← #72321260
Subgroups — #72321260
Order 2048.
705 conjugacy classes of subgroups.
The subgroup lattice has 547 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72321145 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72321124 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72286872 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #72286396 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72234369 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #512934 | C4 | 1 | 1 | yes | characteristic |
| 7 | C2×#13656 | C22 | 1 | 1 | yes | characteristic |
| 8 | C22×#1397 | C22 | 1 | 1 | yes | characteristic |
| 9 | #495879 | — | 2 | 1 | no | — |
| 10 | #483403 | — | 2 | 1 | no | — |
| 11 | #153427 | — | 2 | 1 | no | — |
| 12 | C2×#7511 | C22 | 1 | 2 | yes | — |
| 13 | #152976 | C4 | 1 | 1 | yes | characteristic |
| 14 | #152856 | C4 | 1 | 1 | yes | characteristic |
| 15 | #152835 | — | 2 | 1 | no | — |
| 16 | #152633 | — | 2 | 1 | no | — |
| 17 | #152292 | C4 | 1 | 1 | yes | characteristic |
| 18 | #151996 | C22 | 1 | 1 | yes | characteristic |
| 19 | #151964 | — | 2 | 1 | no | — |
| 20 | #151054 | — | 2 | 4 | no | — |
| 21 | #151037 | — | 2 | 1 | no | — |
| 22 | #151037 | C22 | 1 | 2 | yes | — |
| 23 | #94756 | — | 2 | 1 | no | — |
| 24 | #94613 | — | 2 | 4 | no | — |
| 25 | C2×#2262 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C23×C32 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C23×C32 | D4 | 1 | 1 | yes | characteristic |
| 28 | #33600 | — | 2 | 1 | no | — |
| 29 | C2×#2178 | — | 2 | 1 | no | — |
| 30 | C22×C4×C16 | D4 | 1 | 1 | yes | characteristic |
| 31 | #21544 | — | 4 | 1 | no | — |
| 32 | #17793 | — | 4 | 1 | no | — |
| 33 | C2×M128 | — | 2 | 2 | no | — |
| 34 | #13696 | — | 2 | 2 | no | — |
| 35 | #13695 | — | 2 | 1 | no | — |
| 36 | #13694 | — | 2 | 1 | no | — |
| 37 | #13656 | — | 2 | 2 | no | — |
| 38 | #13656 | — | 2 | 2 | no | — |
| 39 | C2×#1425 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C2×#1425 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | #13633 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C2×#1417 | — | 2 | 1 | no | — |
| 43 | C2×#1417 | — | 2 | 1 | no | — |
| 44 | #13615 | — | 2 | 1 | no | — |
| 45 | C2×#1397 | — | 2 | 2 | no | — |
| 46 | C2×#1397 | — | 2 | 2 | no | — |
| 47 | C2×#1397 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C2×#1397 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×#1397 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×#1397 | C23 | 1 | 1 | yes | characteristic |
| 51 | #13241 | — | 2 | 1 | no | — |
| 52 | #13169 | — | 2 | 1 | no | — |
| 53 | #13151 | — | 4 | 1 | no | — |
| 54 | #13063 | — | 4 | 1 | no | — |
| 55 | #12837 | — | 2 | 1 | no | — |
| 56 | #12670 | — | 2 | 1 | no | — |
| 57 | #12641 | — | 4 | 1 | no | — |
| 58 | #12024 | — | 2 | 2 | no | — |
| 59 | #12024 | — | 4 | 1 | no | — |
| 60 | #12023 | — | 2 | 2 | no | — |
| 61 | #12022 | — | 4 | 1 | no | — |
| 62 | #12008 | — | 2 | 2 | no | — |
| 63 | #12008 | — | 4 | 1 | no | — |
| 64 | C22⋊C64 | — | 2 | 4 | no | — |
| 65 | #7511 | — | 2 | 2 | no | — |
| 66 | #7511 | — | 2 | 2 | no | — |
| 67 | #7473 | — | 2 | 1 | no | — |
| 68 | #7473 | — | 2 | 1 | no | — |
| 69 | #7472 | — | 2 | 1 | no | — |
| 70 | #7463 | — | 2 | 4 | no | — |
| 71 | #7463 | — | 2 | 2 | no | — |
| 72 | #7463 | D4 | 1 | 4 | yes | complemented |
| 73 | C2×#508 | — | 2 | 1 | no | — |
| 74 | C23×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 75 | C23×C16 | SD16 | 1 | 1 | yes | characteristic |
| 76 | #3050 | — | 4 | 1 | no | — |
| 77 | C2×#443 | — | 4 | 1 | no | — |
| 78 | #2929 | — | 8 | 1 | no | — |
| 79 | #2920 | — | 8 | 1 | no | — |
| 80 | C22×C4×C8 | D8 | 1 | 1 | yes | characteristic |
| 81 | #2262 | — | 2 | 2 | no | — |
| 82 | #2262 | — | 2 | 2 | no | — |
| 83 | C2×Q64 | M16 | 1 | 1 | yes | characteristic, complemented |
| 84 | C2×SD64 | — | 2 | 1 | no | — |
| 85 | C2×D32 | M16 | 1 | 1 | yes | characteristic, complemented |
| 86 | C22×C32 | — | 2 | 2 | no | — |
| 87 | C22×C32 | — | 2 | 2 | no | — |
| 88 | C22×C32 | — | 2 | 2 | no | — |
| 89 | C22×C32 | — | 2 | 1 | no | — |
| 90 | C22×C32 | — | 2 | 1 | no | — |
| 91 | C22×C32 | — | 2 | 2 | no | — |
| 92 | C22×C32 | — | 4 | 1 | no | — |
| 93 | C22×C32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 94 | C22×C32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 95 | C22×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 96 | C22×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | #2217 | — | 4 | 2 | no | — |
| 98 | #2216 | — | 2 | 2 | no | — |
| 99 | #2215 | — | 2 | 2 | no | — |
| 100 | #2178 | — | 4 | 1 | no | — |
| 101 | #2178 | — | 4 | 1 | no | — |
| 102 | #2178 | — | 4 | 1 | no | — |
| 103 | #2178 | — | 4 | 1 | no | — |
| 104 | C2×#368 | — | 2 | 1 | no | — |
| 105 | C2×#368 | — | 2 | 1 | no | — |
| 106 | #2158 | — | 2 | 1 | no | — |
| 107 | C2×#359 | — | 4 | 1 | no | — |
| 108 | C2×#359 | — | 4 | 1 | no | — |
| 109 | #2138 | — | 4 | 1 | no | — |
| 110 | C2×C4×C16 | — | 2 | 1 | no | — |
| 111 | C2×C4×C16 | — | 2 | 1 | no | — |
| 112 | C2×C4×C16 | — | 2 | 1 | no | — |
| 113 | C2×C4×C16 | — | 2 | 1 | no | — |
| 114 | C2×C4×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C16 | D8 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C16 | SD16 | 1 | 1 | yes | characteristic |
| 117 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | #1974 | — | 4 | 1 | no | — |
| 119 | #1945 | — | 4 | 1 | no | — |
| 120 | #1937 | — | 8 | 1 | no | — |
| 121 | #1896 | — | 8 | 1 | no | — |
| 122 | #1810 | — | 4 | 1 | no | — |
| 123 | #1772 | — | 4 | 1 | no | — |
| 124 | #1764 | — | 8 | 1 | no | — |
| 125 | #1568 | — | 4 | 2 | no | — |
| 126 | #1568 | — | 8 | 1 | no | — |
| 127 | #1567 | — | 4 | 2 | no | — |
| 128 | #1566 | — | 8 | 1 | no | — |
| 129 | #1564 | — | 4 | 2 | no | — |
| 130 | #1564 | — | 8 | 1 | no | — |
| 131 | M128 | — | 4 | 2 | no | — |
| 132 | M128 | — | 4 | 2 | no | — |
| 133 | C2×C64 | — | 2 | 4 | no | — |
| 134 | #1425 | — | 2 | 2 | no | — |
| 135 | #1425 | — | 2 | 2 | no | — |
| 136 | #1424 | M16 | 1 | 2 | yes | complemented |
| 137 | #1423 | — | 2 | 1 | no | — |
| 138 | #1417 | — | 4 | 2 | no | — |
| 139 | #1417 | — | 4 | 2 | no | — |
| 140 | #1416 | — | 2 | 2 | no | — |
| 141 | #1415 | — | 2 | 2 | no | — |
| 142 | #1397 | — | 2 | 2 | no | — |
| 143 | #1397 | — | 2 | 2 | no | — |
| 144 | #1397 | — | 2 | 1 | no | — |
| 145 | #1397 | — | 2 | 1 | no | — |
| 146 | #1397 | C2×D4 | 1 | 2 | yes | — |
| 147 | #1397 | #41 | 1 | 2 | yes | — |
| 148 | #1382 | — | 4 | 1 | no | — |
| 149 | #1382 | — | 4 | 1 | no | — |
| 150 | #1381 | — | 4 | 1 | no | — |
| 151 | #1372 | — | 2 | 4 | no | — |
| 152 | #1372 | — | 4 | 2 | no | — |
| 153 | #1371 | — | 4 | 2 | no | — |
| 154 | #1371 | — | 4 | 2 | no | — |
| 155 | C2×#135 | — | 4 | 1 | no | — |
| 156 | C2×#131 | — | 8 | 1 | no | — |
| 157 | C23×C8 | #102 | 1 | 1 | yes | characteristic |
| 158 | C23×C8 | SD32 | 1 | 1 | yes | characteristic |
| 159 | #525 | — | 8 | 1 | no | — |
| 160 | C22×C42 | D16 | 1 | 1 | yes | characteristic |
| 161 | #508 | — | 4 | 1 | no | — |
| 162 | #508 | — | 4 | 1 | no | — |
| 163 | #508 | — | 4 | 1 | no | — |
| 164 | #508 | — | 4 | 1 | no | — |
| 165 | C2×Q32 | — | 2 | 1 | no | — |
| 166 | C2×SD32 | — | 4 | 1 | no | — |
| 167 | C2×D16 | — | 2 | 1 | no | — |
| 168 | C22×C16 | — | 2 | 2 | no | — |
| 169 | C22×C16 | — | 2 | 1 | no | — |
| 170 | C22×C16 | — | 2 | 1 | no | — |
| 171 | C22×C16 | — | 2 | 1 | no | — |
| 172 | C22×C16 | — | 2 | 1 | no | — |
| 173 | C22×C16 | — | 2 | 1 | no | — |
| 174 | C22×C16 | — | 2 | 1 | no | — |
| 175 | C22×C16 | — | 2 | 1 | no | — |
| 176 | C22×C16 | — | 2 | 1 | no | — |
| 177 | C22×C16 | — | 4 | 1 | no | — |
| 178 | C22×C16 | #102 | 1 | 1 | yes | characteristic |
| 179 | C22×C16 | #102 | 1 | 1 | yes | characteristic |
| 180 | C22×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 181 | C22×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 182 | #467 | — | 4 | 2 | no | — |
| 183 | #466 | — | 4 | 2 | no | — |
| 184 | #465 | — | 8 | 2 | no | — |
| 185 | #443 | — | 8 | 1 | no | — |
| 186 | #443 | — | 8 | 1 | no | — |
| 187 | #443 | — | 8 | 1 | no | — |
| 188 | #443 | — | 8 | 1 | no | — |
| 189 | #435 | — | 16 | 2 | no | — |
| 190 | C8×D4 | — | 16 | 2 | no | — |
| 191 | #432 | — | 8 | 2 | no | — |
| 192 | #432 | — | 16 | 1 | no | — |
| 193 | #431 | — | 8 | 2 | no | — |
| 194 | #431 | — | 16 | 1 | no | — |
| 195 | C2×#108 | — | 4 | 1 | no | — |
| 196 | C2×#108 | — | 4 | 1 | no | — |
| 197 | #427 | — | 4 | 1 | no | — |
| 198 | #424 | — | 8 | 1 | no | — |
| 199 | #423 | — | 8 | 2 | no | — |
| 200 | C2×#104 | — | 8 | 1 | no | — |
| 201 | C2×#104 | — | 8 | 1 | no | — |
| 202 | #416 | — | 8 | 1 | no | — |
| 203 | #408 | — | 8 | 1 | no | — |
| 204 | #407 | — | 8 | 1 | no | — |
| 205 | #407 | — | 16 | 1 | no | — |
| 206 | #405 | — | 8 | 1 | no | — |
| 207 | C4×M16 | — | 16 | 1 | no | — |
| 208 | C2×C4×C8 | — | 2 | 1 | no | — |
| 209 | C2×C4×C8 | — | 2 | 1 | no | — |
| 210 | C2×C4×C8 | — | 2 | 1 | no | — |
| 211 | C2×C4×C8 | — | 2 | 1 | no | — |
| 212 | C2×C4×C8 | #102 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×C8 | D16 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C8 | SD32 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 216 | Q64 | — | 2 | 2 | no | — |
| 217 | SD64 | — | 4 | 2 | no | — |
| 218 | D32 | — | 2 | 2 | no | — |
| 219 | C2×C32 | — | 2 | 1 | no | — |
| 220 | C2×C32 | — | 2 | 1 | no | — |
| 221 | C2×C32 | — | 2 | 1 | no | — |
| 222 | C2×C32 | — | 2 | 1 | no | — |
| 223 | C2×C32 | — | 2 | 1 | no | — |
| 224 | C2×C32 | — | 2 | 1 | no | — |
| 225 | C2×C32 | — | 2 | 1 | no | — |
| 226 | C2×C32 | — | 4 | 4 | no | — |
| 227 | C2×C32 | — | 4 | 2 | no | — |
| 228 | C2×C32 | — | 4 | 2 | no | — |
| 229 | C2×C32 | #104 | 1 | 2 | yes | — |
| 230 | C2×C32 | C4×D4 | 1 | 2 | yes | — |
| 231 | C2×C32 | #121 | 1 | 2 | yes | — |
| 232 | C2×C32 | C2×M16 | 1 | 1 | yes | characteristic |
| 233 | C2×C32 | C2×M16 | 1 | 1 | yes | characteristic |
| 234 | C2×C32 | #131 | 1 | 2 | yes | — |
| 235 | #368 | — | 4 | 1 | no | — |
| 236 | #368 | — | 4 | 1 | no | — |
| 237 | #368 | — | 4 | 1 | no | — |
| 238 | #368 | — | 4 | 1 | no | — |
| 239 | #367 | — | 4 | 1 | no | — |
| 240 | #366 | — | 2 | 2 | no | — |
| 241 | #359 | — | 8 | 2 | no | — |
| 242 | #359 | — | 8 | 1 | no | — |
| 243 | #359 | — | 8 | 1 | no | — |
| 244 | #358 | — | 4 | 2 | no | — |
| 245 | #357 | — | 4 | 2 | no | — |
| 246 | C4×C16 | — | 2 | 1 | no | — |
| 247 | C4×C16 | — | 2 | 1 | no | — |
| 248 | C4×C16 | — | 2 | 1 | no | — |
| 249 | C4×C16 | — | 2 | 1 | no | — |
| 250 | C4×C16 | — | 2 | 1 | no | — |
| 251 | C4×C16 | — | 2 | 1 | no | — |
| 252 | C4×C16 | #120 | 1 | 1 | yes | characteristic |
| 253 | C4×C16 | #123 | 1 | 1 | yes | characteristic |
| 254 | C4×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 255 | C4×C16 | #137 | 1 | 1 | yes | characteristic |
| 256 | #341 | — | 8 | 1 | no | — |
| 257 | #339 | — | 8 | 1 | no | — |
| 258 | #339 | — | 8 | 1 | no | — |
| 259 | #335 | — | 4 | 4 | no | — |
| 260 | #335 | — | 8 | 2 | no | — |
| 261 | #334 | — | 8 | 2 | no | — |
| 262 | #334 | — | 8 | 2 | no | — |
| 263 | C64 | — | 4 | 4 | no | — |
| 264 | C2×#41 | — | 8 | 1 | no | — |
| 265 | C23×C4 | — | 2 | 1 | no | — |
| 266 | C23×C4 | #357 | 1 | 1 | yes | characteristic |
| 267 | #135 | — | 8 | 1 | no | — |
| 268 | #135 | — | 8 | 1 | no | — |
| 269 | #135 | — | 8 | 1 | no | — |
| 270 | #135 | — | 8 | 1 | no | — |
| 271 | C2×Q16 | — | 4 | 1 | no | — |
| 272 | C2×SD16 | — | 8 | 1 | no | — |
| 273 | C2×D8 | — | 4 | 1 | no | — |
| 274 | #131 | — | 16 | 1 | no | — |
| 275 | #131 | — | 16 | 1 | no | — |
| 276 | #131 | — | 16 | 1 | no | — |
| 277 | #131 | — | 16 | 1 | no | — |
| 278 | C2×M16 | — | 8 | 1 | no | — |
| 279 | C2×M16 | — | 8 | 1 | no | — |
| 280 | C2×M16 | — | 16 | 1 | no | — |
| 281 | C2×M16 | — | 16 | 2 | no | — |
| 282 | C22×C8 | — | 2 | 1 | no | — |
| 283 | C22×C8 | — | 2 | 1 | no | — |
| 284 | C22×C8 | — | 2 | 1 | no | — |
| 285 | C22×C8 | — | 2 | 1 | no | — |
| 286 | C22×C8 | — | 2 | 1 | no | — |
| 287 | C22×C8 | — | 2 | 2 | no | — |
| 288 | C22×C8 | — | 2 | 1 | no | — |
| 289 | C22×C8 | — | 2 | 1 | no | — |
| 290 | C22×C8 | — | 2 | 1 | no | — |
| 291 | C22×C8 | — | 4 | 1 | no | — |
| 292 | C22×C8 | — | 16 | 1 | no | — |
| 293 | C22×C8 | #357 | 1 | 1 | yes | characteristic |
| 294 | C22×C8 | #357 | 1 | 1 | yes | characteristic |
| 295 | C22×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 296 | C22×C8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 297 | #123 | — | 16 | 1 | no | — |
| 298 | C22⋊Q8 | — | 8 | 2 | no | — |
| 299 | #121 | — | 8 | 2 | no | — |
| 300 | #120 | — | 16 | 1 | no | — |
| 301 | C4×D4 | — | 16 | 2 | no | — |
| 302 | #117 | — | 8 | 1 | no | — |
| 303 | C2×C42 | — | 2 | 1 | no | — |
| 304 | C2×C42 | — | 2 | 1 | no | — |
| 305 | C2×C42 | — | 2 | 1 | no | — |
| 306 | C2×C42 | — | 2 | 1 | no | — |
| 307 | C2×C42 | — | 2 | 1 | no | — |
| 308 | C2×C42 | #357 | 1 | 1 | yes | characteristic |
| 309 | C2×C42 | C2×D16 | 1 | 1 | yes | characteristic |
| 310 | Q32 | — | 4 | 1 | no | — |
| 311 | Q32 | — | 4 | 1 | no | — |
| 312 | SD32 | — | 8 | 1 | no | — |
| 313 | SD32 | — | 8 | 1 | no | — |
| 314 | D16 | — | 4 | 1 | no | — |
| 315 | D16 | — | 4 | 1 | no | — |
| 316 | C2×C16 | — | 2 | 1 | no | — |
| 317 | C2×C16 | — | 2 | 1 | no | — |
| 318 | C2×C16 | — | 2 | 1 | no | — |
| 319 | C2×C16 | — | 2 | 1 | no | — |
| 320 | C2×C16 | — | 2 | 1 | no | — |
| 321 | C2×C16 | — | 2 | 1 | no | — |
| 322 | C2×C16 | — | 2 | 1 | no | — |
| 323 | C2×C16 | — | 4 | 2 | no | — |
| 324 | C2×C16 | — | 4 | 2 | no | — |
| 325 | C2×C16 | — | 4 | 1 | no | — |
| 326 | C2×C16 | — | 4 | 1 | no | — |
| 327 | C2×C16 | — | 4 | 1 | no | — |
| 328 | C2×C16 | — | 4 | 1 | no | — |
| 329 | C2×C16 | #359 | 1 | 2 | yes | — |
| 330 | C2×C16 | #386 | 1 | 1 | yes | characteristic |
| 331 | C2×C16 | #407 | 1 | 1 | yes | characteristic |
| 332 | C2×C16 | #408 | 1 | 1 | yes | characteristic |
| 333 | C2×C16 | #417 | 1 | 1 | yes | characteristic |
| 334 | C2×C16 | C2×#104 | 1 | 1 | yes | characteristic |
| 335 | C2×C16 | #421 | 1 | 1 | yes | characteristic |
| 336 | C2×C16 | #448 | 1 | 1 | yes | characteristic |
| 337 | C2×C16 | #481 | 1 | 1 | yes | characteristic |
| 338 | #108 | — | 8 | 1 | no | — |
| 339 | #108 | — | 8 | 1 | no | — |
| 340 | #108 | — | 8 | 1 | no | — |
| 341 | #108 | — | 8 | 1 | no | — |
| 342 | #107 | — | 4 | 2 | no | — |
| 343 | #106 | — | 8 | 1 | no | — |
| 344 | C4⋊C8 | — | 8 | 4 | no | — |
| 345 | C4⋊C8 | — | 16 | 2 | no | — |
| 346 | C4⋊C8 | — | 16 | 2 | no | — |
| 347 | #104 | — | 16 | 1 | no | — |
| 348 | #104 | — | 16 | 1 | no | — |
| 349 | #104 | — | 16 | 1 | no | — |
| 350 | #104 | — | 16 | 1 | no | — |
| 351 | #103 | — | 8 | 2 | no | — |
| 352 | #102 | — | 8 | 2 | no | — |
| 353 | C22⋊C8 | — | 16 | 2 | no | — |
| 354 | C22⋊C8 | — | 16 | 2 | no | — |
| 355 | C22⋊C8 | — | 16 | 2 | no | — |
| 356 | C22⋊C8 | — | 16 | 2 | no | — |
| 357 | #97 | — | 16 | 2 | no | — |
| 358 | #97 | — | 16 | 1 | no | — |
| 359 | C4×C8 | — | 2 | 1 | no | — |
| 360 | C4×C8 | — | 2 | 1 | no | — |
| 361 | C4×C8 | — | 2 | 1 | no | — |
| 362 | C4×C8 | — | 2 | 1 | no | — |
| 363 | C4×C8 | — | 2 | 1 | no | — |
| 364 | C4×C8 | — | 2 | 1 | no | — |
| 365 | C4×C8 | — | 16 | 2 | no | — |
| 366 | C4×C8 | — | 16 | 1 | no | — |
| 367 | C4×C8 | #447 | 1 | 1 | yes | characteristic |
| 368 | C4×C8 | #480 | 1 | 1 | yes | characteristic |
| 369 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 370 | C4×C8 | #510 | 1 | 1 | yes | characteristic |
| 371 | C32 | — | 2 | 2 | no | — |
| 372 | C32 | — | 2 | 2 | no | — |
| 373 | C32 | — | 4 | 1 | no | — |
| 374 | C32 | #435 | 1 | 2 | yes | — |
| 375 | C32 | #436 | 1 | 2 | yes | — |
| 376 | C24 | #1418 | 1 | 1 | yes | characteristic |
| 377 | #41 | — | 16 | 1 | no | — |
| 378 | #41 | — | 16 | 1 | no | — |
| 379 | #41 | — | 16 | 1 | no | — |
| 380 | #41 | — | 16 | 1 | no | — |
| 381 | C2×Q8 | — | 8 | 1 | no | — |
| 382 | C2×D4 | — | 8 | 1 | no | — |
| 383 | C2×D4 | — | 16 | 2 | no | — |
| 384 | C2×D4 | — | 16 | 1 | no | — |
| 385 | C22×C4 | — | 2 | 1 | no | — |
| 386 | C22×C4 | — | 2 | 1 | no | — |
| 387 | C22×C4 | — | 2 | 1 | no | — |
| 388 | C22×C4 | — | 2 | 1 | no | — |
| 389 | C22×C4 | — | 2 | 1 | no | — |
| 390 | C22×C4 | — | 2 | 1 | no | — |
| 391 | C22×C4 | — | 2 | 1 | no | — |
| 392 | C22×C4 | — | 2 | 1 | no | — |
| 393 | C22×C4 | — | 2 | 1 | no | — |
| 394 | C22×C4 | — | 2 | 1 | no | — |
| 395 | C22×C4 | — | 2 | 1 | no | — |
| 396 | C22×C4 | — | 2 | 1 | no | — |
| 397 | C22×C4 | — | 8 | 2 | no | — |
| 398 | C22×C4 | — | 16 | 1 | no | — |
| 399 | C22×C4 | #1418 | 1 | 1 | yes | characteristic |
| 400 | C22×C4 | C2×#357 | 1 | 1 | yes | characteristic |
| 401 | Q16 | — | 8 | 1 | no | — |
| 402 | Q16 | — | 8 | 1 | no | — |
| 403 | SD16 | — | 16 | 1 | no | — |
| 404 | SD16 | — | 16 | 1 | no | — |
| 405 | D8 | — | 8 | 1 | no | — |
| 406 | D8 | — | 8 | 1 | no | — |
| 407 | M16 | — | 16 | 1 | no | — |
| 408 | M16 | — | 16 | 1 | no | — |
| 409 | M16 | — | 16 | 1 | no | — |
| 410 | M16 | — | 16 | 1 | no | — |
| 411 | M16 | — | 32 | 1 | no | — |
| 412 | M16 | — | 32 | 1 | no | — |
| 413 | M16 | — | 32 | 4 | no | — |
| 414 | C2×C8 | — | 2 | 1 | no | — |
| 415 | C2×C8 | — | 2 | 1 | no | — |
| 416 | C2×C8 | — | 2 | 1 | no | — |
| 417 | C2×C8 | — | 2 | 1 | no | — |
| 418 | C2×C8 | — | 2 | 1 | no | — |
| 419 | C2×C8 | — | 2 | 1 | no | — |
| 420 | C2×C8 | — | 2 | 1 | no | — |
| 421 | C2×C8 | — | 4 | 2 | no | — |
| 422 | C2×C8 | — | 4 | 2 | no | — |
| 423 | C2×C8 | — | 4 | 1 | no | — |
| 424 | C2×C8 | — | 4 | 1 | no | — |
| 425 | C2×C8 | — | 4 | 1 | no | — |
| 426 | C2×C8 | — | 4 | 1 | no | — |
| 427 | C2×C8 | — | 16 | 4 | no | — |
| 428 | C2×C8 | — | 16 | 1 | no | — |
| 429 | C2×C8 | — | 16 | 1 | no | — |
| 430 | C2×C8 | — | 32 | 1 | no | — |
| 431 | C2×C8 | — | 32 | 1 | no | — |
| 432 | C2×C8 | #1419 | 1 | 2 | yes | — |
| 433 | C2×C8 | #1486 | 1 | 1 | yes | characteristic |
| 434 | C2×C8 | #1492 | 1 | 1 | yes | characteristic |
| 435 | C2×C8 | #1874 | 1 | 1 | yes | characteristic |
| 436 | C2×C8 | #2139 | 1 | 1 | yes | characteristic |
| 437 | C2×C8 | C2×#359 | 1 | 1 | yes | characteristic |
| 438 | C2×C8 | #2143 | 1 | 1 | yes | characteristic |
| 439 | C2×C8 | #2185 | 1 | 1 | yes | characteristic |
| 440 | C2×C8 | #2233 | 1 | 1 | yes | characteristic |
| 441 | C4⋊C4 | — | 8 | 2 | no | — |
| 442 | C4⋊C4 | — | 16 | 2 | no | — |
| 443 | C22⋊C4 | — | 16 | 2 | no | — |
| 444 | C22⋊C4 | — | 16 | 2 | no | — |
| 445 | C22⋊C4 | — | 16 | 1 | no | — |
| 446 | C42 | — | 2 | 1 | no | — |
| 447 | C42 | — | 2 | 1 | no | — |
| 448 | C42 | — | 2 | 1 | no | — |
| 449 | C42 | — | 2 | 1 | no | — |
| 450 | C42 | — | 2 | 1 | no | — |
| 451 | C42 | — | 2 | 1 | no | — |
| 452 | C42 | — | 16 | 1 | no | — |
| 453 | C42 | #1418 | 1 | 1 | yes | characteristic |
| 454 | C42 | #1418 | 1 | 1 | yes | characteristic |
| 455 | C42 | #2184 | 1 | 1 | yes | characteristic |
| 456 | C42 | #2232 | 1 | 1 | yes | characteristic |
| 457 | C16 | — | 2 | 2 | no | — |
| 458 | C16 | — | 2 | 1 | no | — |
| 459 | C16 | — | 2 | 1 | no | — |
| 460 | C16 | — | 4 | 1 | no | — |
| 461 | C16 | #1489 | 1 | 1 | yes | characteristic |
| 462 | C16 | #1495 | 1 | 1 | yes | characteristic |
| 463 | C16 | #1870 | 1 | 1 | yes | characteristic |
| 464 | C16 | #1871 | 1 | 1 | yes | characteristic |
| 465 | C23 | — | 2 | 1 | no | — |
| 466 | C23 | — | 2 | 1 | no | — |
| 467 | C23 | — | 2 | 1 | no | — |
| 468 | C23 | — | 4 | 2 | no | — |
| 469 | C23 | — | 16 | 1 | no | — |
| 470 | C23 | C2×#1418 | 1 | 1 | yes | characteristic |
| 471 | Q8 | — | 16 | 1 | no | — |
| 472 | Q8 | — | 16 | 1 | no | — |
| 473 | D4 | — | 16 | 1 | no | — |
| 474 | D4 | — | 16 | 1 | no | — |
| 475 | D4 | — | 32 | 4 | no | — |
| 476 | D4 | — | 32 | 1 | no | — |
| 477 | D4 | — | 32 | 1 | no | — |
| 478 | C2×C4 | — | 2 | 1 | no | — |
| 479 | C2×C4 | — | 2 | 1 | no | — |
| 480 | C2×C4 | — | 2 | 1 | no | — |
| 481 | C2×C4 | — | 2 | 1 | no | — |
| 482 | C2×C4 | — | 2 | 1 | no | — |
| 483 | C2×C4 | — | 2 | 1 | no | — |
| 484 | C2×C4 | — | 2 | 1 | no | — |
| 485 | C2×C4 | — | 4 | 2 | no | — |
| 486 | C2×C4 | — | 4 | 2 | no | — |
| 487 | C2×C4 | — | 4 | 1 | no | — |
| 488 | C2×C4 | — | 4 | 1 | no | — |
| 489 | C2×C4 | — | 4 | 1 | no | — |
| 490 | C2×C4 | — | 4 | 1 | no | — |
| 491 | C2×C4 | — | 8 | 1 | no | — |
| 492 | C2×C4 | — | 8 | 1 | no | — |
| 493 | C2×C4 | — | 8 | 1 | no | — |
| 494 | C2×C4 | — | 8 | 1 | no | — |
| 495 | C2×C4 | — | 16 | 2 | no | — |
| 496 | C2×C4 | — | 16 | 1 | no | — |
| 497 | C2×C4 | — | 32 | 1 | no | — |
| 498 | C2×C4 | — | 32 | 1 | no | — |
| 499 | C2×C4 | #11657 | 1 | 1 | yes | characteristic |
| 500 | C2×C4 | #11671 | 1 | 1 | yes | characteristic |
| 501 | C2×C4 | #12991 | 1 | 1 | yes | characteristic |
| 502 | C2×C4 | C2×#1418 | 1 | 1 | yes | characteristic |
| 503 | C2×C4 | C2×#1419 | 1 | 1 | yes | characteristic |
| 504 | C2×C4 | #13625 | 1 | 1 | yes | characteristic |
| 505 | C8 | — | 2 | 1 | no | — |
| 506 | C8 | — | 2 | 1 | no | — |
| 507 | C8 | — | 2 | 2 | no | — |
| 508 | C8 | — | 4 | 1 | no | — |
| 509 | C8 | — | 32 | 4 | no | — |
| 510 | C8 | — | 32 | 1 | no | — |
| 511 | C8 | — | 32 | 1 | no | — |
| 512 | C8 | #8944 | 1 | 1 | yes | characteristic |
| 513 | C8 | #11660 | 1 | 1 | yes | characteristic |
| 514 | C8 | #11674 | 1 | 1 | yes | characteristic |
| 515 | C8 | #12990 | 1 | 1 | yes | characteristic |
| 516 | C22 | — | 2 | 2 | no | — |
| 517 | C22 | — | 2 | 2 | no | — |
| 518 | C22 | — | 2 | 2 | no | — |
| 519 | C22 | — | 4 | 1 | no | — |
| 520 | C22 | — | 4 | 1 | no | — |
| 521 | C22 | — | 4 | 1 | no | — |
| 522 | C22 | — | 4 | 1 | no | — |
| 523 | C22 | — | 4 | 1 | no | — |
| 524 | C22 | — | 32 | 2 | no | — |
| 525 | C22 | — | 32 | 1 | no | — |
| 526 | C22 | #150138 | 1 | 1 | yes | characteristic |
| 527 | C22 | #150157 | 1 | 1 | yes | characteristic |
| 528 | C22 | #152513 | 1 | 1 | yes | characteristic |
| 529 | C4 | — | 4 | 1 | no | — |
| 530 | C4 | — | 4 | 1 | no | — |
| 531 | C4 | — | 4 | 1 | no | — |
| 532 | C4 | — | 4 | 1 | no | — |
| 533 | C4 | — | 4 | 1 | no | — |
| 534 | C4 | — | 32 | 2 | no | — |
| 535 | C4 | — | 32 | 1 | no | — |
| 536 | C4 | #136631 | 1 | 1 | yes | characteristic |
| 537 | C4 | #150141 | 1 | 1 | yes | characteristic |
| 538 | C4 | #150160 | 1 | 1 | yes | characteristic |
| 539 | C4 | #152512 | 1 | 1 | yes | characteristic |
| 540 | C2 | — | 2 | 1 | no | — |
| 541 | C2 | — | 2 | 1 | no | — |
| 542 | C2 | — | 2 | 1 | no | — |
| 543 | C2 | — | 4 | 2 | no | — |
| 544 | C2 | — | 64 | 1 | no | — |
| 545 | C2 | #72321075 | 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