Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
6496 conjugacy classes of subgroups.
The subgroup lattice has 652 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#3531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87139 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #87126 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #87123 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | #87111 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | #86267 | C2 | 1 | 5 | yes | maximal, complemented |
| 7 | #86263 | C2 | 1 | 5 | yes | maximal, complemented |
| 8 | #86177 | C2 | 1 | 5 | yes | maximal, complemented |
| 9 | #86163 | C2 | 1 | 5 | yes | maximal, complemented |
| 10 | #86141 | C2 | 1 | 5 | yes | maximal, complemented |
| 11 | #86127 | C2 | 1 | 5 | yes | maximal, complemented |
| 12 | #63069 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C3×#564 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C3×#563 | C22 | 1 | 5 | yes | complemented |
| 15 | C3×#563 | C22 | 1 | 5 | yes | complemented |
| 16 | C3×#562 | C22 | 1 | 5 | yes | complemented |
| 17 | C3×#533 | C22 | 1 | 5 | yes | complemented |
| 18 | C3×#529 | C22 | 1 | 5 | yes | complemented |
| 19 | C3×#529 | C22 | 1 | 5 | yes | complemented |
| 20 | #5733 | C22 | 1 | 10 | yes | complemented |
| 21 | #5733 | C22 | 1 | 10 | yes | complemented |
| 22 | #5732 | C22 | 1 | 10 | yes | complemented |
| 23 | #5727 | C22 | 1 | 10 | yes | complemented |
| 24 | #5710 | C22 | 1 | 20 | yes | complemented |
| 25 | #5705 | C22 | 1 | 20 | yes | complemented |
| 26 | #5704 | C22 | 1 | 20 | yes | complemented |
| 27 | #5702 | C22 | 1 | 20 | yes | complemented |
| 28 | #5700 | C22 | 1 | 10 | yes | complemented |
| 29 | #5699 | C22 | 1 | 10 | yes | complemented |
| 30 | #5699 | C22 | 1 | 10 | yes | complemented |
| 31 | #5699 | C22 | 1 | 10 | yes | complemented |
| 32 | #5691 | C22 | 1 | 10 | yes | complemented |
| 33 | #5691 | C22 | 1 | 10 | yes | complemented |
| 34 | #5691 | C22 | 1 | 10 | yes | complemented |
| 35 | #5688 | C22 | 1 | 10 | yes | complemented |
| 36 | #5684 | C22 | 1 | 10 | yes | complemented |
| 37 | #5683 | C22 | 1 | 10 | yes | complemented |
| 38 | #5680 | C22 | 1 | 10 | yes | complemented |
| 39 | D3×#124 | C22 | 1 | 10 | yes | complemented |
| 40 | #5662 | C22 | 1 | 20 | yes | complemented |
| 41 | #5658 | C22 | 1 | 20 | yes | complemented |
| 42 | #5657 | C22 | 1 | 20 | yes | complemented |
| 43 | #5654 | C22 | 1 | 20 | yes | complemented |
| 44 | #5644 | C22 | 1 | 10 | yes | complemented |
| 45 | #5643 | C22 | 1 | 20 | yes | complemented |
| 46 | #5641 | C22 | 1 | 10 | yes | complemented |
| 47 | #5637 | C22 | 1 | 20 | yes | complemented |
| 48 | #5637 | C22 | 1 | 20 | yes | complemented |
| 49 | #5634 | C22 | 1 | 10 | yes | complemented |
| 50 | #5633 | C22 | 1 | 10 | yes | complemented |
| 51 | #5628 | C22 | 1 | 20 | yes | complemented |
| 52 | #5617 | C22 | 1 | 10 | yes | complemented |
| 53 | #5616 | C22 | 1 | 10 | yes | complemented |
| 54 | #5612 | C22 | 1 | 10 | yes | complemented |
| 55 | #5605 | C22 | 1 | 10 | yes | complemented |
| 56 | #5585 | C22 | 1 | 5 | yes | complemented |
| 57 | #5585 | C22 | 1 | 10 | yes | complemented |
| 58 | #5584 | C22 | 1 | 5 | yes | complemented |
| 59 | #5584 | C22 | 1 | 10 | yes | complemented |
| 60 | Q8×D12 | C22 | 1 | 5 | yes | complemented |
| 61 | Q8×Dic6 | C22 | 1 | 5 | yes | complemented |
| 62 | #5563 | C22 | 1 | 5 | yes | complemented |
| 63 | #5552 | C22 | 1 | 10 | yes | complemented |
| 64 | #5550 | C22 | 1 | 10 | yes | complemented |
| 65 | D4×D12 | C22 | 1 | 5 | yes | complemented |
| 66 | #5542 | C22 | 1 | 5 | yes | complemented |
| 67 | D4×Dic6 | C22 | 1 | 5 | yes | complemented |
| 68 | #5534 | C22 | 1 | 10 | yes | complemented |
| 69 | #5534 | C22 | 1 | 10 | yes | complemented |
| 70 | #5526 | C22 | 1 | 5 | yes | complemented |
| 71 | #5525 | C22 | 1 | 5 | yes | — |
| 72 | #5521 | C22 | 1 | 5 | yes | complemented |
| 73 | #5516 | C22 | 1 | 5 | yes | complemented |
| 74 | #5477 | C22 | 1 | 5 | yes | — |
| 75 | C2×#875 | C22 | 1 | 5 | yes | complemented |
| 76 | C4×#235 | C22 | 1 | 5 | yes | complemented |
| 77 | #5470 | C22 | 1 | 5 | yes | complemented |
| 78 | #3568 | — | 3 | 10 | no | — |
| 79 | #3561 | — | 3 | 10 | no | — |
| 80 | #3561 | — | 3 | 5 | no | — |
| 81 | #3558 | — | 3 | 5 | no | — |
| 82 | #3550 | — | 3 | 5 | no | — |
| 83 | #3545 | — | 3 | 10 | no | — |
| 84 | #3531 | — | 3 | 2 | no | — |
| 85 | #3531 | D3 | 1 | 1 | yes | characteristic, complemented |
| 86 | #3518 | — | 3 | 5 | no | — |
| 87 | #3514 | — | 3 | 5 | no | — |
| 88 | #3510 | — | 3 | 5 | no | — |
| 89 | C2×D3×Q8 | C23 | 1 | 10 | yes | — |
| 90 | C2×D3×D4 | C23 | 1 | 10 | yes | — |
| 91 | C2×#235 | C23 | 1 | 5 | yes | — |
| 92 | C2×#235 | C23 | 1 | 10 | yes | — |
| 93 | C22×D12 | C23 | 1 | 5 | yes | — |
| 94 | C22×Dic6 | C23 | 1 | 5 | yes | — |
| 95 | C3×C4⋊Q8 | C23 | 1 | 5 | yes | — |
| 96 | C3×C4⋊Q8 | C23 | 1 | 5 | yes | — |
| 97 | C3×#126 | C23 | 1 | 10 | yes | — |
| 98 | C3×#126 | C23 | 1 | 10 | yes | — |
| 99 | C3×#125 | C23 | 1 | 5 | yes | — |
| 100 | C3×#125 | C23 | 1 | 5 | yes | — |
| 101 | C3×#125 | C23 | 1 | 5 | yes | — |
| 102 | C3×#125 | C23 | 1 | 5 | yes | — |
| 103 | C3×#124 | C23 | 1 | 5 | yes | — |
| 104 | C3×#124 | C23 | 1 | 5 | yes | — |
| 105 | C3×#123 | C23 | 1 | 10 | yes | — |
| 106 | C3×#123 | C23 | 1 | 10 | yes | — |
| 107 | C3×C22⋊Q8 | C23 | 1 | 5 | yes | — |
| 108 | C3×C22⋊Q8 | C23 | 1 | 10 | yes | — |
| 109 | C3×C22⋊Q8 | C23 | 1 | 10 | yes | — |
| 110 | C3×C22⋊Q8 | C23 | 1 | 5 | yes | — |
| 111 | C3×#121 | C23 | 1 | 5 | yes | — |
| 112 | C3×#121 | C23 | 1 | 5 | yes | — |
| 113 | C3×C4×Q8 | C23 | 1 | 5 | yes | — |
| 114 | C3×C4×Q8 | C23 | 1 | 5 | yes | — |
| 115 | C3×C4×D4 | C23 | 1 | 5 | yes | — |
| 116 | C3×C4×D4 | C23 | 1 | 5 | yes | — |
| 117 | C3×#117 | C23 | 1 | 5 | yes | — |
| 118 | C3×#117 | C23 | 1 | 5 | yes | — |
| 119 | C2×C3×C42 | C23 | 1 | 5 | yes | — |
| 120 | #947 | C23 | 1 | 10 | yes | — |
| 121 | #947 | C23 | 1 | 20 | yes | — |
| 122 | #946 | C23 | 1 | 20 | yes | — |
| 123 | #946 | C23 | 1 | 10 | yes | — |
| 124 | Q8×Dic3 | C23 | 1 | 10 | yes | — |
| 125 | #939 | C23 | 1 | 20 | yes | — |
| 126 | #938 | C23 | 1 | 10 | yes | — |
| 127 | #937 | C23 | 1 | 20 | yes | — |
| 128 | #936 | C23 | 1 | 10 | yes | — |
| 129 | D4×Dic3 | C23 | 1 | 10 | yes | — |
| 130 | #930 | C23 | 1 | 10 | yes | — |
| 131 | #930 | C23 | 1 | 10 | yes | — |
| 132 | C4×#67 | C23 | 1 | 10 | yes | — |
| 133 | C4×#67 | C23 | 1 | 10 | yes | — |
| 134 | C2×(C2×D3)⋊C4 | C23 | 1 | 10 | yes | — |
| 135 | C2×(C2×D3)⋊C4 | C23 | 1 | 10 | yes | — |
| 136 | #926 | C23 | 1 | 10 | yes | — |
| 137 | #926 | C23 | 1 | 5 | yes | — |
| 138 | #924 | C23 | 1 | 10 | yes | — |
| 139 | #924 | C23 | 1 | 10 | yes | — |
| 140 | #898 | C23 | 1 | 20 | yes | — |
| 141 | #898 | C23 | 1 | 20 | yes | — |
| 142 | #898 | C23 | 1 | 20 | yes | — |
| 143 | #898 | C23 | 1 | 20 | yes | — |
| 144 | #898 | C23 | 1 | 20 | yes | — |
| 145 | #897 | C23 | 1 | 10 | yes | — |
| 146 | #897 | C23 | 1 | 10 | yes | — |
| 147 | #897 | C23 | 1 | 20 | yes | — |
| 148 | #897 | C23 | 1 | 10 | yes | — |
| 149 | #896 | C23 | 1 | 20 | yes | — |
| 150 | #896 | C23 | 1 | 20 | yes | — |
| 151 | #896 | C23 | 1 | 20 | yes | — |
| 152 | #895 | C23 | 1 | 10 | yes | — |
| 153 | #895 | C23 | 1 | 10 | yes | — |
| 154 | #895 | C23 | 1 | 10 | yes | — |
| 155 | #894 | C23 | 1 | 20 | yes | — |
| 156 | #894 | C23 | 1 | 20 | yes | — |
| 157 | #894 | C23 | 1 | 20 | yes | — |
| 158 | #894 | C23 | 1 | 20 | yes | — |
| 159 | #893 | C23 | 1 | 10 | yes | — |
| 160 | #893 | C23 | 1 | 10 | yes | — |
| 161 | #893 | C23 | 1 | 20 | yes | — |
| 162 | #893 | C23 | 1 | 10 | yes | — |
| 163 | #892 | C23 | 1 | 10 | yes | — |
| 164 | #892 | C23 | 1 | 20 | yes | — |
| 165 | #892 | C23 | 1 | 10 | yes | — |
| 166 | #888 | C23 | 1 | 10 | yes | — |
| 167 | #888 | C23 | 1 | 20 | yes | — |
| 168 | #888 | C23 | 1 | 10 | yes | — |
| 169 | #887 | C23 | 1 | 10 | yes | — |
| 170 | #887 | C23 | 1 | 10 | yes | — |
| 171 | #887 | C23 | 1 | 10 | yes | — |
| 172 | #886 | C23 | 1 | 20 | yes | — |
| 173 | #885 | C23 | 1 | 20 | yes | — |
| 174 | #885 | C23 | 1 | 20 | yes | — |
| 175 | #885 | C23 | 1 | 20 | yes | — |
| 176 | #885 | C23 | 1 | 20 | yes | — |
| 177 | #884 | C23 | 1 | 20 | yes | — |
| 178 | #883 | C23 | 1 | 20 | yes | — |
| 179 | #883 | C23 | 1 | 20 | yes | — |
| 180 | #882 | C23 | 1 | 20 | yes | — |
| 181 | #882 | C23 | 1 | 20 | yes | — |
| 182 | #67⋊C4 | C23 | 1 | 20 | yes | — |
| 183 | D3×C22⋊C4 | C23 | 1 | 20 | yes | — |
| 184 | D3×C22⋊C4 | C23 | 1 | 20 | yes | — |
| 185 | #879 | C23 | 1 | 20 | yes | — |
| 186 | #878 | C23 | 1 | 20 | yes | — |
| 187 | #877 | C23 | 1 | 20 | yes | — |
| 188 | #875 | C23 | 1 | 10 | yes | — |
| 189 | #875 | C23 | 1 | 10 | yes | — |
| 190 | #875 | C23 | 1 | 10 | yes | — |
| 191 | #875 | C23 | 1 | 10 | yes | — |
| 192 | #875 | C23 | 1 | 10 | yes | — |
| 193 | #874 | C23 | 1 | 5 | yes | — |
| 194 | C4×D12 | C23 | 1 | 10 | yes | — |
| 195 | C4×D12 | C23 | 1 | 5 | yes | — |
| 196 | C4×D12 | C23 | 1 | 5 | yes | — |
| 197 | C4×D12 | C23 | 1 | 10 | yes | — |
| 198 | #872 | C23 | 1 | 10 | yes | — |
| 199 | C42×D3 | C23 | 1 | 10 | yes | — |
| 200 | #870 | C23 | 1 | 10 | yes | — |
| 201 | #869 | C23 | 1 | 5 | yes | — |
| 202 | #869 | C23 | 1 | 5 | yes | — |
| 203 | #869 | C23 | 1 | 5 | yes | — |
| 204 | C4×Dic6 | C23 | 1 | 10 | yes | — |
| 205 | C4×Dic6 | C23 | 1 | 10 | yes | — |
| 206 | C4×Dic6 | C23 | 1 | 5 | yes | — |
| 207 | C4×Dic6 | C23 | 1 | 5 | yes | — |
| 208 | #564 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 209 | #563 | — | 3 | 10 | no | — |
| 210 | #563 | — | 3 | 10 | no | — |
| 211 | #563 | — | 3 | 10 | no | — |
| 212 | #563 | C2×D3 | 1 | 5 | yes | complemented |
| 213 | #563 | C2×D3 | 1 | 5 | yes | complemented |
| 214 | #562 | — | 3 | 10 | no | — |
| 215 | #562 | — | 3 | 10 | no | — |
| 216 | #562 | C2×D3 | 1 | 5 | yes | complemented |
| 217 | H(3,𝔽4) | — | 3 | 10 | no | — |
| 218 | #559 | — | 3 | 5 | no | — |
| 219 | #559 | — | 3 | 10 | no | — |
| 220 | Q82 | — | 3 | 5 | no | — |
| 221 | #556 | — | 3 | 10 | no | — |
| 222 | #556 | — | 3 | 20 | no | — |
| 223 | #556 | — | 3 | 10 | no | — |
| 224 | #556 | — | 3 | 5 | no | — |
| 225 | #556 | — | 3 | 10 | no | — |
| 226 | #556 | — | 3 | 5 | no | — |
| 227 | #555 | — | 3 | 10 | no | — |
| 228 | #555 | — | 3 | 5 | no | — |
| 229 | #551 | — | 3 | 20 | no | — |
| 230 | #551 | — | 3 | 20 | no | — |
| 231 | #551 | — | 3 | 20 | no | — |
| 232 | #551 | — | 3 | 20 | no | — |
| 233 | D4×Q8 | — | 3 | 10 | no | — |
| 234 | D4×Q8 | — | 3 | 5 | no | — |
| 235 | D4×Q8 | — | 3 | 5 | no | — |
| 236 | #548 | — | 3 | 10 | no | — |
| 237 | #548 | — | 3 | 10 | no | — |
| 238 | #546 | — | 3 | 20 | no | — |
| 239 | #546 | — | 3 | 10 | no | — |
| 240 | #546 | — | 3 | 10 | no | — |
| 241 | D42 | — | 3 | 5 | no | — |
| 242 | #543 | — | 3 | 10 | no | — |
| 243 | #542 | — | 3 | 10 | no | — |
| 244 | #542 | — | 3 | 10 | no | — |
| 245 | #542 | — | 3 | 20 | no | — |
| 246 | #542 | — | 3 | 20 | no | — |
| 247 | #542 | — | 3 | 20 | no | — |
| 248 | #542 | — | 3 | 10 | no | — |
| 249 | #542 | — | 3 | 10 | no | — |
| 250 | #538 | — | 3 | 20 | no | — |
| 251 | #538 | — | 3 | 20 | no | — |
| 252 | #538 | — | 3 | 10 | no | — |
| 253 | #538 | — | 3 | 10 | no | — |
| 254 | #536 | — | 3 | 20 | no | — |
| 255 | #536 | — | 3 | 5 | no | — |
| 256 | #535 | — | 3 | 5 | no | — |
| 257 | #534 | — | 3 | 10 | no | — |
| 258 | #533 | — | 3 | 10 | no | — |
| 259 | #533 | — | 3 | 5 | no | — |
| 260 | #533 | C2×D3 | 1 | 5 | yes | complemented |
| 261 | #532 | — | 3 | 5 | no | — |
| 262 | #529 | — | 3 | 10 | no | — |
| 263 | #529 | — | 3 | 10 | no | — |
| 264 | #529 | — | 3 | 10 | no | — |
| 265 | #529 | — | 3 | 10 | no | — |
| 266 | #529 | C2×D3 | 1 | 5 | yes | complemented |
| 267 | #529 | C2×D3 | 1 | 5 | yes | complemented |
| 268 | C2×#124 | — | 3 | 10 | no | — |
| 269 | C2×#124 | — | 3 | 5 | no | — |
| 270 | #519 | — | 3 | 5 | no | — |
| 271 | #518 | — | 3 | 5 | no | — |
| 272 | C4×#41 | — | 3 | 5 | no | — |
| 273 | C23×D3 | C24 | 1 | 10 | yes | — |
| 274 | C2×C3×Q8 | C24 | 1 | 5 | yes | — |
| 275 | C2×C3×Q8 | C24 | 1 | 5 | yes | — |
| 276 | C2×C3×D4 | C24 | 1 | 5 | yes | — |
| 277 | C2×C3×D4 | C24 | 1 | 5 | yes | — |
| 278 | C22×C3×C4 | C24 | 1 | 5 | yes | — |
| 279 | C22×C3×C4 | C24 | 1 | 5 | yes | — |
| 280 | C22×C3×C4 | C24 | 1 | 5 | yes | — |
| 281 | C2×#67 | C24 | 1 | 20 | yes | — |
| 282 | C2×#67 | C24 | 1 | 10 | yes | — |
| 283 | C22×Dic3 | C24 | 1 | 10 | yes | — |
| 284 | D3×Q8 | — | 8 | 10 | no | — |
| 285 | D3×D4 | — | 8 | 10 | no | — |
| 286 | #235 | — | 4 | 10 | no | — |
| 287 | #235 | — | 8 | 10 | no | — |
| 288 | C2×D12 | — | 4 | 10 | no | — |
| 289 | C2×D12 | C24 | 1 | 5 | yes | — |
| 290 | C2×D12 | C24 | 1 | 10 | yes | — |
| 291 | C2×D12 | C24 | 1 | 10 | yes | — |
| 292 | C2×D12 | C24 | 1 | 10 | yes | — |
| 293 | C2×C4×D3 | C24 | 1 | 10 | yes | — |
| 294 | C2×C4×D3 | C24 | 1 | 10 | yes | — |
| 295 | C2×C4×D3 | C24 | 1 | 10 | yes | — |
| 296 | C2×C4×D3 | C24 | 1 | 20 | yes | — |
| 297 | C2×Dic6 | — | 4 | 10 | no | — |
| 298 | C2×Dic6 | C24 | 1 | 5 | yes | — |
| 299 | C2×Dic6 | C24 | 1 | 10 | yes | — |
| 300 | C2×Dic6 | C24 | 1 | 10 | yes | — |
| 301 | C2×Dic6 | C24 | 1 | 10 | yes | — |
| 302 | C3×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 303 | C3×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 304 | C3×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 305 | C3×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 306 | C3×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 307 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 308 | C3×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 309 | C3×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 310 | C3×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 311 | C3×C4⋊C4 | C24 | 1 | 5 | yes | — |
| 312 | C3×C22⋊C4 | C24 | 1 | 10 | yes | — |
| 313 | C3×C22⋊C4 | C24 | 1 | 10 | yes | — |
| 314 | C3×C22⋊C4 | C24 | 1 | 10 | yes | — |
| 315 | C3×C22⋊C4 | C24 | 1 | 10 | yes | — |
| 316 | C3×C42 | C24 | 1 | 5 | yes | — |
| 317 | C3×C42 | C24 | 1 | 5 | yes | — |
| 318 | C3×C42 | C24 | 1 | 5 | yes | — |
| 319 | C3×C42 | C24 | 1 | 5 | yes | — |
| 320 | #217 | C24 | 1 | 10 | yes | — |
| 321 | #217 | C24 | 1 | 20 | yes | — |
| 322 | (C2×D3)⋊C4 | C24 | 1 | 10 | yes | — |
| 323 | (C2×D3)⋊C4 | C24 | 1 | 10 | yes | — |
| 324 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 325 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 326 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 327 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 328 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 329 | (C2×D3)⋊C4 | C24 | 1 | 20 | yes | — |
| 330 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 331 | C4⋊Dic3 | C24 | 1 | 5 | yes | — |
| 332 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 333 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 334 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 335 | C4⋊Dic3 | C24 | 1 | 10 | yes | — |
| 336 | Dic3⋊C4 | C24 | 1 | 20 | yes | — |
| 337 | Dic3⋊C4 | C24 | 1 | 20 | yes | — |
| 338 | Dic3⋊C4 | C24 | 1 | 10 | yes | — |
| 339 | Dic3⋊C4 | C24 | 1 | 10 | yes | — |
| 340 | C4×Dic3 | C24 | 1 | 20 | yes | — |
| 341 | C4×Dic3 | C24 | 1 | 10 | yes | — |
| 342 | C4×Dic3 | C24 | 1 | 10 | yes | — |
| 343 | C4×Dic3 | C24 | 1 | 10 | yes | — |
| 344 | C2×#41 | — | 3 | 5 | no | — |
| 345 | C2×#41 | — | 3 | 10 | no | — |
| 346 | C22×Q8 | — | 3 | 10 | no | — |
| 347 | C22×Q8 | — | 3 | 5 | no | — |
| 348 | C22×D4 | — | 3 | 10 | no | — |
| 349 | C22×D4 | — | 3 | 5 | no | — |
| 350 | C4⋊Q8 | — | 3 | 10 | no | — |
| 351 | C4⋊Q8 | — | 3 | 10 | no | — |
| 352 | C4⋊Q8 | — | 3 | 20 | no | — |
| 353 | C4⋊Q8 | — | 3 | 5 | no | — |
| 354 | C4⋊Q8 | — | 3 | 5 | no | — |
| 355 | C4⋊Q8 | — | 3 | 5 | no | — |
| 356 | C4⋊Q8 | C22×D3 | 1 | 5 | yes | — |
| 357 | C4⋊Q8 | C22×D3 | 1 | 5 | yes | — |
| 358 | #127 | — | 3 | 5 | no | — |
| 359 | #126 | — | 3 | 20 | no | — |
| 360 | #126 | — | 3 | 20 | no | — |
| 361 | #126 | — | 3 | 20 | no | — |
| 362 | #126 | — | 3 | 20 | no | — |
| 363 | #126 | — | 3 | 20 | no | — |
| 364 | #126 | — | 3 | 20 | no | — |
| 365 | #126 | C22×D3 | 1 | 10 | yes | — |
| 366 | #126 | C22×D3 | 1 | 10 | yes | — |
| 367 | #125 | — | 3 | 10 | no | — |
| 368 | #125 | C22×D3 | 1 | 5 | yes | — |
| 369 | #125 | C22×D3 | 1 | 5 | yes | — |
| 370 | #125 | C22×D3 | 1 | 5 | yes | — |
| 371 | #125 | C22×D3 | 1 | 5 | yes | — |
| 372 | #124 | — | 3 | 10 | no | — |
| 373 | #124 | — | 3 | 20 | no | — |
| 374 | #124 | — | 3 | 10 | no | — |
| 375 | #124 | — | 3 | 20 | no | — |
| 376 | #124 | — | 3 | 20 | no | — |
| 377 | #124 | — | 3 | 20 | no | — |
| 378 | #124 | — | 3 | 20 | no | — |
| 379 | #124 | — | 3 | 10 | no | — |
| 380 | #124 | — | 3 | 10 | no | — |
| 381 | #124 | — | 3 | 10 | no | — |
| 382 | #124 | — | 3 | 10 | no | — |
| 383 | #124 | — | 3 | 10 | no | — |
| 384 | #124 | C22×D3 | 1 | 5 | yes | — |
| 385 | #124 | C22×D3 | 1 | 5 | yes | — |
| 386 | #123 | — | 3 | 20 | no | — |
| 387 | #123 | — | 3 | 20 | no | — |
| 388 | #123 | — | 3 | 20 | no | — |
| 389 | #123 | — | 3 | 20 | no | — |
| 390 | #123 | — | 3 | 20 | no | — |
| 391 | #123 | — | 3 | 20 | no | — |
| 392 | #123 | — | 3 | 20 | no | — |
| 393 | #123 | C22×D3 | 1 | 10 | yes | — |
| 394 | #123 | C22×D3 | 1 | 10 | yes | — |
| 395 | C22⋊Q8 | — | 3 | 10 | no | — |
| 396 | C22⋊Q8 | — | 3 | 20 | no | — |
| 397 | C22⋊Q8 | — | 3 | 10 | no | — |
| 398 | C22⋊Q8 | — | 3 | 10 | no | — |
| 399 | C22⋊Q8 | — | 3 | 10 | no | — |
| 400 | C22⋊Q8 | — | 3 | 10 | no | — |
| 401 | C22⋊Q8 | — | 3 | 10 | no | — |
| 402 | C22⋊Q8 | — | 3 | 20 | no | — |
| 403 | C22⋊Q8 | — | 3 | 20 | no | — |
| 404 | C22⋊Q8 | — | 3 | 20 | no | — |
| 405 | C22⋊Q8 | — | 3 | 20 | no | — |
| 406 | C22⋊Q8 | — | 3 | 20 | no | — |
| 407 | C22⋊Q8 | C22×D3 | 1 | 5 | yes | — |
| 408 | C22⋊Q8 | C22×D3 | 1 | 5 | yes | — |
| 409 | C22⋊Q8 | C22×D3 | 1 | 10 | yes | — |
| 410 | C22⋊Q8 | C22×D3 | 1 | 10 | yes | — |
| 411 | #121 | — | 3 | 10 | no | — |
| 412 | #121 | — | 3 | 20 | no | — |
| 413 | #121 | — | 3 | 10 | no | — |
| 414 | #121 | — | 3 | 10 | no | — |
| 415 | #121 | — | 3 | 10 | no | — |
| 416 | #121 | — | 3 | 10 | no | — |
| 417 | #121 | — | 3 | 10 | no | — |
| 418 | #121 | — | 3 | 20 | no | — |
| 419 | #121 | C22×D3 | 1 | 5 | yes | — |
| 420 | #121 | C22×D3 | 1 | 5 | yes | — |
| 421 | #120 | — | 3 | 20 | no | — |
| 422 | #120 | — | 3 | 20 | no | — |
| 423 | #120 | — | 3 | 20 | no | — |
| 424 | C4×Q8 | — | 3 | 10 | no | — |
| 425 | C4×Q8 | — | 3 | 10 | no | — |
| 426 | C4×Q8 | — | 3 | 10 | no | — |
| 427 | C4×Q8 | — | 3 | 10 | no | — |
| 428 | C4×Q8 | — | 3 | 5 | no | — |
| 429 | C4×Q8 | — | 3 | 5 | no | — |
| 430 | C4×Q8 | — | 3 | 10 | no | — |
| 431 | C4×Q8 | — | 3 | 10 | no | — |
| 432 | C4×Q8 | C22×D3 | 1 | 5 | yes | — |
| 433 | C4×Q8 | C22×D3 | 1 | 5 | yes | — |
| 434 | C4×D4 | — | 3 | 10 | no | — |
| 435 | C4×D4 | — | 3 | 10 | no | — |
| 436 | C4×D4 | — | 3 | 10 | no | — |
| 437 | C4×D4 | — | 3 | 10 | no | — |
| 438 | C4×D4 | — | 3 | 10 | no | — |
| 439 | C4×D4 | — | 3 | 10 | no | — |
| 440 | C4×D4 | — | 3 | 20 | no | — |
| 441 | C4×D4 | — | 3 | 20 | no | — |
| 442 | C4×D4 | — | 3 | 5 | no | — |
| 443 | C4×D4 | — | 3 | 5 | no | — |
| 444 | C4×D4 | — | 3 | 10 | no | — |
| 445 | C4×D4 | — | 3 | 10 | no | — |
| 446 | C4×D4 | C22×D3 | 1 | 5 | yes | — |
| 447 | C4×D4 | C22×D3 | 1 | 5 | yes | — |
| 448 | #117 | — | 3 | 5 | no | — |
| 449 | #117 | — | 3 | 10 | no | — |
| 450 | #117 | — | 3 | 10 | no | — |
| 451 | #117 | — | 3 | 10 | no | — |
| 452 | #117 | — | 3 | 20 | no | — |
| 453 | #117 | — | 3 | 20 | no | — |
| 454 | #117 | — | 3 | 10 | no | — |
| 455 | #117 | C22×D3 | 1 | 5 | yes | — |
| 456 | #117 | C22×D3 | 1 | 5 | yes | — |
| 457 | C2×C22⋊C4 | — | 3 | 10 | no | — |
| 458 | C2×C22⋊C4 | — | 3 | 10 | no | — |
| 459 | C2×C22⋊C4 | — | 3 | 20 | no | — |
| 460 | C2×C22⋊C4 | — | 3 | 20 | no | — |
| 461 | C2×C42 | — | 3 | 10 | no | — |
| 462 | C2×C42 | C22×D3 | 1 | 5 | yes | — |
| 463 | C23×C3 | C25 | 1 | 5 | yes | — |
| 464 | C22×D3 | — | 4 | 10 | no | — |
| 465 | C22×D3 | — | 4 | 10 | no | — |
| 466 | C22×D3 | — | 4 | 10 | no | — |
| 467 | C22×D3 | C25 | 1 | 10 | yes | — |
| 468 | C3×Q8 | — | 4 | 5 | no | — |
| 469 | C3×Q8 | — | 4 | 5 | no | — |
| 470 | C3×D4 | — | 4 | 5 | no | — |
| 471 | C3×D4 | — | 4 | 5 | no | — |
| 472 | C2×C3×C4 | — | 2 | 10 | no | — |
| 473 | C2×C3×C4 | — | 4 | 5 | no | — |
| 474 | C2×C3×C4 | — | 4 | 5 | no | — |
| 475 | C2×C3×C4 | C25 | 1 | 5 | yes | — |
| 476 | C2×C3×C4 | C25 | 1 | 5 | yes | — |
| 477 | C2×C3×C4 | C25 | 1 | 5 | yes | — |
| 478 | C2×C3×C4 | C25 | 1 | 5 | yes | — |
| 479 | C2×C3×C4 | C25 | 1 | 5 | yes | — |
| 480 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 481 | #67 | — | 4 | 10 | no | — |
| 482 | #67 | — | 4 | 20 | no | — |
| 483 | C2×Dic3 | — | 4 | 10 | no | — |
| 484 | C2×Dic3 | C25 | 1 | 2 | yes | — |
| 485 | C2×Dic3 | C25 | 1 | 10 | yes | — |
| 486 | C2×Dic3 | C25 | 1 | 10 | yes | — |
| 487 | D12 | — | 2 | 10 | no | — |
| 488 | D12 | — | 4 | 10 | no | — |
| 489 | D12 | — | 4 | 10 | no | — |
| 490 | D12 | — | 4 | 10 | no | — |
| 491 | C4×D3 | — | 4 | 10 | no | — |
| 492 | C4×D3 | — | 4 | 10 | no | — |
| 493 | C4×D3 | — | 4 | 20 | no | — |
| 494 | C4×D3 | — | 4 | 10 | no | — |
| 495 | Dic6 | — | 2 | 10 | no | — |
| 496 | Dic6 | — | 4 | 10 | no | — |
| 497 | Dic6 | — | 4 | 10 | no | — |
| 498 | Dic6 | — | 4 | 10 | no | — |
| 499 | C24 | — | 3 | 10 | no | — |
| 500 | #41 | — | 12 | 10 | no | — |
| 501 | #41 | — | 24 | 10 | no | — |
| 502 | C2×Q8 | — | 3 | 5 | no | — |
| 503 | C2×Q8 | — | 3 | 10 | no | — |
| 504 | C2×Q8 | — | 3 | 10 | no | — |
| 505 | C2×Q8 | — | 3 | 10 | no | — |
| 506 | C2×Q8 | — | 12 | 10 | no | — |
| 507 | C2×Q8 | — | 24 | 10 | no | — |
| 508 | C2×Q8 | C23×D3 | 1 | 5 | yes | — |
| 509 | C2×Q8 | C23×D3 | 1 | 5 | yes | — |
| 510 | C2×D4 | — | 3 | 10 | no | — |
| 511 | C2×D4 | — | 3 | 20 | no | — |
| 512 | C2×D4 | — | 3 | 5 | no | — |
| 513 | C2×D4 | — | 3 | 10 | no | — |
| 514 | C2×D4 | — | 3 | 10 | no | — |
| 515 | C2×D4 | — | 3 | 10 | no | — |
| 516 | C2×D4 | — | 12 | 10 | no | — |
| 517 | C2×D4 | — | 24 | 10 | no | — |
| 518 | C2×D4 | C23×D3 | 1 | 5 | yes | — |
| 519 | C2×D4 | C23×D3 | 1 | 5 | yes | — |
| 520 | C22×C4 | — | 3 | 10 | no | — |
| 521 | C22×C4 | — | 3 | 10 | no | — |
| 522 | C22×C4 | — | 3 | 10 | no | — |
| 523 | C22×C4 | — | 3 | 10 | no | — |
| 524 | C22×C4 | — | 3 | 20 | no | — |
| 525 | C22×C4 | C23×D3 | 1 | 5 | yes | — |
| 526 | C22×C4 | C23×D3 | 1 | 5 | yes | — |
| 527 | C22×C4 | C23×D3 | 1 | 5 | yes | — |
| 528 | C4⋊C4 | — | 3 | 1 | no | — |
| 529 | C4⋊C4 | — | 3 | 10 | no | — |
| 530 | C4⋊C4 | — | 3 | 10 | no | — |
| 531 | C4⋊C4 | — | 3 | 10 | no | — |
| 532 | C4⋊C4 | — | 3 | 10 | no | — |
| 533 | C4⋊C4 | — | 3 | 5 | no | — |
| 534 | C4⋊C4 | — | 3 | 10 | no | — |
| 535 | C4⋊C4 | — | 3 | 20 | no | — |
| 536 | C4⋊C4 | — | 3 | 20 | no | — |
| 537 | C4⋊C4 | — | 3 | 10 | no | — |
| 538 | C4⋊C4 | C23×D3 | 1 | 5 | yes | — |
| 539 | C4⋊C4 | C23×D3 | 1 | 5 | yes | — |
| 540 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 541 | C4⋊C4 | C23×D3 | 1 | 5 | yes | — |
| 542 | C4⋊C4 | C23×D3 | 1 | 5 | yes | — |
| 543 | C4⋊C4 | C23×D3 | 1 | 5 | yes | — |
| 544 | C4⋊C4 | C23×D3 | 1 | 5 | yes | — |
| 545 | C4⋊C4 | C23×D3 | 1 | 5 | yes | — |
| 546 | C4⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 547 | C4⋊C4 | C23×D3 | 1 | 5 | yes | — |
| 548 | C22⋊C4 | — | 3 | 10 | no | — |
| 549 | C22⋊C4 | — | 3 | 20 | no | — |
| 550 | C22⋊C4 | — | 3 | 10 | no | — |
| 551 | C22⋊C4 | — | 3 | 20 | no | — |
| 552 | C22⋊C4 | — | 3 | 20 | no | — |
| 553 | C22⋊C4 | — | 3 | 20 | no | — |
| 554 | C22⋊C4 | — | 3 | 20 | no | — |
| 555 | C22⋊C4 | — | 3 | 20 | no | — |
| 556 | C22⋊C4 | — | 3 | 20 | no | — |
| 557 | C22⋊C4 | — | 3 | 10 | no | — |
| 558 | C22⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 559 | C22⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 560 | C22⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 561 | C22⋊C4 | C23×D3 | 1 | 10 | yes | — |
| 562 | C42 | — | 3 | 10 | no | — |
| 563 | C42 | — | 3 | 10 | no | — |
| 564 | C42 | — | 3 | 10 | no | — |
| 565 | C42 | — | 3 | 20 | no | — |
| 566 | C42 | C23×D3 | 1 | 5 | yes | — |
| 567 | C42 | C23×D3 | 1 | 5 | yes | — |
| 568 | C42 | C23×D3 | 1 | 5 | yes | — |
| 569 | C42 | C23×D3 | 1 | 5 | yes | — |
| 570 | C22×C3 | — | 2 | 5 | no | — |
| 571 | C22×C3 | — | 2 | 5 | no | — |
| 572 | C22×C3 | — | 2 | 5 | no | — |
| 573 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 574 | C2×D3 | — | 2 | 10 | no | — |
| 575 | C2×D3 | — | 2 | 10 | no | — |
| 576 | C2×D3 | — | 2 | 10 | no | — |
| 577 | C2×D3 | — | 16 | 10 | no | — |
| 578 | C3×C4 | — | 2 | 5 | no | — |
| 579 | C3×C4 | — | 2 | 5 | no | — |
| 580 | C3×C4 | — | 2 | 5 | no | — |
| 581 | C3×C4 | — | 2 | 5 | no | — |
| 582 | C3×C4 | — | 2 | 5 | no | — |
| 583 | C3×C4 | #585 | 1 | 2 | yes | — |
| 584 | Dic3 | — | 2 | 10 | no | — |
| 585 | Dic3 | — | 2 | 10 | no | — |
| 586 | Dic3 | — | 2 | 2 | no | — |
| 587 | C23 | — | 3 | 10 | no | — |
| 588 | C23 | — | 12 | 10 | no | — |
| 589 | C23 | — | 12 | 10 | no | — |
| 590 | C23 | — | 12 | 10 | no | — |
| 591 | C23 | C24×D3 | 1 | 5 | yes | — |
| 592 | Q8 | — | 4 | 5 | no | — |
| 593 | Q8 | — | 4 | 5 | no | — |
| 594 | Q8 | — | 6 | 10 | no | — |
| 595 | Q8 | — | 12 | 10 | no | — |
| 596 | Q8 | — | 12 | 10 | no | — |
| 597 | Q8 | — | 12 | 10 | no | — |
| 598 | D4 | — | 4 | 5 | no | — |
| 599 | D4 | — | 4 | 5 | no | — |
| 600 | D4 | — | 6 | 10 | no | — |
| 601 | D4 | — | 12 | 10 | no | — |
| 602 | D4 | — | 12 | 10 | no | — |
| 603 | D4 | — | 12 | 10 | no | — |
| 604 | D4 | — | 12 | 20 | no | — |
| 605 | D4 | — | 12 | 10 | no | — |
| 606 | C2×C4 | — | 2 | 10 | no | — |
| 607 | C2×C4 | — | 3 | 2 | no | — |
| 608 | C2×C4 | — | 3 | 10 | no | — |
| 609 | C2×C4 | — | 3 | 10 | no | — |
| 610 | C2×C4 | — | 4 | 5 | no | — |
| 611 | C2×C4 | — | 4 | 5 | no | — |
| 612 | C2×C4 | — | 12 | 10 | no | — |
| 613 | C2×C4 | — | 12 | 20 | no | — |
| 614 | C2×C4 | — | 12 | 10 | no | — |
| 615 | C2×C4 | — | 12 | 10 | no | — |
| 616 | C2×C4 | — | 12 | 10 | no | — |
| 617 | C2×C4 | C24×D3 | 1 | 5 | yes | — |
| 618 | C2×C4 | C24×D3 | 1 | 5 | yes | — |
| 619 | C2×C4 | C24×D3 | 1 | 5 | yes | — |
| 620 | C2×C4 | C24×D3 | 1 | 5 | yes | — |
| 621 | C2×C4 | C24×D3 | 1 | 5 | yes | — |
| 622 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 623 | C2×C3 | — | 4 | 5 | no | — |
| 624 | C2×C3 | C2×#585 | 1 | 1 | yes | characteristic |
| 625 | C2×C3 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 626 | C2×C3 | 2−1+6 | 1 | 1 | yes | characteristic |
| 627 | D3 | — | 4 | 10 | no | — |
| 628 | C22 | — | 2 | 5 | no | — |
| 629 | C22 | — | 2 | 5 | no | — |
| 630 | C22 | — | 2 | 5 | no | — |
| 631 | C22 | — | 6 | 10 | no | — |
| 632 | C22 | — | 6 | 10 | no | — |
| 633 | C22 | — | 6 | 10 | no | — |
| 634 | C22 | — | 48 | 10 | no | — |
| 635 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 636 | C4 | — | 2 | 5 | no | — |
| 637 | C4 | — | 2 | 5 | no | — |
| 638 | C4 | — | 2 | 5 | no | — |
| 639 | C4 | — | 2 | 5 | no | — |
| 640 | C4 | — | 2 | 5 | no | — |
| 641 | C4 | — | 6 | 10 | no | — |
| 642 | C4 | — | 6 | 2 | no | — |
| 643 | C4 | — | 6 | 10 | no | — |
| 644 | C4 | #5968 | 1 | 2 | yes | — |
| 645 | C3 | #63069 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 646 | C2 | — | 4 | 5 | no | — |
| 647 | C2 | — | 12 | 10 | no | — |
| 648 | C2 | C2×#5968 | 1 | 1 | yes | characteristic |
| 649 | C2 | #87572 | 1 | 1 | yes | characteristic |
| 650 | C2 | #87574 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Fitting | C3×#3531 | C2 |
| hypercenter | #3531 | D3 |
| hypocenter | C3 | #63069 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #3531 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3531 | C2 | semidirect |
| 2. #87139 | C2 | semidirect |
| 3. #87126 | C2 | semidirect |
| 4. #87123 | C2 | semidirect |
| 5. #87111 | C2 | semidirect |
| 6. #86267 | C2 | semidirect |
| 7. #86263 | C2 | semidirect |
| 8. #86177 | C2 | semidirect |
| 9. #86163 | C2 | semidirect |
| 10. #86141 | C2 | semidirect |
| 11. #86127 | C2 | semidirect |
| 13. C3×#564 | C22 | semidirect |
| 14. C3×#563 | C22 | semidirect |
| 15. C3×#563 | C22 | semidirect |
| 16. C3×#562 | C22 | semidirect |
| 17. C3×#533 | C22 | semidirect |
| 18. C3×#529 | C22 | semidirect |
| 19. C3×#529 | C22 | semidirect |
| 20. #5733 | C22 | semidirect |
| 21. #5733 | C22 | semidirect |
| 22. #5732 | C22 | semidirect |
| 23. #5727 | C22 | semidirect |
| 24. #5710 | C22 | semidirect |
| 25. #5705 | C22 | semidirect |
| 26. #5704 | C22 | semidirect |
| 27. #5702 | C22 | semidirect |
| 28. #5700 | C22 | semidirect |
| 29. #5699 | C22 | semidirect |
| 30. #5699 | C22 | semidirect |
| 31. #5699 | C22 | semidirect |
| 32. #5691 | C22 | semidirect |
| 33. #5691 | C22 | semidirect |
| 34. #5691 | C22 | semidirect |
| 35. #5688 | C22 | semidirect |
| 36. #5684 | C22 | semidirect |
| 37. #5683 | C22 | semidirect |
| 38. #5680 | C22 | semidirect |
| 39. D3×#124 | C22 | semidirect |
| 40. #5662 | C22 | semidirect |
| 41. #5658 | C22 | semidirect |
| 42. #5657 | C22 | semidirect |
| 43. #5654 | C22 | semidirect |
| 44. #5644 | C22 | semidirect |
| 45. #5643 | C22 | semidirect |
| 46. #5641 | C22 | semidirect |
| 47. #5637 | C22 | semidirect |
| 48. #5637 | C22 | semidirect |
| 49. #5634 | C22 | semidirect |
| 50. #5633 | C22 | semidirect |
| 51. #5628 | C22 | semidirect |
| 52. #5617 | C22 | semidirect |
| 53. #5616 | C22 | semidirect |
| 54. #5612 | C22 | semidirect |
| 55. #5605 | C22 | semidirect |
| 56. #5585 | C22 | semidirect |
| 57. #5585 | C22 | semidirect |
| 58. #5584 | C22 | semidirect |
| 59. #5584 | C22 | semidirect |
| 60. Q8×D12 | C22 | semidirect |
| 61. Q8×Dic6 | C22 | semidirect |
| 62. #5563 | C22 | semidirect |
| 63. #5552 | C22 | semidirect |
| 64. #5550 | C22 | semidirect |
| 65. D4×D12 | C22 | semidirect |
| 66. #5542 | C22 | semidirect |
| 67. D4×Dic6 | C22 | semidirect |
| 68. #5534 | C22 | semidirect |
| 69. #5534 | C22 | semidirect |
| 70. #5526 | C22 | semidirect |
| 72. #5521 | C22 | semidirect |
| 73. #5516 | C22 | semidirect |
| 75. C2×#875 | C22 | semidirect |
| 76. C4×#235 | C22 | semidirect |
| 77. #5470 | C22 | semidirect |
| 85. #3531 | D3 | semidirect |
| 208. #564 | C2×D3 | semidirect |
| 212. #563 | C2×D3 | semidirect |
| 213. #563 | C2×D3 | semidirect |
| 216. #562 | C2×D3 | semidirect |
| 260. #533 | C2×D3 | semidirect |
| 266. #529 | C2×D3 | semidirect |
| 267. #529 | C2×D3 | semidirect |
| 645. C3 | #63069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3531 | 2 |
| #87139 | 2 |
| #87126 | 2 |
| #87123 | 2 |
| #87111 | 2 |
| #86267 | 2 |
| #86263 | 2 |
| #86177 | 2 |
| #86163 | 2 |
| #86141 | 2 |
| #86127 | 2 |
| #63069 | 3 |