Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
976 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 976 conjugacy classes of subgroups — too many to draw. Only its 75 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 | #6367518 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #153535 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #153456 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #153435 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #152594 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #152584 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #137581 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #62144 | — | 2 | 1 | no | — |
| 9 | #61934 | — | 2 | 1 | no | — |
| 10 | #23196 | C22 | 1 | 1 | yes | characteristic |
| 11 | #20289 | C4 | 1 | 2 | yes | complemented |
| 12 | #20156 | — | 2 | 1 | no | — |
| 13 | #20152 | — | 2 | 1 | no | — |
| 14 | #20119 | — | 2 | 2 | no | — |
| 15 | #20013 | C4 | 1 | 2 | yes | complemented |
| 16 | #19952 | — | 2 | 2 | no | — |
| 17 | #19654 | C22 | 1 | 1 | yes | characteristic |
| 18 | #19570 | — | 2 | 1 | no | — |
| 19 | #19494 | — | 2 | 1 | no | — |
| 20 | #18688 | C22 | 1 | 1 | yes | characteristic |
| 21 | #18655 | — | 2 | 1 | no | — |
| 22 | #18480 | C22 | 1 | 1 | yes | characteristic |
| 23 | #18019 | — | 2 | 1 | no | — |
| 24 | #13589 | C22 | 1 | 1 | yes | characteristic |
| 25 | #13583 | C22 | 1 | 1 | yes | characteristic |
| 26 | #13272 | — | 2 | 1 | no | — |
| 27 | #12779 | — | 2 | 1 | no | — |
| 28 | #12765 | — | 2 | 1 | no | — |
| 29 | #11920 | C22 | 1 | 1 | yes | characteristic |
| 30 | #7535 | — | 2 | 2 | no | — |
| 31 | #7522 | — | 2 | 2 | no | — |
| 32 | #7516 | — | 2 | 1 | no | — |
| 33 | #7515 | — | 2 | 1 | no | — |
| 34 | #7488 | — | 2 | 1 | no | — |
| 35 | #7482 | — | 2 | 1 | no | — |
| 36 | #7180 | — | 2 | 1 | no | — |
| 37 | #3550 | D4 | 1 | 1 | yes | characteristic |
| 38 | #3509 | — | 2 | 1 | no | — |
| 39 | #3481 | D4 | 1 | 1 | yes | characteristic |
| 40 | #3400 | — | 2 | 2 | no | — |
| 41 | #3398 | — | 4 | 1 | no | — |
| 42 | #3394 | — | 2 | 2 | no | — |
| 43 | #3393 | — | 4 | 1 | no | — |
| 44 | #3381 | — | 2 | 2 | no | — |
| 45 | #3369 | — | 2 | 2 | no | — |
| 46 | #3367 | — | 4 | 1 | no | — |
| 47 | #3365 | — | 2 | 2 | no | — |
| 48 | #3363 | — | 2 | 2 | no | — |
| 49 | #3359 | — | 4 | 1 | no | — |
| 50 | #3356 | — | 2 | 2 | no | — |
| 51 | #3351 | — | 4 | 2 | no | — |
| 52 | #3324 | — | 2 | 2 | no | — |
| 53 | #3323 | — | 4 | 2 | no | — |
| 54 | #3254 | — | 2 | 1 | no | — |
| 55 | #3252 | — | 4 | 1 | no | — |
| 56 | #3233 | — | 4 | 1 | no | — |
| 57 | #3227 | — | 2 | 1 | no | — |
| 58 | #3225 | — | 4 | 2 | no | — |
| 59 | #3209 | — | 2 | 1 | no | — |
| 60 | #3206 | — | 2 | 1 | no | — |
| 61 | C2×#498 | D4 | 1 | 1 | yes | characteristic |
| 62 | #3147 | C23 | 1 | 1 | yes | characteristic |
| 63 | #3121 | — | 4 | 2 | no | — |
| 64 | #3107 | — | 2 | 1 | no | — |
| 65 | #3106 | — | 2 | 1 | no | — |
| 66 | #3101 | — | 4 | 1 | no | — |
| 67 | #3079 | — | 2 | 1 | no | — |
| 68 | #3077 | — | 4 | 1 | no | — |
| 69 | #2991 | — | 2 | 1 | no | — |
| 70 | #2986 | — | 2 | 1 | no | — |
| 71 | #2957 | — | 4 | 1 | no | — |
| 72 | C2×#364 | — | 2 | 1 | no | — |
| 73 | #2132 | — | 2 | 1 | no | — |
| 74 | #2129 | — | 4 | 1 | no | — |
| 75 | #2126 | — | 2 | 1 | no | — |
| 76 | #2120 | — | 4 | 1 | no | — |
| 77 | #1976 | — | 4 | 1 | no | — |
| 78 | #1909 | — | 4 | 1 | no | — |
| 79 | #1891 | — | 4 | 1 | no | — |
| 80 | #1884 | — | 2 | 1 | no | — |
| 81 | #1884 | — | 2 | 1 | no | — |
| 82 | #1772 | — | 2 | 1 | no | — |
| 83 | #1716 | — | 2 | 1 | no | — |
| 84 | #1715 | — | 2 | 1 | no | — |
| 85 | #1708 | C2×C4 | 1 | 2 | yes | — |
| 86 | #1705 | D4 | 1 | 2 | yes | — |
| 87 | #1703 | — | 2 | 2 | no | — |
| 88 | #1702 | — | 2 | 2 | no | — |
| 89 | #1692 | — | 2 | 2 | no | — |
| 90 | #1685 | — | 2 | 2 | no | — |
| 91 | #1684 | — | 2 | 2 | no | — |
| 92 | #1682 | — | 2 | 2 | no | — |
| 93 | #1672 | — | 2 | 2 | no | — |
| 94 | #1666 | — | 2 | 2 | no | — |
| 95 | #1653 | — | 2 | 2 | no | — |
| 96 | #1653 | — | 2 | 2 | no | — |
| 97 | #1652 | — | 2 | 2 | no | — |
| 98 | #1652 | — | 2 | 2 | no | — |
| 99 | #1633 | D4 | 1 | 2 | yes | — |
| 100 | #1632 | — | 2 | 1 | no | — |
| 101 | #1630 | — | 2 | 1 | no | — |
| 102 | #1630 | C2×C4 | 1 | 1 | yes | characteristic |
| 103 | #1629 | C2×C4 | 1 | 1 | yes | characteristic |
| 104 | #1623 | C2×C4 | 1 | 2 | yes | — |
| 105 | #1622 | — | 2 | 1 | no | — |
| 106 | #1620 | — | 2 | 1 | no | — |
| 107 | #1620 | D4 | 1 | 1 | yes | characteristic |
| 108 | #1619 | D4 | 1 | 1 | yes | characteristic |
| 109 | #1590 | — | 2 | 2 | no | — |
| 110 | #1588 | — | 2 | 2 | no | — |
| 111 | #1587 | — | 2 | 2 | no | — |
| 112 | C8×Q16 | — | 2 | 2 | no | — |
| 113 | #1574 | — | 2 | 1 | no | — |
| 114 | #1560 | D4 | 1 | 1 | yes | characteristic |
| 115 | #1546 | — | 2 | 1 | no | — |
| 116 | #1543 | D4 | 1 | 1 | yes | characteristic |
| 117 | #1493 | — | 2 | 1 | no | — |
| 118 | #1476 | — | 2 | 1 | no | — |
| 119 | #1450 | D4 | 1 | 1 | yes | characteristic |
| 120 | #1411 | — | 2 | 1 | no | — |
| 121 | #1410 | — | 2 | 1 | no | — |
| 122 | #1409 | — | 2 | 1 | no | — |
| 123 | #1408 | — | 2 | 1 | no | — |
| 124 | #1386 | — | 4 | 1 | no | — |
| 125 | #1383 | — | 4 | 1 | no | — |
| 126 | #1358 | — | 2 | 1 | no | — |
| 127 | #1357 | — | 2 | 1 | no | — |
| 128 | C2×#135 | — | 4 | 1 | no | — |
| 129 | #568 | — | 2 | 1 | no | — |
| 130 | #568 | — | 2 | 1 | no | — |
| 131 | #563 | — | 4 | 1 | no | — |
| 132 | #559 | — | 2 | 1 | no | — |
| 133 | #559 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 134 | Q82 | C22⋊C4 | 1 | 2 | yes | — |
| 135 | #557 | — | 2 | 2 | no | — |
| 136 | #557 | — | 4 | 1 | no | — |
| 137 | #556 | — | 2 | 2 | no | — |
| 138 | #556 | — | 4 | 1 | no | — |
| 139 | #556 | — | 4 | 1 | no | — |
| 140 | #554 | — | 2 | 1 | no | — |
| 141 | #553 | — | 4 | 1 | no | — |
| 142 | #552 | — | 4 | 2 | no | — |
| 143 | #552 | — | 8 | 1 | no | — |
| 144 | #551 | — | 4 | 1 | no | — |
| 145 | D4×Q8 | — | 4 | 1 | no | — |
| 146 | #546 | — | 4 | 1 | no | — |
| 147 | D42 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 148 | #542 | — | 4 | 2 | no | — |
| 149 | #541 | — | 8 | 1 | no | — |
| 150 | #536 | — | 4 | 1 | no | — |
| 151 | #536 | — | 4 | 1 | no | — |
| 152 | #533 | — | 2 | 1 | no | — |
| 153 | #533 | — | 4 | 1 | no | — |
| 154 | #533 | — | 4 | 1 | no | — |
| 155 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 158 | #529 | — | 4 | 1 | no | — |
| 159 | #525 | — | 4 | 1 | no | — |
| 160 | #519 | — | 4 | 1 | no | — |
| 161 | C4×#41 | — | 2 | 1 | no | — |
| 162 | C2×C4×D4 | — | 4 | 1 | no | — |
| 163 | C2×M32 | — | 4 | 1 | no | — |
| 164 | #499 | — | 4 | 2 | no | — |
| 165 | #498 | — | 2 | 2 | no | — |
| 166 | #498 | — | 2 | 1 | no | — |
| 167 | #498 | — | 4 | 1 | no | — |
| 168 | #498 | C22⋊C4 | 1 | 2 | yes | — |
| 169 | #497 | — | 4 | 2 | no | — |
| 170 | #495 | — | 4 | 1 | no | — |
| 171 | #495 | — | 4 | 2 | no | — |
| 172 | #494 | — | 4 | 1 | no | — |
| 173 | #494 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | #493 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | #492 | — | 2 | 2 | no | — |
| 176 | #492 | C22×C4 | 1 | 1 | yes | characteristic |
| 177 | #492 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | #489 | — | 4 | 2 | no | — |
| 179 | #488 | — | 4 | 2 | no | — |
| 180 | #487 | — | 2 | 2 | no | — |
| 181 | #487 | — | 4 | 2 | no | — |
| 182 | #487 | — | 4 | 1 | no | — |
| 183 | #486 | — | 2 | 2 | no | — |
| 184 | #485 | — | 2 | 2 | no | — |
| 185 | #485 | — | 4 | 2 | no | — |
| 186 | #483 | — | 4 | 2 | no | — |
| 187 | #482 | — | 4 | 2 | no | — |
| 188 | #482 | — | 4 | 1 | no | — |
| 189 | #481 | — | 4 | 2 | no | — |
| 190 | #479 | — | 4 | 2 | no | — |
| 191 | #478 | — | 4 | 2 | no | — |
| 192 | #478 | — | 4 | 2 | no | — |
| 193 | #477 | — | 2 | 1 | no | — |
| 194 | #477 | — | 2 | 2 | no | — |
| 195 | #477 | — | 4 | 2 | no | — |
| 196 | #477 | — | 4 | 1 | no | — |
| 197 | #476 | — | 2 | 1 | no | — |
| 198 | #476 | — | 4 | 1 | no | — |
| 199 | #476 | — | 4 | 1 | no | — |
| 200 | #476 | — | 4 | 1 | no | — |
| 201 | #475 | — | 2 | 1 | no | — |
| 202 | #475 | — | 2 | 2 | no | — |
| 203 | #475 | — | 4 | 2 | no | — |
| 204 | #474 | — | 2 | 1 | no | — |
| 205 | #474 | — | 2 | 2 | no | — |
| 206 | #474 | — | 4 | 1 | no | — |
| 207 | #470 | — | 4 | 2 | no | — |
| 208 | #468 | — | 4 | 2 | no | — |
| 209 | #468 | — | 4 | 2 | no | — |
| 210 | #464 | — | 4 | 2 | no | — |
| 211 | #464 | — | 4 | 2 | no | — |
| 212 | #464 | — | 4 | 2 | no | — |
| 213 | #464 | — | 4 | 2 | no | — |
| 214 | #463 | — | 4 | 2 | no | — |
| 215 | #462 | — | 2 | 1 | no | — |
| 216 | #462 | — | 2 | 2 | no | — |
| 217 | #462 | — | 2 | 2 | no | — |
| 218 | #462 | — | 4 | 2 | no | — |
| 219 | #461 | — | 2 | 1 | no | — |
| 220 | #461 | — | 4 | 2 | no | — |
| 221 | #461 | — | 4 | 1 | no | — |
| 222 | #461 | — | 4 | 1 | no | — |
| 223 | #461 | — | 4 | 1 | no | — |
| 224 | #460 | — | 2 | 2 | no | — |
| 225 | #460 | — | 2 | 1 | no | — |
| 226 | #459 | — | 2 | 1 | no | — |
| 227 | #452 | — | 2 | 2 | no | — |
| 228 | #451 | — | 4 | 2 | no | — |
| 229 | #450 | — | 4 | 2 | no | — |
| 230 | #449 | — | 4 | 1 | no | — |
| 231 | #448 | — | 4 | 2 | no | — |
| 232 | #446 | — | 2 | 2 | no | — |
| 233 | #446 | — | 4 | 1 | no | — |
| 234 | C8×Q8 | — | 2 | 2 | no | — |
| 235 | C8×Q8 | — | 2 | 2 | no | — |
| 236 | C8×Q8 | — | 4 | 1 | no | — |
| 237 | #444 | — | 8 | 2 | no | — |
| 238 | #443 | — | 8 | 2 | no | — |
| 239 | #441 | — | 4 | 2 | no | — |
| 240 | #440 | — | 4 | 2 | no | — |
| 241 | C4×Q16 | — | 2 | 2 | no | — |
| 242 | C4×Q16 | — | 4 | 2 | no | — |
| 243 | C4×SD16 | — | 2 | 2 | no | — |
| 244 | C4×SD16 | — | 4 | 2 | no | — |
| 245 | C4×SD16 | — | 4 | 2 | no | — |
| 246 | C4×SD16 | — | 4 | 1 | no | — |
| 247 | C4×SD16 | — | 4 | 2 | no | — |
| 248 | C4×D8 | — | 4 | 1 | no | — |
| 249 | #436 | — | 2 | 2 | no | — |
| 250 | #436 | — | 4 | 2 | no | — |
| 251 | #433 | — | 4 | 2 | no | — |
| 252 | #431 | — | 2 | 1 | no | — |
| 253 | #431 | — | 2 | 1 | no | — |
| 254 | #431 | — | 4 | 1 | no | — |
| 255 | C2×#108 | — | 2 | 1 | no | — |
| 256 | #428 | — | 4 | 2 | no | — |
| 257 | #428 | — | 4 | 1 | no | — |
| 258 | #427 | — | 2 | 1 | no | — |
| 259 | C2×#106 | — | 4 | 1 | no | — |
| 260 | #423 | — | 2 | 1 | no | — |
| 261 | #423 | — | 4 | 1 | no | — |
| 262 | #421 | — | 4 | 1 | no | — |
| 263 | #421 | — | 4 | 1 | no | — |
| 264 | #419 | — | 8 | 1 | no | — |
| 265 | #418 | — | 4 | 2 | no | — |
| 266 | #417 | — | 4 | 1 | no | — |
| 267 | #413 | — | 4 | 1 | no | — |
| 268 | #410 | — | 2 | 1 | no | — |
| 269 | #410 | — | 2 | 1 | no | — |
| 270 | #410 | — | 4 | 1 | no | — |
| 271 | #407 | — | 8 | 1 | no | — |
| 272 | #405 | — | 4 | 1 | no | — |
| 273 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | #364 | — | 4 | 1 | no | — |
| 275 | #364 | — | 4 | 1 | no | — |
| 276 | #356 | — | 4 | 1 | no | — |
| 277 | #355 | — | 4 | 1 | no | — |
| 278 | #354 | — | 4 | 1 | no | — |
| 279 | #354 | — | 8 | 2 | no | — |
| 280 | #353 | — | 4 | 1 | no | — |
| 281 | #352 | — | 8 | 1 | no | — |
| 282 | AΣL(1,𝔽16) | — | 8 | 1 | no | — |
| 283 | #344 | — | 8 | 1 | no | — |
| 284 | #339 | — | 4 | 1 | no | — |
| 285 | H(3,ℤ/4) | — | 8 | 1 | no | — |
| 286 | #335 | — | 2 | 2 | no | — |
| 287 | #334 | — | 2 | 2 | no | — |
| 288 | #333 | — | 2 | 1 | no | — |
| 289 | #333 | C22⋊C4 | 1 | 2 | yes | — |
| 290 | #332 | — | 2 | 2 | no | — |
| 291 | #332 | — | 2 | 2 | no | — |
| 292 | #331 | — | 2 | 1 | no | — |
| 293 | #331 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 294 | #331 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 295 | Q8⋊C8 | — | 2 | 1 | no | — |
| 296 | Q8⋊C8 | — | 2 | 2 | no | — |
| 297 | Q8⋊C8 | — | 2 | 1 | no | — |
| 298 | Q8⋊C8 | — | 2 | 2 | no | — |
| 299 | D4⋊C8 | — | 2 | 1 | no | — |
| 300 | D4⋊C8 | — | 2 | 1 | no | — |
| 301 | #322 | — | 2 | 1 | no | — |
| 302 | C82 | C22⋊C4 | 1 | 2 | yes | — |
| 303 | C2×#41 | — | 2 | 1 | no | — |
| 304 | C2×#41 | — | 2 | 1 | no | — |
| 305 | C2×#41 | — | 2 | 1 | no | — |
| 306 | C22×Q8 | — | 4 | 1 | no | — |
| 307 | C22×Q8 | — | 4 | 1 | no | — |
| 308 | C22×D4 | — | 4 | 1 | no | — |
| 309 | C23×C4 | — | 4 | 1 | no | — |
| 310 | #135 | — | 8 | 1 | no | — |
| 311 | #135 | — | 8 | 1 | no | — |
| 312 | #135 | — | 8 | 1 | no | — |
| 313 | #135 | — | 8 | 1 | no | — |
| 314 | C2×Q16 | — | 2 | 2 | no | — |
| 315 | C2×Q16 | — | 4 | 1 | no | — |
| 316 | C2×Q16 | — | 4 | 2 | no | — |
| 317 | C2×Q16 | — | 4 | 2 | no | — |
| 318 | C2×SD16 | — | 2 | 2 | no | — |
| 319 | C2×SD16 | — | 4 | 1 | no | — |
| 320 | C2×SD16 | — | 4 | 1 | no | — |
| 321 | C2×SD16 | — | 4 | 2 | no | — |
| 322 | C2×SD16 | — | 4 | 2 | no | — |
| 323 | C2×SD16 | — | 4 | 1 | no | — |
| 324 | C2×SD16 | — | 4 | 2 | no | — |
| 325 | C2×D8 | — | 4 | 1 | no | — |
| 326 | C2×D8 | — | 4 | 1 | no | — |
| 327 | #131 | — | 8 | 2 | no | — |
| 328 | #131 | — | 8 | 2 | no | — |
| 329 | C2×M16 | — | 4 | 2 | no | — |
| 330 | C2×M16 | — | 4 | 1 | no | — |
| 331 | C2×M16 | — | 4 | 1 | no | — |
| 332 | C2×M16 | — | 8 | 1 | no | — |
| 333 | C2×M16 | — | 8 | 1 | no | — |
| 334 | C2×M16 | — | 8 | 1 | no | — |
| 335 | C22×C8 | — | 2 | 1 | no | — |
| 336 | C4⋊Q8 | — | 2 | 1 | no | — |
| 337 | C4⋊Q8 | — | 2 | 1 | no | — |
| 338 | C4⋊Q8 | — | 2 | 2 | no | — |
| 339 | C4⋊Q8 | — | 4 | 1 | no | — |
| 340 | C4⋊Q8 | — | 4 | 1 | no | — |
| 341 | C4⋊Q8 | — | 4 | 2 | no | — |
| 342 | C4⋊Q8 | — | 4 | 2 | no | — |
| 343 | C4⋊Q8 | — | 4 | 2 | no | — |
| 344 | C4⋊Q8 | — | 4 | 1 | no | — |
| 345 | C4⋊Q8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 346 | C4⋊Q8 | #120 | 1 | 1 | yes | characteristic |
| 347 | #127 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 348 | #127 | #120 | 1 | 1 | yes | characteristic |
| 349 | #126 | — | 8 | 1 | no | — |
| 350 | #126 | — | 8 | 2 | no | — |
| 351 | #126 | — | 8 | 2 | no | — |
| 352 | #126 | — | 8 | 2 | no | — |
| 353 | #125 | — | 4 | 1 | no | — |
| 354 | #125 | — | 4 | 2 | no | — |
| 355 | #125 | — | 4 | 1 | no | — |
| 356 | #125 | — | 8 | 1 | no | — |
| 357 | #125 | — | 8 | 2 | no | — |
| 358 | #125 | — | 8 | 2 | no | — |
| 359 | #124 | — | 2 | 1 | no | — |
| 360 | #124 | — | 2 | 1 | no | — |
| 361 | #124 | — | 4 | 1 | no | — |
| 362 | #124 | — | 4 | 2 | no | — |
| 363 | #124 | — | 4 | 2 | no | — |
| 364 | #124 | — | 4 | 2 | no | — |
| 365 | #123 | — | 4 | 1 | no | — |
| 366 | #123 | — | 4 | 1 | no | — |
| 367 | #123 | — | 8 | 1 | no | — |
| 368 | #123 | — | 8 | 1 | no | — |
| 369 | #123 | — | 8 | 2 | no | — |
| 370 | #123 | — | 8 | 1 | no | — |
| 371 | C22⋊Q8 | — | 2 | 2 | no | — |
| 372 | C22⋊Q8 | — | 4 | 1 | no | — |
| 373 | C22⋊Q8 | — | 4 | 1 | no | — |
| 374 | C22⋊Q8 | — | 4 | 2 | no | — |
| 375 | C22⋊Q8 | — | 8 | 1 | no | — |
| 376 | C22⋊Q8 | — | 8 | 2 | no | — |
| 377 | C22⋊Q8 | — | 8 | 1 | no | — |
| 378 | C22⋊Q8 | — | 8 | 1 | no | — |
| 379 | C22⋊Q8 | — | 8 | 1 | no | — |
| 380 | C22⋊Q8 | — | 8 | 1 | no | — |
| 381 | #121 | — | 4 | 1 | no | — |
| 382 | #121 | — | 4 | 1 | no | — |
| 383 | #121 | — | 4 | 1 | no | — |
| 384 | #121 | — | 8 | 1 | no | — |
| 385 | #120 | — | 4 | 1 | no | — |
| 386 | #120 | — | 4 | 1 | no | — |
| 387 | C4×Q8 | — | 2 | 1 | no | — |
| 388 | C4×Q8 | — | 2 | 1 | no | — |
| 389 | C4×Q8 | — | 2 | 2 | no | — |
| 390 | C4×Q8 | — | 4 | 1 | no | — |
| 391 | C4×Q8 | — | 4 | 2 | no | — |
| 392 | C4×Q8 | — | 4 | 2 | no | — |
| 393 | C4×Q8 | — | 4 | 2 | no | — |
| 394 | C4×Q8 | — | 4 | 2 | no | — |
| 395 | C4×Q8 | — | 8 | 1 | no | — |
| 396 | C4×Q8 | — | 8 | 1 | no | — |
| 397 | C4×Q8 | — | 8 | 1 | no | — |
| 398 | C4×D4 | — | 2 | 1 | no | — |
| 399 | C4×D4 | — | 2 | 1 | no | — |
| 400 | C4×D4 | — | 4 | 1 | no | — |
| 401 | C4×D4 | — | 4 | 1 | no | — |
| 402 | C4×D4 | — | 4 | 1 | no | — |
| 403 | C4×D4 | — | 4 | 1 | no | — |
| 404 | C4×D4 | — | 4 | 1 | no | — |
| 405 | C4×D4 | — | 4 | 2 | no | — |
| 406 | C4×D4 | — | 4 | 1 | no | — |
| 407 | C4×D4 | — | 8 | 1 | no | — |
| 408 | C4×D4 | — | 8 | 1 | no | — |
| 409 | #117 | — | 2 | 1 | no | — |
| 410 | #117 | — | 4 | 1 | no | — |
| 411 | #117 | — | 4 | 1 | no | — |
| 412 | #117 | — | 4 | 1 | no | — |
| 413 | #117 | — | 4 | 1 | no | — |
| 414 | #117 | — | 4 | 2 | no | — |
| 415 | #117 | — | 4 | 1 | no | — |
| 416 | #117 | — | 8 | 2 | no | — |
| 417 | #117 | — | 8 | 1 | no | — |
| 418 | #117 | — | 8 | 1 | no | — |
| 419 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 420 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 421 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 422 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 423 | C2×C42 | — | 4 | 1 | no | — |
| 424 | C2×C42 | #120 | 1 | 1 | yes | characteristic |
| 425 | M32 | — | 8 | 1 | no | — |
| 426 | M32 | — | 8 | 1 | no | — |
| 427 | C2×C16 | — | 8 | 1 | no | — |
| 428 | #108 | — | 2 | 2 | no | — |
| 429 | #108 | — | 4 | 1 | no | — |
| 430 | #107 | — | 2 | 2 | no | — |
| 431 | #107 | — | 4 | 2 | no | — |
| 432 | #107 | — | 4 | 2 | no | — |
| 433 | #107 | — | 4 | 1 | no | — |
| 434 | #107 | — | 4 | 1 | no | — |
| 435 | #106 | — | 2 | 2 | no | — |
| 436 | #106 | — | 4 | 2 | no | — |
| 437 | #106 | — | 4 | 1 | no | — |
| 438 | #106 | — | 4 | 2 | no | — |
| 439 | #106 | — | 4 | 2 | no | — |
| 440 | #106 | — | 4 | 2 | no | — |
| 441 | #106 | — | 4 | 1 | no | — |
| 442 | #106 | — | 8 | 1 | no | — |
| 443 | C4⋊C8 | — | 2 | 1 | no | — |
| 444 | C4⋊C8 | — | 2 | 1 | no | — |
| 445 | C4⋊C8 | — | 2 | 1 | no | — |
| 446 | C4⋊C8 | — | 2 | 1 | no | — |
| 447 | C4⋊C8 | — | 2 | 2 | no | — |
| 448 | C4⋊C8 | — | 4 | 1 | no | — |
| 449 | C4⋊C8 | — | 4 | 2 | no | — |
| 450 | C4⋊C8 | — | 4 | 2 | no | — |
| 451 | C4⋊C8 | — | 4 | 2 | no | — |
| 452 | #104 | — | 8 | 2 | no | — |
| 453 | #104 | — | 8 | 2 | no | — |
| 454 | #103 | — | 2 | 2 | no | — |
| 455 | #103 | — | 2 | 2 | no | — |
| 456 | #103 | — | 2 | 2 | no | — |
| 457 | #103 | — | 4 | 2 | no | — |
| 458 | #103 | — | 4 | 2 | no | — |
| 459 | #103 | — | 4 | 2 | no | — |
| 460 | #103 | — | 4 | 2 | no | — |
| 461 | #103 | — | 4 | 2 | no | — |
| 462 | #103 | — | 4 | 1 | no | — |
| 463 | #103 | — | 4 | 2 | no | — |
| 464 | #103 | — | 16 | 2 | no | — |
| 465 | #102 | — | 2 | 2 | no | — |
| 466 | #102 | — | 4 | 2 | no | — |
| 467 | #102 | — | 4 | 1 | no | — |
| 468 | #102 | — | 4 | 1 | no | — |
| 469 | #102 | — | 4 | 2 | no | — |
| 470 | #102 | — | 4 | 2 | no | — |
| 471 | #102 | — | 4 | 2 | no | — |
| 472 | #102 | — | 4 | 1 | no | — |
| 473 | #101 | — | 8 | 1 | no | — |
| 474 | #100 | — | 8 | 1 | no | — |
| 475 | #99 | — | 8 | 1 | no | — |
| 476 | #99 | — | 8 | 1 | no | — |
| 477 | #99 | — | 8 | 1 | no | — |
| 478 | #99 | — | 8 | 1 | no | — |
| 479 | C22⋊C8 | — | 2 | 2 | no | — |
| 480 | C22⋊C8 | — | 4 | 2 | no | — |
| 481 | C22⋊C8 | — | 4 | 1 | no | — |
| 482 | C22⋊C8 | — | 16 | 2 | no | — |
| 483 | #97 | — | 4 | 2 | no | — |
| 484 | #97 | — | 8 | 1 | no | — |
| 485 | C4×C8 | — | 2 | 2 | no | — |
| 486 | C4×C8 | — | 2 | 1 | no | — |
| 487 | C4×C8 | — | 4 | 1 | no | — |
| 488 | C4×C8 | — | 4 | 2 | no | — |
| 489 | C4×C8 | — | 4 | 2 | no | — |
| 490 | C4×C8 | — | 8 | 1 | no | — |
| 491 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 492 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 493 | C24 | — | 4 | 1 | no | — |
| 494 | #41 | — | 8 | 1 | no | — |
| 495 | #41 | — | 8 | 1 | no | — |
| 496 | #41 | — | 8 | 1 | no | — |
| 497 | #41 | — | 8 | 1 | no | — |
| 498 | #41 | — | 8 | 1 | no | — |
| 499 | #41 | — | 8 | 1 | no | — |
| 500 | C2×Q8 | — | 2 | 1 | no | — |
| 501 | C2×Q8 | — | 2 | 2 | no | — |
| 502 | C2×Q8 | — | 2 | 1 | no | — |
| 503 | C2×Q8 | — | 2 | 1 | no | — |
| 504 | C2×Q8 | — | 4 | 2 | no | — |
| 505 | C2×Q8 | — | 4 | 1 | no | — |
| 506 | C2×Q8 | — | 4 | 2 | no | — |
| 507 | C2×Q8 | — | 8 | 1 | no | — |
| 508 | C2×Q8 | — | 16 | 1 | no | — |
| 509 | C2×Q8 | — | 16 | 1 | no | — |
| 510 | C2×Q8 | — | 16 | 1 | no | — |
| 511 | C2×Q8 | — | 16 | 1 | no | — |
| 512 | C2×D4 | — | 2 | 1 | no | — |
| 513 | C2×D4 | — | 2 | 1 | no | — |
| 514 | C2×D4 | — | 2 | 1 | no | — |
| 515 | C2×D4 | — | 4 | 1 | no | — |
| 516 | C2×D4 | — | 4 | 1 | no | — |
| 517 | C2×D4 | — | 4 | 1 | no | — |
| 518 | C2×D4 | — | 4 | 1 | no | — |
| 519 | C2×D4 | — | 4 | 1 | no | — |
| 520 | C2×D4 | — | 8 | 1 | no | — |
| 521 | C2×D4 | — | 8 | 2 | no | — |
| 522 | C2×D4 | — | 16 | 1 | no | — |
| 523 | C22×C4 | — | 2 | 1 | no | — |
| 524 | C22×C4 | — | 4 | 1 | no | — |
| 525 | C22×C4 | — | 4 | 1 | no | — |
| 526 | C22×C4 | — | 4 | 1 | no | — |
| 527 | C22×C4 | — | 4 | 1 | no | — |
| 528 | C22×C4 | — | 4 | 1 | no | — |
| 529 | C22×C4 | — | 4 | 1 | no | — |
| 530 | C22×C4 | — | 8 | 1 | no | — |
| 531 | C22×C4 | — | 8 | 1 | no | — |
| 532 | C22×C4 | — | 8 | 1 | no | — |
| 533 | C22×C4 | — | 16 | 1 | no | — |
| 534 | C22×C4 | — | 16 | 1 | no | — |
| 535 | C22×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 536 | Q16 | — | 8 | 1 | no | — |
| 537 | Q16 | — | 8 | 1 | no | — |
| 538 | Q16 | — | 8 | 2 | no | — |
| 539 | Q16 | — | 16 | 2 | no | — |
| 540 | Q16 | — | 16 | 2 | no | — |
| 541 | SD16 | — | 8 | 1 | no | — |
| 542 | SD16 | — | 8 | 1 | no | — |
| 543 | SD16 | — | 8 | 1 | no | — |
| 544 | SD16 | — | 8 | 1 | no | — |
| 545 | SD16 | — | 8 | 2 | no | — |
| 546 | SD16 | — | 16 | 2 | no | — |
| 547 | SD16 | — | 16 | 2 | no | — |
| 548 | SD16 | — | 16 | 2 | no | — |
| 549 | SD16 | — | 16 | 1 | no | — |
| 550 | D8 | — | 8 | 1 | no | — |
| 551 | D8 | — | 8 | 1 | no | — |
| 552 | D8 | — | 16 | 1 | no | — |
| 553 | M16 | — | 4 | 2 | no | — |
| 554 | M16 | — | 8 | 1 | no | — |
| 555 | M16 | — | 16 | 2 | no | — |
| 556 | M16 | — | 16 | 1 | no | — |
| 557 | M16 | — | 16 | 1 | no | — |
| 558 | M16 | — | 16 | 1 | no | — |
| 559 | M16 | — | 16 | 1 | no | — |
| 560 | M16 | — | 16 | 1 | no | — |
| 561 | C2×C8 | — | 2 | 1 | no | — |
| 562 | C2×C8 | — | 2 | 1 | no | — |
| 563 | C2×C8 | — | 2 | 1 | no | — |
| 564 | C2×C8 | — | 2 | 1 | no | — |
| 565 | C2×C8 | — | 2 | 1 | no | — |
| 566 | C2×C8 | — | 2 | 1 | no | — |
| 567 | C2×C8 | — | 2 | 2 | no | — |
| 568 | C2×C8 | — | 2 | 2 | no | — |
| 569 | C2×C8 | — | 4 | 1 | no | — |
| 570 | C2×C8 | — | 4 | 1 | no | — |
| 571 | C2×C8 | — | 4 | 2 | no | — |
| 572 | C2×C8 | — | 8 | 1 | no | — |
| 573 | C2×C8 | — | 8 | 2 | no | — |
| 574 | C2×C8 | — | 8 | 2 | no | — |
| 575 | C2×C8 | — | 16 | 1 | no | — |
| 576 | C4⋊C4 | — | 2 | 2 | no | — |
| 577 | C4⋊C4 | — | 2 | 1 | no | — |
| 578 | C4⋊C4 | — | 2 | 1 | no | — |
| 579 | C4⋊C4 | — | 4 | 1 | no | — |
| 580 | C4⋊C4 | — | 4 | 1 | no | — |
| 581 | C4⋊C4 | — | 4 | 1 | no | — |
| 582 | C4⋊C4 | — | 4 | 1 | no | — |
| 583 | C4⋊C4 | — | 4 | 1 | no | — |
| 584 | C4⋊C4 | — | 4 | 2 | no | — |
| 585 | C4⋊C4 | — | 4 | 2 | no | — |
| 586 | C4⋊C4 | — | 4 | 1 | no | — |
| 587 | C4⋊C4 | — | 4 | 1 | no | — |
| 588 | C4⋊C4 | — | 4 | 2 | no | — |
| 589 | C4⋊C4 | — | 4 | 2 | no | — |
| 590 | C4⋊C4 | — | 8 | 1 | no | — |
| 591 | C4⋊C4 | — | 8 | 1 | no | — |
| 592 | C4⋊C4 | — | 8 | 1 | no | — |
| 593 | C4⋊C4 | — | 8 | 1 | no | — |
| 594 | C4⋊C4 | — | 8 | 2 | no | — |
| 595 | C4⋊C4 | — | 8 | 2 | no | — |
| 596 | C4⋊C4 | — | 8 | 2 | no | — |
| 597 | C4⋊C4 | — | 8 | 2 | no | — |
| 598 | C4⋊C4 | — | 8 | 2 | no | — |
| 599 | C4⋊C4 | — | 8 | 1 | no | — |
| 600 | C4⋊C4 | — | 16 | 1 | no | — |
| 601 | C22⋊C4 | — | 4 | 1 | no | — |
| 602 | C22⋊C4 | — | 4 | 1 | no | — |
| 603 | C22⋊C4 | — | 4 | 2 | no | — |
| 604 | C22⋊C4 | — | 4 | 1 | no | — |
| 605 | C22⋊C4 | — | 4 | 1 | no | — |
| 606 | C22⋊C4 | — | 4 | 1 | no | — |
| 607 | C22⋊C4 | — | 8 | 1 | no | — |
| 608 | C22⋊C4 | — | 8 | 1 | no | — |
| 609 | C22⋊C4 | — | 8 | 1 | no | — |
| 610 | C22⋊C4 | — | 8 | 1 | no | — |
| 611 | C22⋊C4 | — | 8 | 1 | no | — |
| 612 | C22⋊C4 | — | 8 | 2 | no | — |
| 613 | C22⋊C4 | — | 8 | 2 | no | — |
| 614 | C22⋊C4 | — | 8 | 2 | no | — |
| 615 | C22⋊C4 | — | 8 | 1 | no | — |
| 616 | C22⋊C4 | — | 16 | 1 | no | — |
| 617 | C42 | — | 2 | 1 | no | — |
| 618 | C42 | — | 4 | 1 | no | — |
| 619 | C42 | — | 4 | 2 | no | — |
| 620 | C42 | — | 4 | 1 | no | — |
| 621 | C42 | — | 4 | 2 | no | — |
| 622 | C42 | — | 4 | 1 | no | — |
| 623 | C42 | — | 8 | 1 | no | — |
| 624 | C42 | — | 8 | 2 | no | — |
| 625 | C42 | — | 8 | 2 | no | — |
| 626 | C42 | — | 16 | 1 | no | — |
| 627 | C42 | #379 | 1 | 1 | yes | characteristic |
| 628 | C42 | #458 | 1 | 1 | yes | characteristic |
| 629 | C16 | — | 16 | 1 | no | — |
| 630 | C23 | — | 4 | 1 | no | — |
| 631 | C23 | — | 4 | 1 | no | — |
| 632 | C23 | — | 4 | 1 | no | — |
| 633 | C23 | — | 16 | 1 | no | — |
| 634 | C23 | — | 16 | 2 | no | — |
| 635 | C23 | #2196 | 1 | 1 | yes | characteristic |
| 636 | Q8 | — | 4 | 2 | no | — |
| 637 | Q8 | — | 4 | 2 | no | — |
| 638 | Q8 | — | 4 | 1 | no | — |
| 639 | Q8 | — | 4 | 1 | no | — |
| 640 | Q8 | — | 8 | 1 | no | — |
| 641 | Q8 | — | 8 | 1 | no | — |
| 642 | Q8 | — | 8 | 2 | no | — |
| 643 | Q8 | — | 8 | 2 | no | — |
| 644 | Q8 | — | 8 | 1 | no | — |
| 645 | Q8 | — | 8 | 1 | no | — |
| 646 | Q8 | — | 16 | 2 | no | — |
| 647 | Q8 | — | 16 | 2 | no | — |
| 648 | D4 | — | 4 | 1 | no | — |
| 649 | D4 | — | 4 | 1 | no | — |
| 650 | D4 | — | 8 | 1 | no | — |
| 651 | D4 | — | 8 | 1 | no | — |
| 652 | D4 | — | 8 | 1 | no | — |
| 653 | D4 | — | 8 | 1 | no | — |
| 654 | D4 | — | 8 | 1 | no | — |
| 655 | D4 | — | 8 | 1 | no | — |
| 656 | D4 | — | 16 | 1 | no | — |
| 657 | D4 | — | 16 | 1 | no | — |
| 658 | D4 | — | 16 | 1 | no | — |
| 659 | D4 | — | 16 | 2 | no | — |
| 660 | C2×C4 | — | 2 | 1 | no | — |
| 661 | C2×C4 | — | 2 | 1 | no | — |
| 662 | C2×C4 | — | 2 | 1 | no | — |
| 663 | C2×C4 | — | 2 | 1 | no | — |
| 664 | C2×C4 | — | 4 | 1 | no | — |
| 665 | C2×C4 | — | 4 | 1 | no | — |
| 666 | C2×C4 | — | 4 | 1 | no | — |
| 667 | C2×C4 | — | 4 | 1 | no | — |
| 668 | C2×C4 | — | 4 | 2 | no | — |
| 669 | C2×C4 | — | 4 | 1 | no | — |
| 670 | C2×C4 | — | 4 | 1 | no | — |
| 671 | C2×C4 | — | 4 | 2 | no | — |
| 672 | C2×C4 | — | 4 | 1 | no | — |
| 673 | C2×C4 | — | 8 | 1 | no | — |
| 674 | C2×C4 | — | 8 | 1 | no | — |
| 675 | C2×C4 | — | 8 | 1 | no | — |
| 676 | C2×C4 | — | 8 | 1 | no | — |
| 677 | C2×C4 | — | 8 | 1 | no | — |
| 678 | C2×C4 | — | 8 | 1 | no | — |
| 679 | C2×C4 | — | 8 | 1 | no | — |
| 680 | C2×C4 | — | 8 | 1 | no | — |
| 681 | C2×C4 | — | 8 | 2 | no | — |
| 682 | C2×C4 | — | 16 | 1 | no | — |
| 683 | C2×C4 | — | 16 | 1 | no | — |
| 684 | C2×C4 | — | 16 | 2 | no | — |
| 685 | C2×C4 | — | 16 | 1 | no | — |
| 686 | C2×C4 | — | 32 | 1 | no | — |
| 687 | C2×C4 | — | 32 | 1 | no | — |
| 688 | C2×C4 | — | 32 | 1 | no | — |
| 689 | C2×C4 | #1790 | 1 | 1 | yes | characteristic |
| 690 | C2×C4 | #2196 | 1 | 1 | yes | characteristic |
| 691 | C8 | — | 2 | 1 | no | — |
| 692 | C8 | — | 2 | 1 | no | — |
| 693 | C8 | — | 2 | 1 | no | — |
| 694 | C8 | — | 2 | 1 | no | — |
| 695 | C8 | — | 4 | 2 | no | — |
| 696 | C8 | — | 4 | 2 | no | — |
| 697 | C8 | — | 8 | 2 | no | — |
| 698 | C8 | — | 8 | 1 | no | — |
| 699 | C8 | — | 8 | 1 | no | — |
| 700 | C8 | — | 8 | 2 | no | — |
| 701 | C8 | — | 32 | 1 | no | — |
| 702 | C22 | — | 2 | 1 | no | — |
| 703 | C22 | — | 4 | 1 | no | — |
| 704 | C22 | — | 8 | 1 | no | — |
| 705 | C22 | — | 8 | 1 | no | — |
| 706 | C22 | — | 8 | 1 | no | — |
| 707 | C22 | — | 8 | 1 | no | — |
| 708 | C22 | — | 8 | 1 | no | — |
| 709 | C22 | — | 16 | 1 | no | — |
| 710 | C22 | — | 16 | 1 | no | — |
| 711 | C22 | — | 16 | 2 | no | — |
| 712 | C22 | — | 32 | 1 | no | — |
| 713 | C22 | #12759 | 1 | 1 | yes | characteristic |
| 714 | C4 | — | 2 | 1 | no | — |
| 715 | C4 | — | 2 | 1 | no | — |
| 716 | C4 | — | 2 | 1 | no | — |
| 717 | C4 | — | 4 | 1 | no | — |
| 718 | C4 | — | 8 | 1 | no | — |
| 719 | C4 | — | 8 | 1 | no | — |
| 720 | C4 | — | 8 | 2 | no | — |
| 721 | C4 | — | 8 | 1 | no | — |
| 722 | C4 | — | 8 | 1 | no | — |
| 723 | C4 | — | 8 | 1 | no | — |
| 724 | C4 | — | 8 | 2 | no | — |
| 725 | C4 | — | 16 | 2 | no | — |
| 726 | C4 | — | 32 | 1 | no | — |
| 727 | C4 | — | 64 | 1 | no | — |
| 728 | C4 | #13674 | 1 | 1 | yes | characteristic |
| 729 | C4 | #13676 | 1 | 1 | yes | characteristic |
| 730 | C2 | — | 2 | 1 | no | — |
| 731 | C2 | — | 4 | 1 | no | — |
| 732 | C2 | — | 16 | 1 | no | — |
| 733 | C2 | — | 16 | 1 | no | — |
| 734 | C2 | — | 16 | 1 | no | — |
| 735 | C2 | #152186 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #152186 |
| commutator | #492 | C22×C4 |
| Frattini, cosocle | #3147 | C23 |
| prime radical | #18480 | C22 |
| LCS | G ▷ #492 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #3147 ◁ G | |
| LECS | G ▷ #3147 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #153535 | C2 | semidirect |
| 3. #153456 | C2 | semidirect |
| 5. #152594 | C2 | semidirect |
| 7. #137581 | C2 | semidirect |
| 11. #20289 | C4 | semidirect |
| 15. #20013 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6367518 | 2 |
| #153535 | 2 |
| #153456 | 2 |
| #153435 | 2 |
| #152594 | 2 |
| #152584 | 2 |
| #137581 | 2 |