# Smallest transitive degree

When G acts on a (finite) set, the set is a disjoint union of orbits, the transitive G-sets. There is a natural bijection

 {transitive G-sets up to ≅} ↔ {subgroups of G up to conjugacy} X ↦ stabiliser of a point G/H ↤ H

Transitive G-sets on which G acts faithfully correspond to subgroups H with trivial core (or core-free), that is those where the intersection of H with all of its conjugates is trivial; equivalently, H contains no non-trivial normal subgroup of G. In this case G can be viewed as a transitive subgroup of Sn for n=(G:H), the index of H in G, called the transitive degree. Conversely, all transitive subgroups of Sn arise in this way. The transitive group database in GAP and Magma contains all transitive subgroups of Sn up to conjugacy for n≤31, numbered nTi (or Tn,i).

See all transitive groups of degree up to 15 and up to 31 for the transitive group numbering. The table below orders groups by the smallest n for which G is a transitive subgroup of Sn, provided n≤120. In other words, it is the index of the largest core-free subgroup H of G. (Often H={1}, for example for abelian and many other soluble groups, so G may only act transitively on itself by left multiplication, by the regular action.)

### 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 6

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

### 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 8

dρLabelID
D4Dihedral group; = He2 = AΣL1(𝔽4) = 2+ 1+2 = square symmetries42+D48,3

### Groups of order 12

dρLabelID
A4Alternating group on 4 letters; = PSL2(𝔽3) = L2(3) = tetrahedron rotations43+A412,3

### Groups of order 24

dρLabelID
S4Symmetric group on 4 letters; = PGL2(𝔽3) = Aut(Q8) = Hol(C22) = tetrahedron symmetries = cube/octahedron rotations43+S424,12

### Groups of order 5

dρLabelID
C5Cyclic group; = pentagon rotations51C55,1

### Groups of order 10

dρLabelID
D5Dihedral group; = pentagon symmetries52+D510,1

### Groups of order 20

dρLabelID
F5Frobenius group; = C5C4 = AGL1(𝔽5) = Aut(D5) = Hol(C5) = Sz(2)54+F520,3

### 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

### Groups of order 120

dρLabelID
S5Symmetric group on 5 letters; = PGL2(𝔽5) = Aut(A5) = 5-cell symmetries; almost simple54+S5120,34

### Groups of order 6

dρLabelID
C6Cyclic group; = hexagon rotations61C66,2

### Groups of order 12

dρLabelID
D6Dihedral group; = C2×S3 = hexagon symmetries62+D612,4

### Groups of order 18

dρLabelID
C3×S3Direct product of C3 and S3; = U2(𝔽2)62C3xS318,3

### Groups of order 24

dρLabelID
C2×A4Direct product of C2 and A4; = AΣL1(𝔽8)63+C2xA424,13

### Groups of order 36

dρLabelID
C32⋊C4The semidirect product of C32 and C4 acting faithfully64+C3^2:C436,9
S32Direct product of S3 and S3; = Spin+4(𝔽2) = Hol(S3)64+S3^236,10

### Groups of order 48

dρLabelID
C2×S4Direct product of C2 and S4; = O3(𝔽3) = cube/octahedron symmetries63+C2xS448,48

### Groups of order 72

dρLabelID
S3≀C2Wreath product of S3 by C2; = SO+4(𝔽2)64+S3wrC272,40

### Groups of order 360

dρLabelID
A6Alternating group on 6 letters; = PSL2(𝔽9) = L2(9); 3rd non-abelian simple65+A6360,118

### Groups of order 7

dρLabelID
C7Cyclic group71C77,1

### Groups of order 14

dρLabelID
D7Dihedral group72+D714,1

### Groups of order 21

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

### Groups of order 42

dρLabelID
F7Frobenius group; = C7C6 = AGL1(𝔽7) = Aut(D7) = Hol(C7)76+F742,1

### Groups of order 168

dρLabelID
GL3(𝔽2)General linear group on 𝔽23; = Aut(C23) = L3(2) = L2(7); 2nd non-abelian simple73GL(3,2)168,42

### Groups of order 8

dρLabelID
C8Cyclic group81C88,1
C2×C4Abelian group of type [2,4]8C2xC48,2
Q8Quaternion group; = C4.C2 = Dic2 = 2- 1+282-Q88,4
C23Elementary abelian group of type [2,2,2]8C2^38,5

### Groups of order 16

dρLabelID
C22⋊C4The semidirect product of C22 and C4 acting via C4/C2=C28C2^2:C416,3
M4(2)Modular maximal-cyclic group; = C83C282M4(2)16,6
D8Dihedral group82+D816,7
SD16Semidihedral group; = Q8C2 = QD1682SD1616,8
C2×D4Direct product of C2 and D48C2xD416,11
C4○D4Pauli group = central product of C4 and D482C4oD416,13

### Groups of order 24

dρLabelID
SL2(𝔽3)Special linear group on 𝔽32; = Q8C3 = 2T = <2,3,3> = 1st non-monomial group82-SL(2,3)24,3

### Groups of order 32

dρLabelID
C23⋊C4The semidirect product of C23 and C4 acting faithfully84+C2^3:C432,6
C4.D41st non-split extension by C4 of D4 acting via D4/C22=C284+C4.D432,7
C4≀C2Wreath product of C4 by C282C4wrC232,11
C22≀C2Wreath product of C22 by C28C2^2wrC232,27
C8⋊C22The semidirect product of C8 and C22 acting faithfully; = Aut(D8) = Hol(C8)84+C8:C2^232,43
2+ 1+4Extraspecial group; = D4D484+ES+(2,2)32,49

### Groups of order 48

dρLabelID
GL2(𝔽3)General linear group on 𝔽32; = Q8S3 = Aut(C32)82GL(2,3)48,29

### Groups of order 56

dρLabelID
F8Frobenius group; = C23C7 = AGL1(𝔽8)87+F856,11

### Groups of order 64

dρLabelID
C2≀C4Wreath product of C2 by C4; = AΣL1(𝔽16)84+C2wrC464,32
C42⋊C42nd semidirect product of C42 and C4 acting faithfully84+C4^2:C464,34
D44D43rd semidirect product of D4 and D4 acting via D4/C22=C2; = Hol(D4)84+D4:4D464,134
C2≀C22Wreath product of C2 by C22; = Hol(C2×C4)84+C2wrC2^264,138

### Groups of order 96

dρLabelID
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
C22⋊S4The semidirect product of C22 and S4 acting via S4/C22=S386+C2^2:S496,227

### Groups of order 128

dρLabelID
D4≀C2Wreath product of D4 by C284+D4wrC2128,928

### Groups of order 168

dρLabelID
AΓL1(𝔽8)Affine semilinear group on 𝔽81; = F8C3 = Aut(F8)87+AGammaL(1,8)168,43

### Groups of order 192

dρLabelID
C2≀A4Wreath product of C2 by A484+C2wrA4192,201
C24⋊D61st semidirect product of C24 and D6 acting faithfully; = Aut(C2×Q8)86+C2^4:D6192,955
C23⋊S42nd semidirect product of C23 and S4 acting faithfully; = Aut(C22×C4)84+C2^3:S4192,1493
Q82S42nd semidirect product of Q8 and S4 acting via S4/C22=S3; = Hol(Q8)84+Q8:2S4192,1494

### Groups of order 288

dρLabelID
A4≀C2Wreath product of A4 by C286+A4wrC2288,1025

### Groups of order 336

dρLabelID
PGL2(𝔽7)Projective linear group on 𝔽72; = GL3(𝔽2)C2 = Aut(GL3(𝔽2)); almost simple86+PGL(2,7)336,208

### Groups of order 9

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

### Groups of order 18

dρLabelID
D9Dihedral group92+D918,1
C3⋊S3The semidirect product of C3 and S3 acting via S3/C3=C29C3:S318,4

### Groups of order 27

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

### Groups of order 54

dρLabelID
C32⋊C6The semidirect product of C32 and C6 acting faithfully96+C3^2:C654,5
C9⋊C6The semidirect product of C9 and C6 acting faithfully; = Aut(D9) = Hol(C9)96+C9:C654,6
He3⋊C22nd semidirect product of He3 and C2 acting faithfully; = Aut(3- 1+2)93He3:C254,8

### Groups of order 72

dρLabelID
F9Frobenius group; = C32C8 = AGL1(𝔽9)98+F972,39
PSU3(𝔽2)Projective special unitary group on 𝔽23; = C32Q8 = M998+PSU(3,2)72,41

### Groups of order 81

dρLabelID
C3≀C3Wreath product of C3 by C3; = AΣL1(𝔽27)93C3wrC381,7

### Groups of order 108

dρLabelID
C32⋊D6The semidirect product of C32 and D6 acting faithfully96+C3^2:D6108,17

### Groups of order 144

dρLabelID
AΓL1(𝔽9)Affine semilinear group on 𝔽91; = F9C2 = Aut(C32⋊C4)98+AGammaL(1,9)144,182

### Groups of order 162

dρLabelID
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

### Groups of order 216

dρLabelID
ASL2(𝔽3)Hessian group = Affine special linear group on 𝔽32; = PSU3(𝔽2)C398+ASL(2,3)216,153

### Groups of order 324

dρLabelID
He3⋊D6The semidirect product of He3 and D6 acting faithfully96+He3:D6324,39
C33⋊A4The semidirect product of C33 and A4 acting faithfully94C3^3:A4324,160

### Groups of order 432

dρLabelID
AGL2(𝔽3)Affine linear group on 𝔽32; = PSU3(𝔽2)S3 = Aut(C3⋊S3) = Hol(C32)98+AGL(2,3)432,734

### Groups of order 10

dρLabelID
C10Cyclic group101C1010,2

### Groups of order 20

dρLabelID
D10Dihedral group; = C2×D5102+D1020,4

### Groups of order 40

dρLabelID
C2×F5Direct product of C2 and F5; = Aut(D10) = Hol(C10)104+C2xF540,12

### Groups of order 50

dρLabelID
C5×D5Direct product of C5 and D5; = AΣL1(𝔽25)102C5xD550,3

### Groups of order 80

dρLabelID
C24⋊C5The semidirect product of C24 and C5 acting faithfully105+C2^4:C580,49

### Groups of order 100

dρLabelID
C52⋊C44th semidirect product of C52 and C4 acting faithfully104+C5^2:C4100,12
D52Direct product of D5 and D5104+D5^2100,13

### Groups of order 120

dρLabelID
C2×A5Direct product of C2 and A5; = icosahedron/dodecahedron symmetries103+C2xA5120,35

### Groups of order 160

dρLabelID
C24⋊D5The semidirect product of C24 and D5 acting faithfully105+C2^4:D5160,234
C2×C24⋊C5Direct product of C2 and C24⋊C5; = AΣL1(𝔽32)105+C2xC2^4:C5160,235

### Groups of order 200

dρLabelID
C52⋊C8The semidirect product of C52 and C8 acting faithfully108+C5^2:C8200,40
D5⋊F5The semidirect product of D5 and F5 acting via F5/D5=C2; = Hol(D5)108+D5:F5200,42
D5≀C2Wreath product of D5 by C2104+D5wrC2200,43
C52⋊Q8The semidirect product of C52 and Q8 acting faithfully108+C5^2:Q8200,44

### Groups of order 240

dρLabelID
C2×S5Direct product of C2 and S5; = O3(𝔽5)104+C2xS5240,189

### Groups of order 320

dρLabelID
C24⋊F5The semidirect product of C24 and F5 acting faithfully105+C2^4:F5320,1635
C2×C24⋊D5Direct product of C2 and C24⋊D5105+C2xC2^4:D5320,1636

### Groups of order 400

dρLabelID
C52⋊M4(2)The semidirect product of C52 and M4(2) acting faithfully108+C5^2:M4(2)400,206
D5≀C2⋊C2The semidirect product of D5≀C2 and C2 acting faithfully108+D5wrC2:C2400,207

### Groups of order 11

dρLabelID
C11Cyclic group111C1111,1

### Groups of order 22

dρLabelID
D11Dihedral group112+D1122,1

### Groups of order 55

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

### Groups of order 110

dρLabelID
F11Frobenius group; = C11C10 = AGL1(𝔽11) = Aut(D11) = Hol(C11)1110+F11110,1

### Groups of order 12

dρLabelID
Dic3Dicyclic group; = C3C4122-Dic312,1
C12Cyclic group121C1212,2
C2×C6Abelian group of type [2,6]12C2xC612,5

### Groups of order 24

dρLabelID
C4×S3Direct product of C4 and S3122C4xS324,5
D12Dihedral group122+D1224,6
C3⋊D4The semidirect product of C3 and D4 acting via D4/C22=C2122C3:D424,8
C3×D4Direct product of C3 and D4122C3xD424,10
C22×S3Direct product of C22 and S312C2^2xS324,14

### Groups of order 36

dρLabelID
C3×Dic3Direct product of C3 and Dic3122C3xDic336,6
C3×A4Direct product of C3 and A4123C3xA436,11
S3×C6Direct product of C6 and S3122S3xC636,12

### Groups of order 48

dρLabelID
C42⋊C3The semidirect product of C42 and C3 acting faithfully123C4^2:C348,3
A4⋊C4The semidirect product of A4 and C4 acting via C4/C2=C2; = SL2(ℤ/4ℤ)123A4:C448,30
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
C22⋊A4The semidirect product of C22 and A4 acting via A4/C22=C312C2^2:A448,50

### Groups of order 72

dρLabelID
C6.D62nd non-split extension by C6 of D6 acting via D6/S3=C2124+C6.D672,21
C3⋊D12The semidirect product of C3 and D12 acting via D12/D6=C2124+C3:D1272,23
C3×C3⋊D4Direct product of C3 and C3⋊D4122C3xC3:D472,30
C3×S4Direct product of C3 and S4123C3xS472,42
C3⋊S4The semidirect product of C3 and S4 acting via S4/A4=C2126+C3:S472,43
S3×A4Direct product of S3 and A4126+S3xA472,44
C2×C32⋊C4Direct product of C2 and C32⋊C4124+C2xC3^2:C472,45
C2×S32Direct product of C2, S3 and S3124+C2xS3^272,46

### Groups of order 96

dρLabelID
C23.3A41st non-split extension by C23 of A4 acting via A4/C22=C3126+C2^3.3A496,3
C42⋊S3The semidirect product of C42 and S3 acting faithfully123C4^2:S396,64
C2×C42⋊C3Direct product of C2 and C42⋊C3123C2xC4^2:C396,68
C23.A42nd non-split extension by C23 of A4 acting faithfully126+C2^3.A496,72
C4×S4Direct product of C4 and S4123C4xS496,186
C4⋊S4The semidirect product of C4 and S4 acting via S4/A4=C2126+C4:S496,187
A4⋊D4The semidirect product of A4 and D4 acting via D4/C22=C2; = Aut(C42) = GL2(ℤ/4ℤ)126+A4:D496,195
D4×A4Direct product of D4 and A4126+D4xA496,197
C22×S4Direct product of C22 and S412C2^2xS496,226
C2×C22⋊A4Direct product of C2 and C22⋊A412C2xC2^2:A496,229

### Groups of order 108

dρLabelID
C3×C32⋊C4Direct product of C3 and C32⋊C4124C3xC3^2:C4108,36
C33⋊C42nd semidirect product of C33 and C4 acting faithfully124C3^3:C4108,37
C3×S32Direct product of C3, S3 and S3124C3xS3^2108,38
C324D6The semidirect product of C32 and D6 acting via D6/C3=C22124C3^2:4D6108,40

### Groups of order 144

dρLabelID
S32⋊C4The semidirect product of S32 and C4 acting via C4/C2=C2124+S3^2:C4144,115
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
S3×S4Direct product of S3 and S4; = Hol(C2×C6)126+S3xS4144,183
A42Direct product of A4 and A4; = PΩ+4(𝔽3)129+A4^2144,184
C2×S3≀C2Direct product of C2 and S3≀C2124+C2xS3wrC2144,186

### Groups of order 192

dρLabelID
C23.9S43rd non-split extension by C23 of S4 acting via S4/C22=S3123C2^3.9S4192,182
C4×C42⋊C3Direct product of C4 and C42⋊C3123C4xC4^2:C3192,188
C24⋊C121st semidirect product of C24 and C12 acting via C12/C2=C6126+C2^4:C12192,191
C232D4⋊C3The semidirect product of C232D4 and C3 acting faithfully126+C2^3:2D4:C3192,194
C24.2A42nd non-split extension by C24 of A4 acting faithfully126+C2^4.2A4192,197
C2×C42⋊S3Direct product of C2 and C42⋊S3123C2xC4^2:S3192,944
C42⋊D6The semidirect product of C42 and D6 acting faithfully126+C4^2:D6192,956
C2×C24⋊C6Direct product of C2 and C24⋊C6126+C2xC2^4:C6192,1000
C2×C23.A4Direct product of C2 and C23.A4126+C2xC2^3.A4192,1002
D4×S4Direct product of D4 and S4126+D4xS4192,1472
C244Dic33rd semidirect product of C24 and Dic3 acting via Dic3/C2=S3126+C2^4:4Dic3192,1495
C2×C22⋊S4Direct product of C2 and C22⋊S4126+C2xC2^2:S4192,1538
C22×C22⋊A4Direct product of C22 and C22⋊A412C2^2xC2^2:A4192,1540

### Groups of order 216

dρLabelID
S3×C32⋊C4Direct product of S3 and C32⋊C4128+S3xC3^2:C4216,156
C3×S3≀C2Direct product of C3 and S3≀C2124C3xS3wrC2216,157
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
S33Direct product of S3, S3 and S3; = Hol(C3×S3)128+S3^3216,162

### Groups of order 240

dρLabelID
A5⋊C4The semidirect product of A5 and C4 acting via C4/C2=C2124A5:C4240,91

### Groups of order 288

dρLabelID
D6≀C2Wreath product of D6 by C2124+D6wrC2288,889
PSO4+ (𝔽3)Projective special orthogonal group of + type on 𝔽34; = A4S4 = Hol(A4)129+PSO+(4,3)288,1026

### Groups of order 324

dρLabelID
C3×C33⋊C4Direct product of C3 and C33⋊C4; = AΣL1(𝔽81)124C3xC3^3:C4324,162
C3×C324D6Direct product of C3 and C324D6124C3xC3^2:4D6324,167

### Groups of order 432

dρLabelID
S3×S3≀C2Direct product of S3 and S3≀C2128+S3xS3wrC2432,741

### Groups of order 13

dρLabelID
C13Cyclic group131C1313,1

### Groups of order 26

dρLabelID
D13Dihedral group132+D1326,1

### Groups of order 39

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

### Groups of order 52

dρLabelID
C13⋊C4The semidirect product of C13 and C4 acting faithfully134+C13:C452,3

### Groups of order 78

dρLabelID
C13⋊C6The semidirect product of C13 and C6 acting faithfully136+C13:C678,1

### Groups of order 156

dρLabelID
F13Frobenius group; = C13C12 = AGL1(𝔽13) = Aut(D13) = Hol(C13)1312+F13156,7

### Groups of order 14

dρLabelID
C14Cyclic group141C1414,2

### Groups of order 28

dρLabelID
D14Dihedral group; = C2×D7142+D1428,3

### Groups of order 42

dρLabelID
C2×C7⋊C3Direct product of C2 and C7⋊C3143C2xC7:C342,2

### Groups of order 84

dρLabelID
C2×F7Direct product of C2 and F7; = Aut(D14) = Hol(C14)146+C2xF784,7

### Groups of order 98

dρLabelID
C7×D7Direct product of C7 and D7; = AΣL1(𝔽49)142C7xD798,3

### Groups of order 112

dρLabelID
C2×F8Direct product of C2 and F8147+C2xF8112,41

### Groups of order 196

dρLabelID
C72⋊C4The semidirect product of C72 and C4 acting faithfully144+C7^2:C4196,8
D72Direct product of D7 and D7144+D7^2196,9

### Groups of order 294

dρLabelID
C72⋊S3The semidirect product of C72 and S3 acting faithfully143C7^2:S3294,7
C74F72nd semidirect product of C7 and F7 acting via F7/D7=C3146C7:4F7294,12

### Groups of order 336

dρLabelID
C2×GL3(𝔽2)Direct product of C2 and GL3(𝔽2)143C2xGL(3,2)336,209
C2×AΓL1(𝔽8)Direct product of C2 and AΓL1(𝔽8)147+C2xAGammaL(1,8)336,210

### Groups of order 392

dρLabelID
D7≀C2Wreath product of D7 by C2144+D7wrC2392,37

### Groups of order 448

dρLabelID
C23⋊F82nd semidirect product of C23 and F8 acting via F8/C23=C7147+C2^3:F8448,1394

### Groups of order 15

dρLabelID
C15Cyclic group151C1515,1

### Groups of order 30

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

### Groups of order 60

dρLabelID
C3×F5Direct product of C3 and F5154C3xF560,6
C3⋊F5The semidirect product of C3 and F5 acting via F5/D5=C2154C3:F560,7
S3×D5Direct product of S3 and D5154+S3xD560,8

### Groups of order 75

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

### Groups of order 120

dρLabelID
S3×F5Direct product of S3 and F5; = Aut(D15) = Hol(C15)158+S3xF5120,36

### Groups of order 150

dρLabelID
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

### Groups of order 180

dρLabelID
C3×A5Direct product of C3 and A5; = GL2(𝔽4)153C3xA5180,19

### Groups of order 300

dρLabelID
C52⋊Dic3The semidirect product of C52 and Dic3 acting faithfully1512+C5^2:Dic3300,23
C52⋊C12The semidirect product of C52 and C12 acting faithfully1512+C5^2:C12300,24
C52⋊D6The semidirect product of C52 and D6 acting faithfully156+C5^2:D6300,25

### Groups of order 360

dρLabelID
C3×S5Direct product of C3 and S5154C3xS5360,119
ΓL2(𝔽4)Semilinear group on 𝔽42; = C3S5156GammaL(2,4)360,120
S3×A5Direct product of S3 and A5156+S3xA5360,121

### Groups of order 375

dρLabelID
C5×C52⋊C3Direct product of C5 and C52⋊C3; = AΣL1(𝔽125)153C5xC5^2:C3375,6

### Groups of order 405

dρLabelID
C34⋊C5The semidirect product of C34 and C5 acting faithfully155C3^4:C5405,15

### Groups of order 16

dρLabelID
C16Cyclic group161C1616,1
C42Abelian group of type [4,4]16C4^216,2
C4⋊C4The semidirect product of C4 and C4 acting via C4/C2=C216C4:C416,4
C2×C8Abelian group of type [2,8]16C2xC816,5
Q16Generalised quaternion group; = C8.C2 = Dic4162-Q1616,9
C22×C4Abelian group of type [2,2,4]16C2^2xC416,10
C2×Q8Direct product of C2 and Q816C2xQ816,12
C24Elementary abelian group of type [2,2,2,2]16C2^416,14

### Groups of order 32

dρLabelID
C22⋊C8The semidirect product of C22 and C8 acting via C8/C4=C216C2^2:C832,5
C4.10D42nd non-split extension by C4 of D4 acting via D4/C22=C2164-C4.10D432,8
D4⋊C41st semidirect product of D4 and C4 acting via C4/C2=C216D4:C432,9
C8.C41st non-split extension by C8 of C4 acting via C4/C2=C2162C8.C432,15
M5(2)Modular maximal-cyclic group; = C163C2162M5(2)32,17
D16Dihedral group162+D1632,18
SD32Semidihedral group; = C162C2 = QD32162SD3232,19
C2×C22⋊C4Direct product of C2 and C22⋊C416C2xC2^2:C432,22
C42⋊C21st semidirect product of C42 and C2 acting faithfully16C4^2:C232,24
C4×D4Direct product of C4 and D416C4xD432,25
C4⋊D4The semidirect product of C4 and D4 acting via D4/C22=C216C4:D432,28
C22⋊Q8The semidirect product of C22 and Q8 acting via Q8/C4=C216C2^2:Q832,29
C22.D43rd non-split extension by C22 of D4 acting via D4/C22=C216C2^2.D432,30
C4.4D44th non-split extension by C4 of D4 acting via D4/C4=C216C4.4D432,31
C422C22nd semidirect product of C42 and C2 acting faithfully16C4^2:2C232,33
C41D4The semidirect product of C4 and D4 acting via D4/C4=C216C4:1D432,34
C2×M4(2)Direct product of C2 and M4(2)16C2xM4(2)32,37
C8○D4Central product of C8 and D4162C8oD432,38
C2×D8Direct product of C2 and D816C2xD832,39
C2×SD16Direct product of C2 and SD1616C2xSD1632,40
C4○D8Central product of C4 and D8162C4oD832,42
C8.C22The non-split extension by C8 of C22 acting faithfully164-C8.C2^232,44
C22×D4Direct product of C22 and D416C2^2xD432,46
C2×C4○D4Direct product of C2 and C4○D416C2xC4oD432,48
2- 1+4Gamma matrices = Extraspecial group; = D4Q8164-ES-(2,2)32,50

### Groups of order 48

dρLabelID
CSU2(𝔽3)Conformal special unitary group on 𝔽32; = Q8.S3 = 2O = <2,3,4>162-CSU(2,3)48,28
C2×SL2(𝔽3)Direct product of C2 and SL2(𝔽3)16C2xSL(2,3)48,32
C4.A4The central extension by C4 of A4162C4.A448,33

### Groups of order 64

dρLabelID
C23⋊C8The semidirect product of C23 and C8 acting via C8/C2=C416C2^3:C864,4
C22.SD161st non-split extension by C22 of SD16 acting via SD16/Q8=C216C2^2.SD1664,8
C23.31D42nd non-split extension by C23 of D4 acting via D4/C22=C216C2^3.31D464,9
C4.9C421st central stem extension by C4 of C42164C4.9C4^264,18
C4.10C422nd central stem extension by C4 of C42164C4.10C4^264,19
C426C43rd semidirect product of C42 and C4 acting via C4/C2=C216C4^2:6C464,20
C23.9D42nd non-split extension by C23 of D4 acting via D4/C2=C2216C2^3.9D464,23
M4(2)⋊4C44th semidirect product of M4(2) and C4 acting via C4/C2=C2164M4(2):4C464,25
C16⋊C42nd semidirect product of C16 and C4 acting faithfully164C16:C464,28
C23.C8The non-split extension by C23 of C8 acting via C8/C2=C4164C2^3.C864,30
C23.D42nd non-split extension by C23 of D4 acting faithfully164C2^3.D464,33
C423C43rd semidirect product of C42 and C4 acting faithfully164C4^2:3C464,35
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
D82C42nd semidirect product of D8 and C4 acting via C4/C2=C2164D8:2C464,41
M5(2)⋊C26th semidirect product of M5(2) and C2 acting faithfully164+M5(2):C264,42
C8.C81st non-split extension by C8 of C8 acting via C8/C4=C2162C8.C864,45
C8.Q8The non-split extension by C8 of Q8 acting via Q8/C2=C22164C8.Q864,46
C243C41st semidirect product of C24 and C4 acting via C4/C2=C216C2^4:3C464,60
C24.4C42nd non-split extension by C24 of C4 acting via C4/C2=C216C2^4.4C464,88
C2×C23⋊C4Direct product of C2 and C23⋊C416C2xC2^3:C464,90
C23.C232nd non-split extension by C23 of C23 acting via C23/C2=C22164C2^3.C2^364,91
C2×C4.D4Direct product of C2 and C4.D416C2xC4.D464,92
M4(2).8C223rd non-split extension by M4(2) of C22 acting via C22/C2=C2164M4(2).8C2^264,94
C23.37D48th non-split extension by C23 of D4 acting via D4/C22=C216C2^3.37D464,99
C2×C4≀C2Direct product of C2 and C4≀C216C2xC4wrC264,101
C42⋊C221st semidirect product of C42 and C22 acting faithfully164C4^2:C2^264,102
M4(2).C41st non-split extension by M4(2) of C4 acting via C4/C2=C2164M4(2).C464,111
C8○D8Central product of C8 and D8162C8oD864,124
C8.26D413rd non-split extension by C8 of D4 acting via D4/C22=C2164C8.26D464,125
C22⋊D8The semidirect product of C22 and D8 acting via D8/D4=C216C2^2:D864,128
C22⋊SD16The semidirect product of C22 and SD16 acting via SD16/D4=C216C2^2:SD1664,131
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
D4.10D45th non-split extension by D4 of D4 acting via D4/C22=C2164-D4.10D464,137
C23.7D47th non-split extension by C23 of D4 acting faithfully164C2^3.7D464,139
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
C16⋊C22The semidirect product of C16 and C22 acting faithfully164+C16:C2^264,190
C22.11C247th central extension by C22 of C2416C2^2.11C2^464,199
C2×C22≀C2Direct product of C2 and C22≀C216C2xC2^2wrC264,202
C22.19C245th central stem extension by C22 of C2416C2^2.19C2^464,206
C233D42nd semidirect product of C23 and D4 acting via D4/C2=C2216C2^3:3D464,215
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
C232Q82nd semidirect product of C23 and Q8 acting via Q8/C2=C2216C2^3:2Q864,224
D42Direct product of D4 and D416D4^264,226
D45D41st semidirect product of D4 and D4 acting through Inn(D4)16D4:5D464,227
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
C24⋊C224th semidirect product of C24 and C22 acting faithfully16C2^4:C2^264,242
Q8○M4(2)Central product of Q8 and M4(2)164Q8oM4(2)64,249
C2×C8⋊C22Direct product of C2 and C8⋊C2216C2xC8:C2^264,254
D8⋊C224th semidirect product of D8 and C22 acting via C22/C2=C2164D8:C2^264,256
D4○D8Central product of D4 and D8164+D4oD864,257
D4○SD16Central product of D4 and SD16164D4oSD1664,258
C2×2+ 1+4Direct product of C2 and 2+ 1+416C2xES+(2,2)64,264
C2.C256th central stem extension by C2 of C25164C2.C2^564,266

### Groups of order 96

dρLabelID
C42⋊C61st semidirect product of C42 and C6 acting faithfully166C4^2:C696,71
C2×GL2(𝔽3)Direct product of C2 and GL2(𝔽3)16C2xGL(2,3)96,189
Q8.D62nd non-split extension by Q8 of D6 acting via D6/C2=S3164-Q8.D696,190
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
D4.A4The non-split extension by D4 of A4 acting through Inn(D4)164-D4.A496,202

### Groups of order 128

dρLabelID
C24.4Q83rd non-split extension by C24 of Q8 acting via Q8/C2=C2216C2^4.4Q8128,36
C24⋊C81st semidirect product of C24 and C8 acting via C8/C2=C416C2^4:C8128,48
C24.C82nd non-split extension by C24 of C8 acting via C8/C2=C4164C2^4.C8128,52
C42.C81st non-split extension by C42 of C8 acting via C8/C2=C4164C4^2.C8128,59
C8≀C2Wreath product of C8 by C2162C8wrC2128,67
C8.32D89th non-split extension by C8 of D8 acting via D8/D4=C2164C8.32D8128,68
C23.D81st non-split extension by C23 of D8 acting via D8/C2=D4168+C2^3.D8128,71
C23.SD161st non-split extension by C23 of SD16 acting via SD16/C2=D4168+C2^3.SD16128,73
C24.D41st non-split extension by C24 of D4 acting faithfully16C2^4.D4128,75
C4.C4≀C29th non-split extension by C4 of C4≀C2 acting via C4≀C2/C42=C2168+C4.C4wrC2128,87
C8.24D81st non-split extension by C8 of D8 acting via D8/D4=C2164+C8.24D8128,89
C8.29D86th non-split extension by C8 of D8 acting via D8/D4=C2164C8.29D8128,91
C42.D41st non-split extension by C42 of D4 acting faithfully164+C4^2.D4128,134
C42.2D42nd non-split extension by C42 of D4 acting faithfully164C4^2.2D4128,135
C42.3D43rd non-split extension by C42 of D4 acting faithfully164C4^2.3D4128,136
C42.4D44th non-split extension by C42 of D4 acting faithfully164-C4^2.4D4128,137
C8⋊C4⋊C41st semidirect product of C8⋊C4 and C4 acting faithfully168+C8:C4:C4128,138
C41D4⋊C42nd semidirect product of C41D4 and C4 acting faithfully164+C4:1D4:C4128,140
(C4×C8)⋊6C46th semidirect product of C4×C8 and C4 acting faithfully164(C4xC8):6C4128,141
(C4×C8).C46th non-split extension by C4×C8 of C4 acting faithfully164(C4xC8).C4128,142
C8⋊C45C45th semidirect product of C8⋊C4 and C4 acting faithfully168+C8:C4:5C4128,144
C25.3C43rd non-split extension by C25 of C4 acting faithfully16C2^5.3C4128,194
C24.150D45th non-split extension by C24 of D4 acting via D4/C22=C216C2^4.150D4128,236
C23⋊D8The semidirect product of C23 and D8 acting via D8/C2=D416C2^3:D8128,327
C23⋊SD161st semidirect product of C23 and SD16 acting via SD16/C2=D416C2^3:SD16128,328
C24.9D49th non-split extension by C24 of D4 acting faithfully16C2^4.9D4128,332
C25⋊C41st semidirect product of C25 and C4 acting faithfully16C2^5:C4128,513
C25.C44th non-split extension by C25 of C4 acting faithfully16C2^5.C4128,515
C4○D4.D43rd non-split extension by C4○D4 of D4 acting via D4/C2=C22168+C4oD4.D4128,527
C24.68D423rd non-split extension by C24 of D4 acting via D4/C2=C2216C2^4.68D4128,551
(C2×C42)⋊C48th semidirect product of C2×C42 and C4 acting faithfully164(C2xC4^2):C4128,559
C24.C231st non-split extension by C24 of C23 acting faithfully168+C2^4.C2^3128,560
C24.6(C2×C4)6th non-split extension by C24 of C2×C4 acting faithfully168+C2^4.6(C2xC4)128,561
C8⋊C417C412nd semidirect product of C8⋊C4 and C4 acting via C4/C2=C2164C8:C4:17C4128,573
M4(2).41D45th non-split extension by M4(2) of D4 acting via D4/C22=C2164M4(2).41D4128,593
M4(2)⋊19D46th semidirect product of M4(2) and D4 acting via D4/C22=C2164M4(2):19D4128,616
C24.24D424th non-split extension by C24 of D4 acting faithfully16C2^4.24D4128,619
C25.C229th non-split extension by C25 of C22 acting faithfully16C2^5.C2^2128,621
(C2×C8)⋊D43rd semidirect product of C2×C8 and D4 acting faithfully164(C2xC8):D4128,623
(C2×C4)≀C2Wreath product of C2×C4 by C216(C2xC4)wrC2128,628
C24.78D433rd non-split extension by C24 of D4 acting via D4/C2=C2216C2^4.78D4128,630
M4(2).47D411st non-split extension by M4(2) of D4 acting via D4/C22=C2168+M4(2).47D4128,635
C42.5D45th non-split extension by C42 of D4 acting faithfully168+C4^2.5D4128,636
C42.426D459th non-split extension by C42 of D4 acting via D4/C22=C2164C4^2.426D4128,638
(C2×C8)⋊4D44th semidirect product of C2×C8 and D4 acting faithfully168+(C2xC8):4D4128,642
C42⋊D41st semidirect product of C42 and D4 acting faithfully168+C4^2:D4128,643
C24.28D428th non-split extension by C24 of D4 acting faithfully168+C2^4.28D4128,645
M4(2)⋊21D48th semidirect product of M4(2) and D4 acting via D4/C22=C2168+M4(2):21D4128,646
C42.427D460th non-split extension by C42 of D4 acting via D4/C22=C2164C4^2.427D4128,664
C429D43rd semidirect product of C42 and D4 acting via D4/C2=C2216C4^2:9D4128,734
M4(2)⋊5D45th semidirect product of M4(2) and D4 acting via D4/C2=C22168+M4(2):5D4128,740
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
C242Q81st semidirect product of C24 and Q8 acting via Q8/C2=C2216C2^4:2Q8128,761
C42.8D48th non-split extension by C42 of D4 acting faithfully164C4^2.8D4128,763
C24⋊Q8The semidirect product of C24 and Q8 acting faithfully168+C2^4:Q8128,764
M4(2).8D48th non-split extension by M4(2) of D4 acting via D4/C2=C22168+M4(2).8D4128,780
C42.131D4113rd non-split extension by C42 of D4 acting via D4/C2=C22164C4^2.131D4128,782
C24.Q8The non-split extension by C24 of Q8 acting faithfully168+C2^4.Q8128,801
(C2×C8).D45th non-split extension by C2×C8 of D4 acting faithfully168+(C2xC8).D4128,813
C24.11Q810th non-split extension by C24 of Q8 acting via Q8/C2=C22164C2^4.11Q8128,823
C42.32Q832nd non-split extension by C42 of Q8 acting via Q8/C2=C22164C4^2.32Q8128,834
C24.4C234th non-split extension by C24 of C23 acting faithfully168+C2^4.4C2^3128,836
C2×C2≀C4Direct product of C2 and C2≀C416C2xC2wrC4128,850
C4○C2≀C4Central product of C4 and C2≀C4164C4oC2wrC4128,852
C24.36D436th non-split extension by C24 of D4 acting faithfully168+C2^4.36D4128,853
C2≀C4⋊C26th semidirect product of C2≀C4 and C2 acting faithfully168+C2wrC4:C2128,854
C2×C42⋊C4Direct product of C2 and C42⋊C416C2xC4^2:C4128,856
C4⋊Q829C424th semidirect product of C4⋊Q8 and C4 acting via C4/C2=C2164C4:Q8:29C4128,858
C24.39D439th non-split extension by C24 of D4 acting faithfully168+C2^4.39D4128,859
C4.4D4⋊C46th semidirect product of C4.4D4 and C4 acting faithfully168+C4.4D4:C4128,860
(C2×D4).135D497th non-split extension by C2×D4 of D4 acting via D4/C2=C22164(C2xD4).135D4128,864
C41D4.C45th non-split extension by C41D4 of C4 acting faithfully168+C4:1D4.C4128,866
C8.5M4(2)5th non-split extension by C8 of M4(2) acting via M4(2)/C4=C22164C8.5M4(2)128,897
D16⋊C4The semidirect product of D16 and C4 acting faithfully; = Aut(D16) = Hol(C16)168+D16:C4128,913
D8⋊D4The semidirect product of D8 and D4 acting via D4/C2=C22168+D8:D4128,922
C424D44th semidirect product of C42 and D4 acting faithfully164C4^2:4D4128,929
C42.13D413rd non-split extension by C42 of D4 acting faithfully164C4^2.13D4128,930
C425D45th semidirect product of C42 and D4 acting faithfully168+C4^2:5D4128,931
C426D46th semidirect product of C42 and D4 acting faithfully168+C4^2:6D4128,932
C42.15D415th non-split extension by C42 of D4 acting faithfully168+C4^2.15D4128,934
C42.17D417th non-split extension by C42 of D4 acting faithfully164C4^2.17D4128,936
Q8≀C2Wreath product of Q8 by C2164-Q8wrC2128,937
D83D42nd semidirect product of D8 and D4 acting via D4/C4=C2164+D8:3D4128,945
D83Q83rd semidirect product of D8 and Q8 acting via Q8/C4=C2164D8:3Q8128,962
M5(2).C228th non-split extension by M5(2) of C22 acting faithfully168+M5(2).C2^2128,970
C23≀C2Wreath product of C23 by C216C2^3wrC2128,1578
C23.C243rd non-split extension by C23 of C24 acting via C24/C22=C22168+C2^3.C2^4128,1615
M4(2).24C236th non-split extension by M4(2) of C23 acting via C23/C22=C2168+M4(2).24C2^3128,1620
2- 1+45C44th semidirect product of 2- 1+4 and C4 acting via C4/C2=C2164ES-(2,2):5C4128,1633
M4(2).51D41st non-split extension by M4(2) of D4 acting through Inn(M4(2))164M4(2).51D4128,1688
C24.177D432nd non-split extension by C24 of D4 acting via D4/C22=C216C2^4.177D4128,1735
C2×D44D4Direct product of C2 and D44D416C2xD4:4D4128,1746
C42.313C23174th non-split extension by C42 of C23 acting via C23/C2=C22164C4^2.313C2^3128,1750
M4(2)⋊C233rd semidirect product of M4(2) and C23 acting via C23/C2=C22168+M4(2):C2^3128,1751
C42.12C2312nd non-split extension by C42 of C23 acting faithfully168+C4^2.12C2^3128,1753
C2×C2≀C22Direct product of C2 and C2≀C2216C2xC2wrC2^2128,1755
C23.7C247th non-split extension by C23 of C24 acting via C24/C22=C22164C2^3.7C2^4128,1757
C24⋊C232nd semidirect product of C24 and C23 acting faithfully168+C2^4:C2^3128,1758
C23.9C249th non-split extension by C23 of C24 acting via C24/C22=C22168+C2^3.9C2^4128,1759
M4(2).37D41st non-split extension by M4(2) of D4 acting via D4/C22=C2168+M4(2).37D4128,1800
D811D45th semidirect product of D8 and D4 acting via D4/C22=C2168+D8:11D4128,2020
D86D45th semidirect product of D8 and D4 acting via D4/C4=C2164D8:6D4128,2023
D8○D8Central product of D8 and D8164+D8oD8128,2024
C22.73C2554th central stem extension by C22 of C2516C2^2.73C2^5128,2216
C22.79C2560th central stem extension by C22 of C2516C2^2.79C2^5128,2222
C42⋊C234th semidirect product of C42 and C23 acting faithfully16C4^2:C2^3128,2264
D8⋊C236th semidirect product of D8 and C23 acting via C23/C22=C2168+D8:C2^3128,2317
2+ 1+6Extraspecial group; = D42+ 1+4168+ES+(2,3)128,2326

### Groups of order 192

dρLabelID
C23.SL2(𝔽3)1st non-split extension by C23 of SL2(𝔽3) acting via SL2(𝔽3)/C2=A4164C2^3.SL(2,3)192,4
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
2+ 1+4.C61st non-split extension by 2+ 1+4 of C6 acting faithfully164ES+(2,2).C6192,202
C24.6A46th non-split extension by C24 of A4 acting faithfully1612+C2^4.6A4192,1008
C24⋊A43rd semidirect product of C24 and A4 acting faithfully1612+C2^4:A4192,1009
C24.7A47th non-split extension by C24 of A4 acting faithfully16C2^4.7A4192,1021
C42⋊A4The semidirect product of C42 and A4 acting faithfully1612+C4^2:A4192,1023
C245A45th semidirect product of C24 and A4 acting faithfully16C2^4:5A4192,1024
D4.4S41st non-split extension by D4 of S4 acting through Inn(D4)164D4.4S4192,1485
C23.S44th non-split extension by C23 of S4 acting faithfully164C2^3.S4192,1491
Q8.S42nd non-split extension by Q8 of S4 acting via S4/C22=S3164Q8.S4192,1492
C2×C23⋊A4Direct product of C2 and C23⋊A416C2xC2^3:A4192,1508
2+ 1+4.3C6The non-split extension by 2+ 1+4 of C6 acting via C6/C2=C3164ES+(2,2).3C6192,1509

### Groups of order 240

dρLabelID
F16Frobenius group; = C24C15 = AGL1(𝔽16)1615+F16240,191

### Groups of order 288

dρLabelID
A4×S4Direct product of A4 and S4169+A4xS4288,1024

### Groups of order 336

dρLabelID
SL2(𝔽7)Special linear group on 𝔽72; = C2.GL3(𝔽2)164SL(2,7)336,114

### Groups of order 480

dρLabelID
F16⋊C2The semidirect product of F16 and C2 acting faithfully1615+F16:C2480,1188

### Groups of order 17

dρLabelID
C17Cyclic group171C1717,1

### Groups of order 34

dρLabelID
D17Dihedral group172+D1734,1

### Groups of order 68

dρLabelID
C17⋊C4The semidirect product of C17 and C4 acting faithfully174+C17:C468,3

### Groups of order 136

dρLabelID
C17⋊C8The semidirect product of C17 and C8 acting faithfully178+C17:C8136,12

### Groups of order 272

dρLabelID
F17Frobenius group; = C17C16 = AGL1(𝔽17) = Aut(D17) = Hol(C17)1716+F17272,50

### Groups of order 18

dρLabelID
C18Cyclic group181C1818,2
C3×C6Abelian group of type [3,6]18C3xC618,5

### Groups of order 36

dρLabelID
C3.A4The central extension by C3 of A4183C3.A436,3
D18Dihedral group; = C2×D9182+D1836,4
C2×C3⋊S3Direct product of C2 and C3⋊S318C2xC3:S336,13

### Groups of order 54

dρLabelID
C3×D9Direct product of C3 and D9182C3xD954,3
S3×C9Direct product of C9 and S3182S3xC954,4
C2×He3Direct product of C2 and He3183C2xHe354,10
C2×3- 1+2Direct product of C2 and 3- 1+2183C2xES-(3,1)54,11
S3×C32Direct product of C32 and S318S3xC3^254,12
C3×C3⋊S3Direct product of C3 and C3⋊S318C3xC3:S354,13

### Groups of order 72

dρLabelID
C3.S4The non-split extension by C3 of S4 acting via S4/A4=C2186+C3.S472,15
C2×C3.A4Direct product of C2 and C3.A4183C2xC3.A472,16
C6×A4Direct product of C6 and A4183C6xA472,47

### Groups of order 108

dρLabelID
He3⋊C4The semidirect product of He3 and C4 acting faithfully183He3:C4108,15
S3×D9Direct product of S3 and D9184+S3xD9108,16
C32.A4The non-split extension by C32 of A4 acting via A4/C22=C3183C3^2.A4108,21
C32⋊A4The semidirect product of C32 and A4 acting via A4/C22=C3183C3^2:A4108,22
C2×C32⋊C6Direct product of C2 and C32⋊C6186+C2xC3^2:C6108,25
C2×C9⋊C6Direct product of C2 and C9⋊C6; = Aut(D18) = Hol(C18)186+C2xC9:C6108,26
C2×He3⋊C2Direct product of C2 and He3⋊C2183C2xHe3:C2108,28
S3×C3⋊S3Direct product of S3 and C3⋊S318S3xC3:S3108,39

### Groups of order 144

dρLabelID
C2×C3.S4Direct product of C2 and C3.S4186+C2xC3.S4144,109
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
C6×S4Direct product of C6 and S4183C6xS4144,188
C2×C3⋊S4Direct product of C2 and C3⋊S4186+C2xC3:S4144,189
C2×S3×A4Direct product of C2, S3 and A4186+C2xS3xA4144,190

### Groups of order 162

dρLabelID
C9×D9Direct product of C9 and D9182C9xD9162,3
C32⋊C18The semidirect product of C32 and C18 acting via C18/C3=C6186C3^2:C18162,4
C9⋊C18The semidirect product of C9 and C18 acting via C18/C3=C6186C9:C18162,6
C322D92nd semidirect product of C32 and D9 acting via D9/C3=S3186C3^2:2D9162,17
C2×C3≀C3Direct product of C2 and C3≀C3183C2xC3wrC3162,28
C3×C32⋊C6Direct product of C3 and C32⋊C6186C3xC3^2:C6162,34
S3×He3Direct product of S3 and He3186S3xHe3162,35
C3×C9⋊C6Direct product of C3 and C9⋊C6186C3xC9:C6162,36
S3×3- 1+2Direct product of S3 and 3- 1+2186S3xES-(3,1)162,37
He35S32nd semidirect product of He3 and S3 acting via S3/C3=C2186He3:5S3162,46
C32×C3⋊S3Direct product of C32 and C3⋊S318C3^2xC3:S3162,52

### Groups of order 216

dρLabelID
He3⋊D4The semidirect product of He3 and D4 acting faithfully186+He3:D4216,87
C32.S4The non-split extension by C32 of S4 acting via S4/C22=S3186+C3^2.S4216,90
C62⋊S34th semidirect product of C62 and S3 acting faithfully186+C6^2:S3216,92
C32⋊S42nd semidirect product of C32 and S4 acting via S4/C22=S3183C3^2:S4216,95
C62⋊C63rd semidirect product of C62 and C6 acting faithfully186+C6^2:C6216,99
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
C2×C32⋊A4Direct product of C2 and C32⋊A4183C2xC3^2:A4216,107

### Groups of order 288

dρLabelID
C2×AΓL1(𝔽9)Direct product of C2 and AΓL1(𝔽9)188+C2xAGammaL(1,9)288,1027
C2×S3×S4Direct product of C2, S3 and S4; = Aut(S3×SL2(𝔽3))186+C2xS3xS4288,1028
C2×A42Direct product of C2, A4 and A4189+C2xA4^2288,1029

### Groups of order 324

dρLabelID
C92⋊C4The semidirect product of C92 and C4 acting faithfully184+C9^2:C4324,35
D92Direct product of D9 and D9184+D9^2324,36
C32⋊D18The semidirect product of C32 and D18 acting via D18/C3=D61812+C3^2:D18324,37
C332A41st semidirect product of C33 and A4 acting via A4/C22=C3183C3^3:2A4324,60
C2×C3≀S3Direct product of C2 and C3≀S3183C2xC3wrS3324,68
C2×C33⋊C6Direct product of C2 and C33⋊C6186+C2xC3^3:C6324,69
C2×C33⋊S3Direct product of C2 and C33⋊S3186+C2xC3^3:S3324,77
He34Dic3The semidirect product of He3 and Dic3 acting via Dic3/C3=C4186He3:4Dic3324,113
S3×C32⋊C6Direct product of S3 and C32⋊C61812+S3xC3^2:C6324,116
C3×C32⋊D6Direct product of C3 and C32⋊D6186C3xC3^2:D6324,117
S3×C9⋊C6Direct product of S3 and C9⋊C61812+S3xC9:C6324,118
He35D61st semidirect product of He3 and D6 acting via D6/C3=C221812+He3:5D6324,121
S3×He3⋊C2Direct product of S3 and He3⋊C2186S3xHe3:C2324,122
C344C44th semidirect product of C34 and C4 acting faithfully18C3^4:4C4324,164
C3⋊S32Direct product of C3⋊S3 and C3⋊S318C3:S3^2324,169

### Groups of order 432

dρLabelID
C625D65th semidirect product of C62 and D6 acting faithfully186+C6^2:5D6432,523
C2×C32.S4Direct product of C2 and C32.S4186+C2xC3^2.S4432,533
C2×C62⋊S3Direct product of C2 and C62⋊S3186+C2xC6^2:S3432,535
C2×C32⋊S4Direct product of C2 and C32⋊S4183C2xC3^2:S4432,538
C2×C62⋊C6Direct product of C2 and C62⋊C6186+C2xC6^2:C6432,542
C2×ASL2(𝔽3)Direct product of C2 and ASL2(𝔽3)188+C2xASL(2,3)432,735

### Groups of order 486

dρLabelID
C32⋊C9.S31st non-split extension by C32⋊C9 of S3 acting faithfully186C3^2:C9.S3486,5
C32⋊C9⋊C61st semidirect product of C32⋊C9 and C6 acting faithfully186C3^2:C9:C6486,6
C32⋊C9⋊S31st semidirect product of C32⋊C9 and S3 acting faithfully186C3^2:C9:S3486,7
C331C181st semidirect product of C33 and C18 acting via C18/C3=C6186C3^3:1C18486,18
C331D91st semidirect product of C33 and D9 acting via D9/C3=S3186C3^3:1D9486,19
C34⋊C61st semidirect product of C34 and C6 acting faithfully186C3^4:C6486,102
C34.C64th non-split extension by C34 of C6 acting faithfully186C3^4.C6486,104
C928C68th semidirect product of C92 and C6 acting faithfully186C9^2:8C6486,110
C3×C33⋊C6Direct product of C3 and C33⋊C6186C3xC3^3:C6486,116
S3×C3≀C3Direct product of S3 and C3≀C3186S3xC3wrC3486,117
C343S33rd semidirect product of C34 and S3 acting faithfully186C3^4:3S3486,145
C34.7S37th non-split extension by C34 of S3 acting faithfully186C3^4.7S3486,147
C926S36th semidirect product of C92 and S3 acting faithfully186C9^2:6S3486,153
C3×C33⋊S3Direct product of C3 and C33⋊S3186C3xC3^3:S3486,165
C345S35th semidirect product of C34 and S3 acting faithfully186C3^4:5S3486,166

### Groups of order 19

dρLabelID
C19Cyclic group191C1919,1

### Groups of order 38

dρLabelID
D19Dihedral group192+D1938,1

### Groups of order 57

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

### Groups of order 114

dρLabelID
C19⋊C6The semidirect product of C19 and C6 acting faithfully196+C19:C6114,1

### Groups of order 171

dρLabelID
C19⋊C9The semidirect product of C19 and C9 acting faithfully199C19:C9171,3

### Groups of order 342

dρLabelID
F19Frobenius group; = C19C18 = AGL1(𝔽19) = Aut(D19) = Hol(C19)1918+F19342,7

### Groups of order 20

dρLabelID
Dic5Dicyclic group; = C52C4202-Dic520,1
C20Cyclic group201C2020,2
C2×C10Abelian group of type [2,10]20C2xC1020,5

### Groups of order 40

dρLabelID
C4×D5Direct product of C4 and D5202C4xD540,5
D20Dihedral group202+D2040,6
C5⋊D4The semidirect product of C5 and D4 acting via D4/C22=C2202C5:D440,8
C5×D4Direct product of C5 and D4202C5xD440,10
C22×D5Direct product of C22 and D520C2^2xD540,13

### Groups of order 60

dρLabelID
C5×A4Direct product of C5 and A4203C5xA460,9

### Groups of order 80

dρLabelID
C4×F5Direct product of C4 and F5204C4xF580,30
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×D5Direct product of D4 and D5204+D4xD580,39
C22×F5Direct product of C22 and F520C2^2xF580,50

### Groups of order 100

dρLabelID
C5×Dic5Direct product of C5 and Dic5202C5xDic5100,6
C5×F5Direct product of C5 and F5204C5xF5100,9
D5.D5The non-split extension by D5 of D5 acting via D5/C5=C2204D5.D5100,10
D5×C10Direct product of C10 and D5202D5xC10100,14

### Groups of order 120

dρLabelID
C5×S4Direct product of C5 and S4203C5xS4120,37
C5⋊S4The semidirect product of C5 and S4 acting via S4/A4=C2206+C5:S4120,38
D5×A4Direct product of D5 and A4206+D5xA4120,39

### Groups of order 160

dρLabelID
D4×F5Direct product of D4 and F5; = Aut(D20) = Hol(C20)208+D4xF5160,207

### Groups of order 200

dρLabelID
Dic52D5The semidirect product of Dic5 and D5 acting through Inn(Dic5)204+Dic5:2D5200,23
C5⋊D20The semidirect product of C5 and D20 acting via D20/D10=C2204+C5:D20200,25
C5×C5⋊D4Direct product of C5 and C5⋊D4202C5xC5:D4200,31
D5×F5Direct product of D5 and F5208+D5xF5200,41
C2×C52⋊C4Direct product of C2 and C52⋊C4204+C2xC5^2:C4200,48
C2×D52Direct product of C2, D5 and D5204+C2xD5^2200,49

### Groups of order 240

dρLabelID
C4×A5Direct product of C4 and A5203C4xA5240,92
C22×A5Direct product of C22 and A520C2^2xA5240,190
A4⋊F5The semidirect product of A4 and F5 acting via F5/D5=C22012+A4:F5240,192
A4×F5Direct product of A4 and F52012+A4xF5240,193
D5×S4Direct product of D5 and S4206+D5xS4240,194

### Groups of order 320

dρLabelID
C25.D5The non-split extension by C25 of D5 acting faithfully205C2^5.D5320,1583
C4×C24⋊C5Direct product of C4 and C24⋊C5205C4xC2^4:C5320,1584
C22×C24⋊C5Direct product of C22 and C24⋊C520C2^2xC2^4:C5320,1637

### Groups of order 400

dρLabelID
C523C422nd semidirect product of C52 and C42 acting via C42/C2=C2×C4208+C5^2:3C4^2400,124
D10⋊F52nd semidirect product of D10 and F5 acting via F5/D5=C2208+D10:F5400,125
Dic5⋊F53rd semidirect product of Dic5 and F5 acting via F5/D5=C2208+Dic5:F5400,126
D52⋊C41st semidirect product of D52 and C4 acting via C4/C2=C2204+D5^2:C4400,129
C2.D5≀C22nd central extension by C2 of D5≀C2204C2.D5wrC2400,130
(C5×C10).Q8The non-split extension by C5×C10 of Q8 acting faithfully208+(C5xC10).Q8400,134
C1024C44th semidirect product of C102 and C4 acting faithfully204+C10^2:4C4400,162
D10⋊D103rd semidirect product of D10 and D10 acting via D10/D5=C2204+D10:D10400,180
F52Direct product of F5 and F5; = Hol(F5)2016+F5^2400,205
C2×C52⋊C8Direct product of C2 and C52⋊C8208+C2xC5^2:C8400,208
C2×D5⋊F5Direct product of C2 and D5⋊F5208+C2xD5:F5400,210
C2×D5≀C2Direct product of C2 and D5≀C2204+C2xD5wrC2400,211
C2×C52⋊Q8Direct product of C2 and C52⋊Q8208+C2xC5^2:Q8400,212

### Groups of order 480

dρLabelID
C4×S5Direct product of C4 and S5; = CO3(𝔽5)204C4xS5480,943
C4⋊S5The semidirect product of C4 and S5 acting via S5/A5=C2206C4:S5480,944
C22⋊S5The semidirect product of C22 and S5 acting via S5/A5=C2206+C2^2:S5480,951
D4×A5Direct product of D4 and A5206+D4xA5480,956
C22×S5Direct product of C22 and S520C2^2xS5480,1186
F5×S4Direct product of F5 and S4; = Hol(C2×C10)2012+F5xS4480,1189

### Groups of order 500

dρLabelID
C5×D5.D5Direct product of C5 and D5.D5204C5xD5.D5500,42
C5×C52⋊C4Direct product of C5 and C52⋊C4204C5xC5^2:C4500,44
C536C46th semidirect product of C53 and C4 acting faithfully204C5^3:6C4500,46
C5×D52Direct product of C5, D5 and D5204C5xD5^2500,50
C525D102nd semidirect product of C52 and D10 acting via D10/C5=C22204C5^2:5D10500,52

### Groups of order 21

dρLabelID
C21Cyclic group211C2121,2

### Groups of order 42

dρLabelID
S3×C7Direct product of C7 and S3212S3xC742,3
C3×D7Direct product of C3 and D7212C3xD742,4
D21Dihedral group212+D2142,5

### Groups of order 63

dρLabelID
C3×C7⋊C3Direct product of C3 and C7⋊C3213C3xC7:C363,3

### Groups of order 84

dρLabelID
S3×D7Direct product of S3 and D7214+S3xD784,8

### Groups of order 126

dρLabelID
C3×F7Direct product of C3 and F7216C3xF7126,7
S3×C7⋊C3Direct product of S3 and C7⋊C3216S3xC7:C3126,8
C3⋊F7The semidirect product of C3 and F7 acting via F7/C7⋊C3=C2216+C3:F7126,9

### Groups of order 147

dρLabelID
C7×C7⋊C3Direct product of C7 and C7⋊C3213C7xC7:C3147,3
C723C33rd semidirect product of C72 and C3 acting faithfully213C7^2:3C3147,5

### Groups of order 252

dρLabelID
S3×F7Direct product of S3 and F7; = Aut(D21) = Hol(C21)2112+S3xF7252,26

### Groups of order 294

dρLabelID
C75F7The semidirect product of C7 and F7 acting via F7/C7⋊C3=C2216+C7:5F7294,10
C72⋊C67th semidirect product of C72 and C6 acting faithfully216+C7^2:C6294,14

### Groups of order 441

dρLabelID
C7⋊C32Direct product of C7⋊C3 and C7⋊C3219C7:C3^2441,9

### Groups of order 22

dρLabelID
C22Cyclic group221C2222,2

### Groups of order 44

dρLabelID
D22Dihedral group; = C2×D11222+D2244,3

### Groups of order 110

dρLabelID
C2×C11⋊C5Direct product of C2 and C11⋊C5225C2xC11:C5110,2

### Groups of order 220

dρLabelID
C2×F11Direct product of C2 and F11; = Aut(D22) = Hol(C22)2210+C2xF11220,7

### Groups of order 242

dρLabelID
C11×D11Direct product of C11 and D11; = AΣL1(𝔽121)222C11xD11242,3

### Groups of order 484

dρLabelID
C112⋊C4The semidirect product of C112 and C4 acting faithfully224+C11^2:C4484,8
D112Direct product of D11 and D11224+D11^2484,9

### Groups of order 23

dρLabelID
C23Cyclic group231C2323,1

### Groups of order 46

dρLabelID
D23Dihedral group232+D2346,1

### Groups of order 253

dρLabelID
C23⋊C11The semidirect product of C23 and C11 acting faithfully2311C23:C11253,1

### Groups of order 24

dρLabelID
C3⋊C8The semidirect product of C3 and C8 acting via C8/C4=C2242C3:C824,1
C24Cyclic group241C2424,2
Dic6Dicyclic group; = C3Q8242-Dic624,4
C2×Dic3Direct product of C2 and Dic324C2xDic324,7
C2×C12Abelian group of type [2,12]24C2xC1224,9
C3×Q8Direct product of C3 and Q8242C3xQ824,11
C22×C6Abelian group of type [2,2,6]24C2^2xC624,15

### Groups of order 48

dρLabelID
S3×C8Direct product of C8 and S3242S3xC848,4
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
D24Dihedral group242+D2448,7
C4.Dic3The non-split extension by C4 of Dic3 acting via Dic3/C6=C2242C4.Dic348,10
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
D4.S3The non-split extension by D4 of S3 acting via S3/C3=C2244-D4.S348,16
Q82S3The semidirect product of Q8 and S3 acting via S3/C3=C2244+Q8:2S348,17
C6.D47th non-split extension by C6 of D4 acting via D4/C22=C224C6.D448,19
C3×C22⋊C4Direct product of C3 and C22⋊C424C3xC2^2:C448,21
C3×M4(2)Direct product of C3 and M4(2)242C3xM4(2)48,24
C3×D8Direct product of C3 and D8242C3xD848,25
C3×SD16Direct product of C3 and SD16242C3xSD1648,26
S3×C2×C4Direct product of C2×C4 and S324S3xC2xC448,35
C2×D12Direct product of C2 and D1224C2xD1248,36
C4○D12Central product of C4 and D12242C4oD1248,37
D42S3The semidirect product of D4 and S3 acting through Inn(D4)244-D4:2S348,39
S3×Q8Direct product of S3 and Q8244-S3xQ848,40
Q83S3The semidirect product of Q8 and S3 acting through Inn(Q8)244+Q8:3S348,41
C2×C3⋊D4Direct product of C2 and C3⋊D424C2xC3:D448,43
C6×D4Direct product of C6 and D424C6xD448,45
C3×C4○D4Direct product of C3 and C4○D4242C3xC4oD448,47
S3×C23Direct product of C23 and S324S3xC2^348,51

### Groups of order 72

dρLabelID
C3×C3⋊C8Direct product of C3 and C3⋊C8242C3xC3:C872,12
C322C8The semidirect product of C32 and C8 acting via C8/C2=C4244-C3^2:2C872,19
S3×Dic3Direct product of S3 and Dic3244-S3xDic372,20
D6⋊S31st semidirect product of D6 and S3 acting via S3/C3=C2244-D6:S372,22
C322Q8The semidirect product of C32 and Q8 acting via Q8/C2=C22244-C3^2:2Q872,24
C3×SL2(𝔽3)Direct product of C3 and SL2(𝔽3)242C3xSL(2,3)72,25
C3×Dic6Direct product of C3 and Dic6242C3xDic672,26
S3×C12Direct product of C12 and S3242S3xC1272,27
C3×D12Direct product of C3 and D12242C3xD1272,28
C6×Dic3Direct product of C6 and Dic324C6xDic372,29
S3×C2×C6Direct product of C2×C6 and S324S3xC2xC672,48

### Groups of order 96

dρLabelID
C424S33rd semidirect product of C42 and S3 acting via S3/C3=C2242C4^2:4S396,12
C23.6D61st non-split extension by C23 of D6 acting via D6/C3=C22244C2^3.6D696,13
C12.46D43rd non-split extension by C12 of D4 acting via D4/C22=C2244+C12.46D496,30
D12⋊C44th semidirect product of D12 and C4 acting via C4/C2=C2244D12:C496,32
C12.D48th non-split extension by C12 of D4 acting via D4/C2=C22244C12.D496,40
C23.7D62nd non-split extension by C23 of D6 acting via D6/C3=C22244C2^3.7D696,41
Q83Dic32nd semidirect product of Q8 and Dic3 acting via Dic3/C6=C2244Q8:3Dic396,44
C3×C23⋊C4Direct product of C3 and C23⋊C4244C3xC2^3:C496,49
C3×C4.D4Direct product of C3 and C4.D4244C3xC4.D496,50
C3×C4≀C2Direct product of C3 and C4≀C2242C3xC4wrC296,54
A4⋊C8The semidirect product of A4 and C8 acting via C8/C4=C2243A4:C896,65
U2(𝔽3)Unitary group on 𝔽32; = SL2(𝔽3)2C4242U(2,3)96,67
C8×A4Direct product of C8 and A4243C8xA496,73
S3×C22⋊C4Direct product of S3 and C22⋊C424S3xC2^2:C496,87
D6⋊D41st semidirect product of D6 and D4 acting via D4/C22=C224D6:D496,89
S3×M4(2)Direct product of S3 and M4(2)244S3xM4(2)96,113
C8⋊D61st semidirect product of C8 and D6 acting via D6/C3=C22244+C8:D696,115
S3×D8Direct product of S3 and D8244+S3xD896,117
D8⋊S32nd semidirect product of D8 and S3 acting via S3/C3=C2244D8:S396,118
S3×SD16Direct product of S3 and SD16244S3xSD1696,120
Q83D62nd semidirect product of Q8 and D6 acting via D6/S3=C2244+Q8:3D696,121
D126C224th semidirect product of D12 and C22 acting via C22/C2=C2244D12:6C2^296,139
C232D61st semidirect product of C23 and D6 acting via D6/C3=C2224C2^3:2D696,144
D4⋊D62nd semidirect product of D4 and D6 acting via D6/C6=C2244+D4:D696,156
C244S31st semidirect product of C24 and S3 acting via S3/C3=C224C2^4:4S396,160
C3×C22≀C2Direct product of C3 and C22≀C224C3xC2^2wrC296,167
C3×C8⋊C22Direct product of C3 and C8⋊C22244C3xC8:C2^296,183
A4⋊Q8The semidirect product of A4 and Q8 acting via Q8/C4=C2246-A4:Q896,185
C2×A4⋊C4Direct product of C2 and A4⋊C424C2xA4:C496,194
C2×C4×A4Direct product of C2×C4 and A424C2xC4xA496,196
Q8×A4Direct product of Q8 and A4246-Q8xA496,199
Q8.A4The non-split extension by Q8 of A4 acting through Inn(Q8)244+Q8.A496,201
Q8⋊A41st semidirect product of Q8 and A4 acting via A4/C22=C3246-Q8:A496,203
C2×S3×D4Direct product of C2, S3 and D424C2xS3xD496,209
D46D62nd semidirect product of D4 and D6 acting through Inn(D4)244D4:6D696,211
S3×C4○D4Direct product of S3 and C4○D4244S3xC4oD496,215
D4○D12Central product of D4 and D12244+D4oD1296,216
C3×2+ 1+4Direct product of C3 and 2+ 1+4244C3xES+(2,2)96,224
C23×A4Direct product of C23 and A424C2^3xA496,228

### Groups of order 120

dρLabelID
SL2(𝔽5)Special linear group on 𝔽52; = C2.A5 = 2I = <2,3,5>242-SL(2,5)120,5

### Groups of order 144

dρLabelID
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
C3⋊D24The semidirect product of C3 and D24 acting via D24/D12=C2244+C3:D24144,57
C325SD163rd semidirect product of C32 and SD16 acting via SD16/C4=C22244+C3^2:5SD16144,60
C6.D126th non-split extension by C6 of D12 acting via D12/D6=C224C6.D12144,65
C3×C4.Dic3Direct product of C3 and C4.Dic3242C3xC4.Dic3144,75
C3×D4⋊S3Direct product of C3 and D4⋊S3244C3xD4:S3144,80
C3×D4.S3Direct product of C3 and D4.S3244C3xD4.S3144,81
C3×C6.D4Direct product of C3 and C6.D424C3xC6.D4144,84
C3⋊S3.Q8The non-split extension by C3⋊S3 of Q8 acting via Q8/C2=C22244C3:S3.Q8144,116
C32⋊D8The semidirect product of C32 and D8 acting via D8/C2=D4244C3^2:D8144,117
C322SD16The semidirect product of C32 and SD16 acting via SD16/C2=D4244-C3^2:2SD16144,118
C2.PSU3(𝔽2)The central extension by C2 of PSU3(𝔽2)248+C2.PSU(3,2)144,120
C3×GL2(𝔽3)Direct product of C3 and GL2(𝔽3)242C3xGL(2,3)144,122
C6.6S46th non-split extension by C6 of S4 acting via S4/A4=C2244+C6.6S4144,125
S3×SL2(𝔽3)Direct product of S3 and SL2(𝔽3); = SL2(ℤ/6ℤ)244-S3xSL(2,3)144,128
C3⋊S33C82nd semidirect product of C3⋊S3 and C8 acting via C8/C4=C2244C3:S3:3C8144,130
C32⋊M4(2)The semidirect product of C32 and M4(2) acting via M4(2)/C4=C4244C3^2:M4(2)144,131
C4×C32⋊C4Direct product of C4 and C32⋊C4244C4xC3^2:C4144,132
C4⋊(C32⋊C4)The semidirect product of C4 and C32⋊C4 acting via C32⋊C4/C3⋊S3=C2244C4:(C3^2:C4)144,133
C62.C42nd non-split extension by C62 of C4 acting faithfully244-C6^2.C4144,135
D12⋊S33rd semidirect product of D12 and S3 acting via S3/C3=C2244D12:S3144,139
Dic3.D62nd non-split extension by Dic3 of D6 acting via D6/S3=C2244Dic3.D6144,140
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
C4×S32Direct product of C4, S3 and S3244C4xS3^2144,143
S3×D12Direct product of S3 and D12244+S3xD12144,144
D6⋊D62nd semidirect product of D6 and D6 acting via D6/S3=C2244D6:D6144,145
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
C2×C6.D6Direct product of C2 and C6.D624C2xC6.D6144,149
C2×C3⋊D12Direct product of C2 and C3⋊D1224C2xC3:D12144,151
S3×C3⋊D4Direct product of S3 and C3⋊D4244S3xC3:D4144,153
C3×C4○D12Direct product of C3 and C4○D12242C3xC4oD12144,161
C3×S3×D4Direct product of C3, S3 and D4244C3xS3xD4144,162
C3×D42S3Direct product of C3 and D42S3244C3xD4:2S3144,163
C6×C3⋊D4Direct product of C6 and C3⋊D424C6xC3:D4144,167
C22×C32⋊C4Direct product of C22 and C32⋊C424C2^2xC3^2:C4144,191
C22×S32Direct product of C22, S3 and S324C2^2xS3^2144,192

### Groups of order 168

dρLabelID
C3×F8Direct product of C3 and F8247C3xF8168,44

### Groups of order 192

dρLabelID
C82⋊C3The semidirect product of C82 and C3 acting faithfully243C8^2:C3192,3
C3⋊C2≀C4The semidirect product of C3 and C2≀C4 acting via C2≀C4/C23⋊C4=C2248+C3:C2wrC4192,30
C23.2D122nd non-split extension by C23 of D12 acting via D12/C3=D4248+C2^3.2D12192,33
C23.3D123rd non-split extension by C23 of D12 acting via D12/C3=D4248+C2^3.3D12192,34
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
C3×C2≀C4Direct product of C3 and C2≀C4244C3xC2wrC4192,157
C3×C42⋊C4Direct product of C3 and C42⋊C4244C3xC4^2:C4192,159
C23.7S41st non-split extension by C23 of S4 acting via S4/C22=S3246C2^3.7S4192,180
C23.8S42nd non-split extension by C23 of S4 acting via S4/C22=S3246+C2^3.8S4192,181
C2×C23.3A4Direct product of C2 and C23.3A424C2xC2^3.3A4192,189
C424C4⋊C3The semidirect product of C424C4 and C3 acting faithfully246C4^2:4C4:C3192,190
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
C24.A41st non-split extension by C24 of A4 acting faithfully246C2^4.A4192,195
(C22×C4).A44th non-split extension by C22×C4 of A4 acting faithfully246-(C2^2xC4).A4192,196
C24.3A43rd non-split extension by C24 of A4 acting faithfully246C2^4.3A4192,198
C23.19(C2×A4)12nd non-split extension by C23 of C2×A4 acting via C2×A4/C23=C3246C2^3.19(C2xA4)192,199
C23⋊D12The semidirect product of C23 and D12 acting via D12/C3=D4248+C2^3:D12192,300
S3×C23⋊C4Direct product of S3 and C23⋊C4248+S3xC2^3:C4192,302
S3×C4.D4Direct product of S3 and C4.D4248+S3xC4.D4192,303
D121D41st semidirect product of D12 and D4 acting via D4/C2=C22248+D12:1D4192,306
S3×C4≀C2Direct product of S3 and C4≀C2244S3xC4wrC2192,379
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
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
C3×D44D4Direct product of C3 and D44D4244C3xD4:4D4192,886
C3×C2≀C22Direct product of C3 and C2≀C22244C3xC2wrC2^2192,890
C8×S4Direct product of C8 and S4243C8xS4192,958
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
A4⋊M4(2)The semidirect product of A4 and M4(2) acting via M4(2)/C2×C4=C2246A4:M4(2)192,968
C24.5D64th non-split extension by C24 of D6 acting via D6/C2=S324C2^4.5D6192,972
A4⋊SD16The semidirect product of A4 and SD16 acting via SD16/D4=C2246A4:SD16192,973
D4⋊S4The semidirect product of D4 and S4 acting via S4/A4=C2246+D4:S4192,974
Q83S4The semidirect product of Q8 and S4 acting via S4/A4=C2246Q8:3S4192,976
Q8.5S43rd non-split extension by Q8 of S4 acting via S4/A4=C2244+Q8.5S4192,988
C25.S31st non-split extension by C25 of S3 acting faithfully24C2^5.S3192,991
C22×C42⋊C3Direct product of C22 and C42⋊C324C2^2xC4^2:C3192,992
A4×C22⋊C4Direct product of A4 and C22⋊C424A4xC2^2:C4192,994
C2×C42⋊C6Direct product of C2 and C42⋊C6246C2xC4^2:C6192,1001
A4×M4(2)Direct product of A4 and M4(2)246A4xM4(2)192,1011
A4×D8Direct product of A4 and D8246+A4xD8192,1014
A4×SD16Direct product of A4 and SD16246A4xSD16192,1015
C422A4The semidirect product of C42 and A4 acting via A4/C22=C324C4^2:2A4192,1020
S3×C22≀C2Direct product of S3 and C22≀C224S3xC2^2wrC2192,1147
S3×C8⋊C22Direct product of S3 and C8⋊C22; = Aut(D24) = Hol(C24)248+S3xC8:C2^2192,1331
C2×C4×S4Direct product of C2×C4 and S424C2xC4xS4192,1469
C2×C4⋊S4Direct product of C2 and C4⋊S424C2xC4:S4192,1470
C24.10D69th non-split extension by C24 of D6 acting via D6/C2=S3246C2^4.10D6192,1471
D42S4The semidirect product of D4 and S4 acting through Inn(D4)246D4:2S4192,1473
Q8×S4Direct product of Q8 and S4246-Q8xS4192,1477
Q84S4The semidirect product of Q8 and S4 acting through Inn(Q8)246Q8:4S4192,1478
C2×A4⋊D4Direct product of C2 and A4⋊D424C2xA4:D4192,1488
Q8⋊S41st semidirect product of Q8 and S4 acting via S4/C22=S3246Q8:S4192,1490
C2×D4×A4Direct product of C2, D4 and A424C2xD4xA4192,1497
A4×C4○D4Direct product of A4 and C4○D4246A4xC4oD4192,1501
C4×C22⋊A4Direct product of C4 and C22⋊A424C4xC2^2:A4192,1505
C4○D4⋊A41st semidirect product of C4○D4 and A4 acting via A4/C22=C3246C4oD4:A4192,1507
S3×2+ 1+4Direct product of S3 and 2+ 1+4248+S3xES+(2,2)192,1524
C23×S4Direct product of C23 and S424C2^3xS4192,1537
C26⋊C33rd semidirect product of C26 and C3 acting faithfully24C2^6:C3192,1541

### Groups of order 216

dρLabelID
C3×C322C8Direct product of C3 and C322C8244C3xC3^2:2C8216,117
C334C82nd semidirect product of C33 and C8 acting via C8/C2=C4244C3^3:4C8216,118
C3×S3×Dic3Direct product of C3, S3 and Dic3244C3xS3xDic3216,119
C3×C6.D6Direct product of C3 and C6.D6244C3xC6.D6216,120
C3×D6⋊S3Direct product of C3 and D6⋊S3244C3xD6:S3216,121
C3×C3⋊D12Direct product of C3 and C3⋊D12244C3xC3:D12216,122
C3×C322Q8Direct product of C3 and C322Q8244C3xC3^2:2Q8216,123
C339(C2×C4)6th semidirect product of C33 and C2×C4 acting via C2×C4/C2=C22244C3^3:9(C2xC4)216,131
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
C3×F9Direct product of C3 and F9248C3xF9216,154
C3⋊F9The semidirect product of C3 and F9 acting via F9/C32⋊C4=C2248C3:F9216,155
C3×PSU3(𝔽2)Direct product of C3 and PSU3(𝔽2)248C3xPSU(3,2)216,160
C33⋊Q82nd semidirect product of C33 and Q8 acting faithfully248C3^3:Q8216,161
C3×C3⋊S4Direct product of C3 and C3⋊S4246C3xC3:S4216,164
C3×S3×A4Direct product of C3, S3 and A4246C3xS3xA4216,166
C6×C32⋊C4Direct product of C6 and C32⋊C4244C6xC3^2:C4216,168
C2×C33⋊C4Direct product of C2 and C33⋊C4244C2xC3^3:C4216,169
S32×C6Direct product of C6, S3 and S3244S3^2xC6216,170
C2×C324D6Direct product of C2 and C324D6244C2xC3^2:4D6216,172

### Groups of order 240

dρLabelID
C4.A5The central extension by C4 of A5242C4.A5240,93

### Groups of order 288

dρLabelID
C12.70D121st non-split extension by C12 of D12 acting via D12/D6=C2244+C12.70D12288,207
D124Dic34th semidirect product of D12 and Dic3 acting via Dic3/C6=C2244D12:4Dic3288,216
C62.31D415th non-split extension by C62 of D4 acting via D4/C2=C22244C6^2.31D4288,228
C62.32D416th non-split extension by C62 of D4 acting via D4/C2=C22244C6^2.32D4288,229
C3×C424S3Direct product of C3 and C424S3242C3xC4^2:4S3288,239
C3×C23.6D6Direct product of C3 and C23.6D6244C3xC2^3.6D6288,240
C3×C12.D4Direct product of C3 and C12.D4244C3xC12.D4288,267
C3×C23.7D6Direct product of C3 and C23.7D6244C3xC2^3.7D6288,268
S32⋊C8The semidirect product of S32 and C8 acting via C8/C4=C2244S3^2:C8288,374
C4.S3≀C21st non-split extension by C4 of S3≀C2 acting via S3≀C2/S32=C2244C4.S3wrC2288,375
C3⋊S3.2D81st non-split extension by C3⋊S3 of D8 acting via D8/C4=C22244C3:S3.2D8288,377
C62.2D42nd non-split extension by C62 of D4 acting faithfully244+C6^2.2D4288,386
Dic3≀C2Wreath product of Dic3 by C2244-Dic3wrC2288,389
(C22×S3)⋊A4The semidirect product of C22×S3 and A4 acting faithfully246(C2^2xS3):A4288,411
(C6×C12)⋊C41st semidirect product of C6×C12 and C4 acting faithfully244+(C6xC12):C4288,422
C3⋊S3.5D8The non-split extension by C3⋊S3 of D8 acting via D8/D4=C2248+C3:S3.5D8288,430
(C2×C62)⋊C44th semidirect product of C2×C62 and C4 acting faithfully244(C2xC6^2):C4288,434
(C2×C62).C45th non-split extension by C2×C62 of C4 acting faithfully244(C2xC6^2).C4288,436
C3⋊C820D69th semidirect product of C3⋊C8 and D6 acting via D6/S3=C2244C3:C8:20D6288,466
D1218D62nd semidirect product of D12 and D6 acting via D6/C6=C2244+D12:18D6288,473
D12⋊D64th semidirect product of D12 and D6 acting via D6/C3=C22248+D12:D6288,574
Dic6⋊D64th semidirect product of Dic6 and D6 acting via D6/C3=C22248+Dic6:D6288,578
D125D65th semidirect product of D12 and D6 acting via D6/C3=C22248+D12:5D6288,585
C62.116C23111st non-split extension by C62 of C23 acting via C23/C2=C2224C6^2.116C2^3288,622
C628D45th semidirect product of C62 and D4 acting via D4/C2=C2224C6^2:8D4288,629
C3×C24⋊C6Direct product of C3 and C24⋊C6246C3xC2^4:C6288,634
C3×D126C22Direct product of C3 and D126C22244C3xD12:6C2^2288,703
C3×C244S3Direct product of C3 and C244S324C3xC2^4:4S3288,724
C2.AΓL1(𝔽9)1st central extension by C2 of AΓL1(𝔽9)248+C2.AGammaL(1,9)288,841
S3×GL2(𝔽3)Direct product of S3 and GL2(𝔽3); = GL2(ℤ/6ℤ)244S3xGL(2,3)288,851
A4×SL2(𝔽3)Direct product of A4 and SL2(𝔽3)246-A4xSL(2,3)288,859
Ω4+ (𝔽3)Omega group of + type on 𝔽34; = SL2(𝔽3)A4244+Omega+(4,3)288,860
C22⋊F9The semidirect product of C22 and F9 acting via F9/C32⋊C4=C2248+C2^2:F9288,867
S32⋊Q8The semidirect product of S32 and Q8 acting via Q8/C4=C2244S3^2:Q8288,868
C4.4S3≀C24th non-split extension by C4 of S3≀C2 acting via S3≀C2/C32⋊C4=C2248+C4.4S3wrC2288,869
C32⋊D8⋊C23rd semidirect product of C32⋊D8 and C2 acting faithfully244C3^2:D8:C2288,872
C3⋊S3⋊D8The semidirect product of C3⋊S3 and D8 acting via D8/C4=C22248+C3:S3:D8288,873
C3⋊S32SD16The semidirect product of C3⋊S3 and SD16 acting via SD16/C4=C22248+C3:S3:2SD16288,875
C4×S3≀C2Direct product of C4 and S3≀C2244C4xS3wrC2288,877
S32⋊D4The semidirect product of S32 and D4 acting via D4/C4=C2244S3^2:D4288,878
C4⋊S3≀C2The semidirect product of C4 and S3≀C2 acting via S3≀C2/C32⋊C4=C2248+C4:S3wrC2288,879
C2×S32⋊C4Direct product of C2 and S32⋊C424C2xS3^2:C4288,880
C62.9D49th non-split extension by C62 of D4 acting faithfully244C6^2.9D4288,881
C62.12D412nd non-split extension by C62 of D4 acting faithfully244C6^2.12D4288,884
C62⋊D42nd semidirect product of C62 and D4 acting faithfully248+C6^2:D4288,890
C62⋊Q81st semidirect product of C62 and Q8 acting faithfully248+C6^2:Q8288,895
C3⋊S3⋊M4(2)2nd semidirect product of C3⋊S3 and M4(2) acting via M4(2)/C2×C4=C2244C3:S3:M4(2)288,931
(C6×C12)⋊5C45th semidirect product of C6×C12 and C4 acting faithfully244(C6xC12):5C4288,934
D4×C32⋊C4Direct product of D4 and C32⋊C4248+D4xC3^2:C4288,936
C2×C62⋊C4Direct product of C2 and C62⋊C424C2xC6^2:C4288,941
D1223D67th semidirect product of D12 and D6 acting via D6/C6=C2244D12:23D6288,954
D1227D63rd semidirect product of D12 and D6 acting through Inn(D12)244+D12:27D6288,956
S32×D4Direct product of S3, S3 and D4248+S3^2xD4288,958
Dic612D66th semidirect product of Dic6 and D6 acting via D6/S3=C2248+Dic6:12D6288,960
D1213D67th semidirect product of D12 and D6 acting via D6/S3=C2248+D12:13D6288,962
C2×Dic3⋊D6Direct product of C2 and Dic3⋊D624C2xDic3:D6288,977
C32⋊2+ 1+4The semidirect product of C32 and 2+ 1+4 acting via 2+ 1+4/C23=C22244C3^2:ES+(2,2)288,978
C3×C23⋊A4Direct product of C3 and C23⋊A4244C3xC2^3:A4288,987
C3×D46D6Direct product of C3 and D46D6244C3xD4:6D6288,994
C22×S3≀C2Direct product of C22 and S3≀C224C2^2xS3wrC2288,1031
C3×C22⋊S4Direct product of C3 and C22⋊S4246C3xC2^2:S4288,1035
(C2×C6)⋊S42nd semidirect product of C2×C6 and S4 acting via S4/C22=S3246(C2xC6):S4288,1036

### Groups of order 336

dρLabelID
S3×F8Direct product of S3 and F82414+S3xF8336,211

### Groups of order 432

dρLabelID
D6⋊(C32⋊C4)The semidirect product of D6 and C32⋊C4 acting via C32⋊C4/C3⋊S3=C2248+D6:(C3^2:C4)432,568
C335(C2×C8)2nd semidirect product of C33 and C2×C8 acting via C2×C8/C2=C2×C4248+C3^3:5(C2xC8)432,571
C332M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C2=C2×C4248+C3^3:2M4(2)432,573
C3×S32⋊C4Direct product of C3 and S32⋊C4244C3xS3^2:C4432,574
C3×C32⋊D8Direct product of C3 and C32⋊D8244C3xC3^2:D8432,576
C3×C322SD16Direct product of C3 and C322SD16244C3xC3^2:2SD16432,577
C3⋊S3.2D121st non-split extension by C3⋊S3 of D12 acting via D12/C6=C22244C3:S3.2D12432,579
S32⋊Dic3The semidirect product of S32 and Dic3 acting via Dic3/C6=C2244S3^2:Dic3432,580
C33⋊D82nd semidirect product of C33 and D8 acting via D8/C2=D4244C3^3:D8432,582
C336SD162nd semidirect product of C33 and SD16 acting via SD16/C2=D4244C3^3:6SD16432,583
C337SD163rd semidirect product of C33 and SD16 acting via SD16/C2=D4244C3^3:7SD16432,584
(C3×C6).8D121st non-split extension by C3×C6 of D12 acting via D12/C3=D4248+(C3xC6).8D12432,586
C322D24The semidirect product of C32 and D24 acting via D24/C6=D4248+C3^2:2D24432,588
C338SD164th semidirect product of C33 and SD16 acting via SD16/C2=D4248+C3^3:8SD16432,589
S3×C6.D6Direct product of S3 and C6.D6248+S3xC6.D6432,595
S3×C3⋊D12Direct product of S3 and C3⋊D12248+S3xC3:D12432,598
D64S321st semidirect product of D6 and S32 acting via S32/C3⋊S3=C2248+D6:4S3^2432,599
(S3×C6)⋊D61st semidirect product of S3×C6 and D6 acting via D6/C3=C22248+(S3xC6):D6432,601
C3⋊S34D12The semidirect product of C3⋊S3 and D12 acting via D12/D6=C2248+C3:S3:4D12432,602
C336(C2×Q8)3rd semidirect product of C33 and C2×Q8 acting via C2×Q8/C2=C23248+C3^3:6(C2xQ8)432,605
(S3×C6).D69th non-split extension by S3×C6 of D6 acting via D6/C3=C22248+(S3xC6).D6432,606
D6.3S323rd non-split extension by D6 of S32 acting via S32/C3×S3=C2248+D6.3S3^2432,609
Dic3.S324th non-split extension by Dic3 of S32 acting via S32/C3×S3=C2248+Dic3.S3^2432,612
C3×C62.C4Direct product of C3 and C62.C4244C3xC6^2.C4432,633
C3×C62⋊C4Direct product of C3 and C62⋊C4244C3xC6^2:C4432,634
C3312M4(2)2nd semidirect product of C33 and M4(2) acting via M4(2)/C22=C4244C3^3:12M4(2)432,640
C6211Dic31st semidirect product of C62 and Dic3 acting via Dic3/C3=C4244C6^2:11Dic3432,641
C3×D6.3D6Direct product of C3 and D6.3D6244C3xD6.3D6432,652
C3×D6.4D6Direct product of C3 and D6.4D6244C3xD6.4D6432,653
C3×S3×C3⋊D4Direct product of C3, S3 and C3⋊D4244C3xS3xC3:D4432,658
C3×Dic3⋊D6Direct product of C3 and Dic3⋊D6244C3xDic3:D6432,659
C62.96D644th non-split extension by C62 of D6 acting via D6/C3=C22244C6^2.96D6432,693
C6224D65th semidirect product of C62 and D6 acting via D6/C3=C22244C6^2:24D6432,696
S3×F9Direct product of S3 and F92416+S3xF9432,736
C3×AΓL1(𝔽9)Direct product of C3 and AΓL1(𝔽9)248C3xAGammaL(1,9)432,737
C33⋊SD162nd semidirect product of C33 and SD16 acting faithfully248C3^3:SD16432,738
C333SD163rd semidirect product of C33 and SD16 acting faithfully2416+C3^3:3SD16432,739
F9⋊S3The semidirect product of F9 and S3 acting via S3/C3=C22416+F9:S3432,740
S3×PSU3(𝔽2)Direct product of S3 and PSU3(𝔽2)2416+S3xPSU(3,2)432,742
C62⋊Dic3The semidirect product of C62 and Dic3 acting faithfully2412+C6^2:Dic3432,743
A4×C32⋊C4Direct product of A4 and C32⋊C42412+A4xC3^2:C4432,744
C3×S3×S4Direct product of C3, S3 and S4246C3xS3xS4432,745
S3×C3⋊S4Direct product of S3 and C3⋊S42412+S3xC3:S4432,747
C6210D610th semidirect product of C62 and D6 acting faithfully2412+C6^2:10D6432,748
S32×A4Direct product of S3, S3 and A42412+S3^2xA4432,749
C2×S3×C32⋊C4Direct product of C2, S3 and C32⋊C4248+C2xS3xC3^2:C4432,753
C6×S3≀C2Direct product of C6 and S3≀C2244C6xS3wrC2432,754
C2×C33⋊D4Direct product of C2 and C33⋊D4244C2xC3^3:D4432,755
C2×C322D12Direct product of C2 and C322D12248+C2xC3^2:2D12432,756
C2×S33Direct product of C2, S3, S3 and S3248+C2xS3^3432,759

### Groups of order 480

dρLabelID
GL2(𝔽5)General linear group on 𝔽52; = SL2(𝔽5)1C4 = Aut(C52)244GL(2,5)480,218
A5⋊Q8The semidirect product of A5 and Q8 acting via Q8/C4=C2246A5:Q8480,945
C2×A5⋊C4Direct product of C2 and A5⋊C424C2xA5:C4480,952

### Groups of order 25

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

### Groups of order 50

dρLabelID
D25Dihedral group252+D2550,1
C5⋊D5The semidirect product of C5 and D5 acting via D5/C5=C225C5:D550,4

### Groups of order 100

dρLabelID
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

### Groups of order 125

dρLabelID
He5Heisenberg group; = C52C5 = 5+ 1+2255He5125,3
5- 1+2Extraspecial group255ES-(5,1)125,4

### Groups of order 250

dρLabelID
C52⋊C10The semidirect product of C52 and C10 acting faithfully2510+C5^2:C10250,5
C25⋊C10The semidirect product of C25 and C10 acting faithfully2510+C25:C10250,6
He5⋊C22nd semidirect product of He5 and C2 acting faithfully255He5:C2250,8

### Groups of order 300

dρLabelID
C5×A5Direct product of C5 and A5; = U2(𝔽4)253C5xA5300,22

### Groups of order 500

dρLabelID
C52⋊C20The semidirect product of C52 and C20 acting faithfully2520+C5^2:C20500,17
C25⋊C20The semidirect product of C25 and C20 acting faithfully; = Aut(D25) = Hol(C25)2520+C25:C20500,18
He5⋊C42nd semidirect product of He5 and C4 acting faithfully2520+He5:C4500,21
C52⋊F53rd semidirect product of C52 and F5 acting faithfully2510+C5^2:F5500,23
He54C44th semidirect product of He5 and C4 acting faithfully; = Aut(5- 1+2)255He5:4C4500,25
C52⋊D10The semidirect product of C52 and D10 acting faithfully2510+C5^2:D10500,27

### Groups of order 26

dρLabelID
C26Cyclic group261C2626,2

### Groups of order 52

dρLabelID
D26Dihedral group; = C2×D13262+D2652,4

### Groups of order 78

dρLabelID
C2×C13⋊C3Direct product of C2 and C13⋊C3263C2xC13:C378,2

### Groups of order 104

dρLabelID
C2×C13⋊C4Direct product of C2 and C13⋊C4264+C2xC13:C4104,12

### Groups of order 156

dρLabelID
C2×C13⋊C6Direct product of C2 and C13⋊C6266+C2xC13:C6156,8

### Groups of order 312

dρLabelID
C2×F13Direct product of C2 and F13; = Aut(D26) = Hol(C26)2612+C2xF13312,45

### Groups of order 338

dρLabelID
C13×D13Direct product of C13 and D13; = AΣL1(𝔽169)262C13xD13338,3

### Groups of order 27

dρLabelID
C27Cyclic group271C2727,1
C3×C9Abelian group of type [3,9]27C3xC927,2
C33Elementary abelian group of type [3,3,3]27C3^327,5

### Groups of order 54

dρLabelID
D27Dihedral group272+D2754,1
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

### Groups of order 81

dρLabelID
C32⋊C9The semidirect product of C32 and C9 acting via C9/C3=C327C3^2:C981,3
C27⋊C3The semidirect product of C27 and C3 acting faithfully273C27:C381,6
He3.C3The non-split extension by He3 of C3 acting faithfully273He3.C381,8
He3⋊C32nd semidirect product of He3 and C3 acting faithfully273He3:C381,9
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
C9○He3Central product of C9 and He3273C9oHe381,14

### Groups of order 162

dρLabelID
C32⋊D91st semidirect product of C32 and D9 acting via D9/C3=S327C3^2:D9162,5
C27⋊C6The semidirect product of C27 and C6 acting faithfully276+C27:C6162,9
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⋊S33rd semidirect product of He3 and S3 acting faithfully276+He3:S3162,21
3- 1+2.S3The non-split extension by 3- 1+2 of S3 acting faithfully276+ES-(3,1).S3162,22
He34S31st semidirect product of He3 and S3 acting via S3/C3=C227He3:4S3162,40
C3×He3⋊C2Direct product of C3 and He3⋊C227C3xHe3:C2162,41
C33.S34th non-split extension by C33 of S3 acting faithfully27C3^3.S3162,42
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

### Groups of order 216

dρLabelID
He3⋊C8The semidirect product of He3 and C8 acting faithfully276+He3:C8216,86
SU3(𝔽2)Special unitary group on 𝔽23; = He3Q8273SU(3,2)216,88

### Groups of order 243

dρLabelID
C33⋊C91st semidirect product of C33 and C9 acting via C9/C3=C327C3^3:C9243,13
C9.4He32nd central extension by C9 of He3273C9.4He3243,16
C27⋊C9The semidirect product of C27 and C9 acting faithfully279C27:C9243,22
C92⋊C31st semidirect product of C92 and C3 acting faithfully273C9^2:C3243,25
C922C32nd semidirect product of C92 and C3 acting faithfully273C9^2:2C3243,26
C92.C32nd non-split extension by C92 of C3 acting faithfully273C9^2.C3243,27
C32.He34th non-split extension by C32 of He3 acting via He3/C32=C3279C3^2.He3243,28
C32.5He35th non-split extension by C32 of He3 acting via He3/C32=C3279C3^2.5He3243,29
C32.6He36th non-split extension by C32 of He3 acting via He3/C32=C3279C3^2.6He3243,30
C32⋊He3The semidirect product of C32 and He3 acting via He3/C32=C327C3^2:He3243,37
C34.C33rd non-split extension by C34 of C3 acting faithfully27C3^4.C3243,38
C3×C3≀C3Direct product of C3 and C3≀C327C3xC3wrC3243,51
C9.He31st non-split extension by C9 of He3 acting via He3/C32=C3273C9.He3243,55
C33⋊C322nd semidirect product of C33 and C32 acting faithfully279C3^3:C3^2243,56
He3.C324th non-split extension by He3 of C32 acting via C32/C3=C3279He3.C3^2243,57
He3⋊C323rd semidirect product of He3 and C32 acting via C32/C3=C3279He3:C3^2243,58
C32.C339th non-split extension by C32 of C33 acting via C33/C32=C3279C3^2.C3^3243,59
C9.2He32nd non-split extension by C9 of He3 acting via He3/C32=C3279C9.2He3243,60
3+ 1+4Extraspecial group; = He3He3279ES+(3,2)243,65
3- 1+4Extraspecial group; = He33- 1+2279ES-(3,2)243,66

### Groups of order 324

dρLabelID
He3.D61st non-split extension by He3 of D6 acting faithfully276+He3.D6324,40
He3.2D62nd non-split extension by He3 of D6 acting faithfully276+He3.2D6324,41
He36D62nd semidirect product of He3 and D6 acting via D6/C3=C2227He3:6D6324,124
He3.6D6The non-split extension by He3 of D6 acting via D6/C3=C22276+He3.6D6324,125

### Groups of order 351

dρLabelID
C33⋊C13The semidirect product of C33 and C13 acting faithfully2713C3^3:C13351,12

### Groups of order 432

dρLabelID
He3⋊SD16The semidirect product of He3 and SD16 acting faithfully276+He3:SD16432,520

### Groups of order 486

dρLabelID
C27⋊C18The semidirect product of C27 and C18 acting faithfully; = Aut(D27) = Hol(C27)2718+C27:C18486,31
C92⋊C61st semidirect product of C92 and C6 acting faithfully276+C9^2:C6486,35
C92⋊S31st semidirect product of C92 and S3 acting faithfully276+C9^2:S3486,36
C922C62nd semidirect product of C92 and C6 acting faithfully276+C9^2:2C6486,37
C92.S32nd non-split extension by C92 of S3 acting faithfully276+C9^2.S3486,38
C9⋊C9.S32nd non-split extension by C9⋊C9 of S3 acting faithfully2718+C9:C9.S3486,39
C9⋊C9.3S33rd non-split extension by C9⋊C9 of S3 acting faithfully2718+C9:C9.3S3486,40
C9⋊C9⋊S31st semidirect product of C9⋊C9 and S3 acting faithfully2718+C9:C9:S3486,41
C332D92nd semidirect product of C33 and D9 acting via D9/C3=S327C3^3:2D9486,52
C33.D93rd non-split extension by C33 of D9 acting via D9/C3=S3276+C3^3.D9486,55
C922S32nd semidirect product of C92 and S3 acting faithfully273C9^2:2S3486,61
C34⋊S31st semidirect product of C34 and S3 acting faithfully27C3^4:S3486,103
C34.S34th non-split extension by C34 of S3 acting faithfully27C3^4.S3486,105
C3×C3≀S3Direct product of C3 and C3≀S327C3xC3wrS3486,115
C3≀S33C3The semidirect product of C3≀S3 and C3 acting through Inn(C3≀S3)273C3wrS3:3C3486,125
C3≀C3⋊C62nd semidirect product of C3≀C3 and C6 acting faithfully279C3wrC3:C6486,126
(C3×He3)⋊C68th semidirect product of C3×He3 and C6 acting faithfully2718+(C3xHe3):C6486,127
He3.C3⋊C63rd semidirect product of He3.C3 and C6 acting faithfully279He3.C3:C6486,128
C9⋊S3⋊C322nd semidirect product of C9⋊S3 and C32 acting faithfully2718+C9:S3:C3^2486,129
He3.(C3×C6)6th non-split extension by He3 of C3×C6 acting via C3×C6/C3=C6279He3.(C3xC6)486,130
He3.(C3×S3)5th non-split extension by He3 of C3×S3 acting via C3×S3/C3=S32718+He3.(C3xS3)486,131
C3≀C3.C6The non-split extension by C3≀C3 of C6 acting faithfully279C3wrC3.C6486,132
C344C64th semidirect product of C34 and C6 acting faithfully27C3^4:4C6486,146
C345C65th semidirect product of C34 and C6 acting faithfully27C3^4:5C6486,167
C3≀C3.S3The non-split extension by C3≀C3 of S3 acting via S3/C3=C2276+C3wrC3.S3486,175
C33⋊(C3×S3)4th semidirect product of C33 and C3×S3 acting faithfully2718+C3^3:(C3xS3)486,176
He3.C32C62nd semidirect product of He3.C3 and C6 acting faithfully2718+He3.C3:2C6486,177
He3⋊(C3×S3)4th semidirect product of He3 and C3×S3 acting via C3×S3/C3=S32718+He3:(C3xS3)486,178
C3.He3⋊C6The semidirect product of C3.He3 and C6 acting faithfully2718+C3.He3:C6486,179
C346S36th semidirect product of C34 and S3 acting faithfully27C3^4:6S3486,183
C347S37th semidirect product of C34 and S3 acting faithfully27C3^4:7S3486,185
C3≀C3⋊S32nd semidirect product of C3≀C3 and S3 acting via S3/C3=C2276+C3wrC3:S3486,189
3+ 1+4⋊C21st semidirect product of 3+ 1+4 and C2 acting faithfully2718+ES+(3,2):C2486,236
3+ 1+42C22nd semidirect product of 3+ 1+4 and C2 acting faithfully279ES+(3,2):2C2486,237
3- 1+4⋊C21st semidirect product of 3- 1+4 and C2 acting faithfully2718+ES-(3,2):C2486,238
3- 1+42C22nd semidirect product of 3- 1+4 and C2 acting faithfully279ES-(3,2):2C2486,239
3+ 1+43C23rd semidirect product of 3+ 1+4 and C2 acting faithfully279ES+(3,2):3C2486,249

### Groups of order 28

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

### Groups of order 56

dρLabelID
C4×D7Direct product of C4 and D7282C4xD756,4
D28Dihedral group282+D2856,5
C7⋊D4The semidirect product of C7 and D4 acting via D4/C22=C2282C7:D456,7
C7×D4Direct product of C7 and D4282C7xD456,9
C22×D7Direct product of C22 and D728C2^2xD756,12

### Groups of order 84

dρLabelID
C7⋊C12The semidirect product of C7 and C12 acting via C12/C2=C6286-C7:C1284,1
C4×C7⋊C3Direct product of C4 and C7⋊C3283C4xC7:C384,2
C22×C7⋊C3Direct product of C22 and C7⋊C328C2^2xC7:C384,9
C7×A4Direct product of C7 and A4283C7xA484,10
C7⋊A4The semidirect product of C7 and A4 acting via A4/C22=C3283C7:A484,11

### Groups of order 112

dρLabelID
D4×D7Direct product of D4 and D7284+D4xD7112,31

### Groups of order 168

dρLabelID
C4×F7Direct product of C4 and F7286C4xF7168,8
C4⋊F7The semidirect product of C4 and F7 acting via F7/C7⋊C3=C2286+C4:F7168,9
Dic7⋊C6The semidirect product of Dic7 and C6 acting faithfully286Dic7:C6168,11
D4×C7⋊C3Direct product of D4 and C7⋊C3286D4xC7:C3168,20
C7×S4Direct product of C7 and S4283C7xS4168,45
C7⋊S4The semidirect product of C7 and S4 acting via S4/A4=C2286+C7:S4168,46
C22×F7Direct product of C22 and F728C2^2xF7168,47
A4×D7Direct product of A4 and D7286+A4xD7168,48
D7⋊A4The semidirect product of D7 and A4 acting via A4/C22=C3286+D7:A4168,49

### Groups of order 196

dρLabelID
C7×Dic7Direct product of C7 and Dic7282C7xDic7196,5
D7×C14Direct product of C14 and D7282D7xC14196,10

### Groups of order 224

dρLabelID
C4×F8Direct product of C4 and F8287C4xF8224,173
C22×F8Direct product of C22 and F828C2^2xF8224,195

### Groups of order 252

dρLabelID
A4×C7⋊C3Direct product of A4 and C7⋊C3289A4xC7:C3252,27

### Groups of order 336

dρLabelID
D4×F7Direct product of D4 and F7; = Aut(D28) = Hol(C28)2812+D4xF7336,125
D7×S4Direct product of D7 and S4286+D7xS4336,212

### Groups of order 392

dρLabelID
Dic72D7The semidirect product of Dic7 and D7 acting through Inn(Dic7)284+Dic7:2D7392,19
C7⋊D28The semidirect product of C7 and D28 acting via D28/D14=C2284+C7:D28392,21
C7×C7⋊D4Direct product of C7 and C7⋊D4282C7xC7:D4392,27
C72⋊C8The semidirect product of C72 and C8 acting faithfully288+C7^2:C8392,36
C72⋊Q8The semidirect product of C72 and Q8 acting faithfully288+C7^2:Q8392,38
C2×C72⋊C4Direct product of C2 and C72⋊C4284+C2xC7^2:C4392,40
C2×D72Direct product of C2, D7 and D7284+C2xD7^2392,41

### Groups of order 448

dρLabelID
C43⋊C7The semidirect product of C43 and C7 acting faithfully287C4^3:C7448,178
D4×F8Direct product of D4 and F82814+D4xF8448,1363
C26⋊C72nd semidirect product of C26 and C7 acting faithfully28C2^6:C7448,1393

### Groups of order 29

dρLabelID
C29Cyclic group291C2929,1

### Groups of order 58

dρLabelID
D29Dihedral group292+D2958,1

### Groups of order 116

dρLabelID
C29⋊C4The semidirect product of C29 and C4 acting faithfully294+C29:C4116,3

### Groups of order 203

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

### Groups of order 406

dρLabelID
C29⋊C14The semidirect product of C29 and C14 acting faithfully2914+C29:C14406,1

### Groups of order 30

dρLabelID
C30Cyclic group301C3030,4

### Groups of order 60

dρLabelID
C6×D5Direct product of C6 and D5302C6xD560,10
S3×C10Direct product of C10 and S3302S3xC1060,11
D30Dihedral group; = C2×D15302+D3060,12

### Groups of order 90

dρLabelID
S3×C15Direct product of C15 and S3302S3xC1590,6
C3×D15Direct product of C3 and D15302C3xD1590,7

### Groups of order 120

dρLabelID
C6×F5Direct product of C6 and F5304C6xF5120,40
C2×C3⋊F5Direct product of C2 and C3⋊F5304C2xC3:F5120,41
C2×S3×D5Direct product of C2, S3 and D5304+C2xS3xD5120,42
C10×A4Direct product of C10 and A4303C10xA4120,43

### Groups of order 150

dρLabelID
C2×C52⋊C3Direct product of C2 and C52⋊C3303C2xC5^2:C3150,7
D5×C15Direct product of C15 and D5302D5xC15150,8
C5×D15Direct product of C5 and D15302C5xD15150,11

### Groups of order 180

dρLabelID
C3×C3⋊F5Direct product of C3 and C3⋊F5304C3xC3:F5180,21
C5×C32⋊C4Direct product of C5 and C32⋊C4304C5xC3^2:C4180,23
C32⋊Dic5The semidirect product of C32 and Dic5 acting via Dic5/C5=C4304C3^2:Dic5180,24
C32⋊F5The semidirect product of C32 and F5 acting via F5/C5=C4304+C3^2:F5180,25
C3×S3×D5Direct product of C3, S3 and D5304C3xS3xD5180,26
C5×S32Direct product of C5, S3 and S3304C5xS3^2180,28
S3×D15Direct product of S3 and D15304+S3xD15180,29
D15⋊S3The semidirect product of D15 and S3 acting via S3/C3=C2304D15:S3180,30

### Groups of order 240

dρLabelID
C2×S3×F5Direct product of C2, S3 and F5; = Aut(D30) = Hol(C30)308+C2xS3xF5240,195
C10×S4Direct product of C10 and S4303C10xS4240,196
C2×C5⋊S4Direct product of C2 and C5⋊S4306+C2xC5:S4240,197
C2×D5×A4Direct product of C2, D5 and A4306+C2xD5xA4240,198
C3×C24⋊C5Direct product of C3 and C24⋊C5305C3xC2^4:C5240,199

### Groups of order 300

dρLabelID
C2×C52⋊S3Direct product of C2 and C52⋊S3303C2xC5^2:S3300,26
C2×C52⋊C6Direct product of C2 and C52⋊C6306+C2xC5^2:C6300,27
C3×C52⋊C4Direct product of C3 and C52⋊C4304C3xC5^2:C4300,31
C152F52nd semidirect product of C15 and F5 acting via F5/C5=C4304C15:2F5300,35
C3×D52Direct product of C3, D5 and D5304C3xD5^2300,36
C5×S3×D5Direct product of C5, S3 and D5304C5xS3xD5300,37
D5×D15Direct product of D5 and D15304+D5xD15300,39
D15⋊D5The semidirect product of D15 and D5 acting via D5/C5=C2304D15:D5300,40
C52⋊A4The semidirect product of C52 and A4 acting via A4/C22=C3303C5^2:A4300,43

### Groups of order 360

dρLabelID
C6×A5Direct product of C6 and A5303C6xA5360,122
C3×S3×F5Direct product of C3, S3 and F5308C3xS3xF5360,126
S3×C3⋊F5Direct product of S3 and C3⋊F5308S3xC3:F5360,128
C3⋊F5⋊S3The semidirect product of C3⋊F5 and S3 acting via S3/C3=C2308+C3:F5:S3360,129
D5×C32⋊C4Direct product of D5 and C32⋊C4308+D5xC3^2:C4360,130
C32⋊F5⋊C2The semidirect product of C32⋊F5 and C2 acting faithfully308+C3^2:F5:C2360,131
C5×S3≀C2Direct product of C5 and S3≀C2304C5xS3wrC2360,132
S32⋊D5The semidirect product of S32 and D5 acting via D5/C5=C2304S3^2:D5360,133
C32⋊D20The semidirect product of C32 and D20 acting via D20/C5=D4308+C3^2:D20360,134
S32×D5Direct product of S3, S3 and D5308+S3^2xD5360,137

### Groups of order 450

dρLabelID
C15×D15Direct product of C15 and D15302C15xD15450,29

### Groups of order 480

dρLabelID
C2×F16Direct product of C2 and F163015+C2xF16480,1190
C2×A4⋊F5Direct product of C2 and A4⋊F53012+C2xA4:F5480,1191
C2×A4×F5Direct product of C2, A4 and F53012+C2xA4xF5480,1192
C2×D5×S4Direct product of C2, D5 and S4306+C2xD5xS4480,1193
C3×C24⋊D5Direct product of C3 and C24⋊D5305C3xC2^4:D5480,1194
C24⋊D15The semidirect product of C24 and D15 acting via D15/C3=D53010+C2^4:D15480,1195
S3×C24⋊C5Direct product of S3 and C24⋊C53010+S3xC2^4:C5480,1196
C6×C24⋊C5Direct product of C6 and C24⋊C5305C6xC2^4:C5480,1204

### Groups of order 31

dρLabelID
C31Cyclic group311C3131,1

### Groups of order 62

dρLabelID
D31Dihedral group312+D3162,1

### Groups of order 93

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

### Groups of order 155

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

### Groups of order 186

dρLabelID
C31⋊C6The semidirect product of C31 and C6 acting faithfully316+C31:C6186,1

### Groups of order 310

dρLabelID
C31⋊C10The semidirect product of C31 and C10 acting faithfully3110+C31:C10310,1

### Groups of order 465

dρLabelID
C31⋊C15The semidirect product of C31 and C15 acting faithfully3115C31:C15465,1

### Groups of order 32

dρLabelID
C32Cyclic group321C3232,1
C2.C421st central stem extension by C2 of C4232C2.C4^232,2
C4×C8Abelian group of type [4,8]32C4xC832,3
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⋊C8The semidirect product of C4 and C8 acting via C8/C4=C232C4:C832,12
C4.Q81st non-split extension by C4 of Q8 acting via Q8/C4=C232C4.Q832,13
C2.D82nd central extension by C2 of D832C2.D832,14
C2×C16Abelian group of type [2,16]32C2xC1632,16
Q32Generalised quaternion group; = C16.C2 = Dic8322-Q3232,20
C2×C42Abelian group of type [2,4,4]32C2xC4^232,21
C2×C4⋊C4Direct product of C2 and C4⋊C432C2xC4:C432,23
C4×Q8Direct product of C4 and Q832C4xQ832,26
C42.C24th non-split extension by C42 of C2 acting faithfully32C4^2.C232,32
C4⋊Q8The semidirect product of C4 and Q8 acting via Q8/C4=C232C4:Q832,35
C22×C8Abelian group of type [2,2,8]32C2^2xC832,36
C2×Q16Direct product of C2 and Q1632C2xQ1632,41
C23×C4Abelian group of type [2,2,2,4]32C2^3xC432,45
C22×Q8Direct product of C22 and Q832C2^2xQ832,47
C25Elementary abelian group of type [2,2,2,2,2]32C2^532,51

### Groups of order 64

dρLabelID
C22.M4(2)2nd non-split extension by C22 of M4(2) acting via M4(2)/C2×C4=C232C2^2.M4(2)64,5
D4⋊C8The semidirect product of D4 and C8 acting via C8/C4=C232D4:C864,6
C42.C221st non-split extension by C42 of C22 acting faithfully32C4^2.C2^264,10
C4.D81st non-split extension by C4 of D8 acting via D8/D4=C232C4.D864,12
C4.C423rd non-split extension by C4 of C42 acting via C42/C2×C4=C232C4.C4^264,22
C22.C422nd non-split extension by C22 of C42 acting via C42/C2×C4=C232C2^2.C4^264,24
C22⋊C16The semidirect product of C22 and C16 acting via C16/C8=C232C2^2:C1664,29
D4.C8The non-split extension by D4 of C8 acting via C8/C4=C2322D4.C864,31
C2.D161st central extension by C2 of D1632C2.D1664,38
D8.C41st non-split extension by D8 of C4 acting via C4/C2=C2322D8.C464,40
C8.17D44th non-split extension by C8 of D4 acting via D4/C22=C2324-C8.17D464,43
C8.4Q83rd non-split extension by C8 of Q8 acting via Q8/C4=C2322C8.4Q864,49
M6(2)Modular maximal-cyclic group; = C323C2322M6(2)64,51
D32Dihedral group322+D3264,52
SD64Semidihedral group; = C322C2 = QD64322SD6464,53
C4×C22⋊C4Direct product of C4 and C22⋊C432C4xC2^2:C464,58
C23.7Q82nd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.7Q864,61
C23.34D45th non-split extension by C23 of D4 acting via D4/C22=C232C2^3.34D464,62
C23.8Q83rd non-split extension by C23 of Q8 acting via Q8/C4=C232C2^3.8Q864,66
C23.23D42nd non-split extension by C23 of D4 acting via D4/C4=C232C2^3.23D464,67
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
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
C23.10D43rd non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.10D464,75
C23.Q83rd non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.Q864,77
C23.11D44th non-split extension by C23 of D4 acting via D4/C2=C2232C2^3.11D464,78
C23.4Q84th non-split extension by C23 of Q8 acting via Q8/C2=C2232C2^3.4Q864,80
C4×M4(2)Direct product of C4 and M4(2)32C4xM4(2)64,85
C82M4(2)Central product of C8 and M4(2)32C8o2M4(2)64,86
C2×C22⋊C8Direct product of C2 and C22⋊C832C2xC2^2:C864,87
(C22×C8)⋊C22nd semidirect product of C22×C8 and C2 acting faithfully32(C2^2xC8):C264,89
C2×C4.10D4Direct product of C2 and C4.10D432C2xC4.10D464,93
C2×D4⋊C4Direct product of C2 and D4⋊C432C2xD4:C464,95
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
C4⋊M4(2)The semidirect product of C4 and M4(2) acting via M4(2)/C2×C4=C232C4:M4(2)64,104
C42.6C226th non-split extension by C42 of C22 acting faithfully32C4^2.6C2^264,105
C23.25D44th non-split extension by C23 of D4 acting via D4/C4=C232C2^3.25D464,108
M4(2)⋊C41st semidirect product of M4(2) and C4 acting via C4/C2=C232M4(2):C464,109
C2×C8.C4Direct product of C2 and C8.C432C2xC8.C464,110
C42.12C49th non-split extension by C42 of C4 acting via C4/C2=C232C4^2.12C464,112
C42.6C43rd non-split extension by C42 of C4 acting via C4/C2=C232C4^2.6C464,113
C42.7C227th non-split extension by C42 of C22 acting faithfully32C4^2.7C2^264,114
C8×D4Direct product of C8 and D432C8xD464,115
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×D8Direct product of C4 and D832C4xD864,118
C4×SD16Direct product of C4 and SD1632C4xSD1664,119
SD16⋊C41st semidirect product of SD16 and C4 acting via C4/C2=C232SD16:C464,121
D8⋊C43rd semidirect product of D8 and C4 acting via C4/C2=C2; = Aut(SD32)32D8:C464,123
Q8⋊D41st semidirect product of Q8 and D4 acting via D4/C22=C232Q8:D464,129
D4⋊D42nd semidirect product of D4 and D4 acting via D4/C22=C232D4:D464,130
C22⋊Q16The semidirect product of C22 and Q16 acting via Q16/Q8=C232C2^2:Q1664,132
D4.7D42nd non-split extension by D4 of D4 acting via D4/C22=C232D4.7D464,133
C4⋊D8The semidirect product of C4 and D8 acting via D8/D4=C232C4:D864,140
C4⋊SD16The semidirect product of C4 and SD16 acting via SD16/Q8=C232C4:SD1664,141
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
Q8.D42nd non-split extension by Q8 of D4 acting via D4/C4=C232Q8.D464,145
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
C8.18D45th non-split extension by C8 of D4 acting via D4/C22=C232C8.18D464,148
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
C8.D41st non-split extension by C8 of D4 acting via D4/C2=C2232C8.D464,151
D4.5D45th non-split extension by D4 of D4 acting via D4/C4=C2324-D4.5D464,154
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
D4.Q8The non-split extension by D4 of Q8 acting via Q8/C4=C232D4.Q864,159
C22.D83rd non-split extension by C22 of D8 acting via D8/D4=C232C2^2.D864,161
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
C4.4D84th non-split extension by C4 of D8 acting via D8/C8=C232C4.4D864,167
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
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
C8.12D48th non-split extension by C8 of D4 acting via D4/C4=C232C8.12D464,176
C83D43rd semidirect product of C8 and D4 acting via D4/C2=C2232C8:3D464,177
C8.2D42nd non-split extension by C8 of D4 acting via D4/C2=C2232C8.2D464,178
C2×M5(2)Direct product of C2 and M5(2)32C2xM5(2)64,184
D4○C16Central product of D4 and C16322D4oC1664,185
C2×D16Direct product of C2 and D1632C2xD1664,186
C2×SD32Direct product of C2 and SD3232C2xSD3264,187
C4○D16Central product of C4 and D16322C4oD1664,189
Q32⋊C22nd semidirect product of Q32 and C2 acting faithfully324-Q32:C264,191
C22×C22⋊C4Direct product of C22 and C22⋊C432C2^2xC2^2:C464,193
C2×C42⋊C2Direct product of C2 and C42⋊C232C2xC4^2:C264,195
C2×C4×D4Direct product of C2×C4 and D432C2xC4xD464,196
C4×C4○D4Direct product of C4 and C4○D432C4xC4oD464,198
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
C2×C4⋊D4Direct product of C2 and C4⋊D432C2xC4:D464,203
C2×C22⋊Q8Direct product of C2 and C22⋊Q832C2xC2^2:Q864,204
C2×C22.D4Direct product of C2 and C22.D432C2xC2^2.D464,205
C2×C4.4D4Direct product of C2 and C4.4D432C2xC4.4D464,207
C2×C422C2Direct product of C2 and C422C232C2xC4^2:2C264,209
C23.36C239th non-split extension by C23 of C23 acting via C23/C22=C232C2^3.36C2^364,210
C2×C41D4Direct product of C2 and C41D432C2xC4:1D464,211
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
D46D42nd semidirect product of D4 and D4 acting through Inn(D4)32D4:6D464,228
Q85D41st semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:5D464,229
D4×Q8Direct product of D4 and Q832D4xQ864,230
Q86D42nd semidirect product of Q8 and D4 acting through Inn(Q8)32Q8:6D464,231
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
D43Q8The semidirect product of D4 and Q8 acting through Inn(D4)32D4:3Q864,235
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)Direct product of C22 and M4(2)32C2^2xM4(2)64,247
C2×C8○D4Direct product of C2 and C8○D432C2xC8oD464,248
C22×D8Direct product of C22 and D832C2^2xD864,250
C22×SD16Direct product of C22 and SD1632C2^2xSD1664,251
C2×C4○D8Direct product of C2 and C4○D832C2xC4oD864,253
C2×C8.C22Direct product of C2 and C8.C2232C2xC8.C2^264,255
Q8○D8Central product of Q8 and D8324-Q8oD864,259
D4×C23Direct product of C23 and D432D4xC2^364,261
C22×C4○D4Direct product of C22 and C4○D432C2^2xC4oD464,263
C2×2- 1+4Direct product of C2 and 2- 1+432C2xES-(2,2)64,265

### Groups of order 96

dρLabelID
Q8⋊Dic3The semidirect product of Q8 and Dic3 acting via Dic3/C2=S332Q8:Dic396,66
C4×SL2(𝔽3)Direct product of C4 and SL2(𝔽3)32C4xSL(2,3)96,69
C8.A4The central extension by C8 of A4322C8.A496,74
C2×CSU2(𝔽3)Direct product of C2 and CSU2(𝔽3)32C2xCSU(2,3)96,188
C4.S42nd non-split extension by C4 of S4 acting via S4/A4=C2324-C4.S496,191
C22×SL2(𝔽3)Direct product of C22 and SL2(𝔽3)32C2^2xSL(2,3)96,198
C2×C4.A4Direct product of C2 and C4.A432C2xC4.A496,200

### Groups of order 128

dρLabelID
C421C81st semidirect product of C42 and C8 acting via C8/C2=C432C4^2:1C8128,6
C426C83rd semidirect product of C42 and C8 acting via C8/C4=C232C4^2:6C8128,8
C23.21C423rd non-split extension by C23 of C42 acting via C42/C2×C4=C232C2^3.21C4^2128,14
C24.46D41st non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.46D4128,16
C42.4Q84th non-split extension by C42 of Q8 acting via Q8/C2=C2232C4^2.4Q8128,17
C42.5Q85th non-split extension by C42 of Q8 acting via Q8/C2=C2232C4^2.5Q8128,18
C42.6Q86th non-split extension by C42 of Q8 acting via Q8/C2=C2232C4^2.6Q8128,20
C23.8D81st non-split extension by C23 of D8 acting via D8/C4=C2232C2^3.8D8128,21
C24.2Q81st non-split extension by C24 of Q8 acting via Q8/C2=C2232C2^4.2Q8128,25
C23.30D81st non-split extension by C23 of D8 acting via D8/D4=C232C2^3.30D8128,26
C24.48D43rd non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.48D4128,29
C24.3Q82nd non-split extension by C24 of Q8 acting via Q8/C2=C2232C2^4.3Q8128,30
C42.9Q89th non-split extension by C42 of Q8 acting via Q8/C2=C2232C4^2.9Q8128,32
C42.10Q810th non-split extension by C42 of Q8 acting via Q8/C2=C2232C4^2.10Q8128,35
C23.C422nd non-split extension by C23 of C42 acting via C42/C22=C2232C2^3.C4^2128,37
C23.8C423rd non-split extension by C23 of C42 acting via C42/C22=C2232C2^3.8C4^2128,38
C23⋊C16The semidirect product of C23 and C16 acting via C16/C4=C432C2^3:C16128,46
C23.15M4(2)2nd non-split extension by C23 of M4(2) acting via M4(2)/C22=C432C2^3.15M4(2)128,49
(C2×D4)⋊C82nd semidirect product of C2×D4 and C8 acting via C8/C2=C432(C2xD4):C8128,50
(C2×C42).C46th non-split extension by C2×C42 of C4 acting faithfully32(C2xC4^2).C4128,51
C23.1M4(2)1st non-split extension by C23 of M4(2) acting via M4(2)/C4=C4324C2^3.1M4(2)128,53
C42⋊C82nd semidirect product of C42 and C8 acting via C8/C2=C432C4^2:C8128,56
C423C83rd semidirect product of C42 and C8 acting via C8/C2=C432C4^2:3C8128,57
C23.2M4(2)2nd non-split extension by C23 of M4(2) acting via M4(2)/C4=C432C2^3.2M4(2)128,58
C22⋊C4.C8The non-split extension by C22⋊C4 of C8 acting via C8/C2=C4324C2^2:C4.C8128,60
C23.2D82nd non-split extension by C23 of D8 acting via D8/C2=D4328-C2^3.2D8128,72
C23.2SD162nd non-split extension by C23 of SD16 acting via SD16/C2=D4328-C2^3.2SD16128,74
C23.4D84th non-split extension by C23 of D8 acting via D8/C2=D432C2^3.4D8128,76
C2.C2≀C42nd central stem extension by C2 of C2≀C432C2.C2wrC4128,77
(C2×C4).D84th non-split extension by C2×C4 of D8 acting via D8/C2=D432(C2xC4).D8128,78
C22.SD321st non-split extension by C22 of SD32 acting via SD32/Q16=C232C2^2.SD32128,79
C23.32D83rd non-split extension by C23 of D8 acting via D8/D4=C232C2^3.32D8128,80
C23.Q161st non-split extension by C23 of Q16 acting via Q16/C2=D432C2^3.Q16128,83
C24.4D44th non-split extension by C24 of D4 acting faithfully32C2^4.4D4128,84
(C2×C4).Q161st non-split extension by C2×C4 of Q16 acting via Q16/C2=D432(C2xC4).Q16128,85
C2.7C2≀C44th central stem extension by C2 of C2≀C432C2.7C2wrC4128,86
C42.(C2×C4)2nd non-split extension by C42 of C2×C4 acting faithfully328-C4^2.(C2xC4)128,88
C8.25D82nd non-split extension by C8 of D8 acting via D8/D4=C2324-C8.25D8128,90
C8.1Q161st non-split extension by C8 of Q16 acting via Q16/C4=C22324C8.1Q16128,98
C16.C81st non-split extension by C16 of C8 acting via C8/C2=C4324C16.C8128,101
C16.3C81st non-split extension by C16 of C8 acting via C8/C4=C2322C16.3C8128,105
C42.2C82nd non-split extension by C42 of C8 acting via C8/C2=C432C4^2.2C8128,107
C42.7C84th non-split extension by C42 of C8 acting via C8/C4=C232C4^2.7C8128,108
M4(2).C82nd non-split extension by M4(2) of C8 acting via C8/C4=C2324M4(2).C8128,110
C8.11C425th non-split extension by C8 of C42 acting via C42/C2×C4=C232C8.11C4^2128,115
C23.9D82nd non-split extension by C23 of D8 acting via D8/C4=C22324C2^3.9D8128,116
C8.13C427th non-split extension by C8 of C42 acting via C42/C2×C4=C2324C8.13C4^2128,117
C8.C421st non-split extension by C8 of C42 acting via C42/C22=C2232C8.C4^2128,118
M5(2).C42nd non-split extension by M5(2) of C4 acting via C4/C2=C2324M5(2).C4128,120
C8.4C424th non-split extension by C8 of C42 acting via C42/C22=C22324C8.4C4^2128,121
C24.5D45th non-split extension by C24 of D4 acting faithfully32C2^4.5D4128,122
C23.2C422nd non-split extension by C23 of C42 acting via C42/C4=C4324C2^3.2C4^2128,123
C23.3C423rd non-split extension by C23 of C42 acting via C42/C4=C4324C2^3.3C4^2128,124
C24.6D46th non-split extension by C24 of D4 acting faithfully32C2^4.6D4128,125
(C2×Q8).Q82nd non-split extension by C2×Q8 of Q8 acting via Q8/C2=C2232(C2xQ8).Q8128,126
(C22×C8)⋊C44th semidirect product of C22×C8 and C4 acting faithfully324(C2^2xC8):C4128,127
C32⋊C42nd semidirect product of C32 and C4 acting faithfully324C32:C4128,130
C23.C16The non-split extension by C23 of C16 acting via C16/C4=C4324C2^3.C16128,132
(C2×D4).D44th non-split extension by C2×D4 of D4 acting faithfully328-(C2xD4).D4128,139
(C2×Q8).D46th non-split extension by C2×Q8 of D4 acting faithfully324-(C2xQ8).D4128,143
C8⋊C4.C43rd non-split extension by C8⋊C4 of C4 acting faithfully328-C8:C4.C4128,145
(C4×C8)⋊C43rd semidirect product of C4×C8 and C4 acting faithfully324(C4xC8):C4128,146
D163C42nd semidirect product of D16 and C4 acting via C4/C2=C2324D16:3C4128,150
M6(2)⋊C26th semidirect product of M6(2) and C2 acting faithfully324+M6(2):C2128,151
C8.C161st non-split extension by C8 of C16 acting via C16/C8=C2322C8.C16128,154
C8.Q162nd non-split extension by C8 of Q16 acting via Q16/C4=C22324C8.Q16128,158
C2×C23⋊C8Direct product of C2 and C23⋊C832C2xC2^3:C8128,188
C42.371D44th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.371D4128,190
C23.8M4(2)4th non-split extension by C23 of M4(2) acting via M4(2)/C4=C2232C2^3.8M4(2)128,191
C42.393D426th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.393D4128,192
(C2×C4)⋊M4(2)The semidirect product of C2×C4 and M4(2) acting via M4(2)/C22=C432(C2xC4):M4(2)128,195
C42.42D424th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.42D4128,196
C23⋊M4(2)The semidirect product of C23 and M4(2) acting via M4(2)/C4=C432C2^3:M4(2)128,197
C42.43D425th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.43D4128,198
C23⋊C8⋊C215th semidirect product of C23⋊C8 and C2 acting faithfully32C2^3:C8:C2128,200
C42.395D428th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.395D4128,201
C24.(C2×C4)3rd non-split extension by C24 of C2×C4 acting faithfully32C2^4.(C2xC4)128,203
C24.45(C2×C4)10th non-split extension by C24 of C2×C4 acting via C2×C4/C2=C2232C2^4.45(C2xC4)128,204
C42.372D45th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.372D4128,205
C42.398D431st non-split extension by C42 of D4 acting via D4/C22=C232C4^2.398D4128,210
D4⋊M4(2)1st semidirect product of D4 and M4(2) acting via M4(2)/C2×C4=C232D4:M4(2)128,218
D45M4(2)3rd semidirect product of D4 and M4(2) acting via M4(2)/C2×C4=C232D4:5M4(2)128,222
C2×C22.SD16Direct product of C2 and C22.SD1632C2xC2^2.SD16128,230
C2×C23.31D4Direct product of C2 and C23.31D432C2xC2^3.31D4128,231
C42.375D48th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.375D4128,232
C24.53D48th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.53D4128,233
C42.403D436th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.403D4128,234
C42.404D437th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.404D4128,235
C42.55D437th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.55D4128,237
C42.56D438th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.56D4128,238
C24.54D49th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.54D4128,239
C24.55D410th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.55D4128,240
C42.57D439th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.57D4128,241
C24.56D411st non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.56D4128,242
C24.57D412nd non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.57D4128,243
C42.58D440th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.58D4128,244
C24.58D413rd non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.58D4128,245
C42.59D441st non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.59D4128,246
C42.60D442nd non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.60D4128,247
C24.59D414th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.59D4128,248
C42.61D443rd non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.61D4128,249
C42.62D444th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.62D4128,250
C24.60D415th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.60D4128,251
C24.61D416th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.61D4128,252
C42.63D445th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.63D4128,253
C42.407D440th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.407D4128,259
C42.70D452nd non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.70D4128,265
C42.413D446th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.413D4128,277
C42.82D464th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.82D4128,287
C4⋊C4.D41st non-split extension by C4⋊C4 of D4 acting faithfully32C4:C4.D4128,329
(C2×C4)⋊D8The semidirect product of C2×C4 and D8 acting via D8/C2=D432(C2xC4):D8128,330
(C2×C4)⋊SD161st semidirect product of C2×C4 and SD16 acting via SD16/C2=D432(C2xC4):SD16128,331
C232SD162nd semidirect product of C23 and SD16 acting via SD16/C2=D432C2^3:2SD16128,333
C23⋊Q16The semidirect product of C23 and Q16 acting via Q16/C2=D432C2^3:Q16128,334
C4⋊C4.6D46th non-split extension by C4⋊C4 of D4 acting faithfully32C4:C4.6D4128,335
Q8⋊D4⋊C226th semidirect product of Q8⋊D4 and C2 acting faithfully32Q8:D4:C2128,336
(C2×C4)⋊Q16The semidirect product of C2×C4 and Q16 acting via Q16/C2=D432(C2xC4):Q16128,337
C24.12D412nd non-split extension by C24 of D4 acting faithfully32C2^4.12D4128,338
C23.5D85th non-split extension by C23 of D8 acting via D8/C2=D432C2^3.5D8128,339
C24.14D414th non-split extension by C24 of D4 acting faithfully32C2^4.14D4128,340
C4⋊C4.12D412nd non-split extension by C4⋊C4 of D4 acting faithfully32C4:C4.12D4128,341
(C2×C4).5D85th non-split extension by C2×C4 of D8 acting via D8/C2=D432(C2xC4).5D8128,342
(C2×C4).SD167th non-split extension by C2×C4 of SD16 acting via SD16/C2=D432(C2xC4).SD16128,343
C24.15D415th non-split extension by C24 of D4 acting faithfully32C2^4.15D4128,344
C24.16D416th non-split extension by C24 of D4 acting faithfully32C2^4.16D4128,345
C24.17D417th non-split extension by C24 of D4 acting faithfully32C2^4.17D4128,346
C4⋊C4.18D418th non-split extension by C4⋊C4 of D4 acting faithfully32C4:C4.18D4128,347
C4⋊C4.19D419th non-split extension by C4⋊C4 of D4 acting faithfully32C4:C4.19D4128,348
C4⋊C4.20D420th non-split extension by C4⋊C4 of D4 acting faithfully32C4:C4.20D4128,349
C24.18D418th non-split extension by C24 of D4 acting faithfully32C2^4.18D4128,350
D4⋊D81st semidirect product of D4 and D8 acting via D8/D4=C232D4:D8128,351
D42SD161st semidirect product of D4 and SD16 acting via SD16/D4=C232D4:2SD16128,361
D4.D81st non-split extension by D4 of D8 acting via D8/D4=C232D4.D8128,371
C42.C231st non-split extension by C42 of C23 acting faithfully32C4^2.C2^3128,387
C42.5C235th non-split extension by C42 of C23 acting faithfully32C4^2.5C2^3128,391
C2×C4.9C42Direct product of C2 and C4.9C4232C2xC4.9C4^2128,462
C2×C4.10C42Direct product of C2 and C4.10C4232C2xC4.10C4^2128,463
C2×C426C4Direct product of C2 and C426C432C2xC4^2:6C4128,464
C24.63D418th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.63D4128,465
C24.7Q86th non-split extension by C24 of Q8 acting via Q8/C2=C2232C2^4.7Q8128,470
C2×C23.9D4Direct product of C2 and C23.9D432C2xC2^3.9D4128,471
C24.162C232nd non-split extension by C24 of C23 acting via C23/C2=C2232C2^4.162C2^3128,472
C23.15C4210th non-split extension by C23 of C42 acting via C42/C22=C2232C2^3.15C4^2128,474
C2×M4(2)⋊4C4Direct product of C2 and M4(2)⋊4C432C2xM4(2):4C4128,475
C8.16C4210th non-split extension by C8 of C42 acting via C42/C2×C4=C2324C8.16C4^2128,479
C4×C23⋊C4Direct product of C4 and C23⋊C432C4xC2^3:C4128,486
C4×C4.D4Direct product of C4 and C4.D432C4xC4.D4128,487
C23.5C425th non-split extension by C23 of C42 acting via C42/C4=C4324C2^3.5C4^2128,489
C4×C4≀C2Direct product of C4 and C4≀C232C4xC4wrC2128,490
D4.C421st non-split extension by D4 of C42 acting via C42/C2×C4=C232D4.C4^2128,491
Q8.C422nd non-split extension by Q8 of C42 acting via C42/C2×C4=C232Q8.C4^2128,496
D4.3C423rd non-split extension by D4 of C42 acting via C42/C2×C4=C232D4.3C4^2128,497
C8.14C428th non-split extension by C8 of C42 acting via C42/C2×C4=C232C8.14C4^2128,504
C8.5C425th non-split extension by C8 of C42 acting via C42/C22=C2232C8.5C4^2128,505
C243C81st semidirect product of C24 and C8 acting via C8/C4=C232C2^4:3C8128,511
C24.165C235th non-split extension by C24 of C23 acting via C23/C2=C2232C2^4.165C2^3128,514
C4.C22≀C22nd non-split extension by C4 of C22≀C2 acting via C22≀C2/C2×D4=C232C4.C2^2wrC2128,516
(C23×C4).C420th non-split extension by C23×C4 of C4 acting faithfully32(C2^3xC4).C4128,517
C23.35D86th non-split extension by C23 of D8 acting via D8/D4=C232C2^3.35D8128,518
C24.66D421st non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.66D4128,521
2+ 1+42C41st semidirect product of 2+ 1+4 and C4 acting via C4/C2=C232ES+(2,2):2C4128,522
2+ 1+4.2C4The non-split extension by 2+ 1+4 of C4 acting via C4/C2=C2324ES+(2,2).2C4128,523
2+ 1+43C42nd semidirect product of 2+ 1+4 and C4 acting via C4/C2=C232ES+(2,2):3C4128,524
2- 1+42C41st semidirect product of 2- 1+4 and C4 acting via C4/C2=C232ES-(2,2):2C4128,525
2+ 1+44C43rd semidirect product of 2+ 1+4 and C4 acting via C4/C2=C2324ES+(2,2):4C4128,526
(C22×Q8)⋊C46th semidirect product of C22×Q8 and C4 acting faithfully328-(C2^2xQ8):C4128,528
C24.167C237th non-split extension by C24 of C23 acting via C23/C2=C2232C2^4.167C2^3128,531
C42.96D478th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.96D4128,532
C42.102D484th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.102D4128,538
C24.19Q83rd non-split extension by C24 of Q8 acting via Q8/C4=C232C2^4.19Q8128,542
C24.9Q88th non-split extension by C24 of Q8 acting via Q8/C2=C2232C2^4.9Q8128,543
(C2×D4).24Q85th non-split extension by C2×D4 of Q8 acting via Q8/C4=C2324(C2xD4).24Q8128,544
(C2×C8).103D471st non-split extension by C2×C8 of D4 acting via D4/C2=C22324(C2xC8).103D4128,545
C8○D4⋊C41st semidirect product of C8○D4 and C4 acting via C4/C2=C2324C8oD4:C4128,546
C24.169C239th non-split extension by C24 of C23 acting via C23/C2=C2232C2^4.169C2^3128,552
(C22×C4).275D4160th non-split extension by C22×C4 of D4 acting via D4/C2=C2232(C2^2xC4).275D4128,553
(C22×C4).276D4161st non-split extension by C22×C4 of D4 acting via D4/C2=C2232(C2^2xC4).276D4128,554
C24.70D425th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.70D4128,558
(C2×Q8).211D419th non-split extension by C2×Q8 of D4 acting via D4/C22=C2328-(C2xQ8).211D4128,562
C8.(C4⋊C4)4th non-split extension by C8 of C4⋊C4 acting via C4⋊C4/C22=C22324C8.(C4:C4)128,565
C24.10Q89th non-split extension by C24 of Q8 acting via Q8/C2=C2232C2^4.10Q8128,587
C24.21D421st non-split extension by C24 of D4 acting faithfully32C2^4.21D4128,588
C4.10D42C41st semidirect product of C4.10D4 and C4 acting via C4/C2=C232C4.10D4:2C4128,589
M4(2).40D44th non-split extension by M4(2) of D4 acting via D4/C22=C2324M4(2).40D4128,590
C4≀C2⋊C41st semidirect product of C4≀C2 and C4 acting via C4/C2=C232C4wrC2:C4128,591
C429(C2×C4)4th semidirect product of C42 and C2×C4 acting via C2×C4/C2=C2232C4^2:9(C2xC4)128,592
M4(2).42D46th non-split extension by M4(2) of D4 acting via D4/C22=C232M4(2).42D4128,598
C24.22D422nd non-split extension by C24 of D4 acting faithfully32C2^4.22D4128,599
(C2×D4).Q89th non-split extension by C2×D4 of Q8 acting via Q8/C2=C22324(C2xD4).Q8128,600
C24.72D427th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.72D4128,603
M4(2).43D47th non-split extension by M4(2) of D4 acting via D4/C22=C232M4(2).43D4128,608
M4(2).44D48th non-split extension by M4(2) of D4 acting via D4/C22=C2324M4(2).44D4128,613
C8.C22⋊C42nd semidirect product of C8.C22 and C4 acting via C4/C2=C232C8.C2^2:C4128,614
C8⋊C22⋊C42nd semidirect product of C8⋊C22 and C4 acting via C4/C2=C232C8:C2^2:C4128,615
C24.23D423rd non-split extension by C24 of D4 acting faithfully32C2^4.23D4128,617
C4⋊Q815C410th semidirect product of C4⋊Q8 and C4 acting via C4/C2=C232C4:Q8:15C4128,618
C4.4D413C47th semidirect product of C4.4D4 and C4 acting via C4/C2=C232C4.4D4:13C4128,620
C24.26D426th non-split extension by C24 of D4 acting faithfully32C2^4.26D4128,622
C427D41st semidirect product of C42 and D4 acting via D4/C2=C2232C4^2:7D4128,629
C24.174C2314th non-split extension by C24 of C23 acting via C23/C2=C2232C2^4.174C2^3128,631
M4(2)⋊20D47th semidirect product of M4(2) and D4 acting via D4/C22=C232M4(2):20D4128,632
M4(2).45D49th non-split extension by M4(2) of D4 acting via D4/C22=C232M4(2).45D4128,633
M4(2).46D410th non-split extension by M4(2) of D4 acting via D4/C22=C2328-M4(2).46D4128,634
C42.6D46th non-split extension by C42 of D4 acting faithfully328-C4^2.6D4128,637
M4(2).48D412nd non-split extension by M4(2) of D4 acting via D4/C22=C232M4(2).48D4128,639
C4.(C4×D4)5th non-split extension by C4 of C4×D4 acting via C4×D4/C42=C2328-C4.(C4xD4)128,641
C42.7D47th non-split extension by C42 of D4 acting faithfully328-C4^2.7D4128,644
M4(2).50D414th non-split extension by M4(2) of D4 acting via D4/C22=C2328-M4(2).50D4128,647
M4(2).3Q81st non-split extension by M4(2) of Q8 acting via Q8/C4=C232M4(2).3Q8128,654
M4(2).24D45th non-split extension by M4(2) of D4 acting via D4/C4=C232M4(2).24D4128,661
C4.D43C42nd semidirect product of C4.D4 and C4 acting via C4/C2=C232C4.D4:3C4128,663
C42.428D461st non-split extension by C42 of D4 acting via D4/C22=C232C4^2.428D4128,669
C42.107D489th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.107D4128,670
C42.62Q822nd non-split extension by C42 of Q8 acting via Q8/C4=C232C4^2.62Q8128,677
C42.28Q828th non-split extension by C42 of Q8 acting via Q8/C2=C2232C4^2.28Q8128,678
M4(2).27D48th non-split extension by M4(2) of D4 acting via D4/C4=C2324M4(2).27D4128,685
C43⋊C27th semidirect product of C43 and C2 acting faithfully32C4^3:C2128,694
C428D42nd semidirect product of C42 and D4 acting via D4/C2=C2232C4^2:8D4128,695
C24.175C2315th non-split extension by C24 of C23 acting via C23/C2=C2232C2^4.175C2^3128,696
M4(2)⋊12D46th semidirect product of M4(2) and D4 acting via D4/C4=C232M4(2):12D4128,697
C42.115D497th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.115D4128,699
C42.326D422nd non-split extension by C42 of D4 acting via D4/C4=C232C4^2.326D4128,706
C42.116D498th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.116D4128,707
M4(2).30D411st non-split extension by M4(2) of D4 acting via D4/C4=C2324M4(2).30D4128,708
M4(2).31D412nd non-split extension by M4(2) of D4 acting via D4/C4=C232M4(2).31D4128,709
M4(2).32D413rd non-split extension by M4(2) of D4 acting via D4/C4=C232M4(2).32D4128,710
M4(2)⋊13D47th semidirect product of M4(2) and D4 acting via D4/C4=C232M4(2):13D4128,712
M4(2)⋊7Q85th semidirect product of M4(2) and Q8 acting via Q8/C4=C232M4(2):7Q8128,718
C4216Q83rd semidirect product of C42 and Q8 acting via Q8/C4=C232C4^2:16Q8128,726
C42⋊Q81st semidirect product of C42 and Q8 acting via Q8/C2=C2232C4^2:Q8128,727
C24.176C2316th non-split extension by C24 of C23 acting via C23/C2=C2232C2^4.176C2^3128,728
C42.129D4111st non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.129D4128,735
C4210D44th semidirect product of C42 and D4 acting via D4/C2=C2232C4^2:10D4128,736
C42.130D4112nd non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.130D4128,737
M4(2)⋊D43rd semidirect product of M4(2) and D4 acting via D4/C2=C2232M4(2):D4128,738
M4(2)⋊4D44th semidirect product of M4(2) and D4 acting via D4/C2=C2232M4(2):4D4128,739
M4(2).D43rd non-split extension by M4(2) of D4 acting via D4/C2=C22328-M4(2).D4128,741
(C2×C8).2D42nd non-split extension by C2×C8 of D4 acting faithfully324(C2xC8).2D4128,749
M4(2).4D44th non-split extension by M4(2) of D4 acting via D4/C2=C2232M4(2).4D4128,750
M4(2).5D45th non-split extension by M4(2) of D4 acting via D4/C2=C2232M4(2).5D4128,751
C24.31D431st non-split extension by C24 of D4 acting faithfully32C2^4.31D4128,754
(C2×D4)⋊2Q82nd semidirect product of C2×D4 and Q8 acting via Q8/C2=C2232(C2xD4):2Q8128,759
(C2×Q8)⋊2Q82nd semidirect product of C2×Q8 and Q8 acting via Q8/C2=C2232(C2xQ8):2Q8128,760
C24.180C2320th non-split extension by C24 of C23 acting via C23/C2=C2232C2^4.180C2^3128,762
M4(2)⋊6D46th semidirect product of M4(2) and D4 acting via D4/C2=C2232M4(2):6D4128,769
M4(2).7D47th non-split extension by M4(2) of D4 acting via D4/C2=C2232M4(2).7D4128,770
C4211D45th semidirect product of C42 and D4 acting via D4/C2=C2232C4^2:11D4128,771
C4212D46th semidirect product of C42 and D4 acting via D4/C2=C2232C4^2:12D4128,772
C24.33D433rd non-split extension by C24 of D4 acting faithfully32C2^4.33D4128,776
C4⋊C4.96D451st non-split extension by C4⋊C4 of D4 acting via D4/C2=C2232C4:C4.96D4128,777
C4⋊C4.97D452nd non-split extension by C4⋊C4 of D4 acting via D4/C2=C2232C4:C4.97D4128,778
M4(2).9D49th non-split extension by M4(2) of D4 acting via D4/C2=C22328-M4(2).9D4128,781
M4(2).10D410th non-split extension by M4(2) of D4 acting via D4/C2=C2232M4(2).10D4128,783
C22⋊C4.7D45th non-split extension by C22⋊C4 of D4 acting via D4/C2=C22324C2^2:C4.7D4128,785
M4(2)⋊Q81st semidirect product of M4(2) and Q8 acting via Q8/C2=C2232M4(2):Q8128,792
C423Q83rd semidirect product of C42 and Q8 acting via Q8/C2=C2232C4^2:3Q8128,793
C24.182C2322nd non-split extension by C24 of C23 acting via C23/C2=C2232C2^4.182C2^3128,794
M4(2).12D412nd non-split extension by M4(2) of D4 acting via D4/C2=C2232M4(2).12D4128,795
M4(2).15D415th non-split extension by M4(2) of D4 acting via D4/C2=C22328-M4(2).15D4128,802
C42.9D49th non-split extension by C42 of D4 acting faithfully324C4^2.9D4128,812
(C2×C8).6D46th non-split extension by C2×C8 of D4 acting faithfully328-(C2xC8).6D4128,814
C42.10D410th non-split extension by C42 of D4 acting faithfully324C4^2.10D4128,830
C22⋊C4.Q81st non-split extension by C22⋊C4 of Q8 acting via Q8/C2=C22324C2^2:C4.Q8128,835
C2×C16⋊C4Direct product of C2 and C16⋊C432C2xC16:C4128,841
C8.23C424th central extension by C8 of C42324C8.23C4^2128,842
C24.5C82nd non-split extension by C24 of C8 acting via C8/C4=C232C2^4.5C8128,844
C2×C23.C8Direct product of C2 and C23.C832C2xC2^3.C8128,846
M5(2).19C226th non-split extension by M5(2) of C22 acting via C22/C2=C2324M5(2).19C2^2128,847
M5(2)⋊12C228th semidirect product of M5(2) and C22 acting via C22/C2=C2324M5(2):12C2^2128,849
C2×C23.D4Direct product of C2 and C23.D432C2xC2^3.D4128,851
C23.(C2×D4)6th non-split extension by C23 of C2×D4 acting via C2×D4/C2=D4328-C2^3.(C2xD4)128,855
C2×C423C4Direct product of C2 and C423C432C2xC4^2:3C4128,857
C4⋊Q8⋊C45th semidirect product of C4⋊Q8 and C4 acting faithfully328-C4:Q8:C4128,861
C2×C42.C4Direct product of C2 and C42.C432C2xC4^2.C4128,862
C2×C42.3C4Direct product of C2 and C42.3C432C2xC4^2.3C4128,863
C4⋊Q8.C45th non-split extension by C4⋊Q8 of C4 acting faithfully328-C4:Q8.C4128,865
(C2×D4).137D499th non-split extension by C2×D4 of D4 acting via D4/C2=C22328-(C2xD4).137D4128,867
C23.40D811st non-split extension by C23 of D8 acting via D8/D4=C232C2^3.40D8128,872
C23.20SD1610th non-split extension by C23 of SD16 acting via SD16/C4=C22324C2^3.20SD16128,875
C2×D82C4Direct product of C2 and D82C432C2xD8:2C4128,876
C23.13D86th non-split extension by C23 of D8 acting via D8/C4=C22324C2^3.13D8128,877
C2×M5(2)⋊C2Direct product of C2 and M5(2)⋊C232C2xM5(2):C2128,878
C23.21SD1611st non-split extension by C23 of SD16 acting via SD16/C4=C22324C2^3.21SD16128,880
C2×C8.C8Direct product of C2 and C8.C832C2xC8.C8128,884
M4(2).1C81st non-split extension by M4(2) of C8 acting via C8/C4=C2324M4(2).1C8128,885
C2×C8.Q8Direct product of C2 and C8.Q832C2xC8.Q8128,886
M5(2)⋊3C43rd semidirect product of M5(2) and C4 acting via C4/C2=C2324M5(2):3C4128,887
M5(2).1C41st non-split extension by M5(2) of C4 acting via C4/C2=C2324M5(2).1C4128,893
C8.19M4(2)7th non-split extension by C8 of M4(2) acting via M4(2)/C2×C4=C2324C8.19M4(2)128,898
C16○D8Central product of C16 and D8322C16oD8128,902
D8.C8The non-split extension by D8 of C8 acting via C8/C4=C2324D8.C8128,903
C8○D16Central product of C8 and D16322C8oD16128,910
D165C44th semidirect product of D16 and C4 acting via C4/C2=C2324D16:5C4128,911
Q32⋊C4The semidirect product of Q32 and C4 acting faithfully328-Q32:C4128,912
D87D41st semidirect product of D8 and D4 acting via D4/C22=C232D8:7D4128,916
D8.9D41st non-split extension by D8 of D4 acting via D4/C22=C232D8.9D4128,919
D8.D41st non-split extension by D8 of D4 acting via D4/C2=C22328-D8.D4128,923
Q16.10D43rd non-split extension by Q16 of D4 acting via D4/C22=C2324+Q16.10D4128,924
Q16.D42nd non-split extension by Q16 of D4 acting via D4/C2=C22324Q16.D4128,925
D8.3D43rd non-split extension by D8 of D4 acting via D4/C2=C22324D8.3D4128,926
C42.14D414th non-split extension by C42 of D4 acting faithfully328-C4^2.14D4128,933
C42.16D416th non-split extension by C42 of D4 acting faithfully328-C4^2.16D4128,935
C8.3D83rd non-split extension by C8 of D8 acting via D8/C4=C22324C8.3D8128,944
C8.5D85th non-split extension by C8 of D8 acting via D8/C4=C22324-C8.5D8128,946
D4.3D83rd non-split extension by D4 of D8 acting via D8/C8=C2324+D4.3D8128,953
D4.5D85th non-split extension by D4 of D8 acting via D8/C8=C2324D4.5D8128,955
D8.2Q82nd non-split extension by D8 of Q8 acting via Q8/C4=C2324D8.2Q8128,963
C23.10SD1610th non-split extension by C23 of SD16 acting via SD16/C2=D4328-C2^3.10SD16128,971
C32⋊C22The semidirect product of C32 and C22 acting faithfully324+C32:C2^2128,995
C23⋊C422nd semidirect product of C23 and C42 acting via C42/C22=C2232C2^3:C4^2128,1005
C2×C243C4Direct product of C2 and C243C432C2xC2^4:3C4128,1009
C25.85C226th non-split extension by C25 of C22 acting via C22/C2=C232C2^5.85C2^2128,1012
C4×C22≀C2Direct product of C4 and C22≀C232C4xC2^2wrC2128,1031
C24.90D445th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.90D4128,1040
C23.191C2444th central extension by C23 of C2432C2^3.191C2^4128,1041
C23.194C2447th central extension by C23 of C2432C2^3.194C2^4128,1044
C24.91D446th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.91D4128,1047
C23.203C2456th central extension by C23 of C2432C2^3.203C2^4128,1053
D4×C22⋊C4Direct product of D4 and C22⋊C432D4xC2^2:C4128,1070
C23.224C2477th central extension by C23 of C2432C2^3.224C2^4128,1074
C23.240C2493rd central extension by C23 of C2432C2^3.240C2^4128,1090
C23.257C24110th central extension by C23 of C2432C2^3.257C2^4128,1107
C247D42nd semidirect product of C24 and D4 acting via D4/C2=C2232C2^4:7D4128,1135
C23.304C2421st central stem extension by C23 of C2432C2^3.304C2^4128,1136
C24.94D449th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.94D4128,1137
C23.308C2425th central stem extension by C23 of C2432C2^3.308C2^4128,1140
C248D43rd semidirect product of C24 and D4 acting via D4/C2=C2232C2^4:8D4128,1142
C23.311C2428th central stem extension by C23 of C2432C2^3.311C2^4128,1143
C24.95D450th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.95D4128,1144
C23.318C2435th central stem extension by C23 of C2432C2^3.318C2^4128,1150
C23.324C2441st central stem extension by C23 of C2432C2^3.324C2^4128,1156
C23.333C2450th central stem extension by C23 of C2432C2^3.333C2^4128,1165
C23.335C2452nd central stem extension by C23 of C2432C2^3.335C2^4128,1167
C244Q83rd semidirect product of C24 and Q8 acting via Q8/C2=C2232C2^4:4Q8128,1169
C23.372C2489th central stem extension by C23 of C2432C2^3.372C2^4128,1204
C23.380C2497th central stem extension by C23 of C2432C2^3.380C2^4128,1212
C23.382C2499th central stem extension by C23 of C2432C2^3.382C2^4128,1214
C24.96D451st non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.96D4128,1215
C23.434C24151st central stem extension by C23 of C2432C2^3.434C2^4128,1266
C23.439C24156th central stem extension by C23 of C2432C2^3.439C2^4128,1271
C23.461C24178th central stem extension by C23 of C2432C2^3.461C2^4128,1293
C249D44th semidirect product of C24 and D4 acting via D4/C2=C2232C2^4:9D4128,1345
C2410D45th semidirect product of C24 and D4 acting via D4/C2=C2232C2^4:10D4128,1349
C24.97D452nd non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.97D4128,1354
C245Q84th semidirect product of C24 and Q8 acting via Q8/C2=C2232C2^4:5Q8128,1358
C23.568C24285th central stem extension by C23 of C2432C2^3.568C2^4128,1400
C23.569C24286th central stem extension by C23 of C2432C2^3.569C2^4128,1401
C23.570C24287th central stem extension by C23 of C2432C2^3.570C2^4128,1402
C23.578C24295th central stem extension by C23 of C2432C2^3.578C2^4128,1410
C25⋊C222nd semidirect product of C25 and C22 acting faithfully32C2^5:C2^2128,1411
C23.584C24301st central stem extension by C23 of C2432C2^3.584C2^4128,1416
C23.585C24302nd central stem extension by C23 of C2432C2^3.585C2^4128,1417
C23.597C24314th central stem extension by C23 of C2432C2^3.597C2^4128,1429
C23.635C24352nd central stem extension by C23 of C2432C2^3.635C2^4128,1467
C23.636C24353rd central stem extension by C23 of C2432C2^3.636C2^4128,1468
C2411D46th semidirect product of C24 and D4 acting via D4/C2=C2232C2^4:11D4128,1544
C246Q85th semidirect product of C24 and Q8 acting via Q8/C2=C2232C2^4:6Q8128,1572
C24.15Q814th non-split extension by C24 of Q8 acting via Q8/C2=C2232C2^4.15Q8128,1574
C2413D41st semidirect product of C24 and D4 acting via D4/C4=C232C2^4:13D4128,1579
C248Q81st semidirect product of C24 and Q8 acting via Q8/C4=C232C2^4:8Q8128,1580
C24.166D421st non-split extension by C24 of D4 acting via D4/C22=C232C2^4.166D4128,1581
M4(2)○2M4(2)Central product of M4(2) and M4(2)32M4(2)o2M4(2)128,1605
C2×C24.4C4Direct product of C2 and C24.4C432C2xC2^4.4C4128,1609
C24.73(C2×C4)38th non-split extension by C24 of C2×C4 acting via C2×C4/C2=C2232C2^4.73(C2xC4)128,1611
D4○(C22⋊C8)Central product of D4 and C22⋊C832D4o(C2^2:C8)128,1612
C22×C23⋊C4Direct product of C22 and C23⋊C432C2^2xC2^3:C4128,1613
C2×C23.C23Direct product of C2 and C23.C2332C2xC2^3.C2^3128,1614
C23.4C244th non-split extension by C23 of C24 acting via C24/C22=C22328-C2^3.4C2^4128,1616
C22×C4.D4Direct product of C22 and C4.D432C2^2xC4.D4128,1617
C2×M4(2).8C22Direct product of C2 and M4(2).8C2232C2xM4(2).8C2^2128,1619
M4(2).25C237th non-split extension by M4(2) of C23 acting via C23/C22=C2328-M4(2).25C2^3128,1621
C2×C23.37D4Direct product of C2 and C23.37D432C2xC2^3.37D4128,1625
C24.98D453rd non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.98D4128,1628
2+ 1+45C44th semidirect product of 2+ 1+4 and C4 acting via C4/C2=C232ES+(2,2):5C4128,1629
C22×C4≀C2Direct product of C22 and C4≀C232C2^2xC4wrC2128,1631
C2×C42⋊C22Direct product of C2 and C42⋊C2232C2xC4^2:C2^2128,1632
C42.257C23118th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.257C2^3128,1637
C24.100D455th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.100D4128,1643
C2×M4(2).C4Direct product of C2 and M4(2).C432C2xM4(2).C4128,1647
M4(2).29C2311st non-split extension by M4(2) of C23 acting via C23/C22=C2324M4(2).29C2^3128,1648
C42.677C2392nd non-split extension by C42 of C23 acting via C23/C22=C232C4^2.677C2^3128,1652
C42.259C23120th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.259C2^3128,1653
C42.262C23123rd non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.262C2^3128,1656
C42.264C23125th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.264C2^3128,1661
C42.265C23126th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.265C2^3128,1662
M4(2)⋊22D41st semidirect product of M4(2) and D4 acting through Inn(M4(2))32M4(2):22D4128,1665
D4×M4(2)Direct product of D4 and M4(2)32D4xM4(2)128,1666
C4×C8⋊C22Direct product of C4 and C8⋊C2232C4xC8:C2^2128,1676
C42.275C23136th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.275C2^3128,1678
C42.277C23138th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.277C2^3128,1680
C42.278C23139th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.278C2^3128,1681
C2×C8○D8Direct product of C2 and C8○D832C2xC8oD8128,1685
C2×C8.26D4Direct product of C2 and C8.26D432C2xC8.26D4128,1686
C42.283C23144th non-split extension by C42 of C23 acting via C23/C2=C22324C4^2.283C2^3128,1687
M4(2)○D8Central product of M4(2) and D8324M4(2)oD8128,1689
C42.691C23106th non-split extension by C42 of C23 acting via C23/C22=C232C4^2.691C2^3128,1704
C233M4(2)2nd semidirect product of C23 and M4(2) acting via M4(2)/C4=C2232C2^3:3M4(2)128,1705
D47M4(2)2nd semidirect product of D4 and M4(2) acting through Inn(D4)32D4:7M4(2)128,1706
C42.693C23108th non-split extension by C42 of C23 acting via C23/C22=C232C4^2.693C2^3128,1707
C42.297C23158th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.297C2^3128,1708
C42.298C23159th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.298C2^3128,1709
C42.299C23160th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.299C2^3128,1710
C2×C22⋊D8Direct product of C2 and C22⋊D832C2xC2^2:D8128,1728
C2×C22⋊SD16Direct product of C2 and C22⋊SD1632C2xC2^2:SD16128,1729
C24.103D458th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.103D4128,1734
C24.178D433rd non-split extension by C24 of D4 acting via D4/C22=C232C2^4.178D4128,1736
C24.104D459th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.104D4128,1737
C24.105D460th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.105D4128,1738
C24.106D461st non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.106D4128,1739
C4○D4⋊D41st semidirect product of C4○D4 and D4 acting via D4/C2=C2232C4oD4:D4128,1740
D4.(C2×D4)8th non-split extension by D4 of C2×D4 acting via C2×D4/C23=C232D4.(C2xD4)128,1741
(C2×Q8)⋊16D412nd semidirect product of C2×Q8 and D4 acting via D4/C2=C2232(C2xQ8):16D4128,1742
(C2×D4)⋊21D417th semidirect product of C2×D4 and D4 acting via D4/C2=C2232(C2xD4):21D4128,1744
C2×D4.9D4Direct product of C2 and D4.9D432C2xD4.9D4128,1747
C2×D4.8D4Direct product of C2 and D4.8D432C2xD4.8D4128,1748
C2×D4.10D4Direct product of C2 and D4.10D432C2xD4.10D4128,1749
M4(2).C234th non-split extension by M4(2) of C23 acting via C23/C2=C22328-M4(2).C2^3128,1752
C42.13C2313rd non-split extension by C42 of C23 acting faithfully328-C4^2.13C2^3128,1754
C2×C23.7D4Direct product of C2 and C23.7D432C2xC2^3.7D4128,1756
C23.10C2410th non-split extension by C23 of C24 acting via C24/C22=C22328-C2^3.10C2^4128,1760
C42.211D4193rd non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.211D4128,1768
C42.444D477th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.444D4128,1770
C42.446D479th non-split extension by C42 of D4 acting via D4/C22=C232C4^2.446D4128,1772
C42.14C2314th non-split extension by C42 of C23 acting faithfully32C4^2.14C2^3128,1773
C42.15C2315th non-split extension by C42 of C23 acting faithfully32C4^2.15C2^3128,1774
C42.16C2316th non-split extension by C42 of C23 acting faithfully32C4^2.16C2^3128,1775
C42.18C2318th non-split extension by C42 of C23 acting faithfully32C4^2.18C2^3128,1777
C24.144D413rd non-split extension by C24 of D4 acting via D4/C4=C232C2^4.144D4128,1782
C24.110D465th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.110D4128,1786
M4(2)⋊14D41st semidirect product of M4(2) and D4 acting via D4/C22=C232M4(2):14D4128,1787
M4(2)⋊15D42nd semidirect product of M4(2) and D4 acting via D4/C22=C232M4(2):15D4128,1788
(C2×C8)⋊11D47th semidirect product of C2×C8 and D4 acting via D4/C2=C2232(C2xC8):11D4128,1789
(C2×C8)⋊12D48th semidirect product of C2×C8 and D4 acting via D4/C2=C2232(C2xC8):12D4128,1790
M4(2)⋊16D43rd semidirect product of M4(2) and D4 acting via D4/C22=C232M4(2):16D4128,1794
C2×D4.3D4Direct product of C2 and D4.3D432C2xD4.3D4128,1796
C2×D4.4D4Direct product of C2 and D4.4D432C2xD4.4D4128,1797
M4(2).10C2310th non-split extension by M4(2) of C23 acting via C23/C2=C22324M4(2).10C2^3128,1799
M4(2).38D42nd non-split extension by M4(2) of D4 acting via D4/C22=C2328-M4(2).38D4128,1801
C42.219D4201st non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.219D4128,1809
C42.20C2320th non-split extension by C42 of C23 acting faithfully32C4^2.20C2^3128,1813
C24.115D470th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.115D4128,1823
C24.183D438th non-split extension by C24 of D4 acting via D4/C22=C232C2^4.183D4128,1824
C24.116D471st non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.116D4128,1825
C24.117D472nd non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.117D4128,1826
C24.118D473rd non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.118D4128,1827
(C2×D4).301D454th non-split extension by C2×D4 of D4 acting via D4/C22=C232(C2xD4).301D4128,1828
C42.221D4203rd non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.221D4128,1832
C42.222D4204th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.222D4128,1833
C42.225D4207th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.225D4128,1837
C42.227D4209th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.227D4128,1841
C42.228D4210th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.228D4128,1842
C42.232D4214th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.232D4128,1846
C42.352C23213rd non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.352C2^3128,1850
C42.356C23217th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.356C2^3128,1854
C42.357C23218th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.357C2^3128,1855
C42.366C23227th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.366C2^3128,1868
C42.240D4222nd non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.240D4128,1870
C42.242D4224th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.242D4128,1872
M4(2)⋊7D41st semidirect product of M4(2) and D4 acting via D4/C4=C232M4(2):7D4128,1883
M4(2)⋊9D43rd semidirect product of M4(2) and D4 acting via D4/C4=C232M4(2):9D4128,1885
M4(2)⋊10D44th semidirect product of M4(2) and D4 acting via D4/C4=C232M4(2):10D4128,1886
M4(2)⋊11D45th semidirect product of M4(2) and D4 acting via D4/C4=C232M4(2):11D4128,1887
C233D82nd semidirect product of C23 and D8 acting via D8/C4=C2232C2^3:3D8128,1918
C234SD162nd semidirect product of C23 and SD16 acting via SD16/C4=C2232C2^3:4SD16128,1919
C24.121D476th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.121D4128,1920
C233Q162nd semidirect product of C23 and Q16 acting via Q16/C4=C2232C2^3:3Q16128,1921
C24.123D478th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.123D4128,1922
C24.124D479th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.124D4128,1923
C24.125D480th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.125D4128,1924
C24.126D481st non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.126D4128,1925
C24.127D482nd non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.127D4128,1926
C24.128D483rd non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.128D4128,1927
C24.129D484th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.129D4128,1928
C24.130D485th non-split extension by C24 of D4 acting via D4/C2=C2232C2^4.130D4128,1929
C4.2+ 1+413rd non-split extension by C4 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C232C4.ES+(2,2)128,1930
C4.142+ 1+414th non-split extension by C4 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C232C4.14ES+(2,2)128,1931
C4.152+ 1+415th non-split extension by C4 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C232C4.15ES+(2,2)128,1932
C42.263D4245th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.263D4128,1937
C42.266D4248th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.266D4128,1940
C42.269D4251st non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.269D4128,1943
C42.271D4253rd non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.271D4128,1945
C42.273D4255th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.273D4128,1947
C42.275D4257th non-split extension by C42 of D4 acting via D4/C2=C2232C4^2.275D4128,1949
C42.406C23267th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.406C2^3128,1952
C42.408C23269th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.408C2^3128,1954
C42.410C23271st non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.410C2^3128,1956
D89D43rd semidirect product of D8 and D4 acting via D4/C22=C232D8:9D4128,1996
SD16⋊D41st semidirect product of SD16 and D4 acting via D4/C22=C232SD16:D4128,1997
SD166D42nd semidirect product of SD16 and D4 acting via D4/C22=C232SD16:6D4128,1998
D810D44th semidirect product of D8 and D4 acting via D4/C22=C232D8:10D4128,1999
SD167D43rd semidirect product of SD16 and D4 acting via D4/C22=C232SD16:7D4128,2000
D84D43rd semidirect product of D8 and D4 acting via D4/C4=C232D8:4D4128,2004
D85D44th semidirect product of D8 and D4 acting via D4/C4=C232D8:5D4128,2005
SD161D41st semidirect product of SD16 and D4 acting via D4/C4=C232SD16:1D4128,2006
SD162D42nd semidirect product of SD16 and D4 acting via D4/C4=C232SD16:2D4128,2007
D4×D8Direct product of D4 and D832D4xD8128,2011
D812D41st semidirect product of D8 and D4 acting through Inn(D8)32D8:12D4128,2012
D4×SD16Direct product of D4 and SD1632D4xSD16128,2013
SD1610D41st semidirect product of SD16 and D4 acting through Inn(SD16)32SD16:10D4128,2014
D8.13D45th non-split extension by D8 of D4 acting via D4/C22=C2328-D8.13D4128,2021
D8○SD16Central product of D8 and SD16324D8oSD16128,2022
D8○Q16Central product of D8 and Q16324-D8oQ16128,2025
D44D81st semidirect product of D4 and D8 acting through Inn(D4)32D4:4D8128,2026
D47SD161st semidirect product of D4 and SD16 acting through Inn(D4)32D4:7SD16128,2027
C42.461C23322nd non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.461C2^3128,2028
C42.462C23323rd non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.462C2^3128,2029
C42.41C2341st non-split extension by C42 of C23 acting faithfully32C4^2.41C2^3128,2038
C42.45C2345th non-split extension by C42 of C23 acting faithfully32C4^2.45C2^3128,2042
C42.46C2346th non-split extension by C42 of C23 acting faithfully32C4^2.46C2^3128,2043
C42.49C2349th non-split extension by C42 of C23 acting faithfully32C4^2.49C2^3128,2046
C42.53C2353rd non-split extension by C42 of C23 acting faithfully32C4^2.53C2^3128,2050
C42.54C2354th non-split extension by C42 of C23 acting faithfully32C4^2.54C2^3128,2051
C42.471C23332nd non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.471C2^3128,2054
C42.472C23333rd non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.472C2^3128,2055
C42.473C23334th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.473C2^3128,2056
C42.474C23335th non-split extension by C42 of C23 acting via C23/C2=C2232C4^2.474C2^3128,2057
Q8○M5(2)Central product of Q8 and M5(2)324Q8oM5(2)128,2139
C2×C16⋊C22Direct product of C2 and C16⋊C2232C2xC16:C2^2128,2144
D16⋊C224th semidirect product of D16 and C22 acting via C22/C2=C2324D16:C2^2128,2146
D4○D16Central product of D4 and D16324+D4oD16128,2147
D4○SD32Central product of D4 and SD32324D4oSD32128,2148
C2×C22.11C24Direct product of C2 and C22.11C2432C2xC2^2.11C2^4128,2157
C22.14C2510th central extension by C22 of C2532C2^2.14C2^5128,2160
C4×2+ 1+4Direct product of C4 and 2+ 1+432C4xES+(2,2)128,2161
C22×C22≀C2Direct product of C22 and C22≀C232C2^2xC2^2wrC2128,2163
C2×C22.19C24Direct product of C2 and C22.19C2432C2xC2^2.19C2^4128,2167
C22.33C2514th central stem extension by C22 of C2532C2^2.33C2^5128,2176
C2×C233D4Direct product of C2 and C233D432C2xC2^3:3D4128,2177
C2×C22.29C24Direct product of C2 and C22.29C2432C2xC2^2.29C2^4128,2178
C22.38C2519th central stem extension by C22 of C2532C2^2.38C2^5128,2181
C2×C22.32C24Direct product of C2 and C22.32C2432C2xC2^2.32C2^4128,2182
C22.44C2525th central stem extension by C22 of C2532C2^2.44C2^5128,2187
C2×C232Q8Direct product of C2 and C232Q832C2xC2^3:2Q8128,2188
C22.47C2528th central stem extension by C22 of C2532C2^2.47C2^5128,2190
C22.48C2529th central stem extension by C22 of C2532C2^2.48C2^5128,2191
C22.49C2530th central stem extension by C22 of C2532C2^2.49C2^5128,2192
C2×D42Direct product of C2, D4 and D432C2xD4^2128,2194
C2×D45D4Direct product of C2 and D45D432C2xD4:5D4128,2195
D4×C4○D4Direct product of D4 and C4○D432D4xC4oD4128,2200
C2×C22.45C24Direct product of C2 and C22.45C2432C2xC2^2.45C2^4128,2201
C22.64C2545th central stem extension by C22 of C2532C2^2.64C2^5128,2207
C22.70C2551st central stem extension by C22 of C2532C2^2.70C2^5128,2213
C22.74C2555th central stem extension by C22 of C2532C2^2.74C2^5128,2217
C22.75C2556th central stem extension by C22 of C2532C2^2.75C2^5128,2218
C22.76C2557th central stem extension by C22 of C2532C2^2.76C2^5128,2219
C22.77C2558th central stem extension by C22 of C2532C2^2.77C2^5128,2220
C22.78C2559th central stem extension by C22 of C2532C2^2.78C2^5128,2221
C22.80C2561st central stem extension by C22 of C2532C2^2.80C2^5128,2223
C22.81C2562nd central stem extension by C22 of C2532C2^2.81C2^5128,2224
C22.82C2563rd central stem extension by C22 of C2532C2^2.82C2^5128,2225
C22.83C2564th central stem extension by C22 of C2532C2^2.83C2^5128,2226
C22.84C2565th central stem extension by C22 of C2532C2^2.84C2^5128,2227
C4⋊2+ 1+4The semidirect product of C4 and 2+ 1+4 acting via 2+ 1+4/C2×D4=C232C4:ES+(2,2)128,2228
C22.87C2568th central stem extension by C22 of C2532C2^2.87C2^5128,2230
C22.89C2570th central stem extension by C22 of C2532C2^2.89C2^5128,2232
C22.90C2571st central stem extension by C22 of C2532C2^2.90C2^5128,2233
C22.94C2575th central stem extension by C22 of C2532C2^2.94C2^5128,2237
C22.95C2576th central stem extension by C22 of C2532C2^2.95C2^5128,2238
C22.97C2578th central stem extension by C22 of C2532C2^2.97C2^5128,2240
C22.99C2580th central stem extension by C22 of C2532C2^2.99C2^5128,2242
C22.102C2583rd central stem extension by C22 of C2532C2^2.102C2^5128,2245
C22.103C2584th central stem extension by C22 of C2532C2^2.103C2^5128,2246
C22.108C2589th central stem extension by C22 of C2532C2^2.108C2^5128,2251
C23.144C2444th non-split extension by C23 of C24 acting via C24/C23=C232C2^3.144C2^4128,2252
C22.110C2591st central stem extension by C22 of C2532C2^2.110C2^5128,2253
C2×C22.54C24Direct product of C2 and C22.54C2432C2xC2^2.54C2^4128,2257
C2×C24⋊C22Direct product of C2 and C24⋊C2232C2xC2^4:C2^2128,2258
C22.118C2599th central stem extension by C22 of C2532C2^2.118C2^5128,2261
C22.122C25103rd central stem extension by C22 of C2532C2^2.122C2^5128,2265
C22.123C25104th central stem extension by C22 of C2532C2^2.123C2^5128,2266
C22.124C25105th central stem extension by C22 of C2532C2^2.124C2^5128,2267
C22.125C25106th central stem extension by C22 of C2532C2^2.125C2^5128,2268
C22.126C25107th central stem extension by C22 of C2532C2^2.126C2^5128,2269
C22.127C25108th central stem extension by C22 of C2532C2^2.127C2^5128,2270
C22.128C25109th central stem extension by C22 of C2532C2^2.128C2^5128,2271
C22.129C25110th central stem extension by C22 of C2532C2^2.129C2^5128,2272
C22.130C25111st central stem extension by C22 of C2532C2^2.130C2^5128,2273
C22.131C25112nd central stem extension by C22 of C2532C2^2.131C2^5128,2274
C22.132C25113rd central stem extension by C22 of C2532C2^2.132C2^5128,2275
C22.134C25115th central stem extension by C22 of C2532C2^2.134C2^5128,2277
C22.135C25116th central stem extension by C22 of C2532C2^2.135C2^5128,2278
C22.138C25119th central stem extension by C22 of C2532C2^2.138C2^5128,2281
C22.140C25121st central stem extension by C22 of C2532C2^2.140C2^5128,2283
C22.147C25128th central stem extension by C22 of C2532C2^2.147C2^5128,2290
C22.149C25130th central stem extension by C22 of C2532C2^2.149C2^5128,2292
C22.150C25131st central stem extension by C22 of C2532C2^2.150C2^5128,2293
C22.151C25132nd central stem extension by C22 of C2532C2^2.151C2^5128,2294
C22.153C25134th central stem extension by C22 of C2532C2^2.153C2^5128,2296
C22.155C25136th central stem extension by C22 of C2532C2^2.155C2^5128,2298
C22.157C25138th central stem extension by C22 of C2532C2^2.157C2^5128,2300
C2×Q8○M4(2)Direct product of C2 and Q8○M4(2)32C2xQ8oM4(2)128,2304
C4.22C254th central extension by C4 of C25324C4.22C2^5128,2305
C22×C8⋊C22Direct product of C22 and C8⋊C2232C2^2xC8:C2^2128,2310
C2×D8⋊C22Direct product of C2 and D8⋊C2232C2xD8:C2^2128,2312
C2×D4○D8Direct product of C2 and D4○D832C2xD4oD8128,2313
C2×D4○SD16Direct product of C2 and D4○SD1632C2xD4oSD16128,2314
C8.C246th non-split extension by C8 of C24 acting via C24/C22=C22324C8.C2^4128,2316
C4.C2513rd non-split extension by C4 of C25 acting via C25/C24=C2328-C4.C2^5128,2318
C22×2+ 1+4Direct product of C22 and 2+ 1+432C2^2xES+(2,2)128,2323
C2×C2.C25Direct product of C2 and C2.C2532C2xC2.C2^5128,2325
2- 1+6Extraspecial group; = D42- 1+4328-ES-(2,3)128,2327

### Groups of order 160

dρLabelID
2- 1+4⋊C5The semidirect product of 2- 1+4 and C5 acting faithfully324-ES-(2,2):C5160,199

### Groups of order 192

dρLabelID
C4×GL2(𝔽3)Direct product of C4 and GL2(𝔽3)32C4xGL(2,3)192,951
Q8⋊D12The semidirect product of Q8 and D12 acting via D12/C4=S332Q8:D12192,952
GL2(𝔽3)⋊C41st semidirect product of GL2(𝔽3) and C4 acting via C4/C2=C232GL(2,3):C4192,953
Q8.2D122nd non-split extension by Q8 of D12 acting via D12/C4=S332Q8.2D12192,954
CU2(𝔽3)Conformal unitary group on 𝔽32; = U2(𝔽3)7C2322CU(2,3)192,963
C8.5S45th non-split extension by C8 of S4 acting via S4/A4=C2324C8.5S4192,964
C8.4S44th non-split extension by C8 of S4 acting via S4/A4=C2324C8.4S4192,965
C8.3S43rd non-split extension by C8 of S4 acting via S4/A4=C2324+C8.3S4192,966
C23.14S41st non-split extension by C23 of S4 acting via S4/A4=C232C2^3.14S4192,978
C23.15S42nd non-split extension by C23 of S4 acting via S4/A4=C232C2^3.15S4192,979
C23.16S43rd non-split extension by C23 of S4 acting via S4/A4=C232C2^3.16S4192,980
U2(𝔽3)⋊C26th semidirect product of U2(𝔽3) and C2 acting faithfully324U(2,3):C2192,982
SL2(𝔽3)⋊D42nd semidirect product of SL2(𝔽3) and D4 acting via D4/C22=C232SL(2,3):D4192,986
D4.S42nd non-split extension by D4 of S4 acting via S4/A4=C2324-D4.S4192,989
D4.3S43rd non-split extension by D4 of S4 acting via S4/A4=C2324D4.3S4192,990
(C2×Q8)⋊C12The semidirect product of C2×Q8 and C12 acting via C12/C2=C632(C2xQ8):C12192,998
SL2(𝔽3)⋊5D41st semidirect product of SL2(𝔽3) and D4 acting through Inn(SL2(𝔽3))32SL(2,3):5D4192,1003
D4×SL2(𝔽3)Direct product of D4 and SL2(𝔽3)32D4xSL(2,3)192,1004
M4(2).A4The non-split extension by M4(2) of A4 acting through Inn(M4(2))324M4(2).A4192,1013
SD16.A4The non-split extension by SD16 of A4 acting through Inn(SD16)324SD16.A4192,1018
D8.A4The non-split extension by D8 of A4 acting through Inn(D8)324-D8.A4192,1019
C22×GL2(𝔽3)Direct product of C22 and GL2(𝔽3)32C2^2xGL(2,3)192,1475
C2×Q8.D6Direct product of C2 and Q8.D632C2xQ8.D6192,1476
C2×C4.6S4Direct product of C2 and C4.6S432C2xC4.6S4192,1480
C2×C4.3S4Direct product of C2 and C4.3S432C2xC4.3S4192,1481
GL2(𝔽3)⋊C223rd semidirect product of GL2(𝔽3) and C22 acting via C22/C2=C2324GL(2,3):C2^2192,1482
Q8.6S41st non-split extension by Q8 of S4 acting through Inn(Q8)324Q8.6S4192,1483
Q8.7S42nd non-split extension by Q8 of S4 acting through Inn(Q8)324+Q8.7S4192,1484
D4.5S42nd non-split extension by D4 of S4 acting through Inn(D4)324-D4.5S4192,1486
C2×D4.A4Direct product of C2 and D4.A432C2xD4.A4192,1503
2- 1+43C62nd semidirect product of 2- 1+4 and C6 acting via C6/C2=C3324ES-(2,2):3C6192,1504

### Groups of order 320

dρLabelID
2- 1+4⋊D5The semidirect product of 2- 1+4 and D5 acting faithfully324ES-(2,2):D5320,1582

### Groups of order 33

dρLabelID
C33Cyclic group331C3333,1

### Groups of order 66

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

### Groups of order 132

dρLabelID
S3×D11Direct product of S3 and D11334+S3xD11132,5

### Groups of order 165

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

### Groups of order 330

dρLabelID
C3×F11Direct product of C3 and F113310C3xF11330,1
S3×C11⋊C5Direct product of S3 and C11⋊C53310S3xC11:C5330,2
C3⋊F11The semidirect product of C3 and F11 acting via F11/C11⋊C5=C23310+C3:F11330,3

### Groups of order 363

dρLabelID
C112⋊C3The semidirect product of C112 and C3 acting faithfully333C11^2:C3363,2

### Groups of order 34

dρLabelID
C34Cyclic group341C3434,2

### Groups of order 68

dρLabelID
D34Dihedral group; = C2×D17342+D3468,4

### Groups of order 136

dρLabelID
C2×C17⋊C4Direct product of C2 and C17⋊C4344+C2xC17:C4136,13

### Groups of order 272

dρLabelID
C2×C17⋊C8Direct product of C2 and C17⋊C8348+C2xC17:C8272,51

### Groups of order 35

dρLabelID
C35Cyclic group351C3535,1

### Groups of order 70

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

### Groups of order 105

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

### Groups of order 140

dρLabelID
C7×F5Direct product of C7 and F5354C7xF5140,5
C7⋊F5The semidirect product of C7 and F5 acting via F5/D5=C2354C7:F5140,6
D5×D7Direct product of D5 and D7354+D5xD7140,7

### Groups of order 210

dρLabelID
C5×F7Direct product of C5 and F7356C5xF7210,1
D5×C7⋊C3Direct product of D5 and C7⋊C3356D5xC7:C3210,2
C5⋊F7The semidirect product of C5 and F7 acting via F7/C7⋊C3=C2356+C5:F7210,3

### Groups of order 280

dρLabelID
D7×F5Direct product of D7 and F5358+D7xF5280,32

### Groups of order 420

dρLabelID
C7×A5Direct product of C7 and A5353C7xA5420,13
F5×C7⋊C3Direct product of F5 and C7⋊C33512F5xC7:C3420,14
C35⋊C121st semidirect product of C35 and C12 acting faithfully3512C35:C12420,15
D5×F7Direct product of D5 and F73512+D5xF7420,16

### Groups of order 36

dρLabelID
Dic9Dicyclic group; = C9C4362-Dic936,1
C36Cyclic group361C3636,2
C2×C18Abelian group of type [2,18]36C2xC1836,5
C3⋊Dic3The semidirect product of C3 and Dic3 acting via Dic3/C6=C236C3:Dic336,7
C3×C12Abelian group of type [3,12]36C3xC1236,8
C62Abelian group of type [6,6]36C6^236,14

### Groups of order 72

dρLabelID
C4×D9Direct product of C4 and D9362C4xD972,5
D36Dihedral group362+D3672,6
C9⋊D4The semidirect product of C9 and D4 acting via D4/C22=C2362C9:D472,8
D4×C9Direct product of C9 and D4362D4xC972,10
C22×D9Direct product of C22 and D936C2^2xD972,17
C4×C3⋊S3Direct product of C4 and C3⋊S336C4xC3:S372,32
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
D4×C32Direct product of C32 and D436D4xC3^272,37
C22×C3⋊S3Direct product of C22 and C3⋊S336C2^2xC3:S372,49

### Groups of order 108

dρLabelID
C3×Dic9Direct product of C3 and Dic9362C3xDic9108,6
C9×Dic3Direct product of C9 and Dic3362C9xDic3108,7
C32⋊C12The semidirect product of C32 and C12 acting via C12/C2=C6366-C3^2:C12108,8
C9⋊C12The semidirect product of C9 and C12 acting via C12/C2=C6366-C9:C12108,9
He33C42nd semidirect product of He3 and C4 acting via C4/C2=C2363He3:3C4108,11
C4×He3Direct product of C4 and He3363C4xHe3108,13
C4×3- 1+2Direct product of C4 and 3- 1+2363C4xES-(3,1)108,14
C9×A4Direct product of C9 and A4363C9xA4108,18
C9⋊A4The semidirect product of C9 and A4 acting via A4/C22=C3363C9:A4108,19
C6×D9Direct product of C6 and D9362C6xD9108,23
S3×C18Direct product of C18 and S3362S3xC18108,24
C22×He3Direct product of C22 and He336C2^2xHe3108,30
C22×3- 1+2Direct product of C22 and 3- 1+236C2^2xES-(3,1)108,31
C32×Dic3Direct product of C32 and Dic336C3^2xDic3108,32
C3×C3⋊Dic3Direct product of C3 and C3⋊Dic336C3xC3:Dic3108,33
C32×A4Direct product of C32 and A436C3^2xA4108,41
S3×C3×C6Direct product of C3×C6 and S336S3xC3xC6108,42
C6×C3⋊S3Direct product of C6 and C3⋊S336C6xC3:S3108,43

### Groups of order 144

dρLabelID
C42⋊C9The semidirect product of C42 and C9 acting via C9/C3=C3363C4^2:C9144,3
C6.S43rd non-split extension by C6 of S4 acting via S4/A4=C2366-C6.S4144,33
C4×C3.A4Direct product of C4 and C3.A4363C4xC3.A4144,34
D4×D9Direct product of D4 and D9364+D4xD9144,41
C3×C42⋊C3Direct product of C3 and C42⋊C3363C3xC4^2:C3144,68
C22×C3.A4Direct product of C22 and C3.A436C2^2xC3.A4144,110
C24⋊C92nd semidirect product of C24 and C9 acting via C9/C3=C336C2^4:C9144,111
C3×A4⋊C4Direct product of C3 and A4⋊C4363C3xA4:C4144,123
C6.7S47th non-split extension by C6 of S4 acting via S4/A4=C2366-C6.7S4144,126
Dic3×A4Direct product of Dic3 and A4366-Dic3xA4144,129
C12×A4Direct product of C12 and A4363C12xA4144,155
D4×C3⋊S3Direct product of D4 and C3⋊S336D4xC3:S3144,172