Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
8276 conjugacy classes of subgroups.
The subgroup lattice has 650 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#554 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C4×2−1+4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #36544 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #36492 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #35738 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #35701 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #35672 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #35659 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #35357 | C2 | 1 | 8 | yes | maximal, complemented |
| 10 | #35279 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #35138 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #34963 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #34935 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #34200 | C2 | 1 | 4 | yes | maximal, complemented |
| 15 | #34187 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#554 | — | 2 | 16 | no | — |
| 18 | C2×#554 | C22 | 1 | 8 | yes | — |
| 19 | C2×#554 | C22 | 1 | 8 | yes | — |
| 20 | C22×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 21 | C22×#125 | C22 | 1 | 2 | yes | — |
| 22 | C2×#525 | C22 | 1 | 4 | yes | — |
| 23 | C22×C22⋊Q8 | C22 | 1 | 4 | yes | — |
| 24 | C22×C22⋊Q8 | C22 | 1 | 2 | yes | — |
| 25 | C4×2−1+4 | — | 2 | 16 | no | — |
| 26 | C2×#520 | C22 | 1 | 4 | yes | — |
| 27 | C2×#520 | C22 | 1 | 2 | yes | — |
| 28 | C2×#520 | C22 | 1 | 4 | yes | complemented |
| 29 | C2×#519 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#519 | C22 | 1 | 4 | yes | complemented |
| 31 | C2×C4×#41 | C22 | 1 | 4 | yes | — |
| 32 | C2×C4×#41 | C22 | 1 | 2 | yes | — |
| 33 | C2×C4×#41 | C22 | 1 | 4 | yes | complemented |
| 34 | C22×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 35 | C22×C4×Q8 | C22 | 1 | 4 | yes | complemented |
| 36 | C22×C4×D4 | C22 | 1 | 1 | yes | characteristic |
| 37 | C22×C4×D4 | C22 | 1 | 2 | yes | — |
| 38 | C23×C4⋊C4 | C22 | 1 | 2 | yes | — |
| 39 | #2857 | C22 | 1 | 8 | yes | complemented |
| 40 | #2851 | C22 | 1 | 16 | yes | complemented |
| 41 | #2634 | C22 | 1 | 8 | yes | complemented |
| 42 | #2633 | C22 | 1 | 8 | yes | complemented |
| 43 | #2628 | C22 | 1 | 8 | yes | complemented |
| 44 | #2611 | C22 | 1 | 16 | yes | complemented |
| 45 | #2598 | C22 | 1 | 16 | yes | — |
| 46 | #2584 | C22 | 1 | 8 | yes | complemented |
| 47 | #2580 | C22 | 1 | 8 | yes | — |
| 48 | #2568 | C22 | 1 | 4 | yes | complemented |
| 49 | #2567 | C22 | 1 | 4 | yes | complemented |
| 50 | #2563 | C22 | 1 | 4 | yes | complemented |
| 51 | #2562 | C22 | 1 | 8 | yes | complemented |
| 52 | #2542 | C22 | 1 | 4 | yes | complemented |
| 53 | #2538 | C22 | 1 | 4 | yes | — |
| 54 | #2537 | C22 | 1 | 4 | yes | — |
| 55 | #2536 | C22 | 1 | 4 | yes | — |
| 56 | #2535 | C22 | 1 | 4 | yes | — |
| 57 | #2535 | C22 | 1 | 8 | yes | — |
| 58 | #2534 | C22 | 1 | 8 | yes | — |
| 59 | #2487 | C22 | 1 | 8 | yes | — |
| 60 | #2486 | C22 | 1 | 4 | yes | — |
| 61 | #2484 | C22 | 1 | 8 | yes | — |
| 62 | #2482 | C22 | 1 | 8 | yes | — |
| 63 | #2477 | C22 | 1 | 32 | yes | complemented |
| 64 | #2465 | C22 | 1 | 32 | yes | complemented |
| 65 | #2463 | C22 | 1 | 32 | yes | complemented |
| 66 | #2449 | C22 | 1 | 32 | yes | complemented |
| 67 | #2423 | C22 | 1 | 16 | yes | complemented |
| 68 | #2421 | C22 | 1 | 16 | yes | complemented |
| 69 | #2409 | C22 | 1 | 8 | yes | — |
| 70 | #2409 | C22 | 1 | 16 | yes | complemented |
| 71 | #2408 | C22 | 1 | 4 | yes | — |
| 72 | #2407 | C22 | 1 | 16 | yes | complemented |
| 73 | #2406 | C22 | 1 | 8 | yes | — |
| 74 | #2404 | C22 | 1 | 8 | yes | — |
| 75 | #2398 | C22 | 1 | 8 | yes | — |
| 76 | #2397 | C22 | 1 | 8 | yes | — |
| 77 | #2392 | C22 | 1 | 8 | yes | — |
| 78 | #2361 | C22 | 1 | 16 | yes | complemented |
| 79 | #2360 | C22 | 1 | 16 | yes | complemented |
| 80 | #2356 | C22 | 1 | 8 | yes | complemented |
| 81 | #2355 | C22 | 1 | 8 | yes | complemented |
| 82 | #2352 | C22 | 1 | 16 | yes | complemented |
| 83 | D4×C4⋊C4 | C22 | 1 | 16 | yes | complemented |
| 84 | #2322 | C22 | 1 | 16 | yes | — |
| 85 | #2317 | C22 | 1 | 4 | yes | — |
| 86 | #2313 | C22 | 1 | 4 | yes | — |
| 87 | #2311 | C22 | 1 | 4 | yes | — |
| 88 | #2310 | C22 | 1 | 2 | yes | — |
| 89 | C4×#121 | C22 | 1 | 8 | yes | — |
| 90 | C4×#121 | C22 | 1 | 16 | yes | — |
| 91 | C4×#120 | C22 | 1 | 16 | yes | — |
| 92 | #2285 | C22 | 1 | 2 | yes | — |
| 93 | #2283 | C22 | 1 | 4 | yes | — |
| 94 | #2280 | C22 | 1 | 4 | yes | — |
| 95 | #2274 | C22 | 1 | 2 | yes | — |
| 96 | C2×2−1+4 | — | 2 | 16 | no | — |
| 97 | C2×2−1+4 | — | 2 | 8 | no | — |
| 98 | C22×#41 | C23 | 1 | 4 | yes | — |
| 99 | C22×#41 | C23 | 1 | 4 | yes | — |
| 100 | C22×#41 | C23 | 1 | 2 | yes | — |
| 101 | C23×Q8 | C23 | 1 | 4 | yes | — |
| 102 | C23×Q8 | C23 | 1 | 1 | yes | characteristic |
| 103 | C23×Q8 | C23 | 1 | 2 | yes | — |
| 104 | C23×D4 | C23 | 1 | 1 | yes | characteristic |
| 105 | C24×C4 | C23 | 1 | 2 | yes | — |
| 106 | C24×C4 | C23 | 1 | 4 | yes | — |
| 107 | #554 | — | 2 | 64 | no | — |
| 108 | #554 | — | 2 | 64 | no | — |
| 109 | C2×C4⋊Q8 | — | 2 | 8 | no | — |
| 110 | C2×C4⋊Q8 | C23 | 1 | 4 | yes | — |
| 111 | C2×C4⋊Q8 | C23 | 1 | 4 | yes | — |
| 112 | C2×#125 | — | 2 | 16 | no | — |
| 113 | C2×#125 | C23 | 1 | 8 | yes | — |
| 114 | C2×#125 | C23 | 1 | 8 | yes | — |
| 115 | #525 | — | 2 | 32 | no | — |
| 116 | C2×#123 | C23 | 1 | 8 | yes | — |
| 117 | C2×C22⋊Q8 | — | 2 | 16 | no | — |
| 118 | C2×C22⋊Q8 | — | 2 | 32 | no | — |
| 119 | C2×C22⋊Q8 | C23 | 1 | 8 | yes | — |
| 120 | C2×C22⋊Q8 | C23 | 1 | 16 | yes | — |
| 121 | C2×C22⋊Q8 | C23 | 1 | 32 | yes | — |
| 122 | C2×C22⋊Q8 | C23 | 1 | 16 | yes | — |
| 123 | C2×#121 | C23 | 1 | 8 | yes | — |
| 124 | C2×#121 | C23 | 1 | 8 | yes | — |
| 125 | C2×#120 | C23 | 1 | 8 | yes | — |
| 126 | #520 | — | 2 | 32 | no | — |
| 127 | #520 | — | 2 | 16 | no | — |
| 128 | #520 | — | 2 | 32 | no | — |
| 129 | #519 | — | 2 | 8 | no | — |
| 130 | #519 | — | 2 | 32 | no | — |
| 131 | C4×#41 | — | 2 | 32 | no | — |
| 132 | C4×#41 | — | 2 | 32 | no | — |
| 133 | C4×#41 | — | 2 | 16 | no | — |
| 134 | C2×C4×Q8 | — | 2 | 32 | no | — |
| 135 | C2×C4×Q8 | D4 | 1 | 16 | yes | complemented |
| 136 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 137 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 138 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 139 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 140 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 141 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 142 | C2×C4×Q8 | C23 | 1 | 8 | yes | — |
| 143 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 144 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 145 | C2×C4×Q8 | C23 | 1 | 4 | yes | — |
| 146 | C2×C4×D4 | — | 2 | 16 | no | — |
| 147 | C2×C4×D4 | — | 2 | 8 | no | — |
| 148 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 149 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 150 | C2×C4×D4 | C23 | 1 | 8 | yes | — |
| 151 | C2×C4×D4 | C23 | 1 | 8 | yes | — |
| 152 | C2×C4×D4 | C23 | 1 | 8 | yes | — |
| 153 | C2×C4×D4 | C23 | 1 | 16 | yes | — |
| 154 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 155 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 156 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 157 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 158 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 159 | C2×C4×D4 | C23 | 1 | 4 | yes | — |
| 160 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 161 | C2×C4×D4 | C23 | 1 | 8 | yes | — |
| 162 | C2×C4×D4 | C23 | 1 | 32 | yes | — |
| 163 | C2×#117 | C23 | 1 | 4 | yes | — |
| 164 | C2×#117 | C23 | 1 | 2 | yes | — |
| 165 | C2×#117 | C23 | 1 | 8 | yes | — |
| 166 | C2×#117 | C23 | 1 | 4 | yes | — |
| 167 | C2×#117 | C23 | 1 | 4 | yes | — |
| 168 | C2×#117 | C23 | 1 | 4 | yes | — |
| 169 | C2×#117 | C23 | 1 | 8 | yes | — |
| 170 | C22×C4⋊C4 | — | 2 | 16 | no | — |
| 171 | C22×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 172 | C22×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 173 | C22×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 174 | C22×C4⋊C4 | C23 | 1 | 16 | yes | — |
| 175 | C22×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 176 | C22×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 177 | C22×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 178 | C22×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 179 | C22×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 180 | C22×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 181 | C22×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 182 | C22×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 183 | C22×C42 | C23 | 1 | 8 | yes | — |
| 184 | C22×C42 | C23 | 1 | 4 | yes | — |
| 185 | C22×C42 | C23 | 1 | 2 | yes | — |
| 186 | C22×C42 | C23 | 1 | 1 | yes | characteristic |
| 187 | #400 | C23 | 1 | 16 | yes | — |
| 188 | #400 | C23 | 1 | 16 | yes | — |
| 189 | #399 | C23 | 1 | 16 | yes | — |
| 190 | #399 | C23 | 1 | 16 | yes | — |
| 191 | #398 | C23 | 1 | 16 | yes | — |
| 192 | #398 | C23 | 1 | 8 | yes | — |
| 193 | #397 | C23 | 1 | 8 | yes | — |
| 194 | #397 | C23 | 1 | 16 | yes | — |
| 195 | #396 | C23 | 1 | 16 | yes | — |
| 196 | #395 | C23 | 1 | 16 | yes | — |
| 197 | #395 | C23 | 1 | 16 | yes | — |
| 198 | #394 | C23 | 1 | 16 | yes | — |
| 199 | #394 | C23 | 1 | 8 | yes | — |
| 200 | #394 | C23 | 1 | 16 | yes | — |
| 201 | #393 | C23 | 1 | 16 | yes | — |
| 202 | #393 | C23 | 1 | 16 | yes | — |
| 203 | #392 | C23 | 1 | 8 | yes | — |
| 204 | #392 | C23 | 1 | 16 | yes | — |
| 205 | #391 | C23 | 1 | 16 | yes | — |
| 206 | #391 | C23 | 1 | 8 | yes | — |
| 207 | #391 | C23 | 1 | 16 | yes | — |
| 208 | #390 | C23 | 1 | 8 | yes | — |
| 209 | #390 | C23 | 1 | 8 | yes | — |
| 210 | #389 | C23 | 1 | 16 | yes | — |
| 211 | #389 | C23 | 1 | 16 | yes | — |
| 212 | #389 | C23 | 1 | 32 | yes | — |
| 213 | #389 | C23 | 1 | 8 | yes | — |
| 214 | #388 | C23 | 1 | 32 | yes | — |
| 215 | #388 | C23 | 1 | 32 | yes | — |
| 216 | #388 | C23 | 1 | 16 | yes | — |
| 217 | #387 | C23 | 1 | 32 | yes | — |
| 218 | #387 | C23 | 1 | 32 | yes | — |
| 219 | #387 | C23 | 1 | 32 | yes | — |
| 220 | #386 | C23 | 1 | 16 | yes | — |
| 221 | #386 | C23 | 1 | 32 | yes | — |
| 222 | #386 | C23 | 1 | 32 | yes | — |
| 223 | #386 | C23 | 1 | 16 | yes | — |
| 224 | #385 | C23 | 1 | 16 | yes | — |
| 225 | #385 | C23 | 1 | 32 | yes | — |
| 226 | #385 | C23 | 1 | 32 | yes | — |
| 227 | #385 | C23 | 1 | 32 | yes | — |
| 228 | #384 | C23 | 1 | 8 | yes | — |
| 229 | #384 | C23 | 1 | 4 | yes | — |
| 230 | #383 | C23 | 1 | 8 | yes | — |
| 231 | #382 | C23 | 1 | 8 | yes | — |
| 232 | #382 | C23 | 1 | 8 | yes | — |
| 233 | #382 | C23 | 1 | 4 | yes | — |
| 234 | #381 | C23 | 1 | 8 | yes | — |
| 235 | #381 | C23 | 1 | 8 | yes | — |
| 236 | #380 | C23 | 1 | 8 | yes | — |
| 237 | #380 | C23 | 1 | 16 | yes | — |
| 238 | #380 | C23 | 1 | 16 | yes | — |
| 239 | #380 | C23 | 1 | 4 | yes | — |
| 240 | #380 | C23 | 1 | 8 | yes | — |
| 241 | #380 | C23 | 1 | 8 | yes | — |
| 242 | #380 | C23 | 1 | 4 | yes | — |
| 243 | #379 | C23 | 1 | 8 | yes | — |
| 244 | C4×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 245 | C4×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 246 | C4×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 247 | C4×C4⋊C4 | C23 | 1 | 16 | yes | — |
| 248 | C4×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 249 | C4×C22⋊C4 | C23 | 1 | 32 | yes | — |
| 250 | C4×C22⋊C4 | C23 | 1 | 16 | yes | — |
| 251 | #376 | C23 | 1 | 8 | yes | — |
| 252 | C25 | C24 | 1 | 2 | yes | — |
| 253 | 2−1+4 | — | 2 | 128 | no | — |
| 254 | C2×#41 | — | 2 | 16 | no | — |
| 255 | C2×#41 | — | 2 | 32 | no | — |
| 256 | C2×#41 | — | 2 | 16 | no | — |
| 257 | C2×#41 | — | 2 | 16 | no | — |
| 258 | C2×#41 | — | 2 | 8 | no | — |
| 259 | C2×#41 | — | 2 | 16 | no | — |
| 260 | C2×#41 | — | 2 | 8 | no | — |
| 261 | C2×#41 | #41 | 1 | 16 | yes | — |
| 262 | C22×Q8 | — | 2 | 16 | no | — |
| 263 | C22×Q8 | — | 2 | 16 | no | — |
| 264 | C22×Q8 | — | 2 | 8 | no | — |
| 265 | C22×Q8 | — | 2 | 16 | no | — |
| 266 | C22×Q8 | — | 2 | 8 | no | — |
| 267 | C22×Q8 | — | 8 | 4 | no | — |
| 268 | C22×Q8 | C2×D4 | 1 | 8 | yes | — |
| 269 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 270 | C22×Q8 | C24 | 1 | 4 | yes | — |
| 271 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 272 | C22×Q8 | C24 | 1 | 8 | yes | — |
| 273 | C22×D4 | — | 2 | 8 | no | — |
| 274 | C22×D4 | — | 2 | 4 | no | — |
| 275 | C22×D4 | C24 | 1 | 2 | yes | — |
| 276 | C22×D4 | C24 | 1 | 4 | yes | — |
| 277 | C22×D4 | C24 | 1 | 16 | yes | — |
| 278 | C22×D4 | C24 | 1 | 4 | yes | — |
| 279 | C22×D4 | C24 | 1 | 2 | yes | — |
| 280 | C22×D4 | C24 | 1 | 2 | yes | — |
| 281 | C23×C4 | — | 2 | 8 | no | — |
| 282 | C23×C4 | — | 2 | 16 | no | — |
| 283 | C23×C4 | — | 2 | 16 | no | — |
| 284 | C23×C4 | — | 8 | 8 | no | — |
| 285 | C23×C4 | C24 | 1 | 2 | yes | — |
| 286 | C23×C4 | C24 | 1 | 8 | yes | — |
| 287 | C23×C4 | C24 | 1 | 8 | yes | — |
| 288 | C23×C4 | C24 | 1 | 4 | yes | — |
| 289 | C23×C4 | C24 | 1 | 2 | yes | — |
| 290 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 291 | C23×C4 | C24 | 1 | 4 | yes | — |
| 292 | C23×C4 | C24 | 1 | 4 | yes | — |
| 293 | C23×C4 | C24 | 1 | 8 | yes | — |
| 294 | C23×C4 | C24 | 1 | 4 | yes | — |
| 295 | C23×C4 | C24 | 1 | 16 | yes | — |
| 296 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 297 | C23×C4 | C24 | 1 | 2 | yes | — |
| 298 | C23×C4 | C24 | 1 | 1 | yes | characteristic |
| 299 | C4⋊Q8 | — | 2 | 16 | no | — |
| 300 | C4⋊Q8 | — | 2 | 16 | no | — |
| 301 | #125 | — | 2 | 32 | no | — |
| 302 | #125 | — | 2 | 32 | no | — |
| 303 | #123 | — | 2 | 32 | no | — |
| 304 | C22⋊Q8 | — | 2 | 64 | no | — |
| 305 | C22⋊Q8 | — | 2 | 32 | no | — |
| 306 | C22⋊Q8 | — | 2 | 128 | no | — |
| 307 | C22⋊Q8 | — | 8 | 16 | no | — |
| 308 | #121 | — | 2 | 32 | no | — |
| 309 | #121 | — | 2 | 32 | no | — |
| 310 | #120 | — | 2 | 32 | no | — |
| 311 | C4×Q8 | — | 2 | 16 | no | — |
| 312 | C4×Q8 | — | 2 | 16 | no | — |
| 313 | C4×Q8 | — | 2 | 16 | no | — |
| 314 | C4×Q8 | — | 2 | 32 | no | — |
| 315 | C4×Q8 | — | 2 | 16 | no | — |
| 316 | C4×Q8 | — | 2 | 8 | no | — |
| 317 | C4×Q8 | — | 2 | 16 | no | — |
| 318 | C4×Q8 | — | 2 | 8 | no | — |
| 319 | C4×Q8 | C2×D4 | 1 | 32 | yes | — |
| 320 | C4×Q8 | C2×D4 | 1 | 32 | yes | — |
| 321 | C4×D4 | — | 2 | 16 | no | — |
| 322 | C4×D4 | — | 2 | 16 | no | — |
| 323 | C4×D4 | — | 2 | 32 | no | — |
| 324 | C4×D4 | — | 2 | 64 | no | — |
| 325 | C4×D4 | — | 2 | 16 | no | — |
| 326 | C4×D4 | — | 2 | 32 | no | — |
| 327 | C4×D4 | — | 2 | 32 | no | — |
| 328 | C4×D4 | — | 2 | 16 | no | — |
| 329 | C4×D4 | — | 2 | 32 | no | — |
| 330 | C4×D4 | — | 2 | 16 | no | — |
| 331 | C4×D4 | — | 2 | 16 | no | — |
| 332 | C4×D4 | — | 2 | 8 | no | — |
| 333 | C4×D4 | — | 2 | 16 | no | — |
| 334 | C4×D4 | — | 2 | 8 | no | — |
| 335 | C4×D4 | — | 8 | 32 | no | — |
| 336 | #117 | — | 2 | 16 | no | — |
| 337 | #117 | — | 2 | 8 | no | — |
| 338 | #117 | — | 2 | 16 | no | — |
| 339 | #117 | — | 2 | 16 | no | — |
| 340 | #117 | — | 2 | 32 | no | — |
| 341 | #117 | — | 2 | 32 | no | — |
| 342 | #117 | — | 2 | 16 | no | — |
| 343 | C2×C4⋊C4 | — | 2 | 16 | no | — |
| 344 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 345 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 346 | C2×C4⋊C4 | — | 2 | 8 | no | — |
| 347 | C2×C4⋊C4 | — | 2 | 16 | no | — |
| 348 | C2×C4⋊C4 | — | 2 | 64 | no | — |
| 349 | C2×C4⋊C4 | — | 2 | 16 | no | — |
| 350 | C2×C4⋊C4 | — | 2 | 32 | no | — |
| 351 | C2×C4⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 352 | C2×C4⋊C4 | C2×D4 | 1 | 16 | yes | — |
| 353 | C2×C4⋊C4 | C24 | 1 | 16 | yes | — |
| 354 | C2×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 355 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 356 | C2×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 357 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 358 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 359 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 360 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 361 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 362 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 363 | C2×C4⋊C4 | C24 | 1 | 16 | yes | — |
| 364 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 365 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 366 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 367 | C2×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 368 | C2×C4⋊C4 | C24 | 1 | 16 | yes | — |
| 369 | C2×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 370 | C2×C4⋊C4 | C24 | 1 | 32 | yes | — |
| 371 | C2×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 372 | C2×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 373 | C2×C4⋊C4 | C24 | 1 | 8 | yes | — |
| 374 | C2×C22⋊C4 | — | 2 | 8 | no | — |
| 375 | C2×C22⋊C4 | — | 2 | 16 | no | — |
| 376 | C2×C22⋊C4 | C24 | 1 | 16 | yes | — |
| 377 | C2×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 378 | C2×C22⋊C4 | C24 | 1 | 4 | yes | — |
| 379 | C2×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 380 | C2×C22⋊C4 | C24 | 1 | 4 | yes | — |
| 381 | C2×C22⋊C4 | C24 | 1 | 4 | yes | — |
| 382 | C2×C22⋊C4 | C24 | 1 | 8 | yes | — |
| 383 | C2×C22⋊C4 | C24 | 1 | 16 | yes | — |
| 384 | C2×C22⋊C4 | C24 | 1 | 16 | yes | — |
| 385 | C2×C22⋊C4 | C24 | 1 | 16 | yes | — |
| 386 | C2×C22⋊C4 | C24 | 1 | 16 | yes | — |
| 387 | C2×C22⋊C4 | C24 | 1 | 32 | yes | — |
| 388 | C2×C42 | — | 2 | 32 | no | — |
| 389 | C2×C42 | — | 2 | 16 | no | — |
| 390 | C2×C42 | C2×D4 | 1 | 16 | yes | — |
| 391 | C2×C42 | C2×D4 | 1 | 8 | yes | — |
| 392 | C2×C42 | C24 | 1 | 8 | yes | — |
| 393 | C2×C42 | C24 | 1 | 4 | yes | — |
| 394 | C2×C42 | C24 | 1 | 8 | yes | — |
| 395 | C2×C42 | C24 | 1 | 4 | yes | — |
| 396 | C2×C42 | C24 | 1 | 8 | yes | — |
| 397 | C2×C42 | C24 | 1 | 4 | yes | — |
| 398 | C2×C42 | C24 | 1 | 16 | yes | — |
| 399 | C2×C42 | C24 | 1 | 4 | yes | — |
| 400 | C2×C42 | C24 | 1 | 2 | yes | — |
| 401 | C2×C42 | C24 | 1 | 4 | yes | — |
| 402 | C2×C42 | C24 | 1 | 2 | yes | — |
| 403 | #95 | C24 | 1 | 8 | yes | — |
| 404 | #95 | C24 | 1 | 16 | yes | — |
| 405 | #95 | C24 | 1 | 16 | yes | — |
| 406 | #95 | C24 | 1 | 16 | yes | — |
| 407 | #95 | C24 | 1 | 16 | yes | — |
| 408 | #95 | C24 | 1 | 32 | yes | — |
| 409 | #95 | C24 | 1 | 32 | yes | — |
| 410 | #95 | C24 | 1 | 8 | yes | — |
| 411 | #95 | C24 | 1 | 16 | yes | — |
| 412 | C24 | — | 2 | 4 | no | — |
| 413 | C24 | — | 2 | 8 | no | — |
| 414 | C24 | — | 2 | 8 | no | — |
| 415 | C24 | — | 4 | 4 | no | — |
| 416 | C24 | C25 | 1 | 4 | yes | — |
| 417 | C24 | C25 | 1 | 4 | yes | — |
| 418 | C24 | C25 | 1 | 1 | yes | characteristic |
| 419 | #41 | — | 2 | 128 | no | — |
| 420 | #41 | — | 2 | 128 | no | — |
| 421 | #41 | — | 2 | 64 | no | — |
| 422 | C2×Q8 | — | 2 | 128 | no | — |
| 423 | C2×Q8 | — | 2 | 32 | no | — |
| 424 | C2×Q8 | — | 2 | 8 | no | — |
| 425 | C2×Q8 | — | 2 | 4 | no | — |
| 426 | C2×Q8 | — | 2 | 16 | no | — |
| 427 | C2×Q8 | — | 2 | 16 | no | — |
| 428 | C2×Q8 | — | 2 | 8 | no | — |
| 429 | C2×Q8 | — | 2 | 4 | no | — |
| 430 | C2×Q8 | — | 2 | 8 | no | — |
| 431 | C2×Q8 | — | 4 | 16 | no | — |
| 432 | C2×Q8 | — | 8 | 16 | no | — |
| 433 | C2×Q8 | C22×D4 | 1 | 16 | yes | — |
| 434 | C2×Q8 | C2×#41 | 1 | 8 | yes | — |
| 435 | C2×D4 | — | 2 | 32 | no | — |
| 436 | C2×D4 | — | 2 | 8 | no | — |
| 437 | C2×D4 | — | 2 | 16 | no | — |
| 438 | C2×D4 | — | 2 | 8 | no | — |
| 439 | C2×D4 | — | 2 | 8 | no | — |
| 440 | C2×D4 | — | 2 | 32 | no | — |
| 441 | C2×D4 | — | 2 | 32 | no | — |
| 442 | C2×D4 | — | 2 | 4 | no | — |
| 443 | C2×D4 | — | 2 | 4 | no | — |
| 444 | C2×D4 | — | 2 | 8 | no | — |
| 445 | C2×D4 | — | 2 | 4 | no | — |
| 446 | C2×D4 | — | 2 | 4 | no | — |
| 447 | C2×D4 | — | 2 | 4 | no | — |
| 448 | C2×D4 | — | 4 | 16 | no | — |
| 449 | C2×D4 | C2×#41 | 1 | 16 | yes | — |
| 450 | C2×D4 | C2×#41 | 1 | 8 | yes | — |
| 451 | C2×D4 | 2−1+4 | 1 | 8 | yes | complemented |
| 452 | C22×C4 | — | 2 | 16 | no | — |
| 453 | C22×C4 | — | 2 | 8 | no | — |
| 454 | C22×C4 | — | 2 | 16 | no | — |
| 455 | C22×C4 | — | 2 | 8 | no | — |
| 456 | C22×C4 | — | 2 | 16 | no | — |
| 457 | C22×C4 | — | 2 | 8 | no | — |
| 458 | C22×C4 | — | 2 | 4 | no | — |
| 459 | C22×C4 | — | 2 | 4 | no | — |
| 460 | C22×C4 | — | 2 | 8 | no | — |
| 461 | C22×C4 | — | 2 | 8 | no | — |
| 462 | C22×C4 | — | 2 | 8 | no | — |
| 463 | C22×C4 | — | 2 | 16 | no | — |
| 464 | C22×C4 | — | 2 | 16 | no | — |
| 465 | C22×C4 | — | 2 | 16 | no | — |
| 466 | C22×C4 | — | 2 | 16 | no | — |
| 467 | C22×C4 | — | 2 | 8 | no | — |
| 468 | C22×C4 | — | 2 | 16 | no | — |
| 469 | C22×C4 | — | 2 | 32 | no | — |
| 470 | C22×C4 | — | 4 | 4 | no | — |
| 471 | C22×C4 | — | 4 | 8 | no | — |
| 472 | C22×C4 | — | 4 | 2 | no | — |
| 473 | C22×C4 | — | 4 | 16 | no | — |
| 474 | C22×C4 | — | 4 | 32 | no | — |
| 475 | C22×C4 | — | 4 | 8 | no | — |
| 476 | C22×C4 | — | 4 | 32 | no | — |
| 477 | C22×C4 | — | 8 | 32 | no | — |
| 478 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 479 | C22×C4 | C22×D4 | 1 | 8 | yes | — |
| 480 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 481 | C22×C4 | C22×D4 | 1 | 8 | yes | — |
| 482 | C22×C4 | C22×D4 | 1 | 4 | yes | — |
| 483 | C22×C4 | C2×#41 | 1 | 16 | yes | — |
| 484 | C22×C4 | C2×#41 | 1 | 8 | yes | — |
| 485 | C22×C4 | C25 | 1 | 16 | yes | — |
| 486 | C22×C4 | C25 | 1 | 4 | yes | — |
| 487 | C22×C4 | C25 | 1 | 4 | yes | — |
| 488 | C22×C4 | C25 | 1 | 8 | yes | — |
| 489 | C22×C4 | C25 | 1 | 4 | yes | — |
| 490 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 491 | C22×C4 | C25 | 1 | 4 | yes | — |
| 492 | C22×C4 | C25 | 1 | 4 | yes | — |
| 493 | C22×C4 | C25 | 1 | 2 | yes | — |
| 494 | C22×C4 | C25 | 1 | 4 | yes | — |
| 495 | C22×C4 | C25 | 1 | 2 | yes | — |
| 496 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 497 | C4⋊C4 | — | 2 | 32 | no | — |
| 498 | C4⋊C4 | — | 2 | 16 | no | — |
| 499 | C4⋊C4 | — | 2 | 8 | no | — |
| 500 | C4⋊C4 | — | 2 | 16 | no | — |
| 501 | C4⋊C4 | — | 2 | 8 | no | — |
| 502 | C4⋊C4 | — | 2 | 4 | no | — |
| 503 | C4⋊C4 | — | 2 | 4 | no | — |
| 504 | C4⋊C4 | — | 2 | 4 | no | — |
| 505 | C4⋊C4 | — | 2 | 8 | no | — |
| 506 | C4⋊C4 | — | 2 | 8 | no | — |
| 507 | C4⋊C4 | — | 2 | 32 | no | — |
| 508 | C4⋊C4 | — | 2 | 8 | no | — |
| 509 | C4⋊C4 | — | 2 | 8 | no | — |
| 510 | C4⋊C4 | — | 2 | 4 | no | — |
| 511 | C4⋊C4 | — | 2 | 16 | no | — |
| 512 | C4⋊C4 | — | 2 | 32 | no | — |
| 513 | C4⋊C4 | — | 2 | 16 | no | — |
| 514 | C4⋊C4 | — | 4 | 32 | no | — |
| 515 | C4⋊C4 | — | 4 | 8 | no | — |
| 516 | C4⋊C4 | C22×D4 | 1 | 16 | yes | — |
| 517 | C4⋊C4 | C22×D4 | 1 | 32 | yes | — |
| 518 | C22⋊C4 | — | 2 | 8 | no | — |
| 519 | C22⋊C4 | — | 2 | 16 | no | — |
| 520 | C22⋊C4 | — | 2 | 32 | no | — |
| 521 | C22⋊C4 | — | 2 | 32 | no | — |
| 522 | C22⋊C4 | — | 2 | 16 | no | — |
| 523 | C22⋊C4 | — | 2 | 32 | no | — |
| 524 | C22⋊C4 | — | 2 | 8 | no | — |
| 525 | C22⋊C4 | — | 2 | 16 | no | — |
| 526 | C22⋊C4 | — | 2 | 8 | no | — |
| 527 | C22⋊C4 | — | 2 | 32 | no | — |
| 528 | C22⋊C4 | — | 4 | 16 | no | — |
| 529 | C22⋊C4 | — | 4 | 32 | no | — |
| 530 | C42 | — | 2 | 8 | no | — |
| 531 | C42 | — | 2 | 8 | no | — |
| 532 | C42 | — | 2 | 16 | no | — |
| 533 | C42 | — | 2 | 16 | no | — |
| 534 | C42 | — | 2 | 8 | no | — |
| 535 | C42 | — | 2 | 16 | no | — |
| 536 | C42 | — | 4 | 16 | no | — |
| 537 | C42 | C22×D4 | 1 | 16 | yes | — |
| 538 | C42 | C22×D4 | 1 | 8 | yes | — |
| 539 | C42 | C22×D4 | 1 | 16 | yes | — |
| 540 | C42 | C22×D4 | 1 | 8 | yes | — |
| 541 | C23 | — | 2 | 2 | no | — |
| 542 | C23 | — | 2 | 2 | no | — |
| 543 | C23 | — | 2 | 16 | no | — |
| 544 | C23 | — | 2 | 4 | no | — |
| 545 | C23 | — | 2 | 4 | no | — |
| 546 | C23 | — | 2 | 8 | no | — |
| 547 | C23 | — | 2 | 4 | no | — |
| 548 | C23 | — | 2 | 8 | no | — |
| 549 | C23 | — | 2 | 4 | no | — |
| 550 | C23 | — | 2 | 8 | no | — |
| 551 | C23 | — | 2 | 8 | no | — |
| 552 | C23 | — | 4 | 32 | no | — |
| 553 | C23 | — | 4 | 8 | no | — |
| 554 | C23 | — | 4 | 8 | no | — |
| 555 | C23 | C23×D4 | 1 | 2 | yes | — |
| 556 | C23 | C22×#41 | 1 | 8 | yes | — |
| 557 | C23 | C22×#41 | 1 | 4 | yes | — |
| 558 | C23 | C2×2−1+4 | 1 | 8 | yes | — |
| 559 | C23 | C26 | 1 | 1 | yes | characteristic |
| 560 | Q8 | — | 2 | 32 | no | — |
| 561 | Q8 | — | 2 | 32 | no | — |
| 562 | Q8 | — | 2 | 16 | no | — |
| 563 | Q8 | — | 8 | 16 | no | — |
| 564 | D4 | — | 2 | 16 | no | — |
| 565 | D4 | — | 2 | 32 | no | — |
| 566 | D4 | — | 2 | 32 | no | — |
| 567 | D4 | — | 2 | 16 | no | — |
| 568 | D4 | — | 2 | 16 | no | — |
| 569 | D4 | — | 4 | 64 | no | — |
| 570 | C2×C4 | — | 2 | 64 | no | — |
| 571 | C2×C4 | — | 2 | 4 | no | — |
| 572 | C2×C4 | — | 2 | 8 | no | — |
| 573 | C2×C4 | — | 2 | 4 | no | — |
| 574 | C2×C4 | — | 2 | 2 | no | — |
| 575 | C2×C4 | — | 2 | 8 | no | — |
| 576 | C2×C4 | — | 2 | 4 | no | — |
| 577 | C2×C4 | — | 2 | 16 | no | — |
| 578 | C2×C4 | — | 2 | 32 | no | — |
| 579 | C2×C4 | — | 2 | 8 | no | — |
| 580 | C2×C4 | — | 2 | 4 | no | — |
| 581 | C2×C4 | — | 2 | 4 | no | — |
| 582 | C2×C4 | — | 2 | 4 | no | — |
| 583 | C2×C4 | — | 2 | 8 | no | — |
| 584 | C2×C4 | — | 2 | 16 | no | — |
| 585 | C2×C4 | — | 2 | 8 | no | — |
| 586 | C2×C4 | — | 2 | 8 | no | — |
| 587 | C2×C4 | — | 2 | 16 | no | — |
| 588 | C2×C4 | — | 2 | 16 | no | — |
| 589 | C2×C4 | — | 2 | 8 | no | — |
| 590 | C2×C4 | — | 2 | 16 | no | — |
| 591 | C2×C4 | — | 4 | 8 | no | — |
| 592 | C2×C4 | — | 4 | 4 | no | — |
| 593 | C2×C4 | — | 4 | 16 | no | — |
| 594 | C2×C4 | — | 4 | 8 | no | — |
| 595 | C2×C4 | — | 4 | 32 | no | — |
| 596 | C2×C4 | — | 4 | 16 | no | — |
| 597 | C2×C4 | — | 8 | 16 | no | — |
| 598 | C2×C4 | — | 8 | 8 | no | — |
| 599 | C2×C4 | — | 8 | 32 | no | — |
| 600 | C2×C4 | #525 | 1 | 16 | yes | — |
| 601 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 602 | C2×C4 | C23×D4 | 1 | 8 | yes | — |
| 603 | C2×C4 | C23×D4 | 1 | 8 | yes | — |
| 604 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 605 | C2×C4 | C23×D4 | 1 | 4 | yes | — |
| 606 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 607 | C2×C4 | C22×#41 | 1 | 8 | yes | — |
| 608 | C2×C4 | C22×#41 | 1 | 4 | yes | — |
| 609 | C2×C4 | C22×#41 | 1 | 4 | yes | — |
| 610 | C2×C4 | C2×2−1+4 | 1 | 4 | yes | — |
| 611 | C22 | — | 2 | 8 | no | — |
| 612 | C22 | — | 2 | 2 | no | — |
| 613 | C22 | — | 2 | 2 | no | — |
| 614 | C22 | — | 2 | 16 | no | — |
| 615 | C22 | — | 2 | 16 | no | — |
| 616 | C22 | — | 2 | 8 | no | — |
| 617 | C22 | — | 2 | 8 | no | — |
| 618 | C22 | — | 4 | 32 | no | — |
| 619 | C22 | — | 4 | 8 | no | — |
| 620 | C22 | — | 4 | 8 | no | — |
| 621 | C22 | — | 4 | 4 | no | — |
| 622 | C22 | — | 4 | 4 | no | — |
| 623 | C22 | — | 4 | 4 | no | — |
| 624 | C22 | — | 4 | 4 | no | — |
| 625 | C22 | C2×#525 | 1 | 4 | yes | — |
| 626 | C22 | C24×D4 | 1 | 1 | yes | characteristic |
| 627 | C22 | C23×#41 | 1 | 2 | yes | — |
| 628 | C22 | C22×2−1+4 | 1 | 2 | yes | — |
| 629 | C22 | H(7,𝔽2) | 1 | 2 | yes | — |
| 630 | C4 | — | 2 | 2 | no | — |
| 631 | C4 | — | 2 | 8 | no | — |
| 632 | C4 | — | 2 | 4 | no | — |
| 633 | C4 | — | 2 | 8 | no | — |
| 634 | C4 | — | 2 | 8 | no | — |
| 635 | C4 | — | 4 | 16 | no | — |
| 636 | C4 | — | 4 | 4 | no | — |
| 637 | C4 | — | 4 | 8 | no | — |
| 638 | C4 | — | 4 | 4 | no | — |
| 639 | C4 | — | 4 | 4 | no | — |
| 640 | C4 | C2×#525 | 1 | 8 | yes | — |
| 641 | C4 | #3486 | 1 | 4 | yes | — |
| 642 | C2 | — | 2 | 4 | no | — |
| 643 | C2 | — | 4 | 8 | no | — |
| 644 | C2 | — | 4 | 8 | no | — |
| 645 | C2 | C22×#525 | 1 | 1 | yes | characteristic |
| 646 | C2 | C2×#3486 | 1 | 1 | yes | characteristic |
| 647 | C2 | #62852 | 1 | 1 | yes | characteristic |
| 648 | C2 | #63000 | 1 | 4 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C23 | C26 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#554 | C2 | semidirect |
| 2. C2×C4×2−1+4 | C2 | semidirect |
| 3. #36544 | C2 | semidirect |
| 4. #36492 | C2 | semidirect |
| 5. #35738 | C2 | semidirect |
| 6. #35701 | C2 | semidirect |
| 7. #35672 | C2 | semidirect |
| 8. #35659 | C2 | semidirect |
| 9. #35357 | C2 | semidirect |
| 10. #35279 | C2 | semidirect |
| 11. #35138 | C2 | semidirect |
| 12. #34963 | C2 | semidirect |
| 13. #34935 | C2 | semidirect |
| 14. #34200 | C2 | semidirect |
| 15. #34187 | C2 | semidirect |
| 28. C2×#520 | C22 | semidirect |
| 30. C2×#519 | C22 | semidirect |
| 33. C2×C4×#41 | C22 | semidirect |
| 35. C22×C4×Q8 | C22 | semidirect |
| 39. #2857 | C22 | semidirect |
| 40. #2851 | C22 | semidirect |
| 41. #2634 | C22 | semidirect |
| 42. #2633 | C22 | semidirect |
| 43. #2628 | C22 | semidirect |
| 44. #2611 | C22 | semidirect |
| 46. #2584 | C22 | semidirect |
| 48. #2568 | C22 | semidirect |
| 49. #2567 | C22 | semidirect |
| 50. #2563 | C22 | semidirect |
| 51. #2562 | C22 | semidirect |
| 52. #2542 | C22 | semidirect |
| 63. #2477 | C22 | semidirect |
| 64. #2465 | C22 | semidirect |
| 65. #2463 | C22 | semidirect |
| 66. #2449 | C22 | semidirect |
| 67. #2423 | C22 | semidirect |
| 68. #2421 | C22 | semidirect |
| 70. #2409 | C22 | semidirect |
| 72. #2407 | C22 | semidirect |
| 78. #2361 | C22 | semidirect |
| 79. #2360 | C22 | semidirect |
| 80. #2356 | C22 | semidirect |
| 81. #2355 | C22 | semidirect |
| 82. #2352 | C22 | semidirect |
| 83. D4×C4⋊C4 | C22 | semidirect |
| 135. C2×C4×Q8 | D4 | semidirect |
| 451. C2×D4 | 2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#554 | 2 |
| C2×C4×2−1+4 | 2 |
| #36544 | 2 |
| #36492 | 2 |
| #35738 | 2 |
| #35701 | 2 |
| #35672 | 2 |
| #35659 | 2 |
| #35357 | 2 |
| #35279 | 2 |
| #35138 | 2 |
| #34963 | 2 |
| #34935 | 2 |
| #34200 | 2 |
| #34187 | 2 |