Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596219 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10592836 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10592608 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C32×#349 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589384 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #69121 | — | 3 | 4 | no | maximal |
| 7 | C2×#3828 | — | 2 | 1 | no | — |
| 8 | C2×C32×M16 | C22 | 1 | 1 | yes | characteristic |
| 9 | #64133 | — | 2 | 1 | no | — |
| 10 | #64118 | — | 2 | 2 | no | — |
| 11 | #64117 | — | 2 | 2 | no | — |
| 12 | C2×#3746 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #64113 | — | 2 | 1 | no | — |
| 14 | #64113 | C22 | 1 | 2 | yes | — |
| 15 | C32×M32 | C22 | 1 | 2 | yes | complemented |
| 16 | #63644 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #63643 | — | 2 | 1 | no | — |
| 18 | #63628 | — | 2 | 2 | no | — |
| 19 | #63627 | — | 2 | 2 | no | — |
| 20 | #5748 | — | 3 | 4 | no | — |
| 21 | #5137 | — | 3 | 4 | no | — |
| 22 | #4909 | — | 3 | 8 | no | — |
| 23 | C3×#349 | D3 | 1 | 4 | yes | complemented |
| 24 | #4518 | — | 3 | 8 | no | — |
| 25 | C22×C32×C4 | D4 | 1 | 1 | yes | characteristic |
| 26 | C2×#638 | — | 4 | 1 | no | — |
| 27 | #3828 | — | 2 | 2 | no | — |
| 28 | #3828 | — | 2 | 2 | no | — |
| 29 | #3828 | — | 4 | 1 | no | — |
| 30 | #3828 | — | 4 | 1 | no | — |
| 31 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 32 | C2×C4×C3⋊D3 | — | 4 | 1 | no | — |
| 33 | C2×#634 | — | 2 | 1 | no | — |
| 34 | C2×#634 | — | 2 | 1 | no | — |
| 35 | C32×M16 | — | 2 | 2 | no | — |
| 36 | C2×C32×C8 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 38 | #3757 | — | 4 | 1 | no | — |
| 39 | C4⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 40 | #3750 | — | 4 | 1 | no | — |
| 41 | #3746 | — | 2 | 1 | no | — |
| 42 | #3746 | — | 2 | 2 | no | — |
| 43 | #3746 | D4 | 1 | 2 | yes | — |
| 44 | #3745 | — | 2 | 1 | no | — |
| 45 | #3745 | D4 | 1 | 2 | yes | — |
| 46 | #3744 | — | 2 | 2 | no | — |
| 47 | #3744 | — | 2 | 2 | no | — |
| 48 | C32×C16 | — | 2 | 2 | no | — |
| 49 | #2191 | — | 9 | 1 | no | Sylow |
| 50 | C2×#235 | — | 6 | 4 | no | — |
| 51 | C2×C3×M16 | C2×D3 | 1 | 4 | yes | — |
| 52 | #924 | — | 6 | 4 | no | — |
| 53 | #909 | — | 6 | 8 | no | — |
| 54 | #908 | — | 6 | 8 | no | — |
| 55 | C2×Dic12 | — | 3 | 4 | no | — |
| 56 | #904 | — | 3 | 8 | no | — |
| 57 | #904 | — | 6 | 4 | no | — |
| 58 | C3×M32 | C2×D3 | 1 | 8 | yes | complemented |
| 59 | #817 | — | 3 | 4 | no | — |
| 60 | #816 | — | 6 | 4 | no | — |
| 61 | Dic24 | — | 6 | 8 | no | — |
| 62 | #800 | — | 6 | 8 | no | — |
| 63 | C23×C32 | D8 | 1 | 1 | yes | characteristic |
| 64 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 65 | C2×C32×C4 | — | 2 | 1 | no | — |
| 66 | C2×C32×C4 | — | 2 | 1 | no | — |
| 67 | C2×C32×C4 | D8 | 1 | 1 | yes | characteristic |
| 68 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | #638 | — | 4 | 2 | no | — |
| 70 | #638 | — | 4 | 2 | no | — |
| 71 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 72 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 73 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 74 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 75 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 76 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 77 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 78 | #634 | — | 2 | 2 | no | — |
| 79 | #634 | — | 4 | 1 | no | — |
| 80 | #634 | — | 4 | 1 | no | — |
| 81 | #634 | — | 4 | 1 | no | — |
| 82 | C32×C8 | — | 2 | 1 | no | — |
| 83 | C32×C8 | C2×D4 | 1 | 2 | yes | — |
| 84 | #575 | — | 9 | 1 | no | — |
| 85 | #510 | — | 9 | 2 | no | — |
| 86 | #470 | — | 9 | 1 | no | — |
| 87 | #360 | — | 9 | 2 | no | — |
| 88 | #349 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 89 | C22×C3×C4 | D12 | 1 | 4 | yes | — |
| 90 | C2×#67 | — | 12 | 4 | no | — |
| 91 | #235 | — | 6 | 8 | no | — |
| 92 | #235 | — | 6 | 8 | no | — |
| 93 | #235 | — | 12 | 4 | no | — |
| 94 | #235 | — | 12 | 4 | no | — |
| 95 | C2×D12 | — | 6 | 4 | no | — |
| 96 | C2×C4×D3 | — | 12 | 4 | no | — |
| 97 | C2×Dic6 | — | 6 | 4 | no | — |
| 98 | C2×Dic6 | — | 6 | 4 | no | — |
| 99 | C3×M16 | — | 2 | 8 | no | — |
| 100 | C2×C3×C8 | D12 | 1 | 4 | yes | — |
| 101 | C2×C3×C8 | C22×D3 | 1 | 4 | yes | — |
| 102 | #217 | — | 12 | 4 | no | — |
| 103 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 104 | Dic3⋊C4 | — | 12 | 4 | no | — |
| 105 | Dic12 | — | 3 | 8 | no | — |
| 106 | Dic12 | — | 6 | 4 | no | — |
| 107 | Dic12 | — | 6 | 8 | no | — |
| 108 | D24 | — | 3 | 8 | no | — |
| 109 | D24 | — | 6 | 4 | no | — |
| 110 | #204 | — | 6 | 8 | no | — |
| 111 | #204 | — | 6 | 8 | no | — |
| 112 | C3×C16 | — | 2 | 8 | no | — |
| 113 | C22×C32 | — | 2 | 1 | no | — |
| 114 | C22×C32 | — | 4 | 1 | no | — |
| 115 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 116 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 117 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 118 | C32×C4 | — | 2 | 1 | no | — |
| 119 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 120 | C32×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 121 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 122 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 123 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 124 | C2×#41 | — | 18 | 1 | no | — |
| 125 | #137 | — | 18 | 2 | no | — |
| 126 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 127 | #135 | — | 9 | 2 | no | — |
| 128 | #135 | — | 18 | 1 | no | — |
| 129 | C2×Q16 | — | 9 | 1 | no | — |
| 130 | C2×M16 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 131 | C22⋊Q8 | — | 18 | 1 | no | — |
| 132 | Q32 | — | 18 | 2 | no | — |
| 133 | SD32 | — | 18 | 2 | no | — |
| 134 | M32 | C2×C3⋊D3 | 1 | 2 | yes | complemented |
| 135 | #106 | — | 9 | 1 | no | — |
| 136 | #103 | — | 18 | 1 | no | — |
| 137 | C23×C3 | D24 | 1 | 4 | yes | — |
| 138 | C22×D3 | — | 12 | 4 | no | — |
| 139 | C2×C3×C4 | — | 2 | 4 | no | — |
| 140 | C2×C3×C4 | — | 2 | 4 | no | — |
| 141 | C2×C3×C4 | D24 | 1 | 4 | yes | — |
| 142 | C2×C3×C4 | C2×D12 | 1 | 4 | yes | — |
| 143 | #67 | — | 12 | 8 | no | — |
| 144 | #67 | — | 12 | 8 | no | — |
| 145 | C2×Dic3 | — | 12 | 4 | no | — |
| 146 | C2×Dic3 | — | 12 | 4 | no | — |
| 147 | C2×Dic3 | — | 12 | 4 | no | — |
| 148 | D12 | — | 6 | 8 | no | — |
| 149 | D12 | — | 12 | 4 | no | — |
| 150 | C4×D3 | — | 12 | 8 | no | — |
| 151 | C4×D3 | — | 12 | 8 | no | — |
| 152 | Dic6 | — | 6 | 8 | no | — |
| 153 | Dic6 | — | 12 | 4 | no | — |
| 154 | Dic6 | — | 12 | 4 | no | — |
| 155 | Dic6 | — | 12 | 4 | no | — |
| 156 | C3×C8 | — | 2 | 4 | no | — |
| 157 | C3×C8 | D3×D4 | 1 | 8 | yes | — |
| 158 | C2×C32 | — | 2 | 1 | no | — |
| 159 | C2×C32 | — | 4 | 1 | no | — |
| 160 | C2×C32 | #447 | 1 | 1 | yes | characteristic |
| 161 | C3⋊D3 | — | 8 | 2 | no | — |
| 162 | #41 | — | 18 | 2 | no | — |
| 163 | #41 | — | 18 | 2 | no | — |
| 164 | #41 | — | 36 | 1 | no | — |
| 165 | #41 | — | 36 | 1 | no | — |
| 166 | C2×Q8 | — | 18 | 1 | no | — |
| 167 | C2×Q8 | — | 18 | 1 | no | — |
| 168 | C2×D4 | — | 18 | 1 | no | — |
| 169 | C2×D4 | — | 36 | 1 | no | — |
| 170 | C22×C4 | — | 36 | 1 | no | — |
| 171 | C22×C4 | C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 172 | Q16 | — | 9 | 2 | no | — |
| 173 | Q16 | — | 18 | 1 | no | — |
| 174 | Q16 | — | 18 | 2 | no | — |
| 175 | SD16 | — | 18 | 2 | no | — |
| 176 | SD16 | — | 18 | 2 | no | — |
| 177 | D8 | — | 9 | 2 | no | — |
| 178 | D8 | — | 18 | 1 | no | — |
| 179 | M16 | — | 2 | 2 | no | — |
| 180 | C2×C8 | C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 181 | C2×C8 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 182 | C4⋊C4 | — | 18 | 1 | no | — |
| 183 | C4⋊C4 | — | 36 | 1 | no | — |
| 184 | C22⋊C4 | — | 36 | 1 | no | — |
| 185 | C16 | — | 2 | 2 | no | — |
| 186 | C22×C3 | — | 2 | 4 | no | — |
| 187 | C22×C3 | — | 4 | 4 | no | — |
| 188 | C22×C3 | C2×D24 | 1 | 4 | yes | — |
| 189 | C2×D3 | — | 12 | 8 | no | — |
| 190 | C2×D3 | — | 24 | 8 | no | — |
| 191 | C3×C4 | — | 2 | 4 | no | — |
| 192 | C3×C4 | #882 | 1 | 4 | yes | — |
| 193 | C3×C4 | #908 | 1 | 4 | yes | — |
| 194 | Dic3 | — | 12 | 8 | no | — |
| 195 | Dic3 | — | 24 | 4 | no | — |
| 196 | Dic3 | — | 24 | 4 | no | — |
| 197 | C32 | #2191 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 198 | C23 | — | 36 | 1 | no | — |
| 199 | C23 | #3745 | 1 | 1 | yes | characteristic |
| 200 | Q8 | — | 18 | 2 | no | — |
| 201 | Q8 | — | 36 | 1 | no | — |
| 202 | Q8 | — | 36 | 1 | no | — |
| 203 | Q8 | — | 36 | 1 | no | — |
| 204 | D4 | — | 18 | 2 | no | — |
| 205 | D4 | — | 36 | 1 | no | — |
| 206 | D4 | — | 36 | 2 | no | — |
| 207 | D4 | — | 36 | 2 | no | — |
| 208 | C2×C4 | — | 2 | 1 | no | — |
| 209 | C2×C4 | — | 2 | 1 | no | — |
| 210 | C2×C4 | — | 36 | 2 | no | — |
| 211 | C2×C4 | — | 36 | 1 | no | — |
| 212 | C2×C4 | — | 36 | 2 | no | — |
| 213 | C2×C4 | — | 36 | 1 | no | — |
| 214 | C2×C4 | — | 36 | 1 | no | — |
| 215 | C2×C4 | #3745 | 1 | 1 | yes | characteristic |
| 216 | C2×C4 | C2×C4⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 217 | C8 | — | 2 | 1 | no | — |
| 218 | C8 | D4×C3⋊D3 | 1 | 2 | yes | — |
| 219 | C2×C3 | — | 2 | 4 | no | — |
| 220 | C2×C3 | — | 4 | 4 | no | — |
| 221 | C2×C3 | #4732 | 1 | 4 | yes | — |
| 222 | D3 | — | 24 | 8 | no | — |
| 223 | C22 | — | 2 | 1 | no | — |
| 224 | C22 | — | 4 | 1 | no | — |
| 225 | C22 | — | 36 | 2 | no | — |
| 226 | C22 | — | 72 | 2 | no | — |
| 227 | C22 | C2×#3745 | 1 | 1 | yes | characteristic |
| 228 | C4 | — | 2 | 1 | no | — |
| 229 | C4 | — | 36 | 2 | no | — |
| 230 | C4 | — | 72 | 1 | no | — |
| 231 | C4 | — | 72 | 1 | no | — |
| 232 | C4 | #64091 | 1 | 1 | yes | characteristic |
| 233 | C4 | #64117 | 1 | 1 | yes | characteristic |
| 234 | C3 | #69121 | 1 | 4 | yes | complemented |
| 235 | C2 | — | 2 | 1 | no | — |
| 236 | C2 | — | 4 | 1 | no | — |
| 237 | C2 | — | 72 | 2 | no | — |
| 238 | C2 | #10592431 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10592836 | C2 | semidirect |
| 3. #10592608 | C2 | semidirect |
| 4. C32×#349 | C2 | semidirect |
| 5. #10589384 | C2 | semidirect |
| 12. C2×#3746 | C22 | semidirect |
| 15. C32×M32 | C22 | semidirect |
| 16. #63644 | C22 | semidirect |
| 23. C3×#349 | D3 | semidirect |
| 58. C3×M32 | C2×D3 | semidirect |
| 88. #349 | C3⋊D3 | semidirect |
| 134. M32 | C2×C3⋊D3 | semidirect |
| 197. C32 | #2191 | semidirect |
| 234. C3 | #69121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596219 | 2 |
| #10592836 | 2 |
| #10592608 | 2 |
| C32×#349 | 2 |
| #10589384 | 2 |
| #69121 | 3 |