Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
5961 conjugacy classes of subgroups.
The subgroup lattice has 478 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63069 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62435 | C2 | 1 | 10 | yes | maximal, complemented |
| 3 | #62372 | C2 | 1 | 5 | yes | maximal, complemented |
| 4 | #62091 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | #62088 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | #61944 | C2 | 1 | 10 | yes | maximal, complemented |
| 7 | #61474 | C2 | 1 | 10 | yes | maximal, complemented |
| 8 | #61412 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | #60332 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #3568 | — | 2 | 10 | no | — |
| 11 | #3561 | — | 2 | 10 | no | — |
| 12 | #3561 | C22 | 1 | 10 | yes | complemented |
| 13 | #3558 | C22 | 1 | 10 | yes | complemented |
| 14 | #3550 | C22 | 1 | 10 | yes | complemented |
| 15 | #3545 | — | 2 | 10 | no | — |
| 16 | #3531 | — | 2 | 2 | no | — |
| 17 | #3531 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3518 | C22 | 1 | 10 | yes | complemented |
| 19 | #3514 | C22 | 1 | 10 | yes | complemented |
| 20 | #3510 | C22 | 1 | 10 | yes | complemented |
| 21 | #3403 | C22 | 1 | 20 | yes | complemented |
| 22 | #3402 | C22 | 1 | 20 | yes | complemented |
| 23 | #3401 | C22 | 1 | 20 | yes | complemented |
| 24 | #3394 | C22 | 1 | 10 | yes | complemented |
| 25 | #3394 | C22 | 1 | 20 | yes | complemented |
| 26 | Q8×SD16 | C22 | 1 | 10 | yes | complemented |
| 27 | #3375 | C22 | 1 | 10 | yes | complemented |
| 28 | #3373 | C22 | 1 | 20 | yes | complemented |
| 29 | #3369 | C22 | 1 | 20 | yes | complemented |
| 30 | #3367 | C22 | 1 | 10 | yes | complemented |
| 31 | #3340 | C22 | 1 | 10 | yes | complemented |
| 32 | #3328 | C22 | 1 | 10 | yes | complemented |
| 33 | #3325 | C22 | 1 | 10 | yes | complemented |
| 34 | #3321 | C22 | 1 | 20 | yes | complemented |
| 35 | #3311 | C22 | 1 | 20 | yes | complemented |
| 36 | #3282 | C22 | 1 | 20 | yes | complemented |
| 37 | D4×SD16 | C22 | 1 | 10 | yes | complemented |
| 38 | #3275 | C22 | 1 | 20 | yes | complemented |
| 39 | #3270 | C22 | 1 | 20 | yes | complemented |
| 40 | #3264 | C22 | 1 | 20 | yes | complemented |
| 41 | #3263 | C22 | 1 | 20 | yes | complemented |
| 42 | #3255 | C22 | 1 | 5 | yes | complemented |
| 43 | #3253 | C22 | 1 | 5 | yes | — |
| 44 | #3225 | C22 | 1 | 20 | yes | complemented |
| 45 | #3224 | C22 | 1 | 20 | yes | complemented |
| 46 | #3215 | C22 | 1 | 10 | yes | complemented |
| 47 | #3213 | C22 | 1 | 10 | yes | complemented |
| 48 | #3173 | C22 | 1 | 20 | yes | complemented |
| 49 | #3167 | C22 | 1 | 10 | yes | complemented |
| 50 | #3154 | C22 | 1 | 10 | yes | complemented |
| 51 | C2×#495 | C22 | 1 | 5 | yes | complemented |
| 52 | #3121 | C22 | 1 | 20 | yes | complemented |
| 53 | #3118 | C22 | 1 | 20 | yes | complemented |
| 54 | #3116 | C22 | 1 | 10 | yes | complemented |
| 55 | #3115 | C22 | 1 | 10 | yes | complemented |
| 56 | #3044 | C22 | 1 | 10 | yes | complemented |
| 57 | #3041 | C22 | 1 | 10 | yes | complemented |
| 58 | #3040 | C22 | 1 | 10 | yes | complemented |
| 59 | #2995 | C22 | 1 | 10 | yes | complemented |
| 60 | #2987 | C22 | 1 | 5 | yes | complemented |
| 61 | #2966 | C22 | 1 | 10 | yes | complemented |
| 62 | #2960 | C22 | 1 | 5 | yes | complemented |
| 63 | #2949 | C22 | 1 | 10 | yes | complemented |
| 64 | C4×#135 | C22 | 1 | 5 | yes | complemented |
| 65 | C2×#137 | C23 | 1 | 10 | yes | — |
| 66 | C2×AGL(1,ℤ/8) | C23 | 1 | 10 | yes | — |
| 67 | C2×#135 | C23 | 1 | 5 | yes | — |
| 68 | C22×Q16 | C23 | 1 | 5 | yes | — |
| 69 | C22×SD16 | C23 | 1 | 10 | yes | — |
| 70 | C22×D8 | C23 | 1 | 5 | yes | — |
| 71 | #564 | D4 | 1 | 1 | yes | characteristic |
| 72 | #563 | — | 2 | 10 | no | — |
| 73 | #563 | — | 2 | 10 | no | — |
| 74 | #563 | — | 2 | 10 | no | — |
| 75 | #563 | D4 | 1 | 10 | yes | — |
| 76 | #562 | — | 2 | 10 | no | — |
| 77 | #562 | — | 2 | 10 | no | — |
| 78 | #562 | D4 | 1 | 5 | yes | — |
| 79 | H(3,𝔽4) | — | 2 | 10 | no | — |
| 80 | #559 | C23 | 1 | 20 | yes | — |
| 81 | #559 | C23 | 1 | 10 | yes | — |
| 82 | Q82 | C23 | 1 | 10 | yes | — |
| 83 | #556 | — | 2 | 10 | no | — |
| 84 | #556 | — | 2 | 20 | no | — |
| 85 | #556 | — | 2 | 10 | no | — |
| 86 | #556 | C23 | 1 | 10 | yes | — |
| 87 | #556 | C23 | 1 | 20 | yes | — |
| 88 | #556 | C23 | 1 | 10 | yes | — |
| 89 | #555 | — | 2 | 10 | no | — |
| 90 | #555 | C23 | 1 | 10 | yes | — |
| 91 | #551 | — | 2 | 20 | no | — |
| 92 | #551 | — | 2 | 20 | no | — |
| 93 | #551 | — | 2 | 20 | no | — |
| 94 | #551 | — | 2 | 20 | no | — |
| 95 | D4×Q8 | — | 2 | 10 | no | — |
| 96 | D4×Q8 | C23 | 1 | 10 | yes | — |
| 97 | D4×Q8 | C23 | 1 | 10 | yes | — |
| 98 | #548 | — | 2 | 10 | no | — |
| 99 | #548 | C23 | 1 | 20 | yes | — |
| 100 | #546 | — | 2 | 20 | no | — |
| 101 | #546 | — | 2 | 10 | no | — |
| 102 | #546 | C23 | 1 | 20 | yes | — |
| 103 | D42 | C23 | 1 | 10 | yes | — |
| 104 | #543 | — | 2 | 10 | no | — |
| 105 | #542 | — | 2 | 10 | no | — |
| 106 | #542 | — | 2 | 10 | no | — |
| 107 | #542 | — | 2 | 20 | no | — |
| 108 | #542 | — | 2 | 20 | no | — |
| 109 | #542 | — | 2 | 20 | no | — |
| 110 | #542 | C23 | 1 | 20 | yes | — |
| 111 | #542 | C23 | 1 | 20 | yes | — |
| 112 | #538 | — | 2 | 20 | no | — |
| 113 | #538 | — | 2 | 20 | no | — |
| 114 | #538 | — | 2 | 10 | no | — |
| 115 | #538 | — | 2 | 10 | no | — |
| 116 | #536 | — | 2 | 20 | no | — |
| 117 | #536 | C23 | 1 | 10 | yes | — |
| 118 | #535 | C23 | 1 | 10 | yes | — |
| 119 | #534 | — | 2 | 10 | no | — |
| 120 | #533 | — | 2 | 10 | no | — |
| 121 | #533 | C23 | 1 | 10 | yes | — |
| 122 | #533 | C23 | 1 | 5 | yes | — |
| 123 | #532 | C23 | 1 | 10 | yes | — |
| 124 | #529 | — | 2 | 10 | no | — |
| 125 | #529 | — | 2 | 10 | no | — |
| 126 | #529 | — | 2 | 10 | no | — |
| 127 | #529 | — | 2 | 10 | no | — |
| 128 | #529 | C23 | 1 | 10 | yes | — |
| 129 | C2×#124 | — | 2 | 10 | no | — |
| 130 | C2×#124 | C23 | 1 | 10 | yes | — |
| 131 | #519 | C23 | 1 | 10 | yes | — |
| 132 | #518 | C23 | 1 | 10 | yes | — |
| 133 | C4×#41 | C23 | 1 | 10 | yes | — |
| 134 | #498 | C23 | 1 | 10 | yes | — |
| 135 | #497 | C23 | 1 | 20 | yes | — |
| 136 | #496 | C23 | 1 | 20 | yes | — |
| 137 | #495 | C23 | 1 | 20 | yes | — |
| 138 | #495 | C23 | 1 | 20 | yes | — |
| 139 | #492 | C23 | 1 | 10 | yes | — |
| 140 | #489 | C23 | 1 | 20 | yes | — |
| 141 | #489 | C23 | 1 | 20 | yes | — |
| 142 | #487 | C23 | 1 | 10 | yes | — |
| 143 | #486 | C23 | 1 | 10 | yes | — |
| 144 | #485 | C23 | 1 | 20 | yes | — |
| 145 | #482 | C23 | 1 | 20 | yes | — |
| 146 | #477 | C23 | 1 | 10 | yes | — |
| 147 | #476 | C23 | 1 | 20 | yes | — |
| 148 | #476 | C23 | 1 | 10 | yes | — |
| 149 | #475 | C23 | 1 | 10 | yes | — |
| 150 | #475 | C23 | 1 | 20 | yes | — |
| 151 | #474 | C23 | 1 | 10 | yes | — |
| 152 | #470 | C23 | 1 | 20 | yes | — |
| 153 | #469 | C23 | 1 | 20 | yes | — |
| 154 | #465 | C23 | 1 | 20 | yes | — |
| 155 | #465 | C23 | 1 | 20 | yes | — |
| 156 | #464 | C23 | 1 | 20 | yes | — |
| 157 | #464 | C23 | 1 | 20 | yes | — |
| 158 | #464 | C23 | 1 | 20 | yes | — |
| 159 | #464 | C23 | 1 | 20 | yes | — |
| 160 | #463 | C23 | 1 | 20 | yes | — |
| 161 | #463 | C23 | 1 | 20 | yes | — |
| 162 | #463 | C23 | 1 | 20 | yes | — |
| 163 | #463 | C23 | 1 | 20 | yes | — |
| 164 | #462 | C23 | 1 | 10 | yes | — |
| 165 | #462 | C23 | 1 | 20 | yes | — |
| 166 | #461 | C23 | 1 | 10 | yes | — |
| 167 | #460 | C23 | 1 | 10 | yes | — |
| 168 | #459 | C23 | 1 | 10 | yes | — |
| 169 | #459 | C23 | 1 | 20 | yes | — |
| 170 | #452 | C23 | 1 | 20 | yes | — |
| 171 | #451 | C23 | 1 | 20 | yes | — |
| 172 | #450 | C23 | 1 | 20 | yes | — |
| 173 | #449 | C23 | 1 | 20 | yes | — |
| 174 | #448 | C23 | 1 | 20 | yes | — |
| 175 | #447 | C23 | 1 | 20 | yes | — |
| 176 | #446 | C23 | 1 | 10 | yes | — |
| 177 | #446 | C23 | 1 | 20 | yes | — |
| 178 | C8×Q8 | C23 | 1 | 10 | yes | — |
| 179 | #442 | C23 | 1 | 20 | yes | — |
| 180 | #441 | C23 | 1 | 20 | yes | — |
| 181 | #440 | C23 | 1 | 20 | yes | — |
| 182 | #440 | C23 | 1 | 20 | yes | — |
| 183 | C4×Q16 | C23 | 1 | 10 | yes | — |
| 184 | C4×SD16 | C23 | 1 | 10 | yes | — |
| 185 | C4×SD16 | C23 | 1 | 20 | yes | — |
| 186 | C4×SD16 | C23 | 1 | 20 | yes | — |
| 187 | C4×SD16 | C23 | 1 | 10 | yes | — |
| 188 | C4×D8 | C23 | 1 | 10 | yes | — |
| 189 | #436 | C23 | 1 | 10 | yes | — |
| 190 | #435 | C23 | 1 | 20 | yes | — |
| 191 | C8×D4 | C23 | 1 | 10 | yes | — |
| 192 | #433 | C23 | 1 | 20 | yes | — |
| 193 | #432 | C23 | 1 | 10 | yes | — |
| 194 | #427 | C23 | 1 | 5 | yes | — |
| 195 | #424 | C23 | 1 | 10 | yes | — |
| 196 | #423 | C23 | 1 | 5 | yes | — |
| 197 | #419 | C23 | 1 | 10 | yes | — |
| 198 | #418 | C23 | 1 | 10 | yes | — |
| 199 | #416 | C23 | 1 | 10 | yes | — |
| 200 | #405 | C23 | 1 | 10 | yes | — |
| 201 | C2×C4×C8 | C23 | 1 | 5 | yes | — |
| 202 | C2×#41 | — | 2 | 10 | no | — |
| 203 | C2×#41 | C24 | 1 | 10 | yes | — |
| 204 | C22×Q8 | — | 2 | 10 | no | — |
| 205 | C22×Q8 | C24 | 1 | 10 | yes | — |
| 206 | C22×D4 | — | 2 | 10 | no | — |
| 207 | C22×D4 | C24 | 1 | 10 | yes | — |
| 208 | #137 | — | 8 | 10 | no | — |
| 209 | AGL(1,ℤ/8) | — | 8 | 10 | no | — |
| 210 | #135 | — | 4 | 10 | no | — |
| 211 | C2×Q16 | — | 8 | 5 | no | — |
| 212 | C2×Q16 | C24 | 1 | 20 | yes | — |
| 213 | C2×Q16 | C24 | 1 | 5 | yes | — |
| 214 | C2×SD16 | — | 4 | 20 | no | — |
| 215 | C2×SD16 | C24 | 1 | 10 | yes | — |
| 216 | C2×SD16 | C24 | 1 | 20 | yes | — |
| 217 | C2×SD16 | C24 | 1 | 20 | yes | — |
| 218 | C2×D8 | — | 8 | 5 | no | — |
| 219 | C2×D8 | C24 | 1 | 20 | yes | — |
| 220 | C2×D8 | C24 | 1 | 5 | yes | — |
| 221 | C2×M16 | C24 | 1 | 10 | yes | — |
| 222 | C22×C8 | C24 | 1 | 5 | yes | — |
| 223 | C22×C8 | C24 | 1 | 5 | yes | — |
| 224 | C4⋊Q8 | — | 2 | 10 | no | — |
| 225 | C4⋊Q8 | — | 2 | 10 | no | — |
| 226 | C4⋊Q8 | — | 2 | 20 | no | — |
| 227 | C4⋊Q8 | C2×D4 | 1 | 10 | yes | — |
| 228 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 229 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 230 | C4⋊Q8 | C24 | 1 | 10 | yes | — |
| 231 | #127 | C24 | 1 | 10 | yes | — |
| 232 | #126 | — | 2 | 20 | no | — |
| 233 | #126 | — | 2 | 20 | no | — |
| 234 | #126 | — | 2 | 20 | no | — |
| 235 | #126 | — | 2 | 20 | no | — |
| 236 | #126 | — | 2 | 20 | no | — |
| 237 | #126 | — | 2 | 20 | no | — |
| 238 | #126 | C2×D4 | 1 | 20 | yes | — |
| 239 | #125 | — | 2 | 10 | no | — |
| 240 | #125 | C2×D4 | 1 | 5 | yes | — |
| 241 | #125 | C2×D4 | 1 | 5 | yes | — |
| 242 | #125 | C2×D4 | 1 | 10 | yes | — |
| 243 | #124 | — | 2 | 10 | no | — |
| 244 | #124 | — | 2 | 20 | no | — |
| 245 | #124 | — | 2 | 10 | no | — |
| 246 | #124 | — | 2 | 20 | no | — |
| 247 | #124 | — | 2 | 20 | no | — |
| 248 | #124 | — | 2 | 20 | no | — |
| 249 | #124 | — | 2 | 20 | no | — |
| 250 | #124 | — | 2 | 10 | no | — |
| 251 | #124 | — | 2 | 10 | no | — |
| 252 | #124 | — | 2 | 10 | no | — |
| 253 | #124 | C2×D4 | 1 | 10 | yes | — |
| 254 | #124 | C24 | 1 | 20 | yes | — |
| 255 | #124 | C24 | 1 | 20 | yes | — |
| 256 | #123 | — | 2 | 20 | no | — |
| 257 | #123 | — | 2 | 20 | no | — |
| 258 | #123 | — | 2 | 20 | no | — |
| 259 | #123 | — | 2 | 20 | no | — |
| 260 | #123 | — | 2 | 20 | no | — |
| 261 | #123 | — | 2 | 20 | no | — |
| 262 | #123 | — | 2 | 20 | no | — |
| 263 | #123 | C2×D4 | 1 | 20 | yes | — |
| 264 | C22⋊Q8 | — | 2 | 10 | no | — |
| 265 | C22⋊Q8 | — | 2 | 20 | no | — |
| 266 | C22⋊Q8 | — | 2 | 10 | no | — |
| 267 | C22⋊Q8 | — | 2 | 10 | no | — |
| 268 | C22⋊Q8 | — | 2 | 10 | no | — |
| 269 | C22⋊Q8 | — | 2 | 10 | no | — |
| 270 | C22⋊Q8 | — | 2 | 20 | no | — |
| 271 | C22⋊Q8 | — | 2 | 20 | no | — |
| 272 | C22⋊Q8 | — | 2 | 20 | no | — |
| 273 | C22⋊Q8 | — | 2 | 20 | no | — |
| 274 | C22⋊Q8 | — | 2 | 20 | no | — |
| 275 | C22⋊Q8 | C2×D4 | 1 | 10 | yes | — |
| 276 | C22⋊Q8 | C2×D4 | 1 | 20 | yes | — |
| 277 | C22⋊Q8 | C24 | 1 | 20 | yes | — |
| 278 | #121 | — | 2 | 10 | no | — |
| 279 | #121 | — | 2 | 20 | no | — |
| 280 | #121 | — | 2 | 10 | no | — |
| 281 | #121 | — | 2 | 10 | no | — |
| 282 | #121 | — | 2 | 10 | no | — |
| 283 | #121 | — | 2 | 10 | no | — |
| 284 | #121 | — | 2 | 20 | no | — |
| 285 | #121 | C2×D4 | 1 | 10 | yes | — |
| 286 | #121 | C24 | 1 | 20 | yes | — |
| 287 | #120 | — | 2 | 20 | no | — |
| 288 | #120 | — | 2 | 20 | no | — |
| 289 | #120 | — | 2 | 20 | no | — |
| 290 | C4×Q8 | — | 2 | 10 | no | — |
| 291 | C4×Q8 | — | 2 | 10 | no | — |
| 292 | C4×Q8 | — | 2 | 10 | no | — |
| 293 | C4×Q8 | — | 2 | 10 | no | — |
| 294 | C4×Q8 | — | 2 | 10 | no | — |
| 295 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 296 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 297 | C4×Q8 | C24 | 1 | 20 | yes | — |
| 298 | C4×Q8 | C24 | 1 | 10 | yes | — |
| 299 | C4×D4 | — | 2 | 10 | no | — |
| 300 | C4×D4 | — | 2 | 10 | no | — |
| 301 | C4×D4 | — | 2 | 10 | no | — |
| 302 | C4×D4 | — | 2 | 10 | no | — |
| 303 | C4×D4 | — | 2 | 10 | no | — |
| 304 | C4×D4 | — | 2 | 10 | no | — |
| 305 | C4×D4 | — | 2 | 20 | no | — |
| 306 | C4×D4 | — | 2 | 20 | no | — |
| 307 | C4×D4 | — | 2 | 10 | no | — |
| 308 | C4×D4 | C24 | 1 | 10 | yes | — |
| 309 | C4×D4 | C24 | 1 | 10 | yes | — |
| 310 | C4×D4 | C24 | 1 | 20 | yes | — |
| 311 | C4×D4 | C24 | 1 | 10 | yes | — |
| 312 | #117 | — | 2 | 10 | no | — |
| 313 | #117 | — | 2 | 10 | no | — |
| 314 | #117 | — | 2 | 10 | no | — |
| 315 | #117 | — | 2 | 20 | no | — |
| 316 | #117 | — | 2 | 20 | no | — |
| 317 | #117 | — | 2 | 10 | no | — |
| 318 | #117 | C24 | 1 | 10 | yes | — |
| 319 | #117 | C24 | 1 | 10 | yes | — |
| 320 | C2×C22⋊C4 | — | 2 | 10 | no | — |
| 321 | C2×C22⋊C4 | — | 2 | 10 | no | — |
| 322 | C2×C22⋊C4 | — | 2 | 20 | no | — |
| 323 | C2×C22⋊C4 | — | 2 | 20 | no | — |
| 324 | C2×C42 | — | 2 | 10 | no | — |
| 325 | C2×C42 | C24 | 1 | 5 | yes | — |
| 326 | #107 | C24 | 1 | 10 | yes | — |
| 327 | #106 | C24 | 1 | 1 | yes | characteristic |
| 328 | #106 | C24 | 1 | 5 | yes | — |
| 329 | #106 | C24 | 1 | 20 | yes | — |
| 330 | C4⋊C8 | C24 | 1 | 20 | yes | — |
| 331 | C4⋊C8 | C24 | 1 | 10 | yes | — |
| 332 | C4⋊C8 | C24 | 1 | 10 | yes | — |
| 333 | #103 | C24 | 1 | 10 | yes | — |
| 334 | #103 | C24 | 1 | 10 | yes | — |
| 335 | #103 | C24 | 1 | 20 | yes | — |
| 336 | #103 | C24 | 1 | 20 | yes | — |
| 337 | #102 | C24 | 1 | 10 | yes | — |
| 338 | #102 | C24 | 1 | 10 | yes | — |
| 339 | #102 | C24 | 1 | 20 | yes | — |
| 340 | #102 | C24 | 1 | 20 | yes | — |
| 341 | C22⋊C8 | C24 | 1 | 20 | yes | — |
| 342 | #97 | C24 | 1 | 20 | yes | — |
| 343 | C4×C8 | C24 | 1 | 10 | yes | — |
| 344 | C4×C8 | C24 | 1 | 10 | yes | — |
| 345 | C24 | — | 2 | 10 | no | — |
| 346 | #41 | — | 4 | 10 | no | — |
| 347 | #41 | — | 4 | 10 | no | — |
| 348 | #41 | — | 16 | 10 | no | — |
| 349 | C2×Q8 | — | 2 | 10 | no | — |
| 350 | C2×Q8 | — | 2 | 10 | no | — |
| 351 | C2×Q8 | — | 2 | 10 | no | — |
| 352 | C2×Q8 | — | 4 | 10 | no | — |
| 353 | C2×Q8 | — | 4 | 10 | no | — |
| 354 | C2×Q8 | — | 16 | 10 | no | — |
| 355 | C2×Q8 | C22×D4 | 1 | 10 | yes | — |
| 356 | C2×Q8 | C25 | 1 | 10 | yes | — |
| 357 | C2×D4 | — | 2 | 10 | no | — |
| 358 | C2×D4 | — | 2 | 20 | no | — |
| 359 | C2×D4 | — | 2 | 10 | no | — |
| 360 | C2×D4 | — | 2 | 10 | no | — |
| 361 | C2×D4 | — | 2 | 10 | no | — |
| 362 | C2×D4 | — | 4 | 10 | no | — |
| 363 | C2×D4 | — | 4 | 10 | no | — |
| 364 | C2×D4 | — | 16 | 10 | no | — |
| 365 | C2×D4 | C22×D4 | 1 | 10 | yes | — |
| 366 | C2×D4 | C25 | 1 | 10 | yes | — |
| 367 | C22×C4 | — | 2 | 10 | no | — |
| 368 | C22×C4 | — | 2 | 10 | no | — |
| 369 | C22×C4 | — | 2 | 10 | no | — |
| 370 | C22×C4 | — | 2 | 10 | no | — |
| 371 | C22×C4 | — | 2 | 20 | no | — |
| 372 | C22×C4 | C22×D4 | 1 | 10 | yes | — |
| 373 | C22×C4 | C25 | 1 | 5 | yes | — |
| 374 | Q16 | — | 4 | 20 | no | — |
| 375 | Q16 | — | 4 | 5 | no | — |
| 376 | SD16 | — | 2 | 20 | no | — |
| 377 | SD16 | — | 4 | 20 | no | — |
| 378 | SD16 | — | 4 | 20 | no | — |
| 379 | D8 | — | 4 | 20 | no | — |
| 380 | D8 | — | 4 | 5 | no | — |
| 381 | M16 | — | 4 | 10 | no | — |
| 382 | C2×C8 | — | 2 | 10 | no | — |
| 383 | C2×C8 | — | 4 | 5 | no | — |
| 384 | C2×C8 | C25 | 1 | 5 | yes | — |
| 385 | C2×C8 | C25 | 1 | 10 | yes | — |
| 386 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 387 | C4⋊C4 | — | 2 | 10 | no | — |
| 388 | C4⋊C4 | — | 2 | 10 | no | — |
| 389 | C4⋊C4 | — | 2 | 10 | no | — |
| 390 | C4⋊C4 | — | 2 | 10 | no | — |
| 391 | C4⋊C4 | — | 2 | 10 | no | — |
| 392 | C4⋊C4 | — | 2 | 20 | no | — |
| 393 | C4⋊C4 | — | 2 | 20 | no | — |
| 394 | C4⋊C4 | — | 2 | 10 | no | — |
| 395 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 396 | C4⋊C4 | C22×D4 | 1 | 20 | yes | — |
| 397 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 398 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 399 | C4⋊C4 | C22×D4 | 1 | 10 | yes | — |
| 400 | C4⋊C4 | C25 | 1 | 10 | yes | — |
| 401 | C4⋊C4 | C25 | 1 | 2 | yes | — |
| 402 | C22⋊C4 | — | 2 | 10 | no | — |
| 403 | C22⋊C4 | — | 2 | 20 | no | — |
| 404 | C22⋊C4 | — | 2 | 10 | no | — |
| 405 | C22⋊C4 | — | 2 | 20 | no | — |
| 406 | C22⋊C4 | — | 2 | 20 | no | — |
| 407 | C22⋊C4 | — | 2 | 20 | no | — |
| 408 | C22⋊C4 | — | 2 | 20 | no | — |
| 409 | C22⋊C4 | — | 2 | 20 | no | — |
| 410 | C22⋊C4 | — | 2 | 20 | no | — |
| 411 | C22⋊C4 | — | 2 | 10 | no | — |
| 412 | C22⋊C4 | C22×D4 | 1 | 20 | yes | — |
| 413 | C22⋊C4 | C22×D4 | 1 | 20 | yes | — |
| 414 | C42 | — | 2 | 10 | no | — |
| 415 | C42 | — | 2 | 10 | no | — |
| 416 | C42 | — | 2 | 10 | no | — |
| 417 | C42 | — | 2 | 20 | no | — |
| 418 | C42 | C22×D4 | 1 | 5 | yes | — |
| 419 | C42 | C22×D4 | 1 | 5 | yes | — |
| 420 | C42 | C25 | 1 | 10 | yes | — |
| 421 | C23 | — | 2 | 10 | no | — |
| 422 | C23 | — | 8 | 10 | no | — |
| 423 | C23 | — | 8 | 10 | no | — |
| 424 | C23 | — | 8 | 10 | no | — |
| 425 | C23 | C23×D4 | 1 | 5 | yes | — |
| 426 | Q8 | — | 2 | 10 | no | — |
| 427 | Q8 | — | 2 | 10 | no | — |
| 428 | Q8 | — | 4 | 10 | no | — |
| 429 | Q8 | — | 8 | 10 | no | — |
| 430 | Q8 | — | 8 | 10 | no | — |
| 431 | Q8 | — | 8 | 10 | no | — |
| 432 | D4 | — | 2 | 10 | no | — |
| 433 | D4 | — | 2 | 10 | no | — |
| 434 | D4 | — | 4 | 10 | no | — |
| 435 | D4 | — | 8 | 10 | no | — |
| 436 | D4 | — | 8 | 10 | no | — |
| 437 | D4 | — | 8 | 10 | no | — |
| 438 | D4 | — | 8 | 20 | no | — |
| 439 | D4 | — | 8 | 10 | no | — |
| 440 | C2×C4 | — | 2 | 5 | no | — |
| 441 | C2×C4 | — | 2 | 5 | no | — |
| 442 | C2×C4 | — | 2 | 2 | no | — |
| 443 | C2×C4 | — | 2 | 10 | no | — |
| 444 | C2×C4 | — | 2 | 10 | no | — |
| 445 | C2×C4 | — | 4 | 10 | no | — |
| 446 | C2×C4 | — | 8 | 10 | no | — |
| 447 | C2×C4 | — | 8 | 10 | no | — |
| 448 | C2×C4 | — | 8 | 20 | no | — |
| 449 | C2×C4 | — | 8 | 10 | no | — |
| 450 | C2×C4 | — | 8 | 10 | no | — |
| 451 | C2×C4 | C23×D4 | 1 | 5 | yes | — |
| 452 | C2×C4 | C23×D4 | 1 | 10 | yes | — |
| 453 | C2×C4 | C23×D4 | 1 | 10 | yes | — |
| 454 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 455 | C8 | — | 2 | 5 | no | — |
| 456 | C8 | — | 2 | 10 | no | — |
| 457 | C8 | #585 | 1 | 2 | yes | — |
| 458 | C22 | — | 2 | 5 | no | — |
| 459 | C22 | — | 2 | 10 | no | — |
| 460 | C22 | — | 4 | 10 | no | — |
| 461 | C22 | — | 4 | 10 | no | — |
| 462 | C22 | — | 4 | 10 | no | — |
| 463 | C22 | — | 32 | 10 | no | — |
| 464 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 465 | C4 | — | 2 | 5 | no | — |
| 466 | C4 | — | 2 | 10 | no | — |
| 467 | C4 | — | 2 | 10 | no | — |
| 468 | C4 | — | 4 | 10 | no | — |
| 469 | C4 | — | 4 | 2 | no | — |
| 470 | C4 | — | 4 | 10 | no | — |
| 471 | C4 | C2×#585 | 1 | 1 | yes | characteristic |
| 472 | C4 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 473 | C2 | — | 4 | 5 | no | — |
| 474 | C2 | — | 8 | 10 | no | — |
| 475 | C2 | #63003 | 1 | 1 | yes | characteristic |
| 476 | C2 | #63092 | 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 ◁ #3531 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63069 | C2 | semidirect |
| 2. #62435 | C2 | semidirect |
| 3. #62372 | C2 | semidirect |
| 4. #62091 | C2 | semidirect |
| 5. #62088 | C2 | semidirect |
| 6. #61944 | C2 | semidirect |
| 7. #61474 | C2 | semidirect |
| 8. #61412 | C2 | semidirect |
| 9. #60332 | C2 | semidirect |
| 12. #3561 | C22 | semidirect |
| 13. #3558 | C22 | semidirect |
| 14. #3550 | C22 | semidirect |
| 18. #3518 | C22 | semidirect |
| 19. #3514 | C22 | semidirect |
| 20. #3510 | C22 | semidirect |
| 21. #3403 | C22 | semidirect |
| 22. #3402 | C22 | semidirect |
| 23. #3401 | C22 | semidirect |
| 24. #3394 | C22 | semidirect |
| 25. #3394 | C22 | semidirect |
| 26. Q8×SD16 | C22 | semidirect |
| 27. #3375 | C22 | semidirect |
| 28. #3373 | C22 | semidirect |
| 29. #3369 | C22 | semidirect |
| 30. #3367 | C22 | semidirect |
| 31. #3340 | C22 | semidirect |
| 32. #3328 | C22 | semidirect |
| 33. #3325 | C22 | semidirect |
| 34. #3321 | C22 | semidirect |
| 35. #3311 | C22 | semidirect |
| 36. #3282 | C22 | semidirect |
| 37. D4×SD16 | C22 | semidirect |
| 38. #3275 | C22 | semidirect |
| 39. #3270 | C22 | semidirect |
| 40. #3264 | C22 | semidirect |
| 41. #3263 | C22 | semidirect |
| 42. #3255 | C22 | semidirect |
| 44. #3225 | C22 | semidirect |
| 45. #3224 | C22 | semidirect |
| 46. #3215 | C22 | semidirect |
| 47. #3213 | C22 | semidirect |
| 48. #3173 | C22 | semidirect |
| 49. #3167 | C22 | semidirect |
| 50. #3154 | C22 | semidirect |
| 51. C2×#495 | C22 | semidirect |
| 52. #3121 | C22 | semidirect |
| 53. #3118 | C22 | semidirect |
| 54. #3116 | C22 | semidirect |
| 55. #3115 | C22 | semidirect |
| 56. #3044 | C22 | semidirect |
| 57. #3041 | C22 | semidirect |
| 58. #3040 | C22 | semidirect |
| 59. #2995 | C22 | semidirect |
| 60. #2987 | C22 | semidirect |
| 61. #2966 | C22 | semidirect |
| 62. #2960 | C22 | semidirect |
| 63. #2949 | C22 | semidirect |
| 64. C4×#135 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63069 | 2 |
| #62435 | 2 |
| #62372 | 2 |
| #62091 | 2 |
| #62088 | 2 |
| #61944 | 2 |
| #61474 | 2 |
| #61412 | 2 |
| #60332 | 2 |