Non-abelian groups

A group is non-abelian or non-commutative if it is not abelian, in other words if not all elements of the group commute. See also abelian groups.

Groups of order 6

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

Groups of order 8

dρLabelID
D4Dihedral group; = He2 = AΣL1(𝔽4) = 2+ 1+2 = square symmetries42+D48,3
Q8Quaternion group; = C4.C2 = Dic2 = 2- 1+282-Q88,4

Groups of order 10

dρLabelID
D5Dihedral group; = pentagon symmetries52+D510,1

Groups of order 12

dρLabelID
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

Groups of order 14

dρLabelID
D7Dihedral group72+D714,1

Groups of order 16

dρLabelID
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
C2×D4Direct product of C2 and D48C2xD416,11
C2×Q8Direct product of C2 and Q816C2xQ816,12

Groups of order 18

dρLabelID
D9Dihedral group92+D918,1
C3⋊S3The semidirect product of C3 and S3 acting via S3/C3=C29C3:S318,4
C3×S3Direct product of C3 and S3; = U2(𝔽2)62C3xS318,3

Groups of order 20

dρLabelID
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

Groups of order 21

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

Groups of order 22

dρLabelID
D11Dihedral group112+D1122,1

Groups of order 24

dρLabelID
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×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 26

dρLabelID
D13Dihedral group132+D1326,1

Groups of order 27

dρLabelID
He3Heisenberg group; = C32C3 = 3+ 1+293He327,3
3- 1+2Extraspecial group93ES-(3,1)27,4

Groups of order 28

dρLabelID
D14Dihedral group; = C2×D7142+D1428,3
Dic7Dicyclic group; = C7C4282-Dic728,1

Groups of order 30

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

Groups of order 32

dρLabelID
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+4Extraspecial 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
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 34

dρLabelID
D17Dihedral group172+D1734,1

Groups of order 36

dρLabelID
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
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 38

dρLabelID
D19Dihedral group192+D1938,1

Groups of order 39

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

Groups of order 40

dρLabelID
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×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 42

dρLabelID
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 44

dρLabelID
D22Dihedral group; = C2×D11222+D2244,3
Dic11Dicyclic group; = C11C4442-Dic1144,1

Groups of order 46

dρLabelID
D23Dihedral group232+D2346,1

Groups of order 48

dρLabelID
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
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 50

dρLabelID
D25Dihedral group252+D2550,1
C5⋊D5The semidirect product of C5 and D5 acting via D5/C5=C225C5:D550,4
C5×D5Direct product of C5 and D5; = AΣL1(𝔽25)102C5xD550,3

Groups of order 52

dρLabelID
D26Dihedral group; = C2×D13262+D2652,4
Dic13Dicyclic group; = C132C4522-Dic1352,1
C13⋊C4The semidirect product of C13 and C4 acting faithfully134+C13:C452,3

Groups of order 54

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

Groups of order 56

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

Groups of order 58

dρLabelID
D29Dihedral group292+D2958,1

Groups of order 60

dρLabelID
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
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 62

dρLabelID
D31Dihedral group312+D3162,1

Groups of order 63

dρLabelID
C7⋊C9The semidirect product of C7 and C9 acting via C9/C3=C3633C7:C963,1
C3×C7⋊C3Direct product of C3 and C7⋊C3213C3xC7:C363,3

Groups of order 64

dρLabelID
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
D4○SD16Central product of D4 and SD16164D4oSD1664,258
Q8○M4(2)Central product of Q8 and M4(2)164Q8oM4(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
C23.33C236th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.33C2^364,201
C23.36C239th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.36C2^364,210
C22.26C2412nd central stem extension by C22 of C2432C2^2.26C2^464,213
C23.37C2310th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.37C2^364,214
C23.38C2311st non-split extension by C23 of C23 acting via C23/C22=C232C2^3.38C2^364,217
C22.31C2417th central stem extension by C22 of C2432C2^2.31C2^464,218
C22.33C2419th central stem extension by C22 of C2432C2^2.33C2^464,220
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
C23.41C2314th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.41C2^364,225
C22.46C2432nd central stem extension by C22 of C2432C2^2.46C2^464,233
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
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 66

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

Groups of order 68

dρLabelID
D34Dihedral group; = C2×D17342+D3468,4
Dic17Dicyclic group; = C172C4682-Dic1768,1
C17⋊C4The semidirect product of C17 and C4 acting faithfully174+C17:C468,3

Groups of order 70

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

Groups of order 72

dρLabelID
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
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 74

dρLabelID
D37Dihedral group372+D3774,1

Groups of order 75

dρLabelID
C52⋊C3The semidirect product of C52 and C3 acting faithfully153C5^2:C375,2

Groups of order 76

dρLabelID
D38Dihedral group; = C2×D19382+D3876,3
Dic19Dicyclic group; = C19C4762-Dic1976,1

Groups of order 78

dρLabelID
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 80

dρLabelID
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
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
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
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
D41Dihedral group412+D4182,1

Groups of order 84

dρLabelID
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×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 86

dρLabelID
D43Dihedral group432+D4386,1

Groups of order 88

dρLabelID
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
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 90

dρLabelID
D45Dihedral group452+D4590,3
C3⋊D15The semidirect product of C3 and D15 acting via D15/C15=C245C3:D1590,9
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 92

dρLabelID
D46Dihedral group; = C2×D23462+D4692,3
Dic23Dicyclic group; = C23C4922-Dic2392,1

Groups of order 93

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

Groups of order 94

dρLabelID
D47Dihedral group472+D4794,1

Groups of order 96

dρLabelID
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
D8⋊S32nd semidirect product of D8 and S3 acting via S3/C3=C2244D8:S396,118
D4⋊D62nd semidirect product of D4 and D6 acting via D6/C6=C2244+D4:D696,156
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
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×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 98

dρLabelID
D49Dihedral group492+D4998,1
C7⋊D7The semidirect product of C7 and D7 acting via D7/C7=C249C7:D798,4
C7×D7Direct product of C7 and D7; = AΣL1(𝔽49)142C7xD798,3

Groups of order 100

dρLabelID
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
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 102

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

Groups of order 104

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

Groups of order 106

dρLabelID
D53Dihedral group532+D53106,1

Groups of order 108

dρLabelID
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
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 110

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

Groups of order 112

dρLabelID
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
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 114

dρLabelID
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 116

dρLabelID
D58Dihedral group; = C2×D29582+D58116,4
Dic29Dicyclic group; = C292C41162-Dic29116,1
C29⋊C4The semidirect product of C29 and C4 acting faithfully294+C29:C4116,3

Groups of order 117

dρLabelID
C13⋊C9The semidirect product of C13 and C9 acting via C9/C3=C31173C13:C9117,1
C3×C13⋊C3Direct product of C3 and C13⋊C3393C3xC13:C3117,3

Groups of order 118

dρLabelID
D59Dihedral group592+D59118,1

Groups of order 120

dρLabelID
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×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
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