Group​Names [Beta]

Finite groups of order ≤500, group names, extensions, presentations, properties and character tables.

Order  ≤60≤120≤250≤500

Orders with >300 groups of order n
n = 128, 192, 256, 288, 320, 384, 432, 448, 480.

[non]​abelian, [non]​soluble, super​soluble, [non]​monomial, Z-groups, A-groups, metacyclic, metabelian, p-groups, elementary, hyper​elementary, linear, perfect, simple, almost simple, quasisimple, rational groups.

Groups of order 1

dρLabelID
C1Trivial group11+C11,1

Groups of order 2

dρLabelID
C2Cyclic group21+C22,1

Groups of order 3

dρLabelID
C3Cyclic group; = A3 = triangle rotations31C33,1

Groups of order 4

dρLabelID
C4Cyclic group; = square rotations41C44,1
C22Klein 4-group V4 = elementary abelian group of type [2,2]; = rectangle symmetries4C2^24,2

Groups of order 5

dρLabelID
C5Cyclic group; = pentagon rotations51C55,1

Groups of order 6

dρLabelID
C6Cyclic group; = hexagon rotations61C66,2
S3Symmetric group on 3 letters; = D3 = GL2(𝔽2) = triangle symmetries = 1st non-abelian group32+S36,1

Groups of order 7

dρLabelID
C7Cyclic group71C77,1

Groups of order 8

dρLabelID
C8Cyclic group81C88,1
D4Dihedral group; = He2 = AΣL1(𝔽4) = 2+ 1+2 = square symmetries42+D48,3
Q8Quaternion group; = C4.C2 = Dic2 = 2- 1+282-Q88,4
C23Elementary abelian group of type [2,2,2]8C2^38,5
C2×C4Abelian group of type [2,4]8C2xC48,2

Groups of order 9

dρLabelID
C9Cyclic group91C99,1
C32Elementary abelian group of type [3,3]9C3^29,2

Groups of order 10

dρLabelID
C10Cyclic group101C1010,2
D5Dihedral group; = pentagon symmetries52+D510,1

Groups of order 11

dρLabelID
C11Cyclic group111C1111,1

Groups of order 12

dρLabelID
C12Cyclic group121C1212,2
A4Alternating group on 4 letters; = PSL2(𝔽3) = L2(3) = tetrahedron rotations43+A412,3
D6Dihedral group; = C2×S3 = hexagon symmetries62+D612,4
Dic3Dicyclic group; = C3C4122-Dic312,1
C2×C6Abelian group of type [2,6]12C2xC612,5

Groups of order 13

dρLabelID
C13Cyclic group131C1313,1

Groups of order 14

dρLabelID
C14Cyclic group141C1414,2
D7Dihedral group72+D714,1

Groups of order 15

dρLabelID
C15Cyclic group151C1515,1

Groups of order 16

dρLabelID
C16Cyclic group161C1616,1
D8Dihedral group82+D816,7
Q16Generalised quaternion group; = C8.C2 = Dic4162-Q1616,9
SD16Semidihedral group; = Q8C2 = QD1682SD1616,8
M4(2)Modular maximal-cyclic group; = C83C282M4(2)16,6
C4○D4Pauli group = central product of C4 and D482C4oD416,13
C22⋊C4The semidirect product of C22 and C4 acting via C4/C2=C28C2^2:C416,3
C4⋊C4The semidirect product of C4 and C4 acting via C4/C2=C216C4:C416,4
C42Abelian group of type [4,4]16C4^216,2
C24Elementary abelian group of type [2,2,2,2]16C2^416,14
C2×C8Abelian group of type [2,8]16C2xC816,5
C22×C4Abelian group of type [2,2,4]16C2^2xC416,10
C2×D4Direct product of C2 and D48C2xD416,11
C2×Q8Direct product of C2 and Q816C2xQ816,12

Groups of order 17

dρLabelID
C17Cyclic group171C1717,1

Groups of order 18

dρLabelID
C18Cyclic group181C1818,2
D9Dihedral group92+D918,1
C3⋊S3The semidirect product of C3 and S3 acting via S3/C3=C29C3:S318,4
C3×C6Abelian group of type [3,6]18C3xC618,5
C3×S3Direct product of C3 and S3; = U2(𝔽2)62C3xS318,3

Groups of order 19

dρLabelID
C19Cyclic group191C1919,1

Groups of order 20

dρLabelID
C20Cyclic group201C2020,2
D10Dihedral group; = C2×D5102+D1020,4
F5Frobenius group; = C5C4 = AGL1(𝔽5) = Aut(D5) = Hol(C5) = Sz(2)54+F520,3
Dic5Dicyclic group; = C52C4202-Dic520,1
C2×C10Abelian group of type [2,10]20C2xC1020,5

Groups of order 21

dρLabelID
C21Cyclic group211C2121,2
C7⋊C3The semidirect product of C7 and C3 acting faithfully73C7:C321,1

Groups of order 22

dρLabelID
C22Cyclic group221C2222,2
D11Dihedral group112+D1122,1

Groups of order 23

dρLabelID
C23Cyclic group231C2323,1

Groups of order 24

dρLabelID
C24Cyclic group241C2424,2
S4Symmetric group on 4 letters; = PGL2(𝔽3) = Aut(Q8) = Hol(C22) = tetrahedron symmetries = cube/octahedron rotations43+S424,12
D12Dihedral group122+D1224,6
Dic6Dicyclic group; = C3Q8242-Dic624,4
SL2(𝔽3)Special linear group on 𝔽32; = Q8C3 = 2T = <2,3,3> = 1st non-monomial group82-SL(2,3)24,3
C3⋊D4The semidirect product of C3 and D4 acting via D4/C22=C2122C3:D424,8
C3⋊C8The semidirect product of C3 and C8 acting via C8/C4=C2242C3:C824,1
C2×C12Abelian group of type [2,12]24C2xC1224,9
C22×C6Abelian group of type [2,2,6]24C2^2xC624,15
C2×A4Direct product of C2 and A4; = AΣL1(𝔽8)63+C2xA424,13
C4×S3Direct product of C4 and S3122C4xS324,5
C3×D4Direct product of C3 and D4122C3xD424,10
C22×S3Direct product of C22 and S312C2^2xS324,14
C3×Q8Direct product of C3 and Q8242C3xQ824,11
C2×Dic3Direct product of C2 and Dic324C2xDic324,7

Groups of order 25

dρLabelID
C25Cyclic group251C2525,1
C52Elementary abelian group of type [5,5]25C5^225,2

Groups of order 26

dρLabelID
C26Cyclic group261C2626,2
D13Dihedral group132+D1326,1

Groups of order 27

dρLabelID
C27Cyclic group271C2727,1
He3Heisenberg group; = C32C3 = 3+ 1+293He327,3
3- 1+2Extraspecial group93ES-(3,1)27,4
C33Elementary abelian group of type [3,3,3]27C3^327,5
C3×C9Abelian group of type [3,9]27C3xC927,2

Groups of order 28

dρLabelID
C28Cyclic group281C2828,2
D14Dihedral group; = C2×D7142+D1428,3
Dic7Dicyclic group; = C7C4282-Dic728,1
C2×C14Abelian group of type [2,14]28C2xC1428,4

Groups of order 29

dρLabelID
C29Cyclic group291C2929,1

Groups of order 30

dρLabelID
C30Cyclic group301C3030,4
D15Dihedral group152+D1530,3
C5×S3Direct product of C5 and S3152C5xS330,1
C3×D5Direct product of C3 and D5152C3xD530,2

Groups of order 31

dρLabelID
C31Cyclic group311C3131,1

Groups of order 32

dρLabelID
C32Cyclic group321C3232,1
D16Dihedral group162+D1632,18
Q32Generalised quaternion group; = C16.C2 = Dic8322-Q3232,20
2+ 1+4Extraspecial group; = D4D484+ES+(2,2)32,49
SD32Semidihedral group; = C162C2 = QD32162SD3232,19
2- 1+4Gamma matrices = Extraspecial group; = D4Q8164-ES-(2,2)32,50
M5(2)Modular maximal-cyclic group; = C163C2162M5(2)32,17
C4≀C2Wreath product of C4 by C282C4wrC232,11
C22≀C2Wreath product of C22 by C28C2^2wrC232,27
C8○D4Central product of C8 and D4162C8oD432,38
C4○D8Central product of C4 and D8162C4oD832,42
C23⋊C4The semidirect product of C23 and C4 acting faithfully84+C2^3:C432,6
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)84+C8:C2^232,43
C4⋊D4The semidirect product of C4 and D4 acting via D4/C22=C216C4:D432,28
C41D4The semidirect product of C4 and D4 acting via D4/C4=C216C4:1D432,34
C22⋊C8The semidirect product of C22 and C8 acting via C8/C4=C216C2^2:C832,5
C22⋊Q8The semidirect product of C22 and Q8 acting via Q8/C4=C216C2^2:Q832,29
D4⋊C41st semidirect product of D4 and C4 acting via C4/C2=C216D4:C432,9
C42⋊C21st semidirect product of C42 and C2 acting faithfully16C4^2:C232,24
C422C22nd semidirect product of C42 and C2 acting faithfully16C4^2:2C232,33
C4⋊C8The semidirect product of C4 and C8 acting via C8/C4=C232C4:C832,12
C4⋊Q8The semidirect product of C4 and Q8 acting via Q8/C4=C232C4:Q832,35
C8⋊C43rd semidirect product of C8 and C4 acting via C4/C2=C232C8:C432,4
Q8⋊C41st semidirect product of Q8 and C4 acting via C4/C2=C232Q8:C432,10
C4.D41st non-split extension by C4 of D4 acting via D4/C22=C284+C4.D432,7
C8.C41st non-split extension by C8 of C4 acting via C4/C2=C2162C8.C432,15
C4.4D44th non-split extension by C4 of D4 acting via D4/C4=C216C4.4D432,31
C8.C22The non-split extension by C8 of C22 acting faithfully164-C8.C2^232,44
C4.10D42nd non-split extension by C4 of D4 acting via D4/C22=C2164-C4.10D432,8
C22.D43rd non-split extension by C22 of D4 acting via D4/C22=C216C2^2.D432,30
C2.D82nd central extension by C2 of D832C2.D832,14
C4.Q81st non-split extension by C4 of Q8 acting via Q8/C4=C232C4.Q832,13
C2.C421st central stem extension by C2 of C4232C2.C4^232,2
C42.C24th non-split extension by C42 of C2 acting faithfully32C4^2.C232,32
C25Elementary abelian group of type [2,2,2,2,2]32C2^532,51
C4×C8Abelian group of type [4,8]32C4xC832,3
C2×C16Abelian group of type [2,16]32C2xC1632,16
C2×C42Abelian group of type [2,4,4]32C2xC4^232,21
C22×C8Abelian group of type [2,2,8]32C2^2xC832,36
C23×C4Abelian group of type [2,2,2,4]32C2^3xC432,45
C4×D4Direct product of C4 and D416C4xD432,25
C2×D8Direct product of C2 and D816C2xD832,39
C2×SD16Direct product of C2 and SD1616C2xSD1632,40
C22×D4Direct product of C22 and D416C2^2xD432,46
C2×M4(2)Direct product of C2 and M4(2)16C2xM4(2)32,37
C4×Q8Direct product of C4 and Q832C4xQ832,26
C2×Q16Direct product of C2 and Q1632C2xQ1632,41
C22×Q8Direct product of C22 and Q832C2^2xQ832,47
C2×C4○D4Direct product of C2 and C4○D416C2xC4oD432,48
C2×C22⋊C4Direct product of C2 and C22⋊C416C2xC2^2:C432,22
C2×C4⋊C4Direct product of C2 and C4⋊C432C2xC4:C432,23

Groups of order 33

dρLabelID
C33Cyclic group331C3333,1

Groups of order 34

dρLabelID
C34Cyclic group341C3434,2
D17Dihedral group172+D1734,1

Groups of order 35

dρLabelID
C35Cyclic group351C3535,1

Groups of order 36

dρLabelID
C36Cyclic group361C3636,2
D18Dihedral group; = C2×D9182+D1836,4
Dic9Dicyclic group; = C9C4362-Dic936,1
C32⋊C4The semidirect product of C32 and C4 acting faithfully64+C3^2:C436,9
C3⋊Dic3The semidirect product of C3 and Dic3 acting via Dic3/C6=C236C3:Dic336,7
C3.A4The central extension by C3 of A4183C3.A436,3
C62Abelian group of type [6,6]36C6^236,14
C2×C18Abelian group of type [2,18]36C2xC1836,5
C3×C12Abelian group of type [3,12]36C3xC1236,8
S32Direct product of S3 and S3; = Spin+4(𝔽2) = Hol(S3)64+S3^236,10
S3×C6Direct product of C6 and S3122S3xC636,12
C3×A4Direct product of C3 and A4123C3xA436,11
C3×Dic3Direct product of C3 and Dic3122C3xDic336,6
C2×C3⋊S3Direct product of C2 and C3⋊S318C2xC3:S336,13

Groups of order 37

dρLabelID
C37Cyclic group371C3737,1

Groups of order 38

dρLabelID
C38Cyclic group381C3838,2
D19Dihedral group192+D1938,1

Groups of order 39

dρLabelID
C39Cyclic group391C3939,2
C13⋊C3The semidirect product of C13 and C3 acting faithfully133C13:C339,1

Groups of order 40

dρLabelID
C40Cyclic group401C4040,2
D20Dihedral group202+D2040,6
Dic10Dicyclic group; = C5Q8402-Dic1040,4
C5⋊D4The semidirect product of C5 and D4 acting via D4/C22=C2202C5:D440,8
C5⋊C8The semidirect product of C5 and C8 acting via C8/C2=C4404-C5:C840,3
C52C8The semidirect product of C5 and C8 acting via C8/C4=C2402C5:2C840,1
C2×C20Abelian group of type [2,20]40C2xC2040,9
C22×C10Abelian group of type [2,2,10]40C2^2xC1040,14
C2×F5Direct product of C2 and F5; = Aut(D10) = Hol(C10)104+C2xF540,12
C4×D5Direct product of C4 and D5202C4xD540,5
C5×D4Direct product of C5 and D4202C5xD440,10
C22×D5Direct product of C22 and D520C2^2xD540,13
C5×Q8Direct product of C5 and Q8402C5xQ840,11
C2×Dic5Direct product of C2 and Dic540C2xDic540,7

Groups of order 41

dρLabelID
C41Cyclic group411C4141,1

Groups of order 42

dρLabelID
C42Cyclic group421C4242,6
D21Dihedral group212+D2142,5
F7Frobenius group; = C7C6 = AGL1(𝔽7) = Aut(D7) = Hol(C7)76+F742,1
S3×C7Direct product of C7 and S3212S3xC742,3
C3×D7Direct product of C3 and D7212C3xD742,4
C2×C7⋊C3Direct product of C2 and C7⋊C3143C2xC7:C342,2

Groups of order 43

dρLabelID
C43Cyclic group431C4343,1

Groups of order 44

dρLabelID
C44Cyclic group441C4444,2
D22Dihedral group; = C2×D11222+D2244,3
Dic11Dicyclic group; = C11C4442-Dic1144,1
C2×C22Abelian group of type [2,22]44C2xC2244,4

Groups of order 45

dρLabelID
C45Cyclic group451C4545,1
C3×C15Abelian group of type [3,15]45C3xC1545,2

Groups of order 46

dρLabelID
C46Cyclic group461C4646,2
D23Dihedral group232+D2346,1

Groups of order 47

dρLabelID
C47Cyclic group471C4747,1

Groups of order 48

dρLabelID
C48Cyclic group481C4848,2
D24Dihedral group242+D2448,7
Dic12Dicyclic group; = C31Q16482-Dic1248,8
GL2(𝔽3)General linear group on 𝔽32; = Q8S3 = Aut(C32) = 2O = <2,3,4>82GL(2,3)48,29
CSU2(𝔽3)Conformal special unitary group on 𝔽32; = Q8.S3162-CSU(2,3)48,28
C4○D12Central product of C4 and D12242C4oD1248,37
A4⋊C4The semidirect product of A4 and C4 acting via C4/C2=C2; = SL2(ℤ/4ℤ)123A4:C448,30
C42⋊C3The semidirect product of C42 and C3 acting faithfully123C4^2:C348,3
C22⋊A4The semidirect product of C22 and A4 acting via A4/C22=C312C2^2:A448,50
D6⋊C4The semidirect product of D6 and C4 acting via C4/C2=C224D6:C448,14
D4⋊S3The semidirect product of D4 and S3 acting via S3/C3=C2244+D4:S348,15
C8⋊S33rd semidirect product of C8 and S3 acting via S3/C3=C2242C8:S348,5
C24⋊C22nd semidirect product of C24 and C2 acting faithfully242C24:C248,6
D42S3The semidirect product of D4 and S3 acting through Inn(D4)244-D4:2S348,39
Q82S3The semidirect product of Q8 and S3 acting via S3/C3=C2244+Q8:2S348,17
Q83S3The semidirect product of Q8 and S3 acting through Inn(Q8)244+Q8:3S348,41
C3⋊C16The semidirect product of C3 and C16 acting via C16/C8=C2482C3:C1648,1
C4⋊Dic3The semidirect product of C4 and Dic3 acting via Dic3/C6=C248C4:Dic348,13
C3⋊Q16The semidirect product of C3 and Q16 acting via Q16/Q8=C2484-C3:Q1648,18
Dic3⋊C4The semidirect product of Dic3 and C4 acting via C4/C2=C248Dic3:C448,12
C4.A4The central extension by C4 of A4162C4.A448,33
D4.S3The non-split extension by D4 of S3 acting via S3/C3=C2244-D4.S348,16
C4.Dic3The non-split extension by C4 of Dic3 acting via Dic3/C6=C2242C4.Dic348,10
C6.D47th non-split extension by C6 of D4 acting via D4/C22=C224C6.D448,19
C4×C12Abelian group of type [4,12]48C4xC1248,20
C2×C24Abelian group of type [2,24]48C2xC2448,23
C23×C6Abelian group of type [2,2,2,6]48C2^3xC648,52
C22×C12Abelian group of type [2,2,12]48C2^2xC1248,44
C2×S4Direct product of C2 and S4; = O3(𝔽3) = cube/octahedron symmetries63+C2xS448,48
C4×A4Direct product of C4 and A4123C4xA448,31
S3×D4Direct product of S3 and D4; = Aut(D12) = Hol(C12)124+S3xD448,38
C22×A4Direct product of C22 and A412C2^2xA448,49
C2×SL2(𝔽3)Direct product of C2 and SL2(𝔽3)16C2xSL(2,3)48,32
S3×C8Direct product of C8 and S3242S3xC848,4
C3×D8Direct product of C3 and D8242C3xD848,25
C6×D4Direct product of C6 and D424C6xD448,45
S3×Q8Direct product of S3 and Q8244-S3xQ848,40
C2×D12Direct product of C2 and D1224C2xD1248,36
S3×C23Direct product of C23 and S324S3xC2^348,51
C3×SD16Direct product of C3 and SD16242C3xSD1648,26
C3×M4(2)Direct product of C3 and M4(2)242C3xM4(2)48,24
C6×Q8Direct product of C6 and Q848C6xQ848,46
C3×Q16Direct product of C3 and Q16482C3xQ1648,27
C4×Dic3Direct product of C4 and Dic348C4xDic348,11
C2×Dic6Direct product of C2 and Dic648C2xDic648,34
C22×Dic3Direct product of C22 and Dic348C2^2xDic348,42
S3×C2×C4Direct product of C2×C4 and S324S3xC2xC448,35
C2×C3⋊D4Direct product of C2 and C3⋊D424C2xC3:D448,43
C3×C4○D4Direct product of C3 and C4○D4242C3xC4oD448,47
C3×C22⋊C4Direct product of C3 and C22⋊C424C3xC2^2:C448,21
C2×C3⋊C8Direct product of C2 and C3⋊C848C2xC3:C848,9
C3×C4⋊C4Direct product of C3 and C4⋊C448C3xC4:C448,22

Groups of order 49

dρLabelID
C49Cyclic group491C4949,1
C72Elementary abelian group of type [7,7]49C7^249,2

Groups of order 50

dρLabelID
C50Cyclic group501C5050,2
D25Dihedral group252+D2550,1
C5⋊D5The semidirect product of C5 and D5 acting via D5/C5=C225C5:D550,4
C5×C10Abelian group of type [5,10]50C5xC1050,5
C5×D5Direct product of C5 and D5; = AΣL1(𝔽25)102C5xD550,3

Groups of order 51

dρLabelID
C51Cyclic group511C5151,1

Groups of order 52

dρLabelID
C52Cyclic group521C5252,2
D26Dihedral group; = C2×D13262+D2652,4
Dic13Dicyclic group; = C132C4522-Dic1352,1
C13⋊C4The semidirect product of C13 and C4 acting faithfully134+C13:C452,3
C2×C26Abelian group of type [2,26]52C2xC2652,5

Groups of order 53

dρLabelID
C53Cyclic group531C5353,1

Groups of order 54

dρLabelID
C54Cyclic group541C5454,2
D27Dihedral group272+D2754,1
C9⋊C6The semidirect product of C9 and C6 acting faithfully; = Aut(D9) = Hol(C9)96+C9:C654,6
C32⋊C6The semidirect product of C32 and C6 acting faithfully96+C3^2:C654,5
He3⋊C22nd semidirect product of He3 and C2 acting faithfully; = Aut(3- 1+2)93He3:C254,8
C9⋊S3The semidirect product of C9 and S3 acting via S3/C3=C227C9:S354,7
C33⋊C23rd semidirect product of C33 and C2 acting faithfully27C3^3:C254,14
C3×C18Abelian group of type [3,18]54C3xC1854,9
C32×C6Abelian group of type [3,3,6]54C3^2xC654,15
S3×C9Direct product of C9 and S3182S3xC954,4
C3×D9Direct product of C3 and D9182C3xD954,3
C2×He3Direct product of C2 and He3183C2xHe354,10
S3×C32Direct product of C32 and S318S3xC3^254,12
C2×3- 1+2Direct product of C2 and 3- 1+2183C2xES-(3,1)54,11
C3×C3⋊S3Direct product of C3 and C3⋊S318C3xC3:S354,13

Groups of order 55

dρLabelID
C55Cyclic group551C5555,2
C11⋊C5The semidirect product of C11 and C5 acting faithfully115C11:C555,1

Groups of order 56

dρLabelID
C56Cyclic group561C5656,2
D28Dihedral group282+D2856,5
F8Frobenius group; = C23C7 = AGL1(𝔽8)87+F856,11
Dic14Dicyclic group; = C7Q8562-Dic1456,3
C7⋊D4The semidirect product of C7 and D4 acting via D4/C22=C2282C7:D456,7
C7⋊C8The semidirect product of C7 and C8 acting via C8/C4=C2562C7:C856,1
C2×C28Abelian group of type [2,28]56C2xC2856,8
C22×C14Abelian group of type [2,2,14]56C2^2xC1456,13
C4×D7Direct product of C4 and D7282C4xD756,4
C7×D4Direct product of C7 and D4282C7xD456,9
C22×D7Direct product of C22 and D728C2^2xD756,12
C7×Q8Direct product of C7 and Q8562C7xQ856,10
C2×Dic7Direct product of C2 and Dic756C2xDic756,6

Groups of order 57

dρLabelID
C57Cyclic group571C5757,2
C19⋊C3The semidirect product of C19 and C3 acting faithfully193C19:C357,1

Groups of order 58

dρLabelID
C58Cyclic group581C5858,2
D29Dihedral group292+D2958,1

Groups of order 59

dρLabelID
C59Cyclic group591C5959,1

Groups of order 60

dρLabelID
C60Cyclic group601C6060,4
A5Alternating group on 5 letters; = SL2(𝔽4) = L2(5) = L2(4) = icosahedron/dodecahedron rotations; 1st non-abelian simple53+A560,5
D30Dihedral group; = C2×D15302+D3060,12
Dic15Dicyclic group; = C3Dic5602-Dic1560,3
C3⋊F5The semidirect product of C3 and F5 acting via F5/D5=C2154C3:F560,7
C2×C30Abelian group of type [2,30]60C2xC3060,13
S3×D5Direct product of S3 and D5154+S3xD560,8
C3×F5Direct product of C3 and F5154C3xF560,6
C5×A4Direct product of C5 and A4203C5xA460,9
C6×D5Direct product of C6 and D5302C6xD560,10
S3×C10Direct product of C10 and S3302S3xC1060,11
C5×Dic3Direct product of C5 and Dic3602C5xDic360,1
C3×Dic5Direct product of C3 and Dic5602C3xDic560,2

Groups of order 61

dρLabelID
C61Cyclic group611C6161,1

Groups of order 62

dρLabelID
C62Cyclic group621C6262,2
D31Dihedral group312+D3162,1

Groups of order 63

dρLabelID
C63Cyclic group631C6363,2
C7⋊C9The semidirect product of C7 and C9 acting via C9/C3=C3633C7:C963,1
C3×C21Abelian group of type [3,21]63C3xC2163,4
C3×C7⋊C3Direct product of C3 and C7⋊C3213C3xC7:C363,3

Groups of order 64

dρLabelID
C64Cyclic group641C6464,1
D32Dihedral group322+D3264,52
Q64Generalised quaternion group; = C32.C2 = Dic16642-Q6464,54
SD64Semidihedral group; = C322C2 = QD64322SD6464,53
M6(2)Modular maximal-cyclic group; = C323C2322M6(2)64,51
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)84+C2wrC464,32
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)84+C2wrC2^264,138
C8○D8Central product of C8 and D8162C8oD864,124
D4○D8Central product of D4 and D8164+D4oD864,257
Q8○SD16Central product of Q8 and SD16164Q8oSD1664,258
D4○M4(2)Central product of D4 and M4(2)164D4oM4(2)64,249
Q8○D8Central product of Q8 and D8324-Q8oD864,259
D4○C16Central product of D4 and C16322D4oC1664,185
C4○D16Central product of C4 and D16322C4oD1664,189
C82M4(2)Central product of C8 and M4(2)32C8o2M4(2)64,86
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)84+D4:4D464,134
C42⋊C42nd semidirect product of C42 and C4 acting faithfully84+C4^2:C464,34
C23⋊C8The semidirect product of C23 and C8 acting via C8/C2=C416C2^3:C864,4
C16⋊C42nd semidirect product of C16 and C4 acting faithfully164C16:C464,28
D82C42nd semidirect product of D8 and C4 acting via C4/C2=C2164D8:2C464,41
D45D41st semidirect product of D4 and D4 acting through Inn(D4)16D4:5D464,227
C16⋊C22The semidirect product of C16 and C22 acting faithfully164+C16:C2^264,190
C426C43rd semidirect product of C42 and C4 acting via C4/C2=C216C4^2:6C464,20
C423C43rd semidirect product of C42 and C4 acting faithfully164C4^2:3C464,35
C243C41st semidirect product of C24 and C4 acting via C4/C2=C216C2^4:3C464,60
C22⋊D8The semidirect product of C22 and D8 acting via D8/D4=C216C2^2:D864,128
C233D42nd semidirect product of C23 and D4 acting via D4/C2=C2216C2^3:3D464,215
C232Q82nd semidirect product of C23 and Q8 acting via Q8/C2=C2216C2^3:2Q864,224
D8⋊C224th semidirect product of D8 and C22 acting via C22/C2=C2164D8:C2^264,256
M4(2)⋊4C44th semidirect product of M4(2) and C4 acting via C4/C2=C2164M4(2):4C464,25
M5(2)⋊C26th semidirect product of M5(2) and C2 acting faithfully164+M5(2):C264,42
C42⋊C221st semidirect product of C42 and C22 acting faithfully164C4^2:C2^264,102
C24⋊C224th semidirect product of C24 and C22 acting faithfully16C2^4:C2^264,242
C22⋊SD16The semidirect product of C22 and SD16 acting via SD16/D4=C216C2^2:SD1664,131
D4⋊C8The semidirect product of D4 and C8 acting via C8/C4=C232D4:C864,6
C89D43rd semidirect product of C8 and D4 acting via D4/C22=C232C8:9D464,116
C86D43rd semidirect product of C8 and D4 acting via D4/C4=C232C8:6D464,117
C4⋊D8The semidirect product of C4 and D8 acting via D8/D4=C232C4:D864,140
C88D42nd semidirect product of C8 and D4 acting via D4/C22=C232C8:8D464,146
C87D41st semidirect product of C8 and D4 acting via D4/C22=C232C8:7D464,147
C8⋊D41st semidirect product of C8 and D4 acting via D4/C2=C2232C8:D464,149
C82D42nd semidirect product of C8 and D4 acting via D4/C2=C2232C8:2D464,150
C85D42nd semidirect product of C8 and D4 acting via D4/C4=C232C8:5D464,173
C84D41st semidirect product of C8 and D4 acting via D4/C4=C232C8:4D464,174
C83D43rd semidirect product of C8 and D4 acting via D4/C2=C2232C8:3D464,177
D8⋊C43rd semidirect product of D8 and C4 acting via C4/C2=C2; = Aut(SD32)32D8:C464,123
D4⋊D42nd semidirect product of D4 and D4 acting via D4/C22=C232D4:D464,130
D46D42nd semidirect product of D4 and D4 acting through Inn(D4)32D4:6D464,228
C22⋊C16The semidirect product of C22 and C16 acting via C16/C8=C232C2^2:C1664,29
Q8⋊D41st semidirect product of Q8 and D4 acting via D4/C22=C232Q8:D464,129
D4⋊Q81st semidirect product of D4 and Q8 acting via Q8/C4=C232D4:Q864,155
D42Q82nd semidirect product of D4 and Q8 acting via Q8/C4=C232D4:2Q864,157
Q85D41st semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:5D464,229
Q86D42nd semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:6D464,231
D43Q8The semidirect product of D4 and Q8 acting through Inn(D4)32D4:3Q864,235
Q32⋊C22nd semidirect product of Q32 and C2 acting faithfully324-Q32:C264,191
C4⋊SD16The semidirect product of C4 and SD16 acting via SD16/Q8=C232C4:SD1664,141
C232D41st semidirect product of C23 and D4 acting via D4/C2=C2232C2^3:2D464,73
C23⋊Q81st semidirect product of C23 and Q8 acting via Q8/C2=C2232C2^3:Q864,74
SD16⋊C41st semidirect product of SD16 and C4 acting via C4/C2=C232SD16:C464,121
C4⋊M4(2)The semidirect product of C4 and M4(2) acting via M4(2)/C2×C4=C232C4:M4(2)64,104
C22⋊Q16The semidirect product of C22 and Q16 acting via Q16/Q8=C232C2^2:Q1664,132
M4(2)⋊C41st semidirect product of M4(2) and C4 acting via C4/C2=C232M4(2):C464,109
C8⋊Q8The semidirect product of C8 and Q8 acting via Q8/C2=C2264C8:Q864,182
C4⋊C16The semidirect product of C4 and C16 acting via C16/C8=C264C4:C1664,44
Q8⋊C8The semidirect product of Q8 and C8 acting via C8/C4=C264Q8:C864,7
C8⋊C83rd semidirect product of C8 and C8 acting via C8/C4=C264C8:C864,3
C82C82nd semidirect product of C8 and C8 acting via C8/C4=C264C8:2C864,15
C81C81st semidirect product of C8 and C8 acting via C8/C4=C264C8:1C864,16
C84Q83rd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:4Q864,127
C83Q82nd semidirect product of C8 and Q8 acting via Q8/C4=C264C8:3Q864,179
C82Q81st semidirect product of C8 and Q8 acting via Q8/C4=C264C8:2Q864,181
C165C43rd semidirect product of C16 and C4 acting via C4/C2=C264C16:5C464,27
C163C41st semidirect product of C16 and C4 acting via C4/C2=C264C16:3C464,47
C164C42nd semidirect product of C16 and C4 acting via C4/C2=C264C16:4C464,48
Q8⋊Q81st semidirect product of Q8 and Q8 acting via Q8/C4=C264Q8:Q864,156
Q83Q8The semidirect product of Q8 and Q8 acting through Inn(Q8)64Q8:3Q864,238
C42Q16The semidirect product of C4 and Q16 acting via Q16/Q8=C264C4:2Q1664,143
C4⋊Q16The semidirect product of C4 and Q16 acting via Q16/C8=C264C4:Q1664,175
C424C41st semidirect product of C42 and C4 acting via C4/C2=C264C4^2:4C464,57
C428C45th semidirect product of C42 and C4 acting via C4/C2=C264C4^2:8C464,63
C425C42nd semidirect product of C42 and C4 acting via C4/C2=C264C4^2:5C464,64
C429C46th semidirect product of C42 and C4 acting via C4/C2=C264C4^2:9C464,65
Q16⋊C43rd semidirect product of Q16 and C4 acting via C4/C2=C264Q16:C464,122
(C22×C8)⋊C22nd semidirect product of C22×C8 and C2 acting faithfully32(C2^2xC8):C264,89
C8.Q8The non-split extension by C8 of Q8 acting via Q8/C2=C22164C8.Q864,46
C8.C81st non-split extension by C8 of C8 acting via C8/C4=C2162C8.C864,45
C23.C8The non-split extension by C23 of C8 acting via C8/C2=C4164C2^3.C864,30
D4.8D43rd non-split extension by D4 of D4 acting via D4/C22=C2164D4.8D464,135
D4.9D44th non-split extension by D4 of D4 acting via D4/C22=C2164D4.9D464,136
D4.3D43rd non-split extension by D4 of D4 acting via D4/C4=C2164D4.3D464,152
D4.4D44th non-split extension by D4 of D4 acting via D4/C4=C2164+D4.4D464,153
C8.26D413rd non-split extension by C8 of D4 acting via D4/C22=C2164C8.26D464,125
D4.10D45th non-split extension by D4 of D4 acting via D4/C22=C2164-D4.10D464,137
C4.9C421st central stem extension by C4 of C42164C4.9C4^264,18
C42.C42nd non-split extension by C42 of C4 acting faithfully164C4^2.C464,36
C42.3C43rd non-split extension by C42 of C4 acting faithfully164-C4^2.3C464,37
C24.4C42nd non-split extension by C24 of C4 acting via C4/C2=C216C2^4.4C464,88
C2.C256th central stem extension by C2 of C25164C2.C2^564,266
C23.9D42nd non-split extension by C23 of D4 acting via D4/C2=C2216C2^3.9D464,23
C23.D42nd non-split extension by C23 of D4 acting faithfully164C2^3.D464,33
C23.7D47th non-split extension by C23 of D4 acting faithfully164C2^3.7D464,139
C4.10C422nd central stem extension by C4 of C42164C4.10C4^264,19
C23.31D42nd non-split extension by C23 of D4 acting via D4/C22=C216C2^3.31D464,9
C23.37D48th non-split extension by C23 of D4 acting via D4/C22=C216C2^3.37D464,99
M4(2).C41st non-split extension by M4(2) of C4 acting via C4/C2=C2164M4(2).C464,111
C23.C232nd non-split extension by C23 of C23 acting via C23/C2=C22164C2^3.C2^364,91
C22.SD161st non-split extension by C22 of SD16 acting via SD16/Q8=C216C2^2.SD1664,8
C22.11C247th central extension by C22 of C2416C2^2.11C2^464,199
C22.19C245th central stem extension by C22 of C2416C2^2.19C2^464,206
C22.29C2415th central stem extension by C22 of C2416C2^2.29C2^464,216
C22.32C2418th central stem extension by C22 of C2416C2^2.32C2^464,219
C22.45C2431st central stem extension by C22 of C2416C2^2.45C2^464,232
C22.54C2440th central stem extension by C22 of C2416C2^2.54C2^464,241
M4(2).8C223rd non-split extension by M4(2) of C22 acting via C22/C2=C2164M4(2).8C2^264,94
D4.C8The non-split extension by D4 of C8 acting via C8/C4=C2322D4.C864,31
D4.Q8The non-split extension by D4 of Q8 acting via Q8/C4=C232D4.Q864,159
C4.D81st non-split extension by C4 of D8 acting via D8/D4=C232C4.D864,12
C8.D41st non-split extension by C8 of D4 acting via D4/C2=C2232C8.D464,151
C4.4D84th non-split extension by C4 of D8 acting via D8/C8=C232C4.4D864,167
C8.2D42nd non-split extension by C8 of D4 acting via D4/C2=C2232C8.2D464,178
C8.4Q83rd non-split extension by C8 of Q8 acting via Q8/C4=C2322C8.4Q864,49
D8.C41st non-split extension by D8 of C4 acting via C4/C2=C2322D8.C464,40
D4.7D42nd non-split extension by D4 of D4 acting via D4/C22=C232D4.7D464,133
D4.D41st non-split extension by D4 of D4 acting via D4/C4=C232D4.D464,142
D4.2D42nd non-split extension by D4 of D4 acting via D4/C4=C232D4.2D464,144
D4.5D45th non-split extension by D4 of D4 acting via D4/C4=C2324-D4.5D464,154
C2.D161st central extension by C2 of D1632C2.D1664,38
C8.17D44th non-split extension by C8 of D4 acting via D4/C22=C2324-C8.17D464,43
C8.18D45th non-split extension by C8 of D4 acting via D4/C22=C232C8.18D464,148
C8.12D48th non-split extension by C8 of D4 acting via D4/C4=C232C8.12D464,176
Q8.D42nd non-split extension by Q8 of D4 acting via D4/C4=C232Q8.D464,145
C4.C423rd non-split extension by C4 of C42 acting via C42/C2×C4=C232C4.C4^264,22
C42.6C43rd non-split extension by C42 of C4 acting via C4/C2=C232C4^2.6C464,113
C22.D83rd non-split extension by C22 of D8 acting via D8/D4=C232C2^2.D864,161
C23.7Q82nd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.7Q864,61
C23.8Q83rd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.8Q864,66
C23.Q83rd non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.Q864,77
C23.4Q84th non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.4Q864,80
C42.12C49th non-split extension by C42 of C4 acting via C4/C2=C232C4^2.12C464,112
C23.34D45th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.34D464,62
C23.23D42nd non-split extension by C23 of D4 acting via D4/C4=C232C2^3.23D464,67
C23.10D43rd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.10D464,75
C23.11D44th non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.11D464,78
C23.24D43rd non-split extension by C23 of D4 acting via D4/C4=C232C2^3.24D464,97
C23.36D47th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.36D464,98
C23.38D49th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.38D464,100
C23.25D44th non-split extension by C23 of D4 acting via D4/C4=C232C2^3.25D464,108
C23.46D417th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.46D464,162
C23.19D412nd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.19D464,163
C23.47D418th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.47D464,164
C23.48D419th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.48D464,165
C23.20D413rd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.20D464,166
C42.C221st non-split extension by C42 of C22 acting faithfully32C4^2.C2^264,10
C22.C422nd non-split extension by C22 of C42 acting via C42/C2×C4=C232C2^2.C4^264,24
C24.C222nd non-split extension by C24 of C22 acting faithfully32C2^4.C2^264,69
C24.3C223rd non-split extension by C24 of C22 acting faithfully32C2^4.3C2^264,71
C42.6C226th non-split extension by C42 of C22 acting faithfully32C4^2.6C2^264,105
C42.7C227th non-split extension by C42 of C22 acting faithfully32C4^2.7C2^264,114
C42.78C2221st non-split extension by C42 of C22 acting via C22/C2=C232C4^2.78C2^264,169
C42.28C2228th non-split extension by C42 of C22 acting faithfully32C4^2.28C2^264,170
C42.29C2229th non-split extension by C42 of C22 acting faithfully32C4^2.29C2^264,171
C23.32C235th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.32C2^364,200
C22.13C249th central extension by C22 of C2432C2^2.13C2^464,201
C22.23C249th central stem extension by C22 of C2432C2^2.23C2^464,210
C22.26C2412nd central stem extension by C22 of C2432C2^2.26C2^464,213
C22.27C2413rd central stem extension by C22 of C2432C2^2.27C2^464,214
C22.30C2416th central stem extension by C22 of C2432C2^2.30C2^464,217
C22.31C2417th central stem extension by C22 of C2432C2^2.31C2^464,218
C23.39C2312nd non-split extension by C23 of C23 acting via C23/C22=C232C2^3.39C2^364,220
C22.34C2420th central stem extension by C22 of C2432C2^2.34C2^464,221
C22.35C2421st central stem extension by C22 of C2432C2^2.35C2^464,222
C22.36C2422nd central stem extension by C22 of C2432C2^2.36C2^464,223
C22.38C2424th central stem extension by C22 of C2432C2^2.38C2^464,225
C23.47C2320th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.47C2^364,233
C22.47C2433rd central stem extension by C22 of C2432C2^2.47C2^464,234
C22.49C2435th central stem extension by C22 of C2432C2^2.49C2^464,236
C22.50C2436th central stem extension by C22 of C2432C2^2.50C2^464,237
C22.53C2439th central stem extension by C22 of C2432C2^2.53C2^464,240
C22.56C2442nd central stem extension by C22 of C2432C2^2.56C2^464,243
C22.57C2443rd central stem extension by C22 of C2432C2^2.57C2^464,244
C22.M4(2)2nd non-split extension by C22 of M4(2) acting via M4(2)/C2×C4=C232C2^2.M4(2)64,5
Q8.Q8The non-split extension by Q8 of Q8 acting via Q8/C4=C264Q8.Q864,160
C8.5Q84th non-split extension by C8 of Q8 acting via Q8/C4=C264C8.5Q864,180
C4.10D82nd non-split extension by C4 of D8 acting via D8/D4=C264C4.10D864,13
C4.6Q162nd non-split extension by C4 of Q16 acting via Q16/Q8=C264C4.6Q1664,14
C2.Q321st central extension by C2 of Q3264C2.Q3264,39
C4.Q163rd non-split extension by C4 of Q16 acting via Q16/Q8=C264C4.Q1664,158
C4.SD164th non-split extension by C4 of SD16 acting via SD16/C8=C264C4.SD1664,168
C22.4Q161st central extension by C22 of Q1664C2^2.4Q1664,21
C42.2C222nd non-split extension by C42 of C22 acting faithfully64C4^2.2C2^264,11
C22.7C422nd central extension by C22 of C4264C2^2.7C4^264,17
C23.63C2313rd central extension by C23 of C2364C2^3.63C2^364,68
C23.65C2315th central extension by C23 of C2364C2^3.65C2^364,70
C23.67C2317th central extension by C23 of C2364C2^3.67C2^364,72
C23.78C234th central stem extension by C23 of C2364C2^3.78C2^364,76
C23.81C237th central stem extension by C23 of C2364C2^3.81C2^364,79
C23.83C239th central stem extension by C23 of C2364C2^3.83C2^364,81
C23.84C2310th central stem extension by C23 of C2364C2^3.84C2^364,82
C42.30C2230th non-split extension by C42 of C22 acting faithfully64C4^2.30C2^264,172
C22.58C2444th central stem extension by C22 of C2464C2^2.58C2^464,245
C82Abelian group of type [8,8]64C8^264,2
C43Abelian group of type [4,4,4]64C4^364,55
C26Elementary abelian group of type [2,2,2,2,2,2]64C2^664,267
C4×C16Abelian group of type [4,16]64C4xC1664,26
C2×C32Abelian group of type [2,32]64C2xC3264,50
C23×C8Abelian group of type [2,2,2,8]64C2^3xC864,246
C24×C4Abelian group of type [2,2,2,2,4]64C2^4xC464,260
C22×C16Abelian group of type [2,2,16]64C2^2xC1664,183
C22×C42Abelian group of type [2,2,4,4]64C2^2xC4^264,192
C2×C4×C8Abelian group of type [2,4,8]64C2xC4xC864,83
D42Direct product of D4 and D416D4^264,226
C2×2+ 1+4Direct product of C2 and 2+ 1+416C2xES+(2,2)64,264
C8×D4Direct product of C8 and D432C8xD464,115
C4×D8Direct product of C4 and D832C4xD864,118
D4×Q8Direct product of D4 and Q832D4xQ864,230
C2×D16Direct product of C2 and D1632C2xD1664,186
C4×SD16Direct product of C4 and SD1632C4xSD1664,119
C2×SD32Direct product of C2 and SD3232C2xSD3264,187
C22×D8Direct product of C22 and D832C2^2xD864,250
D4×C23Direct product of C23 and D432D4xC2^364,261
C4×M4(2)Direct product of C4 and M4(2)32C4xM4(2)64,85
C2×M5(2)Direct product of C2 and M5(2)32C2xM5(2)64,184
C22×SD16Direct product of C22 and SD1632C2^2xSD1664,251
C22×M4(2)Direct product of C22 and M4(2)32C2^2xM4(2)64,247
C2×2- 1+4Direct product of C2 and 2- 1+432C2xES-(2,2)64,265
Q82Direct product of Q8 and Q864Q8^264,239
C8×Q8Direct product of C8 and Q864C8xQ864,126
C4×Q16Direct product of C4 and Q1664C4xQ1664,120
C2×Q32Direct product of C2 and Q3264C2xQ3264,188
Q8×C23Direct product of C23 and Q864Q8xC2^364,262
C22×Q16Direct product of C22 and Q1664C2^2xQ1664,252
C2×C4≀C2Direct product of C2 and C4≀C216C2xC4wrC264,101
C2×C23⋊C4Direct product of C2 and C23⋊C416C2xC2^3:C464,90
C2×C8⋊C22Direct product of C2 and C8⋊C2216C2xC8:C2^264,254
C2×C4.D4Direct product of C2 and C4.D416C2xC4.D464,92
C2×C22≀C2Direct product of C2 and C22≀C216C2xC2^2wrC264,202
C2×C4×D4Direct product of C2×C4 and D432C2xC4xD464,196
C4×C4○D4Direct product of C4 and C4○D432C4xC4oD464,198
C2×C8○D4Direct product of C2 and C8○D432C2xC8oD464,248
C2×C4○D8Direct product of C2 and C4○D832C2xC4oD864,253
C2×C4⋊D4Direct product of C2 and C4⋊D432C2xC4:D464,203
C2×D4⋊C4Direct product of C2 and D4⋊C432C2xD4:C464,95
C2×C8.C4Direct product of C2 and C8.C432C2xC8.C464,110
C2×C41D4Direct product of C2 and C41D432C2xC4:1D464,211
C4×C22⋊C4Direct product of C4 and C22⋊C432C4xC2^2:C464,58
C2×C22⋊C8Direct product of C2 and C22⋊C832C2xC2^2:C864,87
C2×C22⋊Q8Direct product of C2 and C22⋊Q832C2xC2^2:Q864,204
C2×C42⋊C2Direct product of C2 and C42⋊C232C2xC4^2:C264,195
C2×C4.4D4Direct product of C2 and C4.4D432C2xC4.4D464,207
C22×C4○D4Direct product of C22 and C4○D432C2^2xC4oD464,263
C2×C8.C22Direct product of C2 and C8.C2232C2xC8.C2^264,255
C2×C422C2Direct product of C2 and C422C232C2xC4^2:2C264,209
C2×C4.10D4Direct product of C2 and C4.10D432C2xC4.10D464,93
C22×C22⋊C4Direct product of C22 and C22⋊C432C2^2xC2^2:C464,193
C2×C22.D4Direct product of C2 and C22.D432C2xC2^2.D464,205
C4×C4⋊C4Direct product of C4 and C4⋊C464C4xC4:C464,59
C2×C4⋊C8Direct product of C2 and C4⋊C864C2xC4:C864,103
C2×C4×Q8Direct product of C2×C4 and Q864C2xC4xQ864,197
C2×C4⋊Q8Direct product of C2 and C4⋊Q864C2xC4:Q864,212
C2×C8⋊C4Direct product of C2 and C8⋊C464C2xC8:C464,84
C22×C4⋊C4Direct product of C22 and C4⋊C464C2^2xC4:C464,194
C2×Q8⋊C4Direct product of C2 and Q8⋊C464C2xQ8:C464,96
C2×C2.D8Direct product of C2 and C2.D864C2xC2.D864,107
C2×C4.Q8Direct product of C2 and C4.Q864C2xC4.Q864,106
C2×C2.C42Direct product of C2 and C2.C4264C2xC2.C4^264,56
C2×C42.C2Direct product of C2 and C42.C264C2xC4^2.C264,208

Groups of order 65

dρLabelID
C65Cyclic group651C6565,1

Groups of order 66

dρLabelID
C66Cyclic group661C6666,4
D33Dihedral group332+D3366,3
S3×C11Direct product of C11 and S3332S3xC1166,1
C3×D11Direct product of C3 and D11332C3xD1166,2

Groups of order 67

dρLabelID
C67Cyclic group671C6767,1

Groups of order 68

dρLabelID
C68Cyclic group681C6868,2
D34Dihedral group; = C2×D17342+D3468,4
Dic17Dicyclic group; = C172C4682-Dic1768,1
C17⋊C4The semidirect product of C17 and C4 acting faithfully174+C17:C468,3
C2×C34Abelian group of type [2,34]68C2xC3468,5

Groups of order 69

dρLabelID
C69Cyclic group691C6969,1

Groups of order 70

dρLabelID
C70Cyclic group701C7070,4
D35Dihedral group352+D3570,3
C7×D5Direct product of C7 and D5352C7xD570,1
C5×D7Direct product of C5 and D7352C5xD770,2

Groups of order 71

dρLabelID
C71Cyclic group711C7171,1

Groups of order 72

dρLabelID
C72Cyclic group721C7272,2
D36Dihedral group362+D3672,6
F9Frobenius group; = C32C8 = AGL1(𝔽9)98+F972,39
Dic18Dicyclic group; = C9Q8722-Dic1872,4
PSU3(𝔽2)Projective special unitary group on 𝔽23; = C32Q8 = M998+PSU(3,2)72,41
S3≀C2Wreath product of S3 by C2; = SO+4(𝔽2)64+S3wrC272,40
C3⋊S4The semidirect product of C3 and S4 acting via S4/A4=C2126+C3:S472,43
C3⋊D12The semidirect product of C3 and D12 acting via D12/D6=C2124+C3:D1272,23
D6⋊S31st semidirect product of D6 and S3 acting via S3/C3=C2244-D6:S372,22
C322C8The semidirect product of C32 and C8 acting via C8/C2=C4244-C3^2:2C872,19
C322Q8The semidirect product of C32 and Q8 acting via Q8/C2=C22244-C3^2:2Q872,24
C9⋊D4The semidirect product of C9 and D4 acting via D4/C22=C2362C9:D472,8
C12⋊S31st semidirect product of C12 and S3 acting via S3/C3=C236C12:S372,33
C327D42nd semidirect product of C32 and D4 acting via D4/C22=C236C3^2:7D472,35
C9⋊C8The semidirect product of C9 and C8 acting via C8/C4=C2722C9:C872,1
Q8⋊C9The semidirect product of Q8 and C9 acting via C9/C3=C3722Q8:C972,3
C324C82nd semidirect product of C32 and C8 acting via C8/C4=C272C3^2:4C872,13
C324Q82nd semidirect product of C32 and Q8 acting via Q8/C4=C272C3^2:4Q872,31
C6.D62nd non-split extension by C6 of D6 acting via D6/S3=C2124+C6.D672,21
C3.S4The non-split extension by C3 of S4 acting via S4/A4=C2186+C3.S472,15
C2×C36Abelian group of type [2,36]72C2xC3672,9
C3×C24Abelian group of type [3,24]72C3xC2472,14
C6×C12Abelian group of type [6,12]72C6xC1272,36
C2×C62Abelian group of type [2,6,6]72C2xC6^272,50
C22×C18Abelian group of type [2,2,18]72C2^2xC1872,18
C3×S4Direct product of C3 and S4123C3xS472,42
S3×A4Direct product of S3 and A4126+S3xA472,44
C6×A4Direct product of C6 and A4183C6xA472,47
S3×C12Direct product of C12 and S3242S3xC1272,27
C3×D12Direct product of C3 and D12242C3xD1272,28
S3×Dic3Direct product of S3 and Dic3244-S3xDic372,20
C3×Dic6Direct product of C3 and Dic6242C3xDic672,26
C6×Dic3Direct product of C6 and Dic324C6xDic372,29
C3×SL2(𝔽3)Direct product of C3 and SL2(𝔽3)242C3xSL(2,3)72,25
C4×D9Direct product of C4 and D9362C4xD972,5
D4×C9Direct product of C9 and D4362D4xC972,10
C22×D9Direct product of C22 and D936C2^2xD972,17
D4×C32Direct product of C32 and D436D4xC3^272,37
Q8×C9Direct product of C9 and Q8722Q8xC972,11
C2×Dic9Direct product of C2 and Dic972C2xDic972,7
Q8×C32Direct product of C32 and Q872Q8xC3^272,38
C2×S32Direct product of C2, S3 and S3124+C2xS3^272,46
C3×C3⋊D4Direct product of C3 and C3⋊D4122C3xC3:D472,30
C2×C32⋊C4Direct product of C2 and C32⋊C4124+C2xC3^2:C472,45
C2×C3.A4Direct product of C2 and C3.A4183C2xC3.A472,16
C3×C3⋊C8Direct product of C3 and C3⋊C8242C3xC3:C872,12
S3×C2×C6Direct product of C2×C6 and S324S3xC2xC672,48
C4×C3⋊S3Direct product of C4 and C3⋊S336C4xC3:S372,32
C22×C3⋊S3Direct product of C22 and C3⋊S336C2^2xC3:S372,49
C2×C3⋊Dic3Direct product of C2 and C3⋊Dic372C2xC3:Dic372,34

Groups of order 73

dρLabelID
C73Cyclic group731C7373,1

Groups of order 74

dρLabelID
C74Cyclic group741C7474,2
D37Dihedral group372+D3774,1

Groups of order 75

dρLabelID
C75Cyclic group751C7575,1
C52⋊C3The semidirect product of C52 and C3 acting faithfully153C5^2:C375,2
C5×C15Abelian group of type [5,15]75C5xC1575,3

Groups of order 76

dρLabelID
C76Cyclic group761C7676,2
D38Dihedral group; = C2×D19382+D3876,3
Dic19Dicyclic group; = C19C4762-Dic1976,1
C2×C38Abelian group of type [2,38]76C2xC3876,4

Groups of order 77

dρLabelID
C77Cyclic group771C7777,1

Groups of order 78

dρLabelID
C78Cyclic group781C7878,6
D39Dihedral group392+D3978,5
C13⋊C6The semidirect product of C13 and C6 acting faithfully136+C13:C678,1
S3×C13Direct product of C13 and S3392S3xC1378,3
C3×D13Direct product of C3 and D13392C3xD1378,4
C2×C13⋊C3Direct product of C2 and C13⋊C3263C2xC13:C378,2

Groups of order 79

dρLabelID
C79Cyclic group791C7979,1

Groups of order 80

dρLabelID
C80Cyclic group801C8080,2
D40Dihedral group402+D4080,7
Dic20Dicyclic group; = C51Q16802-Dic2080,8
C4○D20Central product of C4 and D20402C4oD2080,38
C24⋊C5The semidirect product of C24 and C5 acting faithfully105+C2^4:C580,49
C4⋊F5The semidirect product of C4 and F5 acting via F5/D5=C2204C4:F580,31
C22⋊F5The semidirect product of C22 and F5 acting via F5/D5=C2204+C2^2:F580,34
D4⋊D5The semidirect product of D4 and D5 acting via D5/C5=C2404+D4:D580,15
D5⋊C8The semidirect product of D5 and C8 acting via C8/C4=C2404D5:C880,28
Q8⋊D5The semidirect product of Q8 and D5 acting via D5/C5=C2404+Q8:D580,17
C8⋊D53rd semidirect product of C8 and D5 acting via D5/C5=C2402C8:D580,5
C40⋊C22nd semidirect product of C40 and C2 acting faithfully402C40:C280,6
D42D5The semidirect product of D4 and D5 acting through Inn(D4)404-D4:2D580,40
Q82D5The semidirect product of Q8 and D5 acting through Inn(Q8)404+Q8:2D580,42
D10⋊C41st semidirect product of D10 and C4 acting via C4/C2=C240D10:C480,14
C5⋊C16The semidirect product of C5 and C16 acting via C16/C4=C4804C5:C1680,3
C52C16The semidirect product of C5 and C16 acting via C16/C8=C2802C5:2C1680,1
C4⋊Dic5The semidirect product of C4 and Dic5 acting via Dic5/C10=C280C4:Dic580,13
C5⋊Q16The semidirect product of C5 and Q16 acting via Q16/Q8=C2804-C5:Q1680,18
C4.F5The non-split extension by C4 of F5 acting via F5/D5=C2404C4.F580,29
D4.D5The non-split extension by D4 of D5 acting via D5/C5=C2404-D4.D580,16
C4.Dic5The non-split extension by C4 of Dic5 acting via Dic5/C10=C2402C4.Dic580,10
C23.D5The non-split extension by C23 of D5 acting via D5/C5=C240C2^3.D580,19
C22.F5The non-split extension by C22 of F5 acting via F5/D5=C2404-C2^2.F580,33
C10.D41st non-split extension by C10 of D4 acting via D4/C22=C280C10.D480,12
C4×C20Abelian group of type [4,20]80C4xC2080,20
C2×C40Abelian group of type [2,40]80C2xC4080,23
C22×C20Abelian group of type [2,2,20]80C2^2xC2080,45
C23×C10Abelian group of type [2,2,2,10]80C2^3xC1080,52
D4×D5Direct product of D4 and D5204+D4xD580,39
C4×F5Direct product of C4 and F5204C4xF580,30
C22×F5Direct product of C22 and F520C2^2xF580,50
C8×D5Direct product of C8 and D5402C8xD580,4
C5×D8Direct product of C5 and D8402C5xD880,25
Q8×D5Direct product of Q8 and D5404-Q8xD580,41
C2×D20Direct product of C2 and D2040C2xD2080,37
D4×C10Direct product of C10 and D440D4xC1080,46
C5×SD16Direct product of C5 and SD16402C5xSD1680,26
C23×D5Direct product of C23 and D540C2^3xD580,51
C5×M4(2)Direct product of C5 and M4(2)402C5xM4(2)80,24
C5×Q16Direct product of C5 and Q16802C5xQ1680,27
Q8×C10Direct product of C10 and Q880Q8xC1080,47
C4×Dic5Direct product of C4 and Dic580C4xDic580,11
C2×Dic10Direct product of C2 and Dic1080C2xDic1080,35
C22×Dic5Direct product of C22 and Dic580C2^2xDic580,43
C2×C4×D5Direct product of C2×C4 and D540C2xC4xD580,36
C2×C5⋊D4Direct product of C2 and C5⋊D440C2xC5:D480,44
C5×C4○D4Direct product of C5 and C4○D4402C5xC4oD480,48
C5×C22⋊C4Direct product of C5 and C22⋊C440C5xC2^2:C480,21
C2×C5⋊C8Direct product of C2 and C5⋊C880C2xC5:C880,32
C5×C4⋊C4Direct product of C5 and C4⋊C480C5xC4:C480,22
C2×C52C8Direct product of C2 and C52C880C2xC5:2C880,9

Groups of order 81

dρLabelID
C81Cyclic group811C8181,1
C3≀C3Wreath product of C3 by C3; = AΣL1(𝔽27)93C3wrC381,7
C9○He3Central product of C9 and He3273C9oHe381,14
C27⋊C3The semidirect product of C27 and C3 acting faithfully273C27:C381,6
C32⋊C9The semidirect product of C32 and C9 acting via C9/C3=C327C3^2:C981,3
He3⋊C32nd semidirect product of He3 and C3 acting faithfully273He3:C381,9
C9⋊C9The semidirect product of C9 and C9 acting via C9/C3=C381C9:C981,4
He3.C3The non-split extension by He3 of C3 acting faithfully273He3.C381,8
C3.He34th central stem extension by C3 of He3273C3.He381,10
C92Abelian group of type [9,9]81C9^281,2
C34Elementary abelian group of type [3,3,3,3]81C3^481,15
C3×C27Abelian group of type [3,27]81C3xC2781,5
C32×C9Abelian group of type [3,3,9]81C3^2xC981,11
C3×He3Direct product of C3 and He327C3xHe381,12
C3×3- 1+2Direct product of C3 and 3- 1+227C3xES-(3,1)81,13

Groups of order 82

dρLabelID
C82Cyclic group821C8282,2
D41Dihedral group412+D4182,1

Groups of order 83

dρLabelID
C83Cyclic group831C8383,1

Groups of order 84

dρLabelID
C84Cyclic group841C8484,6
D42Dihedral group; = C2×D21422+D4284,14
Dic21Dicyclic group; = C3Dic7842-Dic2184,5
C7⋊A4The semidirect product of C7 and A4 acting via A4/C22=C3283C7:A484,11
C7⋊C12The semidirect product of C7 and C12 acting via C12/C2=C6286-C7:C1284,1
C2×C42Abelian group of type [2,42]84C2xC4284,15
C2×F7Direct product of C2 and F7; = Aut(D14) = Hol(C14)146+C2xF784,7
S3×D7Direct product of S3 and D7214+S3xD784,8
C7×A4Direct product of C7 and A4283C7xA484,10
C6×D7Direct product of C6 and D7422C6xD784,12
S3×C14Direct product of C14 and S3422S3xC1484,13
C7×Dic3Direct product of C7 and Dic3842C7xDic384,3
C3×Dic7Direct product of C3 and Dic7842C3xDic784,4
C4×C7⋊C3Direct product of C4 and C7⋊C3283C4xC7:C384,2
C22×C7⋊C3Direct product of C22 and C7⋊C328C2^2xC7:C384,9

Groups of order 85

dρLabelID
C85Cyclic group851C8585,1

Groups of order 86

dρLabelID
C86Cyclic group861C8686,2
D43Dihedral group432+D4386,1

Groups of order 87

dρLabelID
C87Cyclic group871C8787,1

Groups of order 88

dρLabelID
C88Cyclic group881C8888,2
D44Dihedral group442+D4488,5
Dic22Dicyclic group; = C11Q8882-Dic2288,3
C11⋊D4The semidirect product of C11 and D4 acting via D4/C22=C2442C11:D488,7
C11⋊C8The semidirect product of C11 and C8 acting via C8/C4=C2882C11:C888,1
C2×C44Abelian group of type [2,44]88C2xC4488,8
C22×C22Abelian group of type [2,2,22]88C2^2xC2288,12
C4×D11Direct product of C4 and D11442C4xD1188,4
D4×C11Direct product of C11 and D4442D4xC1188,9
C22×D11Direct product of C22 and D1144C2^2xD1188,11
Q8×C11Direct product of C11 and Q8882Q8xC1188,10
C2×Dic11Direct product of C2 and Dic1188C2xDic1188,6

Groups of order 89

dρLabelID
C89Cyclic group891C8989,1

Groups of order 90

dρLabelID
C90Cyclic group901C9090,4
D45Dihedral group452+D4590,3
C3⋊D15The semidirect product of C3 and D15 acting via D15/C15=C245C3:D1590,9
C3×C30Abelian group of type [3,30]90C3xC3090,10
S3×C15Direct product of C15 and S3302S3xC1590,6
C3×D15Direct product of C3 and D15302C3xD1590,7
C5×D9Direct product of C5 and D9452C5xD990,1
C9×D5Direct product of C9 and D5452C9xD590,2
C32×D5Direct product of C32 and D545C3^2xD590,5
C5×C3⋊S3Direct product of C5 and C3⋊S345C5xC3:S390,8

Groups of order 91

dρLabelID
C91Cyclic group911C9191,1

Groups of order 92

dρLabelID
C92Cyclic group921C9292,2
D46Dihedral group; = C2×D23462+D4692,3
Dic23Dicyclic group; = C23C4922-Dic2392,1
C2×C46Abelian group of type [2,46]92C2xC4692,4

Groups of order 93

dρLabelID
C93Cyclic group931C9393,2
C31⋊C3The semidirect product of C31 and C3 acting faithfully313C31:C393,1

Groups of order 94

dρLabelID
C94Cyclic group941C9494,2
D47Dihedral group472+D4794,1

Groups of order 95

dρLabelID
C95Cyclic group951C9595,1

Groups of order 96

dρLabelID
C96Cyclic group961C9696,2
D48Dihedral group482+D4896,6
Dic24Dicyclic group; = C31Q32962-Dic2496,8
U2(𝔽3)Unitary group on 𝔽32; = SL2(𝔽3)2C4242U(2,3)96,67
D4○D12Central product of D4 and D12244+D4oD1296,216
C8○D12Central product of C8 and D12482C8oD1296,108
C4○D24Central product of C4 and D24482C4oD2496,111
Q8○D12Central product of Q8 and D12484-Q8oD1296,217
C22⋊S4The semidirect product of C22 and S4 acting via S4/C22=S386+C2^2:S496,227
C24⋊C61st semidirect product of C24 and C6 acting faithfully86+C2^4:C696,70
C23⋊A42nd semidirect product of C23 and A4 acting faithfully84+C2^3:A496,204
C4⋊S4The semidirect product of C4 and S4 acting via S4/A4=C2126+C4:S496,187
C42⋊S3The semidirect product of C42 and S3 acting faithfully123C4^2:S396,64
A4⋊D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(ℤ/4ℤ)126+A4:D496,195
C42⋊C61st semidirect product of C42 and C6 acting faithfully166C4^2:C696,71
A4⋊C8The semidirect product of A4 and C8 acting via C8/C4=C2243A4:C896,65
A4⋊Q8The semidirect product of A4 and Q8 acting via Q8/C4=C2246-A4:Q896,185
C8⋊D61st semidirect product of C8 and D6 acting via D6/C3=C22244+C8:D696,115
D6⋊D41st semidirect product of D6 and D4 acting via D4/C22=C224D6:D496,89
D4⋊D62nd semidirect product of D4 and D6 acting via D6/S3=C2244D4:D696,118
D46D62nd semidirect product of D4 and D6 acting through Inn(D4)244D4:6D696,211
Q83D62nd semidirect product of Q8 and D6 acting via D6/S3=C2244+Q8:3D696,121
Q85D62nd semidirect product of Q8 and D6 acting via D6/C6=C2244+Q8:5D696,156
Q8⋊A41st semidirect product of Q8 and A4 acting via A4/C22=C3246-Q8:A496,203
D12⋊C44th semidirect product of D12 and C4 acting via C4/C2=C2244D12:C496,32
C424S33rd semidirect product of C42 and S3 acting via S3/C3=C2242C4^2:4S396,12
C244S31st semidirect product of C24 and S3 acting via S3/C3=C224C2^4:4S396,160
C232D61st semidirect product of C23 and D6 acting via D6/C3=C2224C2^3:2D696,144
Q83Dic32nd semidirect product of Q8 and Dic3 acting via Dic3/C6=C2244Q8:3Dic396,44
D126C224th semidirect product of D12 and C22 acting via C22/C2=C2244D12:6C2^296,139
M4(2)⋊S33rd semidirect product of M4(2) and S3 acting via S3/C3=C2244+M4(2):S396,30
Q8⋊Dic3The semidirect product of Q8 and Dic3 acting via Dic3/C2=S332Q8:Dic396,66
D6⋊C8The semidirect product of D6 and C8 acting via C8/C4=C248D6:C896,27
C3⋊D16The semidirect product of C3 and D16 acting via D16/D8=C2484+C3:D1696,33
C48⋊C22nd semidirect product of C48 and C2 acting faithfully482C48:C296,7
D83S3The semidirect product of D8 and S3 acting through Inn(D8)484-D8:3S396,119
D63D43rd semidirect product of D6 and D4 acting via D4/C4=C248D6:3D496,145
C4⋊D12The semidirect product of C4 and D12 acting via D12/C12=C248C4:D1296,81
C12⋊D41st semidirect product of C12 and D4 acting via D4/C2=C2248C12:D496,102
C127D41st semidirect product of C12 and D4 acting via D4/C22=C248C12:7D496,137
C123D43rd semidirect product of C12 and D4 acting via D4/C2=C2248C12:3D496,147
D6⋊Q81st semidirect product of D6 and Q8 acting via Q8/C4=C248D6:Q896,103
D63Q83rd semidirect product of D6 and Q8 acting via Q8/C4=C248D6:3Q896,153
D24⋊C25th semidirect product of D24 and C2 acting faithfully484+D24:C296,126
C422S31st semidirect product of C42 and S3 acting via S3/C3=C248C4^2:2S396,79
C427S36th semidirect product of C42 and S3 acting via S3/C3=C248C4^2:7S396,82
C423S32nd semidirect product of C42 and S3 acting via S3/C3=C248C4^2:3S396,83
Q16⋊S32nd semidirect product of Q16 and S3 acting via S3/C3=C2484Q16:S396,125
D4⋊Dic31st semidirect product of D4 and Dic3 acting via Dic3/C6=C248D4:Dic396,39
Dic34D41st semidirect product of Dic3 and D4 acting through Inn(Dic3)48Dic3:4D496,88
Dic3⋊D41st semidirect product of Dic3 and D4 acting via D4/C22=C248Dic3:D496,91
Dic35D42nd semidirect product of Dic3 and D4 acting through Inn(Dic3)48Dic3:5D496,100
C3⋊C32The semidirect product of C3 and C32 acting via C32/C16=C2962C3:C3296,1
C12⋊Q8The semidirect product of C12 and Q8 acting via Q8/C2=C2296C12:Q896,95
C12⋊C81st semidirect product of C12 and C8 acting via C8/C4=C296C12:C896,11
C24⋊C45th semidirect product of C24 and C4 acting via C4/C2=C296C24:C496,22
C241C41st semidirect product of C24 and C4 acting via C4/C2=C296C24:1C496,25
C3⋊Q32The semidirect product of C3 and Q32 acting via Q32/Q16=C2964-C3:Q3296,36
Dic3⋊C8The semidirect product of Dic3 and C8 acting via C8/C4=C296Dic3:C896,21
C122Q81st semidirect product of C12 and Q8 acting via Q8/C4=C296C12:2Q896,76
C8⋊Dic32nd semidirect product of C8 and Dic3 acting via Dic3/C6=C296C8:Dic396,24
Q82Dic31st semidirect product of Q8 and Dic3 acting via Dic3/C6=C296Q8:2Dic396,42
Dic6⋊C45th semidirect product of Dic6 and C4 acting via C4/C2=C296Dic6:C496,94
Dic3⋊Q82nd semidirect product of Dic3 and Q8 acting via Q8/C4=C296Dic3:Q896,151
C4⋊C47S31st semidirect product of C4⋊C4 and S3 acting through Inn(C4⋊C4)48C4:C4:7S396,99
C4⋊C4⋊S36th semidirect product of C4⋊C4 and S3 acting via S3/C3=C248C4:C4:S396,105
C23.3A41st non-split extension by C23 of A4 acting via A4/C22=C3126+C2^3.3A496,3
C23.A42nd non-split extension by C23 of A4 acting faithfully126+C2^3.A496,72
D4.A4The non-split extension by D4 of A4 acting through Inn(D4)164-D4.A496,202
C4.6S43rd central extension by C4 of S4162C4.6S496,192
C4.3S43rd non-split extension by C4 of S4 acting via S4/A4=C2164+C4.3S496,193
Q8.D62nd non-split extension by Q8 of D6 acting via D6/C2=S3164-Q8.D696,190
Q8.A4The non-split extension by Q8 of A4 acting through Inn(Q8)244+Q8.A496,201
C12.D48th non-split extension by C12 of D4 acting via D4/C2=C22244C12.D496,40
C23.6D61st non-split extension by C23 of D6 acting via D6/C3=C22244C2^3.6D696,13
C23.7D62nd non-split extension by C23 of D6 acting via D6/C3=C22244C2^3.7D696,41
C8.A4The central extension by C8 of A4322C8.A496,74
C4.S42nd non-split extension by C4 of S4 acting via S4/A4=C2324-C4.S496,191
D6.C8The non-split extension by D6 of C8 acting via C8/C4=C2482D6.C896,5
D8.S3The non-split extension by D8 of S3 acting via S3/C3=C2484-D8.S396,34
D12.C4The non-split extension by D12 of C4 acting via C4/C2=C2484D12.C496,114
C6.D82nd non-split extension by C6 of D8 acting via D8/D4=C248C6.D896,16
C8.6D63rd non-split extension by C8 of D6 acting via D6/S3=C2484+C8.6D696,35
C8.D61st non-split extension by C8 of D6 acting via D6/C3=C22484-C8.D696,116
C24.C44th non-split extension by C24 of C4 acting via C4/C2=C2482C24.C496,19
D6.D42nd non-split extension by D6 of D4 acting via D4/C22=C248D6.D496,101
D4.D64th non-split extension by D4 of D6 acting via D6/S3=C2484-D4.D696,122
C2.D242nd central extension by C2 of D2448C2.D2496,28
D4.Dic3The non-split extension by D4 of Dic3 acting through Inn(D4)484D4.Dic396,155
Q8.7D62nd non-split extension by Q8 of D6 acting via D6/S3=C2484Q8.7D696,123
C12.53D410th non-split extension by C12 of D4 acting via D4/C22=C2484C12.53D496,29
C12.47D44th non-split extension by C12 of D4 acting via D4/C22=C2484-C12.47D496,31
C12.55D412nd non-split extension by C12 of D4 acting via D4/C22=C248C12.55D496,37
C12.10D410th non-split extension by C12 of D4 acting via D4/C2=C22484C12.10D496,43
C4.D125th non-split extension by C4 of D12 acting via D12/D6=C248C4.D1296,104
C12.48D45th non-split extension by C12 of D4 acting via D4/C22=C248C12.48D496,131
C12.23D423rd non-split extension by C12 of D4 acting via D4/C2=C2248C12.23D496,154
Q8.11D61st non-split extension by Q8 of D6 acting via D6/C6=C2484Q8.11D696,149
Q8.13D63rd non-split extension by Q8 of D6 acting via D6/C6=C2484Q8.13D696,157
Q8.14D64th non-split extension by Q8 of D6 acting via D6/C6=C2484-Q8.14D696,158
Q8.15D61st non-split extension by Q8 of D6 acting through Inn(Q8)484Q8.15D696,214
C8.Dic31st non-split extension by C8 of Dic3 acting via Dic3/C6=C2482C8.Dic396,26
C23.8D63rd non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.8D696,86
C23.9D64th non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.9D696,90
Dic3.D41st non-split extension by Dic3 of D4 acting via D4/C22=C248Dic3.D496,85
C23.16D61st non-split extension by C23 of D6 acting via D6/S3=C248C2^3.16D696,84
C23.11D66th non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.11D696,92
C22.D123rd non-split extension by C22 of D12 acting via D12/D6=C248C2^2.D1296,93
C23.26D62nd non-split extension by C23 of D6 acting via D6/C6=C248C2^3.26D696,133
C23.28D64th non-split extension by C23 of D6 acting via D6/C6=C248C2^3.28D696,136
C23.23D68th non-split extension by C23 of D6 acting via D6/S3=C248C2^3.23D696,142
C23.12D67th non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.12D696,143
C23.14D69th non-split extension by C23 of D6 acting via D6/C3=C2248C2^3.14D696,146
Dic3.Q8The non-split extension by Dic3 of Q8 acting via Q8/C4=C296Dic3.Q896,96
C12.Q81st non-split extension by C12 of Q8 acting via Q8/C2=C2296C12.Q896,14
C6.Q162nd non-split extension by C6 of Q16 acting via Q16/Q8=C296C6.Q1696,17
C12.6Q83rd non-split extension by C12 of Q8 acting via Q8/C4=C296C12.6Q896,77
C12.3Q83rd non-split extension by C12 of Q8 acting via Q8/C2=C2296C12.3Q896,97
C6.C422nd non-split extension by C6 of C42 acting via C42/C2×C4=C296C6.C4^296,10
C4.Dic62nd non-split extension by C4 of Dic6 acting via Dic6/Dic3=C296C4.Dic696,15
C6.SD161st non-split extension by C6 of SD16 acting via SD16/C8=C296C6.SD1696,23
C23.32D61st central extension by C23 of D696C2^3.32D696,38
C4×C24Abelian group of type [4,24]96C4xC2496,46
C2×C48Abelian group of type [2,48]96C2xC4896,59
C24×C6Abelian group of type [2,2,2,2,6]96C2^4xC696,231
C22×C24Abelian group of type [2,2,24]96C2^2xC2496,176
C23×C12Abelian group of type [2,2,2,12]96C2^3xC1296,220
C2×C4×C12Abelian group of type [2,4,12]96C2xC4xC1296,161
C4×S4Direct product of C4 and S4123C4xS496,186
D4×A4Direct product of D4 and A4126+D4xA496,197
C22×S4Direct product of C22 and S412C2^2xS496,226
C2×GL2(𝔽3)Direct product of C2 and GL2(𝔽3)16C2xGL(2,3)96,189
C8×A4Direct product of C8 and A4243C8xA496,73
S3×D8Direct product of S3 and D8244+S3xD896,117
Q8×A4Direct product of Q8 and A4246-Q8xA496,199
C23×A4Direct product of C23 and A424C2^3xA496,228
S3×SD16Direct product of S3 and SD16244S3xSD1696,120
S3×M4(2)Direct product of S3 and M4(2)244S3xM4(2)96,113
C3×2+ 1+4Direct product of C3 and 2+ 1+4244C3xES+(2,2)96,224
C4×SL2(𝔽3)Direct product of C4 and SL2(𝔽3)32C4xSL(2,3)96,69
C2×CSU2(𝔽3)Direct product of C2 and CSU2(𝔽3)32C2xCSU(2,3)96,188
C22×SL2(𝔽3)Direct product of C22 and SL2(𝔽3)32C2^2xSL(2,3)96,198
C6×D8Direct product of C6 and D848C6xD896,179
S3×C16Direct product of C16 and S3482S3xC1696,4
C3×D16Direct product of C3 and D16482C3xD1696,61
C4×D12Direct product of C4 and D1248C4xD1296,80
C2×D24Direct product of C2 and D2448C2xD2496,110
D4×C12Direct product of C12 and D448D4xC1296,165
S3×Q16Direct product of S3 and Q16484-S3xQ1696,124
S3×C42Direct product of C42 and S348S3xC4^296,78
S3×C24Direct product of C24 and S348S3xC2^496,230
C3×SD32Direct product of C3 and SD32482C3xSD3296,62
D4×Dic3Direct product of D4 and Dic348D4xDic396,141
C6×SD16Direct product of C6 and SD1648C6xSD1696,180
C22×D12Direct product of C22 and D1248C2^2xD1296,207
C3×M5(2)Direct product of C3 and M5(2)482C3xM5(2)96,60
C6×M4(2)Direct product of C6 and M4(2)48C6xM4(2)96,177
C3×2- 1+4Direct product of C3 and 2- 1+4484C3xES-(2,2)96,225
C3×Q32Direct product of C3 and Q32962C3xQ3296,63
Q8×C12Direct product of C12 and Q896Q8xC1296,166
C6×Q16Direct product of C6 and Q1696C6xQ1696,181
C8×Dic3Direct product of C8 and Dic396C8xDic396,20
C4×Dic6Direct product of C4 and Dic696C4xDic696,75
Q8×Dic3Direct product of Q8 and Dic396Q8xDic396,152
C2×Dic12Direct product of C2 and Dic1296C2xDic1296,112
C22×Dic6Direct product of C22 and Dic696C2^2xDic696,205
C23×Dic3Direct product of C23 and Dic396C2^3xDic396,218
C2×C42⋊C3Direct product of C2 and C42⋊C3123C2xC4^2:C396,68
C2×C22⋊A4Direct product of C2 and C22⋊A412C2xC2^2:A496,229
C2×C4×A4Direct product of C2×C4 and A424C2xC4xA496,196
C2×S3×D4Direct product of C2, S3 and D424C2xS3xD496,209
C3×C4≀C2Direct product of C3 and C4≀C2242C3xC4wrC296,54
C2×A4⋊C4Direct product of C2 and A4⋊C424C2xA4:C496,194
S3×C4○D4Direct product of S3 and C4○D4244S3xC4oD496,215
C3×C23⋊C4Direct product of C3 and C23⋊C4244C3xC2^3:C496,49
S3×C22⋊C4Direct product of S3 and C22⋊C424S3xC2^2:C496,87
C3×C8⋊C22Direct product of C3 and C8⋊C22244C3xC8:C2^296,183
C3×C4.D4Direct product of C3 and C4.D4244C3xC4.D496,50
C3×C22≀C2Direct product of C3 and C22≀C224C3xC2^2wrC296,167
C2×C4.A4Direct product of C2 and C4.A432C2xC4.A496,200
S3×C2×C8Direct product of C2×C8 and S348S3xC2xC896,106
D4×C2×C6Direct product of C2×C6 and D448D4xC2xC696,221
S3×C4⋊C4Direct product of S3 and C4⋊C448S3xC4:C496,98
C2×S3×Q8Direct product of C2, S3 and Q848C2xS3xQ896,212
C4×C3⋊D4Direct product of C4 and C3⋊D448C4xC3:D496,135
C2×C8⋊S3Direct product of C2 and C8⋊S348C2xC8:S396,107
C2×D6⋊C4Direct product of C2 and D6⋊C448C2xD6:C496,134
C2×D4⋊S3Direct product of C2 and D4⋊S348C2xD4:S396,138
C3×C8○D4Direct product of C3 and C8○D4482C3xC8oD496,178
C3×C4○D8Direct product of C3 and C4○D8482C3xC4oD896,182
C6×C4○D4Direct product of C6 and C4○D448C6xC4oD496,223
C3×C4⋊D4Direct product of C3 and C4⋊D448C3xC4:D496,168
S3×C22×C4Direct product of C22×C4 and S348S3xC2^2xC496,206
C2×C24⋊C2Direct product of C2 and C24⋊C248C2xC24:C296,109
C2×C4○D12Direct product of C2 and C4○D1248C2xC4oD1296,208
C3×D4⋊C4Direct product of C3 and D4⋊C448C3xD4:C496,52
C3×C8.C4Direct product of C3 and C8.C4482C3xC8.C496,58
C3×C41D4Direct product of C3 and C41D448C3xC4:1D496,174
C3×C22⋊C8Direct product of C3 and C22⋊C848C3xC2^2:C896,48
C6×C22⋊C4Direct product of C6 and C22⋊C448C6xC2^2:C496,162
C2×D4.S3Direct product of C2 and D4.S348C2xD4.S396,140
C2×C6.D4Direct product of C2 and C6.D448C2xC6.D496,159
C22×C3⋊D4Direct product of C22 and C3⋊D448C2^2xC3:D496,219
C3×C22⋊Q8Direct product of C3 and C22⋊Q848C3xC2^2:Q896,169
C2×D42S3Direct product of C2 and D42S348C2xD4:2S396,210
C3×C42⋊C2Direct product of C3 and C42⋊C248C3xC4^2:C296,164
C2×Q82S3Direct product of C2 and Q82S348C2xQ8:2S396,148
C2×Q83S3Direct product of C2 and Q83S348C2xQ8:3S396,213
C3×C4.4D4Direct product of C3 and C4.4D448C3xC4.4D496,171
C3×C8.C22Direct product of C3 and C8.C22484C3xC8.C2^296,184
C2×C4.Dic3Direct product of C2 and C4.Dic348C2xC4.Dic396,128
C3×C422C2Direct product of C3 and C422C248C3xC4^2:2C296,173
C3×C4.10D4Direct product of C3 and C4.10D4484C3xC4.10D496,51
C3×C22.D4Direct product of C3 and C22.D448C3xC2^2.D496,170
C4×C3⋊C8Direct product of C4 and C3⋊C896C4xC3:C896,9
C3×C4⋊C8Direct product of C3 and C4⋊C896C3xC4:C896,55
C6×C4⋊C4Direct product of C6 and C4⋊C496C6xC4:C496,163
C2×C3⋊C16Direct product of C2 and C3⋊C1696C2xC3:C1696,18
Q8×C2×C6Direct product of C2×C6 and Q896Q8xC2xC696,222
C3×C4⋊Q8Direct product of C3 and C4⋊Q896C3xC4:Q896,175
C3×C8⋊C4Direct product of C3 and C8⋊C496C3xC8:C496,47
C22×C3⋊C8Direct product of C22 and C3⋊C896C2^2xC3:C896,127
C2×C4×Dic3Direct product of C2×C4 and Dic396C2xC4xDic396,129
C2×C3⋊Q16Direct product of C2 and C3⋊Q1696C2xC3:Q1696,150
C2×C4⋊Dic3Direct product of C2 and C4⋊Dic396C2xC4:Dic396,132
C3×Q8⋊C4Direct product of C3 and Q8⋊C496C3xQ8:C496,53
C3×C2.D8Direct product of C3 and C2.D896C3xC2.D896,57
C3×C4.Q8Direct product of C3 and C4.Q896C3xC4.Q896,56
C2×Dic3⋊C4Direct product of C2 and Dic3⋊C496C2xDic3:C496,130
C3×C2.C42Direct product of C3 and C2.C4296C3xC2.C4^296,45
C3×C42.C2Direct product of C3 and C42.C296C3xC4^2.C296,172

Groups of order 97

dρLabelID
C97Cyclic group971C9797,1

Groups of order 98

dρLabelID
C98Cyclic group981C9898,2
D49Dihedral group492+D4998,1
C7⋊D7The semidirect product of C7 and D7 acting via D7/C7=C249C7:D798,4
C7×C14Abelian group of type [7,14]98C7xC1498,5
C7×D7Direct product of C7 and D7; = AΣL1(𝔽49)142C7xD798,3

Groups of order 99

dρLabelID
C99Cyclic group991C9999,1
C3×C33Abelian group of type [3,33]99C3xC3399,2

Groups of order 100

dρLabelID
C100Cyclic group1001C100100,2
D50Dihedral group; = C2×D25502+D50100,4
Dic25Dicyclic group; = C252C41002-Dic25100,1
C52⋊C44th semidirect product of C52 and C4 acting faithfully104+C5^2:C4100,12
C25⋊C4The semidirect product of C25 and C4 acting faithfully254+C25:C4100,3
C5⋊F51st semidirect product of C5 and F5 acting via F5/C5=C425C5:F5100,11
C526C42nd semidirect product of C52 and C4 acting via C4/C2=C2100C5^2:6C4100,7
D5.D5The non-split extension by D5 of D5 acting via D5/C5=C2204D5.D5100,10
C102Abelian group of type [10,10]100C10^2100,16
C2×C50Abelian group of type [2,50]100C2xC50100,5
C5×C20Abelian group of type [5,20]100C5xC20100,8
D52Direct product of D5 and D5104+D5^2100,13
C5×F5Direct product of C5 and F5204C5xF5100,9
D5×C10Direct product of C10 and D5202D5xC10100,14
C5×Dic5Direct product of C5 and Dic5202C5xDic5100,6
C2×C5⋊D5Direct product of C2 and C5⋊D550C2xC5:D5100,15

Groups of order 101

dρLabelID
C101Cyclic group1011C101101,1

Groups of order 102

dρLabelID
C102Cyclic group1021C102102,4
D51Dihedral group512+D51102,3
S3×C17Direct product of C17 and S3512S3xC17102,1
C3×D17Direct product of C3 and D17512C3xD17102,2

Groups of order 103

dρLabelID
C103Cyclic group1031C103103,1

Groups of order 104

dρLabelID
C104Cyclic group1041C104104,2
D52Dihedral group522+D52104,6
Dic26Dicyclic group; = C13Q81042-Dic26104,4
C13⋊D4The semidirect product of C13 and D4 acting via D4/C22=C2522C13:D4104,8
C13⋊C8The semidirect product of C13 and C8 acting via C8/C2=C41044-C13:C8104,3
C132C8The semidirect product of C13 and C8 acting via C8/C4=C21042C13:2C8104,1
C2×C52Abelian group of type [2,52]104C2xC52104,9
C22×C26Abelian group of type [2,2,26]104C2^2xC26104,14
C4×D13Direct product of C4 and D13522C4xD13104,5
D4×C13Direct product of C13 and D4522D4xC13104,10
C22×D13Direct product of C22 and D1352C2^2xD13104,13
Q8×C13Direct product of C13 and Q81042Q8xC13104,11
C2×Dic13Direct product of C2 and Dic13104C2xDic13104,7
C2×C13⋊C4Direct product of C2 and C13⋊C4264+C2xC13:C4104,12

Groups of order 105

dρLabelID
C105Cyclic group1051C105105,2
C5×C7⋊C3Direct product of C5 and C7⋊C3353C5xC7:C3105,1

Groups of order 106

dρLabelID
C106Cyclic group1061C106106,2
D53Dihedral group532+D53106,1

Groups of order 107

dρLabelID
C107Cyclic group1071C107107,1

Groups of order 108

dρLabelID
C108Cyclic group1081C108108,2
D54Dihedral group; = C2×D27542+D54108,4
Dic27Dicyclic group; = C27C41082-Dic27108,1
C32⋊D6The semidirect product of C32 and D6 acting faithfully96+C3^2:D6108,17
C33⋊C42nd semidirect product of C33 and C4 acting faithfully124C3^3:C4108,37
C324D6The semidirect product of C32 and D6 acting via D6/C3=C22124C3^2:4D6108,40
He3⋊C4The semidirect product of He3 and C4 acting faithfully183He3:C4108,15
C32⋊A4The semidirect product of C32 and A4 acting via A4/C22=C3183C3^2:A4108,22
C9⋊A4The semidirect product of C9 and A4 acting via A4/C22=C3363C9:A4108,19
C9⋊C12The semidirect product of C9 and C12 acting via C12/C2=C6366-C9:C12108,9
C32⋊C12The semidirect product of C32 and C12 acting via C12/C2=C6366-C3^2:C12108,8
He33C42nd semidirect product of He3 and C4 acting via C4/C2=C2363He3:3C4108,11
C9⋊Dic3The semidirect product of C9 and Dic3 acting via Dic3/C6=C2108C9:Dic3108,10
C335C43rd semidirect product of C33 and C4 acting via C4/C2=C2108C3^3:5C4108,34
C32.A4The non-split extension by C32 of A4 acting via A4/C22=C3183C3^2.A4108,21
C9.A4The central extension by C9 of A4543C9.A4108,3
C2×C54Abelian group of type [2,54]108C2xC54108,5
C3×C36Abelian group of type [3,36]108C3xC36108,12
C6×C18Abelian group of type [6,18]108C6xC18108,29
C3×C62Abelian group of type [3,6,6]108C3xC6^2108,45
C32×C12Abelian group of type [3,3,12]108C3^2xC12108,35
S3×D9Direct product of S3 and D9184+S3xD9108,16
C9×A4Direct product of C9 and A4363C9xA4108,18
C6×D9Direct product of C6 and D9362C6xD9108,23
S3×C18Direct product of C18 and S3362S3xC18108,24
C4×He3Direct product of C4 and He3363C4xHe3108,13
C32×A4Direct product of C32 and A436C3^2xA4108,41
C3×Dic9Direct product of C3 and Dic9362C3xDic9108,6
C9×Dic3Direct product of C9 and Dic3362C9xDic3108,7
C22×He3Direct product of C22 and He336C2^2xHe3108,30
C32×Dic3Direct product of C32 and Dic336C3^2xDic3108,32
C4×3- 1+2Direct product of C4 and 3- 1+2363C4xES-(3,1)108,14
C22×3- 1+2Direct product of C22 and 3- 1+236C2^2xES-(3,1)108,31
C3×S32Direct product of C3, S3 and S3124C3xS3^2108,38
C3×C32⋊C4Direct product of C3 and C32⋊C4124C3xC3^2:C4108,36
C2×C9⋊C6Direct product of C2 and C9⋊C6; = Aut(D18) = Hol(C18)186+C2xC9:C6108,26
S3×C3⋊S3Direct product of S3 and C3⋊S318S3xC3:S3108,39
C2×C32⋊C6Direct product of C2 and C32⋊C6186+C2xC3^2:C6108,25
C2×He3⋊C2Direct product of C2 and He3⋊C2183C2xHe3:C2108,28
S3×C3×C6Direct product of C3×C6 and S336S3xC3xC6108,42
C6×C3⋊S3Direct product of C6 and C3⋊S336C6xC3:S3108,43
C3×C3⋊Dic3Direct product of C3 and C3⋊Dic336C3xC3:Dic3108,33
C2×C9⋊S3Direct product of C2 and C9⋊S354C2xC9:S3108,27
C3×C3.A4Direct product of C3 and C3.A454C3xC3.A4108,20
C2×C33⋊C2Direct product of C2 and C33⋊C254C2xC3^3:C2108,44

Groups of order 109

dρLabelID
C109Cyclic group1091C109109,1

Groups of order 110

dρLabelID
C110Cyclic group1101C110110,6
D55Dihedral group552+D55110,5
F11Frobenius group; = C11C10 = AGL1(𝔽11) = Aut(D11) = Hol(C11)1110+F11110,1
D5×C11Direct product of C11 and D5552D5xC11110,3
C5×D11Direct product of C5 and D11552C5xD11110,4
C2×C11⋊C5Direct product of C2 and C11⋊C5225C2xC11:C5110,2

Groups of order 111

dρLabelID
C111Cyclic group1111C111111,2
C37⋊C3The semidirect product of C37 and C3 acting faithfully373C37:C3111,1

Groups of order 112

dρLabelID
C112Cyclic group1121C112112,2
D56Dihedral group562+D56112,6
Dic28Dicyclic group; = C71Q161122-Dic28112,7
C4○D28Central product of C4 and D28562C4oD28112,30
D4⋊D7The semidirect product of D4 and D7 acting via D7/C7=C2564+D4:D7112,14
Q8⋊D7The semidirect product of Q8 and D7 acting via D7/C7=C2564+Q8:D7112,16
D14⋊C4The semidirect product of D14 and C4 acting via C4/C2=C256D14:C4112,13
C8⋊D73rd semidirect product of C8 and D7 acting via D7/C7=C2562C8:D7112,4
C56⋊C22nd semidirect product of C56 and C2 acting faithfully562C56:C2112,5
D42D7The semidirect product of D4 and D7 acting through Inn(D4)564-D4:2D7112,32
Q82D7The semidirect product of Q8 and D7 acting through Inn(Q8)564+Q8:2D7112,34
C7⋊C16The semidirect product of C7 and C16 acting via C16/C8=C21122C7:C16112,1
C4⋊Dic7The semidirect product of C4 and Dic7 acting via Dic7/C14=C2112C4:Dic7112,12
C7⋊Q16The semidirect product of C7 and Q16 acting via Q16/Q8=C21124-C7:Q16112,17
Dic7⋊C4The semidirect product of Dic7 and C4 acting via C4/C2=C2112Dic7:C4112,11
D4.D7The non-split extension by D4 of D7 acting via D7/C7=C2564-D4.D7112,15
C4.Dic7The non-split extension by C4 of Dic7 acting via Dic7/C14=C2562C4.Dic7112,9
C23.D7The non-split extension by C23 of D7 acting via D7/C7=C256C2^3.D7112,18
C4×C28Abelian group of type [4,28]112C4xC28112,19
C2×C56Abelian group of type [2,56]112C2xC56112,22
C22×C28Abelian group of type [2,2,28]112C2^2xC28112,37
C23×C14Abelian group of type [2,2,2,14]112C2^3xC14112,43
C2×F8Direct product of C2 and F8147+C2xF8112,41
D4×D7Direct product of D4 and D7284+D4xD7112,31
C8×D7Direct product of C8 and D7562C8xD7112,3
C7×D8Direct product of C7 and D8562C7xD8112,24
Q8×D7Direct product of Q8 and D7564-Q8xD7112,33
C2×D28Direct product of C2 and D2856C2xD28112,29
D4×C14Direct product of C14 and D456D4xC14112,38
C7×SD16Direct product of C7 and SD16562C7xSD16112,25
C23×D7Direct product of C23 and D756C2^3xD7112,42
C7×M4(2)Direct product of C7 and M4(2)562C7xM4(2)112,23
C7×Q16Direct product of C7 and Q161122C7xQ16112,26
Q8×C14Direct product of C14 and Q8112Q8xC14112,39
C4×Dic7Direct product of C4 and Dic7112C4xDic7112,10
C2×Dic14Direct product of C2 and Dic14112C2xDic14112,27
C22×Dic7Direct product of C22 and Dic7112C2^2xDic7112,35
C2×C4×D7Direct product of C2×C4 and D756C2xC4xD7112,28
C2×C7⋊D4Direct product of C2 and C7⋊D456C2xC7:D4112,36
C7×C4○D4Direct product of C7 and C4○D4562C7xC4oD4112,40
C7×C22⋊C4Direct product of C7 and C22⋊C456C7xC2^2:C4112,20
C2×C7⋊C8Direct product of C2 and C7⋊C8112C2xC7:C8112,8
C7×C4⋊C4Direct product of C7 and C4⋊C4112C7xC4:C4112,21

Groups of order 113

dρLabelID
C113Cyclic group1131C113113,1

Groups of order 114

dρLabelID
C114Cyclic group1141C114114,6
D57Dihedral group572+D57114,5
C19⋊C6The semidirect product of C19 and C6 acting faithfully196+C19:C6114,1
S3×C19Direct product of C19 and S3572S3xC19114,3
C3×D19Direct product of C3 and D19572C3xD19114,4
C2×C19⋊C3Direct product of C2 and C19⋊C3383C2xC19:C3114,2

Groups of order 115

dρLabelID
C115Cyclic group1151C115115,1

Groups of order 116

dρLabelID
C116Cyclic group1161C116116,2
D58Dihedral group; = C2×D29582+D58116,4
Dic29Dicyclic group; = C292C41162-Dic29116,1
C29⋊C4The semidirect product of C29 and C4 acting faithfully294+C29:C4116,3
C2×C58Abelian group of type [2,58]116C2xC58116,5

Groups of order 117

dρLabelID
C117Cyclic group1171C117117,2
C13⋊C9The semidirect product of C13 and C9 acting via C9/C3=C31173C13:C9117,1
C3×C39Abelian group of type [3,39]117C3xC39117,4
C3×C13⋊C3Direct product of C3 and C13⋊C3393C3xC13:C3117,3

Groups of order 118

dρLabelID
C118Cyclic group1181C118118,2
D59Dihedral group592+D59118,1

Groups of order 119

dρLabelID
C119Cyclic group1191C119119,1

Groups of order 120

dρLabelID
C120Cyclic group1201C120120,4
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simple54+S5120,34
D60Dihedral group602+D60120,28
Dic30Dicyclic group; = C152Q81202-Dic30120,26
SL2(𝔽5)Special linear group on 𝔽52; = C2.A5 = 2I = <2,3,5>242-SL(2,5)120,5
C5⋊S4The semidirect product of C5 and S4 acting via S4/A4=C2206+C5:S4120,38
C15⋊D41st semidirect product of C15 and D4 acting via D4/C2=C22604-C15:D4120,11
C3⋊D20The semidirect product of C3 and D20 acting via D20/D10=C2604+C3:D20120,12
C5⋊D12The semidirect product of C5 and D12 acting via D12/D6=C2604+C5:D12120,13
C157D41st semidirect product of C15 and D4 acting via D4/C22=C2602C15:7D4120,30
C15⋊Q8The semidirect product of C15 and Q8 acting via Q8/C2=C221204-C15:Q8120,14
C153C81st semidirect product of C15 and C8 acting via C8/C4=C21202C15:3C8120,3
C15⋊C81st semidirect product of C15 and C8 acting via C8/C2=C41204C15:C8120,7
D30.C2The non-split extension by D30 of C2 acting faithfully604+D30.C2120,10
C2×C60Abelian group of type [2,60]120C2xC60120,31
C22×C30Abelian group of type [2,2,30]120C2^2xC30120,47
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetries103+C2xA5120,35
S3×F5Direct product of S3 and F5; = Aut(D15) = Hol(C15)158+S3xF5120,36
C5×S4Direct product of C5 and S4203C5xS4120,37
D5×A4Direct product of D5 and A4206+D5xA4120,39
C6×F5Direct product of C6 and F5304C6xF5120,40
C10×A4Direct product of C10 and A4303C10xA4120,43
C5×SL2(𝔽3)Direct product of C5 and SL2(𝔽3)402C5xSL(2,3)120,15
S3×C20Direct product of C20 and S3602S3xC20120,22
D5×C12Direct product of C12 and D5602D5xC12120,17
C3×D20Direct product of C3 and D20602C3xD20120,18
C5×D12Direct product of C5 and D12602C5xD12120,23
C4×D15Direct product of C4 and D15602C4xD15120,27
D4×C15Direct product of C15 and D4602D4xC15120,32
D5×Dic3Direct product of D5 and Dic3604-D5xDic3120,8
S3×Dic5Direct product of S3 and Dic5604-S3xDic5120,9
C22×D15Direct product of C22 and D1560C2^2xD15120,46
Q8×C15Direct product of C15 and Q81202Q8xC15120,33
C6×Dic5Direct product of C6 and Dic5120C6xDic5120,19
C5×Dic6Direct product of C5 and Dic61202C5xDic6120,21
C3×Dic10Direct product of C3 and Dic101202C3xDic10120,16
C10×Dic3Direct product of C10 and Dic3120C10xDic3120,24
C2×Dic15Direct product of C2 and Dic15120C2xDic15120,29
C2×S3×D5Direct product of C2, S3 and D5304+C2xS3xD5120,42
C2×C3⋊F5Direct product of C2 and C3⋊F5304C2xC3:F5120,41
D5×C2×C6Direct product of C2×C6 and D560D5xC2xC6120,44
S3×C2×C10Direct product of C2×C10 and S360S3xC2xC10120,45
C3×C5⋊D4Direct product of C3 and C5⋊D4602C3xC5:D4120,20
C5×C3⋊D4Direct product of C5 and C3⋊D4602C5xC3:D4120,25
C5×C3⋊C8Direct product of C5 and C3⋊C81202C5xC3:C8120,1
C3×C5⋊C8Direct product of C3 and C5⋊C81204C3xC5:C8120,6
C3×C52C8Direct product of C3 and C52C81202C3xC5:2C8120,2

Groups of order 121

dρLabelID
C121Cyclic group1211C121121,1
C112Elementary abelian group of type [11,11]121C11^2121,2

Groups of order 122

dρLabelID
C122Cyclic group1221C122122,2
D61Dihedral group612+D61122,1

Groups of order 123

dρLabelID
C123Cyclic group1231C123123,1

Groups of order 124

dρLabelID
C124Cyclic group1241C124124,2
D62Dihedral group; = C2×D31622+D62124,3
Dic31Dicyclic group; = C31C41242-Dic31124,1
C2×C62Abelian group of type [2,62]124C2xC62124,4

Groups of order 125

dρLabelID
C125Cyclic group1251C125125,1
He5Heisenberg group; = C52C5 = 5+ 1+2255He5125,3
5- 1+2Extraspecial group255ES-(5,1)125,4
C53Elementary abelian group of type [5,5,5]125C5^3125,5
C5×C25Abelian group of type [5,25]125C5xC25125,2

Groups of order 126

dρLabelID
C126Cyclic group1261C126126,6
D63Dihedral group632+D63126,5
C3⋊F7The semidirect product of C3 and F7 acting via F7/C7⋊C3=C2216+C3:F7126,9
C7⋊C18The semidirect product of C7 and C18 acting via C18/C3=C6636C7:C18126,1
C3⋊D21The semidirect product of C3 and D21 acting via D21/C21=C263C3:D21126,15
C3×C42Abelian group of type [3,42]126C3xC42126,16
C3×F7Direct product of C3 and F7216C3xF7126,7
S3×C21Direct product of C21 and S3422S3xC21126,12
C3×D21Direct product of C3 and D21422C3xD21126,13
C7×D9Direct product of C7 and D9632C7xD9126,3
C9×D7Direct product of C9 and D7632C9xD7126,4
C32×D7Direct product of C32 and D763C3^2xD7126,11
S3×C7⋊C3Direct product of S3 and C7⋊C3216S3xC7:C3126,8
C6×C7⋊C3Direct product of C6 and C7⋊C3423C6xC7:C3126,10
C7×C3⋊S3Direct product of C7 and C3⋊S363C7xC3:S3126,14
C2×C7⋊C9Direct product of C2 and C7⋊C91263C2xC7:C9126,2

Groups of order 127

dρLabelID
C127Cyclic group1271C127127,1

Groups of order 128

dρLabelID
C128Cyclic group1281C128128,1
D64Dihedral group642+D64128,161
Q128Generalised quaternion group; = C64.C2 = Dic321282-Q128128,163
2+ 1+6Extraspecial group; = Q82- 1+4168+ES+(2,3)128,2326
2- 1+6Extraspecial group; = D42- 1+4328-ES-(2,3)128,2327
SD128Semidihedral group; = C642C2 = QD128642SD128128,162
M7(2)Modular maximal-cyclic group; = C643C2642M7(2)128,160
C2≀D4Wreath product of C2 by D484+C2wrD4128,928
C8≀C2Wreath product of C8 by C2162C8wrC2128,67
Q8≀C2Wreath product of Q8 by C2164-Q8wrC2128,937
C23≀C2Wreath product of C23 by C216C2^3wrC2128,1578
(C2×C4)≀C2Wreath product of C2×C4 by C216(C2xC4)wrC2128,628
D8○D8Central product of D8 and D8164+D8oD8128,2024
C16○D8Central product of C16 and D8322C16oD8128,902
C8○D16Central product of C8 and D16322C8oD16128,910
D4○D16Central product of D4 and D16324+D4oD16128,2147
D8○Q16Central product of D8 and Q16324-D8oQ16128,2025
D8○SD16Central product of D8 and SD16324D8oSD16128,2022
Q8○SD32Central product of Q8 and SD32324Q8oSD32128,2148
M4(2)○D8Central product of M4(2) and D8324M4(2)oD8128,1689
D4○M5(2)Central product of D4 and M5(2)324D4oM5(2)128,2139
M4(2)○2M4(2)Central product of M4(2) and M4(2)32M4(2)o2M4(2)128,1605
D4○C32Central product of D4 and C32642D4oC32128,990
C4○D32Central product of C4 and D32642C4oD32128,994
D4○Q32Central product of D4 and Q32644-D4oQ32128,2149
C162M4(2)Central product of C16 and M4(2)64C16o2M4(2)128,840
C4○C2≀C4Central product of C4 and C2≀C4164C4oC2wrC4128,852
D4○(C22⋊C8)Central product of D4 and C22⋊C832D4o(C2^2:C8)128,1612
D8⋊D4The semidirect product of D8 and D4 acting via D4/C2=C22168+D8:D4128,922
D16⋊C4The semidirect product of D16 and C4 acting faithfully; = Aut(D16) = Hol(C16)168+D16:C4128,913
C23⋊D8The semidirect product of C23 and D8 acting via D8/C2=D416C2^3:D8128,327
C24⋊Q8The semidirect product of C24 and Q8 acting faithfully168+C2^4:Q8128,764
D83D42nd semidirect product of D8 and D4 acting via D4/C4=C2164+D8:3D4128,945
D86D45th semidirect product of D8 and D4 acting via D4/C4=C2164D8:6D4128,2023
D83Q83rd semidirect product of D8 and Q8 acting via Q8/C4=C2164D8:3Q8128,962
D811D45th semidirect product of D8 and D4 acting via D4/C22=C2168+D8:11D4128,2020
C24⋊C81st semidirect product of C24 and C8 acting via C8/C2=C416C2^4:C8128,48
C25⋊C41st semidirect product of C25 and C4 acting faithfully16C2^5:C4128,513
C42⋊D41st semidirect product of C42 and D4 acting faithfully168+C4^2:D4128,643
C429D43rd semidirect product of C42 and D4 acting via D4/C2=C2216C4^2:9D4128,734
C422D42nd semidirect product of C42 and D4 acting faithfully164C4^2:2D4128,742
C24⋊D41st semidirect product of C24 and D4 acting faithfully16C2^4:D4128,753
C424D44th semidirect product of C42 and D4 acting faithfully164C4^2:4D4128,929
C243D43rd semidirect product of C24 and D4 acting faithfully168+C2^4:3D4128,931
C426D46th semidirect product of C42 and D4 acting faithfully168+C4^2:6D4128,932
C242Q81st semidirect product of C24 and Q8 acting via Q8/C2=C2216C2^4:2Q8128,761
D8⋊C236th semidirect product of D8 and C23 acting via C23/C22=C2168+D8:C2^3128,2317
M4(2)⋊5D45th semidirect product of M4(2) and D4 acting via D4/C2=C22168+M4(2):5D4128,740
C24⋊C232nd semidirect product of C24 and C23 acting faithfully168+C2^4:C2^3128,1758
C42⋊C234th semidirect product of C42 and C23 acting faithfully16C4^2:C2^3128,2264

Full list: Groups of order 128 (2328 groups)

Groups of order 129

dρLabelID
C129Cyclic group1291C129129,2
C43⋊C3The semidirect product of C43 and C3 acting faithfully433C43:C3129,1

Groups of order 130

dρLabelID
C130Cyclic group1301C130130,4
D65Dihedral group652+D65130,3
D5×C13Direct product of C13 and D5652D5xC13130,1
C5×D13Direct product of C5 and D13652C5xD13130,2

Groups of order 131

dρLabelID
C131Cyclic group1311C131131,1

Groups of order 132

dρLabelID
C132Cyclic group1321C132132,4
D66Dihedral group; = C2×D33662+D66132,9
Dic33Dicyclic group; = C331C41322-Dic33132,3
C2×C66Abelian group of type [2,66]132C2xC66132,10
S3×D11Direct product of S3 and D11334+S3xD11132,5
C11×A4Direct product of C11 and A4443C11xA4132,6
S3×C22Direct product of C22 and S3662S3xC22132,8
C6×D11Direct product of C6 and D11662C6xD11132,7
C11×Dic3Direct product of C11 and Dic31322C11xDic3132,1
C3×Dic11Direct product of C3 and Dic111322C3xDic11132,2

Groups of order 133

dρLabelID
C133Cyclic group1331C133133,1

Groups of order 134

dρLabelID
C134Cyclic group1341C134134,2
D67Dihedral group672+D67134,1

Groups of order 135

dρLabelID
C135Cyclic group1351C135135,1
C3×C45Abelian group of type [3,45]135C3xC45135,2
C32×C15Abelian group of type [3,3,15]135C3^2xC15135,5
C5×He3Direct product of C5 and He3453C5xHe3135,3
C5×3- 1+2Direct product of C5 and 3- 1+2453C5xES-(3,1)135,4

Groups of order 136

dρLabelID
C136Cyclic group1361C136136,2
D68Dihedral group682+D68136,6
Dic34Dicyclic group; = C17Q81362-Dic34136,4
C17⋊C8The semidirect product of C17 and C8 acting faithfully178+C17:C8136,12
C17⋊D4The semidirect product of C17 and D4 acting via D4/C22=C2682C17:D4136,8
C173C8The semidirect product of C17 and C8 acting via C8/C4=C21362C17:3C8136,1
C172C8The semidirect product of C17 and C8 acting via C8/C2=C41364-C17:2C8136,3
C2×C68Abelian group of type [2,68]136C2xC68136,9
C22×C34Abelian group of type [2,2,34]136C2^2xC34136,15
C4×D17Direct product of C4 and D17682C4xD17136,5
D4×C17Direct product of C17 and D4682D4xC17136,10
C22×D17Direct product of C22 and D1768C2^2xD17136,14
Q8×C17Direct product of C17 and Q81362Q8xC17136,11
C2×Dic17Direct product of C2 and Dic17136C2xDic17136,7
C2×C17⋊C4Direct product of C2 and C17⋊C4344+C2xC17:C4136,13

Groups of order 137

dρLabelID
C137Cyclic group1371C137137,1

Groups of order 138

dρLabelID
C138Cyclic group1381C138138,4
D69Dihedral group692+D69138,3
S3×C23Direct product of C23 and S3692S3xC23138,1
C3×D23Direct product of C3 and D23692C3xD23138,2

Groups of order 139

dρLabelID
C139Cyclic group1391C139139,1

Groups of order 140

dρLabelID
C140Cyclic group1401C140140,4
D70Dihedral group; = C2×D35702+D70140,10
Dic35Dicyclic group; = C7Dic51402-Dic35140,3
C7⋊F5The semidirect product of C7 and F5 acting via F5/D5=C2354C7:F5140,6
C2×C70Abelian group of type [2,70]140C2xC70140,11
D5×D7Direct product of D5 and D7354+D5xD7140,7
C7×F5Direct product of C7 and F5354C7xF5140,5
C10×D7Direct product of C10 and D7702C10xD7140,8
D5×C14Direct product of C14 and D5702D5xC14140,9
C7×Dic5Direct product of C7 and Dic51402C7xDic5140,1
C5×Dic7Direct product of C5 and Dic71402C5xDic7140,2

Groups of order 141

dρLabelID
C141Cyclic group1411C141141,1

Groups of order 142

dρLabelID
C142Cyclic group1421C142142,2
D71Dihedral group712+D71142,1

Groups of order 143

dρLabelID
C143Cyclic group1431C143143,1

Groups of order 144

dρLabelID
C144Cyclic group1441C144144,2
D72Dihedral group722+D72144,8
Dic36Dicyclic group; = C91Q161442-Dic36144,4
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)98+AGammaL(1,9)144,182
C62⋊C41st semidirect product of C62 and C4 acting faithfully124+C6^2:C4144,136
Dic3⋊D62nd semidirect product of Dic3 and D6 acting via D6/S3=C2; = Hol(Dic3)124+Dic3:D6144,154
C32⋊D8The semidirect product of C32 and D8 acting via D8/C2=D4244C3^2:D8144,117
D6⋊D62nd semidirect product of D6 and D6 acting via D6/S3=C2244D6:D6144,145
C3⋊D24The semidirect product of C3 and D24 acting via D24/D12=C2244+C3:D24144,57
D12⋊S33rd semidirect product of D12 and S3 acting via S3/C3=C2244D12:S3144,139
C325SD163rd semidirect product of C32 and SD16 acting via SD16/C4=C22244+C3^2:5SD16144,60
C322SD16The semidirect product of C32 and SD16 acting via SD16/C2=D4244-C3^2:2SD16144,118
C32⋊M4(2)The semidirect product of C32 and M4(2) acting via M4(2)/C4=C4244C3^2:M4(2)144,131
C42⋊C9The semidirect product of C42 and C9 acting via C9/C3=C3363C4^2:C9144,3
C24⋊C92nd semidirect product of C24 and C9 acting via C9/C3=C336C2^4:C9144,111
C32⋊Q16The semidirect product of C32 and Q16 acting via Q16/C2=D4484-C3^2:Q16144,119
D6⋊Dic3The semidirect product of D6 and Dic3 acting via Dic3/C6=C248D6:Dic3144,64
C322D81st semidirect product of C32 and D8 acting via D8/C4=C22484C3^2:2D8144,56
D125S3The semidirect product of D12 and S3 acting through Inn(D12)484-D12:5S3144,138
C322C16The semidirect product of C32 and C16 acting via C16/C4=C4484C3^2:2C16144,51
C322Q161st semidirect product of C32 and Q16 acting via Q16/C4=C22484C3^2:2Q16144,61
C323Q162nd semidirect product of C32 and Q16 acting via Q16/C4=C22484-C3^2:3Q16144,62
Dic3⋊Dic3The semidirect product of Dic3 and Dic3 acting via Dic3/C6=C248Dic3:Dic3144,66
Dic6⋊S32nd semidirect product of Dic6 and S3 acting via S3/C3=C2484Dic6:S3144,58
D4⋊D9The semidirect product of D4 and D9 acting via D9/C9=C2724+D4:D9144,16
Q8⋊D9The semidirect product of Q8 and D9 acting via D9/C3=S3724+Q8:D9144,32
D18⋊C4The semidirect product of D18 and C4 acting via C4/C2=C272D18:C4144,14
C8⋊D93rd semidirect product of C8 and D9 acting via D9/C9=C2722C8:D9144,6
C72⋊C22nd semidirect product of C72 and C2 acting faithfully722C72:C2144,7
C24⋊S35th semidirect product of C24 and S3 acting via S3/C3=C272C24:S3144,86
C242S32nd semidirect product of C24 and S3 acting via S3/C3=C272C24:2S3144,87
D42D9The semidirect product of D4 and D9 acting through Inn(D4)724-D4:2D9144,42
Q82D9The semidirect product of Q8 and D9 acting via D9/C9=C2724+Q8:2D9144,18
Q83D9The semidirect product of Q8 and D9 acting through Inn(Q8)724+Q8:3D9144,44
C325D82nd semidirect product of C32 and D8 acting via D8/C8=C272C3^2:5D8144,88
C327D82nd semidirect product of C32 and D8 acting via D8/D4=C272C3^2:7D8144,96
D365C2The semidirect product of D36 and C2 acting through Inn(D36)722D36:5C2144,40
C625C43rd semidirect product of C62 and C4 acting via C4/C2=C272C6^2:5C4144,100
C329SD162nd semidirect product of C32 and SD16 acting via SD16/D4=C272C3^2:9SD16144,97
C3211SD162nd semidirect product of C32 and SD16 acting via SD16/Q8=C272C3^2:11SD16144,98
C9⋊C16The semidirect product of C9 and C16 acting via C16/C8=C21442C9:C16144,1
C4⋊Dic9The semidirect product of C4 and Dic9 acting via Dic9/C18=C2144C4:Dic9144,13
C9⋊Q16The semidirect product of C9 and Q16 acting via Q16/Q8=C21444-C9:Q16144,17
Dic9⋊C4The semidirect product of Dic9 and C4 acting via C4/C2=C2144Dic9:C4144,12
C325Q162nd semidirect product of C32 and Q16 acting via Q16/C8=C2144C3^2:5Q16144,89
C327Q162nd semidirect product of C32 and Q16 acting via Q16/Q8=C2144C3^2:7Q16144,99
C12⋊Dic31st semidirect product of C12 and Dic3 acting via Dic3/C6=C2144C12:Dic3144,94
S32⋊C4The semidirect product of S32 and C4 acting via C4/C2=C2124+S3^2:C4144,115
C3⋊S33C82nd semidirect product of C3⋊S3 and C8 acting via C8/C4=C2244C3:S3:3C8144,130
C4⋊(C32⋊C4)The semidirect product of C4 and C32⋊C4 acting via C32⋊C4/C3⋊S3=C2244C4:(C3^2:C4)144,133
C6.6S46th non-split extension by C6 of S4 acting via S4/A4=C2244+C6.6S4144,125
D6.D61st non-split extension by D6 of D6 acting via D6/C6=C2244D6.D6144,141
D6.6D62nd non-split extension by D6 of D6 acting via D6/C6=C2244+D6.6D6144,142
D6.3D63rd non-split extension by D6 of D6 acting via D6/S3=C2244D6.3D6144,147
D6.4D64th non-split extension by D6 of D6 acting via D6/S3=C2244-D6.4D6144,148
C12.29D63rd non-split extension by C12 of D6 acting via D6/S3=C2244C12.29D6144,53
C12.31D65th non-split extension by C12 of D6 acting via D6/S3=C2244C12.31D6144,55
C6.D126th non-split extension by C6 of D12 acting via D12/D6=C224C6.D12144,65
C62.C42nd non-split extension by C62 of C4 acting faithfully244-C6^2.C4144,135
Dic3.D62nd non-split extension by Dic3 of D6 acting via D6/S3=C2244Dic3.D6144,140
C2.PSU3(𝔽2)The central extension by C2 of PSU3(𝔽2)248+C2.PSU(3,2)144,120
C6.S43rd non-split extension by C6 of S4 acting via S4/A4=C2366-C6.S4144,33
C6.7S47th non-split extension by C6 of S4 acting via S4/A4=C2366-C6.7S4144,126
C2.F9The central extension by C2 of F9488-C2.F9144,114
C6.5S45th non-split extension by C6 of S4 acting via S4/A4=C2484-C6.5S4144,124
D6.Dic3The non-split extension by D6 of Dic3 acting via Dic3/C6=C2484D6.Dic3144,54
Dic3.A4The non-split extension by Dic3 of A4 acting through Inn(Dic3)484+Dic3.A4144,127
D12.S31st non-split extension by D12 of S3 acting via S3/C3=C2484-D12.S3144,59
C62.C225th non-split extension by C62 of C22 acting faithfully48C6^2.C2^2144,67
D4.D9The non-split extension by D4 of D9 acting via D9/C9=C2724-D4.D9144,15
Q8.C18The non-split extension by Q8 of C18 acting via C18/C6=C3722Q8.C18144,36
C4.Dic9The non-split extension by C4 of Dic9 acting via Dic9/C18=C2722C4.Dic9144,10
C18.D47th non-split extension by C18 of D4 acting via D4/C22=C272C18.D4144,19
C12.58D619th non-split extension by C12 of D6 acting via D6/C6=C272C12.58D6144,91
C6.11D1211st non-split extension by C6 of D12 acting via D12/C12=C272C6.11D12144,95
C12.59D620th non-split extension by C12 of D6 acting via D6/C6=C272C12.59D6144,171
C12.D624th non-split extension by C12 of D6 acting via D6/C3=C2272C12.D6144,173
C12.26D626th non-split extension by C12 of D6 acting via D6/C3=C2272C12.26D6144,175
Q8.D9The non-split extension by Q8 of D9 acting via D9/C3=S31444-Q8.D9144,31
C24.S39th non-split extension by C24 of S3 acting via S3/C3=C2144C24.S3144,29
C6.Dic64th non-split extension by C6 of Dic6 acting via Dic6/C12=C2144C6.Dic6144,93
C3⋊S3.Q8The non-split extension by C3⋊S3 of Q8 acting via Q8/C2=C22244C3:S3.Q8144,116
C122Abelian group of type [12,12]144C12^2144,101
C4×C36Abelian group of type [4,36]144C4xC36144,20
C2×C72Abelian group of type [2,72]144C2xC72144,23
C3×C48Abelian group of type [3,48]144C3xC48144,30
C6×C24Abelian group of type [6,24]144C6xC24144,104
C22×C36Abelian group of type [2,2,36]144C2^2xC36144,47
C23×C18Abelian group of type [2,2,2,18]144C2^3xC18144,113
C22×C62Abelian group of type [2,2,6,6]144C2^2xC6^2144,197
C2×C6×C12Abelian group of type [2,6,12]144C2xC6xC12144,178
A42Direct product of A4 and A4; = PΩ+4(𝔽3)129+A4^2144,184
S3×S4Direct product of S3 and S4; = Hol(C2×C6)126+S3xS4144,183
C6×S4Direct product of C6 and S4183C6xS4144,188
C2×F9Direct product of C2 and F9188+C2xF9144,185
C2×PSU3(𝔽2)Direct product of C2 and PSU3(𝔽2)188+C2xPSU(3,2)144,187
S3×D12Direct product of S3 and D12244+S3xD12144,144
C3×GL2(𝔽3)Direct product of C3 and GL2(𝔽3)242C3xGL(2,3)144,122
S3×SL2(𝔽3)Direct product of S3 and SL2(𝔽3); = SL2(ℤ/6ℤ)244-S3xSL(2,3)144,128
D4×D9Direct product of D4 and D9364+D4xD9144,41
C12×A4Direct product of C12 and A4363C12xA4144,155
Dic3×A4Direct product of Dic3 and A4366-Dic3xA4144,129
S3×C24Direct product of C24 and S3482S3xC24144,69
C3×D24Direct product of C3 and D24482C3xD24144,72
C6×D12Direct product of C6 and D1248C6xD12144,160
Dic32Direct product of Dic3 and Dic348Dic3^2144,63
S3×Dic6Direct product of S3 and Dic6484-S3xDic6144,137
C6×Dic6Direct product of C6 and Dic648C6xDic6144,158
C3×Dic12Direct product of C3 and Dic12482C3xDic12144,73
Dic3×C12Direct product of C12 and Dic348Dic3xC12144,76
C6×SL2(𝔽3)Direct product of C6 and SL2(𝔽3)48C6xSL(2,3)144,156
C3×CSU2(𝔽3)Direct product of C3 and CSU2(𝔽3)482C3xCSU(2,3)144,121
C8×D9Direct product of C8 and D9722C8xD9144,5
C9×D8Direct product of C9 and D8722C9xD8144,25
Q8×D9Direct product of Q8 and D9724-Q8xD9144,43
C2×D36Direct product of C2 and D3672C2xD36144,39
D4×C18Direct product of C18 and D472D4xC18144,48
C9×SD16Direct product of C9 and SD16722C9xSD16144,26
C32×D8Direct product of C32 and D872C3^2xD8144,106
C23×D9Direct product of C23 and D972C2^3xD9144,112
C9×M4(2)Direct product of C9 and M4(2)722C9xM4(2)144,24
C32×SD16Direct product of C32 and SD1672C3^2xSD16144,107
C32×M4(2)Direct product of C32 and M4(2)72C3^2xM4(2)144,105
C9×Q16Direct product of C9 and Q161442C9xQ16144,27
Q8×C18Direct product of C18 and Q8144Q8xC18144,49
C4×Dic9Direct product of C4 and Dic9144C4xDic9144,11
C2×Dic18Direct product of C2 and Dic18144C2xDic18144,37
C32×Q16Direct product of C32 and Q16144C3^2xQ16144,108
C22×Dic9Direct product of C22 and Dic9144C2^2xDic9144,45
C2×S3≀C2Direct product of C2 and S3≀C2124+C2xS3wrC2144,186
C2×S3×A4Direct product of C2, S3 and A4186+C2xS3xA4144,190
C2×C3⋊S4Direct product of C2 and C3⋊S4186+C2xC3:S4144,189
C2×C3.S4Direct product of C2 and C3.S4186+C2xC3.S4144,109
C4×S32Direct product of C4, S3 and S3244C4xS3^2144,143
C3×S3×D4Direct product of C3, S3 and D4244C3xS3xD4144,162
S3×C3⋊D4Direct product of S3 and C3⋊D4244S3xC3:D4144,153
C6×C3⋊D4Direct product of C6 and C3⋊D424C6xC3:D4144,167
C3×D4⋊S3Direct product of C3 and D4⋊S3244C3xD4:S3144,80
C22×S32Direct product of C22, S3 and S324C2^2xS3^2144,192
C4×C32⋊C4Direct product of C4 and C32⋊C4244C4xC3^2:C4144,132
C3×C4○D12Direct product of C3 and C4○D12242C3xC4oD12144,161
C2×C3⋊D12Direct product of C2 and C3⋊D1224C2xC3:D12144,151
C3×D4.S3Direct product of C3 and D4.S3244C3xD4.S3144,81
C3×C6.D4Direct product of C3 and C6.D424C3xC6.D4144,84
C2×C6.D6Direct product of C2 and C6.D624C2xC6.D6144,149
C3×D42S3Direct product of C3 and D42S3244C3xD4:2S3144,163
C22×C32⋊C4Direct product of C22 and C32⋊C424C2^2xC3^2:C4144,191
C3×C4.Dic3Direct product of C3 and C4.Dic3242C3xC4.Dic3144,75
A4×C2×C6Direct product of C2×C6 and A436A4xC2xC6144,193
D4×C3⋊S3Direct product of D4 and C3⋊S336D4xC3:S3144,172
C3×A4⋊C4Direct product of C3 and A4⋊C4363C3xA4:C4144,123
C4×C3.A4Direct product of C4 and C3.A4363C4xC3.A4144,34
C3×C42⋊C3Direct product of C3 and C42⋊C3363C3xC4^2:C3144,68
C3×C22⋊A4Direct product of C3 and C22⋊A436C3xC2^2:A4144,194
C22×C3.A4Direct product of C22 and C3.A436C2^2xC3.A4144,110
C6×C3⋊C8Direct product of C6 and C3⋊C848C6xC3:C8144,74
S3×C3⋊C8Direct product of S3 and C3⋊C8484S3xC3:C8144,52
C3×C3⋊C16Direct product of C3 and C3⋊C16482C3xC3:C16144,28
C3×S3×Q8Direct product of C3, S3 and Q8484C3xS3xQ8144,164
S3×C2×C12Direct product of C2×C12 and S348S3xC2xC12144,159
C3×C8⋊S3Direct product of C3 and C8⋊S3482C3xC8:S3144,70
C3×D6⋊C4Direct product of C3 and D6⋊C448C3xD6:C4144,79
C3×C4.A4Direct product of C3 and C4.A4482C3xC4.A4144,157
S3×C22×C6Direct product of C22×C6 and S348S3xC2^2xC6144,195
C2×S3×Dic3Direct product of C2, S3 and Dic348C2xS3xDic3144,146
Dic3×C2×C6Direct product of C2×C6 and Dic348Dic3xC2xC6144,166
C3×C24⋊C2Direct product of C3 and C24⋊C2482C3xC24:C2144,71
C3×C3⋊Q16Direct product of C3 and C3⋊Q16484C3xC3:Q16144,83
C2×D6⋊S3Direct product of C2 and D6⋊S348C2xD6:S3144,150
C3×C4⋊Dic3Direct product of C3 and C4⋊Dic348C3xC4:Dic3144,78
C3×Dic3⋊C4Direct product of C3 and Dic3⋊C448C3xDic3:C4144,77
C2×C322C8Direct product of C2 and C322C848C2xC3^2:2C8144,134
C3×Q82S3Direct product of C3 and Q82S3484C3xQ8:2S3144,82
C3×Q83S3Direct product of C3 and Q83S3484C3xQ8:3S3144,165
C2×C322Q8Direct product of C2 and C322Q848C2xC3^2:2Q8144,152
C2×C4×D9Direct product of C2×C4 and D972C2xC4xD9144,38
D4×C3×C6Direct product of C3×C6 and D472D4xC3xC6144,179
C8×C3⋊S3Direct product of C8 and C3⋊S372C8xC3:S3144,85
C2×C9⋊D4Direct product of C2 and C9⋊D472C2xC9:D4144,46
Q8×C3⋊S3Direct product of Q8 and C3⋊S372Q8xC3:S3144,174
C9×C4○D4Direct product of C9 and C4○D4722C9xC4oD4144,50
C2×C12⋊S3Direct product of C2 and C12⋊S372C2xC12:S3144,170
C9×C22⋊C4Direct product of C9 and C22⋊C472C9xC2^2:C4144,21
C23×C3⋊S3Direct product of C23 and C3⋊S372C2^3xC3:S3144,196
C32×C4○D4Direct product of C32 and C4○D472C3^2xC4oD4144,181
C2×C327D4Direct product of C2 and C327D472C2xC3^2:7D4144,177
C32×C22⋊C4Direct product of C32 and C22⋊C472C3^2xC2^2:C4144,102
C2×C9⋊C8Direct product of C2 and C9⋊C8144C2xC9:C8144,9
C9×C4⋊C4Direct product of C9 and C4⋊C4144C9xC4:C4144,22
Q8×C3×C6Direct product of C3×C6 and Q8144Q8xC3xC6144,180
C2×Q8⋊C9Direct product of C2 and Q8⋊C9144C2xQ8:C9144,35
C32×C4⋊C4Direct product of C32 and C4⋊C4144C3^2xC4:C4144,103
C4×C3⋊Dic3Direct product of C4 and C3⋊Dic3144C4xC3:Dic3144,92
C2×C324C8Direct product of C2 and C324C8144C2xC3^2:4C8144,90
C2×C324Q8Direct product of C2 and C324Q8144C2xC3^2:4Q8144,168
C22×C3⋊Dic3Direct product of C22 and C3⋊Dic3144C2^2xC3:Dic3144,176
C2×C4×C3⋊S3Direct product of C2×C4 and C3⋊S372C2xC4xC3:S3144,169

Groups of order 145

dρLabelID
C145Cyclic group1451C145145,1

Groups of order 146

dρLabelID
C146Cyclic group1461C146146,2
D73Dihedral group732+D73146,1

Groups of order 147

dρLabelID
C147Cyclic group1471C147147,2
C723C33rd semidirect product of C72 and C3 acting faithfully213C7^2:3C3147,5
C49⋊C3The semidirect product of C49 and C3 acting faithfully493C49:C3147,1
C72⋊C32nd semidirect product of C72 and C3 acting faithfully49C7^2:C3147,4
C7×C21Abelian group of type [7,21]147C7xC21147,6
C7×C7⋊C3Direct product of C7 and C7⋊C3213C7xC7:C3147,3

Groups of order 148

dρLabelID
C148Cyclic group1481C148148,2
D74Dihedral group; = C2×D37742+D74148,4
Dic37Dicyclic group; = C372C41482-Dic37148,1
C37⋊C4The semidirect product of C37 and C4 acting faithfully374+C37:C4148,3
C2×C74Abelian group of type [2,74]148C2xC74148,5

Groups of order 149

dρLabelID
C149Cyclic group1491C149149,1

Groups of order 150

dρLabelID
C150Cyclic group1501C150150,4
D75Dihedral group752+D75150,3
C52⋊S3The semidirect product of C52 and S3 acting faithfully153C5^2:S3150,5
C52⋊C6The semidirect product of C52 and C6 acting faithfully156+C5^2:C6150,6
C5⋊D15The semidirect product of C5 and D15 acting via D15/C15=C275C5:D15150,12
C5×C30Abelian group of type [5,30]150C5xC30150,13
D5×C15Direct product of C15 and D5302D5xC15150,8
C5×D15Direct product of C5 and D15302C5xD15150,11
S3×C25Direct product of C25 and S3752S3xC25150,1
C3×D25Direct product of C3 and D25752C3xD25150,2
S3×C52Direct product of C52 and S375S3xC5^2150,10
C2×C52⋊C3Direct product of C2 and C52⋊C3303C2xC5^2:C3150,7
C3×C5⋊D5Direct product of C3 and C5⋊D575C3xC5:D5150,9

Groups of order 151

dρLabelID
C151Cyclic group1511C151151,1

Groups of order 152

dρLabelID
C152Cyclic group1521C152152,2
D76Dihedral group762+D76152,5
Dic38Dicyclic group; = C19Q81522-Dic38152,3
C19⋊D4The semidirect product of C19 and D4 acting via D4/C22=C2762C19:D4152,7
C19⋊C8The semidirect product of C19 and C8 acting via C8/C4=C21522C19:C8152,1
C2×C76Abelian group of type [2,76]152C2xC76152,8
C22×C38Abelian group of type [2,2,38]152C2^2xC38152,12
C4×D19Direct product of C4 and D19762C4xD19152,4
D4×C19Direct product of C19 and D4762D4xC19152,9
C22×D19Direct product of C22 and D1976C2^2xD19152,11
Q8×C19Direct product of C19 and Q81522Q8xC19152,10
C2×Dic19Direct product of C2 and Dic19152C2xDic19152,6

Groups of order 153

dρLabelID
C153Cyclic group1531C153153,1
C3×C51Abelian group of type [3,51]153C3xC51153,2

Groups of order 154

dρLabelID
C154Cyclic group1541C154154,4
D77Dihedral group772+D77154,3
C11×D7Direct product of C11 and D7772C11xD7154,1
C7×D11Direct product of C7 and D11772C7xD11154,2

Groups of order 155

dρLabelID
C155Cyclic group1551C155155,2
C31⋊C5The semidirect product of C31 and C5 acting faithfully315C31:C5155,1

Groups of order 156

dρLabelID
C156Cyclic group1561C156156,6
D78Dihedral group; = C2×D39782+D78156,17
F13Frobenius group; = C13C12 = AGL1(𝔽13) = Aut(D13) = Hol(C13)1312+F13156,7
Dic39Dicyclic group; = C393C41562-Dic39156,5
C39⋊C41st semidirect product of C39 and C4 acting faithfully394C39:C4156,10
C13⋊A4The semidirect product of C13 and A4 acting via A4/C22=C3523C13:A4156,14
C26.C6The non-split extension by C26 of C6 acting faithfully526-C26.C6156,1
C2×C78Abelian group of type [2,78]156C2xC78156,18
S3×D13Direct product of S3 and D13394+S3xD13156,11
A4×C13Direct product of C13 and A4523A4xC13156,13
S3×C26Direct product of C26 and S3782S3xC26156,16
C6×D13Direct product of C6 and D13782C6xD13156,15
Dic3×C13Direct product of C13 and Dic31562Dic3xC13156,3
C3×Dic13Direct product of C3 and Dic131562C3xDic13156,4
C2×C13⋊C6Direct product of C2 and C13⋊C6266+C2xC13:C6156,8
C3×C13⋊C4Direct product of C3 and C13⋊C4394C3xC13:C4156,9
C4×C13⋊C3Direct product of C4 and C13⋊C3523C4xC13:C3156,2
C22×C13⋊C3Direct product of C22 and C13⋊C352C2^2xC13:C3156,12

Groups of order 157

dρLabelID
C157Cyclic group1571C157157,1

Groups of order 158

dρLabelID
C158Cyclic group1581C158158,2
D79Dihedral group792+D79158,1

Groups of order 159

dρLabelID
C159Cyclic group1591C159159,1

Groups of order 160

dρLabelID
C160Cyclic group1601C160160,2
D80Dihedral group802+D80160,6
Dic40Dicyclic group; = C51Q321602-Dic40160,8
C24⋊D5The semidirect product of C24 and D5 acting faithfully105+C2^4:D5160,234
2- 1+4⋊C5The semidirect product of 2- 1+4 and C5 acting faithfully324-ES-(2,2):C5160,199
C8⋊F53rd semidirect product of C8 and F5 acting via F5/D5=C2404C8:F5160,67
C40⋊C42nd semidirect product of C40 and C4 acting faithfully404C40:C4160,68
C23⋊F5The semidirect product of C23 and F5 acting via F5/C5=C4404C2^3:F5160,86
D8⋊D52nd semidirect product of D8 and D5 acting via D5/C5=C2404D8:D5160,132
C8⋊D101st semidirect product of C8 and D10 acting via D10/C5=C22404+C8:D10160,129
D4⋊F52nd semidirect product of D4 and F5 acting via F5/D5=C2408-D4:F5160,83
Q8⋊F51st semidirect product of Q8 and F5 acting via F5/D5=C2408-Q8:F5160,84
Q82F52nd semidirect product of Q8 and F5 acting via F5/D5=C2408+Q8:2F5160,85
D204C41st semidirect product of D20 and C4 acting via C4/C2=C2402D20:4C4160,12
D207C44th semidirect product of D20 and C4 acting via C4/C2=C2404D20:7C4160,32
D20⋊C41st semidirect product of D20 and C4 acting faithfully408+D20:C4160,82
D40⋊C26th semidirect product of D40 and C2 acting faithfully404+D40:C2160,135
D4⋊D102nd semidirect product of D4 and D10 acting via D10/C10=C2404+D4:D10160,170
D46D102nd semidirect product of D4 and D10 acting through Inn(D4)404D4:6D10160,219
D48D104th semidirect product of D4 and D10 acting through Inn(D4)404+D4:8D10160,224
D5⋊M4(2)The semidirect product of D5 and M4(2) acting via M4(2)/C2×C4=C2404D5:M4(2)160,202
C242D51st semidirect product of C24 and D5 acting via D5/C5=C240C2^4:2D5160,174
C23⋊Dic5The semidirect product of C23 and Dic5 acting via Dic5/C5=C4404C2^3:Dic5160,41
Q82Dic52nd semidirect product of Q8 and Dic5 acting via Dic5/C10=C2404Q8:2Dic5160,44
C22⋊D20The semidirect product of C22 and D20 acting via D20/D10=C240C2^2:D20160,103
C23⋊D101st semidirect product of C23 and D10 acting via D10/C5=C2240C2^3:D10160,158
M4(2)⋊D53rd semidirect product of M4(2) and D5 acting via D5/C5=C2404+M4(2):D5160,30
D5⋊C16The semidirect product of D5 and C16 acting via C16/C8=C2804D5:C16160,64
C5⋊D16The semidirect product of C5 and D16 acting via D16/D8=C2804+C5:D16160,33
C80⋊C25th semidirect product of C80 and C2 acting faithfully802C80:C2160,5
D83D5The semidirect product of D8 and D5 acting through Inn(D8)804-D8:3D5160,133
C16⋊D52nd semidirect product of C16 and D5 acting via D5/C5=C2802C16:D5160,7
C4⋊D20The semidirect product of C4 and D20 acting via D20/C20=C280C4:D20160,95
C42D20The semidirect product of C4 and D20 acting via D20/D10=C280C4:2D20160,116
C207D41st semidirect product of C20 and D4 acting via D4/C22=C280C20:7D4160,151
C202D42nd semidirect product of C20 and D4 acting via D4/C2=C2280C20:2D4160,159
C20⋊D43rd semidirect product of C20 and D4 acting via D4/C2=C2280C20:D4160,161
C5⋊SD32The semidirect product of C5 and SD32 acting via SD32/Q16=C2804+C5:SD32160,35
D206C43rd semidirect product of D20 and C4 acting via C4/C2=C280D20:6C4160,16
D101C81st semidirect product of D10 and C8 acting via C8/C4=C280D10:1C8160,27
D205C42nd semidirect product of D20 and C4 acting via C4/C2=C280D20:5C4160,28
D10⋊C82nd semidirect product of D10 and C8 acting via C8/C4=C280D10:C8160,78
D10⋊D41st semidirect product of D10 and D4 acting via D4/C4=C280D10:D4160,105
D208C45th semidirect product of D20 and C4 acting via C4/C2=C280D20:8C4160,114
D407C2The semidirect product of D40 and C2 acting through Inn(D40)802D40:7C2160,125
D10⋊Q81st semidirect product of D10 and Q8 acting via Q8/C4=C280D10:Q8160,117
D102Q82nd semidirect product of D10 and Q8 acting via Q8/C4=C280D10:2Q8160,118
Q16⋊D52nd semidirect product of Q16 and D5 acting via D5/C5=C2804Q16:D5160,139
D103Q83rd semidirect product of D10 and Q8 acting via Q8/C4=C280D10:3Q8160,167
C42⋊D51st semidirect product of C42 and D5 acting via D5/C5=C280C4^2:D5160,93
C422D52nd semidirect product of C42 and D5 acting via D5/C5=C280C4^2:2D5160,97
D4⋊Dic51st semidirect product of D4 and Dic5 acting via Dic5/C10=C280D4:Dic5160,39
Dic54D41st semidirect product of Dic5 and D4 acting through Inn(Dic5)80Dic5:4D4160,102
SD16⋊D52nd semidirect product of SD16 and D5 acting via D5/C5=C2804-SD16:D5160,136
SD163D5The semidirect product of SD16 and D5 acting through Inn(SD16)804SD16:3D5160,137
Dic5⋊D42nd semidirect product of Dic5 and D4 acting via D4/C22=C280Dic5:D4160,160
C5⋊C32The semidirect product of C5 and C32 acting via C32/C8=C41604C5:C32160,3
C20⋊Q8The semidirect product of C20 and Q8 acting via Q8/C2=C22160C20:Q8160,109
C52C32The semidirect product of C5 and C32 acting via C32/C16=C21602C5:2C32160,1
C203C81st semidirect product of C20 and C8 acting via C8/C4=C2160C20:3C8160,11
C408C44th semidirect product of C40 and C4 acting via C4/C2=C2160C40:8C4160,22
C406C42nd semidirect product of C40 and C4 acting via C4/C2=C2160C40:6C4160,24
C405C41st semidirect product of C40 and C4 acting via C4/C2=C2160C40:5C4160,25
C5⋊Q32The semidirect product of C5 and Q32 acting via Q32/Q16=C21604-C5:Q32160,36
C20⋊C81st semidirect product of C20 and C8 acting via C8/C2=C4160C20:C8160,76
C202Q81st semidirect product of C20 and Q8 acting via Q8/C4=C2160C20:2Q8160,90
Q8⋊Dic51st semidirect product of Q8 and Dic5 acting via Dic5/C10=C2160Q8:Dic5160,42
Dic5⋊C83rd semidirect product of Dic5 and C8 acting via C8/C4=C2160Dic5:C8160,79
Dic53Q8The semidirect product of Dic5 and Q8 acting through Inn(Dic5)160Dic5:3Q8160,108
Dic5⋊Q82nd semidirect product of Dic5 and Q8 acting via Q8/C4=C2160Dic5:Q8160,165
C4⋊C47D51st semidirect product of C4⋊C4 and D5 acting through Inn(C4⋊C4)80C4:C4:7D5160,113
C4⋊C4⋊D56th semidirect product of C4⋊C4 and D5 acting via D5/C5=C280C4:C4:D5160,119
C23.F5The non-split extension by C23 of F5 acting via F5/C5=C4404C2^3.F5160,88
D5.D8The non-split extension by D5 of D8 acting via D8/C8=C2404D5.D8160,69
C20.D48th non-split extension by C20 of D4 acting via D4/C2=C22404C20.D4160,40
D10.D41st non-split extension by D10 of D4 acting via D4/C2=C22404+D10.D4160,74
D4.D101st non-split extension by D4 of D10 acting via D10/C10=C2404D4.D10160,153
D10.3Q83rd non-split extension by D10 of Q8 acting via Q8/C4=C240D10.3Q8160,81
C22.2D201st non-split extension by C22 of D20 acting via D20/D10=C2404C2^2.2D20160,13
D10.C2311st non-split extension by D10 of C23 acting via C23/C22=C2404D10.C2^3160,205
D8.D5The non-split extension by D8 of D5 acting via D5/C5=C2804-D8.D5160,34
D4.F5The non-split extension by D4 of F5 acting through Inn(D4)808-D4.F5160,206
Q8.F5The non-split extension by Q8 of F5 acting through Inn(Q8)808+Q8.F5160,208
C8.F53rd non-split extension by C8 of F5 acting via F5/D5=C2804C8.F5160,65
C40.9C44th non-split extension by C40 of C4 acting via C4/C2=C2802C40.9C4160,19
C40.6C41st non-split extension by C40 of C4 acting via C4/C2=C2802C40.6C4160,26
C40.C42nd non-split extension by C40 of C4 acting faithfully804C40.C4160,70
C20.C81st non-split extension by C20 of C8 acting via C8/C2=C4804C20.C8160,73
C4.D205th non-split extension by C4 of D20 acting via D20/C20=C280C4.D20160,96
C8.D101st non-split extension by C8 of D10 acting via D10/C5=C22804-C8.D10160,130
Q8.Dic5The non-split extension by Q8 of Dic5 acting through Inn(Q8)804Q8.Dic5160,169
D20.3C4The non-split extension by D20 of C4 acting through Inn(D20)802D20.3C4160,122
D20.2C4The non-split extension by D20 of C4 acting via C4/C2=C2804D20.2C4160,128
D4.8D103rd non-split extension by D4 of D10 acting via D10/C10=C2804D4.8D10160,171
D4.9D104th non-split extension by D4 of D10 acting via D10/C10=C2804-D4.9D10160,172
C20.53D410th non-split extension by C20 of D4 acting via D4/C22=C2804C20.53D4160,29
C20.47D44th non-split extension by C20 of D4 acting via D4/C22=C2804-C20.47D4160,31
C20.55D412nd non-split extension by C20 of D4 acting via D4/C22=C280C20.55D4160,37
C20.10D410th non-split extension by C20 of D4 acting via D4/C2=C22804C20.10D4160,43
C20.48D45th non-split extension by C20 of D4 acting via D4/C22=C280C20.48D4160,145
C20.17D417th non-split extension by C20 of D4 acting via D4/C2=C2280C20.17D4160,157
C20.23D423rd non-split extension by C20 of D4 acting via D4/C2=C2280C20.23D4160,168
D10.Q82nd non-split extension by D10 of Q8 acting via Q8/C4=C2804D10.Q8160,71
Q8.D105th non-split extension by Q8 of D10 acting via D10/D5=C2804+Q8.D10160,140
C23.2F51st non-split extension by C23 of F5 acting via F5/D5=C280C2^3.2F5160,87
D10.12D41st non-split extension by D10 of D4 acting via D4/C22=C280D10.12D4160,104
D10.13D42nd non-split extension by D10 of D4 acting via D4/C22=C280D10.13D4160,115
D4.10D10The non-split extension by D4 of D10 acting through Inn(D4)804-D4.10D10160,225
Q8.10D101st non-split extension by Q8 of D10 acting through Inn(Q8)804Q8.10D10160,222
Dic5.D41st non-split extension by Dic5 of D4 acting via D4/C2=C22804-Dic5.D4160,80
Dic5.5D41st non-split extension by Dic5 of D4 acting via D4/C4=C280Dic5.5D4160,106
C23.D103rd non-split extension by C23 of D10 acting via D10/C5=C2280C2^3.D10160,100
C22.D203rd non-split extension by C22 of D20 acting via D20/D10=C280C2^2.D20160,107
C20.C2315th non-split extension by C20 of C23 acting via C23/C2=C22804C20.C2^3160,163
Dic5.14D41st non-split extension by Dic5 of D4 acting via D4/C22=C280Dic5.14D4160,99
C23.11D101st non-split extension by C23 of D10 acting via D10/D5=C280C2^3.11D10160,98
C23.21D102nd non-split extension by C23 of D10 acting via D10/C10=C280C2^3.21D10160,147
C23.23D104th non-split extension by C23 of D10 acting via D10/C10=C280C2^3.23D10160,150
C23.18D108th non-split extension by C23 of D10 acting via D10/D5=C280C2^3.18D10160,156
C10.D81st non-split extension by C10 of D8 acting via D8/D4=C2160C10.D8160,14
C20.Q82nd non-split extension by C20 of Q8 acting via Q8/C2=C22160C20.Q8160,15
C20.8Q85th non-split extension by C20 of Q8 acting via Q8/C4=C2160C20.8Q8160,21
C20.6Q83rd non-split extension by C20 of Q8 acting via Q8/C4=C2160C20.6Q8160,91
C20.44D41st non-split extension by C20 of D4 acting via D4/C22=C2160C20.44D4160,23
C10.Q162nd non-split extension by C10 of Q16 acting via Q16/Q8=C2160C10.Q16160,17
C42.D51st non-split extension by C42 of D5 acting via D5/C5=C2160C4^2.D5160,10
C10.C424th non-split extension by C10 of C42 acting via C42/C4=C4160C10.C4^2160,77
Dic5.Q81st non-split extension by Dic5 of Q8 acting via Q8/C4=C2160Dic5.Q8160,110
C4.Dic103rd non-split extension by C4 of Dic10 acting via Dic10/Dic5=C2160C4.Dic10160,111
C10.10C425th non-split extension by C10 of C42 acting via C42/C2×C4=C2160C10.10C4^2160,38
C4×C40Abelian group of type [4,40]160C4xC40160,46
C2×C80Abelian group of type [2,80]160C2xC80160,59
C22×C40Abelian group of type [2,2,40]160C2^2xC40160,190
C23×C20Abelian group of type [2,2,2,20]160C2^3xC20160,228
C24×C10Abelian group of type [2,2,2,2,10]160C2^4xC10160,238
C2×C4×C20Abelian group of type [2,4,20]160C2xC4xC20160,175
D4×F5Direct product of D4 and F5; = Aut(D20) = Hol(C20)208+D4xF5160,207
D5×D8Direct product of D5 and D8404+D5xD8160,131
C8×F5Direct product of C8 and F5404C8xF5160,66
Q8×F5Direct product of Q8 and F5408-Q8xF5160,209
D5×SD16Direct product of D5 and SD16404D5xSD16160,134
C23×F5Direct product of C23 and F540C2^3xF5160,236
D5×M4(2)Direct product of D5 and M4(2)404D5xM4(2)160,127
C5×2+ 1+4Direct product of C5 and 2+ 1+4404C5xES+(2,2)160,232
D5×C16Direct product of C16 and D5802D5xC16160,4
C5×D16Direct product of C5 and D16802C5xD16160,61
C4×D20Direct product of C4 and D2080C4xD20160,94
C2×D40Direct product of C2 and D4080C2xD40160,124
D4×C20Direct product of C20 and D480D4xC20160,179
C10×D8Direct product of C10 and D880C10xD8160,193
D5×Q16Direct product of D5 and Q16804-D5xQ16160,138
C5×SD32Direct product of C5 and SD32802C5xSD32160,62
D4×Dic5Direct product of D4 and Dic580D4xDic5160,155
D5×C42Direct product of C42 and D580D5xC4^2160,92
D5×C24Direct product of C24 and D580D5xC2^4160,237
C10×SD16Direct product of C10 and SD1680C10xSD16160,194
C22×D20Direct product of C22 and D2080C2^2xD20160,215
C5×M5(2)Direct product of C5 and M5(2)802C5xM5(2)160,60
C10×M4(2)Direct product of C10 and M4(2)80C10xM4(2)160,191
C5×2- 1+4Direct product of C5 and 2- 1+4804C5xES-(2,2)160,233
C5×Q32Direct product of C5 and Q321602C5xQ32160,63
Q8×C20Direct product of C20 and Q8160Q8xC20160,180
C10×Q16Direct product of C10 and Q16160C10xQ16160,195
C8×Dic5Direct product of C8 and Dic5160C8xDic5160,20
Q8×Dic5Direct product of Q8 and Dic5160Q8xDic5160,166
C4×Dic10Direct product of C4 and Dic10160C4xDic10160,89
C2×Dic20Direct product of C2 and Dic20160C2xDic20160,126
C23×Dic5Direct product of C23 and Dic5160C2^3xDic5160,226
C22×Dic10Direct product of C22 and Dic10160C2^2xDic10160,213
C2×C24⋊C5Direct product of C2 and C24⋊C5; = AΣL1(𝔽32)105+C2xC2^4:C5160,235
C2×D4×D5Direct product of C2, D4 and D540C2xD4xD5160,217
C2×C4×F5Direct product of C2×C4 and F540C2xC4xF5160,203
C5×C4≀C2Direct product of C5 and C4≀C2402C5xC4wrC2160,54
C2×C4⋊F5Direct product of C2 and C4⋊F540C2xC4:F5160,204
D5×C4○D4Direct product of D5 and C4○D4404D5xC4oD4160,223
C5×C23⋊C4Direct product of C5 and C23⋊C4404C5xC2^3:C4160,49
C5×C8⋊C22Direct product of C5 and C8⋊C22404C5xC8:C2^2160,197
D5×C22⋊C4Direct product of D5 and C22⋊C440D5xC2^2:C4160,101
C5×C4.D4Direct product of C5 and C4.D4404C5xC4.D4160,50
C2×C22⋊F5Direct product of C2 and C22⋊F540C2xC2^2:F5160,212
C5×C22≀C2Direct product of C5 and C22≀C240C5xC2^2wrC2160,181
D5×C2×C8Direct product of C2×C8 and D580D5xC2xC8160,120
C2×Q8×D5Direct product of C2, Q8 and D580C2xQ8xD5160,220
D5×C4⋊C4Direct product of D5 and C4⋊C480D5xC4:C4160,112
D4×C2×C10Direct product of C2×C10 and D480D4xC2xC10160,229
C4×C5⋊D4Direct product of C4 and C5⋊D480C4xC5:D4160,149
C2×D4⋊D5Direct product of C2 and D4⋊D580C2xD4:D5160,152
C2×D5⋊C8Direct product of C2 and D5⋊C880C2xD5:C8160,200
C5×C8○D4Direct product of C5 and C8○D4802C5xC8oD4160,192
C5×C4○D8Direct product of C5 and C4○D8802C5xC4oD8160,196
C2×C8⋊D5Direct product of C2 and C8⋊D580C2xC8:D5160,121
C5×C4⋊D4Direct product of C5 and C4⋊D480C5xC4:D4160,182
C2×Q8⋊D5Direct product of C2 and Q8⋊D580C2xQ8:D5160,162
C2×C40⋊C2Direct product of C2 and C40⋊C280C2xC40:C2160,123
D5×C22×C4Direct product of C22×C4 and D580D5xC2^2xC4160,214
C2×C4.F5Direct product of C2 and C4.F580C2xC4.F5160,201
C2×C4○D20Direct product of C2 and C4○D2080C2xC4oD20160,216
C10×C4○D4Direct product of C10 and C4○D480C10xC4oD4160,231
C5×D4⋊C4Direct product of C5 and D4⋊C480C5xD4:C4160,52
C5×C8.C4Direct product of C5 and C8.C4802C5xC8.C4160,58
C5×C41D4Direct product of C5 and C41D480C5xC4:1D4160,188
C5×C22⋊C8Direct product of C5 and C22⋊C880C5xC2^2:C8160,48
C2×D4.D5Direct product of C2 and D4.D580C2xD4.D5160,154
C22×C5⋊D4Direct product of C22 and C5⋊D480C2^2xC5:D4160,227
C5×C22⋊Q8Direct product of C5 and C22⋊Q880C5xC2^2:Q8160,183
C2×D10⋊C4Direct product of C2 and D10⋊C480C2xD10:C4160,148
C2×D42D5Direct product of C2 and D42D580C2xD4:2D5160,218
C10×C22⋊C4Direct product of C10 and C22⋊C480C10xC2^2:C4160,176
C5×C42⋊C2Direct product of C5 and C42⋊C280C5xC4^2:C2160,178
C2×Q82D5Direct product of C2 and Q82D580C2xQ8:2D5160,221
C5×C4.4D4Direct product of C5 and C4.4D480C5xC4.4D4160,185
C5×C8.C22Direct product of C5 and C8.C22804C5xC8.C2^2160,198
C2×C4.Dic5Direct product of C2 and C4.Dic580C2xC4.Dic5160,142
C2×C23.D5Direct product of C2 and C23.D580C2xC2^3.D5160,173
C2×C22.F5Direct product of C2 and C22.F580C2xC2^2.F5160,211
C5×C422C2Direct product of C5 and C422C280C5xC4^2:2C2160,187
C5×C4.10D4Direct product of C5 and C4.10D4804C5xC4.10D4160,51
C5×C22.D4Direct product of C5 and C22.D480C5xC2^2.D4160,184
C4×C5⋊C8Direct product of C4 and C5⋊C8160C4xC5:C8160,75
C5×C4⋊C8Direct product of C5 and C4⋊C8160C5xC4:C8160,55
C2×C5⋊C16Direct product of C2 and C5⋊C16160C2xC5:C16160,72
C5×C4⋊Q8Direct product of C5 and C4⋊Q8160C5xC4:Q8160,189
C10×C4⋊C4Direct product of C10 and C4⋊C4160C10xC4:C4160,177
Q8×C2×C10Direct product of C2×C10 and Q8160Q8xC2xC10160,230
C5×C8⋊C4Direct product of C5 and C8⋊C4160C5xC8:C4160,47
C4×C52C8Direct product of C4 and C52C8160C4xC5:2C8160,9
C22×C5⋊C8Direct product of C22 and C5⋊C8160C2^2xC5:C8160,210
C2×C4×Dic5Direct product of C2×C4 and Dic5160C2xC4xDic5160,143
C2×C5⋊Q16Direct product of C2 and C5⋊Q16160C2xC5:Q16160,164
C2×C52C16Direct product of C2 and C52C16160C2xC5:2C16160,18
C2×C4⋊Dic5Direct product of C2 and C4⋊Dic5160C2xC4:Dic5160,146
C5×Q8⋊C4Direct product of C5 and Q8⋊C4160C5xQ8:C4160,53
C5×C2.D8Direct product of C5 and C2.D8160C5xC2.D8160,57
C5×C4.Q8Direct product of C5 and C4.Q8160C5xC4.Q8160,56
C22×C52C8Direct product of C22 and C52C8160C2^2xC5:2C8160,141
C2×C10.D4Direct product of C2 and C10.D4160C2xC10.D4160,144
C5×C2.C42Direct product of C5 and C2.C42160C5xC2.C4^2160,45
C5×C42.C2Direct product of C5 and C42.C2160C5xC4^2.C2160,186

Groups of order 161

dρLabelID
C161Cyclic group1611C161161,1

Groups of order 162

dρLabelID
C162Cyclic group1621C162162,2
D81Dihedral group812+D81162,1
C3≀S3Wreath product of C3 by S393C3wrS3162,10
C33⋊C61st semidirect product of C33 and C6 acting faithfully96+C3^3:C6162,11
C33⋊S32nd semidirect product of C33 and S3 acting faithfully96+C3^3:S3162,19
C9⋊C18The semidirect product of C9 and C18 acting via C18/C3=C6186C9:C18162,6
C32⋊C18The semidirect product of C32 and C18 acting via C18/C3=C6186C3^2:C18162,4
He35S32nd semidirect product of He3 and S3 acting via S3/C3=C2186He3:5S3162,46
C322D92nd semidirect product of C32 and D9 acting via D9/C3=S3186C3^2:2D9162,17
C27⋊C6The semidirect product of C27 and C6 acting faithfully276+C27:C6162,9
He3⋊S33rd semidirect product of He3 and S3 acting faithfully276+He3:S3162,21
He34S31st semidirect product of He3 and S3 acting via S3/C3=C227He3:4S3162,40
C32⋊D91st semidirect product of C32 and D9 acting via D9/C3=S327C3^2:D9162,5
C9⋊D9The semidirect product of C9 and D9 acting via D9/C9=C281C9:D9162,16
C27⋊S3The semidirect product of C27 and S3 acting via S3/C3=C281C27:S3162,18
C34⋊C24th semidirect product of C34 and C2 acting faithfully81C3^4:C2162,54
C324D92nd semidirect product of C32 and D9 acting via D9/C9=C281C3^2:4D9162,45
He3.C61st non-split extension by He3 of C6 acting faithfully273He3.C6162,12
He3.S31st non-split extension by He3 of S3 acting faithfully276+He3.S3162,13
He3.2C62nd non-split extension by He3 of C6 acting faithfully273He3.2C6162,14
He3.2S32nd non-split extension by He3 of S3 acting faithfully276+He3.2S3162,15
He3.3S33rd non-split extension by He3 of S3 acting faithfully276+He3.3S3162,20
He3.4S3The non-split extension by He3 of S3 acting via S3/C3=C2276+He3.4S3162,43
He3.4C6The non-split extension by He3 of C6 acting via C6/C3=C2273He3.4C6162,44
C33.S34th non-split extension by C33 of S3 acting faithfully27C3^3.S3162,42
3- 1+2.S3The non-split extension by 3- 1+2 of S3 acting faithfully276+ES-(3,1).S3162,22
C9×C18Abelian group of type [9,18]162C9xC18162,23
C3×C54Abelian group of type [3,54]162C3xC54162,26
C33×C6Abelian group of type [3,3,3,6]162C3^3xC6162,55
C32×C18Abelian group of type [3,3,18]162C3^2xC18162,47
C9×D9Direct product of C9 and D9182C9xD9162,3
S3×He3Direct product of S3 and He3186S3xHe3162,35
S3×3- 1+2Direct product of S3 and 3- 1+2186S3xES-(3,1)162,37
S3×C27Direct product of C27 and S3542S3xC27162,8
C3×D27Direct product of C3 and D27542C3xD27162,7
C6×He3Direct product of C6 and He354C6xHe3162,48
S3×C33Direct product of C33 and S354S3xC3^3162,51
C32×D9Direct product of C32 and D954C3^2xD9162,32
C6×3- 1+2Direct product of C6 and 3- 1+254C6xES-(3,1)162,49
C3×C9⋊C6Direct product of C3 and C9⋊C6186C3xC9:C6162,36
C2×C3≀C3Direct product of C2 and C3≀C3183C2xC3wrC3162,28
C3×C32⋊C6Direct product of C3 and C32⋊C6186C3xC3^2:C6162,34
C32×C3⋊S3Direct product of C32 and C3⋊S318C3^2xC3:S3162,52
C3×He3⋊C2Direct product of C3 and He3⋊C227C3xHe3:C2162,41
S3×C3×C9Direct product of C3×C9 and S354S3xC3xC9162,33
C3×C9⋊S3Direct product of C3 and C9⋊S354C3xC9:S3162,38
C9×C3⋊S3Direct product of C9 and C3⋊S354C9xC3:S3162,39
C2×C27⋊C3Direct product of C2 and C27⋊C3543C2xC27:C3162,27
C2×C32⋊C9Direct product of C2 and C32⋊C954C2xC3^2:C9162,24
C2×C9○He3Direct product of C2 and C9○He3543C2xC9oHe3162,50
C3×C33⋊C2Direct product of C3 and C33⋊C254C3xC3^3:C2162,53
C2×He3⋊C3Direct product of C2 and He3⋊C3543C2xHe3:C3162,30
C2×He3.C3Direct product of C2 and He3.C3543C2xHe3.C3162,29
C2×C3.He3Direct product of C2 and C3.He3543C2xC3.He3162,31
C2×C9⋊C9Direct product of C2 and C9⋊C9162C2xC9:C9162,25

Groups of order 163

dρLabelID
C163Cyclic group1631C163163,1

Groups of order 164

dρLabelID
C164Cyclic group1641C164164,2
D82Dihedral group; = C2×D41822+D82164,4
Dic41Dicyclic group; = C412C41642-Dic41164,1
C41⋊C4The semidirect product of C41 and C4 acting faithfully414+C41:C4164,3
C2×C82Abelian group of type [2,82]164C2xC82164,5

Groups of order 165

dρLabelID
C165Cyclic group1651C165165,2
C3×C11⋊C5Direct product of C3 and C11⋊C5335C3xC11:C5165,1

Groups of order 166

dρLabelID
C166Cyclic group1661C166166,2
D83Dihedral group832+D83166,1

Groups of order 167

dρLabelID
C167Cyclic group1671C167167,1

Groups of order 168

dρLabelID
C168Cyclic group1681C168168,6
D84Dihedral group842+D84168,36
Dic42Dicyclic group; = C212Q81682-Dic42168,34
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simple73GL(3,2)168,42
AΓL1(𝔽8)Affine semilinear group on 𝔽81; = F8C3 = Aut(F8)87+AGammaL(1,8)168,43
C7⋊S4The semidirect product of C7 and S4 acting via S4/A4=C2286+C7:S4168,46
C4⋊F7The semidirect product of C4 and F7 acting via F7/C7⋊C3=C2286+C4:F7168,9
D7⋊A4The semidirect product of D7 and A4 acting via A4/C22=C3286+D7:A4168,49
Dic7⋊C6The semidirect product of Dic7 and C6 acting faithfully286Dic7:C6168,11
C7⋊C24The semidirect product of C7 and C24 acting via C24/C4=C6566C7:C24168,1
D21⋊C4The semidirect product of D21 and C4 acting via C4/C2=C2844+D21:C4168,14
C21⋊D41st semidirect product of C21 and D4 acting via D4/C2=C22844-C21:D4168,15
C3⋊D28The semidirect product of C3 and D28 acting via D28/D14=C2844+C3:D28168,16
C7⋊D12The semidirect product of C7 and D12 acting via D12/D6=C2844+C7:D12168,17
C217D41st semidirect product of C21 and D4 acting via D4/C22=C2842C21:7D4168,38
C21⋊Q8The semidirect product of C21 and Q8 acting via Q8/C2=C221684-C21:Q8168,18
C21⋊C81st semidirect product of C21 and C8 acting via C8/C4=C21682C21:C8168,5
C4.F7The non-split extension by C4 of F7 acting via F7/C7⋊C3=C2566-C4.F7168,7
C14.A4The non-split extension by C14 of A4 acting via A4/C22=C3566C14.A4168,23
C2×C84Abelian group of type [2,84]168C2xC84168,39
C22×C42Abelian group of type [2,2,42]168C2^2xC42168,57
C3×F8Direct product of C3 and F8247C3xF8168,44
C7×S4Direct product of C7 and S4283C7xS4168,45
A4×D7Direct product of A4 and D7286+A4xD7168,48
C4×F7Direct product of C4 and F7286C4xF7168,8
C22×F7Direct product of C22 and F728C2^2xF7168,47
A4×C14Direct product of C14 and A4423A4xC14168,52
C7×SL2(𝔽3)Direct product of C7 and SL2(𝔽3)562C7xSL(2,3)168,22
S3×C28Direct product of C28 and S3842S3xC28168,30
C12×D7Direct product of C12 and D7842C12xD7168,25
C3×D28Direct product of C3 and D28842C3xD28168,26
C7×D12Direct product of C7 and D12842C7xD12168,31
C4×D21Direct product of C4 and D21842C4xD21168,35
D4×C21Direct product of C21 and D4842D4xC21168,40
Dic3×D7Direct product of Dic3 and D7844-Dic3xD7168,12
S3×Dic7Direct product of S3 and Dic7844-S3xDic7168,13
C22×D21Direct product of C22 and D2184C2^2xD21168,56
Q8×C21Direct product of C21 and Q81682Q8xC21168,41
C6×Dic7Direct product of C6 and Dic7168C6xDic7168,27
C7×Dic6Direct product of C7 and Dic61682C7xDic6168,29
C3×Dic14Direct product of C3 and Dic141682C3xDic14168,24
Dic3×C14Direct product of C14 and Dic3168Dic3xC14168,32
C2×Dic21Direct product of C2 and Dic21168C2xDic21168,37
D4×C7⋊C3Direct product of D4 and C7⋊C3286D4xC7:C3168,20
C2×C7⋊A4Direct product of C2 and C7⋊A4423C2xC7:A4168,53
C2×S3×D7Direct product of C2, S3 and D7424+C2xS3xD7168,50
C8×C7⋊C3Direct product of C8 and C7⋊C3563C8xC7:C3168,2
Q8×C7⋊C3Direct product of Q8 and C7⋊C3566Q8xC7:C3168,21
C2×C7⋊C12Direct product of C2 and C7⋊C1256C2xC7:C12168,10
C23×C7⋊C3Direct product of C23 and C7⋊C356C2^3xC7:C3168,51
C2×C6×D7Direct product of C2×C6 and D784C2xC6xD7168,54
S3×C2×C14Direct product of C2×C14 and S384S3xC2xC14168,55
C3×C7⋊D4Direct product of C3 and C7⋊D4842C3xC7:D4168,28
C7×C3⋊D4Direct product of C7 and C3⋊D4842C7xC3:D4168,33
C7×C3⋊C8Direct product of C7 and C3⋊C81682C7xC3:C8168,3
C3×C7⋊C8Direct product of C3 and C7⋊C81682C3xC7:C8168,4
C2×C4×C7⋊C3Direct product of C2×C4 and C7⋊C356C2xC4xC7:C3168,19

Groups of order 169

dρLabelID
C169Cyclic group1691C169169,1
C132Elementary abelian group of type [13,13]169C13^2169,2

Groups of order 170

dρLabelID
C170Cyclic group1701C170170,4
D85Dihedral group852+D85170,3
D5×C17Direct product of C17 and D5852D5xC17170,1
C5×D17Direct product of C5 and D17852C5xD17170,2

Groups of order 171

dρLabelID
C171Cyclic group1711C171171,2
C19⋊C9The semidirect product of C19 and C9 acting faithfully199C19:C9171,3
C192C9The semidirect product of C19 and C9 acting via C9/C3=C31713C19:2C9171,1
C3×C57Abelian group of type [3,57]171C3xC57171,5
C3×C19⋊C3Direct product of C3 and C19⋊C3573C3xC19:C3171,4

Groups of order 172

dρLabelID
C172Cyclic group1721C172172,2
D86Dihedral group; = C2×D43862+D86172,3
Dic43Dicyclic group; = C43C41722-Dic43172,1
C2×C86Abelian group of type [2,86]172C2xC86172,4

Groups of order 173

dρLabelID
C173Cyclic group1731C173173,1

Groups of order 174

dρLabelID
C174Cyclic group1741C174174,4
D87Dihedral group872+D87174,3
S3×C29Direct product of C29 and S3872S3xC29174,1
C3×D29Direct product of C3 and D29872C3xD29174,2

Groups of order 175

dρLabelID
C175Cyclic group1751C175175,1
C5×C35Abelian group of type [5,35]175C5xC35175,2

Groups of order 176

dρLabelID
C176Cyclic group1761C176176,2
D88Dihedral group882+D88176,6
Dic44Dicyclic group; = C111Q161762-Dic44176,7
D22⋊C4The semidirect product of D22 and C4 acting via C4/C2=C288D22:C4176,13
D4⋊D11The semidirect product of D4 and D11 acting via D11/C11=C2884+D4:D11176,14
Q8⋊D11The semidirect product of Q8 and D11 acting via D11/C11=C2884+Q8:D11176,16
C88⋊C24th semidirect product of C88 and C2 acting faithfully882C88:C2176,4
C8⋊D112nd semidirect product of C8 and D11 acting via D11/C11=C2882C8:D11176,5
D445C2The semidirect product of D44 and C2 acting through Inn(D44)882D44:5C2176,30
D42D11The semidirect product of D4 and D11 acting through Inn(D4)884-D4:2D11176,32
D44⋊C24th semidirect product of D44 and C2 acting faithfully884+D44:C2176,34
C11⋊C16The semidirect product of C11 and C16 acting via C16/C8=C21762C11:C16176,1
C44⋊C41st semidirect product of C44 and C4 acting via C4/C2=C2176C44:C4176,12
C11⋊Q16The semidirect product of C11 and Q16 acting via Q16/Q8=C21764-C11:Q16176,17
Dic11⋊C4The semidirect product of Dic11 and C4 acting via C4/C2=C2176Dic11:C4176,11
D4.D11The non-split extension by D4 of D11 acting via D11/C11=C2884-D4.D11176,15
C44.C41st non-split extension by C44 of C4 acting via C4/C2=C2882C44.C4176,9
C23.D11The non-split extension by C23 of D11 acting via D11/C11=C288C2^3.D11176,18
C4×C44Abelian group of type [4,44]176C4xC44176,19
C2×C88Abelian group of type [2,88]176C2xC88176,22
C22×C44Abelian group of type [2,2,44]176C2^2xC44176,37
C23×C22Abelian group of type [2,2,2,22]176C2^3xC22176,42
D4×D11Direct product of D4 and D11444+D4xD11176,31
C8×D11Direct product of C8 and D11882C8xD11176,3
C11×D8Direct product of C11 and D8882C11xD8176,24
C2×D44Direct product of C2 and D4488C2xD44176,29
D4×C22Direct product of C22 and D488D4xC22176,38
Q8×D11Direct product of Q8 and D11884-Q8xD11176,33
C11×SD16Direct product of C11 and SD16882C11xSD16176,25
C23×D11Direct product of C23 and D1188C2^3xD11176,41
C11×M4(2)Direct product of C11 and M4(2)882C11xM4(2)176,23
Q8×C22Direct product of C22 and Q8176Q8xC22176,39
C11×Q16Direct product of C11 and Q161762C11xQ16176,26
C4×Dic11Direct product of C4 and Dic11176C4xDic11176,10
C2×Dic22Direct product of C2 and Dic22176C2xDic22176,27
C22×Dic11Direct product of C22 and Dic11176C2^2xDic11176,35
C2×C4×D11Direct product of C2×C4 and D1188C2xC4xD11176,28
C2×C11⋊D4Direct product of C2 and C11⋊D488C2xC11:D4176,36
C11×C4○D4Direct product of C11 and C4○D4882C11xC4oD4176,40
C11×C22⋊C4Direct product of C11 and C22⋊C488C11xC2^2:C4176,20
C2×C11⋊C8Direct product of C2 and C11⋊C8176C2xC11:C8176,8
C11×C4⋊C4Direct product of C11 and C4⋊C4176C11xC4:C4176,21

Groups of order 177

dρLabelID
C177Cyclic group1771C177177,1

Groups of order 178

dρLabelID
C178Cyclic group1781C178178,2
D89Dihedral group892+D89178,1

Groups of order 179

dρLabelID
C179Cyclic group1791C179179,1

Groups of order 180

dρLabelID
C180Cyclic group1801C180180,4
D90Dihedral group; = C2×D45902+D90180,11
Dic45Dicyclic group; = C9Dic51802-Dic45180,3
C32⋊F5The semidirect product of C32 and F5 acting via F5/C5=C4304+C3^2:F5180,25
D15⋊S3The semidirect product of D15 and S3 acting via S3/C3=C2304D15:S3180,30
C32⋊Dic5The semidirect product of C32 and Dic5 acting via Dic5/C5=C4304C3^2:Dic5180,24
C9⋊F5The semidirect product of C9 and F5 acting via F5/D5=C2454C9:F5180,6
C323F52nd semidirect product of C32 and F5 acting via F5/D5=C245C3^2:3F5180,22
C3⋊Dic15The semidirect product of C3 and Dic15 acting via Dic15/C30=C2180C3:Dic15180,17
C2×C90Abelian group of type [2,90]180C2xC90180,12
C3×C60Abelian group of type [3,60]180C3xC60180,18
C6×C30Abelian group of type [6,30]180C6xC30180,37
C3×A5Direct product of C3 and A5; = GL2(𝔽4)153C3xA5180,19
S3×D15Direct product of S3 and D15304+S3xD15180,29
D5×D9Direct product of D5 and D9454+D5xD9180,7
C9×F5Direct product of C9 and F5454C9xF5180,5
C32×F5Direct product of C32 and F545C3^2xF5180,20
S3×C30Direct product of C30 and S3602S3xC30180,33
A4×C15Direct product of C15 and A4603A4xC15180,31
C6×D15Direct product of C6 and D15602C6xD15180,34
Dic3×C15Direct product of C15 and Dic3602Dic3xC15180,14
C3×Dic15Direct product of C3 and Dic15602C3xDic15180,15
D5×C18Direct product of C18 and D5902D5xC18180,9
C10×D9Direct product of C10 and D9902C10xD9180,10
C5×Dic9Direct product of C5 and Dic91802C5xDic9180,1
C9×Dic5Direct product of C9 and Dic51802C9xDic5180,2
C32×Dic5Direct product of C32 and Dic5180C3^2xDic5180,13
C5×S32Direct product of C5, S3 and S3304C5xS3^2180,28
C3×S3×D5Direct product of C3, S3 and D5304C3xS3xD5180,26
C3×C3⋊F5Direct product of C3 and C3⋊F5304C3xC3:F5180,21
C5×C32⋊C4Direct product of C5 and C32⋊C4304C5xC3^2:C4180,23
D5×C3⋊S3Direct product of D5 and C3⋊S345D5xC3:S3180,27
D5×C3×C6Direct product of C3×C6 and D590D5xC3xC6180,32
C10×C3⋊S3Direct product of C10 and C3⋊S390C10xC3:S3180,35
C2×C3⋊D15Direct product of C2 and C3⋊D1590C2xC3:D15180,36
C5×C3.A4Direct product of C5 and C3.A4903C5xC3.A4180,8
C5×C3⋊Dic3Direct product of C5 and C3⋊Dic3180C5xC3:Dic3180,16

Groups of order 181

dρLabelID
C181Cyclic group1811C181181,1

Groups of order 182

dρLabelID
C182Cyclic group1821C182182,4
D91Dihedral group912+D91182,3
C13×D7Direct product of C13 and D7912C13xD7182,1
C7×D13Direct product of C7 and D13912C7xD13182,2

Groups of order 183

dρLabelID
C183Cyclic group1831C183183,2
C61⋊C3The semidirect product of C61 and C3 acting faithfully613C61:C3183,1

Groups of order 184

dρLabelID
C184Cyclic group1841C184184,2
D92Dihedral group922+D92184,5
Dic46Dicyclic group; = C23Q81842-Dic46184,3
C23⋊D4The semidirect product of C23 and D4 acting via D4/C22=C2922C23:D4184,7
C23⋊C8The semidirect product of C23 and C8 acting via C8/C4=C21842C23:C8184,1
C2×C92Abelian group of type [2,92]184C2xC92184,8
C22×C46Abelian group of type [2,2,46]184C2^2xC46184,12
C4×D23Direct product of C4 and D23922C4xD23184,4
D4×C23Direct product of C23 and D4922D4xC23184,9
C22×D23Direct product of C22 and D2392C2^2xD23184,11
Q8×C23Direct product of C23 and Q81842Q8xC23184,10
C2×Dic23Direct product of C2 and Dic23184C2xDic23184,6

Groups of order 185

dρLabelID
C185Cyclic group1851C185185,1

Groups of order 186

dρLabelID
C186Cyclic group1861C186186,6
D93Dihedral group932+D93186,5
C31⋊C6The semidirect product of C31 and C6 acting faithfully316+C31:C6186,1
S3×C31Direct product of C31 and S3932S3xC31186,3
C3×D31Direct product of C3 and D31932C3xD31186,4
C2×C31⋊C3Direct product of C2 and C31⋊C3623C2xC31:C3186,2

Groups of order 187

dρLabelID
C187Cyclic group1871C187187,1

Groups of order 188

dρLabelID
C188Cyclic group1881C188188,2
D94Dihedral group; = C2×D47942+D94188,3
Dic47Dicyclic group; = C47C41882-Dic47188,1
C2×C94Abelian group of type [2,94]188C2xC94188,4

Groups of order 189

dρLabelID
C189Cyclic group1891C189189,2
C7⋊He3The semidirect product of C7 and He3 acting via He3/C32=C3633C7:He3189,8
C63⋊C32nd semidirect product of C63 and C3 acting faithfully633C63:C3189,4
C633C33rd semidirect product of C63 and C3 acting faithfully633C63:3C3189,5
C7⋊C27The semidirect product of C7 and C27 acting via C27/C9=C31893C7:C27189,1
C21.C325th non-split extension by C21 of C32 acting via C32/C3=C3633C21.C3^2189,7
C3×C63Abelian group of type [3,63]189C3xC63189,9
C32×C21Abelian group of type [3,3,21]189C3^2xC21189,13
C7×He3Direct product of C7 and He3633C7xHe3189,10
C7×3- 1+2Direct product of C7 and 3- 1+2633C7xES-(3,1)189,11
C9×C7⋊C3Direct product of C9 and C7⋊C3633C9xC7:C3189,3
C32×C7⋊C3Direct product of C32 and C7⋊C363C3^2xC7:C3189,12
C3×C7⋊C9Direct product of C3 and C7⋊C9189C3xC7:C9189,6

Groups of order 190

dρLabelID
C190Cyclic group1901C190190,4
D95Dihedral group952+D95190,3
D5×C19Direct product of C19 and D5952D5xC19190,1
C5×D19Direct product of C5 and D19952C5xD19190,2

Groups of order 191

dρLabelID
C191Cyclic group1911C191191,1

Groups of order 192

dρLabelID
C192Cyclic group1921C192192,2
D96Dihedral group962+D96192,7
Dic48Dicyclic group; = C31Q641922-Dic48192,9
CU2(𝔽3)Conformal unitary group on 𝔽32; = U2(𝔽3)7C2322CU(2,3)192,963
C2≀A4Wreath product of C2 by A484+C2wrA4192,201
Q82S42nd semidirect product of Q8 and S4 acting via S4/C22=S3; = Hol(Q8)84+Q8:2S4192,1494
C23⋊S42nd semidirect product of C23 and S4 acting faithfully; = Aut(C22×C4)84+C2^3:S4192,1493
C24⋊D61st semidirect product of C24 and D6 acting faithfully; = Aut(C2×Q8)86+C2^4:D6192,955
C42⋊D6The semidirect product of C42 and D6 acting faithfully126+C4^2:D6192,956
C24⋊C121st semidirect product of C24 and C12 acting via C12/C2=C6126+C2^4:C12192,191
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3126+C2^4:4Dic3192,1495
C42⋊A4The semidirect product of C42 and A4 acting faithfully1612+C4^2:A4192,1023
C24⋊A43rd semidirect product of C24 and A4 acting faithfully1612+C2^4:A4192,1009
C245A45th semidirect product of C24 and A4 acting faithfully16C2^4:5A4192,1024
C24⋊Dic3The semidirect product of C24 and Dic3 acting faithfully1612+C2^4:Dic3192,184
C42⋊Dic3The semidirect product of C42 and Dic3 acting faithfully1612+C4^2:Dic3192,185
D4⋊S4The semidirect product of D4 and S4 acting via S4/A4=C2246+D4:S4192,974
C82⋊C3The semidirect product of C82 and C3 acting faithfully243C8^2:C3192,3
C8⋊S43rd semidirect product of C8 and S4 acting via S4/A4=C2246C8:S4192,959
C82S42nd semidirect product of C8 and S4 acting via S4/A4=C2246C8:2S4192,960
A4⋊D8The semidirect product of A4 and D8 acting via D8/C8=C2246+A4:D8192,961
D42S4The semidirect product of D4 and S4 acting through Inn(D4)246D4:2S4192,1473
C26⋊C33rd semidirect product of C26 and C3 acting faithfully24C2^6:C3192,1541
Q83S4The semidirect product of Q8 and S4 acting via S4/A4=C2246Q8:3S4192,976
Q84S4The semidirect product of Q8 and S4 acting through Inn(Q8)246Q8:4S4192,1478
Q8⋊S41st semidirect product of Q8 and S4 acting via S4/C22=S3246Q8:S4192,1490
C23⋊D12The semidirect product of C23 and D12 acting via D12/C3=D4248+C2^3:D12192,300
D121D41st semidirect product of D12 and D4 acting via D4/C2=C22248+D12:1D4192,306
C422A4The semidirect product of C42 and A4 acting via A4/C22=C324C4^2:2A4192,1020
Q85D123rd semidirect product of Q8 and D12 acting via D12/D6=C2244+Q8:5D12192,381
C246D61st semidirect product of C24 and D6 acting via D6/C3=C22244C2^4:6D6192,591
C428D66th semidirect product of C42 and D6 acting via D6/C3=C22244C4^2:8D6192,636
D1218D46th semidirect product of D12 and D4 acting via D4/C22=C2248+D12:18D4192,757
C42⋊C121st semidirect product of C42 and C12 acting via C12/C2=C6246C4^2:C12192,192
C422C122nd semidirect product of C42 and C12 acting via C12/C2=C6246-C4^2:2C12192,193
A4⋊SD16The semidirect product of A4 and SD16 acting via SD16/D4=C2246A4:SD16192,973
A4⋊M4(2)The semidirect product of A4 and M4(2) acting via M4(2)/C2×C4=C2246A4:M4(2)192,968
C245Dic31st semidirect product of C24 and Dic3 acting via Dic3/C3=C4244C2^4:5Dic3192,95
C425Dic33rd semidirect product of C42 and Dic3 acting via Dic3/C3=C4244C4^2:5Dic3192,104
2+ 1+46S31st semidirect product of 2+ 1+4 and S3 acting via S3/C3=C2248+ES+(2,2):6S3192,800
2+ 1+47S32nd semidirect product of 2+ 1+4 and S3 acting via S3/C3=C2248+ES+(2,2):7S3192,803
Q8⋊D12The semidirect product of Q8 and D12 acting via D12/C4=S332Q8:D12192,952
U2(𝔽3)⋊C26th semidirect product of U2(𝔽3) and C2 acting faithfully324U(2,3):C2192,982
GL2(𝔽3)⋊C41st semidirect product of GL2(𝔽3) and C4 acting via C4/C2=C232GL(2,3):C4192,953
SL2(𝔽3)⋊D42nd semidirect product of SL2(𝔽3) and D4 acting via D4/C22=C232SL(2,3):D4192,986
SL2(𝔽3)⋊5D41st semidirect product of SL2(𝔽3) and D4 acting through Inn(SL2(𝔽3))32SL(2,3):5D4192,1003
2+ 1+44C62nd semidirect product of 2+ 1+4 and C6 acting via C6/C2=C3324ES+(2,2):4C6192,1504
GL2(𝔽3)⋊C223rd semidirect product of GL2(𝔽3) and C22 acting via C22/C2=C2324GL(2,3):C2^2192,1482
A4⋊C16The semidirect product of A4 and C16 acting via C16/C8=C2483A4:C16192,186
C48⋊C42nd semidirect product of C48 and C4 acting faithfully484C48:C4192,71

Full list: Groups of order 192 (1543 groups)

Groups of order 193

dρLabelID
C193Cyclic group1931C193193,1

Groups of order 194

dρLabelID
C194Cyclic group1941C194194,2
D97Dihedral group972+D97194,1

Groups of order 195

dρLabelID
C195Cyclic group1951C195195,2
C5×C13⋊C3Direct product of C5 and C13⋊C3653C5xC13:C3195,1

Groups of order 196

dρLabelID
C196Cyclic group1961C196196,2
D98Dihedral group; = C2×D49982+D98196,3
Dic49Dicyclic group; = C49C41962-Dic49196,1
C72⋊C4The semidirect product of C72 and C4 acting faithfully144+C7^2:C4196,8
C7⋊Dic7The semidirect product of C7 and Dic7 acting via Dic7/C14=C2196C7:Dic7196,6
C142Abelian group of type [14,14]196C14^2196,12
C2×C98Abelian group of type [2,98]196C2xC98196,4
C7×C28Abelian group of type [7,28]196C7xC28196,7
D72Direct product of D7 and D7144+D7^2196,9
D7×C14Direct product of C14 and D7282D7xC14196,10
C7×Dic7Direct product of C7 and Dic7282C7xDic7196,5
C2×C7⋊D7Direct product of C2 and C7⋊D798C2xC7:D7196,11

Groups of order 197

dρLabelID
C197Cyclic group1971C197197,1

Groups of order 198

dρLabelID
C198Cyclic group1981C198198,4
D99Dihedral group992+D99198,3
C3⋊D33The semidirect product of C3 and D33 acting via D33/C33=C299C3:D33198,9
C3×C66Abelian group of type [3,66]198C3xC66198,10
S3×C33Direct product of C33 and S3662S3xC33198,6
C3×D33Direct product of C3 and D33662C3xD33198,7
C11×D9Direct product of C11 and D9992C11xD9198,1
C9×D11Direct product of C9 and D11992C9xD11198,2
C32×D11Direct product of C32 and D1199C3^2xD11198,5
C11×C3⋊S3Direct product of C11 and C3⋊S399C11xC3:S3198,8

Groups of order 199

dρLabelID
C199Cyclic group1991C199199,1

Groups of order 200

dρLabelID
C200Cyclic group2001C200200,2
D100Dihedral group1002+D100200,6
Dic50Dicyclic group; = C25Q82002-Dic50200,4
D5≀C2Wreath product of D5 by C2104+D5wrC2200,43
D5⋊F5The semidirect product of D5 and F5 acting via F5/D5=C2; = Hol(D5)108+D5:F5200,42
C52⋊C8The semidirect product of C52 and C8 acting faithfully108+C5^2:C8200,40
C52⋊Q8The semidirect product of C52 and Q8 acting faithfully108+C5^2:Q8200,44
C5⋊D20The semidirect product of C5 and D20 acting via D20/D10=C2204+C5:D20200,25
Dic52D5The semidirect product of Dic5 and D5 acting through Inn(Dic5)204+Dic5:2D5200,23
C523C82nd semidirect product of C52 and C8 acting via C8/C2=C4404C5^2:3C8200,19
C525C84th semidirect product of C52 and C8 acting via C8/C2=C4404-C5^2:5C8200,21
C522D41st semidirect product of C52 and D4 acting via D4/C2=C22404-C5^2:2D4200,24
C522Q8The semidirect product of C52 and Q8 acting via Q8/C2=C22404-C5^2:2Q8200,26
C25⋊D4The semidirect product of C25 and D4 acting via D4/C22=C21002C25:D4200,8
C20⋊D51st semidirect product of C20 and D5 acting via D5/C5=C2100C20:D5200,34
C527D42nd semidirect product of C52 and D4 acting via D4/C22=C2100C5^2:7D4200,36
C25⋊C8The semidirect product of C25 and C8 acting via C8/C2=C42004-C25:C8200,3
C252C8The semidirect product of C25 and C8 acting via C8/C4=C22002C25:2C8200,1
C527C82nd semidirect product of C52 and C8 acting via C8/C4=C2200C5^2:7C8200,16
C524C83rd semidirect product of C52 and C8 acting via C8/C2=C4200C5^2:4C8200,20
C524Q82nd semidirect product of C52 and Q8 acting via Q8/C4=C2200C5^2:4Q8200,32
C5×C40Abelian group of type [5,40]200C5xC40200,17
C2×C100Abelian group of type [2,100]200C2xC100200,9
C10×C20Abelian group of type [10,20]200C10xC20200,37
C22×C50Abelian group of type [2,2,50]200C2^2xC50200,14
C2×C102Abelian group of type [2,10,10]200C2xC10^2200,52
D5×F5Direct product of D5 and F5208+D5xF5200,41
D5×C20Direct product of C20 and D5402D5xC20200,28
C5×D20Direct product of C5 and D20402C5xD20200,29
C10×F5Direct product of C10 and F5404C10xF5200,45
D5×Dic5Direct product of D5 and Dic5404-D5xDic5200,22
C5×Dic10Direct product of C5 and Dic10402C5xDic10200,27
C10×Dic5Direct product of C10 and Dic540C10xDic5200,30
C4×D25Direct product of C4 and D251002C4xD25200,5
D4×C25Direct product of C25 and D41002D4xC25200,10
D4×C52Direct product of C52 and D4100D4xC5^2200,38
C22×D25Direct product of C22 and D25100C2^2xD25200,13
Q8×C25Direct product of C25 and Q82002Q8xC25200,11
Q8×C52Direct product of C52 and Q8200Q8xC5^2200,39
C2×Dic25Direct product of C2 and Dic25200C2xDic25200,7
C2×D52Direct product of C2, D5 and D5204+C2xD5^2200,49
C5×C5⋊D4Direct product of C5 and C5⋊D4202C5xC5:D4200,31
C2×C52⋊C4Direct product of C2 and C52⋊C4204+C2xC5^2:C4200,48
C5×C5⋊C8Direct product of C5 and C5⋊C8404C5xC5:C8200,18
D5×C2×C10Direct product of C2×C10 and D540D5xC2xC10200,50
C5×C52C8Direct product of C5 and C52C8402C5xC5:2C8200,15
C2×D5.D5Direct product of C2 and D5.D5404C2xD5.D5200,46
C2×C25⋊C4Direct product of C2 and C25⋊C4504+C2xC25:C4200,12
C2×C5⋊F5Direct product of C2 and C5⋊F550C2xC5:F5200,47
C4×C5⋊D5Direct product of C4 and C5⋊D5100C4xC5:D5200,33
C22×C5⋊D5Direct product of C22 and C5⋊D5100C2^2xC5:D5200,51
C2×C526C4Direct product of C2 and C526C4200C2xC5^2:6C4200,35

Groups of order 201

dρLabelID
C201Cyclic group2011C201201,2
C67⋊C3The semidirect product of C67 and C3 acting faithfully673C67:C3201,1

Groups of order 202

dρLabelID
C202Cyclic group2021C202202,2
D101Dihedral group1012+D101202,1

Groups of order 203

dρLabelID
C203Cyclic group2031C203203,2
C29⋊C7The semidirect product of C29 and C7 acting faithfully297C29:C7203,1

Groups of order 204

dρLabelID
C204Cyclic group2041C204204,4
D102Dihedral group; = C2×D511022+D102204,11
Dic51Dicyclic group; = C513C42042-Dic51204,3
C51⋊C41st semidirect product of C51 and C4 acting faithfully514C51:C4204,6
C2×C102Abelian group of type [2,102]204C2xC102204,12
S3×D17Direct product of S3 and D17514+S3xD17204,7
A4×C17Direct product of C17 and A4683A4xC17204,8
S3×C34Direct product of C34 and S31022S3xC34204,10
C6×D17Direct product of C6 and D171022C6xD17204,9
Dic3×C17Direct product of C17 and Dic32042Dic3xC17204,1
C3×Dic17Direct product of C3 and Dic172042C3xDic17204,2
C3×C17⋊C4Direct product of C3 and C17⋊C4514C3xC17:C4204,5

Groups of order 205

dρLabelID
C205Cyclic group2051C205205,2
C41⋊C5The semidirect product of C41 and C5 acting faithfully415C41:C5205,1

Groups of order 206

dρLabelID
C206Cyclic group2061C206206,2
D103Dihedral group1032+D103206,1

Groups of order 207

dρLabelID
C207Cyclic group2071C207207,1
C3×C69Abelian group of type [3,69]207C3xC69207,2

Groups of order 208

dρLabelID
C208Cyclic group2081C208208,2
D104Dihedral group1042+D104208,7
Dic52Dicyclic group; = C131Q162082-Dic52208,8
C52⋊C41st semidirect product of C52 and C4 acting faithfully524C52:C4208,31
D4⋊D13The semidirect product of D4 and D13 acting via D13/C13=C21044+D4:D13208,15
D13⋊C8The semidirect product of D13 and C8 acting via C8/C4=C21044D13:C8208,28
Q8⋊D13The semidirect product of Q8 and D13 acting via D13/C13=C21044+Q8:D13208,17
C8⋊D133rd semidirect product of C8 and D13 acting via D13/C13=C21042C8:D13208,5
C104⋊C22nd semidirect product of C104 and C2 acting faithfully1042C104:C2208,6
D26⋊C41st semidirect product of D26 and C4 acting via C4/C2=C2104D26:C4208,14
D525C2The semidirect product of D52 and C2 acting through Inn(D52)1042D52:5C2208,38
D42D13The semidirect product of D4 and D13 acting through Inn(D4)1044-D4:2D13208,40
D52⋊C24th semidirect product of D52 and C2 acting faithfully1044+D52:C2208,42
C13⋊M4(2)The semidirect product of C13 and M4(2) acting via M4(2)/C22=C41044-C13:M4(2)208,33
C13⋊C16The semidirect product of C13 and C16 acting via C16/C4=C42084C13:C16208,3
C523C41st semidirect product of C52 and C4 acting via C4/C2=C2208C52:3C4208,13
C132C16The semidirect product of C13 and C16 acting via C16/C8=C22082C13:2C16208,1
C13⋊Q16The semidirect product of C13 and Q16 acting via Q16/Q8=C22084-C13:Q16208,18
D13.D4The non-split extension by D13 of D4 acting via D4/C22=C2524+D13.D4208,34
D4.D13The non-split extension by D4 of D13 acting via D13/C13=C21044-D4.D13208,16
C52.4C41st non-split extension by C52 of C4 acting via C4/C2=C21042C52.4C4208,10
C52.C41st non-split extension by C52 of C4 acting faithfully1044C52.C4208,29
C23.D13The non-split extension by C23 of D13 acting via D13/C13=C2104C2^3.D13208,19
C26.D41st non-split extension by C26 of D4 acting via D4/C22=C2208C26.D4208,12
C4×C52Abelian group of type [4,52]208C4xC52208,20
C2×C104Abelian group of type [2,104]208C2xC104208,23
C22×C52Abelian group of type [2,2,52]208C2^2xC52208,45
C23×C26Abelian group of type [2,2,2,26]208C2^3xC26208,51
D4×D13Direct product of D4 and D13524+D4xD13208,39
C8×D13Direct product of C8 and D131042C8xD13208,4
C13×D8Direct product of C13 and D81042C13xD8208,25
C2×D52Direct product of C2 and D52104C2xD52208,37
D4×C26Direct product of C26 and D4104D4xC26208,46
Q8×D13Direct product of Q8 and D131044-Q8xD13208,41
C13×SD16Direct product of C13 and SD161042C13xSD16208,26
C23×D13Direct product of C23 and D13104C2^3xD13208,50
C13×M4(2)Direct product of C13 and M4(2)1042C13xM4(2)208,24
Q8×C26Direct product of C26 and Q8208Q8xC26208,47
C13×Q16Direct product of C13 and Q162082C13xQ16208,27
C4×Dic13Direct product of C4 and Dic13208C4xDic13208,11
C2×Dic26Direct product of C2 and Dic26208C2xDic26208,35
C22×Dic13Direct product of C22 and Dic13208C2^2xDic13208,43
C4×C13⋊C4Direct product of C4 and C13⋊C4524C4xC13:C4208,30
C22×C13⋊C4Direct product of C22 and C13⋊C452C2^2xC13:C4208,49
C2×C4×D13Direct product of C2×C4 and D13104C2xC4xD13208,36
C2×C13⋊D4Direct product of C2 and C13⋊D4104C2xC13:D4208,44
C13×C4○D4Direct product of C13 and C4○D41042C13xC4oD4208,48
C13×C22⋊C4Direct product of C13 and C22⋊C4104C13xC2^2:C4208,21
C2×C13⋊C8Direct product of C2 and C13⋊C8208C2xC13:C8208,32
C13×C4⋊C4Direct product of C13 and C4⋊C4208C13xC4:C4208,22
C2×C132C8Direct product of C2 and C132C8208C2xC13:2C8208,9

Groups of order 209

dρLabelID
C209Cyclic group2091C209209,1

Groups of order 210

dρLabelID
C210Cyclic group2101C210210,12
D105Dihedral group1052+D105210,11
C5⋊F7The semidirect product of C5 and F7 acting via F7/C7⋊C3=C2356+C5:F7210,3
C5×F7Direct product of C5 and F7356C5xF7210,1
S3×C35Direct product of C35 and S31052S3xC35210,8
D7×C15Direct product of C15 and D71052D7xC15210,5
D5×C21Direct product of C21 and D51052D5xC21210,6
C3×D35Direct product of C3 and D351052C3xD35210,7
C5×D21Direct product of C5 and D211052C5xD21210,9
C7×D15Direct product of C7 and D151052C7xD15210,10
D5×C7⋊C3Direct product of D5 and C7⋊C3356D5xC7:C3210,2
C10×C7⋊C3Direct product of C10 and C7⋊C3703C10xC7:C3210,4

Groups of order 211

dρLabelID
C211Cyclic group2111C211211,1

Groups of order 212

dρLabelID
C212Cyclic group2121C212212,2
D106Dihedral group; = C2×D531062+D106212,4
Dic53Dicyclic group; = C532C42122-Dic53212,1
C53⋊C4The semidirect product of C53 and C4 acting faithfully534+C53:C4212,3
C2×C106Abelian group of type [2,106]212C2xC106212,5

Groups of order 213

dρLabelID
C213Cyclic group2131C213213,1

Groups of order 214

dρLabelID
C214Cyclic group2141C214214,2
D107Dihedral group1072+D107214,1

Groups of order 215

dρLabelID
C215Cyclic group2151C215215,1

Groups of order 216

dρLabelID
C216Cyclic group2161C216216,2
D108Dihedral group1082+D108216,6
Dic54Dicyclic group; = C27Q82162-Dic54216,4
SU3(𝔽2)Special unitary group on 𝔽23; = He3Q8273SU(3,2)216,88
ASL2(𝔽3)Hessian group = Affine special linear group on 𝔽32; = PSU3(𝔽2)C398+ASL(2,3)216,153
C33⋊D42nd semidirect product of C33 and D4 acting faithfully124C3^3:D4216,158
C322D12The semidirect product of C32 and D12 acting via D12/C3=D4128+C3^2:2D12216,159
He3⋊D4The semidirect product of He3 and D4 acting faithfully186+He3:D4216,87
C32⋊S41st semidirect product of C32 and S4 acting via S4/C22=S3186+C3^2:S4216,92
C62⋊S35th semidirect product of C62 and S3 acting faithfully183C6^2:S3216,95
C62⋊C63rd semidirect product of C62 and C6 acting faithfully186+C6^2:C6216,99
C3⋊F9The semidirect product of C3 and F9 acting via F9/C32⋊C4=C2248C3:F9216,155
C334C82nd semidirect product of C33 and C8 acting via C8/C2=C4244C3^3:4C8216,118
C339D46th semidirect product of C33 and D4 acting via D4/C2=C22244C3^3:9D4216,132
C335Q83rd semidirect product of C33 and Q8 acting via Q8/C2=C22244C3^3:5Q8216,133
C33⋊Q82nd semidirect product of C33 and Q8 acting faithfully248C3^3:Q8216,161
He3⋊C8The semidirect product of He3 and C8 acting faithfully276+He3:C8216,86
C9⋊S4The semidirect product of C9 and S4 acting via S4/A4=C2366+C9:S4216,93
D9⋊A4The semidirect product of D9 and A4 acting via A4/C22=C3366+D9:A4216,96
D36⋊C3The semidirect product of D36 and C3 acting faithfully366+D36:C3216,54
C3⋊D36The semidirect product of C3 and D36 acting via D36/D18=C2364+C3:D36216,29
C9⋊D12The semidirect product of C9 and D12 acting via D12/D6=C2364+C9:D12216,32
Dic9⋊C6The semidirect product of Dic9 and C6 acting faithfully366Dic9:C6216,62
He32D41st semidirect product of He3 and D4 acting via D4/C2=C22366+He3:2D4216,35
He33D42nd semidirect product of He3 and D4 acting via D4/C2=C22366He3:3D4216,37
He34D41st semidirect product of He3 and D4 acting via D4/C4=C2366+He3:4D4216,51
He36D41st semidirect product of He3 and D4 acting via D4/C22=C2366He3:6D4216,60
He35D42nd semidirect product of He3 and D4 acting via D4/C4=C2366He3:5D4216,68
He37D42nd semidirect product of He3 and D4 acting via D4/C22=C2366He3:7D4216,72
C337D44th semidirect product of C33 and D4 acting via D4/C2=C2236C3^3:7D4216,128
C338D45th semidirect product of C33 and D4 acting via D4/C2=C2236C3^3:8D4216,129
C629S39th semidirect product of C62 and S3 acting faithfully36C6^2:9S3216,165
C9⋊C24The semidirect product of C9 and C24 acting via C24/C4=C6726C9:C24216,15
Q8⋊He3The semidirect product of Q8 and He3 acting via He3/C32=C3726Q8:He3216,42
D6⋊D91st semidirect product of D6 and D9 acting via D9/C9=C2724-D6:D9216,31
He33C81st semidirect product of He3 and C8 acting via C8/C4=C2726He3:3C8216,14
He34C82nd semidirect product of He3 and C8 acting via C8/C4=C2723He3:4C8216,17
He32C8The semidirect product of He3 and C8 acting via C8/C2=C4723He3:2C8216,25
He32Q8The semidirect product of He3 and Q8 acting via Q8/C2=C22726-He3:2Q8216,33
He33Q81st semidirect product of He3 and Q8 acting via Q8/C4=C2726-He3:3Q8216,49
He34Q82nd semidirect product of He3 and Q8 acting via Q8/C4=C2726He3:4Q8216,66
C336D43rd semidirect product of C33 and D4 acting via D4/C2=C2272C3^3:6D4216,127
C334Q82nd semidirect product of C33 and Q8 acting via Q8/C2=C2272C3^3:4Q8216,130
C9⋊Dic6The semidirect product of C9 and Dic6 acting via Dic6/Dic3=C2724-C9:Dic6216,26
Q8⋊3- 1+2The semidirect product of Q8 and 3- 1+2 acting via 3- 1+2/C32=C3726Q8:ES-(3,1)216,41
C27⋊D4The semidirect product of C27 and D4 acting via D4/C22=C21082C27:D4216,8
C36⋊S31st semidirect product of C36 and S3 acting via S3/C3=C2108C36:S3216,65
C3312D43rd semidirect product of C33 and D4 acting via D4/C4=C2108C3^3:12D4216,147
C3315D43rd semidirect product of C33 and D4 acting via D4/C22=C2108C3^3:15D4216,149
C27⋊C8The semidirect product of C27 and C8 acting via C8/C4=C22162C27:C8216,1
Q8⋊C27The semidirect product of Q8 and C27 acting via C27/C9=C32162Q8:C27216,3
C337C83rd semidirect product of C33 and C8 acting via C8/C4=C2216C3^3:7C8216,84
C338Q83rd semidirect product of C33 and Q8 acting via Q8/C4=C2216C3^3:8Q8216,145
C339(C2×C4)6th semidirect product of C33 and C2×C4 acting via C2×C4/C2=C22244C3^3:9(C2xC4)216,131
He3⋊(C2×C4)2nd semidirect product of He3 and C2×C4 acting via C2×C4/C2=C22366-He3:(C2xC4)216,36
C338(C2×C4)5th semidirect product of C33 and C2×C4 acting via C2×C4/C2=C2236C3^3:8(C2xC4)216,126
C32.S4The non-split extension by C32 of S4 acting via S4/C22=S3186+C3^2.S4216,90
C18.D63rd non-split extension by C18 of D6 acting via D6/S3=C2364+C18.D6216,28
C9.S4The non-split extension by C9 of S4 acting via S4/A4=C2546+C9.S4216,21
C62.S37th non-split extension by C62 of S3 acting faithfully54C6^2.S3216,94
C18.A4The non-split extension by C18 of A4 acting via A4/C22=C3726C18.A4216,39
C36.C61st non-split extension by C36 of C6 acting faithfully726-C36.C6216,52
C6.D1811st non-split extension by C6 of D18 acting via D18/C18=C2108C6.D18216,70
C36.S36th non-split extension by C36 of S3 acting via S3/C3=C2216C36.S3216,16
C12.D93rd non-split extension by C12 of D9 acting via D9/C9=C2216C12.D9216,63
C6.S322nd non-split extension by C6 of S32 acting via S32/C3⋊S3=C2366C6.S3^2216,34
C63Abelian group of type [6,6,6]216C6^3216,177
C3×C72Abelian group of type [3,72]216C3xC72216,18
C6×C36Abelian group of type [6,36]216C6xC36216,73
C2×C108Abelian group of type [2,108]216C2xC108216,9
C22×C54Abelian group of type [2,2,54]216C2^2xC54216,24
C32×C24Abelian group of type [3,3,24]216C3^2xC24216,85
C2×C6×C18Abelian group of type [2,6,18]216C2xC6xC18216,114
C3×C6×C12Abelian group of type [3,6,12]216C3xC6xC12216,150
C3×F9Direct product of C3 and F9248C3xF9216,154
C3×PSU3(𝔽2)Direct product of C3 and PSU3(𝔽2)248C3xPSU(3,2)216,160
C9×S4Direct product of C9 and S4363C9xS4216,89
A4×D9Direct product of A4 and D9366+A4xD9216,97
D4×He3Direct product of D4 and He3366D4xHe3216,77
C32×S4Direct product of C32 and S436C3^2xS4216,163
D4×3- 1+2Direct product of D4 and 3- 1+2366D4xES-(3,1)216,78
A4×C18Direct product of C18 and A4543A4xC18216,103
S3×C36Direct product of C36 and S3722S3xC36216,47
C12×D9Direct product of C12 and D9722C12xD9216,45
C3×D36Direct product of C3 and D36722C3xD36216,46
C9×D12Direct product of C9 and D12722C9xD12216,48
C8×He3Direct product of C8 and He3723C8xHe3216,19
Q8×He3Direct product of Q8 and He3726Q8xHe3216,80
S3×C62Direct product of C62 and S372S3xC6^2216,174
Dic3×D9Direct product of Dic3 and D9724-Dic3xD9216,27
S3×Dic9Direct product of S3 and Dic9724-S3xDic9216,30
C9×Dic6Direct product of C9 and Dic6722C9xDic6216,44
C6×Dic9Direct product of C6 and Dic972C6xDic9216,55
C3×Dic18Direct product of C3 and Dic18722C3xDic18216,43
Dic3×C18Direct product of C18 and Dic372Dic3xC18216,56
C32×D12Direct product of C32 and D1272C3^2xD12216,137
C23×He3Direct product of C23 and He372C2^3xHe3216,115
C32×Dic6Direct product of C32 and Dic672C3^2xDic6216,135
C9×SL2(𝔽3)Direct product of C9 and SL2(𝔽3)722C9xSL(2,3)216,38
C8×3- 1+2Direct product of C8 and 3- 1+2723C8xES-(3,1)216,20
Q8×3- 1+2Direct product of Q8 and 3- 1+2726Q8xES-(3,1)216,81
C32×SL2(𝔽3)Direct product of C32 and SL2(𝔽3)72C3^2xSL(2,3)216,134
C23×3- 1+2Direct product of C23 and 3- 1+272C2^3xES-(3,1)216,116
C4×D27Direct product of C4 and D271082C4xD27216,5
D4×C27Direct product of C27 and D41082D4xC27216,10
D4×C33Direct product of C33 and D4108D4xC3^3216,151
C22×D27Direct product of C22 and D27108C2^2xD27216,23
Q8×C27Direct product of C27 and Q82162Q8xC27216,11
Q8×C33Direct product of C33 and Q8216Q8xC3^3216,152
C2×Dic27Direct product of C2 and Dic27216C2xDic27216,7
S33Direct product of S3, S3 and S3; = Hol(C3×S3)128+S3^3216,162
C3×S3≀C2Direct product of C3 and S3≀C2124C3xS3wrC2216,157
S3×C32⋊C4Direct product of S3 and C32⋊C4128+S3xC3^2:C4216,156
C2×C32⋊A4Direct product of C2 and C32⋊A4183C2xC3^2:A4216,107
C2×C32⋊D6Direct product of C2 and C32⋊D6186+C2xC3^2:D6216,102
C2×C32.A4Direct product of C2 and C32.A4183C2xC3^2.A4216,106
S32×C6Direct product of C6, S3 and S3244S3^2xC6216,170
C3×S3×A4Direct product of C3, S3 and A4246C3xS3xA4216,166
C3×C3⋊S4Direct product of C3 and C3⋊S4246C3xC3:S4216,164
C6×C32⋊C4Direct product of C6 and C32⋊C4244C6xC3^2:C4216,168
C3×S3×Dic3Direct product of C3, S3 and Dic3244C3xS3xDic3216,119
C3×D6⋊S3Direct product of C3 and D6⋊S3244C3xD6:S3216,121
C3×C3⋊D12Direct product of C3 and C3⋊D12244C3xC3:D12216,122
C2×C33⋊C4Direct product of C2 and C33⋊C4244C2xC3^3:C4216,169
C3×C6.D6Direct product of C3 and C6.D6244C3xC6.D6216,120
C3×C322C8Direct product of C3 and C322C8244C3xC3^2:2C8216,117
C3×C322Q8Direct product of C3 and C322Q8244C3xC3^2:2Q8216,123
C2×C324D6Direct product of C2 and C324D6244C2xC3^2:4D6216,172
C2×S3×D9Direct product of C2, S3 and D9364+C2xS3xD9216,101
C4×C9⋊C6Direct product of C4 and C9⋊C6366C4xC9:C6216,53
A4×C3⋊S3Direct product of A4 and C3⋊S336A4xC3:S3216,167
C3×C9⋊D4Direct product of C3 and C9⋊D4362C3xC9:D4216,57
C9×C3⋊D4Direct product of C9 and C3⋊D4362C9xC3:D4216,58
C3×C3.S4Direct product of C3 and C3.S4366C3xC3.S4216,91
S3×C3.A4Direct product of S3 and C3.A4366S3xC3.A4216,98
C2×He3⋊C4Direct product of C2 and He3⋊C4363C2xHe3:C4216,100
C4×C32⋊C6Direct product of C4 and C32⋊C6366C4xC3^2:C6216,50
C22×C9⋊C6Direct product of C22 and C9⋊C636C2^2xC9:C6216,111
C4×He3⋊C2Direct product of C4 and He3⋊C2363C4xHe3:C2216,67
C32×C3⋊D4Direct product of C32 and C3⋊D436C3^2xC3:D4216,139
C3×C327D4Direct product of C3 and C327D436C3xC3^2:7D4216,144
C22×C32⋊C6Direct product of C22 and C32⋊C636C2^2xC3^2:C6216,110
C22×He3⋊C2Direct product of C22 and He3⋊C236C2^2xHe3:C2216,113
A4×C3×C6Direct product of C3×C6 and A454A4xC3xC6216,173
C2×C9⋊A4Direct product of C2 and C9⋊A4543C2xC9:A4216,104
C2×C9.A4Direct product of C2 and C9.A4543C2xC9.A4216,22
C6×C3.A4Direct product of C6 and C3.A454C6xC3.A4216,105
C3×C9⋊C8Direct product of C3 and C9⋊C8722C3xC9:C8216,12
C9×C3⋊C8Direct product of C9 and C3⋊C8722C9xC3:C8216,13
C2×C6×D9Direct product of C2×C6 and D972C2xC6xD9216,108
S3×C2×C18Direct product of C2×C18 and S372S3xC2xC18216,109
S3×C3×C12Direct product of C3×C12 and S372S3xC3xC12216,136
C2×C9⋊C12Direct product of C2 and C9⋊C1272C2xC9:C12216,61
C2×C4×He3Direct product of C2×C4 and He372C2xC4xHe3216,74
C12×C3⋊S3Direct product of C12 and C3⋊S372C12xC3:S3216,141
C32×C3⋊C8Direct product of C32 and C3⋊C872C3^2xC3:C8216,82
Dic3×C3×C6Direct product of C3×C6 and Dic372Dic3xC3xC6216,138
C3×C12⋊S3Direct product of C3 and C12⋊S372C3xC12:S3216,142
S3×C3⋊Dic3Direct product of S3 and C3⋊Dic372S3xC3:Dic3216,124
Dic3×C3⋊S3Direct product of Dic3 and C3⋊S372Dic3xC3:S3216,125
C6×C3⋊Dic3Direct product of C6 and C3⋊Dic372C6xC3:Dic3216,143
C2×C32⋊C12Direct product of C2 and C32⋊C1272C2xC3^2:C12216,59
C2×He33C4Direct product of C2 and He33C472C2xHe3:3C4216,71
C3×C324C8Direct product of C3 and C324C872C3xC3^2:4C8216,83
C3×C324Q8Direct product of C3 and C324Q872C3xC3^2:4Q8216,140
C2×C4×3- 1+2Direct product of C2×C4 and 3- 1+272C2xC4xES-(3,1)216,75
D4×C3×C9Direct product of C3×C9 and D4108D4xC3xC9216,76
C4×C9⋊S3Direct product of C4 and C9⋊S3108C4xC9:S3216,64
C22×C9⋊S3Direct product of C22 and C9⋊S3108C2^2xC9:S3216,112
C4×C33⋊C2Direct product of C4 and C33⋊C2108C4xC3^3:C2216,146
C22×C33⋊C2Direct product of C22 and C33⋊C2108C2^2xC3^3:C2216,176
Q8×C3×C9Direct product of C3×C9 and Q8216Q8xC3xC9216,79
C3×Q8⋊C9Direct product of C3 and Q8⋊C9216C3xQ8:C9216,40
C2×C9⋊Dic3Direct product of C2 and C9⋊Dic3216C2xC9:Dic3216,69
C2×C335C4Direct product of C2 and C335C4216C2xC3^3:5C4216,148
C2×S3×C3⋊S3Direct product of C2, S3 and C3⋊S336C2xS3xC3:S3216,171
C2×C6×C3⋊S3Direct product of C2×C6 and C3⋊S372C2xC6xC3:S3216,175

Groups of order 217

dρLabelID
C217Cyclic group2171C217217,1

Groups of order 218

dρLabelID
C218Cyclic group2181C218218,2
D109Dihedral group109</