Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
6216 conjugacy classes of subgroups.
The subgroup lattice has 573 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 | #62364 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #62363 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #62362 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #62361 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #62360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #62359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #62358 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #62357 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #61393 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | Q8×#135 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #61303 | C2 | 1 | 8 | yes | maximal, complemented |
| 13 | #60900 | C2 | 1 | 6 | yes | maximal, complemented |
| 14 | #60673 | C2 | 1 | 6 | yes | maximal, complemented |
| 15 | C22×C8×Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #3523 | C22 | 1 | 8 | yes | — |
| 17 | #3522 | C22 | 1 | 8 | yes | — |
| 18 | #3516 | — | 2 | 8 | no | — |
| 19 | #3507 | C22 | 1 | 12 | yes | — |
| 20 | #3502 | C22 | 1 | 2 | yes | — |
| 21 | #3497 | C22 | 1 | 2 | yes | — |
| 22 | #3492 | — | 2 | 6 | no | — |
| 23 | #3486 | — | 2 | 2 | no | — |
| 24 | #3482 | — | 2 | 8 | no | — |
| 25 | #3480 | C22 | 1 | 8 | yes | — |
| 26 | Q8×#41 | C22 | 1 | 8 | yes | — |
| 27 | #3461 | — | 2 | 6 | no | — |
| 28 | #3444 | C22 | 1 | 12 | yes | — |
| 29 | C4×2−1+4 | — | 2 | 2 | no | — |
| 30 | C22×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 31 | #3396 | C22 | 1 | 12 | yes | complemented |
| 32 | #3395 | C22 | 1 | 4 | yes | complemented |
| 33 | #3394 | C22 | 1 | 24 | yes | complemented |
| 34 | #3393 | C22 | 1 | 12 | yes | complemented |
| 35 | #3392 | C22 | 1 | 8 | yes | complemented |
| 36 | #3391 | C22 | 1 | 4 | yes | complemented |
| 37 | #3383 | C22 | 1 | 12 | yes | complemented |
| 38 | Q8×Q16 | C22 | 1 | 4 | yes | complemented |
| 39 | #3381 | C22 | 1 | 24 | yes | complemented |
| 40 | #3380 | C22 | 1 | 12 | yes | complemented |
| 41 | Q8×SD16 | C22 | 1 | 8 | yes | complemented |
| 42 | Q8×D8 | C22 | 1 | 4 | yes | complemented |
| 43 | #3365 | C22 | 1 | 24 | yes | complemented |
| 44 | #3364 | C22 | 1 | 24 | yes | complemented |
| 45 | #3363 | C22 | 1 | 8 | yes | complemented |
| 46 | #3362 | C22 | 1 | 8 | yes | complemented |
| 47 | #3361 | C22 | 1 | 24 | yes | complemented |
| 48 | #3360 | C22 | 1 | 24 | yes | complemented |
| 49 | #3359 | C22 | 1 | 8 | yes | complemented |
| 50 | #3358 | C22 | 1 | 8 | yes | complemented |
| 51 | #3250 | C22 | 1 | 24 | yes | — |
| 52 | #3249 | C22 | 1 | 6 | yes | — |
| 53 | #3248 | C22 | 1 | 24 | yes | — |
| 54 | #3247 | C22 | 1 | 24 | yes | — |
| 55 | #3246 | C22 | 1 | 12 | yes | — |
| 56 | #3245 | C22 | 1 | 6 | yes | — |
| 57 | #3170 | C22 | 1 | 6 | yes | — |
| 58 | #3170 | C22 | 1 | 6 | yes | — |
| 59 | #3169 | C22 | 1 | 6 | yes | — |
| 60 | #3169 | C22 | 1 | 6 | yes | — |
| 61 | #3168 | C22 | 1 | 12 | yes | — |
| 62 | #3168 | C22 | 1 | 12 | yes | — |
| 63 | #3168 | C22 | 1 | 12 | yes | — |
| 64 | #3168 | C22 | 1 | 12 | yes | — |
| 65 | #3167 | C22 | 1 | 12 | yes | — |
| 66 | #3167 | C22 | 1 | 12 | yes | — |
| 67 | #3160 | C22 | 1 | 6 | yes | — |
| 68 | #3147 | C22 | 1 | 6 | yes | — |
| 69 | #3131 | C22 | 1 | 12 | yes | — |
| 70 | #3076 | C22 | 1 | 24 | yes | — |
| 71 | #3050 | C22 | 1 | 4 | yes | — |
| 72 | #3050 | C22 | 1 | 12 | yes | — |
| 73 | #3035 | C22 | 1 | 24 | yes | — |
| 74 | C2×C8×Q8 | C22 | 1 | 4 | yes | — |
| 75 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 76 | C2×C8×Q8 | C22 | 1 | 3 | yes | — |
| 77 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 78 | C2×C8×Q8 | C22 | 1 | 3 | yes | — |
| 79 | C2×C8×Q8 | C22 | 1 | 4 | yes | — |
| 80 | C2×C8×Q8 | C22 | 1 | 4 | yes | — |
| 81 | C2×C8×Q8 | C22 | 1 | 4 | yes | — |
| 82 | C4×#135 | C22 | 1 | 12 | yes | — |
| 83 | C4×#135 | C22 | 1 | 12 | yes | — |
| 84 | C22×C4⋊C8 | C22 | 1 | 3 | yes | — |
| 85 | C22×C4×C8 | C22 | 1 | 3 | yes | — |
| 86 | C2×2−1+4 | — | 2 | 2 | no | — |
| 87 | C23×Q8 | D4 | 1 | 1 | yes | characteristic |
| 88 | C2×#135 | C23 | 1 | 4 | yes | — |
| 89 | C2×#135 | C23 | 1 | 12 | yes | — |
| 90 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 91 | C23×C8 | C23 | 1 | 3 | yes | — |
| 92 | #559 | C23 | 1 | 24 | yes | — |
| 93 | Q82 | C23 | 1 | 8 | yes | — |
| 94 | #557 | — | 2 | 8 | no | — |
| 95 | #557 | C23 | 1 | 8 | yes | — |
| 96 | #557 | C23 | 1 | 24 | yes | — |
| 97 | #556 | — | 2 | 24 | no | — |
| 98 | #556 | C23 | 1 | 24 | yes | — |
| 99 | #554 | — | 2 | 24 | no | — |
| 100 | #554 | C23 | 1 | 24 | yes | — |
| 101 | #553 | — | 2 | 24 | no | — |
| 102 | #552 | — | 2 | 24 | no | — |
| 103 | #552 | — | 2 | 24 | no | — |
| 104 | #550 | C23 | 1 | 8 | yes | — |
| 105 | D4×Q8 | — | 2 | 8 | no | — |
| 106 | D4×Q8 | — | 2 | 8 | no | — |
| 107 | D4×Q8 | C23 | 1 | 8 | yes | — |
| 108 | #548 | — | 2 | 8 | no | — |
| 109 | #548 | — | 2 | 8 | no | — |
| 110 | #548 | — | 2 | 8 | no | — |
| 111 | #547 | — | 2 | 24 | no | — |
| 112 | #544 | — | 2 | 6 | no | — |
| 113 | #542 | — | 2 | 24 | no | — |
| 114 | #541 | — | 2 | 24 | no | — |
| 115 | #539 | — | 2 | 24 | no | — |
| 116 | #537 | — | 2 | 6 | no | — |
| 117 | #536 | — | 2 | 12 | no | — |
| 118 | #533 | — | 2 | 24 | no | — |
| 119 | #533 | C23 | 1 | 12 | yes | — |
| 120 | #533 | C23 | 1 | 12 | yes | — |
| 121 | #533 | C23 | 1 | 12 | yes | — |
| 122 | #532 | C23 | 1 | 12 | yes | — |
| 123 | #532 | C23 | 1 | 12 | yes | — |
| 124 | #532 | C23 | 1 | 12 | yes | — |
| 125 | #529 | — | 2 | 24 | no | — |
| 126 | #529 | — | 2 | 12 | no | — |
| 127 | #529 | — | 2 | 12 | no | — |
| 128 | #529 | — | 2 | 12 | no | — |
| 129 | #529 | — | 2 | 12 | no | — |
| 130 | #529 | C23 | 1 | 24 | yes | — |
| 131 | #529 | C23 | 1 | 24 | yes | — |
| 132 | #525 | — | 2 | 12 | no | — |
| 133 | #525 | — | 2 | 12 | no | — |
| 134 | #525 | C23 | 1 | 8 | yes | — |
| 135 | #520 | — | 2 | 8 | no | — |
| 136 | #520 | — | 2 | 12 | no | — |
| 137 | #519 | — | 2 | 2 | no | — |
| 138 | #519 | — | 2 | 8 | no | — |
| 139 | C4×#41 | — | 2 | 8 | no | — |
| 140 | C4×#41 | — | 2 | 12 | no | — |
| 141 | C4×#41 | — | 2 | 12 | no | — |
| 142 | C4×#41 | C23 | 1 | 24 | yes | — |
| 143 | C2×C4×Q8 | — | 2 | 8 | no | — |
| 144 | C2×C4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 145 | C2×C4×Q8 | D4 | 1 | 3 | yes | — |
| 146 | C2×C4×Q8 | D4 | 1 | 4 | yes | — |
| 147 | C2×C4×Q8 | D4 | 1 | 4 | yes | — |
| 148 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 149 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 151 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 152 | C22×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 153 | C22×C42 | C23 | 1 | 3 | yes | — |
| 154 | #500 | C23 | 1 | 6 | yes | — |
| 155 | #500 | C23 | 1 | 6 | yes | — |
| 156 | #499 | C23 | 1 | 12 | yes | — |
| 157 | #499 | C23 | 1 | 12 | yes | — |
| 158 | #498 | C23 | 1 | 12 | yes | — |
| 159 | #495 | C23 | 1 | 12 | yes | — |
| 160 | #495 | C23 | 1 | 12 | yes | — |
| 161 | #494 | C23 | 1 | 6 | yes | — |
| 162 | #493 | C23 | 1 | 6 | yes | — |
| 163 | #492 | C23 | 1 | 12 | yes | — |
| 164 | #488 | C23 | 1 | 24 | yes | — |
| 165 | #488 | C23 | 1 | 24 | yes | — |
| 166 | #487 | C23 | 1 | 12 | yes | — |
| 167 | #487 | C23 | 1 | 12 | yes | — |
| 168 | #486 | C23 | 1 | 12 | yes | — |
| 169 | #486 | C23 | 1 | 12 | yes | — |
| 170 | #479 | C23 | 1 | 48 | yes | — |
| 171 | #478 | C23 | 1 | 48 | yes | — |
| 172 | #477 | C23 | 1 | 24 | yes | — |
| 173 | #476 | C23 | 1 | 24 | yes | — |
| 174 | #475 | C23 | 1 | 24 | yes | — |
| 175 | #474 | C23 | 1 | 24 | yes | — |
| 176 | #467 | C23 | 1 | 4 | yes | — |
| 177 | #467 | C23 | 1 | 4 | yes | — |
| 178 | #467 | C23 | 1 | 12 | yes | — |
| 179 | #467 | C23 | 1 | 12 | yes | — |
| 180 | #466 | C23 | 1 | 4 | yes | — |
| 181 | #466 | C23 | 1 | 4 | yes | — |
| 182 | #466 | C23 | 1 | 12 | yes | — |
| 183 | #466 | C23 | 1 | 12 | yes | — |
| 184 | #465 | C23 | 1 | 8 | yes | — |
| 185 | #465 | C23 | 1 | 8 | yes | — |
| 186 | #465 | C23 | 1 | 24 | yes | — |
| 187 | #465 | C23 | 1 | 24 | yes | — |
| 188 | #464 | C23 | 1 | 48 | yes | — |
| 189 | #463 | C23 | 1 | 48 | yes | — |
| 190 | #462 | C23 | 1 | 24 | yes | — |
| 191 | #461 | C23 | 1 | 24 | yes | — |
| 192 | #460 | C23 | 1 | 24 | yes | — |
| 193 | #459 | C23 | 1 | 24 | yes | — |
| 194 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 195 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 196 | C8×Q8 | C23 | 1 | 12 | yes | — |
| 197 | C8×Q8 | C23 | 1 | 12 | yes | — |
| 198 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 199 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 200 | C8×Q8 | C23 | 1 | 12 | yes | — |
| 201 | C8×Q8 | C23 | 1 | 12 | yes | — |
| 202 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 203 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 204 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 205 | C4×Q16 | C23 | 1 | 12 | yes | — |
| 206 | C4×SD16 | C23 | 1 | 24 | yes | — |
| 207 | C4×SD16 | C23 | 1 | 24 | yes | — |
| 208 | C4×SD16 | C23 | 1 | 24 | yes | — |
| 209 | C4×SD16 | C23 | 1 | 24 | yes | — |
| 210 | C4×D8 | C23 | 1 | 12 | yes | — |
| 211 | C4×D8 | C23 | 1 | 12 | yes | — |
| 212 | C4×D8 | C23 | 1 | 12 | yes | — |
| 213 | C4×D8 | C23 | 1 | 12 | yes | — |
| 214 | #427 | C23 | 1 | 12 | yes | — |
| 215 | #427 | C23 | 1 | 4 | yes | — |
| 216 | C2×C4⋊C8 | C23 | 1 | 12 | yes | — |
| 217 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 218 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 219 | C2×C4⋊C8 | C23 | 1 | 12 | yes | — |
| 220 | C2×C4⋊C8 | C23 | 1 | 6 | yes | — |
| 221 | #416 | C23 | 1 | 24 | yes | — |
| 222 | #416 | C23 | 1 | 8 | yes | — |
| 223 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 224 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 225 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 226 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 227 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 228 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 229 | C2×C4×C8 | C23 | 1 | 6 | yes | — |
| 230 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 231 | 2−1+4 | — | 4 | 16 | no | — |
| 232 | C2×#41 | — | 2 | 8 | no | — |
| 233 | C2×#41 | — | 2 | 12 | no | — |
| 234 | C2×#41 | — | 2 | 12 | no | — |
| 235 | C2×#41 | C24 | 1 | 8 | yes | — |
| 236 | C22×Q8 | — | 2 | 8 | no | — |
| 237 | C22×Q8 | — | 2 | 8 | no | — |
| 238 | C22×Q8 | C2×D4 | 1 | 3 | yes | — |
| 239 | C22×Q8 | C2×D4 | 1 | 4 | yes | — |
| 240 | C22×Q8 | C2×D4 | 1 | 4 | yes | — |
| 241 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 243 | C23×C4 | C2×D4 | 1 | 3 | yes | — |
| 244 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 245 | #135 | — | 2 | 16 | no | — |
| 246 | #135 | — | 4 | 24 | no | — |
| 247 | C2×Q16 | C24 | 1 | 4 | yes | — |
| 248 | C2×Q16 | C24 | 1 | 12 | yes | — |
| 249 | C2×SD16 | C24 | 1 | 8 | yes | — |
| 250 | C2×SD16 | C24 | 1 | 24 | yes | — |
| 251 | C2×D8 | C24 | 1 | 4 | yes | — |
| 252 | C2×D8 | C24 | 1 | 12 | yes | — |
| 253 | C22×C8 | — | 2 | 4 | no | — |
| 254 | C22×C8 | — | 4 | 6 | no | — |
| 255 | C22×C8 | C24 | 1 | 6 | yes | — |
| 256 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 257 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 258 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 259 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 260 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 261 | C22×C8 | C24 | 1 | 3 | yes | — |
| 262 | C22×C8 | C24 | 1 | 6 | yes | — |
| 263 | C22×C8 | C24 | 1 | 3 | yes | — |
| 264 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 265 | C4⋊Q8 | — | 2 | 24 | no | — |
| 266 | C4⋊Q8 | — | 2 | 24 | no | — |
| 267 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 268 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 269 | C4⋊Q8 | C24 | 1 | 12 | yes | — |
| 270 | #127 | C24 | 1 | 12 | yes | — |
| 271 | #126 | — | 2 | 48 | no | — |
| 272 | #126 | — | 2 | 24 | no | — |
| 273 | #126 | — | 2 | 24 | no | — |
| 274 | #125 | — | 2 | 24 | no | — |
| 275 | #125 | — | 2 | 48 | no | — |
| 276 | #125 | — | 2 | 12 | no | — |
| 277 | #125 | — | 2 | 12 | no | — |
| 278 | #125 | C24 | 1 | 24 | yes | — |
| 279 | #124 | — | 2 | 24 | no | — |
| 280 | #124 | — | 2 | 12 | no | — |
| 281 | #124 | — | 2 | 12 | no | — |
| 282 | #124 | C24 | 1 | 24 | yes | — |
| 283 | #123 | — | 2 | 24 | no | — |
| 284 | #123 | — | 2 | 24 | no | — |
| 285 | #123 | — | 2 | 8 | no | — |
| 286 | #123 | — | 2 | 48 | no | — |
| 287 | C22⋊Q8 | — | 2 | 24 | no | — |
| 288 | C22⋊Q8 | — | 2 | 24 | no | — |
| 289 | C22⋊Q8 | — | 2 | 12 | no | — |
| 290 | C22⋊Q8 | — | 2 | 12 | no | — |
| 291 | C22⋊Q8 | — | 2 | 12 | no | — |
| 292 | C22⋊Q8 | — | 2 | 12 | no | — |
| 293 | C22⋊Q8 | — | 2 | 24 | no | — |
| 294 | C22⋊Q8 | — | 2 | 48 | no | — |
| 295 | C22⋊Q8 | C24 | 1 | 8 | yes | — |
| 296 | C22⋊Q8 | C24 | 1 | 8 | yes | — |
| 297 | #121 | — | 2 | 12 | no | — |
| 298 | #121 | — | 2 | 12 | no | — |
| 299 | #121 | — | 2 | 12 | no | — |
| 300 | #121 | — | 2 | 12 | no | — |
| 301 | #121 | — | 2 | 24 | no | — |
| 302 | #121 | C24 | 1 | 8 | yes | — |
| 303 | #121 | C24 | 1 | 8 | yes | — |
| 304 | #120 | — | 2 | 8 | no | — |
| 305 | C4×Q8 | — | 2 | 8 | no | — |
| 306 | C4×Q8 | — | 2 | 8 | no | — |
| 307 | C4×Q8 | — | 2 | 24 | no | — |
| 308 | C4×Q8 | — | 2 | 12 | no | — |
| 309 | C4×Q8 | — | 2 | 12 | no | — |
| 310 | C4×Q8 | — | 2 | 12 | no | — |
| 311 | C4×Q8 | — | 2 | 12 | no | — |
| 312 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 313 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 314 | C4×Q8 | C2×D4 | 1 | 12 | yes | — |
| 315 | C4×Q8 | C2×D4 | 1 | 12 | yes | — |
| 316 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 317 | C4×Q8 | C2×D4 | 1 | 12 | yes | — |
| 318 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 319 | C4×Q8 | C24 | 1 | 24 | yes | — |
| 320 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 321 | C4×Q8 | C24 | 1 | 12 | yes | — |
| 322 | C4×D4 | — | 2 | 8 | no | — |
| 323 | C4×D4 | — | 2 | 8 | no | — |
| 324 | C4×D4 | — | 2 | 24 | no | — |
| 325 | C4×D4 | — | 2 | 24 | no | — |
| 326 | C4×D4 | — | 2 | 24 | no | — |
| 327 | C4×D4 | — | 2 | 24 | no | — |
| 328 | C4×D4 | — | 2 | 24 | no | — |
| 329 | C4×D4 | — | 2 | 12 | no | — |
| 330 | C4×D4 | — | 2 | 12 | no | — |
| 331 | C4×D4 | — | 2 | 12 | no | — |
| 332 | C4×D4 | — | 2 | 12 | no | — |
| 333 | C4×D4 | C24 | 1 | 24 | yes | — |
| 334 | C4×D4 | C24 | 1 | 24 | yes | — |
| 335 | #117 | — | 2 | 12 | no | — |
| 336 | #117 | — | 2 | 12 | no | — |
| 337 | #117 | — | 2 | 24 | no | — |
| 338 | #117 | — | 2 | 24 | no | — |
| 339 | #117 | — | 2 | 24 | no | — |
| 340 | #117 | — | 2 | 24 | no | — |
| 341 | #117 | C24 | 1 | 8 | yes | — |
| 342 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 343 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 344 | C2×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 345 | C2×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 346 | C2×C4⋊C4 | C2×D4 | 1 | 12 | yes | — |
| 347 | C2×C4⋊C4 | C2×D4 | 1 | 12 | yes | — |
| 348 | C2×C42 | — | 2 | 24 | no | — |
| 349 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 350 | C2×C42 | C2×D4 | 1 | 6 | yes | — |
| 351 | C2×C42 | C2×D4 | 1 | 6 | yes | — |
| 352 | C2×C42 | C2×D4 | 1 | 3 | yes | — |
| 353 | C2×C42 | C24 | 1 | 6 | yes | — |
| 354 | C2×C42 | C24 | 1 | 3 | yes | — |
| 355 | C2×C42 | C24 | 1 | 6 | yes | — |
| 356 | C2×C42 | C24 | 1 | 3 | yes | — |
| 357 | #107 | C24 | 1 | 4 | yes | — |
| 358 | #107 | C24 | 1 | 4 | yes | — |
| 359 | #107 | C24 | 1 | 12 | yes | — |
| 360 | #107 | C24 | 1 | 12 | yes | — |
| 361 | #106 | C24 | 1 | 8 | yes | — |
| 362 | #106 | C24 | 1 | 24 | yes | — |
| 363 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 364 | C4⋊C8 | C24 | 1 | 12 | yes | — |
| 365 | C4⋊C8 | C24 | 1 | 24 | yes | — |
| 366 | #103 | C24 | 1 | 8 | yes | — |
| 367 | #103 | C24 | 1 | 8 | yes | — |
| 368 | #103 | C24 | 1 | 24 | yes | — |
| 369 | #103 | C24 | 1 | 24 | yes | — |
| 370 | #102 | C24 | 1 | 8 | yes | — |
| 371 | #102 | C24 | 1 | 8 | yes | — |
| 372 | #102 | C24 | 1 | 24 | yes | — |
| 373 | #102 | C24 | 1 | 24 | yes | — |
| 374 | C4×C8 | C24 | 1 | 6 | yes | — |
| 375 | C4×C8 | C24 | 1 | 6 | yes | — |
| 376 | C4×C8 | C24 | 1 | 6 | yes | — |
| 377 | C4×C8 | C24 | 1 | 6 | yes | — |
| 378 | C4×C8 | C24 | 1 | 6 | yes | — |
| 379 | C4×C8 | C24 | 1 | 6 | yes | — |
| 380 | C4×C8 | C24 | 1 | 6 | yes | — |
| 381 | C4×C8 | C24 | 1 | 6 | yes | — |
| 382 | C24 | C22×D4 | 1 | 1 | yes | characteristic |
| 383 | #41 | — | 2 | 16 | no | — |
| 384 | #41 | — | 2 | 16 | no | — |
| 385 | #41 | — | 4 | 32 | no | — |
| 386 | #41 | — | 4 | 48 | no | — |
| 387 | #41 | — | 8 | 24 | no | — |
| 388 | C2×Q8 | — | 2 | 16 | no | — |
| 389 | C2×Q8 | — | 2 | 16 | no | — |
| 390 | C2×Q8 | — | 2 | 12 | no | — |
| 391 | C2×Q8 | — | 2 | 12 | no | — |
| 392 | C2×Q8 | — | 2 | 12 | no | — |
| 393 | C2×Q8 | — | 4 | 32 | no | — |
| 394 | C2×Q8 | #135 | 1 | 8 | yes | complemented |
| 395 | C2×Q8 | C22×D4 | 1 | 12 | yes | — |
| 396 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 397 | C2×Q8 | C25 | 1 | 8 | yes | — |
| 398 | C2×D4 | — | 2 | 8 | no | — |
| 399 | C2×D4 | — | 2 | 8 | no | — |
| 400 | C2×D4 | — | 2 | 8 | no | — |
| 401 | C2×D4 | — | 2 | 12 | no | — |
| 402 | C2×D4 | — | 2 | 12 | no | — |
| 403 | C2×D4 | C25 | 1 | 8 | yes | — |
| 404 | C22×C4 | — | 2 | 12 | no | — |
| 405 | C22×C4 | — | 2 | 2 | no | — |
| 406 | C22×C4 | — | 2 | 2 | no | — |
| 407 | C22×C4 | — | 2 | 24 | no | — |
| 408 | C22×C4 | — | 2 | 8 | no | — |
| 409 | C22×C4 | — | 2 | 24 | no | — |
| 410 | C22×C4 | — | 4 | 6 | no | — |
| 411 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 412 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 413 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 414 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 415 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 416 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 417 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 418 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 419 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 420 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 421 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 422 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 423 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 424 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 425 | Q16 | — | 2 | 8 | no | — |
| 426 | Q16 | — | 4 | 12 | no | — |
| 427 | SD16 | — | 2 | 16 | no | — |
| 428 | SD16 | — | 4 | 24 | no | — |
| 429 | D8 | — | 2 | 8 | no | — |
| 430 | D8 | — | 4 | 12 | no | — |
| 431 | C2×C8 | — | 2 | 2 | no | — |
| 432 | C2×C8 | — | 2 | 12 | no | — |
| 433 | C2×C8 | — | 2 | 2 | no | — |
| 434 | C2×C8 | — | 2 | 2 | no | — |
| 435 | C2×C8 | — | 2 | 2 | no | — |
| 436 | C2×C8 | — | 2 | 2 | no | — |
| 437 | C2×C8 | — | 4 | 3 | no | — |
| 438 | C2×C8 | — | 4 | 6 | no | — |
| 439 | C2×C8 | — | 4 | 3 | no | — |
| 440 | C2×C8 | 2−1+4 | 1 | 4 | yes | complemented |
| 441 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 442 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 443 | C2×C8 | C25 | 1 | 6 | yes | — |
| 444 | C2×C8 | C25 | 1 | 6 | yes | — |
| 445 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 446 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 447 | C4⋊C4 | — | 2 | 12 | no | — |
| 448 | C4⋊C4 | — | 2 | 24 | no | — |
| 449 | C4⋊C4 | — | 2 | 12 | no | — |
| 450 | C4⋊C4 | — | 2 | 8 | no | — |
| 451 | C4⋊C4 | — | 2 | 8 | no | — |
| 452 | C4⋊C4 | — | 2 | 12 | no | — |
| 453 | C4⋊C4 | — | 2 | 12 | no | — |
| 454 | C4⋊C4 | — | 2 | 24 | no | — |
| 455 | C4⋊C4 | — | 2 | 24 | no | — |
| 456 | C4⋊C4 | — | 2 | 24 | no | — |
| 457 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 458 | C4⋊C4 | C22×D4 | 1 | 12 | yes | — |
| 459 | C4⋊C4 | C22×D4 | 1 | 24 | yes | — |
| 460 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 461 | C4⋊C4 | C25 | 1 | 8 | yes | — |
| 462 | C22⋊C4 | — | 2 | 8 | no | — |
| 463 | C22⋊C4 | — | 2 | 8 | no | — |
| 464 | C22⋊C4 | — | 2 | 8 | no | — |
| 465 | C22⋊C4 | — | 2 | 24 | no | — |
| 466 | C22⋊C4 | — | 2 | 8 | no | — |
| 467 | C22⋊C4 | — | 2 | 8 | no | — |
| 468 | C22⋊C4 | — | 2 | 24 | no | — |
| 469 | C22⋊C4 | — | 2 | 24 | no | — |
| 470 | C22⋊C4 | — | 2 | 24 | no | — |
| 471 | C42 | — | 2 | 24 | no | — |
| 472 | C42 | — | 2 | 24 | no | — |
| 473 | C42 | — | 2 | 8 | no | — |
| 474 | C42 | C22×D4 | 1 | 6 | yes | — |
| 475 | C42 | C22×D4 | 1 | 6 | yes | — |
| 476 | C42 | C22×D4 | 1 | 6 | yes | — |
| 477 | C42 | C22×D4 | 1 | 6 | yes | — |
| 478 | C42 | C22×D4 | 1 | 6 | yes | — |
| 479 | C42 | C22×D4 | 1 | 6 | yes | — |
| 480 | C42 | C25 | 1 | 6 | yes | — |
| 481 | C42 | C25 | 1 | 6 | yes | — |
| 482 | C23 | — | 2 | 2 | no | — |
| 483 | C23 | — | 2 | 2 | no | — |
| 484 | C23 | — | 2 | 2 | no | — |
| 485 | C23 | — | 2 | 8 | no | — |
| 486 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 487 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 488 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 489 | Q8 | — | 2 | 24 | no | — |
| 490 | Q8 | — | 2 | 8 | no | — |
| 491 | Q8 | — | 2 | 8 | no | — |
| 492 | Q8 | — | 4 | 24 | no | — |
| 493 | Q8 | — | 8 | 12 | no | — |
| 494 | Q8 | C2×#135 | 1 | 16 | yes | — |
| 495 | D4 | — | 2 | 8 | no | — |
| 496 | D4 | — | 2 | 8 | no | — |
| 497 | D4 | — | 4 | 16 | no | — |
| 498 | D4 | — | 4 | 16 | no | — |
| 499 | D4 | — | 4 | 16 | no | — |
| 500 | D4 | — | 4 | 24 | no | — |
| 501 | D4 | — | 8 | 12 | no | — |
| 502 | C2×C4 | — | 2 | 12 | no | — |
| 503 | C2×C4 | — | 2 | 2 | no | — |
| 504 | C2×C4 | — | 2 | 6 | no | — |
| 505 | C2×C4 | — | 2 | 1 | no | — |
| 506 | C2×C4 | — | 2 | 1 | no | — |
| 507 | C2×C4 | — | 2 | 1 | no | — |
| 508 | C2×C4 | — | 2 | 1 | no | — |
| 509 | C2×C4 | — | 2 | 2 | no | — |
| 510 | C2×C4 | — | 2 | 2 | no | — |
| 511 | C2×C4 | — | 2 | 12 | no | — |
| 512 | C2×C4 | — | 2 | 12 | no | — |
| 513 | C2×C4 | — | 2 | 8 | no | — |
| 514 | C2×C4 | — | 2 | 8 | no | — |
| 515 | C2×C4 | — | 2 | 8 | no | — |
| 516 | C2×C4 | — | 4 | 3 | no | — |
| 517 | C2×C4 | — | 4 | 6 | no | — |
| 518 | C2×C4 | — | 4 | 3 | no | — |
| 519 | C2×C4 | — | 4 | 16 | no | — |
| 520 | C2×C4 | — | 4 | 48 | no | — |
| 521 | C2×C4 | — | 8 | 24 | no | — |
| 522 | C2×C4 | C2×#135 | 1 | 12 | yes | — |
| 523 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 524 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 526 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 527 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 528 | C2×C4 | C23×D4 | 1 | 6 | yes | — |
| 529 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 530 | C2×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 531 | C2×C4 | #585 | 1 | 2 | yes | — |
| 532 | C2×C4 | C26 | 1 | 1 | yes | characteristic |
| 533 | C8 | — | 2 | 1 | no | — |
| 534 | C8 | — | 2 | 1 | no | — |
| 535 | C8 | — | 2 | 6 | no | — |
| 536 | C8 | — | 2 | 6 | no | — |
| 537 | C8 | C2×2−1+4 | 1 | 2 | yes | — |
| 538 | C8 | C2×2−1+4 | 1 | 2 | yes | — |
| 539 | C22 | — | 2 | 8 | no | — |
| 540 | C22 | — | 2 | 1 | no | — |
| 541 | C22 | — | 2 | 1 | no | — |
| 542 | C22 | — | 2 | 1 | no | — |
| 543 | C22 | — | 2 | 1 | no | — |
| 544 | C22 | — | 2 | 1 | no | — |
| 545 | C22 | — | 2 | 1 | no | — |
| 546 | C22 | — | 4 | 8 | no | — |
| 547 | C22 | — | 4 | 8 | no | — |
| 548 | C22 | — | 4 | 8 | no | — |
| 549 | C22 | #3497 | 1 | 2 | yes | — |
| 550 | C22 | C22×#135 | 1 | 2 | yes | — |
| 551 | C22 | #3584 | 1 | 2 | yes | — |
| 552 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 553 | C4 | — | 2 | 1 | no | — |
| 554 | C4 | — | 2 | 1 | no | — |
| 555 | C4 | — | 2 | 6 | no | — |
| 556 | C4 | — | 2 | 6 | no | — |
| 557 | C4 | — | 2 | 6 | no | — |
| 558 | C4 | — | 4 | 8 | no | — |
| 559 | C4 | — | 4 | 8 | no | — |
| 560 | C4 | — | 4 | 8 | no | — |
| 561 | C4 | #3497 | 1 | 2 | yes | — |
| 562 | C4 | C22×#135 | 1 | 12 | yes | — |
| 563 | C4 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 564 | C4 | C2×#585 | 1 | 1 | yes | characteristic |
| 565 | C2 | — | 2 | 2 | no | — |
| 566 | C2 | — | 2 | 2 | no | — |
| 567 | C2 | — | 2 | 2 | no | — |
| 568 | C2 | — | 8 | 8 | no | — |
| 569 | C2 | C2×#3497 | 1 | 1 | yes | characteristic |
| 570 | C2 | C23×#135 | 1 | 1 | yes | characteristic |
| 571 | C2 | C2×#3584 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C26 |
| socle | C22 | C24×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ 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. #62364 | C2 | semidirect |
| 3. #62363 | C2 | semidirect |
| 4. #62362 | C2 | semidirect |
| 5. #62361 | C2 | semidirect |
| 6. #62360 | C2 | semidirect |
| 7. #62359 | C2 | semidirect |
| 8. #62358 | C2 | semidirect |
| 9. #62357 | C2 | semidirect |
| 10. #61393 | C2 | semidirect |
| 11. Q8×#135 | C2 | semidirect |
| 12. #61303 | C2 | semidirect |
| 13. #60900 | C2 | semidirect |
| 14. #60673 | C2 | semidirect |
| 15. C22×C8×Q8 | C2 | semidirect |
| 31. #3396 | C22 | semidirect |
| 32. #3395 | C22 | semidirect |
| 33. #3394 | C22 | semidirect |
| 34. #3393 | C22 | semidirect |
| 35. #3392 | C22 | semidirect |
| 36. #3391 | C22 | semidirect |
| 37. #3383 | C22 | semidirect |
| 38. Q8×Q16 | C22 | semidirect |
| 39. #3381 | C22 | semidirect |
| 40. #3380 | C22 | semidirect |
| 41. Q8×SD16 | C22 | semidirect |
| 42. Q8×D8 | C22 | semidirect |
| 43. #3365 | C22 | semidirect |
| 44. #3364 | C22 | semidirect |
| 45. #3363 | C22 | semidirect |
| 46. #3362 | C22 | semidirect |
| 47. #3361 | C22 | semidirect |
| 48. #3360 | C22 | semidirect |
| 49. #3359 | C22 | semidirect |
| 50. #3358 | C22 | semidirect |
| 394. C2×Q8 | #135 | semidirect |
| 440. C2×C8 | 2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62788 | 2 |
| #62364 | 2 |
| #62363 | 2 |
| #62362 | 2 |
| #62361 | 2 |
| #62360 | 2 |
| #62359 | 2 |
| #62358 | 2 |
| #62357 | 2 |
| #61393 | 2 |
| Q8×#135 | 2 |
| #61303 | 2 |
| #60900 | 2 |
| #60673 | 2 |
| C22×C8×Q8 | 2 |