← #34179838
Subgroups — #34179838
Order 20224.
710 conjugacy classes of subgroups.
The subgroup lattice has 462 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #23764337 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #23763396 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #23762090 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23762077 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #23761855 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #23761851 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C79×#3507 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #19098587 | C22 | 1 | 1 | yes | characteristic |
| 9 | #19098587 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C4⋊(C79⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#14579080 | — | 2 | 1 | no | — |
| 12 | C2×C4×C79⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 13 | #19098332 | — | 2 | 1 | no | — |
| 14 | #19098318 | — | 2 | 2 | no | — |
| 15 | #19098312 | — | 2 | 1 | no | — |
| 16 | #19098309 | — | 2 | 1 | no | — |
| 17 | #19098309 | — | 2 | 1 | no | — |
| 18 | #19098307 | — | 2 | 1 | no | — |
| 19 | Q8⋊(C79⋊C8) | — | 2 | 2 | no | — |
| 20 | D4⋊(C79⋊C8) | — | 2 | 2 | no | — |
| 21 | #559×C79 | — | 2 | 1 | no | — |
| 22 | #557×C79 | — | 2 | 1 | no | — |
| 23 | #556×C79 | — | 2 | 1 | no | — |
| 24 | #556×C79 | — | 2 | 2 | no | — |
| 25 | #554×C79 | — | 2 | 1 | no | — |
| 26 | #552×C79 | — | 2 | 2 | no | — |
| 27 | #539×C79 | C4 | 1 | 4 | yes | — |
| 28 | #536×C79 | — | 2 | 1 | no | — |
| 29 | #533×C79 | C22 | 1 | 1 | yes | characteristic |
| 30 | #532×C79 | C22 | 1 | 1 | yes | characteristic |
| 31 | #529×C79 | — | 2 | 2 | no | — |
| 32 | #520×C79 | — | 2 | 1 | no | — |
| 33 | C2×C4×Q8×C79 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#11929608 | — | 2 | 1 | no | — |
| 35 | C2×#11929608 | — | 2 | 1 | no | — |
| 36 | C22×C79⋊C8 | — | 2 | 1 | no | — |
| 37 | C22×C79⋊C8 | — | 2 | 1 | no | — |
| 38 | C4⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 39 | C4⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 40 | C4⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 41 | C4⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 42 | C4⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 43 | C4⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 44 | #14579080 | — | 4 | 2 | no | — |
| 45 | C4×C79⋊C8 | — | 2 | 1 | no | — |
| 46 | C4×C79⋊C8 | — | 2 | 1 | no | — |
| 47 | C2×#41×C79 | — | 2 | 1 | no | — |
| 48 | C22×Q8×C79 | D4 | 1 | 1 | yes | characteristic |
| 49 | C4⋊Q8×C79 | — | 2 | 2 | no | — |
| 50 | C4⋊Q8×C79 | D4 | 1 | 1 | yes | characteristic |
| 51 | C4⋊Q8×C79 | D4 | 1 | 1 | yes | characteristic |
| 52 | C4⋊Q8×C79 | D4 | 1 | 1 | yes | characteristic |
| 53 | #127×C79 | D4 | 1 | 1 | yes | characteristic |
| 54 | #126×C79 | — | 2 | 4 | no | — |
| 55 | #126×C79 | — | 2 | 4 | no | — |
| 56 | #125×C79 | — | 2 | 2 | no | — |
| 57 | #125×C79 | — | 2 | 4 | no | — |
| 58 | #125×C79 | — | 2 | 1 | no | — |
| 59 | #124×C79 | — | 2 | 2 | no | — |
| 60 | #124×C79 | — | 2 | 2 | no | — |
| 61 | #124×C79 | — | 2 | 1 | no | — |
| 62 | #123×C79 | — | 2 | 4 | no | — |
| 63 | #123×C79 | — | 2 | 4 | no | — |
| 64 | C22⋊Q8×C79 | — | 2 | 2 | no | — |
| 65 | C22⋊Q8×C79 | — | 2 | 2 | no | — |
| 66 | C22⋊Q8×C79 | — | 2 | 4 | no | — |
| 67 | C22⋊Q8×C79 | — | 2 | 1 | no | — |
| 68 | C22⋊Q8×C79 | C2×C4 | 1 | 2 | yes | — |
| 69 | #121×C79 | — | 2 | 1 | no | — |
| 70 | #121×C79 | C2×C4 | 1 | 2 | yes | — |
| 71 | C4×Q8×C79 | — | 2 | 2 | no | — |
| 72 | C4×Q8×C79 | — | 2 | 2 | no | — |
| 73 | C4×Q8×C79 | — | 2 | 1 | no | — |
| 74 | C4×Q8×C79 | — | 2 | 1 | no | — |
| 75 | C4×Q8×C79 | — | 2 | 1 | no | — |
| 76 | C4×Q8×C79 | — | 2 | 1 | no | — |
| 77 | C4×Q8×C79 | — | 2 | 1 | no | — |
| 78 | C4×Q8×C79 | D4 | 1 | 2 | yes | — |
| 79 | C4×D4×C79 | — | 2 | 2 | no | — |
| 80 | C4×D4×C79 | — | 2 | 2 | no | — |
| 81 | C4×D4×C79 | — | 2 | 4 | no | — |
| 82 | C4×D4×C79 | — | 2 | 1 | no | — |
| 83 | C4×D4×C79 | D4 | 1 | 2 | yes | — |
| 84 | #117×C79 | — | 2 | 2 | no | — |
| 85 | #117×C79 | — | 2 | 4 | no | — |
| 86 | #117×C79 | — | 2 | 1 | no | — |
| 87 | C2×C4⋊C4×C79 | — | 2 | 2 | no | — |
| 88 | C2×C4⋊C4×C79 | C2×C4 | 1 | 2 | yes | — |
| 89 | C2×C4⋊C4×C79 | D4 | 1 | 1 | yes | characteristic |
| 90 | C2×C42×C79 | D4 | 1 | 2 | yes | — |
| 91 | C2×C42×C79 | C23 | 1 | 1 | yes | characteristic |
| 92 | #11929608 | — | 4 | 1 | no | — |
| 93 | #11929608 | — | 4 | 1 | no | — |
| 94 | #11929608 | — | 4 | 1 | no | — |
| 95 | #11929608 | — | 4 | 1 | no | — |
| 96 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 97 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 98 | C2×C79⋊C8 | — | 4 | 2 | no | — |
| 99 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 100 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 101 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 102 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 103 | #41×C79 | — | 4 | 1 | no | — |
| 104 | #41×C79 | — | 4 | 1 | no | — |
| 105 | #41×C79 | — | 4 | 1 | no | — |
| 106 | #41×C79 | — | 4 | 1 | no | — |
| 107 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 108 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 109 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 110 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 111 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 112 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 113 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 114 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 115 | C2×Q8×C79 | C22⋊C4 | 1 | 2 | yes | — |
| 116 | C2×D4×C79 | — | 2 | 2 | no | — |
| 117 | C2×D4×C79 | — | 2 | 1 | no | — |
| 118 | C2×D4×C79 | — | 2 | 1 | no | — |
| 119 | C2×D4×C79 | C22⋊C4 | 1 | 2 | yes | — |
| 120 | C22×C4×C79 | — | 2 | 4 | no | — |
| 121 | C22×C4×C79 | — | 2 | 2 | no | — |
| 122 | C22×C4×C79 | C22⋊C4 | 1 | 2 | yes | — |
| 123 | C22×C4×C79 | C22⋊C4 | 1 | 2 | yes | — |
| 124 | C22×C4×C79 | C22×C4 | 1 | 1 | yes | characteristic |
| 125 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C4⋊C4×C79 | — | 2 | 4 | no | — |
| 128 | C4⋊C4×C79 | — | 2 | 4 | no | — |
| 129 | C4⋊C4×C79 | — | 2 | 4 | no | — |
| 130 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 131 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 132 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 133 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 134 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 135 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 136 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 137 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 138 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 139 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 140 | C4⋊C4×C79 | C22⋊C4 | 1 | 2 | yes | — |
| 141 | C4⋊C4×C79 | C22⋊C4 | 1 | 2 | yes | — |
| 142 | C22⋊C4×C79 | — | 2 | 4 | no | — |
| 143 | C22⋊C4×C79 | — | 2 | 4 | no | — |
| 144 | C22⋊C4×C79 | — | 2 | 4 | no | — |
| 145 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 146 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 147 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 148 | C42×C79 | — | 2 | 4 | no | — |
| 149 | C42×C79 | — | 2 | 2 | no | — |
| 150 | C42×C79 | — | 2 | 2 | no | — |
| 151 | C42×C79 | — | 2 | 2 | no | — |
| 152 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C23×C79 | — | 2 | 2 | no | — |
| 157 | C23×C79 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 158 | Q8×C79 | — | 4 | 2 | no | — |
| 159 | Q8×C79 | — | 4 | 1 | no | — |
| 160 | Q8×C79 | — | 4 | 1 | no | — |
| 161 | Q8×C79 | — | 4 | 1 | no | — |
| 162 | Q8×C79 | — | 4 | 1 | no | — |
| 163 | Q8×C79 | — | 4 | 1 | no | — |
| 164 | Q8×C79 | — | 4 | 1 | no | — |
| 165 | Q8×C79 | — | 4 | 1 | no | — |
| 166 | Q8×C79 | — | 4 | 1 | no | — |
| 167 | D4×C79 | — | 4 | 2 | no | — |
| 168 | D4×C79 | — | 4 | 2 | no | — |
| 169 | D4×C79 | — | 4 | 2 | no | — |
| 170 | D4×C79 | — | 4 | 1 | no | — |
| 171 | D4×C79 | — | 4 | 1 | no | — |
| 172 | D4×C79 | — | 4 | 1 | no | — |
| 173 | D4×C79 | — | 4 | 1 | no | — |
| 174 | C2×C4×C79 | — | 2 | 1 | no | — |
| 175 | C2×C4×C79 | — | 2 | 1 | no | — |
| 176 | C2×C4×C79 | — | 2 | 2 | no | — |
| 177 | C2×C4×C79 | — | 2 | 2 | no | — |
| 178 | C2×C4×C79 | — | 2 | 2 | no | — |
| 179 | C2×C4×C79 | — | 2 | 2 | no | — |
| 180 | C2×C4×C79 | — | 2 | 2 | no | — |
| 181 | C2×C4×C79 | — | 2 | 2 | no | — |
| 182 | C2×C4×C79 | — | 2 | 2 | no | — |
| 183 | C2×C4×C79 | — | 4 | 1 | no | — |
| 184 | C2×C4×C79 | — | 4 | 2 | no | — |
| 185 | C2×C4×C79 | — | 4 | 2 | no | — |
| 186 | C2×C4×C79 | — | 4 | 2 | no | — |
| 187 | C2×C4×C79 | — | 8 | 4 | no | — |
| 188 | C2×C4×C79 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 189 | C2×C4×C79 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 190 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 191 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 192 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 193 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 194 | C2×C4×C79 | #135 | 1 | 1 | yes | characteristic |
| 195 | C2×C4×C79 | #135 | 1 | 1 | yes | characteristic |
| 196 | C2×C4×C79 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 197 | C2×C4×C79 | #137 | 1 | 1 | yes | characteristic |
| 198 | C79⋊C8 | — | 4 | 2 | no | — |
| 199 | C79⋊C8 | — | 8 | 1 | no | — |
| 200 | C79⋊C8 | — | 8 | 1 | no | — |
| 201 | C79⋊C8 | — | 8 | 1 | no | — |
| 202 | C22×C79 | — | 2 | 1 | no | — |
| 203 | C22×C79 | — | 2 | 1 | no | — |
| 204 | C22×C79 | — | 4 | 2 | no | — |
| 205 | C22×C79 | — | 4 | 2 | no | — |
| 206 | C22×C79 | — | 4 | 2 | no | — |
| 207 | C22×C79 | #379 | 1 | 1 | yes | characteristic |
| 208 | C22×C79 | #416 | 1 | 1 | yes | characteristic |
| 209 | C22×C79 | #417 | 1 | 1 | yes | characteristic |
| 210 | C4×C79 | — | 2 | 1 | no | — |
| 211 | C4×C79 | — | 2 | 1 | no | — |
| 212 | C4×C79 | — | 2 | 1 | no | — |
| 213 | C4×C79 | — | 4 | 2 | no | — |
| 214 | C4×C79 | — | 4 | 2 | no | — |
| 215 | C4×C79 | — | 4 | 2 | no | — |
| 216 | C4×C79 | — | 4 | 2 | no | — |
| 217 | C4×C79 | — | 4 | 2 | no | — |
| 218 | C4×C79 | #449 | 1 | 1 | yes | characteristic |
| 219 | C4×C79 | #449 | 1 | 1 | yes | characteristic |
| 220 | C4×C79 | #452 | 1 | 1 | yes | characteristic |
| 221 | C4×C79 | #452 | 1 | 1 | yes | characteristic |
| 222 | C4×C79 | #454 | 1 | 1 | yes | characteristic |
| 223 | C4×C79 | #456 | 1 | 1 | yes | characteristic |
| 224 | #8357 | — | 79 | 1 | no | maximal, Sylow |
| 225 | C2×C79 | — | 2 | 1 | no | — |
| 226 | C2×C79 | — | 2 | 1 | no | — |
| 227 | C2×C79 | — | 8 | 2 | no | — |
| 228 | C2×C79 | #1788 | 1 | 1 | yes | characteristic |
| 229 | C2×C79 | #1791 | 1 | 1 | yes | characteristic |
| 230 | C2×C79 | #1793 | 1 | 1 | yes | characteristic |
| 231 | #3507 | D79 | 1 | 1 | yes | characteristic |
| 232 | #1984 | — | 79 | 1 | no | — |
| 233 | #1801 | — | 79 | 1 | no | — |
| 234 | #1550 | — | 79 | 1 | no | — |
| 235 | #1547 | — | 79 | 1 | no | — |
| 236 | #1493 | — | 79 | 1 | no | — |
| 237 | #1492 | — | 79 | 1 | no | — |
| 238 | C79 | #8357 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 239 | #559 | — | 2 | 1 | no | — |
| 240 | #557 | — | 2 | 1 | no | — |
| 241 | #556 | — | 2 | 1 | no | — |
| 242 | #556 | — | 2 | 2 | no | — |
| 243 | #554 | — | 2 | 1 | no | — |
| 244 | #552 | — | 2 | 2 | no | — |
| 245 | #539 | Dic79 | 1 | 4 | yes | — |
| 246 | #536 | — | 2 | 1 | no | — |
| 247 | #533 | C2×D79 | 1 | 1 | yes | characteristic |
| 248 | #532 | C2×D79 | 1 | 1 | yes | characteristic |
| 249 | #529 | — | 2 | 2 | no | — |
| 250 | #520 | — | 2 | 1 | no | — |
| 251 | C2×C4×Q8 | C2×D79 | 1 | 1 | yes | characteristic |
| 252 | #423 | — | 79 | 1 | no | — |
| 253 | #423 | — | 79 | 1 | no | — |
| 254 | C2×C4⋊C8 | — | 79 | 1 | no | — |
| 255 | C2×#101 | — | 158 | 1 | no | — |
| 256 | C2×C4×C8 | — | 79 | 1 | no | — |
| 257 | #343 | — | 158 | 1 | no | — |
| 258 | #336 | — | 158 | 2 | no | — |
| 259 | #333 | — | 158 | 1 | no | — |
| 260 | #332 | — | 158 | 1 | no | — |
| 261 | #332 | — | 158 | 1 | no | — |
| 262 | #331 | — | 158 | 1 | no | — |
| 263 | Q8⋊C8 | — | 158 | 2 | no | — |
| 264 | D4⋊C8 | — | 158 | 2 | no | — |
| 265 | C2×#41 | — | 2 | 1 | no | — |
| 266 | C22×Q8 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 267 | C2×M16 | — | 158 | 1 | no | — |
| 268 | C2×M16 | — | 158 | 1 | no | — |
| 269 | C22×C8 | — | 158 | 1 | no | — |
| 270 | C22×C8 | — | 158 | 1 | no | — |
| 271 | C4⋊Q8 | — | 2 | 2 | no | — |
| 272 | C4⋊Q8 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 273 | C4⋊Q8 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 274 | C4⋊Q8 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 275 | #127 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 276 | #126 | — | 2 | 4 | no | — |
| 277 | #126 | — | 2 | 4 | no | — |
| 278 | #125 | — | 2 | 2 | no | — |
| 279 | #125 | — | 2 | 4 | no | — |
| 280 | #125 | — | 2 | 1 | no | — |
| 281 | #124 | — | 2 | 2 | no | — |
| 282 | #124 | — | 2 | 2 | no | — |
| 283 | #124 | — | 2 | 1 | no | — |
| 284 | #123 | — | 2 | 4 | no | — |
| 285 | #123 | — | 2 | 4 | no | — |
| 286 | C22⋊Q8 | — | 2 | 2 | no | — |
| 287 | C22⋊Q8 | — | 2 | 2 | no | — |
| 288 | C22⋊Q8 | — | 2 | 4 | no | — |
| 289 | C22⋊Q8 | — | 2 | 1 | no | — |
| 290 | C22⋊Q8 | C2×Dic79 | 1 | 2 | yes | — |
| 291 | #121 | — | 2 | 1 | no | — |
| 292 | #121 | C2×Dic79 | 1 | 2 | yes | — |
| 293 | C4×Q8 | — | 2 | 2 | no | — |
| 294 | C4×Q8 | — | 2 | 2 | no | — |
| 295 | C4×Q8 | — | 2 | 1 | no | — |
| 296 | C4×Q8 | — | 2 | 1 | no | — |
| 297 | C4×Q8 | — | 2 | 1 | no | — |
| 298 | C4×Q8 | — | 2 | 1 | no | — |
| 299 | C4×Q8 | — | 2 | 1 | no | — |
| 300 | C4×Q8 | C22⋊D79 | 1 | 2 | yes | — |
| 301 | C4×D4 | — | 2 | 2 | no | — |
| 302 | C4×D4 | — | 2 | 2 | no | — |
| 303 | C4×D4 | — | 2 | 4 | no | — |
| 304 | C4×D4 | — | 2 | 1 | no | — |
| 305 | C4×D4 | C22⋊D79 | 1 | 2 | yes | — |
| 306 | #117 | — | 2 | 2 | no | — |
| 307 | #117 | — | 2 | 4 | no | — |
| 308 | #117 | — | 2 | 1 | no | — |
| 309 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 310 | C2×C4⋊C4 | C2×Dic79 | 1 | 2 | yes | — |
| 311 | C2×C4⋊C4 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 312 | C2×C42 | C22⋊D79 | 1 | 2 | yes | — |
| 313 | C2×C42 | C22×D79 | 1 | 1 | yes | characteristic |
| 314 | C4⋊C8 | — | 158 | 1 | no | — |
| 315 | C4⋊C8 | — | 158 | 1 | no | — |
| 316 | C4⋊C8 | — | 158 | 1 | no | — |
| 317 | C4⋊C8 | — | 158 | 1 | no | — |
| 318 | C4⋊C8 | — | 158 | 1 | no | — |
| 319 | C4⋊C8 | — | 158 | 1 | no | — |
| 320 | #101 | — | 316 | 2 | no | — |
| 321 | C4×C8 | — | 158 | 1 | no | — |
| 322 | C4×C8 | — | 158 | 1 | no | — |
| 323 | #41 | — | 4 | 1 | no | — |
| 324 | #41 | — | 4 | 1 | no | — |
| 325 | #41 | — | 4 | 1 | no | — |
| 326 | #41 | — | 4 | 1 | no | — |
| 327 | C2×Q8 | — | 2 | 1 | no | — |
| 328 | C2×Q8 | — | 2 | 1 | no | — |
| 329 | C2×Q8 | — | 2 | 1 | no | — |
| 330 | C2×Q8 | — | 2 | 1 | no | — |
| 331 | C2×Q8 | — | 2 | 1 | no | — |
| 332 | C2×Q8 | — | 2 | 1 | no | — |
| 333 | C2×Q8 | — | 2 | 1 | no | — |
| 334 | C2×Q8 | — | 2 | 1 | no | — |
| 335 | C2×Q8 | C22⋊Dic79 | 1 | 2 | yes | — |
| 336 | C2×D4 | — | 2 | 2 | no | — |
| 337 | C2×D4 | — | 2 | 1 | no | — |
| 338 | C2×D4 | — | 2 | 1 | no | — |
| 339 | C2×D4 | C22⋊Dic79 | 1 | 2 | yes | — |
| 340 | C22×C4 | — | 2 | 4 | no | — |
| 341 | C22×C4 | — | 2 | 2 | no | — |
| 342 | C22×C4 | C22⋊Dic79 | 1 | 2 | yes | — |
| 343 | C22×C4 | C22⋊Dic79 | 1 | 2 | yes | — |
| 344 | C22×C4 | C22×Dic79 | 1 | 1 | yes | characteristic |
| 345 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 346 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 347 | M16 | — | 316 | 1 | no | — |
| 348 | M16 | — | 316 | 1 | no | — |
| 349 | M16 | — | 316 | 1 | no | — |
| 350 | M16 | — | 316 | 1 | no | — |
| 351 | C2×C8 | — | 316 | 1 | no | — |
| 352 | C2×C8 | — | 316 | 1 | no | — |
| 353 | C2×C8 | — | 316 | 2 | no | — |
| 354 | C2×C8 | — | 316 | 1 | no | — |
| 355 | C2×C8 | — | 316 | 1 | no | — |
| 356 | C2×C8 | — | 316 | 1 | no | — |
| 357 | C2×C8 | — | 158 | 2 | no | — |
| 358 | C4⋊C4 | — | 2 | 4 | no | — |
| 359 | C4⋊C4 | — | 2 | 4 | no | — |
| 360 | C4⋊C4 | — | 2 | 4 | no | — |
| 361 | C4⋊C4 | — | 2 | 2 | no | — |
| 362 | C4⋊C4 | — | 2 | 2 | no | — |
| 363 | C4⋊C4 | — | 2 | 2 | no | — |
| 364 | C4⋊C4 | — | 2 | 1 | no | — |
| 365 | C4⋊C4 | — | 2 | 1 | no | — |
| 366 | C4⋊C4 | — | 2 | 1 | no | — |
| 367 | C4⋊C4 | — | 2 | 1 | no | — |
| 368 | C4⋊C4 | — | 2 | 2 | no | — |
| 369 | C4⋊C4 | — | 2 | 1 | no | — |
| 370 | C4⋊C4 | — | 2 | 1 | no | — |
| 371 | C4⋊C4 | C22⋊Dic79 | 1 | 2 | yes | — |
| 372 | C4⋊C4 | C22⋊Dic79 | 1 | 2 | yes | — |
| 373 | C22⋊C4 | — | 2 | 4 | no | — |
| 374 | C22⋊C4 | — | 2 | 4 | no | — |
| 375 | C22⋊C4 | — | 2 | 4 | no | — |
| 376 | C22⋊C4 | — | 2 | 2 | no | — |
| 377 | C22⋊C4 | — | 2 | 2 | no | — |
| 378 | C22⋊C4 | — | 2 | 2 | no | — |
| 379 | C42 | — | 2 | 4 | no | — |
| 380 | C42 | — | 2 | 2 | no | — |
| 381 | C42 | — | 2 | 2 | no | — |
| 382 | C42 | — | 2 | 2 | no | — |
| 383 | C42 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 384 | C42 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 385 | C42 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 386 | C42 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 387 | C23 | — | 2 | 2 | no | — |
| 388 | C23 | C2×C22⋊Dic79 | 1 | 1 | yes | characteristic |
| 389 | Q8 | — | 4 | 2 | no | — |
| 390 | Q8 | — | 4 | 1 | no | — |
| 391 | Q8 | — | 4 | 1 | no | — |
| 392 | Q8 | — | 4 | 1 | no | — |
| 393 | Q8 | — | 4 | 1 | no | — |
| 394 | Q8 | — | 4 | 1 | no | — |
| 395 | Q8 | — | 4 | 1 | no | — |
| 396 | Q8 | — | 4 | 1 | no | — |
| 397 | Q8 | — | 4 | 1 | no | — |
| 398 | D4 | — | 4 | 2 | no | — |
| 399 | D4 | — | 4 | 2 | no | — |
| 400 | D4 | — | 4 | 2 | no | — |
| 401 | D4 | — | 4 | 1 | no | — |
| 402 | D4 | — | 4 | 1 | no | — |
| 403 | D4 | — | 4 | 1 | no | — |
| 404 | D4 | — | 4 | 1 | no | — |
| 405 | C2×C4 | — | 2 | 1 | no | — |
| 406 | C2×C4 | — | 2 | 1 | no | — |
| 407 | C2×C4 | — | 2 | 2 | no | — |
| 408 | C2×C4 | — | 2 | 2 | no | — |
| 409 | C2×C4 | — | 2 | 2 | no | — |
| 410 | C2×C4 | — | 2 | 2 | no | — |
| 411 | C2×C4 | — | 2 | 2 | no | — |
| 412 | C2×C4 | — | 2 | 2 | no | — |
| 413 | C2×C4 | — | 2 | 2 | no | — |
| 414 | C2×C4 | — | 4 | 1 | no | — |
| 415 | C2×C4 | — | 4 | 2 | no | — |
| 416 | C2×C4 | — | 4 | 2 | no | — |
| 417 | C2×C4 | — | 4 | 2 | no | — |
| 418 | C2×C4 | — | 8 | 4 | no | — |
| 419 | C2×C4 | C2×C22⋊Dic79 | 1 | 1 | yes | characteristic |
| 420 | C2×C4 | C2×C22⋊Dic79 | 1 | 1 | yes | characteristic |
| 421 | C2×C4 | #14579130 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | #14579130 | 1 | 1 | yes | characteristic |
| 423 | C2×C4 | #14579130 | 1 | 1 | yes | characteristic |
| 424 | C2×C4 | #14579130 | 1 | 1 | yes | characteristic |
| 425 | C2×C4 | #14579181 | 1 | 1 | yes | characteristic |
| 426 | C2×C4 | #14579181 | 1 | 1 | yes | characteristic |
| 427 | C2×C4 | #14579186 | 1 | 1 | yes | characteristic |
| 428 | C2×C4 | #14579191 | 1 | 1 | yes | characteristic |
| 429 | C8 | — | 316 | 2 | no | — |
| 430 | C8 | — | 632 | 1 | no | — |
| 431 | C8 | — | 632 | 1 | no | — |
| 432 | C8 | — | 632 | 1 | no | — |
| 433 | C22 | — | 2 | 1 | no | — |
| 434 | C22 | — | 2 | 1 | no | — |
| 435 | C22 | — | 4 | 2 | no | — |
| 436 | C22 | — | 4 | 2 | no | — |
| 437 | C22 | — | 4 | 2 | no | — |
| 438 | C22 | #19098419 | 1 | 1 | yes | characteristic |
| 439 | C22 | #19098559 | 1 | 1 | yes | characteristic |
| 440 | C22 | #19098564 | 1 | 1 | yes | characteristic |
| 441 | C4 | — | 2 | 1 | no | — |
| 442 | C4 | — | 2 | 1 | no | — |
| 443 | C4 | — | 2 | 1 | no | — |
| 444 | C4 | — | 4 | 2 | no | — |
| 445 | C4 | — | 4 | 2 | no | — |
| 446 | C4 | — | 4 | 2 | no | — |
| 447 | C4 | — | 4 | 2 | no | — |
| 448 | C4 | — | 4 | 2 | no | — |
| 449 | C4 | #19098708 | 1 | 1 | yes | characteristic |
| 450 | C4 | #19098708 | 1 | 1 | yes | characteristic |
| 451 | C4 | #19098725 | 1 | 1 | yes | characteristic |
| 452 | C4 | #19098725 | 1 | 1 | yes | characteristic |
| 453 | C4 | #19098736 | 1 | 1 | yes | characteristic |
| 454 | C4 | #19098746 | 1 | 1 | yes | characteristic |
| 455 | C2 | — | 2 | 1 | no | — |
| 456 | C2 | — | 2 | 1 | no | — |
| 457 | C2 | — | 8 | 2 | no | — |
| 458 | C2 | #23763340 | 1 | 1 | yes | characteristic |
| 459 | C2 | #23763351 | 1 | 1 | yes | characteristic |
| 460 | C2 | #23763359 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta