Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
401 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #10592850 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10590902 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#4562 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10589116 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10589102 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69183 | — | 3 | 2 | no | maximal |
| 7 | C2×C32×D8 | C22 | 1 | 1 | yes | characteristic |
| 8 | #64149 | — | 2 | 1 | no | — |
| 9 | C2×#3753 | — | 2 | 1 | no | — |
| 10 | C2×#3745 | C22 | 1 | 1 | yes | characteristic |
| 11 | #63919 | — | 2 | 1 | no | — |
| 12 | C8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#818 | C22 | 1 | 2 | yes | — |
| 14 | C2×C3×C3⋊C16 | C22 | 1 | 2 | yes | — |
| 15 | #63576 | — | 2 | 1 | no | — |
| 16 | #5151 | — | 3 | 2 | no | — |
| 17 | #5151 | — | 6 | 1 | no | — |
| 18 | #4874 | — | 3 | 2 | no | — |
| 19 | C3×#357 | — | 3 | 2 | no | — |
| 20 | #4562 | D3 | 1 | 2 | yes | complemented |
| 21 | #4509 | — | 3 | 2 | no | — |
| 22 | Dic3×C16 | — | 3 | 2 | no | — |
| 23 | #4491 | — | 3 | 2 | no | — |
| 24 | C2×C32×D4 | — | 2 | 1 | no | — |
| 25 | C2×#638 | — | 4 | 1 | no | — |
| 26 | C2×#638 | — | 4 | 1 | no | — |
| 27 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 28 | C2×#627 | — | 4 | 1 | no | — |
| 29 | C32×D8 | — | 2 | 2 | no | — |
| 30 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 31 | #3753 | — | 4 | 2 | no | — |
| 32 | C4×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 34 | #3745 | — | 2 | 2 | no | — |
| 35 | C3×C4⋊Dic3 | — | 2 | 2 | no | — |
| 36 | #3724 | — | 4 | 1 | no | — |
| 37 | C3×C3⋊C16 | — | 2 | 2 | no | — |
| 38 | #2240 | — | 9 | 1 | no | Sylow |
| 39 | C2×C3×D8 | — | 2 | 1 | no | — |
| 40 | C2×C3×D8 | C2×D3 | 1 | 2 | yes | — |
| 41 | #940 | — | 6 | 2 | no | — |
| 42 | #940 | — | 6 | 2 | no | — |
| 43 | C2×#213 | — | 6 | 2 | no | — |
| 44 | C2×#213 | — | 6 | 2 | no | — |
| 45 | C2×D24 | — | 3 | 2 | no | — |
| 46 | C2×D24 | — | 6 | 1 | no | — |
| 47 | #888 | — | 6 | 2 | no | — |
| 48 | C2×C3×C16 | — | 3 | 2 | no | — |
| 49 | C3×#107 | — | 3 | 2 | no | — |
| 50 | #818 | C2×D3 | 1 | 2 | yes | — |
| 51 | C8×Dic3 | — | 3 | 2 | no | — |
| 52 | C8×Dic3 | — | 6 | 1 | no | — |
| 53 | C2×C3⋊C16 | C2×D3 | 1 | 2 | yes | — |
| 54 | #807 | — | 6 | 2 | no | — |
| 55 | C23×C32 | — | 4 | 1 | no | — |
| 56 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 57 | C32×D4 | — | 4 | 1 | no | — |
| 58 | C32×D4 | — | 4 | 1 | no | — |
| 59 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 60 | #638 | — | 8 | 2 | no | — |
| 61 | #638 | — | 8 | 2 | no | — |
| 62 | C2×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 63 | C2×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 64 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 65 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 66 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 67 | #627 | — | 8 | 2 | no | — |
| 68 | C32×C8 | #41 | 1 | 2 | yes | — |
| 69 | C3⋊(C3⋊C8) | SD16 | 1 | 2 | yes | — |
| 70 | #500 | — | 9 | 1 | no | — |
| 71 | #493 | — | 9 | 1 | no | — |
| 72 | #357 | — | 3 | 2 | no | — |
| 73 | #357 | — | 9 | 2 | no | — |
| 74 | C4×C16 | — | 9 | 1 | no | — |
| 75 | C2×C3×D4 | — | 2 | 2 | no | — |
| 76 | C2×C3×D4 | — | 2 | 2 | no | — |
| 77 | C2×#67 | — | 12 | 2 | no | — |
| 78 | C2×#67 | — | 12 | 2 | no | — |
| 79 | C2×#67 | — | 12 | 2 | no | — |
| 80 | C2×#67 | — | 12 | 2 | no | — |
| 81 | C2×D12 | — | 6 | 2 | no | — |
| 82 | C2×D12 | — | 6 | 2 | no | — |
| 83 | C2×Dic6 | — | 12 | 2 | no | — |
| 84 | C3×D8 | — | 2 | 2 | no | — |
| 85 | C3×D8 | — | 2 | 2 | no | — |
| 86 | C3×D8 | — | 4 | 2 | no | — |
| 87 | C2×C3×C8 | — | 2 | 1 | no | — |
| 88 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 89 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 90 | #213 | — | 12 | 4 | no | — |
| 91 | #213 | — | 12 | 4 | no | — |
| 92 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 93 | Dic3⋊C4 | — | 12 | 2 | no | — |
| 94 | C4×Dic3 | — | 3 | 2 | no | — |
| 95 | C4×Dic3 | — | 6 | 1 | no | — |
| 96 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 97 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 98 | D24 | — | 6 | 2 | no | — |
| 99 | D24 | — | 6 | 2 | no | — |
| 100 | D24 | — | 12 | 2 | no | — |
| 101 | C3×C16 | — | 6 | 2 | no | — |
| 102 | C3⋊C16 | — | 2 | 2 | no | — |
| 103 | C22×C32 | — | 8 | 1 | no | — |
| 104 | C22×C32 | — | 8 | 1 | no | — |
| 105 | C22×C32 | — | 8 | 1 | no | — |
| 106 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 107 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 108 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 109 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 110 | C32×C4 | #124 | 1 | 1 | yes | characteristic |
| 111 | C32×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 112 | C3⋊Dic3 | D16 | 1 | 2 | yes | — |
| 113 | C3⋊Dic3 | SD32 | 1 | 2 | yes | — |
| 114 | C3×Dic3 | — | 8 | 2 | no | — |
| 115 | C2×D8 | — | 9 | 1 | no | — |
| 116 | C2×D8 | — | 18 | 1 | no | — |
| 117 | C2×D8 | D32 | 1 | 1 | yes | characteristic |
| 118 | C4⋊Q8 | — | 18 | 1 | no | — |
| 119 | #127 | — | 18 | 1 | no | — |
| 120 | C2×C16 | — | 3 | 2 | no | — |
| 121 | #107 | — | 3 | 2 | no | — |
| 122 | #107 | — | 18 | 1 | no | — |
| 123 | C4×C8 | — | 9 | 1 | no | — |
| 124 | C23×C3 | — | 4 | 2 | no | — |
| 125 | C23×C3 | — | 4 | 2 | no | — |
| 126 | C22×D3 | — | 12 | 2 | no | — |
| 127 | C22×D3 | — | 12 | 2 | no | — |
| 128 | C3×D4 | — | 4 | 2 | no | — |
| 129 | C3×D4 | — | 4 | 2 | no | — |
| 130 | C3×D4 | — | 4 | 2 | no | — |
| 131 | C3×D4 | — | 4 | 2 | no | — |
| 132 | C2×C3×C4 | — | 2 | 1 | no | — |
| 133 | C2×C3×C4 | — | 12 | 2 | no | — |
| 134 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 135 | #67 | — | 24 | 4 | no | — |
| 136 | #67 | — | 24 | 4 | no | — |
| 137 | #67 | — | 24 | 4 | no | — |
| 138 | #67 | — | 24 | 4 | no | — |
| 139 | C2×Dic3 | — | 3 | 2 | no | — |
| 140 | C2×Dic3 | — | 3 | 2 | no | — |
| 141 | C2×Dic3 | — | 4 | 2 | no | — |
| 142 | C2×Dic3 | — | 6 | 1 | no | — |
| 143 | C2×Dic3 | — | 6 | 1 | no | — |
| 144 | D12 | — | 12 | 2 | no | — |
| 145 | D12 | — | 12 | 2 | no | — |
| 146 | D12 | — | 12 | 2 | no | — |
| 147 | D12 | — | 12 | 2 | no | — |
| 148 | Dic6 | — | 24 | 4 | no | — |
| 149 | C3×C8 | — | 2 | 2 | no | — |
| 150 | C3×C8 | #235 | 1 | 2 | yes | — |
| 151 | C3×C8 | #237 | 1 | 2 | yes | — |
| 152 | C3⋊C8 | — | 3 | 4 | no | — |
| 153 | C3⋊C8 | — | 6 | 2 | no | — |
| 154 | C2×C32 | — | 16 | 1 | no | — |
| 155 | C2×C32 | #486 | 1 | 1 | yes | characteristic |
| 156 | C2×C32 | C2×D16 | 1 | 1 | yes | characteristic |
| 157 | C2×C32 | C2×SD32 | 1 | 1 | yes | characteristic |
| 158 | C3⋊D3 | — | 16 | 1 | no | — |
| 159 | C2×Q8 | — | 36 | 1 | no | — |
| 160 | C2×D4 | — | 2 | 1 | no | — |
| 161 | C2×D4 | — | 18 | 1 | no | — |
| 162 | C2×D4 | — | 36 | 1 | no | — |
| 163 | C2×D4 | — | 36 | 1 | no | — |
| 164 | D8 | — | 2 | 2 | no | — |
| 165 | D8 | — | 18 | 2 | no | — |
| 166 | D8 | — | 36 | 2 | no | — |
| 167 | C2×C8 | — | 9 | 1 | no | — |
| 168 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 169 | C4⋊C4 | — | 6 | 2 | no | — |
| 170 | C4⋊C4 | — | 36 | 1 | no | — |
| 171 | C42 | — | 9 | 1 | no | — |
| 172 | C16 | — | 6 | 2 | no | — |
| 173 | C22×C3 | — | 2 | 1 | no | — |
| 174 | C22×C3 | — | 8 | 2 | no | — |
| 175 | C22×C3 | — | 8 | 2 | no | — |
| 176 | C22×C3 | — | 8 | 2 | no | — |
| 177 | C22×C3 | — | 8 | 2 | no | — |
| 178 | C22×C3 | — | 8 | 2 | no | — |
| 179 | C22×C3 | — | 8 | 2 | no | — |
| 180 | C22×C3 | D3×D8 | 1 | 2 | yes | — |
| 181 | C2×D3 | — | 24 | 2 | no | — |
| 182 | C2×D3 | — | 24 | 2 | no | — |
| 183 | C2×D3 | — | 24 | 2 | no | — |
| 184 | C2×D3 | — | 24 | 2 | no | — |
| 185 | C2×D3 | — | 24 | 2 | no | — |
| 186 | C2×D3 | — | 24 | 2 | no | — |
| 187 | C3×C4 | — | 2 | 1 | no | — |
| 188 | C3×C4 | — | 2 | 1 | no | — |
| 189 | C3×C4 | — | 24 | 2 | no | — |
| 190 | C3×C4 | #885 | 1 | 2 | yes | — |
| 191 | C3×C4 | D3×SD16 | 1 | 2 | yes | — |
| 192 | Dic3 | — | 3 | 4 | no | — |
| 193 | Dic3 | — | 3 | 4 | no | — |
| 194 | Dic3 | — | 6 | 2 | no | — |
| 195 | Dic3 | — | 6 | 2 | no | — |
| 196 | Dic3 | — | 8 | 2 | no | — |
| 197 | C32 | #2240 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 198 | C23 | — | 4 | 1 | no | — |
| 199 | C23 | — | 36 | 1 | no | — |
| 200 | Q8 | — | 72 | 2 | no | — |
| 201 | D4 | — | 4 | 1 | no | — |
| 202 | D4 | — | 4 | 1 | no | — |
| 203 | D4 | — | 36 | 1 | no | — |
| 204 | D4 | — | 36 | 1 | no | — |
| 205 | D4 | — | 72 | 2 | no | — |
| 206 | D4 | — | 72 | 2 | no | — |
| 207 | C2×C4 | — | 9 | 1 | no | — |
| 208 | C2×C4 | — | 9 | 1 | no | — |
| 209 | C2×C4 | — | 12 | 2 | no | — |
| 210 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 211 | C8 | — | 9 | 2 | no | — |
| 212 | C8 | #3804 | 1 | 2 | yes | — |
| 213 | C2×C3 | — | 2 | 1 | no | — |
| 214 | C2×C3 | — | 2 | 1 | no | — |
| 215 | C2×C3 | — | 2 | 1 | no | — |
| 216 | C2×C3 | — | 16 | 2 | no | — |
| 217 | C2×C3 | — | 16 | 2 | no | — |
| 218 | C2×C3 | #4760 | 1 | 2 | yes | — |
| 219 | C2×C3 | D3×D16 | 1 | 2 | yes | — |
| 220 | C2×C3 | D3×SD32 | 1 | 2 | yes | — |
| 221 | D3 | — | 48 | 2 | no | — |
| 222 | D3 | — | 48 | 2 | no | — |
| 223 | C22 | — | 8 | 1 | no | — |
| 224 | C22 | — | 8 | 1 | no | — |
| 225 | C22 | — | 8 | 1 | no | — |
| 226 | C22 | — | 72 | 1 | no | — |
| 227 | C22 | — | 72 | 1 | no | — |
| 228 | C22 | — | 72 | 1 | no | — |
| 229 | C22 | #63926 | 1 | 1 | yes | characteristic |
| 230 | C4 | — | 9 | 2 | no | — |
| 231 | C4 | — | 9 | 2 | no | — |
| 232 | C4 | — | 24 | 2 | no | — |
| 233 | C4 | #63930 | 1 | 1 | yes | characteristic |
| 234 | C4 | #63953 | 1 | 1 | yes | characteristic |
| 235 | C3 | — | 2 | 1 | no | — |
| 236 | C3 | #69183 | 1 | 2 | yes | complemented |
| 237 | C2 | — | 16 | 1 | no | — |
| 238 | C2 | — | 144 | 1 | no | — |
| 239 | C2 | #10591025 | 1 | 1 | yes | characteristic |
| 240 | C2 | #10591029 | 1 | 1 | yes | characteristic |
| 241 | C2 | #10591402 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10590902 | C2 | semidirect |
| 3. C3×#4562 | C2 | semidirect |
| 4. #10589116 | C2 | semidirect |
| 5. #10589102 | C2 | semidirect |
| 20. #4562 | D3 | semidirect |
| 197. C32 | #2240 | semidirect |
| 236. C3 | #69183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592850 | 2 |
| #10590902 | 2 |
| C3×#4562 | 2 |
| #10589116 | 2 |
| #10589102 | 2 |
| #69183 | 3 |