← #11664448
Subgroups — #11664448
Order 768.
2050 conjugacy classes of subgroups.
The subgroup lattice has 424 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #85735 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #85725 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3×#405 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83768 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#5113 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #78575 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #78563 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #78497 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #78463 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #60612 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C22×#235 | C22 | 1 | 2 | yes | — |
| 12 | C22×C3×M16 | C22 | 1 | 1 | yes | characteristic |
| 13 | C23×C3×C8 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×#117 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#926 | C22 | 1 | 2 | yes | — |
| 16 | #5526 | C22 | 1 | 4 | yes | — |
| 17 | #5525 | C22 | 1 | 4 | yes | — |
| 18 | #5524 | — | 2 | 4 | no | — |
| 19 | #5519 | C22 | 1 | 8 | yes | complemented |
| 20 | #5517 | — | 2 | 4 | no | — |
| 21 | #5510 | — | 2 | 2 | no | — |
| 22 | #5500 | — | 2 | 2 | no | — |
| 23 | #5493 | — | 2 | 2 | no | — |
| 24 | #5483 | — | 2 | 2 | no | — |
| 25 | #5477 | C22 | 1 | 4 | yes | — |
| 26 | #5470 | C22 | 1 | 4 | yes | complemented |
| 27 | C3×#405 | C22 | 1 | 8 | yes | complemented |
| 28 | C2×C3×#97 | C22 | 1 | 2 | yes | complemented |
| 29 | C2×C3×C4×C8 | C22 | 1 | 2 | yes | complemented |
| 30 | #5133 | C22 | 1 | 8 | yes | — |
| 31 | #5131 | C22 | 1 | 4 | yes | complemented |
| 32 | #5120 | C22 | 1 | 4 | yes | complemented |
| 33 | #5113 | C22 | 1 | 8 | yes | — |
| 34 | #5113 | C22 | 1 | 4 | yes | complemented |
| 35 | #5113 | C22 | 1 | 4 | yes | complemented |
| 36 | #5113 | C22 | 1 | 8 | yes | complemented |
| 37 | C2×#821 | C22 | 1 | 4 | yes | complemented |
| 38 | C2×#816 | C22 | 1 | 4 | yes | complemented |
| 39 | #4714 | C22 | 1 | 16 | yes | complemented |
| 40 | #4713 | C22 | 1 | 8 | yes | complemented |
| 41 | #4703 | C22 | 1 | 8 | yes | complemented |
| 42 | #4697 | C22 | 1 | 16 | yes | complemented |
| 43 | #4694 | C22 | 1 | 8 | yes | complemented |
| 44 | #4681 | C22 | 1 | 8 | yes | complemented |
| 45 | #3458 | — | 3 | 1 | no | — |
| 46 | #3449 | — | 3 | 1 | no | — |
| 47 | #3137 | — | 3 | 8 | no | — |
| 48 | #3136 | — | 3 | 8 | no | — |
| 49 | #3135 | — | 3 | 4 | no | — |
| 50 | #3131 | — | 3 | 4 | no | — |
| 51 | #2896 | — | 3 | 2 | no | — |
| 52 | C2×#416 | — | 3 | 2 | no | — |
| 53 | C2×#405 | D3 | 1 | 1 | yes | characteristic, complemented |
| 54 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 55 | C22×#67 | — | 2 | 2 | no | — |
| 56 | C2×#235 | — | 2 | 2 | no | — |
| 57 | C2×#235 | — | 2 | 2 | no | — |
| 58 | C2×#235 | — | 2 | 8 | no | — |
| 59 | C2×#235 | — | 2 | 8 | no | — |
| 60 | C2×#235 | C23 | 1 | 4 | yes | — |
| 61 | C2×#235 | C23 | 1 | 4 | yes | — |
| 62 | C22×D12 | C23 | 1 | 2 | yes | — |
| 63 | C22×C4×D3 | — | 2 | 2 | no | — |
| 64 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 65 | C2×C3×M16 | — | 2 | 4 | no | — |
| 66 | C2×C3×M16 | C23 | 1 | 4 | yes | — |
| 67 | C22×C3×C8 | — | 2 | 4 | no | — |
| 68 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×C3×C8 | C23 | 1 | 4 | yes | — |
| 71 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 72 | C3×#117 | D4 | 1 | 4 | yes | — |
| 73 | C3×#117 | C23 | 1 | 4 | yes | — |
| 74 | C2×C3×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 75 | C2×C3×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 76 | C2×C3×C42 | C23 | 1 | 2 | yes | — |
| 77 | C2×#217 | — | 2 | 2 | no | — |
| 78 | #930 | — | 2 | 8 | no | — |
| 79 | #926 | — | 2 | 2 | no | — |
| 80 | #926 | — | 2 | 2 | no | — |
| 81 | #926 | C23 | 1 | 4 | yes | — |
| 82 | #926 | C23 | 1 | 4 | yes | — |
| 83 | C2×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 84 | #924 | — | 2 | 8 | no | — |
| 85 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 86 | #897 | — | 2 | 8 | no | — |
| 87 | #895 | — | 2 | 8 | no | — |
| 88 | #890 | — | 2 | 8 | no | — |
| 89 | #888 | — | 2 | 8 | no | — |
| 90 | #886 | — | 2 | 8 | no | — |
| 91 | #882 | — | 2 | 8 | no | — |
| 92 | #878 | — | 2 | 16 | no | — |
| 93 | #875 | C23 | 1 | 8 | yes | — |
| 94 | #874 | C23 | 1 | 4 | yes | — |
| 95 | C4×D12 | — | 2 | 8 | no | — |
| 96 | #870 | C23 | 1 | 8 | yes | — |
| 97 | #869 | C23 | 1 | 4 | yes | — |
| 98 | #869 | C23 | 1 | 8 | yes | — |
| 99 | C4×Dic6 | — | 2 | 8 | no | — |
| 100 | C3×#97 | C23 | 1 | 8 | yes | — |
| 101 | C3×C4×C8 | C23 | 1 | 8 | yes | — |
| 102 | #821 | C23 | 1 | 16 | yes | — |
| 103 | #821 | C23 | 1 | 8 | yes | — |
| 104 | #821 | C23 | 1 | 8 | yes | — |
| 105 | #816 | C23 | 1 | 16 | yes | — |
| 106 | #816 | C23 | 1 | 8 | yes | — |
| 107 | #816 | C23 | 1 | 8 | yes | — |
| 108 | C22×#41 | — | 3 | 2 | no | — |
| 109 | C22×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 110 | C23×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 111 | #544 | — | 3 | 8 | no | — |
| 112 | #544 | — | 6 | 2 | no | — |
| 113 | #543 | — | 6 | 2 | no | — |
| 114 | #537 | — | 6 | 2 | no | — |
| 115 | #536 | — | 3 | 4 | no | — |
| 116 | #535 | — | 3 | 4 | no | — |
| 117 | #534 | — | 6 | 2 | no | — |
| 118 | #533 | — | 3 | 4 | no | — |
| 119 | #533 | — | 6 | 4 | no | — |
| 120 | #532 | — | 3 | 4 | no | — |
| 121 | #525 | — | 6 | 4 | no | — |
| 122 | C2×#117 | — | 3 | 2 | no | — |
| 123 | C2×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 124 | #491 | — | 3 | 8 | no | — |
| 125 | #490 | — | 3 | 8 | no | — |
| 126 | #489 | — | 3 | 16 | no | — |
| 127 | #488 | — | 3 | 16 | no | — |
| 128 | #487 | — | 3 | 8 | no | — |
| 129 | #486 | — | 3 | 8 | no | — |
| 130 | #419 | — | 3 | 4 | no | — |
| 131 | #418 | — | 3 | 4 | no | — |
| 132 | #417 | — | 3 | 8 | no | — |
| 133 | #416 | — | 3 | 4 | no | — |
| 134 | #416 | — | 3 | 8 | no | — |
| 135 | #416 | — | 3 | 4 | no | — |
| 136 | #416 | — | 3 | 8 | no | — |
| 137 | C2×#103 | — | 3 | 4 | no | — |
| 138 | C2×#102 | — | 3 | 4 | no | — |
| 139 | #405 | C2×D3 | 1 | 8 | yes | complemented |
| 140 | C2×#97 | C2×D3 | 1 | 2 | yes | complemented |
| 141 | C2×C4×C8 | C2×D3 | 1 | 2 | yes | complemented |
| 142 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C23×D3 | — | 2 | 2 | no | — |
| 144 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 145 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 146 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C22×C3×C4 | #41 | 1 | 4 | yes | — |
| 148 | C22×C3×C4 | #41 | 1 | 4 | yes | — |
| 149 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 150 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 151 | C2×#67 | — | 2 | 4 | no | — |
| 152 | C2×#67 | — | 2 | 4 | no | — |
| 153 | C2×#67 | — | 4 | 8 | no | — |
| 154 | C22×Dic3 | — | 2 | 2 | no | — |
| 155 | C22×Dic3 | — | 2 | 4 | no | — |
| 156 | #235 | — | 2 | 8 | no | — |
| 157 | #235 | — | 2 | 8 | no | — |
| 158 | #235 | — | 2 | 8 | no | — |
| 159 | #235 | — | 2 | 8 | no | — |
| 160 | #235 | — | 4 | 8 | no | — |
| 161 | #235 | — | 4 | 8 | no | — |
| 162 | C2×D12 | — | 2 | 4 | no | — |
| 163 | C2×D12 | — | 2 | 4 | no | — |
| 164 | C2×D12 | — | 2 | 2 | no | — |
| 165 | C2×D12 | — | 2 | 8 | no | — |
| 166 | C2×D12 | C24 | 1 | 4 | yes | — |
| 167 | C2×C4×D3 | — | 2 | 4 | no | — |
| 168 | C2×C4×D3 | — | 2 | 4 | no | — |
| 169 | C2×C4×D3 | — | 4 | 8 | no | — |
| 170 | C2×Dic6 | — | 2 | 4 | no | — |
| 171 | C2×Dic6 | — | 2 | 4 | no | — |
| 172 | C2×Dic6 | — | 2 | 2 | no | — |
| 173 | C2×Dic6 | — | 2 | 8 | no | — |
| 174 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 175 | C3×M16 | — | 2 | 8 | no | — |
| 176 | C2×C3×C8 | — | 2 | 8 | no | — |
| 177 | C2×C3×C8 | — | 2 | 2 | no | — |
| 178 | C2×C3×C8 | — | 2 | 2 | no | — |
| 179 | C2×C3×C8 | — | 2 | 4 | no | — |
| 180 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 181 | C2×C3×C8 | C24 | 1 | 4 | yes | — |
| 182 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 183 | C3×C4⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 184 | C3×C22⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 185 | C3×C42 | C2×D4 | 1 | 4 | yes | — |
| 186 | C3×C42 | C24 | 1 | 4 | yes | — |
| 187 | #217 | — | 2 | 4 | no | — |
| 188 | #217 | — | 2 | 4 | no | — |
| 189 | (C2×D3)⋊C4 | — | 2 | 16 | no | — |
| 190 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 191 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 192 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 193 | C4⋊Dic3 | C24 | 1 | 8 | yes | — |
| 194 | Dic3⋊C4 | — | 2 | 16 | no | — |
| 195 | C4×Dic3 | — | 2 | 4 | no | — |
| 196 | C4×Dic3 | — | 2 | 4 | no | — |
| 197 | C2×#41 | — | 3 | 4 | no | — |
| 198 | C2×#41 | — | 3 | 4 | no | — |
| 199 | C2×#41 | — | 6 | 2 | no | — |
| 200 | C2×#41 | — | 6 | 2 | no | — |
| 201 | C2×#41 | — | 6 | 8 | no | — |
| 202 | C2×#41 | — | 6 | 8 | no | — |
| 203 | C22×Q8 | — | 3 | 2 | no | — |
| 204 | C22×D4 | — | 3 | 2 | no | — |
| 205 | C22×D4 | — | 6 | 2 | no | — |
| 206 | C23×C4 | — | 6 | 2 | no | — |
| 207 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 208 | C2×M16 | — | 2 | 4 | no | — |
| 209 | C2×M16 | C22×D3 | 1 | 4 | yes | — |
| 210 | C22×C8 | — | 2 | 4 | no | — |
| 211 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 212 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 213 | C22×C8 | C22×D3 | 1 | 4 | yes | — |
| 214 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 215 | C4⋊Q8 | — | 3 | 8 | no | — |
| 216 | C4⋊Q8 | — | 3 | 4 | no | — |
| 217 | C4⋊Q8 | — | 6 | 8 | no | — |
| 218 | #127 | — | 3 | 4 | no | — |
| 219 | #125 | — | 3 | 8 | no | — |
| 220 | #125 | — | 6 | 8 | no | — |
| 221 | #124 | — | 3 | 8 | no | — |
| 222 | #123 | — | 6 | 8 | no | — |
| 223 | C22⋊Q8 | — | 6 | 8 | no | — |
| 224 | C22⋊Q8 | — | 6 | 8 | no | — |
| 225 | C22⋊Q8 | — | 6 | 16 | no | — |
| 226 | #121 | — | 6 | 8 | no | — |
| 227 | #121 | — | 6 | 8 | no | — |
| 228 | #120 | — | 6 | 8 | no | — |
| 229 | C4×Q8 | — | 6 | 8 | no | — |
| 230 | C4×D4 | — | 6 | 8 | no | — |
| 231 | #117 | — | 3 | 4 | no | — |
| 232 | #117 | — | 3 | 4 | no | — |
| 233 | #117 | — | 6 | 2 | no | — |
| 234 | #117 | — | 6 | 2 | no | — |
| 235 | #117 | D12 | 1 | 4 | yes | — |
| 236 | #117 | C22×D3 | 1 | 4 | yes | — |
| 237 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 238 | C2×C4⋊C4 | D12 | 1 | 2 | yes | — |
| 239 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 240 | C2×C22⋊C4 | D12 | 1 | 2 | yes | — |
| 241 | C2×C42 | — | 6 | 2 | no | — |
| 242 | C2×C42 | C22×D3 | 1 | 2 | yes | — |
| 243 | #103 | — | 3 | 8 | no | — |
| 244 | #103 | — | 3 | 8 | no | — |
| 245 | #103 | — | 3 | 16 | no | — |
| 246 | #102 | — | 3 | 8 | no | — |
| 247 | #102 | — | 3 | 8 | no | — |
| 248 | #102 | — | 3 | 16 | no | — |
| 249 | #97 | C22×D3 | 1 | 8 | yes | — |
| 250 | C4×C8 | C22×D3 | 1 | 8 | yes | — |
| 251 | C23×C3 | — | 4 | 2 | no | — |
| 252 | C23×C3 | #124 | 1 | 4 | yes | — |
| 253 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 254 | C23×C3 | C22×D4 | 1 | 2 | yes | — |
| 255 | C22×D3 | — | 2 | 4 | no | — |
| 256 | C22×D3 | — | 4 | 4 | no | — |
| 257 | C22×D3 | — | 8 | 4 | no | — |
| 258 | C2×C3×C4 | — | 4 | 4 | no | — |
| 259 | C2×C3×C4 | #124 | 1 | 8 | yes | — |
| 260 | C2×C3×C4 | #124 | 1 | 4 | yes | — |
| 261 | C2×C3×C4 | C22×D4 | 1 | 8 | yes | — |
| 262 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 263 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 264 | C2×C3×C4 | C2×#41 | 1 | 4 | yes | — |
| 265 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 266 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 267 | C2×C3×C4 | C2×#41 | 1 | 4 | yes | — |
| 268 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 269 | #67 | — | 4 | 8 | no | — |
| 270 | #67 | — | 4 | 8 | no | — |
| 271 | C2×Dic3 | — | 2 | 8 | no | — |
| 272 | C2×Dic3 | — | 2 | 4 | no | — |
| 273 | C2×Dic3 | — | 4 | 4 | no | — |
| 274 | C2×Dic3 | — | 8 | 4 | no | — |
| 275 | D12 | — | 2 | 4 | no | — |
| 276 | D12 | — | 2 | 4 | no | — |
| 277 | D12 | — | 4 | 4 | no | — |
| 278 | D12 | — | 8 | 8 | no | — |
| 279 | C4×D3 | — | 4 | 8 | no | — |
| 280 | C4×D3 | — | 4 | 8 | no | — |
| 281 | Dic6 | — | 2 | 4 | no | — |
| 282 | Dic6 | — | 2 | 4 | no | — |
| 283 | Dic6 | — | 4 | 4 | no | — |
| 284 | Dic6 | — | 8 | 8 | no | — |
| 285 | C3×C8 | — | 2 | 2 | no | — |
| 286 | C3×C8 | — | 2 | 2 | no | — |
| 287 | C3×C8 | — | 2 | 4 | no | — |
| 288 | C24 | — | 6 | 2 | no | — |
| 289 | C24 | C2×D12 | 1 | 1 | yes | characteristic |
| 290 | #41 | — | 6 | 8 | no | — |
| 291 | #41 | — | 6 | 8 | no | — |
| 292 | #41 | — | 6 | 8 | no | — |
| 293 | #41 | — | 6 | 8 | no | — |
| 294 | #41 | — | 12 | 8 | no | — |
| 295 | #41 | — | 12 | 8 | no | — |
| 296 | C2×Q8 | — | 3 | 4 | no | — |
| 297 | C2×Q8 | — | 6 | 2 | no | — |
| 298 | C2×Q8 | — | 6 | 8 | no | — |
| 299 | C2×Q8 | — | 6 | 4 | no | — |
| 300 | C2×Q8 | — | 6 | 4 | no | — |
| 301 | C2×D4 | — | 3 | 4 | no | — |
| 302 | C2×D4 | — | 6 | 4 | no | — |
| 303 | C2×D4 | — | 6 | 4 | no | — |
| 304 | C2×D4 | — | 6 | 2 | no | — |
| 305 | C2×D4 | — | 6 | 8 | no | — |
| 306 | C2×D4 | — | 6 | 4 | no | — |
| 307 | C2×D4 | — | 6 | 4 | no | — |
| 308 | C2×D4 | — | 12 | 8 | no | — |
| 309 | C22×C4 | — | 6 | 2 | no | — |
| 310 | C22×C4 | — | 6 | 4 | no | — |
| 311 | C22×C4 | — | 6 | 4 | no | — |
| 312 | C22×C4 | — | 6 | 4 | no | — |
| 313 | C22×C4 | — | 12 | 8 | no | — |
| 314 | C22×C4 | C2×D12 | 1 | 4 | yes | — |
| 315 | C22×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 316 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 317 | C22×C4 | #235 | 1 | 4 | yes | — |
| 318 | C22×C4 | #235 | 1 | 4 | yes | — |
| 319 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 320 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 321 | M16 | — | 2 | 8 | no | — |
| 322 | C2×C8 | — | 2 | 8 | no | — |
| 323 | C2×C8 | — | 2 | 2 | no | — |
| 324 | C2×C8 | — | 2 | 2 | no | — |
| 325 | C2×C8 | — | 2 | 4 | no | — |
| 326 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 327 | C2×C8 | C23×D3 | 1 | 4 | yes | — |
| 328 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 329 | C4⋊C4 | — | 3 | 8 | no | — |
| 330 | C4⋊C4 | — | 6 | 4 | no | — |
| 331 | C4⋊C4 | — | 6 | 8 | no | — |
| 332 | C4⋊C4 | — | 6 | 16 | no | — |
| 333 | C4⋊C4 | — | 6 | 8 | no | — |
| 334 | C4⋊C4 | C2×D12 | 1 | 8 | yes | — |
| 335 | C22⋊C4 | — | 6 | 4 | no | — |
| 336 | C22⋊C4 | — | 6 | 4 | no | — |
| 337 | C22⋊C4 | — | 6 | 16 | no | — |
| 338 | C22⋊C4 | C2×D12 | 1 | 8 | yes | — |
| 339 | C42 | — | 6 | 4 | no | — |
| 340 | C42 | — | 6 | 4 | no | — |
| 341 | C42 | C2×D12 | 1 | 4 | yes | — |
| 342 | C42 | C23×D3 | 1 | 4 | yes | — |
| 343 | C22×C3 | — | 2 | 4 | no | — |
| 344 | C22×C3 | — | 2 | 2 | no | — |
| 345 | C22×C3 | — | 4 | 4 | no | — |
| 346 | C22×C3 | C2×#124 | 1 | 4 | yes | — |
| 347 | C22×C3 | C2×#124 | 1 | 2 | yes | — |
| 348 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 349 | C2×D3 | — | 4 | 8 | no | — |
| 350 | C2×D3 | — | 4 | 4 | no | — |
| 351 | C2×D3 | — | 8 | 8 | no | — |
| 352 | C3×C4 | — | 2 | 8 | no | — |
| 353 | C3×C4 | C2×#124 | 1 | 4 | yes | — |
| 354 | C3×C4 | C2×#124 | 1 | 2 | yes | — |
| 355 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 356 | C3×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 357 | Dic3 | — | 4 | 8 | no | — |
| 358 | Dic3 | — | 4 | 4 | no | — |
| 359 | C23 | — | 4 | 2 | no | — |
| 360 | C23 | — | 6 | 4 | no | — |
| 361 | C23 | — | 12 | 4 | no | — |
| 362 | C23 | — | 24 | 4 | no | — |
| 363 | C23 | #875 | 1 | 4 | yes | — |
| 364 | C23 | C22×D12 | 1 | 1 | yes | characteristic |
| 365 | C23 | C22×D12 | 1 | 2 | yes | — |
| 366 | Q8 | — | 6 | 4 | no | — |
| 367 | Q8 | — | 6 | 4 | no | — |
| 368 | Q8 | — | 12 | 4 | no | — |
| 369 | Q8 | — | 24 | 8 | no | — |
| 370 | D4 | — | 6 | 4 | no | — |
| 371 | D4 | — | 6 | 4 | no | — |
| 372 | D4 | — | 12 | 8 | no | — |
| 373 | D4 | — | 12 | 8 | no | — |
| 374 | D4 | — | 12 | 4 | no | — |
| 375 | D4 | — | 24 | 8 | no | — |
| 376 | C2×C4 | — | 4 | 4 | no | — |
| 377 | C2×C4 | — | 6 | 8 | no | — |
| 378 | C2×C4 | — | 6 | 4 | no | — |
| 379 | C2×C4 | — | 12 | 4 | no | — |
| 380 | C2×C4 | — | 12 | 8 | no | — |
| 381 | C2×C4 | — | 12 | 8 | no | — |
| 382 | C2×C4 | — | 24 | 4 | no | — |
| 383 | C2×C4 | #875 | 1 | 8 | yes | — |
| 384 | C2×C4 | #875 | 1 | 4 | yes | — |
| 385 | C2×C4 | C22×D12 | 1 | 8 | yes | — |
| 386 | C2×C4 | C22×D12 | 1 | 2 | yes | — |
| 387 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 388 | C2×C4 | C2×#235 | 1 | 4 | yes | — |
| 389 | C2×C4 | C2×#235 | 1 | 2 | yes | — |
| 390 | C2×C4 | C2×#235 | 1 | 2 | yes | — |
| 391 | C2×C4 | C2×#235 | 1 | 4 | yes | — |
| 392 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 393 | C8 | — | 2 | 2 | no | — |
| 394 | C8 | — | 2 | 2 | no | — |
| 395 | C8 | — | 2 | 4 | no | — |
| 396 | C2×C3 | — | 2 | 4 | no | — |
| 397 | C2×C3 | — | 2 | 2 | no | — |
| 398 | C2×C3 | C22×#124 | 1 | 1 | yes | characteristic |
| 399 | C2×C3 | #3584 | 1 | 2 | yes | — |
| 400 | D3 | — | 8 | 4 | no | — |
| 401 | C22 | — | 2 | 2 | no | — |
| 402 | C22 | — | 2 | 4 | no | — |
| 403 | C22 | — | 4 | 4 | no | — |
| 404 | C22 | — | 12 | 8 | no | — |
| 405 | C22 | — | 12 | 4 | no | — |
| 406 | C22 | — | 24 | 8 | no | — |
| 407 | C22 | C2×#875 | 1 | 4 | yes | — |
| 408 | C22 | C2×#875 | 1 | 2 | yes | — |
| 409 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 410 | C4 | — | 2 | 8 | no | — |
| 411 | C4 | — | 12 | 8 | no | — |
| 412 | C4 | — | 12 | 4 | no | — |
| 413 | C4 | C2×#875 | 1 | 2 | yes | — |
| 414 | C4 | C2×#875 | 1 | 4 | yes | — |
| 415 | C4 | C22×#235 | 1 | 1 | yes | characteristic |
| 416 | C4 | C22×#235 | 1 | 1 | yes | characteristic |
| 417 | C3 | #60612 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 418 | C2 | — | 2 | 4 | no | — |
| 419 | C2 | — | 2 | 2 | no | — |
| 420 | C2 | — | 24 | 4 | no | — |
| 421 | C2 | C22×#875 | 1 | 1 | yes | characteristic |
| 422 | C2 | #87163 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta