Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
5665 conjugacy classes of subgroups.
The subgroup lattice has 675 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #59933 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #58890 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #58010 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | #52957 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #52421 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #47814 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #45319 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #45244 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #42909 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #42838 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #42057 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | #39745 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #36694 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #35757 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | C22×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#559 | C22 | 1 | 3 | yes | — |
| 17 | C2×#550 | C22 | 1 | 3 | yes | — |
| 18 | C2×#548 | C22 | 1 | 6 | yes | — |
| 19 | C2×#537 | C22 | 1 | 3 | yes | — |
| 20 | #2867 | C22 | 1 | 1 | yes | characteristic |
| 21 | #2844 | C22 | 1 | 1 | yes | characteristic |
| 22 | #2832 | C22 | 1 | 3 | yes | — |
| 23 | #2832 | C22 | 1 | 3 | yes | — |
| 24 | #2829 | C22 | 1 | 12 | yes | — |
| 25 | #2828 | C22 | 1 | 6 | yes | — |
| 26 | #2828 | C22 | 1 | 6 | yes | — |
| 27 | #2824 | C22 | 1 | 6 | yes | — |
| 28 | #2819 | C22 | 1 | 3 | yes | — |
| 29 | #2816 | C22 | 1 | 6 | yes | — |
| 30 | #2813 | C22 | 1 | 12 | yes | — |
| 31 | #2799 | C22 | 1 | 6 | yes | — |
| 32 | #2784 | C22 | 1 | 6 | yes | — |
| 33 | #2780 | C22 | 1 | 12 | yes | — |
| 34 | #2748 | C22 | 1 | 6 | yes | — |
| 35 | #2712 | C22 | 1 | 12 | yes | — |
| 36 | #2710 | C22 | 1 | 12 | yes | — |
| 37 | #2710 | C22 | 1 | 12 | yes | — |
| 38 | #2708 | C22 | 1 | 12 | yes | — |
| 39 | #2687 | C22 | 1 | 12 | yes | — |
| 40 | #2683 | C22 | 1 | 6 | yes | — |
| 41 | #2682 | C22 | 1 | 12 | yes | — |
| 42 | #2676 | C22 | 1 | 12 | yes | — |
| 43 | #2675 | C22 | 1 | 6 | yes | — |
| 44 | #2675 | C22 | 1 | 6 | yes | — |
| 45 | #2673 | C22 | 1 | 12 | yes | — |
| 46 | #2673 | C22 | 1 | 12 | yes | — |
| 47 | #2673 | C22 | 1 | 12 | yes | — |
| 48 | #2673 | C22 | 1 | 12 | yes | — |
| 49 | #2671 | C22 | 1 | 12 | yes | — |
| 50 | #2671 | C22 | 1 | 12 | yes | — |
| 51 | #2661 | C22 | 1 | 12 | yes | — |
| 52 | #2657 | C22 | 1 | 6 | yes | — |
| 53 | #2656 | C22 | 1 | 6 | yes | — |
| 54 | #2649 | C22 | 1 | 12 | yes | — |
| 55 | #2644 | C22 | 1 | 2 | yes | — |
| 56 | #2635 | C22 | 1 | 6 | yes | — |
| 57 | #2615 | C22 | 1 | 6 | yes | — |
| 58 | #2615 | C22 | 1 | 1 | yes | characteristic |
| 59 | #2615 | C22 | 1 | 3 | yes | — |
| 60 | #2612 | C22 | 1 | 6 | yes | — |
| 61 | #2589 | C22 | 1 | 12 | yes | — |
| 62 | #2582 | C22 | 1 | 6 | yes | — |
| 63 | #2564 | C22 | 1 | 6 | yes | — |
| 64 | #2557 | C22 | 1 | 12 | yes | — |
| 65 | #2555 | C22 | 1 | 6 | yes | — |
| 66 | #2548 | C22 | 1 | 3 | yes | — |
| 67 | #2544 | C22 | 1 | 6 | yes | — |
| 68 | #2541 | C22 | 1 | 6 | yes | — |
| 69 | #2541 | C22 | 1 | 3 | yes | — |
| 70 | #2537 | C22 | 1 | 6 | yes | — |
| 71 | #2522 | C22 | 1 | 12 | yes | — |
| 72 | #2501 | C22 | 1 | 3 | yes | — |
| 73 | #2497 | C22 | 1 | 6 | yes | — |
| 74 | #2487 | C22 | 1 | 3 | yes | — |
| 75 | #2464 | C22 | 1 | 12 | yes | — |
| 76 | #2463 | C22 | 1 | 6 | yes | — |
| 77 | #2459 | C22 | 1 | 12 | yes | — |
| 78 | #2450 | C22 | 1 | 12 | yes | — |
| 79 | #2436 | C22 | 1 | 3 | yes | — |
| 80 | #2436 | C22 | 1 | 6 | yes | — |
| 81 | #2431 | C22 | 1 | 6 | yes | — |
| 82 | #2431 | C22 | 1 | 6 | yes | — |
| 83 | #2431 | C22 | 1 | 12 | yes | — |
| 84 | #2428 | C22 | 1 | 6 | yes | — |
| 85 | #2428 | C22 | 1 | 6 | yes | — |
| 86 | #2428 | C22 | 1 | 12 | yes | — |
| 87 | #2426 | C22 | 1 | 6 | yes | — |
| 88 | #2425 | C22 | 1 | 12 | yes | — |
| 89 | #2423 | C22 | 1 | 6 | yes | — |
| 90 | #2422 | C22 | 1 | 6 | yes | — |
| 91 | #2416 | C22 | 1 | 6 | yes | — |
| 92 | #2409 | C22 | 1 | 6 | yes | — |
| 93 | #2409 | C22 | 1 | 3 | yes | — |
| 94 | #2407 | C22 | 1 | 6 | yes | — |
| 95 | #2407 | C22 | 1 | 12 | yes | — |
| 96 | #2398 | C22 | 1 | 6 | yes | — |
| 97 | #2388 | C22 | 1 | 6 | yes | — |
| 98 | #2388 | C22 | 1 | 3 | yes | — |
| 99 | #2388 | C22 | 1 | 3 | yes | — |
| 100 | #2372 | C22 | 1 | 6 | yes | — |
| 101 | #2360 | C22 | 1 | 6 | yes | — |
| 102 | #2341 | C22 | 1 | 3 | yes | — |
| 103 | Q8×C22⋊C4 | C22 | 1 | 6 | yes | — |
| 104 | #2339 | C22 | 1 | 3 | yes | — |
| 105 | #2328 | C22 | 1 | 6 | yes | — |
| 106 | #2326 | C22 | 1 | 6 | yes | — |
| 107 | C4×#124 | C22 | 1 | 3 | yes | — |
| 108 | #2295 | C22 | 1 | 3 | yes | — |
| 109 | C2×2−1+4 | — | 4 | 12 | no | — |
| 110 | C22×#41 | C23 | 1 | 3 | yes | — |
| 111 | C22×#41 | C23 | 1 | 3 | yes | — |
| 112 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 113 | C22×#41 | C23 | 1 | 6 | yes | — |
| 114 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 115 | C23×Q8 | C23 | 1 | 3 | yes | — |
| 116 | C23×Q8 | C23 | 1 | 2 | yes | — |
| 117 | #559 | — | 4 | 12 | no | — |
| 118 | #550 | — | 4 | 12 | no | — |
| 119 | #548 | — | 4 | 24 | no | — |
| 120 | #537 | — | 4 | 12 | no | — |
| 121 | C2×#127 | C23 | 1 | 2 | yes | — |
| 122 | C2×#127 | C23 | 1 | 3 | yes | — |
| 123 | C2×#127 | C23 | 1 | 3 | yes | — |
| 124 | C2×#127 | C23 | 1 | 6 | yes | — |
| 125 | C2×#127 | C23 | 1 | 6 | yes | — |
| 126 | C2×#127 | C23 | 1 | 6 | yes | — |
| 127 | C2×#124 | C23 | 1 | 3 | yes | — |
| 128 | C2×#124 | C23 | 1 | 6 | yes | — |
| 129 | C2×#124 | C23 | 1 | 6 | yes | — |
| 130 | C2×#124 | C23 | 1 | 12 | yes | — |
| 131 | C2×#124 | C23 | 1 | 6 | yes | — |
| 132 | C2×#123 | C23 | 1 | 12 | yes | — |
| 133 | C2×#123 | C23 | 1 | 12 | yes | — |
| 134 | C2×#123 | C23 | 1 | 12 | yes | — |
| 135 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 136 | C2×C22⋊Q8 | C23 | 1 | 6 | yes | — |
| 137 | C2×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 138 | C2×#121 | C23 | 1 | 6 | yes | — |
| 139 | C2×#121 | C23 | 1 | 3 | yes | — |
| 140 | C2×#121 | C23 | 1 | 6 | yes | — |
| 141 | C2×#121 | C23 | 1 | 12 | yes | — |
| 142 | C2×#121 | C23 | 1 | 6 | yes | — |
| 143 | C2×#121 | C23 | 1 | 3 | yes | — |
| 144 | C2×#121 | C23 | 1 | 6 | yes | — |
| 145 | C2×#121 | C23 | 1 | 12 | yes | — |
| 146 | C2×#121 | C23 | 1 | 6 | yes | — |
| 147 | C2×#121 | C23 | 1 | 12 | yes | — |
| 148 | C2×#121 | C23 | 1 | 12 | yes | — |
| 149 | C2×#121 | C23 | 1 | 12 | yes | — |
| 150 | C2×#121 | C23 | 1 | 12 | yes | — |
| 151 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 152 | C2×C4×Q8 | C23 | 1 | 6 | yes | — |
| 153 | C2×C4×Q8 | C23 | 1 | 3 | yes | — |
| 154 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 155 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 156 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 157 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 158 | C2×C4×D4 | C23 | 1 | 3 | yes | — |
| 159 | C2×C4×D4 | C23 | 1 | 12 | yes | — |
| 160 | C22×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 161 | #400 | C23 | 1 | 6 | yes | — |
| 162 | #400 | C23 | 1 | 12 | yes | — |
| 163 | #400 | C23 | 1 | 6 | yes | — |
| 164 | #400 | C23 | 1 | 6 | yes | — |
| 165 | #399 | C23 | 1 | 6 | yes | — |
| 166 | #399 | C23 | 1 | 6 | yes | — |
| 167 | #399 | C23 | 1 | 6 | yes | — |
| 168 | #399 | C23 | 1 | 12 | yes | — |
| 169 | #398 | C23 | 1 | 12 | yes | — |
| 170 | #398 | C23 | 1 | 12 | yes | — |
| 171 | #398 | C23 | 1 | 12 | yes | — |
| 172 | #397 | C23 | 1 | 12 | yes | — |
| 173 | #397 | C23 | 1 | 6 | yes | — |
| 174 | #397 | C23 | 1 | 6 | yes | — |
| 175 | #397 | C23 | 1 | 12 | yes | — |
| 176 | #396 | C23 | 1 | 12 | yes | — |
| 177 | #396 | C23 | 1 | 12 | yes | — |
| 178 | #396 | C23 | 1 | 4 | yes | — |
| 179 | #396 | C23 | 1 | 12 | yes | — |
| 180 | #395 | C23 | 1 | 3 | yes | — |
| 181 | #395 | C23 | 1 | 3 | yes | — |
| 182 | #395 | C23 | 1 | 6 | yes | — |
| 183 | #394 | C23 | 1 | 12 | yes | — |
| 184 | #394 | C23 | 1 | 12 | yes | — |
| 185 | #394 | C23 | 1 | 12 | yes | — |
| 186 | #394 | C23 | 1 | 3 | yes | — |
| 187 | #394 | C23 | 1 | 6 | yes | — |
| 188 | #394 | C23 | 1 | 3 | yes | — |
| 189 | #394 | C23 | 1 | 12 | yes | — |
| 190 | #394 | C23 | 1 | 12 | yes | — |
| 191 | #394 | C23 | 1 | 6 | yes | — |
| 192 | #394 | C23 | 1 | 12 | yes | — |
| 193 | #394 | C23 | 1 | 6 | yes | — |
| 194 | #394 | C23 | 1 | 6 | yes | — |
| 195 | #394 | C23 | 1 | 12 | yes | — |
| 196 | #394 | C23 | 1 | 12 | yes | — |
| 197 | #394 | C23 | 1 | 12 | yes | — |
| 198 | #393 | C23 | 1 | 2 | yes | — |
| 199 | #393 | C23 | 1 | 3 | yes | — |
| 200 | #393 | C23 | 1 | 6 | yes | — |
| 201 | #393 | C23 | 1 | 6 | yes | — |
| 202 | #393 | C23 | 1 | 3 | yes | — |
| 203 | #393 | C23 | 1 | 6 | yes | — |
| 204 | #393 | C23 | 1 | 6 | yes | — |
| 205 | #393 | C23 | 1 | 6 | yes | — |
| 206 | #393 | C23 | 1 | 6 | yes | — |
| 207 | #392 | C23 | 1 | 6 | yes | — |
| 208 | #392 | C23 | 1 | 6 | yes | — |
| 209 | #392 | C23 | 1 | 6 | yes | — |
| 210 | #392 | C23 | 1 | 3 | yes | — |
| 211 | #392 | C23 | 1 | 3 | yes | — |
| 212 | #392 | C23 | 1 | 12 | yes | — |
| 213 | #392 | C23 | 1 | 12 | yes | — |
| 214 | #392 | C23 | 1 | 12 | yes | — |
| 215 | #392 | C23 | 1 | 6 | yes | — |
| 216 | #392 | C23 | 1 | 6 | yes | — |
| 217 | #392 | C23 | 1 | 12 | yes | — |
| 218 | #392 | C23 | 1 | 12 | yes | — |
| 219 | #392 | C23 | 1 | 12 | yes | — |
| 220 | #392 | C23 | 1 | 12 | yes | — |
| 221 | #392 | C23 | 1 | 12 | yes | — |
| 222 | #392 | C23 | 1 | 6 | yes | — |
| 223 | #391 | C23 | 1 | 3 | yes | — |
| 224 | #391 | C23 | 1 | 6 | yes | — |
| 225 | #391 | C23 | 1 | 6 | yes | — |
| 226 | #391 | C23 | 1 | 12 | yes | — |
| 227 | #391 | C23 | 1 | 12 | yes | — |
| 228 | #391 | C23 | 1 | 12 | yes | — |
| 229 | #390 | C23 | 1 | 3 | yes | — |
| 230 | #390 | C23 | 1 | 6 | yes | — |
| 231 | #390 | C23 | 1 | 12 | yes | — |
| 232 | #390 | C23 | 1 | 6 | yes | — |
| 233 | #390 | C23 | 1 | 6 | yes | — |
| 234 | #390 | C23 | 1 | 6 | yes | — |
| 235 | #390 | C23 | 1 | 12 | yes | — |
| 236 | #389 | C23 | 1 | 12 | yes | — |
| 237 | #389 | C23 | 1 | 6 | yes | — |
| 238 | #389 | C23 | 1 | 6 | yes | — |
| 239 | #389 | C23 | 1 | 12 | yes | — |
| 240 | #388 | C23 | 1 | 6 | yes | — |
| 241 | #388 | C23 | 1 | 6 | yes | — |
| 242 | #388 | C23 | 1 | 12 | yes | — |
| 243 | #388 | C23 | 1 | 12 | yes | — |
| 244 | #388 | C23 | 1 | 12 | yes | — |
| 245 | #388 | C23 | 1 | 12 | yes | — |
| 246 | #388 | C23 | 1 | 12 | yes | — |
| 247 | #387 | C23 | 1 | 12 | yes | — |
| 248 | #387 | C23 | 1 | 12 | yes | — |
| 249 | #387 | C23 | 1 | 12 | yes | — |
| 250 | #387 | C23 | 1 | 12 | yes | — |
| 251 | #386 | C23 | 1 | 12 | yes | — |
| 252 | #386 | C23 | 1 | 12 | yes | — |
| 253 | #386 | C23 | 1 | 12 | yes | — |
| 254 | #386 | C23 | 1 | 12 | yes | — |
| 255 | #386 | C23 | 1 | 12 | yes | — |
| 256 | #386 | C23 | 1 | 12 | yes | — |
| 257 | #386 | C23 | 1 | 6 | yes | — |
| 258 | #386 | C23 | 1 | 6 | yes | — |
| 259 | #386 | C23 | 1 | 12 | yes | — |
| 260 | #386 | C23 | 1 | 12 | yes | — |
| 261 | #386 | C23 | 1 | 12 | yes | — |
| 262 | #386 | C23 | 1 | 12 | yes | — |
| 263 | #385 | C23 | 1 | 12 | yes | — |
| 264 | #385 | C23 | 1 | 6 | yes | — |
| 265 | #385 | C23 | 1 | 12 | yes | — |
| 266 | #385 | C23 | 1 | 12 | yes | — |
| 267 | #385 | C23 | 1 | 12 | yes | — |
| 268 | #385 | C23 | 1 | 6 | yes | — |
| 269 | #385 | C23 | 1 | 12 | yes | — |
| 270 | #384 | C23 | 1 | 6 | yes | — |
| 271 | #382 | C23 | 1 | 3 | yes | — |
| 272 | #381 | C23 | 1 | 6 | yes | — |
| 273 | #380 | C23 | 1 | 12 | yes | — |
| 274 | #380 | C23 | 1 | 3 | yes | — |
| 275 | #380 | C23 | 1 | 12 | yes | — |
| 276 | #380 | C23 | 1 | 6 | yes | — |
| 277 | #380 | C23 | 1 | 3 | yes | — |
| 278 | #380 | C23 | 1 | 6 | yes | — |
| 279 | C4×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 280 | C4×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 281 | C4×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 282 | C4×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 283 | C4×C22⋊C4 | C23 | 1 | 12 | yes | — |
| 284 | C4×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 285 | C4×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 286 | C4×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 287 | C4×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 288 | #376 | C23 | 1 | 2 | yes | — |
| 289 | #376 | C23 | 1 | 6 | yes | — |
| 290 | C2×#95 | C23 | 1 | 6 | yes | — |
| 291 | C43 | C23 | 1 | 1 | yes | characteristic |
| 292 | 2−1+4 | — | 4 | 64 | no | — |
| 293 | C2×#41 | — | 2 | 12 | no | — |
| 294 | C2×#41 | — | 2 | 12 | no | — |
| 295 | C2×#41 | — | 4 | 6 | no | — |
| 296 | C2×#41 | — | 4 | 12 | no | — |
| 297 | C2×#41 | — | 4 | 6 | no | — |
| 298 | C2×#41 | — | 4 | 12 | no | — |
| 299 | C2×#41 | — | 4 | 24 | no | — |
| 300 | C2×#41 | — | 4 | 12 | no | — |
| 301 | C22×Q8 | — | 2 | 24 | no | — |
| 302 | C22×Q8 | — | 4 | 6 | no | — |
| 303 | C22×Q8 | — | 4 | 12 | no | — |
| 304 | C22×Q8 | C24 | 1 | 6 | yes | — |
| 305 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 306 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 307 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 308 | C22×Q8 | C24 | 1 | 1 | yes | characteristic |
| 309 | C22×D4 | C24 | 1 | 3 | yes | — |
| 310 | C22×D4 | C24 | 1 | 1 | yes | characteristic |
| 311 | C22×D4 | C24 | 1 | 3 | yes | — |
| 312 | C22×D4 | C24 | 1 | 6 | yes | — |
| 313 | C22×D4 | C24 | 1 | 6 | yes | — |
| 314 | C22×D4 | C24 | 1 | 6 | yes | — |
| 315 | C22×D4 | C24 | 1 | 6 | yes | — |
| 316 | C22×D4 | C24 | 1 | 6 | yes | — |
| 317 | C22×D4 | C24 | 1 | 12 | yes | — |
| 318 | C22×D4 | C24 | 1 | 6 | yes | — |
| 319 | C22×D4 | C24 | 1 | 12 | yes | — |
| 320 | C22×D4 | C24 | 1 | 3 | yes | — |
| 321 | C22×D4 | C24 | 1 | 6 | yes | — |
| 322 | C22×D4 | C24 | 1 | 6 | yes | — |
| 323 | C22×D4 | C24 | 1 | 6 | yes | — |
| 324 | C22×D4 | C24 | 1 | 3 | yes | — |
| 325 | C23×C4 | C24 | 1 | 3 | yes | — |
| 326 | C23×C4 | C24 | 1 | 3 | yes | — |
| 327 | C23×C4 | C24 | 1 | 6 | yes | — |
| 328 | C23×C4 | C24 | 1 | 6 | yes | — |
| 329 | C23×C4 | C24 | 1 | 6 | yes | — |
| 330 | C23×C4 | C24 | 1 | 6 | yes | — |
| 331 | C23×C4 | C24 | 1 | 12 | yes | — |
| 332 | #127 | — | 2 | 8 | no | — |
| 333 | #127 | — | 4 | 12 | no | — |
| 334 | #127 | — | 4 | 6 | no | — |
| 335 | #127 | — | 4 | 6 | no | — |
| 336 | #127 | — | 8 | 6 | no | — |
| 337 | #127 | — | 8 | 6 | no | — |
| 338 | #124 | — | 2 | 24 | no | — |
| 339 | #124 | — | 2 | 12 | no | — |
| 340 | #124 | — | 4 | 12 | no | — |
| 341 | #124 | — | 4 | 24 | no | — |
| 342 | #124 | — | 8 | 6 | no | — |
| 343 | #123 | — | 4 | 24 | no | — |
| 344 | #123 | — | 8 | 12 | no | — |
| 345 | #123 | — | 8 | 12 | no | — |
| 346 | C22⋊Q8 | — | 2 | 24 | no | — |
| 347 | C22⋊Q8 | — | 4 | 24 | no | — |
| 348 | C22⋊Q8 | — | 4 | 12 | no | — |
| 349 | #121 | — | 4 | 12 | no | — |
| 350 | #121 | — | 4 | 24 | no | — |
| 351 | #121 | — | 4 | 24 | no | — |
| 352 | #121 | — | 4 | 12 | no | — |
| 353 | #121 | — | 4 | 12 | no | — |
| 354 | #121 | — | 4 | 6 | no | — |
| 355 | #121 | — | 4 | 6 | no | — |
| 356 | #121 | — | 4 | 12 | no | — |
| 357 | #121 | — | 4 | 12 | no | — |
| 358 | #121 | — | 8 | 12 | no | — |
| 359 | #121 | — | 8 | 12 | no | — |
| 360 | #121 | — | 8 | 12 | no | — |
| 361 | #121 | — | 8 | 12 | no | — |
| 362 | C4×Q8 | — | 2 | 12 | no | — |
| 363 | C4×Q8 | — | 4 | 6 | no | — |
| 364 | C4×Q8 | — | 4 | 12 | no | — |
| 365 | C4×D4 | — | 4 | 12 | no | — |
| 366 | C4×D4 | — | 4 | 12 | no | — |
| 367 | C4×D4 | — | 4 | 12 | no | — |
| 368 | C4×D4 | — | 4 | 12 | no | — |
| 369 | C4×D4 | — | 4 | 6 | no | — |
| 370 | C4×D4 | — | 4 | 24 | no | — |
| 371 | C2×C4⋊C4 | — | 4 | 6 | no | — |
| 372 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 373 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 374 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 375 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 376 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 377 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 378 | C2×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 379 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 380 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 381 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 382 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 383 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 384 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 385 | C2×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 386 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 387 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 388 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 389 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 390 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 391 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 392 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 393 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 394 | C2×C22⋊C4 | C24 | 1 | 3 | yes | — |
| 395 | C2×C22⋊C4 | C24 | 1 | 3 | yes | — |
| 396 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 397 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 398 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 399 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 400 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 401 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 402 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 403 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 404 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 405 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 406 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 407 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 408 | C2×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 409 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 410 | C2×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 411 | C2×C42 | C24 | 1 | 6 | yes | — |
| 412 | C2×C42 | C24 | 1 | 6 | yes | — |
| 413 | C2×C42 | C24 | 1 | 3 | yes | — |
| 414 | C2×C42 | C24 | 1 | 12 | yes | — |
| 415 | C2×C42 | C24 | 1 | 6 | yes | — |
| 416 | C2×C42 | C24 | 1 | 3 | yes | — |
| 417 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 418 | #95 | C24 | 1 | 3 | yes | — |
| 419 | #95 | C24 | 1 | 6 | yes | — |
| 420 | #95 | C24 | 1 | 12 | yes | — |
| 421 | #95 | C24 | 1 | 12 | yes | — |
| 422 | #95 | C24 | 1 | 2 | yes | — |
| 423 | #95 | C24 | 1 | 6 | yes | — |
| 424 | #95 | C24 | 1 | 12 | yes | — |
| 425 | #95 | C24 | 1 | 3 | yes | — |
| 426 | #95 | C24 | 1 | 3 | yes | — |
| 427 | #95 | C24 | 1 | 6 | yes | — |
| 428 | #95 | C24 | 1 | 3 | yes | — |
| 429 | #95 | C24 | 1 | 12 | yes | — |
| 430 | #95 | C24 | 1 | 6 | yes | — |
| 431 | #95 | C24 | 1 | 6 | yes | — |
| 432 | #95 | C24 | 1 | 6 | yes | — |
| 433 | #95 | C24 | 1 | 6 | yes | — |
| 434 | #95 | C24 | 1 | 12 | yes | — |
| 435 | #95 | C24 | 1 | 12 | yes | — |
| 436 | #95 | C24 | 1 | 6 | yes | — |
| 437 | #95 | C24 | 1 | 12 | yes | — |
| 438 | C24 | C25 | 1 | 6 | yes | — |
| 439 | C24 | C25 | 1 | 3 | yes | — |
| 440 | C24 | C25 | 1 | 3 | yes | — |
| 441 | C24 | C25 | 1 | 2 | yes | — |
| 442 | #41 | — | 4 | 48 | no | — |
| 443 | #41 | — | 4 | 96 | no | — |
| 444 | #41 | — | 4 | 16 | no | — |
| 445 | #41 | — | 8 | 8 | no | — |
| 446 | #41 | — | 8 | 24 | no | — |
| 447 | C2×Q8 | — | 2 | 12 | no | — |
| 448 | C2×Q8 | — | 2 | 24 | no | — |
| 449 | C2×Q8 | — | 2 | 6 | no | — |
| 450 | C2×Q8 | — | 4 | 6 | no | — |
| 451 | C2×Q8 | — | 4 | 3 | no | — |
| 452 | C2×Q8 | — | 4 | 3 | no | — |
| 453 | C2×Q8 | — | 4 | 3 | no | — |
| 454 | C2×Q8 | — | 4 | 3 | no | — |
| 455 | C2×Q8 | — | 4 | 48 | no | — |
| 456 | C2×Q8 | — | 4 | 32 | no | — |
| 457 | C2×Q8 | H(5,𝔽2) | 1 | 12 | yes | — |
| 458 | C2×D4 | — | 2 | 12 | no | — |
| 459 | C2×D4 | — | 2 | 6 | no | — |
| 460 | C2×D4 | — | 2 | 12 | no | — |
| 461 | C2×D4 | — | 2 | 6 | no | — |
| 462 | C2×D4 | — | 2 | 12 | no | — |
| 463 | C2×D4 | — | 2 | 6 | no | — |
| 464 | C2×D4 | — | 2 | 12 | no | — |
| 465 | C2×D4 | — | 2 | 12 | no | — |
| 466 | C2×D4 | — | 4 | 12 | no | — |
| 467 | C2×D4 | — | 4 | 3 | no | — |
| 468 | C2×D4 | — | 4 | 6 | no | — |
| 469 | C2×D4 | — | 4 | 6 | no | — |
| 470 | C2×D4 | — | 4 | 12 | no | — |
| 471 | C2×D4 | — | 4 | 6 | no | — |
| 472 | C2×D4 | — | 4 | 6 | no | — |
| 473 | C2×D4 | — | 4 | 3 | no | — |
| 474 | C2×D4 | — | 4 | 6 | no | — |
| 475 | C2×D4 | — | 4 | 3 | no | — |
| 476 | C2×D4 | — | 4 | 12 | no | — |
| 477 | C2×D4 | — | 4 | 6 | no | — |
| 478 | C2×D4 | — | 4 | 6 | no | — |
| 479 | C2×D4 | — | 4 | 12 | no | — |
| 480 | C2×D4 | — | 4 | 12 | no | — |
| 481 | C2×D4 | — | 4 | 6 | no | — |
| 482 | C2×D4 | — | 4 | 3 | no | — |
| 483 | C2×D4 | — | 4 | 6 | no | — |
| 484 | C2×D4 | — | 4 | 12 | no | — |
| 485 | C2×D4 | — | 4 | 6 | no | — |
| 486 | C2×D4 | — | 4 | 6 | no | — |
| 487 | C2×D4 | — | 4 | 6 | no | — |
| 488 | C2×D4 | — | 4 | 12 | no | — |
| 489 | C2×D4 | — | 4 | 12 | no | — |
| 490 | C2×D4 | — | 4 | 12 | no | — |
| 491 | C2×D4 | — | 4 | 12 | no | — |
| 492 | C2×D4 | — | 4 | 12 | no | — |
| 493 | C2×D4 | — | 4 | 12 | no | — |
| 494 | C2×D4 | — | 4 | 6 | no | — |
| 495 | C22×C4 | — | 2 | 6 | no | — |
| 496 | C22×C4 | — | 2 | 12 | no | — |
| 497 | C22×C4 | — | 2 | 24 | no | — |
| 498 | C22×C4 | — | 2 | 12 | no | — |
| 499 | C22×C4 | — | 2 | 12 | no | — |
| 500 | C22×C4 | — | 2 | 6 | no | — |
| 501 | C22×C4 | — | 2 | 12 | no | — |
| 502 | C22×C4 | — | 4 | 6 | no | — |
| 503 | C22×C4 | — | 4 | 12 | no | — |
| 504 | C22×C4 | — | 4 | 12 | no | — |
| 505 | C22×C4 | — | 4 | 6 | no | — |
| 506 | C22×C4 | — | 4 | 12 | no | — |
| 507 | C22×C4 | — | 4 | 12 | no | — |
| 508 | C22×C4 | — | 4 | 12 | no | — |
| 509 | C22×C4 | — | 4 | 12 | no | — |
| 510 | C22×C4 | C25 | 1 | 3 | yes | — |
| 511 | C22×C4 | C25 | 1 | 6 | yes | — |
| 512 | C22×C4 | C25 | 1 | 3 | yes | — |
| 513 | C22×C4 | C25 | 1 | 6 | yes | — |
| 514 | C22×C4 | C25 | 1 | 12 | yes | — |
| 515 | C22×C4 | C25 | 1 | 6 | yes | — |
| 516 | C22×C4 | C25 | 1 | 3 | yes | — |
| 517 | C22×C4 | C25 | 1 | 6 | yes | — |
| 518 | C22×C4 | C25 | 1 | 3 | yes | — |
| 519 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 520 | C4⋊C4 | — | 2 | 12 | no | — |
| 521 | C4⋊C4 | — | 2 | 6 | no | — |
| 522 | C4⋊C4 | — | 2 | 24 | no | — |
| 523 | C4⋊C4 | — | 2 | 12 | no | — |
| 524 | C4⋊C4 | — | 4 | 6 | no | — |
| 525 | C4⋊C4 | — | 4 | 3 | no | — |
| 526 | C4⋊C4 | — | 4 | 3 | no | — |
| 527 | C4⋊C4 | — | 4 | 6 | no | — |
| 528 | C4⋊C4 | — | 4 | 12 | no | — |
| 529 | C4⋊C4 | — | 4 | 6 | no | — |
| 530 | C4⋊C4 | — | 4 | 12 | no | — |
| 531 | C4⋊C4 | — | 4 | 12 | no | — |
| 532 | C4⋊C4 | — | 4 | 12 | no | — |
| 533 | C4⋊C4 | — | 4 | 12 | no | — |
| 534 | C22⋊C4 | — | 2 | 24 | no | — |
| 535 | C22⋊C4 | — | 2 | 24 | no | — |
| 536 | C22⋊C4 | — | 2 | 24 | no | — |
| 537 | C22⋊C4 | — | 2 | 12 | no | — |
| 538 | C22⋊C4 | — | 2 | 12 | no | — |
| 539 | C22⋊C4 | — | 4 | 6 | no | — |
| 540 | C22⋊C4 | — | 4 | 6 | no | — |
| 541 | C22⋊C4 | — | 4 | 6 | no | — |
| 542 | C22⋊C4 | — | 4 | 3 | no | — |
| 543 | C22⋊C4 | — | 4 | 3 | no | — |
| 544 | C22⋊C4 | — | 4 | 12 | no | — |
| 545 | C22⋊C4 | — | 4 | 6 | no | — |
| 546 | C22⋊C4 | — | 4 | 12 | no | — |
| 547 | C22⋊C4 | — | 4 | 12 | no | — |
| 548 | C22⋊C4 | — | 4 | 6 | no | — |
| 549 | C22⋊C4 | — | 4 | 6 | no | — |
| 550 | C22⋊C4 | — | 4 | 12 | no | — |
| 551 | C22⋊C4 | — | 4 | 6 | no | — |
| 552 | C22⋊C4 | — | 4 | 6 | no | — |
| 553 | C22⋊C4 | — | 4 | 12 | no | — |
| 554 | C22⋊C4 | — | 4 | 12 | no | — |
| 555 | C22⋊C4 | — | 4 | 6 | no | — |
| 556 | C22⋊C4 | — | 4 | 6 | no | — |
| 557 | C22⋊C4 | — | 4 | 12 | no | — |
| 558 | C22⋊C4 | — | 4 | 12 | no | — |
| 559 | C42 | — | 2 | 12 | no | — |
| 560 | C42 | — | 2 | 12 | no | — |
| 561 | C42 | — | 2 | 6 | no | — |
| 562 | C42 | — | 4 | 12 | no | — |
| 563 | C42 | — | 4 | 6 | no | — |
| 564 | C42 | — | 4 | 3 | no | — |
| 565 | C42 | 2−1+4 | 1 | 4 | yes | complemented |
| 566 | C23 | — | 2 | 12 | no | — |
| 567 | C23 | — | 2 | 6 | no | — |
| 568 | C23 | — | 2 | 6 | no | — |
| 569 | C23 | — | 2 | 6 | no | — |
| 570 | C23 | — | 2 | 3 | no | — |
| 571 | C23 | — | 2 | 3 | no | — |
| 572 | C23 | — | 2 | 6 | no | — |
| 573 | C23 | — | 2 | 3 | no | — |
| 574 | C23 | — | 2 | 3 | no | — |
| 575 | C23 | — | 2 | 6 | no | — |
| 576 | C23 | — | 2 | 2 | no | — |
| 577 | C23 | — | 2 | 6 | no | — |
| 578 | C23 | — | 2 | 6 | no | — |
| 579 | C23 | — | 2 | 6 | no | — |
| 580 | C23 | — | 2 | 6 | no | — |
| 581 | C23 | — | 2 | 3 | no | — |
| 582 | C23 | — | 2 | 3 | no | — |
| 583 | C23 | — | 2 | 12 | no | — |
| 584 | C23 | C26 | 1 | 1 | yes | characteristic |
| 585 | Q8 | — | 2 | 24 | no | — |
| 586 | Q8 | — | 4 | 24 | no | — |
| 587 | Q8 | — | 4 | 4 | no | — |
| 588 | Q8 | — | 8 | 6 | no | — |
| 589 | Q8 | — | 8 | 2 | no | — |
| 590 | D4 | — | 4 | 24 | no | — |
| 591 | D4 | — | 4 | 12 | no | — |
| 592 | D4 | — | 4 | 4 | no | — |
| 593 | D4 | — | 4 | 12 | no | — |
| 594 | D4 | — | 8 | 6 | no | — |
| 595 | D4 | — | 8 | 12 | no | — |
| 596 | D4 | — | 8 | 12 | no | — |
| 597 | D4 | — | 8 | 12 | no | — |
| 598 | D4 | — | 8 | 12 | no | — |
| 599 | D4 | — | 8 | 24 | no | — |
| 600 | D4 | — | 8 | 6 | no | — |
| 601 | D4 | — | 16 | 6 | no | — |
| 602 | D4 | — | 16 | 6 | no | — |
| 603 | D4 | — | 16 | 12 | no | — |
| 604 | D4 | — | 16 | 6 | no | — |
| 605 | D4 | — | 16 | 6 | no | — |
| 606 | C2×C4 | — | 2 | 3 | no | — |
| 607 | C2×C4 | — | 2 | 12 | no | — |
| 608 | C2×C4 | — | 2 | 3 | no | — |
| 609 | C2×C4 | — | 2 | 6 | no | — |
| 610 | C2×C4 | — | 2 | 6 | no | — |
| 611 | C2×C4 | — | 2 | 6 | no | — |
| 612 | C2×C4 | — | 2 | 3 | no | — |
| 613 | C2×C4 | — | 2 | 12 | no | — |
| 614 | C2×C4 | — | 2 | 6 | no | — |
| 615 | C2×C4 | — | 2 | 3 | no | — |
| 616 | C2×C4 | — | 2 | 3 | no | — |
| 617 | C2×C4 | — | 2 | 6 | no | — |
| 618 | C2×C4 | — | 2 | 6 | no | — |
| 619 | C2×C4 | — | 2 | 12 | no | — |
| 620 | C2×C4 | — | 2 | 6 | no | — |
| 621 | C2×C4 | — | 2 | 6 | no | — |
| 622 | C2×C4 | — | 2 | 6 | no | — |
| 623 | C2×C4 | — | 2 | 6 | no | — |
| 624 | C2×C4 | — | 2 | 12 | no | — |
| 625 | C2×C4 | — | 2 | 12 | no | — |
| 626 | C2×C4 | — | 4 | 24 | no | — |
| 627 | C2×C4 | — | 4 | 24 | no | — |
| 628 | C2×C4 | — | 4 | 12 | no | — |
| 629 | C2×C4 | — | 4 | 12 | no | — |
| 630 | C2×C4 | — | 8 | 12 | no | — |
| 631 | C2×C4 | — | 16 | 12 | no | — |
| 632 | C2×C4 | — | 16 | 6 | no | — |
| 633 | C2×C4 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 634 | C2×C4 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 635 | C2×C4 | C2×2−1+4 | 1 | 6 | yes | — |
| 636 | C22 | — | 4 | 3 | no | — |
| 637 | C22 | — | 4 | 12 | no | — |
| 638 | C22 | — | 4 | 6 | no | — |
| 639 | C22 | — | 4 | 6 | no | — |
| 640 | C22 | — | 4 | 6 | no | — |
| 641 | C22 | — | 4 | 3 | no | — |
| 642 | C22 | — | 4 | 6 | no | — |
| 643 | C22 | — | 4 | 12 | no | — |
| 644 | C22 | — | 4 | 6 | no | — |
| 645 | C22 | — | 4 | 3 | no | — |
| 646 | C22 | — | 4 | 3 | no | — |
| 647 | C22 | — | 4 | 6 | no | — |
| 648 | C22 | — | 4 | 6 | no | — |
| 649 | C22 | — | 4 | 6 | no | — |
| 650 | C22 | — | 4 | 3 | no | — |
| 651 | C22 | — | 4 | 2 | no | — |
| 652 | C22 | — | 4 | 3 | no | — |
| 653 | C22 | — | 4 | 6 | no | — |
| 654 | C22 | C22×H(5,𝔽2) | 1 | 3 | yes | — |
| 655 | C22 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 656 | C22 | H(7,𝔽2) | 1 | 3 | yes | — |
| 657 | C4 | — | 2 | 6 | no | — |
| 658 | C4 | — | 2 | 12 | no | — |
| 659 | C4 | — | 4 | 6 | no | — |
| 660 | C4 | — | 4 | 6 | no | — |
| 661 | C4 | — | 4 | 12 | no | — |
| 662 | C4 | — | 4 | 3 | no | — |
| 663 | C4 | — | 4 | 6 | no | — |
| 664 | C4 | — | 4 | 3 | no | — |
| 665 | C4 | — | 4 | 3 | no | — |
| 666 | C4 | #3532 | 1 | 4 | yes | — |
| 667 | C2 | — | 8 | 3 | no | — |
| 668 | C2 | — | 8 | 6 | no | — |
| 669 | C2 | — | 8 | 3 | no | — |
| 670 | C2 | — | 8 | 2 | no | — |
| 671 | C2 | C2×#3532 | 1 | 1 | yes | characteristic |
| 672 | C2 | #62917 | 1 | 3 | yes | — |
| 673 | C2 | #63066 | 1 | 3 | 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. #59933 | C2 | semidirect |
| 2. #58890 | C2 | semidirect |
| 3. #58010 | C2 | semidirect |
| 4. #52957 | C2 | semidirect |
| 5. #52421 | C2 | semidirect |
| 6. #47814 | C2 | semidirect |
| 7. #45319 | C2 | semidirect |
| 8. #45244 | C2 | semidirect |
| 9. #42909 | C2 | semidirect |
| 10. #42838 | C2 | semidirect |
| 11. #42057 | C2 | semidirect |
| 12. #39745 | C2 | semidirect |
| 13. #36694 | C2 | semidirect |
| 14. #35757 | C2 | semidirect |
| 565. C42 | 2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #59933 | 2 |
| #58890 | 2 |
| #58010 | 2 |
| #52957 | 2 |
| #52421 | 2 |
| #47814 | 2 |
| #45319 | 2 |
| #45244 | 2 |
| #42909 | 2 |
| #42838 | 2 |
| #42057 | 2 |
| #39745 | 2 |
| #36694 | 2 |
| #35757 | 2 |