Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6383 conjugacy classes of subgroups.
The subgroup lattice has 593 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63048 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62437 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #62329 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #62275 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #62091 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #61674 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #61646 | C2 | 1 | 12 | yes | maximal, complemented |
| 8 | #61478 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #61090 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #61053 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #60307 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#578 | C22 | 1 | 3 | yes | — |
| 13 | C2×#576 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C23×Q16 | C22 | 1 | 2 | yes | complemented |
| 15 | #3561 | — | 2 | 12 | no | — |
| 16 | #3561 | C22 | 1 | 12 | yes | complemented |
| 17 | #3550 | — | 2 | 6 | no | — |
| 18 | #3550 | C22 | 1 | 6 | yes | — |
| 19 | #3540 | — | 2 | 12 | no | — |
| 20 | #3540 | C22 | 1 | 12 | yes | complemented |
| 21 | #3529 | — | 2 | 2 | no | — |
| 22 | #3529 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3518 | C22 | 1 | 12 | yes | complemented |
| 24 | #3500 | C22 | 1 | 6 | yes | — |
| 25 | #3486 | C22 | 1 | 12 | yes | complemented |
| 26 | #3402 | C22 | 1 | 12 | yes | complemented |
| 27 | #3393 | C22 | 1 | 6 | yes | complemented |
| 28 | Q8×Q16 | C22 | 1 | 2 | yes | complemented |
| 29 | #3369 | C22 | 1 | 12 | yes | complemented |
| 30 | #3342 | C22 | 1 | 12 | yes | complemented |
| 31 | #3341 | C22 | 1 | 6 | yes | complemented |
| 32 | #3329 | C22 | 1 | 12 | yes | complemented |
| 33 | #3328 | C22 | 1 | 24 | yes | complemented |
| 34 | #3321 | C22 | 1 | 24 | yes | complemented |
| 35 | #3313 | C22 | 1 | 24 | yes | complemented |
| 36 | #3311 | C22 | 1 | 24 | yes | complemented |
| 37 | D4×Q16 | C22 | 1 | 6 | yes | complemented |
| 38 | D4×Q16 | C22 | 1 | 12 | yes | complemented |
| 39 | #3285 | C22 | 1 | 12 | yes | complemented |
| 40 | #3285 | C22 | 1 | 12 | yes | complemented |
| 41 | #3280 | C22 | 1 | 12 | yes | complemented |
| 42 | #3277 | C22 | 1 | 12 | yes | complemented |
| 43 | #3275 | C22 | 1 | 24 | yes | complemented |
| 44 | #3270 | C22 | 1 | 24 | yes | complemented |
| 45 | #3270 | C22 | 1 | 24 | yes | complemented |
| 46 | #3266 | C22 | 1 | 24 | yes | complemented |
| 47 | #3263 | C22 | 1 | 12 | yes | complemented |
| 48 | #3255 | C22 | 1 | 6 | yes | complemented |
| 49 | #3225 | C22 | 1 | 24 | yes | complemented |
| 50 | #3215 | C22 | 1 | 12 | yes | complemented |
| 51 | #3202 | C22 | 1 | 6 | yes | complemented |
| 52 | #3202 | C22 | 1 | 6 | yes | complemented |
| 53 | #3200 | C22 | 1 | 12 | yes | complemented |
| 54 | #3197 | C22 | 1 | 12 | yes | complemented |
| 55 | #3175 | C22 | 1 | 12 | yes | complemented |
| 56 | #3170 | C22 | 1 | 6 | yes | complemented |
| 57 | #3156 | C22 | 1 | 6 | yes | complemented |
| 58 | C2×#495 | C22 | 1 | 3 | yes | complemented |
| 59 | #3121 | C22 | 1 | 24 | yes | complemented |
| 60 | #3116 | C22 | 1 | 12 | yes | complemented |
| 61 | #3059 | C22 | 1 | 6 | yes | complemented |
| 62 | #3059 | C22 | 1 | 3 | yes | complemented |
| 63 | #3058 | C22 | 1 | 3 | yes | — |
| 64 | #3050 | C22 | 1 | 6 | yes | complemented |
| 65 | #3044 | C22 | 1 | 12 | yes | complemented |
| 66 | #3040 | C22 | 1 | 6 | yes | complemented |
| 67 | #3011 | C22 | 1 | 12 | yes | complemented |
| 68 | #3010 | C22 | 1 | 6 | yes | — |
| 69 | #3009 | C22 | 1 | 6 | yes | complemented |
| 70 | #3004 | C22 | 1 | 12 | yes | complemented |
| 71 | #2995 | C22 | 1 | 6 | yes | complemented |
| 72 | #2980 | C22 | 1 | 3 | yes | — |
| 73 | #2978 | C22 | 1 | 6 | yes | complemented |
| 74 | #2966 | C22 | 1 | 6 | yes | complemented |
| 75 | #2950 | C22 | 1 | 6 | yes | complemented |
| 76 | C4×#135 | C22 | 1 | 3 | yes | complemented |
| 77 | #2931 | C22 | 1 | 3 | yes | — |
| 78 | #2929 | C22 | 1 | 6 | yes | complemented |
| 79 | C2×2−1+4 | C23 | 1 | 6 | yes | — |
| 80 | C2×H(5,𝔽2) | C23 | 1 | 2 | yes | — |
| 81 | C23×Q8 | C23 | 1 | 4 | yes | — |
| 82 | #578 | — | 4 | 12 | no | — |
| 83 | #576 | — | 4 | 4 | no | — |
| 84 | C2×#137 | C23 | 1 | 12 | yes | — |
| 85 | C2×#137 | C23 | 1 | 6 | yes | — |
| 86 | C2×#137 | C23 | 1 | 12 | yes | — |
| 87 | C2×AGL(1,ℤ/8) | C23 | 1 | 6 | yes | — |
| 88 | C2×#135 | C23 | 1 | 3 | yes | — |
| 89 | C2×#135 | C23 | 1 | 6 | yes | — |
| 90 | C22×Q16 | — | 4 | 8 | no | — |
| 91 | C22×Q16 | C23 | 1 | 6 | yes | — |
| 92 | C22×Q16 | C23 | 1 | 3 | yes | — |
| 93 | C22×Q16 | C23 | 1 | 6 | yes | — |
| 94 | C22×Q16 | C23 | 1 | 12 | yes | — |
| 95 | C22×SD16 | C23 | 1 | 6 | yes | — |
| 96 | C22×D8 | C23 | 1 | 3 | yes | — |
| 97 | C2×#131 | C23 | 1 | 3 | yes | — |
| 98 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 99 | C23×C8 | C23 | 1 | 2 | yes | — |
| 100 | #563 | — | 2 | 12 | no | — |
| 101 | #563 | — | 2 | 6 | no | — |
| 102 | #563 | — | 2 | 6 | no | — |
| 103 | #563 | D4 | 1 | 3 | yes | — |
| 104 | #562 | — | 2 | 12 | no | — |
| 105 | #562 | D4 | 1 | 6 | yes | — |
| 106 | H(3,𝔽4) | — | 2 | 12 | no | — |
| 107 | H(3,𝔽4) | D4 | 1 | 1 | yes | characteristic |
| 108 | #560 | — | 2 | 12 | no | — |
| 109 | #560 | D4 | 1 | 6 | yes | — |
| 110 | #559 | — | 2 | 6 | no | — |
| 111 | #559 | — | 2 | 12 | no | — |
| 112 | Q82 | — | 2 | 6 | no | — |
| 113 | Q82 | C23 | 1 | 4 | yes | — |
| 114 | #556 | — | 2 | 24 | no | — |
| 115 | #556 | — | 2 | 12 | no | — |
| 116 | #556 | C23 | 1 | 12 | yes | — |
| 117 | #556 | C23 | 1 | 24 | yes | — |
| 118 | #555 | — | 2 | 12 | no | — |
| 119 | #555 | C23 | 1 | 12 | yes | — |
| 120 | #551 | — | 2 | 24 | no | — |
| 121 | #551 | — | 2 | 12 | no | — |
| 122 | D4×Q8 | — | 2 | 24 | no | — |
| 123 | D4×Q8 | C23 | 1 | 24 | yes | — |
| 124 | D4×Q8 | C23 | 1 | 12 | yes | — |
| 125 | #548 | — | 2 | 24 | no | — |
| 126 | #548 | C23 | 1 | 24 | yes | — |
| 127 | #548 | C23 | 1 | 24 | yes | — |
| 128 | #546 | — | 2 | 24 | no | — |
| 129 | #546 | C23 | 1 | 24 | yes | — |
| 130 | #543 | — | 2 | 12 | no | — |
| 131 | #542 | — | 2 | 24 | no | — |
| 132 | #542 | — | 2 | 24 | no | — |
| 133 | #542 | — | 2 | 24 | no | — |
| 134 | #542 | — | 2 | 24 | no | — |
| 135 | #542 | C23 | 1 | 24 | yes | — |
| 136 | #538 | — | 2 | 12 | no | — |
| 137 | #538 | — | 2 | 24 | no | — |
| 138 | #536 | — | 2 | 6 | no | — |
| 139 | #536 | — | 2 | 12 | no | — |
| 140 | #536 | — | 2 | 12 | no | — |
| 141 | #536 | C23 | 1 | 12 | yes | — |
| 142 | #536 | C23 | 1 | 12 | yes | — |
| 143 | #536 | C23 | 1 | 6 | yes | — |
| 144 | #535 | — | 2 | 6 | no | — |
| 145 | #535 | C23 | 1 | 6 | yes | — |
| 146 | #533 | — | 2 | 12 | no | — |
| 147 | #533 | C23 | 1 | 12 | yes | — |
| 148 | #532 | — | 2 | 6 | no | — |
| 149 | #532 | C23 | 1 | 3 | yes | — |
| 150 | #529 | — | 2 | 12 | no | — |
| 151 | #529 | C23 | 1 | 6 | yes | — |
| 152 | C2×#124 | — | 2 | 6 | no | — |
| 153 | C2×#124 | C23 | 1 | 6 | yes | — |
| 154 | #525 | — | 2 | 12 | no | — |
| 155 | #525 | — | 2 | 12 | no | — |
| 156 | #525 | C23 | 1 | 12 | yes | — |
| 157 | #525 | C23 | 1 | 6 | yes | — |
| 158 | #519 | C23 | 1 | 12 | yes | — |
| 159 | C4×#41 | C23 | 1 | 6 | yes | — |
| 160 | #500 | C23 | 1 | 6 | yes | — |
| 161 | #497 | C23 | 1 | 24 | yes | — |
| 162 | #495 | C23 | 1 | 12 | yes | — |
| 163 | #495 | C23 | 1 | 12 | yes | — |
| 164 | #494 | C23 | 1 | 6 | yes | — |
| 165 | #489 | C23 | 1 | 24 | yes | — |
| 166 | #487 | C23 | 1 | 12 | yes | — |
| 167 | #485 | C23 | 1 | 24 | yes | — |
| 168 | #485 | C23 | 1 | 24 | yes | — |
| 169 | #482 | C23 | 1 | 24 | yes | — |
| 170 | #477 | C23 | 1 | 12 | yes | — |
| 171 | #476 | C23 | 1 | 12 | yes | — |
| 172 | #475 | C23 | 1 | 24 | yes | — |
| 173 | #470 | C23 | 1 | 12 | yes | — |
| 174 | #470 | C23 | 1 | 12 | yes | — |
| 175 | #470 | C23 | 1 | 12 | yes | — |
| 176 | #469 | C23 | 1 | 12 | yes | — |
| 177 | #468 | C23 | 1 | 24 | yes | — |
| 178 | #467 | C23 | 1 | 12 | yes | — |
| 179 | #467 | C23 | 1 | 12 | yes | — |
| 180 | #467 | C23 | 1 | 12 | yes | — |
| 181 | #466 | C23 | 1 | 12 | yes | — |
| 182 | #465 | C23 | 1 | 24 | yes | — |
| 183 | #464 | C23 | 1 | 24 | yes | — |
| 184 | #464 | C23 | 1 | 24 | yes | — |
| 185 | #464 | C23 | 1 | 24 | yes | — |
| 186 | #463 | C23 | 1 | 24 | yes | — |
| 187 | #462 | C23 | 1 | 24 | yes | — |
| 188 | #462 | C23 | 1 | 12 | yes | — |
| 189 | #461 | C23 | 1 | 12 | yes | — |
| 190 | #452 | C23 | 1 | 24 | yes | — |
| 191 | #452 | C23 | 1 | 24 | yes | — |
| 192 | #451 | C23 | 1 | 24 | yes | — |
| 193 | #451 | C23 | 1 | 24 | yes | — |
| 194 | #451 | C23 | 1 | 24 | yes | — |
| 195 | #450 | C23 | 1 | 24 | yes | — |
| 196 | #449 | C23 | 1 | 24 | yes | — |
| 197 | #448 | C23 | 1 | 24 | yes | — |
| 198 | #448 | C23 | 1 | 24 | yes | — |
| 199 | #446 | C23 | 1 | 6 | yes | — |
| 200 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 201 | #441 | C23 | 1 | 24 | yes | — |
| 202 | #440 | C23 | 1 | 24 | yes | — |
| 203 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 204 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 205 | C4×Q16 | C23 | 1 | 6 | yes | — |
| 206 | C4×SD16 | C23 | 1 | 12 | yes | — |
| 207 | C4×D8 | C23 | 1 | 6 | yes | — |
| 208 | #436 | C23 | 1 | 12 | yes | — |
| 209 | #436 | C23 | 1 | 6 | yes | — |
| 210 | #435 | C23 | 1 | 12 | yes | — |
| 211 | #435 | C23 | 1 | 12 | yes | — |
| 212 | #435 | C23 | 1 | 12 | yes | — |
| 213 | C8×D4 | C23 | 1 | 6 | yes | — |
| 214 | C8×D4 | C23 | 1 | 12 | yes | — |
| 215 | #433 | C23 | 1 | 12 | yes | — |
| 216 | #432 | C23 | 1 | 6 | yes | — |
| 217 | #427 | C23 | 1 | 6 | yes | — |
| 218 | #427 | C23 | 1 | 3 | yes | — |
| 219 | #424 | C23 | 1 | 6 | yes | — |
| 220 | #423 | C23 | 1 | 3 | yes | — |
| 221 | #419 | C23 | 1 | 6 | yes | — |
| 222 | #419 | C23 | 1 | 12 | yes | — |
| 223 | #419 | C23 | 1 | 12 | yes | — |
| 224 | #418 | C23 | 1 | 6 | yes | — |
| 225 | #416 | C23 | 1 | 6 | yes | — |
| 226 | #416 | C23 | 1 | 12 | yes | — |
| 227 | #408 | C23 | 1 | 6 | yes | — |
| 228 | #408 | C23 | 1 | 3 | yes | — |
| 229 | #408 | C23 | 1 | 3 | yes | — |
| 230 | #407 | C23 | 1 | 6 | yes | — |
| 231 | #405 | C23 | 1 | 6 | yes | — |
| 232 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 233 | 2−1+4 | — | 4 | 12 | no | — |
| 234 | 2−1+4 | — | 8 | 6 | no | — |
| 235 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 236 | H(5,𝔽2) | — | 8 | 2 | no | — |
| 237 | C2×#41 | — | 2 | 2 | no | — |
| 238 | C2×#41 | — | 2 | 6 | no | — |
| 239 | C2×#41 | — | 2 | 12 | no | — |
| 240 | C2×#41 | C24 | 1 | 6 | yes | — |
| 241 | C2×#41 | C24 | 1 | 12 | yes | — |
| 242 | C2×#41 | C24 | 1 | 3 | yes | — |
| 243 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 244 | C22×Q8 | — | 2 | 6 | no | — |
| 245 | C22×Q8 | — | 2 | 12 | no | — |
| 246 | C22×Q8 | — | 4 | 8 | no | — |
| 247 | C22×Q8 | — | 8 | 4 | no | — |
| 248 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 249 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 250 | C22×Q8 | C24 | 1 | 12 | yes | — |
| 251 | C22×D4 | — | 2 | 6 | no | — |
| 252 | C22×D4 | C24 | 1 | 6 | yes | — |
| 253 | C23×C4 | — | 2 | 4 | no | — |
| 254 | C23×C4 | C24 | 1 | 2 | yes | — |
| 255 | #137 | — | 4 | 24 | no | — |
| 256 | #137 | — | 4 | 12 | no | — |
| 257 | #137 | — | 8 | 12 | no | — |
| 258 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 259 | #135 | — | 2 | 12 | no | — |
| 260 | #135 | — | 4 | 12 | no | — |
| 261 | C2×Q16 | — | 2 | 24 | no | — |
| 262 | C2×Q16 | — | 4 | 12 | no | — |
| 263 | C2×Q16 | — | 4 | 6 | no | — |
| 264 | C2×Q16 | — | 4 | 24 | no | — |
| 265 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 266 | C2×Q16 | C24 | 1 | 12 | yes | — |
| 267 | C2×Q16 | C24 | 1 | 12 | yes | — |
| 268 | C2×Q16 | C24 | 1 | 6 | yes | — |
| 269 | C2×Q16 | C24 | 1 | 12 | yes | — |
| 270 | C2×Q16 | C24 | 1 | 1 | yes | characteristic |
| 271 | C2×SD16 | — | 8 | 6 | no | — |
| 272 | C2×SD16 | C24 | 1 | 6 | yes | — |
| 273 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 274 | C2×SD16 | C24 | 1 | 12 | yes | — |
| 275 | C2×D8 | — | 4 | 6 | no | — |
| 276 | C2×D8 | C24 | 1 | 3 | yes | — |
| 277 | C2×D8 | C24 | 1 | 6 | yes | — |
| 278 | #131 | — | 4 | 2 | no | — |
| 279 | #131 | — | 4 | 6 | no | — |
| 280 | C2×M16 | C24 | 1 | 3 | yes | — |
| 281 | C2×M16 | C24 | 1 | 6 | yes | — |
| 282 | C2×M16 | C24 | 1 | 3 | yes | — |
| 283 | C2×M16 | C24 | 1 | 6 | yes | — |
| 284 | C22×C8 | — | 4 | 4 | no | — |
| 285 | C22×C8 | C24 | 1 | 6 | yes | — |
| 286 | C22×C8 | C24 | 1 | 3 | yes | — |
| 287 | C22×C8 | C24 | 1 | 6 | yes | — |
| 288 | C22×C8 | C24 | 1 | 3 | yes | — |
| 289 | C4⋊Q8 | — | 2 | 6 | no | — |
| 290 | C4⋊Q8 | — | 2 | 12 | no | — |
| 291 | C4⋊Q8 | — | 2 | 12 | no | — |
| 292 | C4⋊Q8 | — | 2 | 12 | no | — |
| 293 | C4⋊Q8 | — | 2 | 24 | no | — |
| 294 | C4⋊Q8 | C2×D4 | 1 | 3 | yes | — |
| 295 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 296 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 297 | #127 | — | 2 | 6 | no | — |
| 298 | #127 | C2×D4 | 1 | 3 | yes | — |
| 299 | #126 | — | 2 | 24 | no | — |
| 300 | #126 | — | 2 | 24 | no | — |
| 301 | #126 | — | 2 | 24 | no | — |
| 302 | #126 | — | 2 | 24 | no | — |
| 303 | #126 | C2×D4 | 1 | 12 | yes | — |
| 304 | #125 | — | 2 | 12 | no | — |
| 305 | #125 | C2×D4 | 1 | 6 | yes | — |
| 306 | #124 | — | 2 | 6 | no | — |
| 307 | #124 | — | 2 | 6 | no | — |
| 308 | #124 | — | 2 | 12 | no | — |
| 309 | #124 | — | 2 | 24 | no | — |
| 310 | #124 | — | 2 | 24 | no | — |
| 311 | #124 | — | 2 | 24 | no | — |
| 312 | #124 | — | 2 | 24 | no | — |
| 313 | #124 | — | 2 | 24 | no | — |
| 314 | #124 | — | 2 | 6 | no | — |
| 315 | #124 | — | 2 | 6 | no | — |
| 316 | #124 | C2×D4 | 1 | 3 | yes | — |
| 317 | #124 | C2×D4 | 1 | 6 | yes | — |
| 318 | #124 | C2×D4 | 1 | 3 | yes | — |
| 319 | #124 | C24 | 1 | 24 | yes | — |
| 320 | #123 | — | 2 | 12 | no | — |
| 321 | #123 | — | 2 | 12 | no | — |
| 322 | #123 | — | 2 | 12 | no | — |
| 323 | #123 | — | 2 | 12 | no | — |
| 324 | #123 | — | 2 | 24 | no | — |
| 325 | #123 | — | 2 | 12 | no | — |
| 326 | #123 | — | 2 | 12 | no | — |
| 327 | #123 | — | 2 | 24 | no | — |
| 328 | #123 | C2×D4 | 1 | 6 | yes | — |
| 329 | #123 | C2×D4 | 1 | 6 | yes | — |
| 330 | #123 | C2×D4 | 1 | 12 | yes | — |
| 331 | C22⋊Q8 | — | 2 | 12 | no | — |
| 332 | C22⋊Q8 | — | 2 | 12 | no | — |
| 333 | C22⋊Q8 | — | 2 | 24 | no | — |
| 334 | C22⋊Q8 | — | 2 | 24 | no | — |
| 335 | C22⋊Q8 | — | 2 | 24 | no | — |
| 336 | C22⋊Q8 | — | 2 | 24 | no | — |
| 337 | C22⋊Q8 | — | 2 | 24 | no | — |
| 338 | C22⋊Q8 | — | 2 | 24 | no | — |
| 339 | C22⋊Q8 | — | 2 | 24 | no | — |
| 340 | C22⋊Q8 | C2×D4 | 1 | 12 | yes | — |
| 341 | C22⋊Q8 | C2×D4 | 1 | 6 | yes | — |
| 342 | C22⋊Q8 | C24 | 1 | 24 | yes | — |
| 343 | C22⋊Q8 | C24 | 1 | 24 | yes | — |
| 344 | #121 | — | 2 | 24 | no | — |
| 345 | #121 | — | 2 | 24 | no | — |
| 346 | #121 | — | 2 | 12 | no | — |
| 347 | #121 | — | 2 | 24 | no | — |
| 348 | #121 | C2×D4 | 1 | 12 | yes | — |
| 349 | #121 | C2×D4 | 1 | 6 | yes | — |
| 350 | #121 | C2×D4 | 1 | 12 | yes | — |
| 351 | #121 | C24 | 1 | 24 | yes | — |
| 352 | #120 | — | 2 | 12 | no | — |
| 353 | #120 | — | 2 | 24 | no | — |
| 354 | #120 | — | 2 | 12 | no | — |
| 355 | #120 | C2×D4 | 1 | 6 | yes | — |
| 356 | #120 | C2×D4 | 1 | 6 | yes | — |
| 357 | C4×Q8 | — | 2 | 4 | no | — |
| 358 | C4×Q8 | — | 2 | 24 | no | — |
| 359 | C4×Q8 | — | 2 | 24 | no | — |
| 360 | C4×Q8 | — | 2 | 12 | no | — |
| 361 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 362 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 363 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 364 | C4×D4 | — | 2 | 12 | no | — |
| 365 | C4×D4 | — | 2 | 24 | no | — |
| 366 | C4×D4 | — | 2 | 12 | no | — |
| 367 | C4×D4 | — | 2 | 24 | no | — |
| 368 | C4×D4 | — | 2 | 24 | no | — |
| 369 | C4×D4 | — | 2 | 24 | no | — |
| 370 | C4×D4 | C24 | 1 | 12 | yes | — |
| 371 | C4×D4 | C24 | 1 | 6 | yes | — |
| 372 | C4×D4 | C24 | 1 | 12 | yes | — |
| 373 | #117 | — | 2 | 12 | no | — |
| 374 | #117 | — | 2 | 12 | no | — |
| 375 | #117 | — | 2 | 12 | no | — |
| 376 | #117 | — | 2 | 12 | no | — |
| 377 | #117 | — | 2 | 12 | no | — |
| 378 | #117 | — | 2 | 6 | no | — |
| 379 | #117 | C24 | 1 | 6 | yes | — |
| 380 | #117 | C24 | 1 | 12 | yes | — |
| 381 | #117 | C24 | 1 | 6 | yes | — |
| 382 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 383 | C2×C22⋊C4 | — | 2 | 24 | no | — |
| 384 | C2×C42 | — | 2 | 6 | no | — |
| 385 | C2×C42 | C24 | 1 | 3 | yes | — |
| 386 | #107 | C24 | 1 | 6 | yes | — |
| 387 | #107 | C24 | 1 | 12 | yes | — |
| 388 | #106 | C24 | 1 | 6 | yes | — |
| 389 | #106 | C24 | 1 | 12 | yes | — |
| 390 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 391 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 392 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 393 | #103 | C24 | 1 | 12 | yes | — |
| 394 | #103 | C24 | 1 | 24 | yes | — |
| 395 | #103 | C24 | 1 | 24 | yes | — |
| 396 | #103 | C24 | 1 | 24 | yes | — |
| 397 | #102 | C24 | 1 | 24 | yes | — |
| 398 | #102 | C24 | 1 | 12 | yes | — |
| 399 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 400 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 401 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 402 | #97 | C24 | 1 | 12 | yes | — |
| 403 | C4×C8 | C24 | 1 | 6 | yes | — |
| 404 | C4×C8 | C24 | 1 | 6 | yes | — |
| 405 | C24 | — | 2 | 6 | no | — |
| 406 | C24 | C22×D4 | 1 | 2 | yes | — |
| 407 | #41 | — | 2 | 12 | no | — |
| 408 | #41 | — | 4 | 1 | no | — |
| 409 | #41 | — | 4 | 3 | no | — |
| 410 | #41 | — | 4 | 1 | no | — |
| 411 | #41 | — | 4 | 3 | no | — |
| 412 | #41 | — | 4 | 6 | no | — |
| 413 | #41 | — | 4 | 12 | no | — |
| 414 | #41 | — | 4 | 12 | no | — |
| 415 | #41 | — | 8 | 12 | no | — |
| 416 | #41 | — | 8 | 4 | no | — |
| 417 | #41 | — | 8 | 24 | no | — |
| 418 | C2×Q8 | — | 2 | 12 | no | — |
| 419 | C2×Q8 | — | 2 | 12 | no | — |
| 420 | C2×Q8 | — | 2 | 12 | no | — |
| 421 | C2×Q8 | — | 2 | 6 | no | — |
| 422 | C2×Q8 | — | 2 | 24 | no | — |
| 423 | C2×Q8 | — | 4 | 12 | no | — |
| 424 | C2×Q8 | — | 4 | 6 | no | — |
| 425 | C2×Q8 | — | 4 | 12 | no | — |
| 426 | C2×Q8 | — | 4 | 6 | no | — |
| 427 | C2×Q8 | — | 4 | 12 | no | — |
| 428 | C2×Q8 | — | 8 | 24 | no | — |
| 429 | C2×Q8 | — | 8 | 12 | no | — |
| 430 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 431 | C2×Q8 | C22×D4 | 1 | 3 | yes | — |
| 432 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 433 | C2×Q8 | C25 | 1 | 12 | yes | — |
| 434 | C2×Q8 | C25 | 1 | 2 | yes | — |
| 435 | C2×D4 | — | 2 | 6 | no | — |
| 436 | C2×D4 | — | 2 | 24 | no | — |
| 437 | C2×D4 | — | 2 | 12 | no | — |
| 438 | C2×D4 | — | 2 | 6 | no | — |
| 439 | C2×D4 | — | 4 | 6 | no | — |
| 440 | C2×D4 | — | 4 | 6 | no | — |
| 441 | C2×D4 | — | 8 | 12 | no | — |
| 442 | C2×D4 | C22×D4 | 1 | 12 | yes | — |
| 443 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 444 | C2×D4 | C22×D4 | 1 | 6 | yes | — |
| 445 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 446 | C2×D4 | C22×D4 | 1 | 3 | yes | — |
| 447 | C2×D4 | C25 | 1 | 6 | yes | — |
| 448 | C22×C4 | — | 2 | 12 | no | — |
| 449 | C22×C4 | — | 2 | 6 | no | — |
| 450 | C22×C4 | — | 2 | 12 | no | — |
| 451 | C22×C4 | — | 2 | 6 | no | — |
| 452 | C22×C4 | — | 2 | 12 | no | — |
| 453 | C22×C4 | — | 2 | 12 | no | — |
| 454 | C22×C4 | — | 4 | 2 | no | — |
| 455 | C22×C4 | — | 4 | 2 | no | — |
| 456 | C22×C4 | — | 8 | 8 | no | — |
| 457 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 458 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 459 | C22×C4 | C25 | 1 | 3 | yes | — |
| 460 | C22×C4 | C25 | 1 | 6 | yes | — |
| 461 | Q16 | — | 2 | 24 | no | — |
| 462 | Q16 | — | 2 | 12 | no | — |
| 463 | Q16 | — | 4 | 12 | no | — |
| 464 | Q16 | — | 4 | 6 | no | — |
| 465 | Q16 | — | 4 | 12 | no | — |
| 466 | Q16 | H(5,𝔽2) | 1 | 4 | yes | — |
| 467 | SD16 | — | 2 | 12 | no | — |
| 468 | SD16 | — | 4 | 24 | no | — |
| 469 | SD16 | — | 4 | 12 | no | — |
| 470 | D8 | — | 2 | 6 | no | — |
| 471 | D8 | — | 4 | 6 | no | — |
| 472 | M16 | — | 4 | 3 | no | — |
| 473 | M16 | — | 4 | 3 | no | — |
| 474 | M16 | — | 4 | 6 | no | — |
| 475 | M16 | — | 4 | 6 | no | — |
| 476 | C2×C8 | — | 2 | 12 | no | — |
| 477 | C2×C8 | — | 2 | 6 | no | — |
| 478 | C2×C8 | — | 4 | 6 | no | — |
| 479 | C2×C8 | — | 4 | 3 | no | — |
| 480 | C2×C8 | C25 | 1 | 6 | yes | — |
| 481 | C2×C8 | C25 | 1 | 3 | yes | — |
| 482 | C2×C8 | C25 | 1 | 6 | yes | — |
| 483 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 484 | C4⋊C4 | — | 2 | 12 | no | — |
| 485 | C4⋊C4 | — | 2 | 12 | no | — |
| 486 | C4⋊C4 | — | 2 | 12 | no | — |
| 487 | C4⋊C4 | — | 2 | 24 | no | — |
| 488 | C4⋊C4 | — | 2 | 12 | no | — |
| 489 | C4⋊C4 | — | 2 | 24 | no | — |
| 490 | C4⋊C4 | — | 2 | 24 | no | — |
| 491 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 492 | C4⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 493 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 494 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 495 | C4⋊C4 | C25 | 1 | 12 | yes | — |
| 496 | C22⋊C4 | — | 2 | 24 | no | — |
| 497 | C22⋊C4 | — | 2 | 12 | no | — |
| 498 | C22⋊C4 | — | 2 | 6 | no | — |
| 499 | C22⋊C4 | — | 2 | 24 | no | — |
| 500 | C22⋊C4 | — | 2 | 24 | no | — |
| 501 | C22⋊C4 | — | 2 | 24 | no | — |
| 502 | C22⋊C4 | — | 2 | 24 | no | — |
| 503 | C22⋊C4 | — | 2 | 12 | no | — |
| 504 | C22⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 505 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 506 | C22⋊C4 | C22×D4 | 1 | 6 | yes | — |
| 507 | C22⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 508 | C22⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 509 | C42 | — | 2 | 12 | no | — |
| 510 | C42 | — | 2 | 6 | no | — |
| 511 | C42 | — | 2 | 24 | no | — |
| 512 | C42 | — | 2 | 12 | no | — |
| 513 | C42 | C22×D4 | 1 | 3 | yes | — |
| 514 | C42 | C22×D4 | 1 | 3 | yes | — |
| 515 | C42 | C25 | 1 | 6 | yes | — |
| 516 | C23 | — | 2 | 6 | no | — |
| 517 | C23 | — | 4 | 2 | no | — |
| 518 | C23 | — | 4 | 4 | no | — |
| 519 | C23 | — | 8 | 6 | no | — |
| 520 | C23 | — | 8 | 12 | no | — |
| 521 | C23 | C23×D4 | 1 | 3 | yes | — |
| 522 | C23 | C23×D4 | 1 | 6 | yes | — |
| 523 | Q8 | — | 2 | 2 | no | — |
| 524 | Q8 | — | 2 | 12 | no | — |
| 525 | Q8 | — | 2 | 12 | no | — |
| 526 | Q8 | — | 4 | 3 | no | — |
| 527 | Q8 | — | 4 | 2 | no | — |
| 528 | Q8 | — | 4 | 1 | no | — |
| 529 | Q8 | — | 4 | 24 | no | — |
| 530 | Q8 | — | 8 | 12 | no | — |
| 531 | Q8 | — | 8 | 12 | no | — |
| 532 | Q8 | — | 8 | 6 | no | — |
| 533 | Q8 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 534 | D4 | — | 2 | 6 | no | — |
| 535 | D4 | — | 2 | 6 | no | — |
| 536 | D4 | — | 4 | 3 | no | — |
| 537 | D4 | — | 4 | 6 | no | — |
| 538 | D4 | — | 4 | 12 | no | — |
| 539 | D4 | — | 4 | 3 | no | — |
| 540 | D4 | — | 4 | 6 | no | — |
| 541 | D4 | — | 4 | 12 | no | — |
| 542 | D4 | — | 8 | 6 | no | — |
| 543 | D4 | — | 8 | 24 | no | — |
| 544 | D4 | — | 8 | 12 | no | — |
| 545 | C2×C4 | — | 2 | 2 | no | — |
| 546 | C2×C4 | — | 2 | 6 | no | — |
| 547 | C2×C4 | — | 2 | 3 | no | — |
| 548 | C2×C4 | — | 2 | 3 | no | — |
| 549 | C2×C4 | — | 2 | 6 | no | — |
| 550 | C2×C4 | — | 2 | 12 | no | — |
| 551 | C2×C4 | — | 2 | 12 | no | — |
| 552 | C2×C4 | — | 4 | 6 | no | — |
| 553 | C2×C4 | — | 4 | 6 | no | — |
| 554 | C2×C4 | — | 4 | 12 | no | — |
| 555 | C2×C4 | — | 4 | 24 | no | — |
| 556 | C2×C4 | — | 8 | 12 | no | — |
| 557 | C2×C4 | — | 8 | 12 | no | — |
| 558 | C2×C4 | — | 8 | 12 | no | — |
| 559 | C2×C4 | — | 8 | 6 | no | — |
| 560 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 561 | C2×C4 | C23×D4 | 1 | 3 | yes | — |
| 562 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 563 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 564 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 565 | C8 | — | 2 | 6 | no | — |
| 566 | C8 | — | 2 | 3 | no | — |
| 567 | C8 | — | 2 | 6 | no | — |
| 568 | C8 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 569 | C22 | — | 2 | 6 | no | — |
| 570 | C22 | — | 2 | 3 | no | — |
| 571 | C22 | — | 2 | 6 | no | — |
| 572 | C22 | — | 2 | 12 | no | — |
| 573 | C22 | — | 4 | 8 | no | — |
| 574 | C22 | — | 4 | 6 | no | — |
| 575 | C22 | — | 4 | 12 | no | — |
| 576 | C22 | — | 32 | 6 | no | — |
| 577 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 578 | C4 | — | 2 | 3 | no | — |
| 579 | C4 | — | 2 | 6 | no | — |
| 580 | C4 | — | 2 | 4 | no | — |
| 581 | C4 | — | 2 | 6 | no | — |
| 582 | C4 | — | 2 | 6 | no | — |
| 583 | C4 | — | 4 | 12 | no | — |
| 584 | C4 | — | 4 | 12 | no | — |
| 585 | C4 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 586 | C4 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 587 | C2 | — | 4 | 6 | no | — |
| 588 | C2 | — | 4 | 3 | no | — |
| 589 | C2 | — | 8 | 6 | no | — |
| 590 | C2 | D4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 591 | C2 | #63093 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #3529 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63048 | C2 | semidirect |
| 2. #62437 | C2 | semidirect |
| 3. #62329 | C2 | semidirect |
| 4. #62275 | C2 | semidirect |
| 5. #62091 | C2 | semidirect |
| 6. #61674 | C2 | semidirect |
| 7. #61646 | C2 | semidirect |
| 8. #61478 | C2 | semidirect |
| 9. #61090 | C2 | semidirect |
| 10. #61053 | C2 | semidirect |
| 11. #60307 | C2 | semidirect |
| 13. C2×#576 | C22 | semidirect |
| 14. C23×Q16 | C22 | semidirect |
| 16. #3561 | C22 | semidirect |
| 20. #3540 | C22 | semidirect |
| 23. #3518 | C22 | semidirect |
| 25. #3486 | C22 | semidirect |
| 26. #3402 | C22 | semidirect |
| 27. #3393 | C22 | semidirect |
| 28. Q8×Q16 | C22 | semidirect |
| 29. #3369 | C22 | semidirect |
| 30. #3342 | C22 | semidirect |
| 31. #3341 | C22 | semidirect |
| 32. #3329 | C22 | semidirect |
| 33. #3328 | C22 | semidirect |
| 34. #3321 | C22 | semidirect |
| 35. #3313 | C22 | semidirect |
| 36. #3311 | C22 | semidirect |
| 37. D4×Q16 | C22 | semidirect |
| 38. D4×Q16 | C22 | semidirect |
| 39. #3285 | C22 | semidirect |
| 40. #3285 | C22 | semidirect |
| 41. #3280 | C22 | semidirect |
| 42. #3277 | C22 | semidirect |
| 43. #3275 | C22 | semidirect |
| 44. #3270 | C22 | semidirect |
| 45. #3270 | C22 | semidirect |
| 46. #3266 | C22 | semidirect |
| 47. #3263 | C22 | semidirect |
| 48. #3255 | C22 | semidirect |
| 49. #3225 | C22 | semidirect |
| 50. #3215 | C22 | semidirect |
| 51. #3202 | C22 | semidirect |
| 52. #3202 | C22 | semidirect |
| 53. #3200 | C22 | semidirect |
| 54. #3197 | C22 | semidirect |
| 55. #3175 | C22 | semidirect |
| 56. #3170 | C22 | semidirect |
| 57. #3156 | C22 | semidirect |
| 58. C2×#495 | C22 | semidirect |
| 59. #3121 | C22 | semidirect |
| 60. #3116 | C22 | semidirect |
| 61. #3059 | C22 | semidirect |
| 62. #3059 | C22 | semidirect |
| 64. #3050 | C22 | semidirect |
| 65. #3044 | C22 | semidirect |
| 66. #3040 | C22 | semidirect |
| 67. #3011 | C22 | semidirect |
| 69. #3009 | C22 | semidirect |
| 70. #3004 | C22 | semidirect |
| 71. #2995 | C22 | semidirect |
| 73. #2978 | C22 | semidirect |
| 74. #2966 | C22 | semidirect |
| 75. #2950 | C22 | semidirect |
| 76. C4×#135 | C22 | semidirect |
| 78. #2929 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63048 | 2 |
| #62437 | 2 |
| #62329 | 2 |
| #62275 | 2 |
| #62091 | 2 |
| #61674 | 2 |
| #61646 | 2 |
| #61478 | 2 |
| #61090 | 2 |
| #61053 | 2 |
| #60307 | 2 |