Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6075 conjugacy classes of subgroups.
The subgroup lattice has 510 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62788 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #62361 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #62360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #62359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #62358 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #62357 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #61887 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #61886 | C2 | 1 | 8 | yes | maximal, complemented |
| 9 | #61824 | C2 | 1 | 8 | yes | maximal, complemented |
| 10 | #61823 | C2 | 1 | 8 | yes | maximal, complemented |
| 11 | #60948 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | #60944 | C2 | 1 | 6 | yes | maximal, complemented |
| 13 | C2×#2982 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #3523 | C22 | 1 | 8 | yes | — |
| 15 | #3522 | C22 | 1 | 8 | yes | — |
| 16 | #3516 | — | 2 | 8 | no | — |
| 17 | #3507 | C22 | 1 | 12 | yes | — |
| 18 | #3502 | C22 | 1 | 2 | yes | — |
| 19 | #3497 | C22 | 1 | 2 | yes | — |
| 20 | #3492 | — | 2 | 6 | no | — |
| 21 | #3486 | — | 2 | 2 | no | — |
| 22 | #3482 | — | 2 | 8 | no | — |
| 23 | #3480 | C22 | 1 | 8 | yes | — |
| 24 | Q8×#41 | C22 | 1 | 8 | yes | — |
| 25 | #3461 | — | 2 | 6 | no | — |
| 26 | #3444 | C22 | 1 | 12 | yes | — |
| 27 | C4×2−1+4 | — | 2 | 2 | no | — |
| 28 | C22×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 29 | #3396 | C22 | 1 | 12 | yes | complemented |
| 30 | #3395 | C22 | 1 | 4 | yes | complemented |
| 31 | #3394 | C22 | 1 | 24 | yes | complemented |
| 32 | #3393 | C22 | 1 | 12 | yes | complemented |
| 33 | #3392 | C22 | 1 | 8 | yes | complemented |
| 34 | #3391 | C22 | 1 | 4 | yes | complemented |
| 35 | #3383 | C22 | 1 | 12 | yes | complemented |
| 36 | Q8×Q16 | C22 | 1 | 4 | yes | complemented |
| 37 | #3381 | C22 | 1 | 24 | yes | complemented |
| 38 | #3380 | C22 | 1 | 12 | yes | complemented |
| 39 | Q8×SD16 | C22 | 1 | 8 | yes | complemented |
| 40 | Q8×D8 | C22 | 1 | 4 | yes | complemented |
| 41 | #3365 | C22 | 1 | 24 | yes | complemented |
| 42 | #3364 | C22 | 1 | 24 | yes | complemented |
| 43 | #3363 | C22 | 1 | 8 | yes | complemented |
| 44 | #3362 | C22 | 1 | 8 | yes | complemented |
| 45 | #3361 | C22 | 1 | 24 | yes | complemented |
| 46 | #3360 | C22 | 1 | 24 | yes | complemented |
| 47 | #3359 | C22 | 1 | 8 | yes | complemented |
| 48 | #3358 | C22 | 1 | 8 | yes | complemented |
| 49 | #3250 | C22 | 1 | 12 | yes | — |
| 50 | #3250 | C22 | 1 | 12 | yes | — |
| 51 | #3249 | C22 | 1 | 6 | yes | — |
| 52 | #3246 | C22 | 1 | 12 | yes | — |
| 53 | #3245 | C22 | 1 | 6 | yes | — |
| 54 | #3233 | C22 | 1 | 24 | yes | — |
| 55 | #3231 | C22 | 1 | 12 | yes | — |
| 56 | #3228 | C22 | 1 | 12 | yes | — |
| 57 | #3212 | C22 | 1 | 24 | yes | — |
| 58 | #3210 | C22 | 1 | 12 | yes | — |
| 59 | #3207 | C22 | 1 | 12 | yes | — |
| 60 | #3191 | C22 | 1 | 4 | yes | — |
| 61 | #3191 | C22 | 1 | 12 | yes | — |
| 62 | #3170 | C22 | 1 | 6 | yes | — |
| 63 | #3169 | C22 | 1 | 6 | yes | — |
| 64 | #3168 | C22 | 1 | 24 | yes | — |
| 65 | #3167 | C22 | 1 | 12 | yes | — |
| 66 | #3107 | C22 | 1 | 24 | yes | — |
| 67 | #3106 | C22 | 1 | 24 | yes | — |
| 68 | #3102 | C22 | 1 | 24 | yes | — |
| 69 | #3102 | C22 | 1 | 24 | yes | — |
| 70 | #2982 | C22 | 1 | 8 | yes | — |
| 71 | #2982 | C22 | 1 | 8 | yes | — |
| 72 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 73 | C2×C8×Q8 | C22 | 1 | 3 | yes | — |
| 74 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 75 | C2×C8×Q8 | C22 | 1 | 3 | yes | — |
| 76 | C2×#431 | C22 | 1 | 3 | yes | — |
| 77 | C2×#431 | C22 | 1 | 3 | yes | — |
| 78 | C2×2−1+4 | — | 2 | 2 | no | — |
| 79 | C23×Q8 | D4 | 1 | 1 | yes | characteristic |
| 80 | #559 | C23 | 1 | 24 | yes | — |
| 81 | Q82 | C23 | 1 | 8 | yes | — |
| 82 | #557 | — | 2 | 8 | no | — |
| 83 | #557 | C23 | 1 | 8 | yes | — |
| 84 | #557 | C23 | 1 | 24 | yes | — |
| 85 | #556 | — | 2 | 24 | no | — |
| 86 | #556 | C23 | 1 | 24 | yes | — |
| 87 | #554 | — | 2 | 24 | no | — |
| 88 | #554 | C23 | 1 | 24 | yes | — |
| 89 | #553 | — | 2 | 24 | no | — |
| 90 | #552 | — | 2 | 24 | no | — |
| 91 | #552 | — | 2 | 24 | no | — |
| 92 | #550 | C23 | 1 | 8 | yes | — |
| 93 | D4×Q8 | — | 2 | 8 | no | — |
| 94 | D4×Q8 | — | 2 | 8 | no | — |
| 95 | D4×Q8 | C23 | 1 | 8 | yes | — |
| 96 | #548 | — | 2 | 8 | no | — |
| 97 | #548 | — | 2 | 8 | no | — |
| 98 | #548 | — | 2 | 8 | no | — |
| 99 | #547 | — | 2 | 24 | no | — |
| 100 | #544 | — | 2 | 6 | no | — |
| 101 | #542 | — | 2 | 24 | no | — |
| 102 | #541 | — | 2 | 24 | no | — |
| 103 | #539 | — | 2 | 24 | no | — |
| 104 | #537 | — | 2 | 6 | no | — |
| 105 | #536 | — | 2 | 12 | no | — |
| 106 | #533 | — | 2 | 24 | no | — |
| 107 | #533 | C23 | 1 | 12 | yes | — |
| 108 | #533 | C23 | 1 | 12 | yes | — |
| 109 | #533 | C23 | 1 | 12 | yes | — |
| 110 | #532 | C23 | 1 | 12 | yes | — |
| 111 | #532 | C23 | 1 | 12 | yes | — |
| 112 | #532 | C23 | 1 | 12 | yes | — |
| 113 | #529 | — | 2 | 24 | no | — |
| 114 | #529 | — | 2 | 12 | no | — |
| 115 | #529 | — | 2 | 12 | no | — |
| 116 | #529 | — | 2 | 12 | no | — |
| 117 | #529 | — | 2 | 12 | no | — |
| 118 | #529 | C23 | 1 | 24 | yes | — |
| 119 | #529 | C23 | 1 | 24 | yes | — |
| 120 | #525 | — | 2 | 12 | no | — |
| 121 | #525 | — | 2 | 12 | no | — |
| 122 | #525 | C23 | 1 | 8 | yes | — |
| 123 | #520 | — | 2 | 8 | no | — |
| 124 | #520 | — | 2 | 12 | no | — |
| 125 | #519 | — | 2 | 2 | no | — |
| 126 | #519 | — | 2 | 8 | no | — |
| 127 | C4×#41 | — | 2 | 8 | no | — |
| 128 | C4×#41 | — | 2 | 12 | no | — |
| 129 | C4×#41 | — | 2 | 12 | no | — |
| 130 | C4×#41 | C23 | 1 | 24 | yes | — |
| 131 | C2×C4×Q8 | — | 2 | 8 | no | — |
| 132 | C2×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 133 | C2×C4×Q8 | D4 | 1 | 3 | yes | — |
| 134 | C2×C4×Q8 | D4 | 1 | 8 | yes | — |
| 135 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 137 | C2×C4×Q8 | C23 | 1 | 8 | yes | — |
| 138 | C22×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 139 | C22×C42 | C23 | 1 | 3 | yes | — |
| 140 | #500 | C23 | 1 | 6 | yes | — |
| 141 | #500 | C23 | 1 | 6 | yes | — |
| 142 | #499 | C23 | 1 | 24 | yes | — |
| 143 | #498 | C23 | 1 | 12 | yes | — |
| 144 | #495 | C23 | 1 | 24 | yes | — |
| 145 | #494 | C23 | 1 | 6 | yes | — |
| 146 | #493 | C23 | 1 | 6 | yes | — |
| 147 | #492 | C23 | 1 | 12 | yes | — |
| 148 | #488 | C23 | 1 | 48 | yes | — |
| 149 | #487 | C23 | 1 | 12 | yes | — |
| 150 | #487 | C23 | 1 | 12 | yes | — |
| 151 | #486 | C23 | 1 | 12 | yes | — |
| 152 | #486 | C23 | 1 | 12 | yes | — |
| 153 | #485 | C23 | 1 | 8 | yes | — |
| 154 | #485 | C23 | 1 | 24 | yes | — |
| 155 | #482 | C23 | 1 | 8 | yes | — |
| 156 | #482 | C23 | 1 | 24 | yes | — |
| 157 | #479 | C23 | 1 | 24 | yes | — |
| 158 | #479 | C23 | 1 | 24 | yes | — |
| 159 | #478 | C23 | 1 | 24 | yes | — |
| 160 | #478 | C23 | 1 | 24 | yes | — |
| 161 | #477 | C23 | 1 | 24 | yes | — |
| 162 | #476 | C23 | 1 | 24 | yes | — |
| 163 | #475 | C23 | 1 | 24 | yes | — |
| 164 | #474 | C23 | 1 | 24 | yes | — |
| 165 | #467 | C23 | 1 | 12 | yes | — |
| 166 | #467 | C23 | 1 | 4 | yes | — |
| 167 | #466 | C23 | 1 | 12 | yes | — |
| 168 | #466 | C23 | 1 | 4 | yes | — |
| 169 | #465 | C23 | 1 | 8 | yes | — |
| 170 | #465 | C23 | 1 | 24 | yes | — |
| 171 | #464 | C23 | 1 | 24 | yes | — |
| 172 | #464 | C23 | 1 | 24 | yes | — |
| 173 | #463 | C23 | 1 | 24 | yes | — |
| 174 | #463 | C23 | 1 | 24 | yes | — |
| 175 | #462 | C23 | 1 | 24 | yes | — |
| 176 | #461 | C23 | 1 | 24 | yes | — |
| 177 | #460 | C23 | 1 | 24 | yes | — |
| 178 | #459 | C23 | 1 | 24 | yes | — |
| 179 | #452 | C23 | 1 | 8 | yes | — |
| 180 | #452 | C23 | 1 | 24 | yes | — |
| 181 | #449 | C23 | 1 | 8 | yes | — |
| 182 | #449 | C23 | 1 | 24 | yes | — |
| 183 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 184 | C8×Q8 | C23 | 1 | 8 | yes | — |
| 185 | C8×Q8 | C23 | 1 | 12 | yes | — |
| 186 | C8×Q8 | C23 | 1 | 24 | yes | — |
| 187 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 188 | C8×Q8 | C23 | 1 | 12 | yes | — |
| 189 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 190 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 191 | C4×Q16 | C23 | 1 | 24 | yes | — |
| 192 | C4×SD16 | C23 | 1 | 24 | yes | — |
| 193 | C4×SD16 | C23 | 1 | 24 | yes | — |
| 194 | C4×SD16 | C23 | 1 | 48 | yes | — |
| 195 | C4×D8 | C23 | 1 | 12 | yes | — |
| 196 | C4×D8 | C23 | 1 | 12 | yes | — |
| 197 | C4×D8 | C23 | 1 | 24 | yes | — |
| 198 | #431 | C23 | 1 | 12 | yes | — |
| 199 | #431 | C23 | 1 | 12 | yes | — |
| 200 | #431 | C23 | 1 | 24 | yes | — |
| 201 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 202 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 203 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 204 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 205 | C2×C22⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 206 | C2×C22⋊C8 | C23 | 1 | 3 | yes | — |
| 207 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 208 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 209 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 210 | 2−1+4 | — | 4 | 16 | no | — |
| 211 | C2×#41 | — | 2 | 8 | no | — |
| 212 | C2×#41 | — | 2 | 12 | no | — |
| 213 | C2×#41 | — | 2 | 12 | no | — |
| 214 | C2×#41 | C24 | 1 | 8 | yes | — |
| 215 | C22×Q8 | — | 2 | 8 | no | — |
| 216 | C22×Q8 | — | 2 | 8 | no | — |
| 217 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 218 | C22×Q8 | C2×D4 | 1 | 8 | yes | — |
| 219 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 221 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 222 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 223 | C2×Q16 | C24 | 1 | 12 | yes | — |
| 224 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 225 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 226 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 227 | C2×D8 | C24 | 1 | 12 | yes | — |
| 228 | C2×D8 | C24 | 1 | 4 | yes | — |
| 229 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 230 | C22×C8 | C24 | 1 | 3 | yes | — |
| 231 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 232 | C22×C8 | C24 | 1 | 3 | yes | — |
| 233 | C4⋊Q8 | — | 2 | 24 | no | — |
| 234 | C4⋊Q8 | — | 2 | 24 | no | — |
| 235 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 236 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 237 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 238 | #127 | C24 | 1 | 12 | yes | — |
| 239 | #126 | — | 2 | 48 | no | — |
| 240 | #126 | — | 2 | 24 | no | — |
| 241 | #126 | — | 2 | 24 | no | — |
| 242 | #125 | — | 2 | 24 | no | — |
| 243 | #125 | — | 2 | 48 | no | — |
| 244 | #125 | — | 2 | 12 | no | — |
| 245 | #125 | — | 2 | 12 | no | — |
| 246 | #125 | C24 | 1 | 24 | yes | — |
| 247 | #124 | — | 2 | 24 | no | — |
| 248 | #124 | — | 2 | 12 | no | — |
| 249 | #124 | — | 2 | 12 | no | — |
| 250 | #124 | C24 | 1 | 24 | yes | — |
| 251 | #123 | — | 2 | 24 | no | — |
| 252 | #123 | — | 2 | 24 | no | — |
| 253 | #123 | — | 2 | 8 | no | — |
| 254 | #123 | — | 2 | 48 | no | — |
| 255 | C22⋊Q8 | — | 2 | 24 | no | — |
| 256 | C22⋊Q8 | — | 2 | 24 | no | — |
| 257 | C22⋊Q8 | — | 2 | 12 | no | — |
| 258 | C22⋊Q8 | — | 2 | 12 | no | — |
| 259 | C22⋊Q8 | — | 2 | 12 | no | — |
| 260 | C22⋊Q8 | — | 2 | 12 | no | — |
| 261 | C22⋊Q8 | — | 2 | 24 | no | — |
| 262 | C22⋊Q8 | — | 2 | 48 | no | — |
| 263 | C22⋊Q8 | C24 | 1 | 8 | yes | — |
| 264 | C22⋊Q8 | C24 | 1 | 8 | yes | — |
| 265 | #121 | — | 2 | 12 | no | — |
| 266 | #121 | — | 2 | 12 | no | — |
| 267 | #121 | — | 2 | 12 | no | — |
| 268 | #121 | — | 2 | 12 | no | — |
| 269 | #121 | — | 2 | 24 | no | — |
| 270 | #121 | C24 | 1 | 8 | yes | — |
| 271 | #121 | C24 | 1 | 8 | yes | — |
| 272 | #120 | — | 2 | 8 | no | — |
| 273 | C4×Q8 | — | 2 | 8 | no | — |
| 274 | C4×Q8 | — | 2 | 8 | no | — |
| 275 | C4×Q8 | — | 2 | 24 | no | — |
| 276 | C4×Q8 | — | 2 | 12 | no | — |
| 277 | C4×Q8 | — | 2 | 12 | no | — |
| 278 | C4×Q8 | — | 2 | 12 | no | — |
| 279 | C4×Q8 | — | 2 | 12 | no | — |
| 280 | C4×Q8 | C2×D4 | 1 | 8 | yes | — |
| 281 | C4×Q8 | C2×D4 | 1 | 24 | yes | — |
| 282 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 283 | C4×Q8 | C2×D4 | 1 | 12 | yes | — |
| 284 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 285 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 286 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 287 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 288 | C4×D4 | — | 2 | 8 | no | — |
| 289 | C4×D4 | — | 2 | 8 | no | — |
| 290 | C4×D4 | — | 2 | 24 | no | — |
| 291 | C4×D4 | — | 2 | 24 | no | — |
| 292 | C4×D4 | — | 2 | 24 | no | — |
| 293 | C4×D4 | — | 2 | 24 | no | — |
| 294 | C4×D4 | — | 2 | 24 | no | — |
| 295 | C4×D4 | — | 2 | 12 | no | — |
| 296 | C4×D4 | — | 2 | 12 | no | — |
| 297 | C4×D4 | — | 2 | 12 | no | — |
| 298 | C4×D4 | — | 2 | 12 | no | — |
| 299 | C4×D4 | C24 | 1 | 24 | yes | — |
| 300 | C4×D4 | C24 | 1 | 24 | yes | — |
| 301 | #117 | — | 2 | 12 | no | — |
| 302 | #117 | — | 2 | 12 | no | — |
| 303 | #117 | — | 2 | 24 | no | — |
| 304 | #117 | — | 2 | 24 | no | — |
| 305 | #117 | — | 2 | 24 | no | — |
| 306 | #117 | — | 2 | 24 | no | — |
| 307 | #117 | C24 | 1 | 8 | yes | — |
| 308 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 309 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 310 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 311 | C2×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 312 | C2×C4⋊C4 | C2×D4 | 1 | 24 | yes | — |
| 313 | C2×C42 | — | 2 | 24 | no | — |
| 314 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 315 | C2×C42 | C2×D4 | 1 | 12 | yes | — |
| 316 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 317 | C2×C42 | C24 | 1 | 12 | yes | — |
| 318 | C2×C42 | C24 | 1 | 3 | yes | — |
| 319 | C2×C42 | C24 | 1 | 3 | yes | — |
| 320 | #107 | C24 | 1 | 4 | yes | — |
| 321 | #107 | C24 | 1 | 12 | yes | — |
| 322 | #107 | C24 | 1 | 12 | yes | — |
| 323 | #107 | C24 | 1 | 4 | yes | — |
| 324 | #106 | C24 | 1 | 24 | yes | — |
| 325 | #106 | C24 | 1 | 8 | yes | — |
| 326 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 327 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 328 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 329 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 330 | C4⋊C8 | C24 | 1 | 6 | yes | — |
| 331 | #103 | C24 | 1 | 8 | yes | — |
| 332 | #103 | C24 | 1 | 24 | yes | — |
| 333 | #103 | C24 | 1 | 24 | yes | — |
| 334 | #103 | C24 | 1 | 8 | yes | — |
| 335 | #102 | C24 | 1 | 8 | yes | — |
| 336 | #102 | C24 | 1 | 24 | yes | — |
| 337 | #102 | C24 | 1 | 24 | yes | — |
| 338 | #102 | C24 | 1 | 8 | yes | — |
| 339 | C22⋊C8 | C24 | 1 | 2 | yes | — |
| 340 | C22⋊C8 | C24 | 1 | 12 | yes | — |
| 341 | C22⋊C8 | C24 | 1 | 2 | yes | — |
| 342 | C4×C8 | C24 | 1 | 6 | yes | — |
| 343 | C4×C8 | C24 | 1 | 6 | yes | — |
| 344 | C4×C8 | C24 | 1 | 24 | yes | — |
| 345 | C4×C8 | C24 | 1 | 12 | yes | — |
| 346 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 347 | #41 | — | 4 | 8 | no | — |
| 348 | #41 | — | 4 | 8 | no | — |
| 349 | #41 | — | 4 | 32 | no | — |
| 350 | #41 | — | 4 | 48 | no | — |
| 351 | #41 | — | 8 | 24 | no | — |
| 352 | C2×Q8 | — | 2 | 32 | no | — |
| 353 | C2×Q8 | — | 2 | 12 | no | — |
| 354 | C2×Q8 | — | 2 | 12 | no | — |
| 355 | C2×Q8 | — | 2 | 12 | no | — |
| 356 | C2×Q8 | — | 4 | 32 | no | — |
| 357 | C2×Q8 | #135 | 1 | 8 | yes | — |
| 358 | C2×Q8 | C22×D4 | 1 | 12 | yes | — |
| 359 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 360 | C2×Q8 | C25 | 1 | 8 | yes | — |
| 361 | C2×D4 | — | 2 | 8 | no | — |
| 362 | C2×D4 | — | 2 | 8 | no | — |
| 363 | C2×D4 | — | 2 | 8 | no | — |
| 364 | C2×D4 | — | 2 | 12 | no | — |
| 365 | C2×D4 | — | 2 | 12 | no | — |
| 366 | C2×D4 | C25 | 1 | 8 | yes | — |
| 367 | C22×C4 | — | 2 | 12 | no | — |
| 368 | C22×C4 | — | 2 | 8 | no | — |
| 369 | C22×C4 | — | 2 | 24 | no | — |
| 370 | C22×C4 | — | 2 | 24 | no | — |
| 371 | C22×C4 | — | 4 | 1 | no | — |
| 372 | C22×C4 | — | 4 | 1 | no | — |
| 373 | C22×C4 | — | 8 | 3 | no | — |
| 374 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 375 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 376 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 377 | C22×C4 | C22×D4 | 1 | 2 | yes | — |
| 378 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 379 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 380 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 381 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 382 | C22×C4 | C25 | 1 | 2 | yes | — |
| 383 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 384 | Q16 | — | 4 | 12 | no | — |
| 385 | Q16 | — | 4 | 4 | no | — |
| 386 | SD16 | — | 4 | 8 | no | — |
| 387 | SD16 | — | 4 | 24 | no | — |
| 388 | D8 | — | 4 | 4 | no | — |
| 389 | D8 | — | 4 | 12 | no | — |
| 390 | C2×C8 | — | 4 | 1 | no | — |
| 391 | C2×C8 | — | 4 | 3 | no | — |
| 392 | C2×C8 | — | 4 | 1 | no | — |
| 393 | C2×C8 | — | 4 | 3 | no | — |
| 394 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 395 | C2×C8 | C25 | 1 | 6 | yes | — |
| 396 | C2×C8 | C25 | 1 | 2 | yes | — |
| 397 | C2×C8 | C25 | 1 | 6 | yes | — |
| 398 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 399 | C4⋊C4 | — | 2 | 12 | no | — |
| 400 | C4⋊C4 | — | 2 | 24 | no | — |
| 401 | C4⋊C4 | — | 2 | 12 | no | — |
| 402 | C4⋊C4 | — | 2 | 8 | no | — |
| 403 | C4⋊C4 | — | 2 | 8 | no | — |
| 404 | C4⋊C4 | — | 2 | 12 | no | — |
| 405 | C4⋊C4 | — | 2 | 12 | no | — |
| 406 | C4⋊C4 | — | 2 | 24 | no | — |
| 407 | C4⋊C4 | — | 2 | 24 | no | — |
| 408 | C4⋊C4 | — | 2 | 24 | no | — |
| 409 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 410 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 411 | C4⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 412 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 413 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 414 | C22⋊C4 | — | 2 | 8 | no | — |
| 415 | C22⋊C4 | — | 2 | 8 | no | — |
| 416 | C22⋊C4 | — | 2 | 8 | no | — |
| 417 | C22⋊C4 | — | 2 | 24 | no | — |
| 418 | C22⋊C4 | — | 2 | 8 | no | — |
| 419 | C22⋊C4 | — | 2 | 8 | no | — |
| 420 | C22⋊C4 | — | 2 | 24 | no | — |
| 421 | C22⋊C4 | — | 2 | 24 | no | — |
| 422 | C22⋊C4 | — | 2 | 24 | no | — |
| 423 | C42 | — | 2 | 8 | no | — |
| 424 | C42 | — | 2 | 24 | no | — |
| 425 | C42 | — | 2 | 24 | no | — |
| 426 | C42 | C22×D4 | 1 | 12 | yes | — |
| 427 | C42 | C22×D4 | 1 | 6 | yes | — |
| 428 | C42 | C22×D4 | 1 | 12 | yes | — |
| 429 | C42 | C22×D4 | 1 | 6 | yes | — |
| 430 | C42 | C25 | 1 | 6 | yes | — |
| 431 | C42 | C25 | 1 | 6 | yes | — |
| 432 | C23 | — | 2 | 2 | no | — |
| 433 | C23 | — | 2 | 8 | no | — |
| 434 | C23 | — | 4 | 1 | no | — |
| 435 | C23 | — | 4 | 1 | no | — |
| 436 | C23 | C23×D4 | 1 | 2 | yes | — |
| 437 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 438 | Q8 | — | 2 | 24 | no | — |
| 439 | Q8 | — | 2 | 8 | no | — |
| 440 | Q8 | — | 2 | 8 | no | — |
| 441 | Q8 | — | 4 | 24 | no | — |
| 442 | Q8 | — | 8 | 12 | no | — |
| 443 | Q8 | C2×#135 | 1 | 16 | yes | — |
| 444 | D4 | — | 2 | 8 | no | — |
| 445 | D4 | — | 2 | 8 | no | — |
| 446 | D4 | — | 4 | 16 | no | — |
| 447 | D4 | — | 4 | 16 | no | — |
| 448 | D4 | — | 4 | 16 | no | — |
| 449 | D4 | — | 4 | 24 | no | — |
| 450 | D4 | — | 8 | 12 | no | — |
| 451 | C2×C4 | — | 2 | 6 | no | — |
| 452 | C2×C4 | — | 2 | 1 | no | — |
| 453 | C2×C4 | — | 2 | 1 | no | — |
| 454 | C2×C4 | — | 2 | 2 | no | — |
| 455 | C2×C4 | — | 2 | 2 | no | — |
| 456 | C2×C4 | — | 2 | 24 | no | — |
| 457 | C2×C4 | — | 2 | 8 | no | — |
| 458 | C2×C4 | — | 2 | 8 | no | — |
| 459 | C2×C4 | — | 2 | 8 | no | — |
| 460 | C2×C4 | — | 4 | 1 | no | — |
| 461 | C2×C4 | — | 4 | 2 | no | — |
| 462 | C2×C4 | — | 4 | 3 | no | — |
| 463 | C2×C4 | — | 4 | 3 | no | — |
| 464 | C2×C4 | — | 4 | 12 | no | — |
| 465 | C2×C4 | — | 4 | 16 | no | — |
| 466 | C2×C4 | — | 4 | 48 | no | — |
| 467 | C2×C4 | — | 8 | 24 | no | — |
| 468 | C2×C4 | C2×#135 | 1 | 12 | yes | — |
| 469 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 470 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 471 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 472 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 473 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 474 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 475 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 476 | C8 | — | 2 | 1 | no | — |
| 477 | C8 | — | 2 | 6 | no | — |
| 478 | C8 | — | 2 | 6 | no | — |
| 479 | C8 | — | 2 | 2 | no | — |
| 480 | C8 | — | 2 | 1 | no | — |
| 481 | C22 | — | 2 | 1 | no | — |
| 482 | C22 | — | 2 | 1 | no | — |
| 483 | C22 | — | 2 | 2 | no | — |
| 484 | C22 | — | 2 | 2 | no | — |
| 485 | C22 | — | 2 | 2 | no | — |
| 486 | C22 | — | 4 | 4 | no | — |
| 487 | C22 | — | 4 | 8 | no | — |
| 488 | C22 | — | 4 | 8 | no | — |
| 489 | C22 | — | 4 | 8 | no | — |
| 490 | C22 | C22×#135 | 1 | 2 | yes | — |
| 491 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 492 | C4 | — | 2 | 6 | no | — |
| 493 | C4 | — | 2 | 6 | no | — |
| 494 | C4 | — | 2 | 6 | no | — |
| 495 | C4 | — | 2 | 2 | no | — |
| 496 | C4 | — | 2 | 1 | no | — |
| 497 | C4 | — | 4 | 8 | no | — |
| 498 | C4 | — | 4 | 8 | no | — |
| 499 | C4 | — | 4 | 8 | no | — |
| 500 | C4 | C22×#135 | 1 | 12 | yes | — |
| 501 | C4 | 2−1+6 | 1 | 1 | yes | characteristic |
| 502 | C4 | 2−1+6 | 1 | 1 | yes | characteristic |
| 503 | C2 | — | 2 | 2 | no | — |
| 504 | C2 | — | 4 | 2 | no | — |
| 505 | C2 | — | 8 | 8 | no | — |
| 506 | C2 | #62848 | 1 | 1 | yes | characteristic |
| 507 | C2 | C23×#135 | 1 | 1 | yes | characteristic |
| 508 | C2 | #63090 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4×Q8 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62788 | C2 | semidirect |
| 2. #62361 | C2 | semidirect |
| 3. #62360 | C2 | semidirect |
| 4. #62359 | C2 | semidirect |
| 5. #62358 | C2 | semidirect |
| 6. #62357 | C2 | semidirect |
| 7. #61887 | C2 | semidirect |
| 8. #61886 | C2 | semidirect |
| 9. #61824 | C2 | semidirect |
| 10. #61823 | C2 | semidirect |
| 11. #60948 | C2 | semidirect |
| 12. #60944 | C2 | semidirect |
| 13. C2×#2982 | C2 | semidirect |
| 29. #3396 | C22 | semidirect |
| 30. #3395 | C22 | semidirect |
| 31. #3394 | C22 | semidirect |
| 32. #3393 | C22 | semidirect |
| 33. #3392 | C22 | semidirect |
| 34. #3391 | C22 | semidirect |
| 35. #3383 | C22 | semidirect |
| 36. Q8×Q16 | C22 | semidirect |
| 37. #3381 | C22 | semidirect |
| 38. #3380 | C22 | semidirect |
| 39. Q8×SD16 | C22 | semidirect |
| 40. Q8×D8 | C22 | semidirect |
| 41. #3365 | C22 | semidirect |
| 42. #3364 | C22 | semidirect |
| 43. #3363 | C22 | semidirect |
| 44. #3362 | C22 | semidirect |
| 45. #3361 | C22 | semidirect |
| 46. #3360 | C22 | semidirect |
| 47. #3359 | C22 | semidirect |
| 48. #3358 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62788 | 2 |
| #62361 | 2 |
| #62360 | 2 |
| #62359 | 2 |
| #62358 | 2 |
| #62357 | 2 |
| #61887 | 2 |
| #61886 | 2 |
| #61824 | 2 |
| #61823 | 2 |
| #60948 | 2 |
| #60944 | 2 |
| C2×#2982 | 2 |