← #72322120
Subgroups — #72322120
Order 2048.
464 conjugacy classes of subgroups.
The subgroup lattice has 418 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72321574 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72321140 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72321119 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72320488 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72286519 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#94754 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72232025 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #512761 | C22 | 1 | 1 | yes | characteristic |
| 9 | #483832 | — | 2 | 1 | no | — |
| 10 | #153562 | C4 | 1 | 1 | yes | characteristic |
| 11 | #153560 | C4 | 1 | 1 | yes | characteristic |
| 12 | C2×#7511 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#7511 | C22 | 1 | 1 | yes | characteristic |
| 14 | #151996 | C22 | 1 | 1 | yes | characteristic |
| 15 | #151129 | — | 2 | 1 | no | — |
| 16 | #151128 | — | 2 | 1 | no | — |
| 17 | #151127 | — | 2 | 2 | no | — |
| 18 | C2×#7464 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#7463 | C22 | 1 | 1 | yes | characteristic |
| 20 | #150063 | — | 2 | 1 | no | — |
| 21 | #149496 | C22 | 1 | 1 | yes | characteristic |
| 22 | #140349 | — | 2 | 1 | no | — |
| 23 | #94770 | C4 | 1 | 1 | yes | characteristic |
| 24 | #94765 | C4 | 1 | 1 | yes | characteristic |
| 25 | #94754 | — | 2 | 2 | no | — |
| 26 | #94615 | — | 2 | 1 | no | — |
| 27 | #94614 | — | 2 | 1 | no | — |
| 28 | #94053 | — | 2 | 1 | no | — |
| 29 | C2×#2262 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C4×#508 | — | 2 | 1 | no | — |
| 31 | #17898 | — | 4 | 1 | no | — |
| 32 | C2×M128 | — | 2 | 1 | no | — |
| 33 | C2×M128 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C2×M128 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | #13654 | D4 | 1 | 1 | yes | characteristic |
| 36 | #13654 | Q8 | 1 | 1 | yes | characteristic |
| 37 | #13653 | D4 | 1 | 1 | yes | characteristic |
| 38 | #13653 | Q8 | 1 | 1 | yes | characteristic |
| 39 | #13652 | — | 2 | 1 | no | — |
| 40 | #13652 | — | 2 | 1 | no | — |
| 41 | C2×#1425 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #13633 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | #13633 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | #13615 | — | 2 | 1 | no | — |
| 45 | C4×M64 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×#1397 | C23 | 1 | 1 | yes | characteristic |
| 47 | #13164 | — | 4 | 1 | no | — |
| 48 | #12670 | — | 2 | 1 | no | — |
| 49 | #12086 | — | 2 | 2 | no | — |
| 50 | #12085 | — | 2 | 2 | no | — |
| 51 | #12082 | — | 4 | 2 | no | — |
| 52 | C2×#1373 | — | 2 | 1 | no | — |
| 53 | C2×#1372 | — | 2 | 1 | no | — |
| 54 | #11592 | — | 4 | 1 | no | — |
| 55 | #11399 | D4 | 1 | 1 | yes | characteristic |
| 56 | #7540 | — | 2 | 2 | no | — |
| 57 | #7539 | — | 2 | 2 | no | — |
| 58 | #7511 | — | 2 | 1 | no | — |
| 59 | #7511 | — | 2 | 1 | no | — |
| 60 | #7511 | — | 2 | 1 | no | — |
| 61 | #7511 | — | 2 | 1 | no | — |
| 62 | #7473 | — | 2 | 1 | no | — |
| 63 | #7464 | — | 2 | 1 | no | — |
| 64 | #7464 | — | 2 | 1 | no | — |
| 65 | #7463 | — | 2 | 1 | no | — |
| 66 | #7463 | D4 | 1 | 2 | yes | — |
| 67 | #7386 | — | 2 | 2 | no | — |
| 68 | #7385 | — | 2 | 2 | no | — |
| 69 | #7330 | — | 2 | 1 | no | — |
| 70 | #7330 | — | 2 | 1 | no | — |
| 71 | #7181 | — | 4 | 1 | no | — |
| 72 | C2×#508 | — | 2 | 1 | no | — |
| 73 | #2989 | — | 8 | 1 | no | — |
| 74 | C4×#135 | — | 4 | 1 | no | — |
| 75 | #2262 | — | 2 | 1 | no | — |
| 76 | #2262 | — | 2 | 1 | no | — |
| 77 | #2262 | — | 2 | 1 | no | — |
| 78 | #2262 | — | 2 | 1 | no | — |
| 79 | C2×Q64 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 80 | C2×SD64 | — | 2 | 1 | no | — |
| 81 | C2×D32 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 82 | C2×M64 | — | 2 | 1 | no | — |
| 83 | C22×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 84 | C22×C32 | #41 | 1 | 1 | yes | characteristic |
| 85 | C4×Q32 | — | 2 | 1 | no | — |
| 86 | C4×Q32 | — | 2 | 1 | no | — |
| 87 | C4×SD32 | — | 4 | 1 | no | — |
| 88 | C4×SD32 | — | 4 | 1 | no | — |
| 89 | C4×D16 | — | 2 | 1 | no | — |
| 90 | C4×D16 | — | 2 | 1 | no | — |
| 91 | C2×#368 | — | 2 | 1 | no | — |
| 92 | #2158 | — | 2 | 1 | no | — |
| 93 | #2158 | — | 2 | 1 | no | — |
| 94 | #2153 | — | 8 | 1 | no | — |
| 95 | C2×#364 | — | 4 | 1 | no | — |
| 96 | #2138 | — | 4 | 1 | no | — |
| 97 | C4×M32 | D8 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | #1772 | — | 4 | 1 | no | — |
| 100 | #1592 | — | 8 | 2 | no | — |
| 101 | #1591 | — | 4 | 2 | no | — |
| 102 | #1589 | — | 4 | 2 | no | — |
| 103 | C2×#335 | — | 4 | 1 | no | — |
| 104 | #1477 | — | 8 | 1 | no | — |
| 105 | #1450 | D8 | 1 | 1 | yes | characteristic |
| 106 | M128 | — | 2 | 1 | no | — |
| 107 | M128 | — | 2 | 1 | no | — |
| 108 | M128 | — | 2 | 1 | no | — |
| 109 | M128 | — | 4 | 1 | no | — |
| 110 | M128 | — | 4 | 1 | no | — |
| 111 | M128 | M16 | 1 | 2 | yes | complemented |
| 112 | C2×C64 | — | 2 | 1 | no | — |
| 113 | C2×C64 | — | 2 | 2 | no | — |
| 114 | C2×C64 | — | 2 | 1 | no | — |
| 115 | #1425 | — | 2 | 1 | no | — |
| 116 | #1425 | M16 | 1 | 2 | yes | complemented |
| 117 | #1424 | — | 2 | 1 | no | — |
| 118 | #1424 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 119 | #1424 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 120 | #1423 | — | 2 | 1 | no | — |
| 121 | #1423 | — | 2 | 1 | no | — |
| 122 | #1416 | — | 2 | 1 | no | — |
| 123 | #1416 | — | 2 | 1 | no | — |
| 124 | #1415 | — | 2 | 1 | no | — |
| 125 | #1415 | — | 2 | 1 | no | — |
| 126 | #1397 | — | 2 | 1 | no | — |
| 127 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | #1397 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | #1397 | C2×Q8 | 1 | 1 | yes | characteristic |
| 130 | #1397 | #41 | 1 | 1 | yes | characteristic |
| 131 | C4×C32 | — | 2 | 1 | no | — |
| 132 | #1382 | — | 4 | 1 | no | — |
| 133 | #1378 | — | 8 | 1 | no | — |
| 134 | #1373 | — | 4 | 1 | no | — |
| 135 | #1373 | — | 4 | 1 | no | — |
| 136 | #1372 | — | 2 | 2 | no | — |
| 137 | #1372 | — | 4 | 1 | no | — |
| 138 | #1332 | — | 4 | 2 | no | — |
| 139 | #1331 | — | 4 | 2 | no | — |
| 140 | #1311 | — | 2 | 1 | no | — |
| 141 | C8×C16 | — | 2 | 1 | no | — |
| 142 | C2×#135 | — | 4 | 1 | no | — |
| 143 | C4×#41 | — | 8 | 1 | no | — |
| 144 | #508 | — | 4 | 1 | no | — |
| 145 | #508 | — | 4 | 1 | no | — |
| 146 | #508 | — | 4 | 1 | no | — |
| 147 | #508 | — | 4 | 1 | no | — |
| 148 | C2×Q32 | — | 2 | 1 | no | — |
| 149 | C2×SD32 | — | 4 | 1 | no | — |
| 150 | C2×D16 | — | 2 | 1 | no | — |
| 151 | C2×M32 | — | 2 | 1 | no | — |
| 152 | C2×M32 | — | 8 | 1 | no | — |
| 153 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 154 | C22×C16 | #135 | 1 | 1 | yes | characteristic |
| 155 | #446 | — | 8 | 2 | no | — |
| 156 | C4×Q16 | — | 4 | 1 | no | — |
| 157 | C4×Q16 | — | 4 | 1 | no | — |
| 158 | C4×SD16 | — | 8 | 1 | no | — |
| 159 | C4×SD16 | — | 8 | 1 | no | — |
| 160 | C4×D8 | — | 4 | 1 | no | — |
| 161 | C4×D8 | — | 4 | 1 | no | — |
| 162 | #436 | — | 8 | 2 | no | — |
| 163 | #435 | — | 16 | 2 | no | — |
| 164 | #432 | — | 16 | 1 | no | — |
| 165 | #431 | — | 2 | 1 | no | — |
| 166 | C2×#108 | — | 4 | 1 | no | — |
| 167 | #427 | — | 4 | 1 | no | — |
| 168 | #427 | — | 4 | 1 | no | — |
| 169 | #423 | — | 16 | 1 | no | — |
| 170 | C2×C4⋊C8 | — | 8 | 1 | no | — |
| 171 | #416 | — | 8 | 1 | no | — |
| 172 | #405 | — | 8 | 1 | no | — |
| 173 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 174 | Q64 | — | 2 | 1 | no | — |
| 175 | Q64 | — | 2 | 1 | no | — |
| 176 | SD64 | — | 4 | 1 | no | — |
| 177 | SD64 | — | 4 | 1 | no | — |
| 178 | D32 | — | 2 | 1 | no | — |
| 179 | D32 | — | 2 | 1 | no | — |
| 180 | M64 | — | 2 | 2 | no | — |
| 181 | M64 | — | 4 | 1 | no | — |
| 182 | C2×C32 | — | 2 | 1 | no | — |
| 183 | C2×C32 | — | 2 | 1 | no | — |
| 184 | C2×C32 | — | 4 | 1 | no | — |
| 185 | C2×C32 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 186 | C2×C32 | C4×D4 | 1 | 1 | yes | characteristic |
| 187 | C2×C32 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 188 | C2×C32 | #123 | 1 | 1 | yes | characteristic |
| 189 | C2×C32 | C2×M16 | 1 | 1 | yes | characteristic |
| 190 | C2×C32 | C2×M16 | 1 | 1 | yes | characteristic |
| 191 | C2×C32 | #131 | 1 | 1 | yes | characteristic |
| 192 | C2×C32 | #131 | 1 | 1 | yes | characteristic |
| 193 | #368 | — | 2 | 2 | no | — |
| 194 | #368 | — | 4 | 1 | no | — |
| 195 | #367 | — | 4 | 1 | no | — |
| 196 | #367 | — | 4 | 1 | no | — |
| 197 | #366 | — | 2 | 1 | no | — |
| 198 | #366 | — | 2 | 1 | no | — |
| 199 | #366 | — | 4 | 1 | no | — |
| 200 | #364 | — | 8 | 1 | no | — |
| 201 | #364 | — | 8 | 1 | no | — |
| 202 | #364 | — | 16 | 2 | no | — |
| 203 | #358 | — | 4 | 1 | no | — |
| 204 | #358 | — | 4 | 1 | no | — |
| 205 | #357 | — | 4 | 1 | no | — |
| 206 | #357 | — | 4 | 1 | no | — |
| 207 | #346 | — | 2 | 1 | no | — |
| 208 | C4×C16 | — | 2 | 1 | no | — |
| 209 | C4×C16 | #120 | 1 | 1 | yes | characteristic |
| 210 | C4×C16 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 211 | C4×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 212 | C4×C16 | #137 | 1 | 1 | yes | characteristic |
| 213 | #339 | — | 8 | 1 | no | — |
| 214 | #335 | — | 4 | 2 | no | — |
| 215 | #335 | — | 8 | 1 | no | — |
| 216 | Q8⋊C8 | — | 8 | 2 | no | — |
| 217 | D4⋊C8 | — | 8 | 2 | no | — |
| 218 | #322 | SD32 | 1 | 2 | yes | — |
| 219 | C82 | — | 2 | 1 | no | — |
| 220 | C64 | — | 2 | 2 | no | — |
| 221 | C64 | — | 4 | 2 | no | — |
| 222 | C64 | — | 4 | 1 | no | — |
| 223 | C2×#41 | — | 8 | 1 | no | — |
| 224 | #135 | — | 8 | 1 | no | — |
| 225 | #135 | — | 8 | 1 | no | — |
| 226 | #135 | — | 8 | 1 | no | — |
| 227 | #135 | — | 8 | 1 | no | — |
| 228 | C2×Q16 | — | 4 | 1 | no | — |
| 229 | C2×SD16 | — | 8 | 1 | no | — |
| 230 | C2×D8 | — | 4 | 1 | no | — |
| 231 | C2×M16 | — | 8 | 1 | no | — |
| 232 | C2×M16 | — | 16 | 2 | no | — |
| 233 | C22×C8 | — | 16 | 1 | no | — |
| 234 | C22×C8 | C4×D8 | 1 | 1 | yes | characteristic |
| 235 | C22×C8 | #509 | 1 | 1 | yes | characteristic |
| 236 | C4×Q8 | — | 8 | 1 | no | — |
| 237 | C4×Q8 | — | 8 | 1 | no | — |
| 238 | C4×D4 | — | 8 | 1 | no | — |
| 239 | C4×D4 | — | 8 | 1 | no | — |
| 240 | C4×D4 | — | 16 | 1 | no | — |
| 241 | C4×D4 | — | 16 | 1 | no | — |
| 242 | #117 | — | 8 | 1 | no | — |
| 243 | #117 | — | 8 | 1 | no | — |
| 244 | #117 | — | 16 | 1 | no | — |
| 245 | C2×C42 | — | 16 | 1 | no | — |
| 246 | C2×C42 | #509 | 1 | 1 | yes | characteristic |
| 247 | Q32 | — | 4 | 1 | no | — |
| 248 | Q32 | — | 4 | 1 | no | — |
| 249 | SD32 | — | 8 | 1 | no | — |
| 250 | SD32 | — | 8 | 1 | no | — |
| 251 | D16 | — | 4 | 1 | no | — |
| 252 | D16 | — | 4 | 1 | no | — |
| 253 | M32 | — | 4 | 1 | no | — |
| 254 | M32 | — | 4 | 1 | no | — |
| 255 | M32 | — | 16 | 1 | no | — |
| 256 | M32 | — | 16 | 1 | no | — |
| 257 | C2×C16 | — | 2 | 1 | no | — |
| 258 | C2×C16 | — | 2 | 1 | no | — |
| 259 | C2×C16 | — | 4 | 1 | no | — |
| 260 | C2×C16 | — | 16 | 1 | no | — |
| 261 | C2×C16 | #385 | 1 | 1 | yes | characteristic |
| 262 | C2×C16 | #435 | 1 | 1 | yes | characteristic |
| 263 | C2×C16 | #436 | 1 | 1 | yes | characteristic |
| 264 | C2×C16 | #440 | 1 | 1 | yes | characteristic |
| 265 | C2×C16 | #443 | 1 | 1 | yes | characteristic |
| 266 | C2×C16 | #444 | 1 | 1 | yes | characteristic |
| 267 | C2×C16 | #452 | 1 | 1 | yes | characteristic |
| 268 | C2×C16 | #478 | 1 | 1 | yes | characteristic |
| 269 | #108 | — | 4 | 2 | no | — |
| 270 | #108 | — | 8 | 1 | no | — |
| 271 | #107 | — | 4 | 1 | no | — |
| 272 | #107 | — | 4 | 1 | no | — |
| 273 | #107 | — | 8 | 1 | no | — |
| 274 | #106 | — | 8 | 1 | no | — |
| 275 | #106 | — | 8 | 1 | no | — |
| 276 | C4⋊C8 | — | 4 | 1 | no | — |
| 277 | C4⋊C8 | — | 8 | 2 | no | — |
| 278 | C4⋊C8 | — | 16 | 1 | no | — |
| 279 | C4⋊C8 | — | 16 | 2 | no | — |
| 280 | #103 | — | 8 | 1 | no | — |
| 281 | #103 | — | 8 | 1 | no | — |
| 282 | #102 | — | 8 | 1 | no | — |
| 283 | #102 | — | 8 | 1 | no | — |
| 284 | C22⋊C8 | — | 4 | 1 | no | — |
| 285 | C22⋊C8 | — | 16 | 2 | no | — |
| 286 | #97 | — | 16 | 1 | no | — |
| 287 | #97 | — | 16 | 2 | no | — |
| 288 | C4×C8 | — | 2 | 2 | no | — |
| 289 | C4×C8 | — | 16 | 1 | no | — |
| 290 | C4×C8 | #447 | 1 | 1 | yes | characteristic |
| 291 | C4×C8 | #474 | 1 | 1 | yes | characteristic |
| 292 | C4×C8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 293 | C4×C8 | #508 | 1 | 1 | yes | characteristic |
| 294 | C32 | — | 2 | 1 | no | — |
| 295 | C32 | — | 2 | 1 | no | — |
| 296 | C32 | — | 4 | 2 | no | — |
| 297 | C32 | #423 | 1 | 1 | yes | characteristic |
| 298 | C32 | #424 | 1 | 1 | yes | characteristic |
| 299 | C32 | #435 | 1 | 1 | yes | characteristic |
| 300 | C32 | #436 | 1 | 1 | yes | characteristic |
| 301 | #41 | — | 16 | 1 | no | — |
| 302 | #41 | — | 16 | 1 | no | — |
| 303 | #41 | — | 16 | 1 | no | — |
| 304 | #41 | — | 16 | 1 | no | — |
| 305 | C2×Q8 | — | 8 | 1 | no | — |
| 306 | C2×D4 | — | 8 | 1 | no | — |
| 307 | C2×D4 | — | 16 | 1 | no | — |
| 308 | C22×C4 | — | 2 | 1 | no | — |
| 309 | C22×C4 | — | 16 | 1 | no | — |
| 310 | C22×C4 | — | 16 | 1 | no | — |
| 311 | C22×C4 | — | 16 | 1 | no | — |
| 312 | C22×C4 | #2177 | 1 | 1 | yes | characteristic |
| 313 | Q16 | — | 8 | 1 | no | — |
| 314 | Q16 | — | 8 | 1 | no | — |
| 315 | SD16 | — | 16 | 1 | no | — |
| 316 | SD16 | — | 16 | 1 | no | — |
| 317 | D8 | — | 8 | 1 | no | — |
| 318 | D8 | — | 8 | 1 | no | — |
| 319 | M16 | — | 8 | 2 | no | — |
| 320 | M16 | — | 16 | 1 | no | — |
| 321 | M16 | — | 64 | 2 | no | — |
| 322 | C2×C8 | — | 2 | 1 | no | — |
| 323 | C2×C8 | — | 2 | 1 | no | — |
| 324 | C2×C8 | — | 4 | 2 | no | — |
| 325 | C2×C8 | — | 16 | 1 | no | — |
| 326 | C2×C8 | — | 16 | 2 | no | — |
| 327 | C2×C8 | — | 64 | 1 | no | — |
| 328 | C2×C8 | #1581 | 1 | 1 | yes | characteristic |
| 329 | C2×C8 | #1589 | 1 | 1 | yes | characteristic |
| 330 | C2×C8 | #1862 | 1 | 1 | yes | characteristic |
| 331 | C2×C8 | C4×SD32 | 1 | 1 | yes | characteristic |
| 332 | C2×C8 | #2178 | 1 | 1 | yes | characteristic |
| 333 | C2×C8 | #2179 | 1 | 1 | yes | characteristic |
| 334 | C2×C8 | #2186 | 1 | 1 | yes | characteristic |
| 335 | C2×C8 | #2226 | 1 | 1 | yes | characteristic |
| 336 | C4⋊C4 | — | 8 | 1 | no | — |
| 337 | C4⋊C4 | — | 8 | 1 | no | — |
| 338 | C4⋊C4 | — | 16 | 1 | no | — |
| 339 | C4⋊C4 | — | 16 | 1 | no | — |
| 340 | C4⋊C4 | — | 16 | 1 | no | — |
| 341 | C22⋊C4 | — | 16 | 1 | no | — |
| 342 | C22⋊C4 | — | 16 | 1 | no | — |
| 343 | C22⋊C4 | — | 16 | 1 | no | — |
| 344 | C22⋊C4 | — | 16 | 1 | no | — |
| 345 | C42 | — | 2 | 1 | no | — |
| 346 | C42 | — | 16 | 1 | no | — |
| 347 | C42 | — | 16 | 1 | no | — |
| 348 | C42 | — | 16 | 1 | no | — |
| 349 | C42 | — | 16 | 1 | no | — |
| 350 | C42 | #2187 | 1 | 1 | yes | characteristic |
| 351 | C42 | #2228 | 1 | 1 | yes | characteristic |
| 352 | C16 | — | 2 | 1 | no | — |
| 353 | C16 | — | 2 | 1 | no | — |
| 354 | C16 | — | 8 | 1 | no | — |
| 355 | C16 | — | 32 | 1 | no | — |
| 356 | C16 | #1588 | 1 | 1 | yes | characteristic |
| 357 | C16 | #1592 | 1 | 1 | yes | characteristic |
| 358 | C16 | #1851 | 1 | 1 | yes | characteristic |
| 359 | C16 | #1866 | 1 | 1 | yes | characteristic |
| 360 | C23 | — | 16 | 1 | no | — |
| 361 | C23 | #13658 | 1 | 1 | yes | characteristic |
| 362 | Q8 | — | 16 | 1 | no | — |
| 363 | Q8 | — | 16 | 1 | no | — |
| 364 | D4 | — | 16 | 1 | no | — |
| 365 | D4 | — | 16 | 1 | no | — |
| 366 | D4 | — | 32 | 1 | no | — |
| 367 | D4 | — | 32 | 1 | no | — |
| 368 | C2×C4 | — | 2 | 1 | no | — |
| 369 | C2×C4 | — | 2 | 1 | no | — |
| 370 | C2×C4 | — | 8 | 1 | no | — |
| 371 | C2×C4 | — | 16 | 1 | no | — |
| 372 | C2×C4 | — | 16 | 1 | no | — |
| 373 | C2×C4 | — | 16 | 1 | no | — |
| 374 | C2×C4 | — | 32 | 1 | no | — |
| 375 | C2×C4 | — | 32 | 1 | no | — |
| 376 | C2×C4 | — | 32 | 1 | no | — |
| 377 | C2×C4 | — | 32 | 1 | no | — |
| 378 | C2×C4 | — | 32 | 1 | no | — |
| 379 | C2×C4 | — | 64 | 1 | no | — |
| 380 | C2×C4 | #12073 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | #12086 | 1 | 1 | yes | characteristic |
| 382 | C2×C4 | #12937 | 1 | 1 | yes | characteristic |
| 383 | C2×C4 | #13657 | 1 | 1 | yes | characteristic |
| 384 | C2×C4 | #13658 | 1 | 1 | yes | characteristic |
| 385 | C2×C4 | #13658 | 1 | 1 | yes | characteristic |
| 386 | C8 | — | 2 | 1 | no | — |
| 387 | C8 | — | 2 | 1 | no | — |
| 388 | C8 | — | 8 | 2 | no | — |
| 389 | C8 | — | 16 | 2 | no | — |
| 390 | C8 | — | 32 | 2 | no | — |
| 391 | C8 | #8847 | 1 | 1 | yes | characteristic |
| 392 | C8 | #12071 | 1 | 1 | yes | characteristic |
| 393 | C8 | #12082 | 1 | 1 | yes | characteristic |
| 394 | C8 | #12939 | 1 | 1 | yes | characteristic |
| 395 | C22 | — | 4 | 1 | no | — |
| 396 | C22 | — | 32 | 1 | no | — |
| 397 | C22 | — | 32 | 1 | no | — |
| 398 | C22 | — | 32 | 1 | no | — |
| 399 | C22 | #151117 | 1 | 1 | yes | characteristic |
| 400 | C22 | #151129 | 1 | 1 | yes | characteristic |
| 401 | C22 | #152454 | 1 | 1 | yes | characteristic |
| 402 | C4 | — | 4 | 1 | no | — |
| 403 | C4 | — | 4 | 1 | no | — |
| 404 | C4 | — | 32 | 1 | no | — |
| 405 | C4 | — | 32 | 1 | no | — |
| 406 | C4 | — | 32 | 1 | no | — |
| 407 | C4 | — | 64 | 1 | no | — |
| 408 | C4 | #135921 | 1 | 1 | yes | characteristic |
| 409 | C4 | #151115 | 1 | 1 | yes | characteristic |
| 410 | C4 | #151127 | 1 | 1 | yes | characteristic |
| 411 | C4 | #152453 | 1 | 1 | yes | characteristic |
| 412 | C2 | — | 2 | 1 | no | — |
| 413 | C2 | — | 2 | 1 | no | — |
| 414 | C2 | — | 2 | 1 | no | — |
| 415 | C2 | — | 64 | 1 | no | — |
| 416 | C2 | #72321047 | 1 | 1 | yes | characteristic |
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