Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1692 conjugacy classes of subgroups.
The subgroup lattice has 634 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62375 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #62245 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #61680 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20054 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20029 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #19777 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #19757 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #19712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #19511 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #19347 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #19259 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #18948 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #18846 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #17989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #17905 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3550 | C22 | 1 | 2 | yes | complemented |
| 17 | #3496 | C22 | 1 | 2 | yes | — |
| 18 | #3396 | — | 2 | 1 | no | — |
| 19 | #3393 | C22 | 1 | 2 | yes | complemented |
| 20 | Q8×Q16 | — | 2 | 1 | no | — |
| 21 | Q8×D8 | C22 | 1 | 2 | yes | complemented |
| 22 | #3375 | — | 2 | 2 | no | — |
| 23 | #3367 | C22 | 1 | 4 | yes | complemented |
| 24 | #3334 | — | 2 | 1 | no | — |
| 25 | #3334 | C22 | 1 | 2 | yes | — |
| 26 | #3324 | C22 | 1 | 4 | yes | complemented |
| 27 | #3311 | — | 2 | 4 | no | — |
| 28 | #3302 | C22 | 1 | 4 | yes | complemented |
| 29 | #3294 | — | 2 | 2 | no | — |
| 30 | #3294 | C22 | 1 | 4 | yes | — |
| 31 | D4×SD16 | C22 | 1 | 4 | yes | complemented |
| 32 | D4×D8 | — | 2 | 1 | no | — |
| 33 | D4×D8 | C22 | 1 | 2 | yes | — |
| 34 | #3276 | C22 | 1 | 4 | yes | complemented |
| 35 | #3266 | — | 2 | 4 | no | — |
| 36 | #3262 | — | 2 | 2 | no | — |
| 37 | #3254 | C22 | 1 | 2 | yes | complemented |
| 38 | #3245 | C22 | 1 | 2 | yes | — |
| 39 | #3228 | C22 | 1 | 2 | yes | complemented |
| 40 | #3216 | C22 | 1 | 2 | yes | complemented |
| 41 | #3210 | C22 | 1 | 2 | yes | complemented |
| 42 | #3201 | — | 2 | 4 | no | — |
| 43 | #3186 | — | 2 | 2 | no | — |
| 44 | #3175 | — | 2 | 2 | no | — |
| 45 | #3170 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 47 | #3169 | C22 | 1 | 1 | yes | characteristic |
| 48 | #3110 | C22 | 1 | 2 | yes | — |
| 49 | #3101 | C22 | 1 | 1 | yes | characteristic |
| 50 | C2×#466 | — | 2 | 2 | no | — |
| 51 | #3009 | — | 2 | 4 | no | — |
| 52 | #2981 | C22 | 1 | 2 | yes | complemented |
| 53 | #2960 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | C2×C8×D4 | C22 | 1 | 1 | yes | characteristic |
| 55 | #1723 | C22 | 1 | 2 | yes | complemented |
| 56 | #1722 | C22 | 1 | 2 | yes | complemented |
| 57 | #1720 | C22 | 1 | 2 | yes | complemented |
| 58 | #1717 | C22 | 1 | 2 | yes | complemented |
| 59 | #1699 | C22 | 1 | 4 | yes | complemented |
| 60 | #1694 | C22 | 1 | 2 | yes | complemented |
| 61 | #1688 | C22 | 1 | 2 | yes | complemented |
| 62 | #1685 | C22 | 1 | 4 | yes | complemented |
| 63 | #1682 | C22 | 1 | 4 | yes | complemented |
| 64 | #1681 | C22 | 1 | 4 | yes | complemented |
| 65 | #1679 | C22 | 1 | 4 | yes | complemented |
| 66 | #1673 | C22 | 1 | 2 | yes | complemented |
| 67 | #1669 | C22 | 1 | 4 | yes | complemented |
| 68 | #1669 | C22 | 1 | 2 | yes | complemented |
| 69 | #1654 | C22 | 1 | 4 | yes | complemented |
| 70 | #1652 | C22 | 1 | 4 | yes | complemented |
| 71 | #1649 | C22 | 1 | 4 | yes | complemented |
| 72 | #1647 | C22 | 1 | 4 | yes | complemented |
| 73 | #1639 | C22 | 1 | 4 | yes | complemented |
| 74 | #1639 | C22 | 1 | 4 | yes | complemented |
| 75 | #1628 | C22 | 1 | 4 | yes | complemented |
| 76 | #1627 | C22 | 1 | 4 | yes | complemented |
| 77 | #1586 | C22 | 1 | 4 | yes | complemented |
| 78 | #1585 | C22 | 1 | 4 | yes | complemented |
| 79 | #1581 | C22 | 1 | 4 | yes | complemented |
| 80 | SD16⋊C8 | C22 | 1 | 4 | yes | complemented |
| 81 | #1571 | C22 | 1 | 1 | yes | characteristic, complemented |
| 82 | #1568 | C22 | 1 | 1 | yes | characteristic, complemented |
| 83 | #1557 | C22 | 1 | 2 | yes | complemented |
| 84 | #1552 | C22 | 1 | 2 | yes | complemented |
| 85 | #1496 | C22 | 1 | 2 | yes | complemented |
| 86 | #1486 | C22 | 1 | 1 | yes | characteristic |
| 87 | #1481 | C22 | 1 | 1 | yes | characteristic, complemented |
| 88 | #1452 | C22 | 1 | 1 | yes | characteristic, complemented |
| 89 | C2×H(5,𝔽2) | — | 2 | 2 | no | — |
| 90 | C2×#137 | — | 2 | 4 | no | — |
| 91 | C22×SD16 | — | 2 | 4 | no | — |
| 92 | C22×D8 | — | 2 | 2 | no | — |
| 93 | C23×C8 | — | 2 | 1 | no | — |
| 94 | #563 | — | 4 | 2 | no | — |
| 95 | #559 | — | 2 | 2 | no | — |
| 96 | Q82 | — | 2 | 2 | no | — |
| 97 | #556 | — | 2 | 2 | no | — |
| 98 | #556 | C23 | 1 | 4 | yes | — |
| 99 | D4×Q8 | — | 2 | 2 | no | — |
| 100 | D4×Q8 | C23 | 1 | 4 | yes | — |
| 101 | #547 | — | 2 | 2 | no | — |
| 102 | #547 | C23 | 1 | 4 | yes | — |
| 103 | #546 | — | 2 | 4 | no | — |
| 104 | #546 | — | 4 | 2 | no | — |
| 105 | D42 | — | 2 | 2 | no | — |
| 106 | D42 | C23 | 1 | 4 | yes | — |
| 107 | #542 | — | 2 | 4 | no | — |
| 108 | #542 | — | 4 | 2 | no | — |
| 109 | #537 | — | 2 | 2 | no | — |
| 110 | #536 | — | 2 | 4 | no | — |
| 111 | #534 | — | 4 | 2 | no | — |
| 112 | #533 | C23 | 1 | 2 | yes | — |
| 113 | #533 | C23 | 1 | 1 | yes | characteristic |
| 114 | #532 | C23 | 1 | 2 | yes | — |
| 115 | #532 | C23 | 1 | 2 | yes | — |
| 116 | C2×#121 | — | 2 | 4 | no | — |
| 117 | C2×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 118 | #500 | — | 2 | 2 | no | — |
| 119 | #500 | D4 | 1 | 1 | yes | characteristic |
| 120 | #500 | C23 | 1 | 1 | yes | characteristic |
| 121 | #500 | C23 | 1 | 1 | yes | characteristic |
| 122 | #500 | C23 | 1 | 2 | yes | — |
| 123 | #498 | C23 | 1 | 2 | yes | — |
| 124 | #497 | — | 2 | 2 | no | — |
| 125 | #495 | — | 2 | 2 | no | — |
| 126 | #494 | C23 | 1 | 1 | yes | characteristic |
| 127 | #494 | C23 | 1 | 2 | yes | — |
| 128 | #493 | D4 | 1 | 1 | yes | characteristic |
| 129 | #493 | C23 | 1 | 1 | yes | characteristic |
| 130 | #492 | C23 | 1 | 2 | yes | — |
| 131 | #489 | — | 2 | 2 | no | — |
| 132 | #489 | — | 2 | 4 | no | — |
| 133 | #487 | C23 | 1 | 2 | yes | — |
| 134 | #487 | C23 | 1 | 2 | yes | — |
| 135 | #486 | D4 | 1 | 2 | yes | — |
| 136 | #486 | C23 | 1 | 2 | yes | — |
| 137 | #486 | C23 | 1 | 2 | yes | — |
| 138 | #486 | C23 | 1 | 2 | yes | — |
| 139 | #486 | C23 | 1 | 2 | yes | — |
| 140 | #485 | — | 2 | 4 | no | — |
| 141 | #484 | — | 2 | 2 | no | — |
| 142 | #483 | D4 | 1 | 2 | yes | — |
| 143 | #482 | — | 2 | 4 | no | — |
| 144 | #482 | — | 4 | 2 | no | — |
| 145 | #480 | — | 2 | 4 | no | — |
| 146 | #480 | — | 2 | 4 | no | — |
| 147 | #478 | — | 4 | 2 | no | — |
| 148 | #477 | — | 2 | 2 | no | — |
| 149 | #477 | — | 2 | 4 | no | — |
| 150 | #476 | D4 | 1 | 2 | yes | — |
| 151 | #474 | — | 2 | 2 | no | — |
| 152 | #474 | — | 2 | 4 | no | — |
| 153 | #474 | C23 | 1 | 4 | yes | — |
| 154 | #474 | C23 | 1 | 4 | yes | — |
| 155 | #474 | C23 | 1 | 4 | yes | — |
| 156 | #470 | — | 2 | 4 | no | — |
| 157 | #468 | — | 2 | 4 | no | — |
| 158 | #468 | — | 2 | 4 | no | — |
| 159 | #467 | — | 2 | 1 | no | — |
| 160 | #467 | — | 2 | 1 | no | — |
| 161 | #467 | — | 2 | 4 | no | — |
| 162 | #466 | — | 2 | 2 | no | — |
| 163 | #466 | — | 2 | 1 | no | — |
| 164 | #466 | — | 2 | 1 | no | — |
| 165 | #466 | — | 2 | 4 | no | — |
| 166 | #466 | — | 2 | 2 | no | — |
| 167 | #466 | — | 2 | 4 | no | — |
| 168 | #466 | D4 | 1 | 2 | yes | — |
| 169 | #466 | D4 | 1 | 2 | yes | — |
| 170 | #465 | — | 2 | 4 | no | — |
| 171 | #464 | — | 2 | 4 | no | — |
| 172 | #464 | — | 2 | 4 | no | — |
| 173 | #463 | — | 2 | 4 | no | — |
| 174 | #462 | C23 | 1 | 4 | yes | — |
| 175 | #461 | D4 | 1 | 2 | yes | — |
| 176 | #461 | C23 | 1 | 4 | yes | — |
| 177 | #461 | C23 | 1 | 4 | yes | — |
| 178 | #460 | — | 2 | 2 | no | — |
| 179 | #460 | C23 | 1 | 4 | yes | — |
| 180 | #459 | — | 2 | 2 | no | — |
| 181 | #459 | C23 | 1 | 4 | yes | — |
| 182 | #452 | — | 2 | 4 | no | — |
| 183 | #452 | — | 2 | 4 | no | — |
| 184 | #452 | — | 2 | 4 | no | — |
| 185 | #452 | — | 2 | 4 | no | — |
| 186 | #451 | — | 2 | 4 | no | — |
| 187 | #450 | — | 2 | 2 | no | — |
| 188 | #450 | — | 2 | 4 | no | — |
| 189 | #450 | — | 2 | 4 | no | — |
| 190 | #450 | D4 | 1 | 2 | yes | — |
| 191 | #448 | — | 2 | 4 | no | — |
| 192 | #447 | — | 2 | 4 | no | — |
| 193 | #447 | — | 2 | 4 | no | — |
| 194 | #446 | — | 2 | 1 | no | — |
| 195 | #446 | C23 | 1 | 2 | yes | — |
| 196 | C8×Q8 | — | 2 | 1 | no | — |
| 197 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 198 | #440 | — | 2 | 4 | no | — |
| 199 | #440 | — | 2 | 4 | no | — |
| 200 | C4×Q16 | — | 2 | 2 | no | — |
| 201 | C4×Q16 | — | 2 | 1 | no | — |
| 202 | C4×Q16 | — | 2 | 1 | no | — |
| 203 | C4×SD16 | C23 | 1 | 4 | yes | — |
| 204 | C4×D8 | — | 2 | 2 | no | — |
| 205 | C4×D8 | — | 2 | 1 | no | — |
| 206 | C4×D8 | — | 2 | 1 | no | — |
| 207 | C4×D8 | C23 | 1 | 2 | yes | — |
| 208 | C4×D8 | C23 | 1 | 2 | yes | — |
| 209 | #436 | C23 | 1 | 4 | yes | — |
| 210 | #435 | — | 2 | 4 | no | — |
| 211 | C8×D4 | — | 2 | 1 | no | — |
| 212 | C8×D4 | — | 2 | 1 | no | — |
| 213 | C8×D4 | C23 | 1 | 2 | yes | — |
| 214 | C8×D4 | C23 | 1 | 2 | yes | — |
| 215 | C8×D4 | C23 | 1 | 4 | yes | — |
| 216 | #432 | C23 | 1 | 2 | yes | — |
| 217 | #431 | C23 | 1 | 1 | yes | characteristic |
| 218 | #431 | C23 | 1 | 1 | yes | characteristic |
| 219 | C2×#107 | — | 2 | 2 | no | — |
| 220 | #424 | — | 2 | 1 | no | — |
| 221 | #423 | C23 | 1 | 1 | yes | characteristic |
| 222 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 223 | #418 | — | 2 | 4 | no | — |
| 224 | #416 | — | 2 | 4 | no | — |
| 225 | C2×#102 | — | 2 | 4 | no | — |
| 226 | #408 | — | 2 | 4 | no | — |
| 227 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 228 | #405 | — | 2 | 1 | no | — |
| 229 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 230 | #335 | C23 | 1 | 2 | yes | — |
| 231 | #335 | C23 | 1 | 4 | yes | — |
| 232 | #334 | C23 | 1 | 2 | yes | — |
| 233 | #332 | C23 | 1 | 4 | yes | — |
| 234 | #332 | C23 | 1 | 4 | yes | — |
| 235 | #332 | C23 | 1 | 4 | yes | — |
| 236 | #331 | C23 | 1 | 4 | yes | — |
| 237 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 238 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 239 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 240 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 241 | #322 | C23 | 1 | 2 | yes | — |
| 242 | #322 | C23 | 1 | 2 | yes | — |
| 243 | H(5,𝔽2) | — | 8 | 8 | no | — |
| 244 | C2×#41 | — | 2 | 2 | no | — |
| 245 | C2×#41 | — | 2 | 4 | no | — |
| 246 | C2×#41 | — | 2 | 2 | no | — |
| 247 | C2×#41 | — | 4 | 2 | no | — |
| 248 | C22×Q8 | — | 2 | 4 | no | — |
| 249 | C22×D4 | — | 2 | 4 | no | — |
| 250 | C22×D4 | — | 2 | 4 | no | — |
| 251 | C22×D4 | — | 4 | 2 | no | — |
| 252 | C22×D4 | — | 4 | 4 | no | — |
| 253 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C23×C4 | — | 2 | 1 | no | — |
| 255 | #137 | — | 8 | 8 | no | — |
| 256 | C2×Q16 | — | 2 | 4 | no | — |
| 257 | C2×Q16 | — | 2 | 1 | no | — |
| 258 | C2×Q16 | — | 2 | 4 | no | — |
| 259 | C2×Q16 | — | 2 | 1 | no | — |
| 260 | C2×SD16 | — | 2 | 4 | no | — |
| 261 | C2×SD16 | — | 2 | 4 | no | — |
| 262 | C2×SD16 | — | 2 | 4 | no | — |
| 263 | C2×SD16 | — | 2 | 4 | no | — |
| 264 | C2×SD16 | — | 8 | 8 | no | — |
| 265 | C2×SD16 | C2×D4 | 1 | 4 | yes | — |
| 266 | C2×D8 | — | 2 | 4 | no | — |
| 267 | C2×D8 | — | 2 | 1 | no | — |
| 268 | C2×D8 | — | 2 | 1 | no | — |
| 269 | C2×D8 | — | 8 | 4 | no | — |
| 270 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 271 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 272 | C2×M16 | — | 2 | 1 | no | — |
| 273 | C2×M16 | — | 2 | 4 | no | — |
| 274 | C22×C8 | — | 2 | 1 | no | — |
| 275 | C22×C8 | — | 2 | 2 | no | — |
| 276 | C22×C8 | — | 2 | 2 | no | — |
| 277 | C22×C8 | — | 2 | 4 | no | — |
| 278 | C22×C8 | — | 8 | 2 | no | — |
| 279 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C4⋊Q8 | — | 2 | 4 | no | — |
| 282 | C4⋊Q8 | — | 4 | 2 | no | — |
| 283 | C4⋊Q8 | — | 4 | 4 | no | — |
| 284 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 285 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 286 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 288 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 289 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 290 | #127 | C2×D4 | 1 | 2 | yes | — |
| 291 | #127 | C24 | 1 | 2 | yes | — |
| 292 | #126 | — | 4 | 4 | no | — |
| 293 | #126 | — | 4 | 4 | no | — |
| 294 | #125 | — | 2 | 1 | no | — |
| 295 | #125 | — | 2 | 2 | no | — |
| 296 | #124 | — | 2 | 4 | no | — |
| 297 | #124 | — | 2 | 2 | no | — |
| 298 | #124 | — | 2 | 2 | no | — |
| 299 | #124 | — | 4 | 4 | no | — |
| 300 | #124 | — | 4 | 2 | no | — |
| 301 | #123 | — | 4 | 4 | no | — |
| 302 | #123 | — | 4 | 4 | no | — |
| 303 | #123 | — | 4 | 4 | no | — |
| 304 | #123 | — | 4 | 4 | no | — |
| 305 | C22⋊Q8 | — | 2 | 1 | no | — |
| 306 | C22⋊Q8 | — | 2 | 4 | no | — |
| 307 | C22⋊Q8 | — | 2 | 2 | no | — |
| 308 | C22⋊Q8 | — | 2 | 2 | no | — |
| 309 | C22⋊Q8 | — | 2 | 4 | no | — |
| 310 | C22⋊Q8 | — | 2 | 4 | no | — |
| 311 | C22⋊Q8 | — | 4 | 4 | no | — |
| 312 | C22⋊Q8 | — | 4 | 4 | no | — |
| 313 | C22⋊Q8 | — | 4 | 2 | no | — |
| 314 | C22⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 315 | #121 | — | 2 | 2 | no | — |
| 316 | #121 | — | 2 | 4 | no | — |
| 317 | #121 | — | 2 | 2 | no | — |
| 318 | #121 | — | 2 | 2 | no | — |
| 319 | #121 | — | 2 | 4 | no | — |
| 320 | #121 | — | 2 | 4 | no | — |
| 321 | #121 | — | 4 | 4 | no | — |
| 322 | #121 | — | 4 | 2 | no | — |
| 323 | #121 | — | 4 | 4 | no | — |
| 324 | #121 | C2×D4 | 1 | 4 | yes | — |
| 325 | #120 | — | 4 | 4 | no | — |
| 326 | #120 | — | 4 | 4 | no | — |
| 327 | C4×Q8 | — | 2 | 1 | no | — |
| 328 | C4×Q8 | — | 2 | 4 | no | — |
| 329 | C4×Q8 | — | 2 | 2 | no | — |
| 330 | C4×Q8 | — | 2 | 2 | no | — |
| 331 | C4×Q8 | — | 4 | 2 | no | — |
| 332 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 333 | C4×D4 | — | 2 | 4 | no | — |
| 334 | C4×D4 | — | 2 | 1 | no | — |
| 335 | C4×D4 | — | 2 | 2 | no | — |
| 336 | C4×D4 | — | 2 | 2 | no | — |
| 337 | C4×D4 | — | 2 | 1 | no | — |
| 338 | C4×D4 | — | 2 | 2 | no | — |
| 339 | C4×D4 | — | 4 | 2 | no | — |
| 340 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 341 | C4×D4 | C24 | 1 | 2 | yes | — |
| 342 | C4×D4 | C24 | 1 | 4 | yes | — |
| 343 | #117 | — | 2 | 1 | no | — |
| 344 | #117 | — | 2 | 2 | no | — |
| 345 | #117 | — | 2 | 4 | no | — |
| 346 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 347 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 348 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 349 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 350 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 351 | #107 | — | 2 | 1 | no | — |
| 352 | #107 | — | 2 | 1 | no | — |
| 353 | #107 | — | 2 | 1 | no | — |
| 354 | #107 | — | 2 | 1 | no | — |
| 355 | #107 | — | 2 | 4 | no | — |
| 356 | #107 | — | 2 | 4 | no | — |
| 357 | #107 | — | 2 | 4 | no | — |
| 358 | #107 | — | 4 | 2 | no | — |
| 359 | #107 | C2×D4 | 1 | 2 | yes | — |
| 360 | #107 | C2×D4 | 1 | 2 | yes | — |
| 361 | #106 | — | 4 | 2 | no | — |
| 362 | #106 | C2×D4 | 1 | 4 | yes | — |
| 363 | C4⋊C8 | — | 2 | 2 | no | — |
| 364 | C4⋊C8 | — | 2 | 2 | no | — |
| 365 | C4⋊C8 | — | 2 | 1 | no | — |
| 366 | C4⋊C8 | — | 2 | 1 | no | — |
| 367 | C4⋊C8 | — | 2 | 1 | no | — |
| 368 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 369 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 370 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 371 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 372 | #103 | — | 2 | 4 | no | — |
| 373 | #103 | — | 2 | 2 | no | — |
| 374 | #103 | — | 2 | 2 | no | — |
| 375 | #103 | — | 2 | 4 | no | — |
| 376 | #103 | — | 2 | 4 | no | — |
| 377 | #103 | — | 2 | 4 | no | — |
| 378 | #103 | C2×D4 | 1 | 4 | yes | — |
| 379 | #102 | — | 2 | 4 | no | — |
| 380 | #102 | — | 2 | 4 | no | — |
| 381 | #102 | — | 2 | 4 | no | — |
| 382 | #102 | — | 2 | 2 | no | — |
| 383 | #102 | — | 2 | 4 | no | — |
| 384 | #102 | — | 2 | 2 | no | — |
| 385 | #102 | — | 2 | 4 | no | — |
| 386 | #102 | — | 2 | 4 | no | — |
| 387 | #102 | — | 4 | 2 | no | — |
| 388 | #102 | — | 4 | 2 | no | — |
| 389 | #102 | C2×D4 | 1 | 4 | yes | — |
| 390 | #102 | C2×D4 | 1 | 4 | yes | — |
| 391 | #102 | C2×D4 | 1 | 4 | yes | — |
| 392 | C22⋊C8 | — | 2 | 2 | no | — |
| 393 | C22⋊C8 | — | 2 | 1 | no | — |
| 394 | C22⋊C8 | — | 2 | 2 | no | — |
| 395 | C22⋊C8 | — | 2 | 2 | no | — |
| 396 | C22⋊C8 | — | 2 | 4 | no | — |
| 397 | C22⋊C8 | — | 2 | 4 | no | — |
| 398 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 399 | #97 | — | 2 | 2 | no | — |
| 400 | #97 | — | 2 | 2 | no | — |
| 401 | C4×C8 | — | 2 | 2 | no | — |
| 402 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 403 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 404 | C4×C8 | C24 | 1 | 2 | yes | — |
| 405 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 406 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 407 | C4×C8 | C24 | 1 | 2 | yes | — |
| 408 | C24 | — | 2 | 1 | no | — |
| 409 | C24 | — | 4 | 4 | no | — |
| 410 | #41 | — | 4 | 8 | no | — |
| 411 | #41 | — | 8 | 4 | no | — |
| 412 | #41 | — | 8 | 4 | no | — |
| 413 | #41 | — | 8 | 4 | no | — |
| 414 | #41 | — | 8 | 8 | no | — |
| 415 | C2×Q8 | — | 2 | 1 | no | — |
| 416 | C2×Q8 | — | 2 | 2 | no | — |
| 417 | C2×Q8 | — | 2 | 2 | no | — |
| 418 | C2×Q8 | — | 2 | 2 | no | — |
| 419 | C2×Q8 | — | 2 | 2 | no | — |
| 420 | C2×Q8 | — | 4 | 4 | no | — |
| 421 | C2×Q8 | — | 8 | 4 | no | — |
| 422 | C2×Q8 | — | 8 | 4 | no | — |
| 423 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 424 | C2×D4 | — | 2 | 4 | no | — |
| 425 | C2×D4 | — | 2 | 4 | no | — |
| 426 | C2×D4 | — | 2 | 1 | no | — |
| 427 | C2×D4 | — | 2 | 2 | no | — |
| 428 | C2×D4 | — | 2 | 2 | no | — |
| 429 | C2×D4 | — | 2 | 2 | no | — |
| 430 | C2×D4 | — | 2 | 2 | no | — |
| 431 | C2×D4 | — | 2 | 2 | no | — |
| 432 | C2×D4 | — | 4 | 4 | no | — |
| 433 | C2×D4 | — | 4 | 4 | no | — |
| 434 | C2×D4 | — | 4 | 8 | no | — |
| 435 | C2×D4 | — | 4 | 4 | no | — |
| 436 | C2×D4 | — | 4 | 2 | no | — |
| 437 | C2×D4 | — | 8 | 4 | no | — |
| 438 | C2×D4 | — | 8 | 4 | no | — |
| 439 | C2×D4 | — | 8 | 4 | no | — |
| 440 | C2×D4 | — | 8 | 8 | no | — |
| 441 | C2×D4 | — | 8 | 16 | no | — |
| 442 | C2×D4 | C22×D4 | 1 | 4 | yes | — |
| 443 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 444 | C22×C4 | — | 2 | 1 | no | — |
| 445 | C22×C4 | — | 2 | 2 | no | — |
| 446 | C22×C4 | — | 2 | 4 | no | — |
| 447 | C22×C4 | — | 2 | 2 | no | — |
| 448 | C22×C4 | — | 4 | 4 | no | — |
| 449 | C22×C4 | — | 4 | 4 | no | — |
| 450 | C22×C4 | — | 4 | 2 | no | — |
| 451 | C22×C4 | — | 8 | 1 | no | — |
| 452 | C22×C4 | — | 8 | 1 | no | — |
| 453 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 454 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 455 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 456 | Q16 | — | 4 | 2 | no | — |
| 457 | Q16 | — | 8 | 1 | no | — |
| 458 | Q16 | — | 8 | 4 | no | — |
| 459 | Q16 | — | 8 | 4 | no | — |
| 460 | SD16 | — | 2 | 8 | no | — |
| 461 | SD16 | — | 4 | 8 | no | — |
| 462 | SD16 | — | 8 | 4 | no | — |
| 463 | SD16 | — | 8 | 4 | no | — |
| 464 | SD16 | — | 8 | 4 | no | — |
| 465 | D8 | — | 4 | 2 | no | — |
| 466 | D8 | — | 4 | 2 | no | — |
| 467 | D8 | — | 4 | 2 | no | — |
| 468 | D8 | — | 8 | 1 | no | — |
| 469 | D8 | — | 8 | 4 | no | — |
| 470 | M16 | — | 8 | 4 | no | — |
| 471 | M16 | — | 8 | 1 | no | — |
| 472 | C2×C8 | — | 2 | 2 | no | — |
| 473 | C2×C8 | — | 2 | 4 | no | — |
| 474 | C2×C8 | — | 2 | 2 | no | — |
| 475 | C2×C8 | — | 2 | 2 | no | — |
| 476 | C2×C8 | — | 4 | 1 | no | — |
| 477 | C2×C8 | — | 4 | 1 | no | — |
| 478 | C2×C8 | — | 4 | 4 | no | — |
| 479 | C2×C8 | — | 8 | 2 | no | — |
| 480 | C2×C8 | — | 8 | 4 | no | — |
| 481 | C2×C8 | — | 8 | 1 | no | — |
| 482 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 483 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 484 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 485 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 486 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 487 | C4⋊C4 | — | 2 | 1 | no | — |
| 488 | C4⋊C4 | — | 2 | 1 | no | — |
| 489 | C4⋊C4 | — | 2 | 1 | no | — |
| 490 | C4⋊C4 | — | 2 | 2 | no | — |
| 491 | C4⋊C4 | — | 2 | 1 | no | — |
| 492 | C4⋊C4 | — | 2 | 2 | no | — |
| 493 | C4⋊C4 | — | 2 | 2 | no | — |
| 494 | C4⋊C4 | — | 2 | 2 | no | — |
| 495 | C4⋊C4 | — | 2 | 2 | no | — |
| 496 | C4⋊C4 | — | 2 | 2 | no | — |
| 497 | C4⋊C4 | — | 2 | 2 | no | — |
| 498 | C4⋊C4 | — | 2 | 2 | no | — |
| 499 | C4⋊C4 | — | 2 | 2 | no | — |
| 500 | C4⋊C4 | — | 4 | 4 | no | — |
| 501 | C4⋊C4 | — | 4 | 4 | no | — |
| 502 | C4⋊C4 | — | 4 | 4 | no | — |
| 503 | C4⋊C4 | — | 4 | 2 | no | — |
| 504 | C4⋊C4 | — | 4 | 2 | no | — |
| 505 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 506 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 507 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 508 | C22⋊C4 | — | 2 | 2 | no | — |
| 509 | C22⋊C4 | — | 2 | 2 | no | — |
| 510 | C22⋊C4 | — | 2 | 4 | no | — |
| 511 | C22⋊C4 | — | 2 | 2 | no | — |
| 512 | C22⋊C4 | — | 2 | 4 | no | — |
| 513 | C22⋊C4 | — | 4 | 4 | no | — |
| 514 | C22⋊C4 | — | 4 | 4 | no | — |
| 515 | C22⋊C4 | — | 4 | 4 | no | — |
| 516 | C22⋊C4 | — | 4 | 4 | no | — |
| 517 | C22⋊C4 | — | 4 | 4 | no | — |
| 518 | C22⋊C4 | — | 4 | 2 | no | — |
| 519 | C22⋊C4 | — | 4 | 2 | no | — |
| 520 | C22⋊C4 | — | 4 | 2 | no | — |
| 521 | C42 | — | 2 | 2 | no | — |
| 522 | C42 | — | 4 | 4 | no | — |
| 523 | C42 | — | 4 | 2 | no | — |
| 524 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 525 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 526 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 527 | C42 | C25 | 1 | 1 | yes | characteristic |
| 528 | C23 | — | 2 | 4 | no | — |
| 529 | C23 | — | 2 | 2 | no | — |
| 530 | C23 | — | 2 | 4 | no | — |
| 531 | C23 | — | 4 | 2 | no | — |
| 532 | C23 | — | 8 | 1 | no | — |
| 533 | C23 | — | 8 | 1 | no | — |
| 534 | C23 | — | 8 | 8 | no | — |
| 535 | C23 | — | 16 | 4 | no | — |
| 536 | C23 | — | 16 | 4 | no | — |
| 537 | C23 | D42 | 1 | 1 | yes | characteristic |
| 538 | Q8 | — | 2 | 4 | no | — |
| 539 | Q8 | — | 4 | 2 | no | — |
| 540 | Q8 | — | 4 | 2 | no | — |
| 541 | Q8 | — | 4 | 2 | no | — |
| 542 | Q8 | — | 4 | 4 | no | — |
| 543 | Q8 | — | 4 | 4 | no | — |
| 544 | Q8 | — | 8 | 2 | no | — |
| 545 | Q8 | — | 16 | 4 | no | — |
| 546 | D4 | — | 2 | 4 | no | — |
| 547 | D4 | — | 2 | 4 | no | — |
| 548 | D4 | — | 2 | 4 | no | — |
| 549 | D4 | — | 2 | 2 | no | — |
| 550 | D4 | — | 4 | 2 | no | — |
| 551 | D4 | — | 4 | 2 | no | — |
| 552 | D4 | — | 4 | 4 | no | — |
| 553 | D4 | — | 8 | 2 | no | — |
| 554 | D4 | — | 8 | 2 | no | — |
| 555 | D4 | — | 8 | 2 | no | — |
| 556 | D4 | — | 8 | 4 | no | — |
| 557 | D4 | — | 8 | 8 | no | — |
| 558 | D4 | — | 8 | 8 | no | — |
| 559 | D4 | — | 8 | 4 | no | — |
| 560 | D4 | — | 16 | 4 | no | — |
| 561 | D4 | #576 | 1 | 4 | yes | — |
| 562 | C2×C4 | — | 2 | 1 | no | — |
| 563 | C2×C4 | — | 2 | 1 | no | — |
| 564 | C2×C4 | — | 2 | 2 | no | — |
| 565 | C2×C4 | — | 2 | 2 | no | — |
| 566 | C2×C4 | — | 2 | 2 | no | — |
| 567 | C2×C4 | — | 2 | 4 | no | — |
| 568 | C2×C4 | — | 2 | 2 | no | — |
| 569 | C2×C4 | — | 4 | 1 | no | — |
| 570 | C2×C4 | — | 4 | 2 | no | — |
| 571 | C2×C4 | — | 4 | 2 | no | — |
| 572 | C2×C4 | — | 4 | 4 | no | — |
| 573 | C2×C4 | — | 4 | 4 | no | — |
| 574 | C2×C4 | — | 4 | 2 | no | — |
| 575 | C2×C4 | — | 4 | 2 | no | — |
| 576 | C2×C4 | — | 4 | 2 | no | — |
| 577 | C2×C4 | — | 8 | 2 | no | — |
| 578 | C2×C4 | — | 8 | 4 | no | — |
| 579 | C2×C4 | — | 8 | 1 | no | — |
| 580 | C2×C4 | — | 8 | 8 | no | — |
| 581 | C2×C4 | — | 16 | 4 | no | — |
| 582 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 583 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 584 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 585 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 586 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 587 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 588 | C8 | — | 2 | 1 | no | — |
| 589 | C8 | — | 2 | 1 | no | — |
| 590 | C8 | — | 2 | 1 | no | — |
| 591 | C8 | — | 2 | 1 | no | — |
| 592 | C8 | — | 2 | 4 | no | — |
| 593 | C8 | — | 4 | 2 | no | — |
| 594 | C8 | — | 4 | 2 | no | — |
| 595 | C8 | — | 4 | 2 | no | — |
| 596 | C8 | — | 4 | 4 | no | — |
| 597 | C22 | — | 2 | 1 | no | — |
| 598 | C22 | — | 2 | 4 | no | — |
| 599 | C22 | — | 2 | 1 | no | — |
| 600 | C22 | — | 2 | 1 | no | — |
| 601 | C22 | — | 4 | 2 | no | — |
| 602 | C22 | — | 4 | 2 | no | — |
| 603 | C22 | — | 4 | 4 | no | — |
| 604 | C22 | — | 4 | 4 | no | — |
| 605 | C22 | — | 4 | 4 | no | — |
| 606 | C22 | — | 8 | 4 | no | — |
| 607 | C22 | — | 8 | 2 | no | — |
| 608 | C22 | — | 8 | 2 | no | — |
| 609 | C22 | — | 8 | 2 | no | — |
| 610 | C22 | — | 32 | 8 | no | — |
| 611 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 612 | C4 | — | 2 | 1 | no | — |
| 613 | C4 | — | 2 | 1 | no | — |
| 614 | C4 | — | 2 | 1 | no | — |
| 615 | C4 | — | 2 | 1 | no | — |
| 616 | C4 | — | 4 | 4 | no | — |
| 617 | C4 | — | 4 | 2 | no | — |
| 618 | C4 | — | 4 | 2 | no | — |
| 619 | C4 | — | 4 | 2 | no | — |
| 620 | C4 | — | 8 | 2 | no | — |
| 621 | C4 | — | 8 | 2 | no | — |
| 622 | C4 | — | 8 | 2 | no | — |
| 623 | C4 | C2×#576 | 1 | 2 | yes | — |
| 624 | C4 | #3585 | 1 | 1 | yes | characteristic |
| 625 | C4 | #3586 | 1 | 1 | yes | characteristic |
| 626 | C2 | — | 4 | 1 | no | — |
| 627 | C2 | — | 4 | 4 | no | — |
| 628 | C2 | — | 8 | 4 | no | — |
| 629 | C2 | — | 16 | 2 | no | — |
| 630 | C2 | #61049 | 1 | 1 | yes | characteristic |
| 631 | C2 | #61080 | 1 | 1 | yes | characteristic |
| 632 | C2 | #61108 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C42 | C25 |
| prime radical | #62245 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62375 | C2 | semidirect |
| 3. #61680 | C2 | semidirect |
| 4. #20054 | C2 | semidirect |
| 5. #20029 | C2 | semidirect |
| 6. #19777 | C2 | semidirect |
| 7. #19757 | C2 | semidirect |
| 8. #19712 | C2 | semidirect |
| 9. #19511 | C2 | semidirect |
| 10. #19347 | C2 | semidirect |
| 11. #19259 | C2 | semidirect |
| 12. #18948 | C2 | semidirect |
| 13. #18846 | C2 | semidirect |
| 14. #17989 | C2 | semidirect |
| 15. #17905 | C2 | semidirect |
| 16. #3550 | C22 | semidirect |
| 19. #3393 | C22 | semidirect |
| 21. Q8×D8 | C22 | semidirect |
| 23. #3367 | C22 | semidirect |
| 26. #3324 | C22 | semidirect |
| 28. #3302 | C22 | semidirect |
| 31. D4×SD16 | C22 | semidirect |
| 34. #3276 | C22 | semidirect |
| 37. #3254 | C22 | semidirect |
| 39. #3228 | C22 | semidirect |
| 40. #3216 | C22 | semidirect |
| 41. #3210 | C22 | semidirect |
| 45. #3170 | C22 | semidirect |
| 52. #2981 | C22 | semidirect |
| 53. #2960 | C22 | semidirect |
| 55. #1723 | C22 | semidirect |
| 56. #1722 | C22 | semidirect |
| 57. #1720 | C22 | semidirect |
| 58. #1717 | C22 | semidirect |
| 59. #1699 | C22 | semidirect |
| 60. #1694 | C22 | semidirect |
| 61. #1688 | C22 | semidirect |
| 62. #1685 | C22 | semidirect |
| 63. #1682 | C22 | semidirect |
| 64. #1681 | C22 | semidirect |
| 65. #1679 | C22 | semidirect |
| 66. #1673 | C22 | semidirect |
| 67. #1669 | C22 | semidirect |
| 68. #1669 | C22 | semidirect |
| 69. #1654 | C22 | semidirect |
| 70. #1652 | C22 | semidirect |
| 71. #1649 | C22 | semidirect |
| 72. #1647 | C22 | semidirect |
| 73. #1639 | C22 | semidirect |
| 74. #1639 | C22 | semidirect |
| 75. #1628 | C22 | semidirect |
| 76. #1627 | C22 | semidirect |
| 77. #1586 | C22 | semidirect |
| 78. #1585 | C22 | semidirect |
| 79. #1581 | C22 | semidirect |
| 80. SD16⋊C8 | C22 | semidirect |
| 81. #1571 | C22 | semidirect |
| 82. #1568 | C22 | semidirect |
| 83. #1557 | C22 | semidirect |
| 84. #1552 | C22 | semidirect |
| 85. #1496 | C22 | semidirect |
| 87. #1481 | C22 | semidirect |
| 88. #1452 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62375 | 2 |
| #62245 | 2 |
| #61680 | 2 |
| #20054 | 2 |
| #20029 | 2 |
| #19777 | 2 |
| #19757 | 2 |
| #19712 | 2 |
| #19511 | 2 |
| #19347 | 2 |
| #19259 | 2 |
| #18948 | 2 |
| #18846 | 2 |
| #17989 | 2 |
| #17905 | 2 |