Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
689 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 689 conjugacy classes of subgroups — too many to draw. Only its 100 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 | C2×D8×C3⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10590714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#63544 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#4562 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10589116 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #69190 | — | 3 | 2 | no | maximal |
| 7 | C2×D4×C3⋊D3 | — | 2 | 1 | no | — |
| 8 | C2×C32×D8 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#3753 | — | 2 | 1 | no | — |
| 10 | D8×C3⋊D3 | — | 2 | 2 | no | — |
| 11 | D8×C3⋊D3 | C4 | 1 | 4 | yes | complemented |
| 12 | C2×#3745 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 14 | #63849 | — | 2 | 1 | no | — |
| 15 | C3×#818 | C22 | 1 | 2 | yes | complemented |
| 16 | C2×C3×C3⋊C16 | C22 | 1 | 2 | yes | complemented |
| 17 | #63574 | — | 2 | 1 | no | — |
| 18 | #63544 | — | 2 | 2 | no | — |
| 19 | C2×D3×D8 | — | 3 | 2 | no | — |
| 20 | C2×D3×D8 | — | 6 | 1 | no | — |
| 21 | C2×#798 | — | 3 | 2 | no | — |
| 22 | #4880 | — | 3 | 2 | no | — |
| 23 | C3×#357 | — | 3 | 2 | no | — |
| 24 | #4562 | D3 | 1 | 2 | yes | complemented |
| 25 | #4509 | — | 3 | 2 | no | — |
| 26 | #4491 | — | 3 | 2 | no | — |
| 27 | C23×C3⋊D3 | — | 4 | 1 | no | — |
| 28 | C2×C32×D4 | — | 2 | 1 | no | — |
| 29 | C2×#638 | — | 4 | 1 | no | — |
| 30 | D4×C3⋊D3 | — | 2 | 4 | no | — |
| 31 | D4×C3⋊D3 | — | 4 | 2 | no | — |
| 32 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 33 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 34 | C32×D8 | — | 2 | 1 | no | — |
| 35 | C32×D8 | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 37 | #3753 | — | 2 | 4 | no | — |
| 38 | C2×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 39 | #3745 | — | 2 | 1 | no | — |
| 40 | #3745 | C2×C4 | 1 | 2 | yes | — |
| 41 | C8×C3⋊D3 | C2×C4 | 1 | 2 | yes | — |
| 42 | C8×C3⋊D3 | D4 | 1 | 2 | yes | — |
| 43 | C3×C4⋊Dic3 | — | 2 | 2 | no | — |
| 44 | #3722 | — | 4 | 1 | no | — |
| 45 | Dic32 | — | 4 | 1 | no | — |
| 46 | C3×C3⋊C16 | — | 2 | 2 | no | — |
| 47 | #2140 | — | 9 | 1 | no | Sylow |
| 48 | C2×D3×D4 | — | 6 | 2 | no | — |
| 49 | C2×D3×D4 | — | 6 | 2 | no | — |
| 50 | C2×C3×D8 | — | 2 | 1 | no | — |
| 51 | C2×C3×D8 | C2×D3 | 1 | 2 | yes | — |
| 52 | C2×#213 | — | 6 | 2 | no | — |
| 53 | C2×#213 | — | 6 | 2 | no | — |
| 54 | D3×D8 | — | 3 | 8 | no | — |
| 55 | D3×D8 | — | 6 | 4 | no | — |
| 56 | D3×D8 | — | 6 | 4 | no | — |
| 57 | D3×D8 | — | 6 | 4 | no | — |
| 58 | C2×D24 | — | 3 | 2 | no | — |
| 59 | C2×D24 | — | 6 | 1 | no | — |
| 60 | C2×D3×C8 | — | 3 | 2 | no | — |
| 61 | C2×D3×C8 | — | 6 | 1 | no | — |
| 62 | #892 | — | 6 | 2 | no | — |
| 63 | C2×C3×C16 | — | 3 | 2 | no | — |
| 64 | C3×#107 | — | 3 | 2 | no | — |
| 65 | #818 | C2×D3 | 1 | 2 | yes | complemented |
| 66 | C2×C3⋊C16 | C2×D3 | 1 | 2 | yes | complemented |
| 67 | #808 | — | 6 | 2 | no | — |
| 68 | #798 | — | 6 | 4 | no | — |
| 69 | C23×C32 | — | 4 | 1 | no | — |
| 70 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 71 | C22×C3⋊D3 | — | 4 | 4 | no | — |
| 72 | C22×C3⋊D3 | — | 8 | 4 | no | — |
| 73 | C22×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 74 | C32×D4 | — | 2 | 2 | no | — |
| 75 | C32×D4 | — | 4 | 1 | no | — |
| 76 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | #638 | — | 4 | 4 | no | — |
| 78 | C2×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 79 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 80 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 81 | C4×C3⋊D3 | C22⋊C4 | 1 | 2 | yes | — |
| 82 | C4×C3⋊D3 | SD16 | 1 | 2 | yes | — |
| 83 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 84 | C32×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 85 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C3⋊(C3⋊C8) | C22⋊C4 | 1 | 2 | yes | — |
| 87 | C22×D8 | — | 9 | 1 | no | — |
| 88 | C2×M32 | — | 9 | 1 | no | — |
| 89 | #427 | — | 9 | 1 | no | — |
| 90 | #357 | — | 3 | 2 | no | — |
| 91 | #357 | — | 9 | 2 | no | — |
| 92 | C23×D3 | — | 12 | 2 | no | — |
| 93 | C23×D3 | — | 12 | 2 | no | — |
| 94 | C2×C3×D4 | — | 2 | 2 | no | — |
| 95 | C2×C3×D4 | — | 2 | 2 | no | — |
| 96 | C2×#67 | — | 12 | 2 | no | — |
| 97 | C2×#67 | — | 12 | 2 | no | — |
| 98 | D3×D4 | — | 6 | 8 | no | — |
| 99 | D3×D4 | — | 6 | 8 | no | — |
| 100 | D3×D4 | — | 12 | 4 | no | — |
| 101 | D3×D4 | — | 12 | 4 | no | — |
| 102 | C2×D12 | — | 6 | 2 | no | — |
| 103 | C2×D12 | — | 6 | 2 | no | — |
| 104 | C2×C4×D3 | — | 3 | 2 | no | — |
| 105 | C2×C4×D3 | — | 6 | 1 | no | — |
| 106 | C3×D8 | — | 2 | 2 | no | — |
| 107 | C3×D8 | — | 2 | 2 | no | — |
| 108 | C3×D8 | — | 2 | 2 | no | — |
| 109 | C3×D8 | C4×D3 | 1 | 4 | yes | — |
| 110 | C2×C3×C8 | — | 2 | 1 | no | — |
| 111 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 112 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 113 | #213 | — | 6 | 8 | no | — |
| 114 | #213 | — | 6 | 8 | no | — |
| 115 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 116 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 117 | C4×Dic3 | — | 12 | 2 | no | — |
| 118 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 119 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 120 | D24 | — | 3 | 4 | no | — |
| 121 | D24 | — | 6 | 2 | no | — |
| 122 | D24 | — | 6 | 2 | no | — |
| 123 | D24 | — | 6 | 2 | no | — |
| 124 | D3×C8 | — | 3 | 4 | no | — |
| 125 | D3×C8 | — | 3 | 4 | no | — |
| 126 | D3×C8 | — | 6 | 2 | no | — |
| 127 | D3×C8 | — | 6 | 2 | no | — |
| 128 | C3×C16 | — | 6 | 2 | no | — |
| 129 | C3⋊C16 | — | 2 | 2 | no | — |
| 130 | C22×C32 | — | 4 | 2 | no | — |
| 131 | C22×C32 | — | 8 | 2 | no | — |
| 132 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 133 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 134 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 135 | C2×C3⋊D3 | — | 8 | 8 | no | — |
| 136 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 137 | C2×C3⋊D3 | #102 | 1 | 2 | yes | — |
| 138 | C32×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C32×C4 | C2×SD16 | 1 | 1 | yes | characteristic |
| 140 | C3⋊Dic3 | #102 | 1 | 2 | yes | — |
| 141 | C3×Dic3 | — | 8 | 2 | no | — |
| 142 | C22×D4 | — | 18 | 1 | no | — |
| 143 | C2×D8 | — | 9 | 4 | no | — |
| 144 | C2×D8 | — | 9 | 1 | no | — |
| 145 | C2×D8 | — | 18 | 2 | no | — |
| 146 | C2×D8 | — | 18 | 1 | no | — |
| 147 | C2×D8 | D32 | 1 | 1 | yes | characteristic |
| 148 | C22×C8 | — | 9 | 1 | no | — |
| 149 | #117 | — | 18 | 1 | no | — |
| 150 | M32 | — | 18 | 2 | no | — |
| 151 | C2×C16 | — | 3 | 2 | no | — |
| 152 | #107 | — | 3 | 2 | no | — |
| 153 | #106 | — | 18 | 1 | no | — |
| 154 | C23×C3 | — | 4 | 2 | no | — |
| 155 | C23×C3 | — | 4 | 2 | no | — |
| 156 | C22×D3 | — | 3 | 2 | no | — |
| 157 | C22×D3 | — | 6 | 1 | no | — |
| 158 | C22×D3 | — | 12 | 8 | no | — |
| 159 | C22×D3 | — | 12 | 8 | no | — |
| 160 | C22×D3 | — | 12 | 2 | no | — |
| 161 | C22×D3 | — | 12 | 2 | no | — |
| 162 | C22×D3 | — | 24 | 8 | no | — |
| 163 | C22×D3 | — | 24 | 4 | no | — |
| 164 | C22×D3 | — | 24 | 4 | no | — |
| 165 | C3×D4 | — | 2 | 4 | no | — |
| 166 | C3×D4 | — | 2 | 4 | no | — |
| 167 | C3×D4 | — | 4 | 2 | no | — |
| 168 | C3×D4 | — | 4 | 2 | no | — |
| 169 | C2×C3×C4 | — | 2 | 1 | no | — |
| 170 | C2×C3×C4 | — | 12 | 2 | no | — |
| 171 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 172 | #67 | — | 12 | 8 | no | — |
| 173 | #67 | — | 12 | 8 | no | — |
| 174 | C2×Dic3 | — | 3 | 2 | no | — |
| 175 | C2×Dic3 | — | 4 | 2 | no | — |
| 176 | C2×Dic3 | — | 6 | 1 | no | — |
| 177 | D12 | — | 6 | 4 | no | — |
| 178 | D12 | — | 6 | 4 | no | — |
| 179 | D12 | — | 12 | 2 | no | — |
| 180 | D12 | — | 12 | 2 | no | — |
| 181 | C4×D3 | — | 3 | 4 | no | — |
| 182 | C4×D3 | — | 3 | 4 | no | — |
| 183 | C4×D3 | — | 6 | 2 | no | — |
| 184 | C4×D3 | — | 6 | 2 | no | — |
| 185 | C3×C8 | — | 2 | 1 | no | — |
| 186 | C3×C8 | — | 2 | 1 | no | — |
| 187 | C3×C8 | C2×C4×D3 | 1 | 2 | yes | — |
| 188 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 189 | C3⋊C8 | — | 3 | 4 | no | — |
| 190 | C3⋊C8 | — | 6 | 2 | no | — |
| 191 | C2×C32 | — | 8 | 2 | no | — |
| 192 | C2×C32 | C2×#102 | 1 | 1 | yes | characteristic |
| 193 | C2×C32 | #509 | 1 | 2 | yes | — |
| 194 | C3⋊D3 | — | 2 | 2 | no | — |
| 195 | C3⋊D3 | — | 8 | 2 | no | — |
| 196 | C24 | — | 36 | 1 | no | — |
| 197 | C2×D4 | — | 2 | 1 | no | — |
| 198 | C2×D4 | — | 18 | 4 | no | — |
| 199 | C2×D4 | — | 18 | 1 | no | — |
| 200 | C2×D4 | — | 36 | 2 | no | — |
| 201 | C2×D4 | — | 36 | 1 | no | — |
| 202 | C22×C4 | — | 9 | 1 | no | — |
| 203 | D8 | — | 2 | 1 | no | — |
| 204 | D8 | — | 9 | 2 | no | — |
| 205 | D8 | — | 18 | 4 | no | — |
| 206 | D8 | — | 18 | 1 | no | — |
| 207 | D8 | #624 | 1 | 2 | yes | — |
| 208 | C2×C8 | — | 9 | 1 | no | — |
| 209 | C2×C8 | — | 9 | 2 | no | — |
| 210 | C2×C8 | — | 9 | 2 | no | — |
| 211 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 212 | C4⋊C4 | — | 6 | 2 | no | — |
| 213 | C22⋊C4 | — | 36 | 1 | no | — |
| 214 | C42 | — | 36 | 1 | no | — |
| 215 | C16 | — | 6 | 2 | no | — |
| 216 | C22×C3 | — | 2 | 1 | no | — |
| 217 | C22×C3 | — | 4 | 4 | no | — |
| 218 | C22×C3 | — | 4 | 4 | no | — |
| 219 | C22×C3 | — | 8 | 4 | no | — |
| 220 | C22×C3 | — | 8 | 2 | no | — |
| 221 | C22×C3 | — | 8 | 2 | no | — |
| 222 | C22×C3 | D3×D8 | 1 | 2 | yes | — |
| 223 | C2×D3 | — | 3 | 4 | no | — |
| 224 | C2×D3 | — | 6 | 2 | no | — |
| 225 | C2×D3 | — | 6 | 4 | no | — |
| 226 | C2×D3 | — | 6 | 2 | no | — |
| 227 | C2×D3 | — | 6 | 2 | no | — |
| 228 | C2×D3 | — | 12 | 4 | no | — |
| 229 | C2×D3 | — | 12 | 4 | no | — |
| 230 | C2×D3 | — | 24 | 16 | no | — |
| 231 | C2×D3 | — | 24 | 16 | no | — |
| 232 | C2×D3 | — | 24 | 4 | no | — |
| 233 | C2×D3 | — | 24 | 2 | no | — |
| 234 | C2×D3 | — | 24 | 2 | no | — |
| 235 | C3×C4 | — | 2 | 1 | no | — |
| 236 | C3×C4 | — | 2 | 1 | no | — |
| 237 | C3×C4 | — | 24 | 2 | no | — |
| 238 | C3×C4 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 239 | C3×C4 | D3×SD16 | 1 | 2 | yes | — |
| 240 | Dic3 | — | 3 | 4 | no | — |
| 241 | Dic3 | — | 6 | 2 | no | — |
| 242 | Dic3 | — | 8 | 2 | no | — |
| 243 | C32 | #2140 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 244 | C23 | — | 4 | 1 | no | — |
| 245 | C23 | — | 9 | 1 | no | — |
| 246 | C23 | — | 36 | 4 | no | — |
| 247 | C23 | — | 36 | 1 | no | — |
| 248 | C23 | — | 72 | 4 | no | — |
| 249 | D4 | — | 2 | 2 | no | — |
| 250 | D4 | — | 4 | 1 | no | — |
| 251 | D4 | — | 18 | 2 | no | — |
| 252 | D4 | — | 36 | 4 | no | — |
| 253 | D4 | — | 36 | 1 | no | — |
| 254 | C2×C4 | — | 9 | 1 | no | — |
| 255 | C2×C4 | — | 9 | 2 | no | — |
| 256 | C2×C4 | — | 9 | 2 | no | — |
| 257 | C2×C4 | — | 12 | 2 | no | — |
| 258 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 259 | C8 | — | 9 | 2 | no | — |
| 260 | C8 | C2×#624 | 1 | 1 | yes | characteristic |
| 261 | C8 | #3811 | 1 | 1 | yes | characteristic |
| 262 | C2×C3 | — | 2 | 2 | no | — |
| 263 | C2×C3 | — | 2 | 1 | no | — |
| 264 | C2×C3 | — | 8 | 4 | no | — |
| 265 | C2×C3 | — | 8 | 4 | no | — |
| 266 | C2×C3 | D3×#102 | 1 | 2 | yes | — |
| 267 | C2×C3 | #4911 | 1 | 2 | yes | — |
| 268 | C2×C3 | #4914 | 1 | 2 | yes | — |
| 269 | D3 | — | 6 | 4 | no | — |
| 270 | D3 | — | 6 | 4 | no | — |
| 271 | D3 | — | 24 | 4 | no | — |
| 272 | D3 | — | 24 | 4 | no | — |
| 273 | C22 | — | 4 | 2 | no | — |
| 274 | C22 | — | 8 | 2 | no | — |
| 275 | C22 | — | 9 | 2 | no | — |
| 276 | C22 | — | 18 | 2 | no | — |
| 277 | C22 | — | 36 | 2 | no | — |
| 278 | C22 | — | 72 | 8 | no | — |
| 279 | C22 | — | 72 | 2 | no | — |
| 280 | C22 | #63926 | 1 | 1 | yes | characteristic |
| 281 | C4 | — | 9 | 2 | no | — |
| 282 | C4 | — | 24 | 2 | no | — |
| 283 | C4 | #63930 | 1 | 1 | yes | characteristic |
| 284 | C4 | #63974 | 1 | 1 | yes | characteristic |
| 285 | C3 | — | 2 | 1 | no | — |
| 286 | C3 | #69190 | 1 | 2 | yes | complemented |
| 287 | C2 | — | 8 | 2 | no | — |
| 288 | C2 | — | 18 | 2 | no | — |
| 289 | C2 | — | 72 | 2 | no | — |
| 290 | C2 | #10591036 | 1 | 2 | yes | — |
| 291 | C2 | #10591416 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10590714 | C2 | semidirect |
| 3. C2×#63544 | C2 | semidirect |
| 4. C3×#4562 | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 11. D8×C3⋊D3 | C4 | semidirect |
| 15. C3×#818 | C22 | semidirect |
| 16. C2×C3×C3⋊C16 | C22 | semidirect |
| 24. #4562 | D3 | semidirect |
| 65. #818 | C2×D3 | semidirect |
| 66. C2×C3⋊C16 | C2×D3 | semidirect |
| 243. C32 | #2140 | semidirect |
| 286. C3 | #69190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×C3⋊D3 | 2 |
| #10590714 | 2 |
| C2×#63544 | 2 |
| C3×#4562 | 2 |
| #10589116 | 2 |
| #69190 | 3 |