Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
6588 conjugacy classes of subgroups.
The subgroup lattice has 600 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#3504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #87023 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #87019 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #86957 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #86939 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #86603 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #86288 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #86286 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #86103 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #85896 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #85853 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #63070 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C3×#557 | C22 | 1 | 4 | yes | — |
| 14 | C3×#554 | C22 | 1 | 12 | yes | — |
| 15 | C3×#544 | C22 | 1 | 6 | yes | — |
| 16 | C3×#533 | C22 | 1 | 3 | yes | — |
| 17 | C2×C3×#125 | C22 | 1 | 3 | yes | — |
| 18 | C3×#520 | C22 | 1 | 2 | yes | — |
| 19 | C3×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 20 | #5834 | C22 | 1 | 4 | yes | — |
| 21 | #5735 | C22 | 1 | 12 | yes | — |
| 22 | #5730 | C22 | 1 | 12 | yes | — |
| 23 | #5729 | C22 | 1 | 12 | yes | — |
| 24 | #5726 | C22 | 1 | 12 | yes | — |
| 25 | #5726 | C22 | 1 | 12 | yes | — |
| 26 | #5725 | C22 | 1 | 12 | yes | — |
| 27 | #5700 | C22 | 1 | 3 | yes | — |
| 28 | #5700 | C22 | 1 | 6 | yes | — |
| 29 | #5699 | C22 | 1 | 6 | yes | — |
| 30 | #5697 | C22 | 1 | 12 | yes | — |
| 31 | #5697 | C22 | 1 | 12 | yes | — |
| 32 | #5695 | C22 | 1 | 12 | yes | — |
| 33 | #5695 | C22 | 1 | 12 | yes | — |
| 34 | #5692 | C22 | 1 | 24 | yes | — |
| 35 | #5690 | C22 | 1 | 12 | yes | — |
| 36 | #5690 | C22 | 1 | 12 | yes | — |
| 37 | #5689 | C22 | 1 | 12 | yes | — |
| 38 | D3×#125 | C22 | 1 | 12 | yes | — |
| 39 | C3⋊#564 | C22 | 1 | 1 | yes | characteristic |
| 40 | #5647 | C22 | 1 | 12 | yes | — |
| 41 | #5647 | C22 | 1 | 24 | yes | — |
| 42 | #5646 | C22 | 1 | 12 | yes | — |
| 43 | #5638 | C22 | 1 | 24 | yes | — |
| 44 | #5631 | C22 | 1 | 24 | yes | — |
| 45 | #5629 | C22 | 1 | 24 | yes | — |
| 46 | #5629 | C22 | 1 | 24 | yes | — |
| 47 | #5580 | C22 | 1 | 12 | yes | — |
| 48 | #5579 | C22 | 1 | 12 | yes | — |
| 49 | #5578 | C22 | 1 | 12 | yes | — |
| 50 | #5577 | C22 | 1 | 12 | yes | — |
| 51 | #5577 | C22 | 1 | 2 | yes | — |
| 52 | #5577 | C22 | 1 | 4 | yes | — |
| 53 | #5574 | C22 | 1 | 4 | yes | — |
| 54 | #5574 | C22 | 1 | 4 | yes | — |
| 55 | C4×#239 | C22 | 1 | 4 | yes | — |
| 56 | #5570 | C22 | 1 | 2 | yes | — |
| 57 | #5569 | C22 | 1 | 4 | yes | — |
| 58 | #5562 | C22 | 1 | 12 | yes | — |
| 59 | #5562 | C22 | 1 | 12 | yes | — |
| 60 | #5558 | C22 | 1 | 12 | yes | — |
| 61 | #5553 | C22 | 1 | 6 | yes | — |
| 62 | #5553 | C22 | 1 | 12 | yes | — |
| 63 | #5551 | C22 | 1 | 6 | yes | — |
| 64 | #5548 | C22 | 1 | 12 | yes | — |
| 65 | #5535 | C22 | 1 | 12 | yes | — |
| 66 | #5530 | C22 | 1 | 12 | yes | — |
| 67 | #5528 | C22 | 1 | 12 | yes | — |
| 68 | #5515 | C22 | 1 | 12 | yes | — |
| 69 | #5514 | C22 | 1 | 12 | yes | — |
| 70 | #5510 | C22 | 1 | 12 | yes | — |
| 71 | #5507 | C22 | 1 | 12 | yes | — |
| 72 | #5507 | C22 | 1 | 24 | yes | — |
| 73 | #5479 | C22 | 1 | 6 | yes | — |
| 74 | #5477 | C22 | 1 | 6 | yes | — |
| 75 | #3559 | — | 3 | 12 | no | — |
| 76 | #3559 | — | 3 | 12 | no | — |
| 77 | #3559 | — | 3 | 6 | no | — |
| 78 | #3548 | — | 3 | 12 | no | — |
| 79 | #3548 | — | 3 | 3 | no | — |
| 80 | #3531 | — | 3 | 3 | no | — |
| 81 | #3517 | — | 3 | 4 | no | — |
| 82 | #3517 | — | 3 | 4 | no | — |
| 83 | #3517 | — | 3 | 2 | no | — |
| 84 | #3504 | — | 3 | 4 | no | — |
| 85 | #3504 | D3 | 1 | 1 | yes | characteristic, complemented |
| 86 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×#239 | C23 | 1 | 4 | yes | — |
| 88 | C2×#239 | C23 | 1 | 24 | yes | — |
| 89 | C2×#235 | C23 | 1 | 12 | yes | — |
| 90 | C2×#235 | C23 | 1 | 24 | yes | — |
| 91 | C3×C4⋊Q8 | C23 | 1 | 12 | yes | — |
| 92 | C3×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 93 | C3×#125 | C23 | 1 | 1 | yes | characteristic |
| 94 | C3×#125 | C23 | 1 | 12 | yes | — |
| 95 | C3×#125 | C23 | 1 | 12 | yes | — |
| 96 | C3×#125 | C23 | 1 | 6 | yes | — |
| 97 | C3×#125 | C23 | 1 | 3 | yes | — |
| 98 | C3×C22⋊Q8 | C23 | 1 | 24 | yes | — |
| 99 | C3×C22⋊Q8 | C23 | 1 | 12 | yes | — |
| 100 | C3×C4×Q8 | C23 | 1 | 4 | yes | — |
| 101 | C3×C4×Q8 | C23 | 1 | 2 | yes | — |
| 102 | C3×C4×Q8 | C23 | 1 | 12 | yes | — |
| 103 | C3×C4×D4 | C23 | 1 | 12 | yes | — |
| 104 | C3×C4×D4 | C23 | 1 | 6 | yes | — |
| 105 | C3×#117 | C23 | 1 | 6 | yes | — |
| 106 | C3×#117 | C23 | 1 | 3 | yes | — |
| 107 | C2×C3×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 108 | C2×C3×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 109 | C2×C3×C42 | C23 | 1 | 3 | yes | — |
| 110 | #947 | C23 | 1 | 12 | yes | — |
| 111 | #946 | C23 | 1 | 12 | yes | — |
| 112 | #946 | C23 | 1 | 24 | yes | — |
| 113 | #946 | C23 | 1 | 12 | yes | — |
| 114 | Q8×Dic3 | C23 | 1 | 4 | yes | — |
| 115 | #944 | C23 | 1 | 12 | yes | — |
| 116 | #940 | C23 | 1 | 12 | yes | — |
| 117 | #938 | C23 | 1 | 12 | yes | — |
| 118 | #930 | C23 | 1 | 6 | yes | — |
| 119 | #930 | C23 | 1 | 24 | yes | — |
| 120 | #930 | C23 | 1 | 12 | yes | — |
| 121 | #930 | C23 | 1 | 12 | yes | — |
| 122 | #929 | C23 | 1 | 24 | yes | — |
| 123 | #929 | C23 | 1 | 12 | yes | — |
| 124 | C4×#67 | C23 | 1 | 24 | yes | — |
| 125 | C4×#67 | C23 | 1 | 12 | yes | — |
| 126 | #924 | C23 | 1 | 6 | yes | — |
| 127 | #898 | C23 | 1 | 12 | yes | — |
| 128 | #898 | C23 | 1 | 12 | yes | — |
| 129 | #898 | C23 | 1 | 12 | yes | — |
| 130 | #897 | C23 | 1 | 24 | yes | — |
| 131 | #897 | C23 | 1 | 12 | yes | — |
| 132 | #896 | C23 | 1 | 12 | yes | — |
| 133 | #896 | C23 | 1 | 24 | yes | — |
| 134 | #896 | C23 | 1 | 12 | yes | — |
| 135 | #896 | C23 | 1 | 24 | yes | — |
| 136 | #896 | C23 | 1 | 12 | yes | — |
| 137 | #895 | C23 | 1 | 24 | yes | — |
| 138 | #895 | C23 | 1 | 12 | yes | — |
| 139 | #895 | C23 | 1 | 24 | yes | — |
| 140 | #895 | C23 | 1 | 12 | yes | — |
| 141 | #895 | C23 | 1 | 12 | yes | — |
| 142 | #895 | C23 | 1 | 24 | yes | — |
| 143 | #895 | C23 | 1 | 12 | yes | — |
| 144 | #894 | C23 | 1 | 24 | yes | — |
| 145 | #894 | C23 | 1 | 24 | yes | — |
| 146 | #894 | C23 | 1 | 12 | yes | — |
| 147 | #894 | C23 | 1 | 12 | yes | — |
| 148 | #894 | C23 | 1 | 24 | yes | — |
| 149 | #894 | C23 | 1 | 12 | yes | — |
| 150 | #893 | C23 | 1 | 24 | yes | — |
| 151 | #893 | C23 | 1 | 12 | yes | — |
| 152 | #893 | C23 | 1 | 12 | yes | — |
| 153 | #893 | C23 | 1 | 12 | yes | — |
| 154 | #892 | C23 | 1 | 12 | yes | — |
| 155 | D3×C4⋊C4 | C23 | 1 | 24 | yes | — |
| 156 | D3×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 157 | D3×C4⋊C4 | C23 | 1 | 24 | yes | — |
| 158 | D3×C4⋊C4 | C23 | 1 | 12 | yes | — |
| 159 | #890 | C23 | 1 | 4 | yes | — |
| 160 | #890 | C23 | 1 | 12 | yes | — |
| 161 | #890 | C23 | 1 | 12 | yes | — |
| 162 | #889 | C23 | 1 | 24 | yes | — |
| 163 | #889 | C23 | 1 | 12 | yes | — |
| 164 | #889 | C23 | 1 | 4 | yes | — |
| 165 | #889 | C23 | 1 | 4 | yes | — |
| 166 | #888 | C23 | 1 | 12 | yes | — |
| 167 | #888 | C23 | 1 | 12 | yes | — |
| 168 | #885 | C23 | 1 | 12 | yes | — |
| 169 | #884 | C23 | 1 | 24 | yes | — |
| 170 | #884 | C23 | 1 | 12 | yes | — |
| 171 | #884 | C23 | 1 | 24 | yes | — |
| 172 | #884 | C23 | 1 | 24 | yes | — |
| 173 | #883 | C23 | 1 | 24 | yes | — |
| 174 | #883 | C23 | 1 | 12 | yes | — |
| 175 | #879 | C23 | 1 | 12 | yes | — |
| 176 | #876 | C23 | 1 | 12 | yes | — |
| 177 | #875 | C23 | 1 | 6 | yes | — |
| 178 | #874 | C23 | 1 | 6 | yes | — |
| 179 | #874 | C23 | 1 | 12 | yes | — |
| 180 | C4×D12 | C23 | 1 | 12 | yes | — |
| 181 | C4×D12 | C23 | 1 | 12 | yes | — |
| 182 | C4×D12 | C23 | 1 | 12 | yes | — |
| 183 | C4×D12 | C23 | 1 | 6 | yes | — |
| 184 | C4×D12 | C23 | 1 | 12 | yes | — |
| 185 | C4×D12 | C23 | 1 | 12 | yes | — |
| 186 | #872 | C23 | 1 | 12 | yes | — |
| 187 | #872 | C23 | 1 | 12 | yes | — |
| 188 | C42×D3 | C23 | 1 | 12 | yes | — |
| 189 | #870 | C23 | 1 | 2 | yes | — |
| 190 | #870 | C23 | 1 | 12 | yes | — |
| 191 | #869 | C23 | 1 | 6 | yes | — |
| 192 | C4×Dic6 | C23 | 1 | 6 | yes | — |
| 193 | C4×Dic6 | C23 | 1 | 12 | yes | — |
| 194 | #564 | — | 3 | 1 | no | — |
| 195 | #563 | — | 3 | 12 | no | — |
| 196 | #563 | — | 3 | 6 | no | — |
| 197 | #563 | — | 3 | 12 | no | — |
| 198 | #562 | — | 3 | 3 | no | — |
| 199 | #562 | — | 3 | 6 | no | — |
| 200 | #562 | — | 3 | 12 | no | — |
| 201 | #562 | — | 3 | 24 | no | — |
| 202 | #557 | — | 3 | 4 | no | — |
| 203 | #557 | — | 3 | 2 | no | — |
| 204 | #557 | C2×D3 | 1 | 4 | yes | — |
| 205 | #554 | — | 3 | 12 | no | — |
| 206 | #554 | — | 3 | 12 | no | — |
| 207 | #554 | — | 3 | 12 | no | — |
| 208 | #554 | — | 3 | 12 | no | — |
| 209 | #554 | C2×D3 | 1 | 12 | yes | — |
| 210 | #553 | — | 3 | 12 | no | — |
| 211 | #553 | — | 3 | 12 | no | — |
| 212 | #553 | — | 3 | 12 | no | — |
| 213 | #553 | — | 3 | 12 | no | — |
| 214 | #553 | — | 3 | 12 | no | — |
| 215 | #550 | — | 3 | 4 | no | — |
| 216 | #550 | — | 3 | 4 | no | — |
| 217 | #550 | — | 3 | 2 | no | — |
| 218 | #550 | — | 3 | 12 | no | — |
| 219 | #550 | — | 3 | 12 | no | — |
| 220 | #550 | — | 3 | 6 | no | — |
| 221 | #547 | — | 3 | 12 | no | — |
| 222 | #547 | — | 3 | 12 | no | — |
| 223 | #547 | — | 3 | 24 | no | — |
| 224 | #547 | — | 3 | 6 | no | — |
| 225 | #547 | — | 3 | 12 | no | — |
| 226 | #547 | — | 3 | 24 | no | — |
| 227 | #544 | — | 3 | 12 | no | — |
| 228 | #544 | — | 3 | 12 | no | — |
| 229 | #544 | C2×D3 | 1 | 6 | yes | — |
| 230 | #540 | — | 3 | 12 | no | — |
| 231 | #540 | — | 3 | 12 | no | — |
| 232 | #540 | — | 3 | 12 | no | — |
| 233 | #540 | — | 3 | 12 | no | — |
| 234 | #540 | — | 3 | 12 | no | — |
| 235 | #539 | — | 3 | 24 | no | — |
| 236 | #539 | — | 3 | 24 | no | — |
| 237 | #539 | — | 3 | 12 | no | — |
| 238 | #537 | — | 3 | 24 | no | — |
| 239 | #537 | — | 3 | 24 | no | — |
| 240 | #537 | — | 3 | 12 | no | — |
| 241 | #533 | — | 3 | 12 | no | — |
| 242 | #533 | C2×D3 | 1 | 3 | yes | — |
| 243 | #532 | — | 3 | 12 | no | — |
| 244 | #532 | — | 3 | 12 | no | — |
| 245 | #532 | — | 3 | 6 | no | — |
| 246 | #529 | — | 3 | 12 | no | — |
| 247 | #529 | — | 3 | 12 | no | — |
| 248 | #529 | — | 3 | 6 | no | — |
| 249 | C2×#125 | — | 3 | 12 | no | — |
| 250 | C2×#125 | C2×D3 | 1 | 3 | yes | — |
| 251 | #520 | — | 3 | 4 | no | — |
| 252 | #520 | — | 3 | 4 | no | — |
| 253 | #520 | C2×D3 | 1 | 2 | yes | — |
| 254 | C4×#41 | — | 3 | 4 | no | — |
| 255 | C4×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 256 | C3×#41 | — | 2 | 4 | no | — |
| 257 | C2×C3×Q8 | C24 | 1 | 12 | yes | — |
| 258 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 259 | C2×C3×D4 | C24 | 1 | 3 | yes | — |
| 260 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 261 | C22×C3×C4 | C24 | 1 | 6 | yes | — |
| 262 | C22×C3×C4 | C24 | 1 | 12 | yes | — |
| 263 | C2×#67 | C24 | 1 | 24 | yes | — |
| 264 | C2×#67 | C24 | 1 | 12 | yes | — |
| 265 | #239 | — | 2 | 16 | no | — |
| 266 | #239 | — | 8 | 24 | no | — |
| 267 | #235 | — | 8 | 24 | no | — |
| 268 | #235 | — | 8 | 12 | no | — |
| 269 | C2×D12 | C24 | 1 | 12 | yes | — |
| 270 | C2×D12 | C24 | 1 | 6 | yes | — |
| 271 | C2×D12 | C24 | 1 | 12 | yes | — |
| 272 | C2×D12 | C24 | 1 | 12 | yes | — |
| 273 | C2×D12 | C24 | 1 | 24 | yes | — |
| 274 | C2×C4×D3 | C24 | 1 | 12 | yes | — |
| 275 | C2×C4×D3 | C24 | 1 | 12 | yes | — |
| 276 | C2×C4×D3 | C24 | 1 | 12 | yes | — |
| 277 | C2×C4×D3 | C24 | 1 | 24 | yes | — |
| 278 | C2×C4×D3 | C24 | 1 | 24 | yes | — |
| 279 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 280 | C2×Dic6 | C24 | 1 | 12 | yes | — |
| 281 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 282 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 283 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 284 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 285 | C3×C4⋊C4 | C24 | 1 | 12 | yes | — |
| 286 | C3×C4⋊C4 | C24 | 1 | 24 | yes | — |
| 287 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 288 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 289 | C3×C22⋊C4 | C24 | 1 | 12 | yes | — |
| 290 | C3×C22⋊C4 | C24 | 1 | 6 | yes | — |
| 291 | C3×C42 | C24 | 1 | 6 | yes | — |
| 292 | C3×C42 | C24 | 1 | 12 | yes | — |
| 293 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 294 | C3×C42 | C24 | 1 | 3 | yes | — |
| 295 | #217 | C24 | 1 | 12 | yes | — |
| 296 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 297 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 298 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 299 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 300 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 301 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 302 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 303 | (C2×D3)⋊C4 | C24 | 1 | 24 | yes | — |
| 304 | (C2×D3)⋊C4 | C24 | 1 | 12 | yes | — |
| 305 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 306 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 307 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 308 | C4⋊Dic3 | C24 | 1 | 12 | yes | — |
| 309 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 310 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 311 | Dic3⋊C4 | C24 | 1 | 4 | yes | — |
| 312 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 313 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 314 | Dic3⋊C4 | C24 | 1 | 4 | yes | — |
| 315 | Dic3⋊C4 | C24 | 1 | 4 | yes | — |
| 316 | Dic3⋊C4 | C24 | 1 | 24 | yes | — |
| 317 | Dic3⋊C4 | C24 | 1 | 4 | yes | — |
| 318 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 319 | Dic3⋊C4 | C24 | 1 | 12 | yes | — |
| 320 | C4×Dic3 | C24 | 1 | 12 | yes | — |
| 321 | C4×Dic3 | C24 | 1 | 4 | yes | — |
| 322 | C4×Dic3 | C24 | 1 | 12 | yes | — |
| 323 | C2×#41 | — | 3 | 4 | no | — |
| 324 | C2×#41 | — | 3 | 24 | no | — |
| 325 | C2×#41 | — | 3 | 24 | no | — |
| 326 | C2×#41 | — | 3 | 12 | no | — |
| 327 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 328 | C4⋊Q8 | — | 3 | 12 | no | — |
| 329 | C4⋊Q8 | — | 3 | 12 | no | — |
| 330 | C4⋊Q8 | — | 3 | 12 | no | — |
| 331 | C4⋊Q8 | — | 3 | 6 | no | — |
| 332 | C4⋊Q8 | C22×D3 | 1 | 12 | yes | — |
| 333 | C4⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 334 | #127 | — | 3 | 12 | no | — |
| 335 | #127 | — | 3 | 12 | no | — |
| 336 | #127 | — | 3 | 6 | no | — |
| 337 | #126 | — | 3 | 12 | no | — |
| 338 | #126 | — | 3 | 12 | no | — |
| 339 | #126 | — | 3 | 12 | no | — |
| 340 | #126 | — | 3 | 12 | no | — |
| 341 | #126 | — | 3 | 12 | no | — |
| 342 | #125 | — | 3 | 12 | no | — |
| 343 | #125 | — | 3 | 24 | no | — |
| 344 | #125 | — | 3 | 12 | no | — |
| 345 | #125 | — | 3 | 12 | no | — |
| 346 | #125 | — | 3 | 4 | no | — |
| 347 | #125 | — | 3 | 4 | no | — |
| 348 | #125 | — | 3 | 4 | no | — |
| 349 | #125 | — | 3 | 12 | no | — |
| 350 | #125 | — | 3 | 2 | no | — |
| 351 | #125 | C22×D3 | 1 | 12 | yes | — |
| 352 | #125 | C22×D3 | 1 | 3 | yes | — |
| 353 | #125 | C22×D3 | 1 | 6 | yes | — |
| 354 | #125 | C22×D3 | 1 | 12 | yes | — |
| 355 | #125 | C22×D3 | 1 | 1 | yes | characteristic |
| 356 | #124 | — | 3 | 12 | no | — |
| 357 | #124 | — | 3 | 12 | no | — |
| 358 | #124 | — | 3 | 6 | no | — |
| 359 | #123 | — | 3 | 12 | no | — |
| 360 | #123 | — | 3 | 24 | no | — |
| 361 | #123 | — | 3 | 12 | no | — |
| 362 | #123 | — | 3 | 12 | no | — |
| 363 | #123 | — | 3 | 12 | no | — |
| 364 | #123 | — | 3 | 24 | no | — |
| 365 | #123 | — | 3 | 24 | no | — |
| 366 | #123 | — | 3 | 24 | no | — |
| 367 | #123 | — | 3 | 12 | no | — |
| 368 | #123 | — | 3 | 24 | no | — |
| 369 | C22⋊Q8 | — | 3 | 12 | no | — |
| 370 | C22⋊Q8 | — | 3 | 12 | no | — |
| 371 | C22⋊Q8 | — | 3 | 24 | no | — |
| 372 | C22⋊Q8 | — | 3 | 6 | no | — |
| 373 | C22⋊Q8 | — | 3 | 12 | no | — |
| 374 | C22⋊Q8 | — | 3 | 12 | no | — |
| 375 | C22⋊Q8 | — | 3 | 12 | no | — |
| 376 | C22⋊Q8 | — | 3 | 12 | no | — |
| 377 | C22⋊Q8 | — | 3 | 24 | no | — |
| 378 | C22⋊Q8 | — | 3 | 24 | no | — |
| 379 | C22⋊Q8 | — | 3 | 24 | no | — |
| 380 | C22⋊Q8 | C22×D3 | 1 | 12 | yes | — |
| 381 | C22⋊Q8 | C22×D3 | 1 | 24 | yes | — |
| 382 | #121 | — | 3 | 12 | no | — |
| 383 | #121 | — | 3 | 6 | no | — |
| 384 | #121 | — | 3 | 12 | no | — |
| 385 | #121 | — | 3 | 12 | no | — |
| 386 | #121 | — | 3 | 24 | no | — |
| 387 | #121 | — | 3 | 12 | no | — |
| 388 | #121 | — | 3 | 24 | no | — |
| 389 | #121 | — | 3 | 12 | no | — |
| 390 | #121 | — | 3 | 12 | no | — |
| 391 | #121 | — | 3 | 12 | no | — |
| 392 | #121 | — | 3 | 24 | no | — |
| 393 | #121 | — | 3 | 24 | no | — |
| 394 | #121 | — | 3 | 12 | no | — |
| 395 | #121 | — | 3 | 24 | no | — |
| 396 | #121 | — | 3 | 24 | no | — |
| 397 | #121 | — | 3 | 24 | no | — |
| 398 | C4×Q8 | — | 3 | 4 | no | — |
| 399 | C4×Q8 | — | 3 | 12 | no | — |
| 400 | C4×Q8 | — | 3 | 6 | no | — |
| 401 | C4×Q8 | C22×D3 | 1 | 4 | yes | — |
| 402 | C4×Q8 | C22×D3 | 1 | 2 | yes | — |
| 403 | C4×Q8 | C22×D3 | 1 | 12 | yes | — |
| 404 | C4×D4 | — | 3 | 12 | no | — |
| 405 | C4×D4 | — | 3 | 24 | no | — |
| 406 | C4×D4 | — | 3 | 12 | no | — |
| 407 | C4×D4 | — | 3 | 12 | no | — |
| 408 | C4×D4 | — | 3 | 12 | no | — |
| 409 | C4×D4 | — | 3 | 24 | no | — |
| 410 | C4×D4 | — | 3 | 12 | no | — |
| 411 | C4×D4 | — | 3 | 12 | no | — |
| 412 | C4×D4 | — | 3 | 12 | no | — |
| 413 | C4×D4 | — | 3 | 12 | no | — |
| 414 | C4×D4 | — | 3 | 6 | no | — |
| 415 | C4×D4 | — | 3 | 12 | no | — |
| 416 | C4×D4 | C22×D3 | 1 | 6 | yes | — |
| 417 | C4×D4 | C22×D3 | 1 | 12 | yes | — |
| 418 | #117 | — | 3 | 12 | no | — |
| 419 | #117 | — | 3 | 12 | no | — |
| 420 | #117 | — | 3 | 12 | no | — |
| 421 | #117 | C22×D3 | 1 | 3 | yes | — |
| 422 | #117 | C22×D3 | 1 | 6 | yes | — |
| 423 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 424 | C2×C4⋊C4 | — | 3 | 12 | no | — |
| 425 | C2×C4⋊C4 | — | 3 | 24 | no | — |
| 426 | C2×C4⋊C4 | — | 3 | 24 | no | — |
| 427 | C2×C4⋊C4 | C22×D3 | 1 | 6 | yes | — |
| 428 | C2×C4⋊C4 | C22×D3 | 1 | 12 | yes | — |
| 429 | C2×C42 | — | 3 | 12 | no | — |
| 430 | C2×C42 | C22×D3 | 1 | 3 | yes | — |
| 431 | C23×C3 | C25 | 1 | 3 | yes | — |
| 432 | C22×D3 | C25 | 1 | 12 | yes | — |
| 433 | C3×Q8 | — | 4 | 12 | no | — |
| 434 | C3×Q8 | 2−1+4 | 1 | 4 | yes | — |
| 435 | C3×D4 | — | 2 | 6 | no | — |
| 436 | C2×C3×C4 | — | 2 | 6 | no | — |
| 437 | C2×C3×C4 | — | 4 | 6 | no | — |
| 438 | C2×C3×C4 | — | 4 | 12 | no | — |
| 439 | C2×C3×C4 | C25 | 1 | 4 | yes | — |
| 440 | C2×C3×C4 | C25 | 1 | 12 | yes | — |
| 441 | C2×C3×C4 | C25 | 1 | 6 | yes | — |
| 442 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 443 | C2×C3×C4 | C25 | 1 | 2 | yes | — |
| 444 | C2×C3×C4 | C25 | 1 | 3 | yes | — |
| 445 | #67 | — | 4 | 12 | no | — |
| 446 | #67 | — | 4 | 24 | no | — |
| 447 | C2×Dic3 | C25 | 1 | 4 | yes | — |
| 448 | C2×Dic3 | C25 | 1 | 4 | yes | — |
| 449 | C2×Dic3 | C25 | 1 | 12 | yes | — |
| 450 | D12 | — | 2 | 24 | no | — |
| 451 | D12 | — | 4 | 6 | no | — |
| 452 | D12 | — | 4 | 24 | no | — |
| 453 | D12 | — | 4 | 12 | no | — |
| 454 | D12 | — | 4 | 12 | no | — |
| 455 | C4×D3 | — | 2 | 24 | no | — |
| 456 | C4×D3 | — | 4 | 12 | no | — |
| 457 | C4×D3 | — | 4 | 24 | no | — |
| 458 | C4×D3 | — | 4 | 24 | no | — |
| 459 | C4×D3 | — | 4 | 12 | no | — |
| 460 | Dic6 | — | 4 | 12 | no | — |
| 461 | Dic6 | — | 4 | 6 | no | — |
| 462 | #41 | — | 2 | 4 | no | — |
| 463 | #41 | — | 6 | 16 | no | — |
| 464 | #41 | — | 24 | 12 | no | — |
| 465 | #41 | — | 24 | 24 | no | — |
| 466 | #41 | — | 24 | 24 | no | — |
| 467 | C2×Q8 | — | 3 | 12 | no | — |
| 468 | C2×Q8 | — | 3 | 6 | no | — |
| 469 | C2×Q8 | C23×D3 | 1 | 12 | yes | — |
| 470 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 471 | C2×D4 | — | 3 | 24 | no | — |
| 472 | C2×D4 | — | 3 | 12 | no | — |
| 473 | C2×D4 | — | 3 | 12 | no | — |
| 474 | C2×D4 | — | 3 | 24 | no | — |
| 475 | C2×D4 | — | 3 | 12 | no | — |
| 476 | C2×D4 | — | 3 | 12 | no | — |
| 477 | C2×D4 | — | 3 | 6 | no | — |
| 478 | C2×D4 | C23×D3 | 1 | 3 | yes | — |
| 479 | C22×C4 | — | 3 | 12 | no | — |
| 480 | C22×C4 | — | 3 | 12 | no | — |
| 481 | C22×C4 | — | 3 | 12 | no | — |
| 482 | C22×C4 | — | 3 | 24 | no | — |
| 483 | C22×C4 | — | 3 | 24 | no | — |
| 484 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 485 | C22×C4 | C23×D3 | 1 | 6 | yes | — |
| 486 | C22×C4 | C23×D3 | 1 | 12 | yes | — |
| 487 | C4⋊C4 | — | 3 | 12 | no | — |
| 488 | C4⋊C4 | — | 3 | 12 | no | — |
| 489 | C4⋊C4 | — | 3 | 12 | no | — |
| 490 | C4⋊C4 | — | 3 | 24 | no | — |
| 491 | C4⋊C4 | — | 3 | 12 | no | — |
| 492 | C4⋊C4 | — | 3 | 12 | no | — |
| 493 | C4⋊C4 | — | 3 | 12 | no | — |
| 494 | C4⋊C4 | — | 3 | 12 | no | — |
| 495 | C4⋊C4 | — | 3 | 4 | no | — |
| 496 | C4⋊C4 | — | 3 | 4 | no | — |
| 497 | C4⋊C4 | — | 3 | 4 | no | — |
| 498 | C4⋊C4 | — | 3 | 4 | no | — |
| 499 | C4⋊C4 | — | 3 | 2 | no | — |
| 500 | C4⋊C4 | — | 3 | 4 | no | — |
| 501 | C4⋊C4 | — | 3 | 2 | no | — |
| 502 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 503 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 504 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 505 | C4⋊C4 | C23×D3 | 1 | 24 | yes | — |
| 506 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 507 | C4⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 508 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 509 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 510 | C22⋊C4 | — | 3 | 12 | no | — |
| 511 | C22⋊C4 | — | 3 | 12 | no | — |
| 512 | C22⋊C4 | — | 3 | 12 | no | — |
| 513 | C22⋊C4 | — | 3 | 12 | no | — |
| 514 | C22⋊C4 | — | 3 | 12 | no | — |
| 515 | C22⋊C4 | — | 3 | 24 | no | — |
| 516 | C22⋊C4 | — | 3 | 12 | no | — |
| 517 | C22⋊C4 | — | 3 | 12 | no | — |
| 518 | C22⋊C4 | — | 3 | 12 | no | — |
| 519 | C22⋊C4 | — | 3 | 12 | no | — |
| 520 | C22⋊C4 | C23×D3 | 1 | 12 | yes | — |
| 521 | C22⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 522 | C42 | — | 3 | 4 | no | — |
| 523 | C42 | — | 3 | 12 | no | — |
| 524 | C42 | — | 3 | 12 | no | — |
| 525 | C42 | C23×D3 | 1 | 12 | yes | — |
| 526 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 527 | C42 | C23×D3 | 1 | 6 | yes | — |
| 528 | C42 | C23×D3 | 1 | 3 | yes | — |
| 529 | C22×C3 | — | 2 | 3 | no | — |
| 530 | C22×C3 | — | 2 | 6 | no | — |
| 531 | C22×C3 | C26 | 1 | 1 | yes | characteristic |
| 532 | C2×D3 | — | 2 | 12 | no | — |
| 533 | C2×D3 | — | 2 | 12 | no | — |
| 534 | C2×D3 | — | 2 | 12 | no | — |
| 535 | C3×C4 | — | 2 | 1 | no | — |
| 536 | C3×C4 | — | 2 | 2 | no | — |
| 537 | C3×C4 | — | 2 | 12 | no | — |
| 538 | C3×C4 | — | 2 | 6 | no | — |
| 539 | C3×C4 | — | 2 | 4 | no | — |
| 540 | C3×C4 | C2×2−1+4 | 1 | 6 | yes | — |
| 541 | Dic3 | — | 2 | 4 | no | — |
| 542 | Dic3 | — | 2 | 4 | no | — |
| 543 | Dic3 | — | 2 | 12 | no | — |
| 544 | C23 | — | 3 | 12 | no | — |
| 545 | C23 | C24×D3 | 1 | 3 | yes | — |
| 546 | Q8 | — | 4 | 12 | no | — |
| 547 | Q8 | — | 12 | 6 | no | — |
| 548 | Q8 | — | 12 | 12 | no | — |
| 549 | Q8 | #1007 | 1 | 4 | yes | — |
| 550 | D4 | — | 2 | 6 | no | — |
| 551 | D4 | — | 6 | 24 | no | — |
| 552 | D4 | — | 12 | 6 | no | — |
| 553 | D4 | — | 12 | 24 | no | — |
| 554 | D4 | — | 12 | 12 | no | — |
| 555 | D4 | — | 12 | 12 | no | — |
| 556 | D4 | — | 12 | 24 | no | — |
| 557 | D4 | — | 12 | 12 | no | — |
| 558 | C2×C4 | — | 2 | 6 | no | — |
| 559 | C2×C4 | — | 3 | 4 | no | — |
| 560 | C2×C4 | — | 3 | 4 | no | — |
| 561 | C2×C4 | — | 3 | 12 | no | — |
| 562 | C2×C4 | — | 4 | 6 | no | — |
| 563 | C2×C4 | — | 4 | 12 | no | — |
| 564 | C2×C4 | — | 6 | 24 | no | — |
| 565 | C2×C4 | — | 12 | 24 | no | — |
| 566 | C2×C4 | — | 12 | 12 | no | — |
| 567 | C2×C4 | — | 12 | 24 | no | — |
| 568 | C2×C4 | — | 12 | 12 | no | — |
| 569 | C2×C4 | C24×D3 | 1 | 4 | yes | — |
| 570 | C2×C4 | C24×D3 | 1 | 12 | yes | — |
| 571 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 572 | C2×C4 | C24×D3 | 1 | 2 | yes | — |
| 573 | C2×C4 | C24×D3 | 1 | 6 | yes | — |
| 574 | C2×C4 | C24×D3 | 1 | 3 | yes | — |
| 575 | C2×C3 | — | 4 | 3 | no | — |
| 576 | C2×C3 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 577 | C2×C3 | H(7,𝔽2) | 1 | 2 | yes | — |
| 578 | D3 | — | 4 | 12 | no | — |
| 579 | C22 | — | 2 | 3 | no | — |
| 580 | C22 | — | 2 | 6 | no | — |
| 581 | C22 | — | 6 | 12 | no | — |
| 582 | C22 | — | 6 | 12 | no | — |
| 583 | C22 | — | 6 | 12 | no | — |
| 584 | C22 | C25×D3 | 1 | 1 | yes | characteristic |
| 585 | C4 | — | 2 | 1 | no | — |
| 586 | C4 | — | 2 | 2 | no | — |
| 587 | C4 | — | 2 | 12 | no | — |
| 588 | C4 | — | 2 | 6 | no | — |
| 589 | C4 | — | 2 | 4 | no | — |
| 590 | C4 | — | 6 | 4 | no | — |
| 591 | C4 | — | 6 | 12 | no | — |
| 592 | C4 | — | 6 | 4 | no | — |
| 593 | C4 | C2×#1007 | 1 | 6 | yes | — |
| 594 | C3 | #63070 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 595 | C2 | — | 4 | 3 | no | — |
| 596 | C2 | — | 12 | 12 | no | — |
| 597 | C2 | C22×#1007 | 1 | 1 | yes | characteristic |
| 598 | C2 | #87574 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D3 |
| commutator, socle, cosocle | C22×C3 | C26 |
| Fitting | C3×#3504 | C2 |
| hypercenter | #3504 | D3 |
| hypocenter | C3 | #63070 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #3504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#3504 | C2 | semidirect |
| 2. #87023 | C2 | semidirect |
| 3. #87019 | C2 | semidirect |
| 4. #86957 | C2 | semidirect |
| 5. #86939 | C2 | semidirect |
| 6. #86603 | C2 | semidirect |
| 7. #86288 | C2 | semidirect |
| 8. #86286 | C2 | semidirect |
| 9. #86103 | C2 | semidirect |
| 10. #85896 | C2 | semidirect |
| 11. #85853 | C2 | semidirect |
| 85. #3504 | D3 | semidirect |
| 594. C3 | #63070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3504 | 2 |
| #87023 | 2 |
| #87019 | 2 |
| #86957 | 2 |
| #86939 | 2 |
| #86603 | 2 |
| #86288 | 2 |
| #86286 | 2 |
| #86103 | 2 |
| #85896 | 2 |
| #85853 | 2 |
| #63070 | 3 |