Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
874 conjugacy classes of subgroups.
The subgroup lattice has 726 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86765 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #81592 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #81114 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #81072 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#1637 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71917 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71236 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71159 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #71141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #68463 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #68429 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #68254 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #68240 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68197 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68177 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #18709 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C3×D4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 18 | #5817 | — | 2 | 1 | no | — |
| 19 | #5816 | — | 2 | 1 | no | — |
| 20 | #5733 | — | 2 | 1 | no | — |
| 21 | #5730 | — | 2 | 1 | no | — |
| 22 | #5728 | C22 | 1 | 1 | yes | characteristic |
| 23 | #5725 | C22 | 1 | 1 | yes | characteristic |
| 24 | #5721 | C22 | 1 | 1 | yes | characteristic |
| 25 | #5647 | — | 2 | 2 | no | — |
| 26 | #5643 | — | 2 | 1 | no | — |
| 27 | #5638 | — | 2 | 2 | no | — |
| 28 | #5631 | — | 2 | 1 | no | — |
| 29 | #5585 | C22 | 1 | 1 | yes | characteristic |
| 30 | #5578 | C22 | 1 | 1 | yes | characteristic |
| 31 | #5562 | — | 2 | 1 | no | — |
| 32 | #5559 | — | 2 | 1 | no | — |
| 33 | #5557 | C22 | 1 | 1 | yes | characteristic |
| 34 | #5553 | C22 | 1 | 1 | yes | characteristic |
| 35 | C3×#487 | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×#477 | C22 | 1 | 1 | yes | characteristic |
| 37 | C3×#476 | C22 | 1 | 1 | yes | characteristic |
| 38 | #5091 | C22 | 1 | 1 | yes | characteristic |
| 39 | #5091 | C22 | 1 | 1 | yes | characteristic |
| 40 | #5085 | C22 | 1 | 1 | yes | characteristic |
| 41 | #5080 | C22 | 1 | 1 | yes | characteristic |
| 42 | #5020 | C22 | 1 | 1 | yes | characteristic |
| 43 | #5019 | C22 | 1 | 1 | yes | characteristic |
| 44 | #4888 | — | 2 | 1 | no | — |
| 45 | #4876 | — | 2 | 1 | no | — |
| 46 | #4867 | — | 2 | 1 | no | — |
| 47 | #4857 | — | 2 | 1 | no | — |
| 48 | #4851 | C22 | 1 | 1 | yes | characteristic |
| 49 | #4849 | C22 | 1 | 1 | yes | characteristic |
| 50 | #4837 | C22 | 1 | 1 | yes | characteristic |
| 51 | #4835 | C22 | 1 | 1 | yes | characteristic |
| 52 | #4815 | — | 2 | 1 | no | — |
| 53 | #4807 | — | 2 | 2 | no | — |
| 54 | #4797 | — | 2 | 1 | no | — |
| 55 | #4788 | — | 2 | 2 | no | — |
| 56 | #4780 | — | 2 | 1 | no | — |
| 57 | #4767 | — | 2 | 1 | no | — |
| 58 | #4694 | C22 | 1 | 1 | yes | characteristic |
| 59 | C4×D3×C8 | C22 | 1 | 1 | yes | characteristic |
| 60 | C3×#332 | C22 | 1 | 1 | yes | characteristic |
| 61 | C3×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 62 | C3×D4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 63 | #4547 | C22 | 1 | 1 | yes | characteristic |
| 64 | #4535 | C22 | 1 | 1 | yes | characteristic |
| 65 | D4⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 66 | #4485 | C22 | 1 | 1 | yes | characteristic |
| 67 | #4485 | C22 | 1 | 1 | yes | characteristic |
| 68 | #4484 | C22 | 1 | 1 | yes | characteristic |
| 69 | #4484 | C22 | 1 | 1 | yes | characteristic |
| 70 | #4456 | C22 | 1 | 1 | yes | characteristic |
| 71 | #4456 | C22 | 1 | 1 | yes | characteristic |
| 72 | #3554 | — | 3 | 1 | no | — |
| 73 | #3252 | — | 3 | 1 | no | — |
| 74 | #3237 | — | 3 | 1 | no | — |
| 75 | #3167 | — | 3 | 1 | no | — |
| 76 | #1653 | — | 3 | 1 | no | — |
| 77 | #1651 | — | 3 | 1 | no | — |
| 78 | #1642 | — | 3 | 1 | no | — |
| 79 | #1640 | — | 3 | 1 | no | — |
| 80 | #1637 | D3 | 1 | 1 | yes | characteristic, complemented |
| 81 | #1636 | — | 3 | 1 | no | — |
| 82 | #1631 | — | 3 | 1 | no | — |
| 83 | #1630 | — | 3 | 1 | no | — |
| 84 | #1557 | — | 3 | 1 | no | — |
| 85 | #1494 | — | 3 | 1 | no | — |
| 86 | #1493 | — | 3 | 1 | no | — |
| 87 | C22×C3×Q8 | — | 2 | 1 | no | — |
| 88 | C2×#239 | — | 2 | 1 | no | — |
| 89 | C2×#235 | — | 2 | 1 | no | — |
| 90 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 91 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 92 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 93 | C3×C22⋊Q8 | — | 2 | 2 | no | — |
| 94 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 95 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 96 | C3×C4×D4 | — | 2 | 1 | no | — |
| 97 | C3×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 98 | #947 | — | 2 | 2 | no | — |
| 99 | #947 | — | 2 | 1 | no | — |
| 100 | #947 | — | 2 | 1 | no | — |
| 101 | #946 | — | 2 | 2 | no | — |
| 102 | #946 | — | 2 | 2 | no | — |
| 103 | #946 | — | 2 | 2 | no | — |
| 104 | #946 | — | 2 | 1 | no | — |
| 105 | #946 | D4 | 1 | 1 | yes | characteristic |
| 106 | Q8×Dic3 | — | 2 | 1 | no | — |
| 107 | Q8×Dic3 | — | 2 | 1 | no | — |
| 108 | #944 | — | 2 | 1 | no | — |
| 109 | #944 | D4 | 1 | 1 | yes | characteristic |
| 110 | C2×#215 | — | 2 | 2 | no | — |
| 111 | #940 | — | 2 | 1 | no | — |
| 112 | #938 | D4 | 1 | 1 | yes | characteristic |
| 113 | #936 | D4 | 1 | 1 | yes | characteristic |
| 114 | C2×#214 | — | 2 | 1 | no | — |
| 115 | #930 | — | 2 | 2 | no | — |
| 116 | #930 | — | 2 | 1 | no | — |
| 117 | #929 | — | 2 | 2 | no | — |
| 118 | #929 | — | 2 | 2 | no | — |
| 119 | C4×#67 | — | 2 | 2 | no | — |
| 120 | C4×#67 | — | 2 | 1 | no | — |
| 121 | #926 | — | 2 | 1 | no | — |
| 122 | C2×Dic12 | — | 2 | 1 | no | — |
| 123 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 124 | C2×D3×C8 | — | 2 | 1 | no | — |
| 125 | #898 | — | 2 | 2 | no | — |
| 126 | #897 | — | 2 | 2 | no | — |
| 127 | #897 | — | 2 | 1 | no | — |
| 128 | #897 | D4 | 1 | 1 | yes | characteristic |
| 129 | #897 | D4 | 1 | 1 | yes | characteristic |
| 130 | #896 | — | 2 | 1 | no | — |
| 131 | #895 | — | 2 | 1 | no | — |
| 132 | #895 | D4 | 1 | 2 | yes | — |
| 133 | #894 | — | 2 | 2 | no | — |
| 134 | #894 | — | 2 | 2 | no | — |
| 135 | #893 | — | 2 | 1 | no | — |
| 136 | #893 | — | 2 | 1 | no | — |
| 137 | #893 | — | 2 | 1 | no | — |
| 138 | #893 | D4 | 1 | 2 | yes | — |
| 139 | #892 | — | 2 | 1 | no | — |
| 140 | D3×C4⋊C4 | — | 2 | 2 | no | — |
| 141 | #890 | — | 2 | 1 | no | — |
| 142 | #890 | — | 2 | 1 | no | — |
| 143 | #890 | D4 | 1 | 1 | yes | characteristic |
| 144 | #889 | — | 2 | 2 | no | — |
| 145 | #889 | — | 2 | 1 | no | — |
| 146 | #888 | D4 | 1 | 1 | yes | characteristic |
| 147 | #887 | — | 2 | 1 | no | — |
| 148 | #887 | — | 2 | 1 | no | — |
| 149 | #885 | — | 2 | 2 | no | — |
| 150 | #884 | — | 2 | 2 | no | — |
| 151 | #884 | — | 2 | 2 | no | — |
| 152 | #883 | — | 2 | 2 | no | — |
| 153 | #883 | — | 2 | 2 | no | — |
| 154 | #883 | — | 2 | 1 | no | — |
| 155 | #879 | — | 2 | 1 | no | — |
| 156 | #875 | — | 2 | 1 | no | — |
| 157 | #874 | C23 | 1 | 1 | yes | characteristic |
| 158 | C4×D12 | — | 2 | 1 | no | — |
| 159 | #872 | — | 2 | 1 | no | — |
| 160 | C42×D3 | C23 | 1 | 1 | yes | characteristic |
| 161 | #869 | C23 | 1 | 1 | yes | characteristic |
| 162 | C4×Dic6 | — | 2 | 1 | no | — |
| 163 | C4×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 164 | C4×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 165 | C3×#107 | — | 2 | 1 | no | — |
| 166 | C3×#106 | — | 2 | 1 | no | — |
| 167 | C3×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 168 | C3×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 169 | C3×#103 | — | 2 | 1 | no | — |
| 170 | C3×#103 | — | 2 | 2 | no | — |
| 171 | C3×#102 | — | 2 | 1 | no | — |
| 172 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 173 | #835 | — | 2 | 1 | no | — |
| 174 | #821 | — | 2 | 2 | no | — |
| 175 | (C2×D3)⋊C8 | — | 2 | 1 | no | — |
| 176 | #817 | — | 2 | 1 | no | — |
| 177 | #816 | — | 2 | 1 | no | — |
| 178 | #816 | — | 2 | 1 | no | — |
| 179 | #815 | — | 2 | 1 | no | — |
| 180 | Dic3⋊C8 | — | 2 | 1 | no | — |
| 181 | C8×Dic3 | — | 2 | 1 | no | — |
| 182 | #810 | — | 2 | 1 | no | — |
| 183 | #810 | — | 2 | 1 | no | — |
| 184 | #810 | — | 2 | 1 | no | — |
| 185 | #808 | — | 2 | 1 | no | — |
| 186 | #808 | — | 2 | 2 | no | — |
| 187 | #807 | — | 2 | 1 | no | — |
| 188 | #807 | — | 2 | 1 | no | — |
| 189 | C4⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 190 | C4⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 191 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 192 | #562 | — | 6 | 2 | no | — |
| 193 | #559 | — | 3 | 1 | no | — |
| 194 | #559 | — | 6 | 1 | no | — |
| 195 | #557 | — | 3 | 1 | no | — |
| 196 | #554 | — | 6 | 1 | no | — |
| 197 | #550 | — | 3 | 1 | no | — |
| 198 | D4×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 199 | #548 | — | 6 | 1 | no | — |
| 200 | #547 | — | 6 | 1 | no | — |
| 201 | #542 | — | 6 | 1 | no | — |
| 202 | #542 | — | 6 | 1 | no | — |
| 203 | #540 | — | 6 | 1 | no | — |
| 204 | #539 | — | 6 | 2 | no | — |
| 205 | #536 | — | 6 | 1 | no | — |
| 206 | #533 | — | 3 | 1 | no | — |
| 207 | #533 | — | 3 | 1 | no | — |
| 208 | #532 | — | 3 | 1 | no | — |
| 209 | #529 | — | 3 | 1 | no | — |
| 210 | #501 | — | 6 | 1 | no | — |
| 211 | #498 | — | 3 | 1 | no | — |
| 212 | #492 | — | 3 | 1 | no | — |
| 213 | #491 | — | 6 | 1 | no | — |
| 214 | #487 | C2×D3 | 1 | 1 | yes | characteristic |
| 215 | #486 | — | 3 | 1 | no | — |
| 216 | #485 | — | 6 | 1 | no | — |
| 217 | #485 | — | 6 | 1 | no | — |
| 218 | #479 | — | 6 | 1 | no | — |
| 219 | #477 | — | 3 | 1 | no | — |
| 220 | #477 | — | 3 | 1 | no | — |
| 221 | #477 | C2×D3 | 1 | 1 | yes | characteristic |
| 222 | #476 | C2×D3 | 1 | 1 | yes | characteristic |
| 223 | #475 | — | 3 | 1 | no | — |
| 224 | #475 | — | 3 | 1 | no | — |
| 225 | #470 | — | 6 | 1 | no | — |
| 226 | #468 | — | 6 | 1 | no | — |
| 227 | #465 | — | 6 | 2 | no | — |
| 228 | #464 | — | 6 | 1 | no | — |
| 229 | #462 | — | 3 | 1 | no | — |
| 230 | #461 | — | 3 | 1 | no | — |
| 231 | C4×SD16 | — | 6 | 2 | no | — |
| 232 | #432 | — | 3 | 1 | no | — |
| 233 | #423 | — | 3 | 1 | no | — |
| 234 | C2×C4×C8 | — | 3 | 1 | no | — |
| 235 | #332 | — | 3 | 1 | no | — |
| 236 | #332 | C2×D3 | 1 | 1 | yes | characteristic |
| 237 | #331 | — | 3 | 1 | no | — |
| 238 | #331 | — | 3 | 1 | no | — |
| 239 | Q8⋊C8 | — | 3 | 1 | no | — |
| 240 | Q8⋊C8 | — | 3 | 1 | no | — |
| 241 | Q8⋊C8 | — | 3 | 1 | no | — |
| 242 | Q8⋊C8 | — | 3 | 1 | no | — |
| 243 | Q8⋊C8 | — | 3 | 1 | no | — |
| 244 | Q8⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 245 | D4⋊C8 | — | 3 | 1 | no | — |
| 246 | D4⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 247 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 248 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 249 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 250 | C2×C3×Q8 | — | 8 | 1 | no | — |
| 251 | C2×C3×Q8 | — | 8 | 1 | no | — |
| 252 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C22×C3×C4 | — | 2 | 2 | no | — |
| 255 | C22×C3×C4 | — | 2 | 1 | no | — |
| 256 | C2×#67 | — | 2 | 2 | no | — |
| 257 | C2×#67 | — | 2 | 2 | no | — |
| 258 | C2×#67 | — | 2 | 1 | no | — |
| 259 | #239 | — | 8 | 1 | no | — |
| 260 | #239 | — | 8 | 1 | no | — |
| 261 | #235 | — | 8 | 1 | no | — |
| 262 | #235 | — | 8 | 1 | no | — |
| 263 | C2×D12 | — | 2 | 1 | no | — |
| 264 | C2×D12 | — | 2 | 1 | no | — |
| 265 | C2×D12 | — | 2 | 2 | no | — |
| 266 | C2×D12 | C2×D4 | 1 | 2 | yes | — |
| 267 | C2×C4×D3 | — | 2 | 2 | no | — |
| 268 | C2×C4×D3 | — | 2 | 2 | no | — |
| 269 | C2×C4×D3 | — | 2 | 2 | no | — |
| 270 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 271 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 273 | C2×Dic6 | — | 2 | 1 | no | — |
| 274 | C2×Dic6 | — | 2 | 1 | no | — |
| 275 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 276 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C2×C3×C8 | — | 2 | 1 | no | — |
| 278 | C2×C3×C8 | — | 2 | 1 | no | — |
| 279 | C2×C3×C8 | — | 2 | 1 | no | — |
| 280 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 281 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 282 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 283 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 284 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 285 | C3×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 286 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 288 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 289 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 290 | C3×C42 | — | 2 | 1 | no | — |
| 291 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 292 | #217 | — | 2 | 1 | no | — |
| 293 | #217 | — | 2 | 1 | no | — |
| 294 | #217 | — | 2 | 1 | no | — |
| 295 | #215 | — | 4 | 4 | no | — |
| 296 | #214 | — | 8 | 1 | no | — |
| 297 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 298 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 299 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 300 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 301 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 302 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 303 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 304 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 305 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 306 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 307 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 308 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 309 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 310 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 311 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 312 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 313 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 314 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 315 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 316 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 317 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 318 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 319 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 320 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 321 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 322 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 323 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 324 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 325 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 326 | C4×Dic3 | — | 2 | 2 | no | — |
| 327 | C4×Dic3 | — | 2 | 1 | no | — |
| 328 | C4×Dic3 | — | 2 | 1 | no | — |
| 329 | C4×Dic3 | — | 4 | 1 | no | — |
| 330 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 331 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 332 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 333 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 334 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 335 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 336 | Dic12 | — | 8 | 1 | no | — |
| 337 | ΓL(1,𝔽25) | — | 8 | 1 | no | — |
| 338 | D3×C8 | — | 4 | 2 | no | — |
| 339 | C2×#41 | — | 6 | 1 | no | — |
| 340 | C2×#41 | — | 6 | 1 | no | — |
| 341 | C22×Q8 | — | 2 | 1 | no | — |
| 342 | C2×Q16 | — | 6 | 1 | no | — |
| 343 | C2×SD16 | — | 6 | 2 | no | — |
| 344 | C2×SD16 | — | 6 | 1 | no | — |
| 345 | C2×M16 | — | 6 | 1 | no | — |
| 346 | C22×C8 | — | 6 | 1 | no | — |
| 347 | C4⋊Q8 | — | 2 | 1 | no | — |
| 348 | C4⋊Q8 | — | 3 | 1 | no | — |
| 349 | C4⋊Q8 | — | 3 | 1 | no | — |
| 350 | C4⋊Q8 | — | 3 | 1 | no | — |
| 351 | C4⋊Q8 | — | 6 | 1 | no | — |
| 352 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 353 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 354 | #127 | — | 3 | 1 | no | — |
| 355 | #127 | — | 6 | 1 | no | — |
| 356 | #126 | — | 6 | 1 | no | — |
| 357 | #126 | — | 6 | 2 | no | — |
| 358 | #125 | — | 3 | 1 | no | — |
| 359 | #125 | — | 6 | 1 | no | — |
| 360 | #125 | — | 6 | 1 | no | — |
| 361 | #125 | — | 6 | 1 | no | — |
| 362 | #125 | — | 6 | 2 | no | — |
| 363 | #124 | — | 3 | 1 | no | — |
| 364 | #124 | — | 6 | 1 | no | — |
| 365 | #124 | — | 6 | 1 | no | — |
| 366 | #124 | — | 6 | 2 | no | — |
| 367 | #124 | — | 6 | 2 | no | — |
| 368 | #124 | — | 6 | 1 | no | — |
| 369 | #123 | — | 6 | 1 | no | — |
| 370 | #123 | — | 6 | 2 | no | — |
| 371 | #123 | — | 6 | 2 | no | — |
| 372 | #123 | — | 6 | 2 | no | — |
| 373 | #123 | — | 6 | 2 | no | — |
| 374 | #123 | — | 6 | 2 | no | — |
| 375 | #123 | — | 6 | 2 | no | — |
| 376 | C22⋊Q8 | — | 2 | 2 | no | — |
| 377 | C22⋊Q8 | — | 2 | 1 | no | — |
| 378 | C22⋊Q8 | — | 3 | 1 | no | — |
| 379 | C22⋊Q8 | — | 3 | 1 | no | — |
| 380 | C22⋊Q8 | — | 3 | 1 | no | — |
| 381 | C22⋊Q8 | — | 6 | 1 | no | — |
| 382 | C22⋊Q8 | — | 6 | 2 | no | — |
| 383 | C22⋊Q8 | — | 6 | 2 | no | — |
| 384 | C22⋊Q8 | — | 6 | 2 | no | — |
| 385 | C22⋊Q8 | — | 6 | 2 | no | — |
| 386 | C22⋊Q8 | — | 6 | 1 | no | — |
| 387 | C22⋊Q8 | — | 6 | 1 | no | — |
| 388 | #121 | — | 3 | 1 | no | — |
| 389 | #121 | — | 3 | 2 | no | — |
| 390 | #121 | — | 6 | 2 | no | — |
| 391 | #121 | — | 6 | 2 | no | — |
| 392 | #121 | — | 6 | 1 | no | — |
| 393 | #121 | — | 6 | 1 | no | — |
| 394 | #121 | — | 6 | 2 | no | — |
| 395 | C4×Q8 | — | 3 | 1 | no | — |
| 396 | C4×Q8 | — | 3 | 1 | no | — |
| 397 | C4×Q8 | — | 6 | 1 | no | — |
| 398 | C4×Q8 | — | 6 | 1 | no | — |
| 399 | C4×Q8 | — | 6 | 1 | no | — |
| 400 | C4×Q8 | — | 6 | 1 | no | — |
| 401 | C4×Q8 | — | 6 | 1 | no | — |
| 402 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 403 | C4×D4 | — | 2 | 1 | no | — |
| 404 | C4×D4 | — | 3 | 2 | no | — |
| 405 | C4×D4 | — | 6 | 1 | no | — |
| 406 | C4×D4 | — | 6 | 1 | no | — |
| 407 | C4×D4 | — | 6 | 1 | no | — |
| 408 | C4×D4 | — | 6 | 2 | no | — |
| 409 | C4×D4 | — | 6 | 1 | no | — |
| 410 | C4×D4 | — | 6 | 1 | no | — |
| 411 | C4×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 412 | #117 | — | 6 | 1 | no | — |
| 413 | #117 | — | 6 | 1 | no | — |
| 414 | #117 | — | 6 | 1 | no | — |
| 415 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 416 | C2×C42 | — | 3 | 1 | no | — |
| 417 | #107 | — | 2 | 1 | no | — |
| 418 | #107 | — | 6 | 1 | no | — |
| 419 | #107 | — | 6 | 1 | no | — |
| 420 | #106 | — | 2 | 1 | no | — |
| 421 | #106 | — | 6 | 1 | no | — |
| 422 | #106 | — | 6 | 2 | no | — |
| 423 | #106 | — | 6 | 1 | no | — |
| 424 | C4⋊C8 | — | 3 | 1 | no | — |
| 425 | C4⋊C8 | — | 3 | 1 | no | — |
| 426 | C4⋊C8 | — | 6 | 1 | no | — |
| 427 | C4⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 428 | C4⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 429 | #103 | — | 2 | 1 | no | — |
| 430 | #103 | — | 2 | 2 | no | — |
| 431 | #103 | — | 6 | 1 | no | — |
| 432 | #103 | — | 6 | 1 | no | — |
| 433 | #103 | — | 6 | 1 | no | — |
| 434 | #103 | — | 6 | 1 | no | — |
| 435 | #103 | — | 6 | 1 | no | — |
| 436 | #103 | — | 6 | 1 | no | — |
| 437 | #102 | — | 2 | 1 | no | — |
| 438 | #102 | — | 6 | 2 | no | — |
| 439 | C22⋊C8 | — | 6 | 1 | no | — |
| 440 | #97 | — | 6 | 1 | no | — |
| 441 | C4×C8 | — | 3 | 1 | no | — |
| 442 | C4×C8 | — | 6 | 1 | no | — |
| 443 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 444 | C23×C3 | — | 2 | 1 | no | — |
| 445 | C22×D3 | — | 2 | 2 | no | — |
| 446 | C22×D3 | #120 | 1 | 1 | yes | characteristic |
| 447 | C3×Q8 | — | 2 | 1 | no | — |
| 448 | C3×Q8 | — | 2 | 1 | no | — |
| 449 | C3×Q8 | — | 4 | 2 | no | — |
| 450 | C3×Q8 | — | 4 | 1 | no | — |
| 451 | C3×Q8 | — | 4 | 1 | no | — |
| 452 | C3×Q8 | — | 8 | 2 | no | — |
| 453 | C3×D4 | — | 2 | 1 | no | — |
| 454 | C3×D4 | — | 2 | 1 | no | — |
| 455 | C2×C3×C4 | — | 2 | 2 | no | — |
| 456 | C2×C3×C4 | — | 2 | 1 | no | — |
| 457 | C2×C3×C4 | — | 2 | 1 | no | — |
| 458 | C2×C3×C4 | — | 2 | 1 | no | — |
| 459 | C2×C3×C4 | — | 4 | 1 | no | — |
| 460 | C2×C3×C4 | — | 4 | 1 | no | — |
| 461 | C2×C3×C4 | — | 4 | 1 | no | — |
| 462 | C2×C3×C4 | — | 8 | 2 | no | — |
| 463 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 464 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 465 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 466 | #67 | — | 8 | 1 | no | — |
| 467 | #67 | — | 8 | 2 | no | — |
| 468 | #67 | — | 8 | 2 | no | — |
| 469 | C2×Dic3 | — | 2 | 1 | no | — |
| 470 | C2×Dic3 | — | 2 | 1 | no | — |
| 471 | C2×Dic3 | — | 2 | 1 | no | — |
| 472 | C2×Dic3 | — | 2 | 1 | no | — |
| 473 | C2×Dic3 | — | 4 | 1 | no | — |
| 474 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 475 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 476 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 477 | D12 | — | 4 | 2 | no | — |
| 478 | D12 | — | 4 | 1 | no | — |
| 479 | D12 | — | 4 | 1 | no | — |
| 480 | D12 | — | 4 | 1 | no | — |
| 481 | D12 | — | 4 | 1 | no | — |
| 482 | D12 | — | 8 | 2 | no | — |
| 483 | C4×D3 | — | 2 | 1 | no | — |
| 484 | C4×D3 | — | 2 | 1 | no | — |
| 485 | C4×D3 | — | 2 | 1 | no | — |
| 486 | C4×D3 | — | 2 | 1 | no | — |
| 487 | C4×D3 | — | 4 | 1 | no | — |
| 488 | C4×D3 | — | 8 | 2 | no | — |
| 489 | C4×D3 | — | 8 | 2 | no | — |
| 490 | C4×D3 | — | 8 | 2 | no | — |
| 491 | Dic6 | — | 2 | 1 | no | — |
| 492 | Dic6 | — | 2 | 1 | no | — |
| 493 | Dic6 | — | 2 | 1 | no | — |
| 494 | Dic6 | — | 2 | 1 | no | — |
| 495 | Dic6 | — | 4 | 1 | no | — |
| 496 | Dic6 | — | 4 | 1 | no | — |
| 497 | Dic6 | — | 8 | 1 | no | — |
| 498 | C3×C8 | — | 4 | 1 | no | — |
| 499 | C3×C8 | — | 4 | 1 | no | — |
| 500 | C3×C8 | — | 4 | 1 | no | — |
| 501 | C3⋊C8 | — | 2 | 2 | no | — |
| 502 | C3⋊C8 | — | 4 | 1 | no | — |
| 503 | C3⋊C8 | — | 4 | 1 | no | — |
| 504 | #41 | — | 24 | 1 | no | — |
| 505 | #41 | — | 24 | 1 | no | — |
| 506 | #41 | — | 24 | 1 | no | — |
| 507 | #41 | — | 24 | 1 | no | — |
| 508 | C2×Q8 | — | 2 | 2 | no | — |
| 509 | C2×Q8 | — | 2 | 1 | no | — |
| 510 | C2×Q8 | — | 2 | 1 | no | — |
| 511 | C2×Q8 | — | 3 | 1 | no | — |
| 512 | C2×Q8 | — | 3 | 1 | no | — |
| 513 | C2×Q8 | — | 6 | 1 | no | — |
| 514 | C2×Q8 | — | 6 | 1 | no | — |
| 515 | C2×Q8 | — | 8 | 1 | no | — |
| 516 | C2×Q8 | — | 8 | 1 | no | — |
| 517 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 518 | C2×D4 | — | 3 | 2 | no | — |
| 519 | C2×D4 | — | 6 | 2 | no | — |
| 520 | C2×D4 | — | 6 | 1 | no | — |
| 521 | C2×D4 | — | 6 | 2 | no | — |
| 522 | C2×D4 | — | 6 | 2 | no | — |
| 523 | C2×D4 | — | 6 | 1 | no | — |
| 524 | C2×D4 | — | 6 | 1 | no | — |
| 525 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 526 | C22×C4 | — | 2 | 2 | no | — |
| 527 | C22×C4 | — | 2 | 1 | no | — |
| 528 | C22×C4 | — | 3 | 1 | no | — |
| 529 | C22×C4 | — | 3 | 1 | no | — |
| 530 | C22×C4 | — | 3 | 1 | no | — |
| 531 | C22×C4 | — | 6 | 2 | no | — |
| 532 | C22×C4 | — | 6 | 2 | no | — |
| 533 | C22×C4 | — | 6 | 2 | no | — |
| 534 | Q16 | — | 24 | 1 | no | — |
| 535 | SD16 | — | 12 | 4 | no | — |
| 536 | SD16 | — | 24 | 1 | no | — |
| 537 | M16 | — | 24 | 1 | no | — |
| 538 | C2×C8 | — | 2 | 1 | no | — |
| 539 | C2×C8 | — | 2 | 1 | no | — |
| 540 | C2×C8 | — | 2 | 1 | no | — |
| 541 | C2×C8 | — | 6 | 1 | no | — |
| 542 | C2×C8 | — | 6 | 1 | no | — |
| 543 | C2×C8 | — | 6 | 1 | no | — |
| 544 | C2×C8 | — | 12 | 2 | no | — |
| 545 | C4⋊C4 | — | 2 | 2 | no | — |
| 546 | C4⋊C4 | — | 2 | 1 | no | — |
| 547 | C4⋊C4 | — | 2 | 1 | no | — |
| 548 | C4⋊C4 | — | 2 | 1 | no | — |
| 549 | C4⋊C4 | — | 2 | 1 | no | — |
| 550 | C4⋊C4 | — | 3 | 1 | no | — |
| 551 | C4⋊C4 | — | 3 | 1 | no | — |
| 552 | C4⋊C4 | — | 6 | 1 | no | — |
| 553 | C4⋊C4 | — | 6 | 1 | no | — |
| 554 | C4⋊C4 | — | 6 | 1 | no | — |
| 555 | C4⋊C4 | — | 6 | 1 | no | — |
| 556 | C4⋊C4 | — | 6 | 1 | no | — |
| 557 | C4⋊C4 | — | 6 | 1 | no | — |
| 558 | C4⋊C4 | — | 6 | 1 | no | — |
| 559 | C4⋊C4 | — | 6 | 1 | no | — |
| 560 | C4⋊C4 | — | 6 | 2 | no | — |
| 561 | C4⋊C4 | — | 6 | 2 | no | — |
| 562 | C4⋊C4 | — | 6 | 2 | no | — |
| 563 | C4⋊C4 | — | 6 | 1 | no | — |
| 564 | C4⋊C4 | — | 6 | 1 | no | — |
| 565 | C4⋊C4 | — | 6 | 1 | no | — |
| 566 | C4⋊C4 | — | 6 | 1 | no | — |
| 567 | C4⋊C4 | — | 12 | 1 | no | — |
| 568 | C4⋊C4 | — | 12 | 1 | no | — |
| 569 | C4⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 570 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 571 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 572 | C22⋊C4 | — | 2 | 2 | no | — |
| 573 | C22⋊C4 | — | 2 | 1 | no | — |
| 574 | C22⋊C4 | — | 6 | 2 | no | — |
| 575 | C22⋊C4 | — | 6 | 2 | no | — |
| 576 | C22⋊C4 | — | 6 | 1 | no | — |
| 577 | C22⋊C4 | — | 6 | 1 | no | — |
| 578 | C22⋊C4 | — | 6 | 1 | no | — |
| 579 | C22⋊C4 | — | 6 | 2 | no | — |
| 580 | C22⋊C4 | — | 6 | 2 | no | — |
| 581 | C22⋊C4 | — | 6 | 2 | no | — |
| 582 | C22⋊C4 | — | 6 | 2 | no | — |
| 583 | C22⋊C4 | — | 6 | 1 | no | — |
| 584 | C22⋊C4 | — | 6 | 1 | no | — |
| 585 | C22⋊C4 | — | 6 | 1 | no | — |
| 586 | C22⋊C4 | — | 12 | 1 | no | — |
| 587 | C42 | — | 2 | 1 | no | — |
| 588 | C42 | — | 3 | 1 | no | — |
| 589 | C42 | — | 3 | 1 | no | — |
| 590 | C42 | — | 3 | 1 | no | — |
| 591 | C42 | — | 6 | 2 | no | — |
| 592 | C42 | — | 6 | 1 | no | — |
| 593 | C42 | — | 6 | 1 | no | — |
| 594 | C42 | — | 12 | 1 | no | — |
| 595 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 596 | C22×C3 | — | 4 | 1 | no | — |
| 597 | C22×C3 | — | 4 | 1 | no | — |
| 598 | C22×C3 | — | 4 | 1 | no | — |
| 599 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 600 | C2×D3 | — | 2 | 1 | no | — |
| 601 | C2×D3 | — | 2 | 1 | no | — |
| 602 | C2×D3 | — | 2 | 1 | no | — |
| 603 | C2×D3 | — | 4 | 2 | no | — |
| 604 | C2×D3 | — | 4 | 2 | no | — |
| 605 | C2×D3 | — | 4 | 2 | no | — |
| 606 | C3×C4 | — | 2 | 1 | no | — |
| 607 | C3×C4 | — | 4 | 1 | no | — |
| 608 | C3×C4 | — | 4 | 2 | no | — |
| 609 | C3×C4 | — | 4 | 1 | no | — |
| 610 | C3×C4 | — | 4 | 1 | no | — |
| 611 | C3×C4 | — | 8 | 1 | no | — |
| 612 | C3×C4 | #577 | 1 | 1 | yes | characteristic |
| 613 | C3×C4 | #577 | 1 | 1 | yes | characteristic |
| 614 | C3×C4 | #577 | 1 | 1 | yes | characteristic |
| 615 | C3×C4 | #578 | 1 | 1 | yes | characteristic |
| 616 | Dic3 | — | 2 | 1 | no | — |
| 617 | Dic3 | — | 2 | 1 | no | — |
| 618 | Dic3 | — | 2 | 1 | no | — |
| 619 | Dic3 | — | 4 | 1 | no | — |
| 620 | Dic3 | — | 4 | 1 | no | — |
| 621 | Dic3 | — | 4 | 1 | no | — |
| 622 | Dic3 | — | 4 | 1 | no | — |
| 623 | Dic3 | — | 8 | 1 | no | — |
| 624 | C23 | — | 2 | 1 | no | — |
| 625 | C23 | — | 3 | 1 | no | — |
| 626 | C23 | — | 6 | 2 | no | — |
| 627 | Q8 | — | 2 | 1 | no | — |
| 628 | Q8 | — | 2 | 1 | no | — |
| 629 | Q8 | — | 4 | 2 | no | — |
| 630 | Q8 | — | 4 | 1 | no | — |
| 631 | Q8 | — | 4 | 1 | no | — |
| 632 | Q8 | — | 6 | 1 | no | — |
| 633 | Q8 | — | 6 | 1 | no | — |
| 634 | Q8 | — | 6 | 1 | no | — |
| 635 | Q8 | — | 6 | 1 | no | — |
| 636 | Q8 | — | 8 | 2 | no | — |
| 637 | Q8 | — | 12 | 1 | no | — |
| 638 | Q8 | — | 12 | 1 | no | — |
| 639 | Q8 | — | 24 | 1 | no | — |
| 640 | D4 | — | 2 | 1 | no | — |
| 641 | D4 | — | 2 | 1 | no | — |
| 642 | D4 | — | 12 | 2 | no | — |
| 643 | D4 | — | 12 | 1 | no | — |
| 644 | D4 | — | 12 | 1 | no | — |
| 645 | D4 | — | 12 | 1 | no | — |
| 646 | D4 | — | 12 | 1 | no | — |
| 647 | D4 | — | 24 | 2 | no | — |
| 648 | D4 | — | 24 | 1 | no | — |
| 649 | D4 | — | 24 | 2 | no | — |
| 650 | D4 | — | 24 | 2 | no | — |
| 651 | C2×C4 | — | 2 | 1 | no | — |
| 652 | C2×C4 | — | 2 | 1 | no | — |
| 653 | C2×C4 | — | 2 | 2 | no | — |
| 654 | C2×C4 | — | 2 | 1 | no | — |
| 655 | C2×C4 | — | 3 | 1 | no | — |
| 656 | C2×C4 | — | 3 | 1 | no | — |
| 657 | C2×C4 | — | 3 | 1 | no | — |
| 658 | C2×C4 | — | 4 | 1 | no | — |
| 659 | C2×C4 | — | 4 | 1 | no | — |
| 660 | C2×C4 | — | 4 | 1 | no | — |
| 661 | C2×C4 | — | 6 | 1 | no | — |
| 662 | C2×C4 | — | 6 | 1 | no | — |
| 663 | C2×C4 | — | 6 | 1 | no | — |
| 664 | C2×C4 | — | 6 | 1 | no | — |
| 665 | C2×C4 | — | 6 | 1 | no | — |
| 666 | C2×C4 | — | 6 | 1 | no | — |
| 667 | C2×C4 | — | 6 | 1 | no | — |
| 668 | C2×C4 | — | 6 | 1 | no | — |
| 669 | C2×C4 | — | 8 | 2 | no | — |
| 670 | C2×C4 | — | 12 | 1 | no | — |
| 671 | C2×C4 | — | 12 | 1 | no | — |
| 672 | C2×C4 | — | 24 | 2 | no | — |
| 673 | C2×C4 | — | 24 | 2 | no | — |
| 674 | C2×C4 | — | 24 | 2 | no | — |
| 675 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 676 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 677 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 678 | C8 | — | 4 | 1 | no | — |
| 679 | C8 | — | 4 | 1 | no | — |
| 680 | C8 | — | 4 | 1 | no | — |
| 681 | C8 | — | 6 | 2 | no | — |
| 682 | C8 | — | 12 | 1 | no | — |
| 683 | C8 | — | 12 | 1 | no | — |
| 684 | C2×C3 | — | 8 | 1 | no | — |
| 685 | C2×C3 | #3009 | 1 | 1 | yes | characteristic |
| 686 | C2×C3 | #3013 | 1 | 1 | yes | characteristic |
| 687 | C2×C3 | #3018 | 1 | 1 | yes | characteristic |
| 688 | D3 | — | 4 | 1 | no | — |
| 689 | D3 | — | 8 | 2 | no | — |
| 690 | C22 | — | 4 | 1 | no | — |
| 691 | C22 | — | 4 | 1 | no | — |
| 692 | C22 | — | 4 | 1 | no | — |
| 693 | C22 | — | 6 | 1 | no | — |
| 694 | C22 | — | 6 | 1 | no | — |
| 695 | C22 | — | 6 | 1 | no | — |
| 696 | C22 | — | 12 | 2 | no | — |
| 697 | C22 | — | 12 | 2 | no | — |
| 698 | C22 | — | 12 | 2 | no | — |
| 699 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 700 | C4 | — | 2 | 1 | no | — |
| 701 | C4 | — | 4 | 1 | no | — |
| 702 | C4 | — | 4 | 1 | no | — |
| 703 | C4 | — | 4 | 2 | no | — |
| 704 | C4 | — | 4 | 1 | no | — |
| 705 | C4 | — | 6 | 1 | no | — |
| 706 | C4 | — | 6 | 1 | no | — |
| 707 | C4 | — | 6 | 1 | no | — |
| 708 | C4 | — | 8 | 1 | no | — |
| 709 | C4 | — | 12 | 1 | no | — |
| 710 | C4 | — | 12 | 1 | no | — |
| 711 | C4 | — | 12 | 1 | no | — |
| 712 | C4 | — | 12 | 1 | no | — |
| 713 | C4 | — | 24 | 1 | no | — |
| 714 | C4 | #5762 | 1 | 1 | yes | characteristic |
| 715 | C4 | #5766 | 1 | 1 | yes | characteristic |
| 716 | C4 | #5775 | 1 | 1 | yes | characteristic |
| 717 | C4 | #5778 | 1 | 1 | yes | characteristic |
| 718 | C3 | #18709 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 719 | C2 | — | 8 | 1 | no | — |
| 720 | C2 | — | 12 | 1 | no | — |
| 721 | C2 | — | 24 | 2 | no | — |
| 722 | C2 | #80148 | 1 | 1 | yes | characteristic |
| 723 | C2 | #80186 | 1 | 1 | yes | characteristic |
| 724 | C2 | #80284 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #81592 | C2 | semidirect |
| 3. #81114 | C2 | semidirect |
| 4. #81072 | C2 | semidirect |
| 5. C3×#1637 | C2 | semidirect |
| 6. #71917 | C2 | semidirect |
| 7. #71236 | C2 | semidirect |
| 8. #71159 | C2 | semidirect |
| 9. #71141 | C2 | semidirect |
| 10. #68463 | C2 | semidirect |
| 11. #68429 | C2 | semidirect |
| 12. #68254 | C2 | semidirect |
| 13. #68240 | C2 | semidirect |
| 14. #68197 | C2 | semidirect |
| 15. #68177 | C2 | semidirect |
| 80. #1637 | D3 | semidirect |
| 718. C3 | #18709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86765 | 2 |
| #81592 | 2 |
| #81114 | 2 |
| #81072 | 2 |
| C3×#1637 | 2 |
| #71917 | 2 |
| #71236 | 2 |
| #71159 | 2 |
| #71141 | 2 |
| #68463 | 2 |
| #68429 | 2 |
| #68254 | 2 |
| #68240 | 2 |
| #68197 | 2 |
| #68177 | 2 |
| #18709 | 3 |