← #13511380
Subgroups — #13511380
Order 1792.
464 conjugacy classes of subgroups.
The subgroup lattice has 266 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11736858 | C2 | 1 | 2 | yes | maximal |
| 2 | C7×#2169 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11729201 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11729182 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11727051 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11726854 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11726853 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C4×Dic56 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11726799 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #90232 | — | 2 | 2 | no | — |
| 11 | C2×C7×M32 | C22 | 1 | 2 | yes | — |
| 12 | C7×C8×D4 | C22 | 1 | 1 | yes | characteristic |
| 13 | #89888 | C22 | 1 | 2 | yes | — |
| 14 | #89888 | C22 | 1 | 2 | yes | — |
| 15 | #89878 | C22 | 1 | 2 | yes | — |
| 16 | C2×#6392 | C22 | 1 | 2 | yes | — |
| 17 | C2×Dic56 | C22 | 1 | 1 | yes | characteristic |
| 18 | #89601 | — | 2 | 2 | no | — |
| 19 | #89495 | — | 2 | 2 | no | — |
| 20 | #89493 | — | 2 | 2 | no | — |
| 21 | C4×Dic28 | C22 | 1 | 2 | yes | — |
| 22 | #89455 | C22 | 1 | 2 | yes | — |
| 23 | C7×C4⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 24 | C7×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 25 | C4×C7×C16 | C22 | 1 | 1 | yes | characteristic |
| 26 | #89300 | C22 | 1 | 2 | yes | — |
| 27 | #89300 | C22 | 1 | 2 | yes | — |
| 28 | #89299 | C22 | 1 | 1 | yes | characteristic |
| 29 | #89299 | C22 | 1 | 2 | yes | — |
| 30 | #89299 | C22 | 1 | 1 | yes | characteristic |
| 31 | #89299 | C22 | 1 | 1 | yes | characteristic |
| 32 | #89298 | C22 | 1 | 2 | yes | — |
| 33 | #89298 | C22 | 1 | 2 | yes | — |
| 34 | #89298 | C22 | 1 | 2 | yes | — |
| 35 | #33919 | — | 7 | 1 | no | maximal, Sylow |
| 36 | C22×C7×C8 | C23 | 1 | 2 | yes | — |
| 37 | C4×C7×D4 | D4 | 1 | 1 | yes | characteristic |
| 38 | #6498 | — | 4 | 2 | no | — |
| 39 | #6489 | — | 2 | 2 | no | — |
| 40 | C2×C4⋊Dic7 | — | 2 | 2 | no | — |
| 41 | #6487 | — | 2 | 2 | no | — |
| 42 | #6487 | — | 2 | 2 | no | — |
| 43 | C2×Dic28 | C23 | 1 | 2 | yes | — |
| 44 | #6452 | — | 4 | 2 | no | — |
| 45 | #6442 | — | 4 | 2 | no | — |
| 46 | #6440 | — | 4 | 2 | no | — |
| 47 | #6433 | — | 2 | 2 | no | — |
| 48 | C4×Dic14 | — | 2 | 2 | no | — |
| 49 | C7×M32 | — | 2 | 4 | no | — |
| 50 | C2×C7×C16 | C23 | 1 | 2 | yes | — |
| 51 | C2×C7×C16 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×C7×C16 | C23 | 1 | 1 | yes | characteristic |
| 53 | C7×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 54 | C7×C22⋊C8 | D4 | 1 | 2 | yes | — |
| 55 | C4×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 56 | #6392 | — | 2 | 2 | no | — |
| 57 | #6392 | C23 | 1 | 2 | yes | — |
| 58 | #6392 | C23 | 1 | 2 | yes | — |
| 59 | #6392 | C23 | 1 | 2 | yes | — |
| 60 | #6391 | — | 2 | 2 | no | — |
| 61 | #6391 | — | 2 | 2 | no | — |
| 62 | #6390 | — | 2 | 2 | no | — |
| 63 | #6390 | — | 2 | 2 | no | — |
| 64 | #6390 | — | 2 | 2 | no | — |
| 65 | Dic56 | — | 2 | 2 | no | — |
| 66 | #3336 | — | 7 | 2 | no | — |
| 67 | #2253 | — | 7 | 1 | no | — |
| 68 | #2237 | — | 7 | 2 | no | — |
| 69 | #2236 | — | 7 | 2 | no | — |
| 70 | #2229 | — | 7 | 2 | no | — |
| 71 | #2219 | — | 7 | 2 | no | — |
| 72 | C4×Q32 | — | 7 | 1 | no | — |
| 73 | #2169 | D7 | 1 | 1 | yes | characteristic |
| 74 | #2159 | — | 7 | 2 | no | — |
| 75 | C2×C7×D4 | D8 | 1 | 1 | yes | characteristic |
| 76 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 77 | C22×Dic7 | — | 4 | 2 | no | — |
| 78 | C2×Dic14 | — | 2 | 2 | no | — |
| 79 | C2×C7×C8 | — | 2 | 2 | no | — |
| 80 | C2×C7×C8 | — | 2 | 2 | no | — |
| 81 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 83 | C2×C7×C8 | C24 | 1 | 1 | yes | characteristic |
| 84 | C7×C4⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 85 | C7×C22⋊C4 | D8 | 1 | 2 | yes | — |
| 86 | C42×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 88 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 89 | C22⋊Dic7 | — | 4 | 2 | no | — |
| 90 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 91 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 92 | C4⋊Dic7 | — | 2 | 2 | no | — |
| 93 | C4⋊Dic7 | — | 4 | 2 | no | — |
| 94 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 95 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 96 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 97 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 98 | Dic7⋊C4 | — | 4 | 2 | no | — |
| 99 | C4×Dic7 | — | 4 | 2 | no | — |
| 100 | C4×Dic7 | — | 4 | 2 | no | — |
| 101 | Dic28 | — | 2 | 2 | no | — |
| 102 | Dic28 | — | 2 | 2 | no | — |
| 103 | C7×C16 | — | 2 | 2 | no | — |
| 104 | C7×C16 | — | 2 | 1 | no | — |
| 105 | C7×C16 | #41 | 1 | 2 | yes | — |
| 106 | #552 | — | 14 | 2 | no | — |
| 107 | C2×Q32 | — | 7 | 1 | no | — |
| 108 | C2×M32 | C2×D7 | 1 | 2 | yes | — |
| 109 | #499 | — | 7 | 2 | no | — |
| 110 | #485 | — | 14 | 2 | no | — |
| 111 | #483 | — | 14 | 2 | no | — |
| 112 | #479 | — | 14 | 2 | no | — |
| 113 | #467 | — | 7 | 2 | no | — |
| 114 | #467 | — | 7 | 2 | no | — |
| 115 | C4×Q16 | — | 7 | 2 | no | — |
| 116 | C8×D4 | C2×D7 | 1 | 1 | yes | characteristic |
| 117 | #427 | — | 7 | 2 | no | — |
| 118 | C2×#107 | — | 7 | 2 | no | — |
| 119 | #367 | — | 7 | 2 | no | — |
| 120 | #367 | — | 7 | 2 | no | — |
| 121 | #366 | — | 7 | 1 | no | — |
| 122 | #366 | — | 7 | 2 | no | — |
| 123 | #366 | — | 7 | 1 | no | — |
| 124 | #366 | — | 7 | 1 | no | — |
| 125 | C4⋊C16 | C2×D7 | 1 | 1 | yes | characteristic |
| 126 | #358 | — | 7 | 2 | no | — |
| 127 | #358 | — | 7 | 2 | no | — |
| 128 | #358 | — | 7 | 2 | no | — |
| 129 | C22⋊C16 | C2×D7 | 1 | 2 | yes | — |
| 130 | C4×C16 | C2×D7 | 1 | 1 | yes | characteristic |
| 131 | C23×C7 | C2×D8 | 1 | 2 | yes | — |
| 132 | C7×D4 | — | 4 | 1 | no | — |
| 133 | C2×C4×C7 | — | 2 | 2 | no | — |
| 134 | C2×C4×C7 | — | 2 | 2 | no | — |
| 135 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C7 | C2×D8 | 1 | 2 | yes | — |
| 137 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×Dic7 | — | 4 | 2 | no | — |
| 140 | C2×Dic7 | — | 4 | 2 | no | — |
| 141 | C2×Dic7 | — | 4 | 2 | no | — |
| 142 | C2×Dic7 | — | 4 | 2 | no | — |
| 143 | C2×Dic7 | — | 8 | 4 | no | — |
| 144 | Dic14 | — | 4 | 2 | no | — |
| 145 | Dic14 | — | 4 | 2 | no | — |
| 146 | C7×C8 | — | 2 | 2 | no | — |
| 147 | C7×C8 | — | 2 | 1 | no | — |
| 148 | C7×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 149 | C7×C8 | 2−1+4 | 1 | 1 | yes | characteristic |
| 150 | C2×Q16 | — | 7 | 2 | no | — |
| 151 | C22×C8 | C22×D7 | 1 | 2 | yes | — |
| 152 | #126 | — | 28 | 2 | no | — |
| 153 | #125 | — | 14 | 2 | no | — |
| 154 | #125 | — | 28 | 2 | no | — |
| 155 | #123 | — | 28 | 2 | no | — |
| 156 | C22⋊Q8 | — | 14 | 2 | no | — |
| 157 | C22⋊Q8 | — | 14 | 2 | no | — |
| 158 | C4×Q8 | — | 14 | 2 | no | — |
| 159 | C4×D4 | D28 | 1 | 1 | yes | characteristic |
| 160 | #117 | — | 14 | 2 | no | — |
| 161 | #117 | — | 28 | 2 | no | — |
| 162 | C2×C4⋊C4 | — | 14 | 2 | no | — |
| 163 | Q32 | — | 14 | 2 | no | — |
| 164 | M32 | — | 2 | 4 | no | — |
| 165 | C2×C16 | C22×D7 | 1 | 1 | yes | characteristic |
| 166 | C2×C16 | C22×D7 | 1 | 2 | yes | — |
| 167 | C2×C16 | C22×D7 | 1 | 1 | yes | characteristic |
| 168 | #107 | — | 7 | 2 | no | — |
| 169 | #107 | — | 7 | 2 | no | — |
| 170 | #107 | — | 7 | 2 | no | — |
| 171 | #107 | — | 14 | 2 | no | — |
| 172 | #106 | — | 14 | 2 | no | — |
| 173 | #106 | — | 14 | 2 | no | — |
| 174 | C4⋊C8 | D28 | 1 | 1 | yes | characteristic |
| 175 | #103 | — | 14 | 2 | no | — |
| 176 | #103 | — | 14 | 2 | no | — |
| 177 | #103 | — | 14 | 2 | no | — |
| 178 | C22⋊C8 | D28 | 1 | 2 | yes | — |
| 179 | C4×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 180 | C22×C7 | — | 2 | 2 | no | — |
| 181 | C22×C7 | — | 2 | 2 | no | — |
| 182 | C22×C7 | — | 2 | 2 | no | — |
| 183 | C22×C7 | C22×D8 | 1 | 1 | yes | characteristic |
| 184 | C4×C7 | — | 2 | 2 | no | — |
| 185 | C4×C7 | — | 2 | 1 | no | — |
| 186 | C4×C7 | — | 2 | 1 | no | — |
| 187 | C4×C7 | #547 | 1 | 1 | yes | characteristic |
| 188 | C4×C7 | #578 | 1 | 1 | yes | characteristic |
| 189 | Dic7 | — | 8 | 2 | no | — |
| 190 | Dic7 | — | 8 | 2 | no | — |
| 191 | Dic7 | — | 8 | 2 | no | — |
| 192 | Dic7 | — | 8 | 2 | no | — |
| 193 | C2×Q8 | — | 14 | 2 | no | — |
| 194 | C2×D4 | D56 | 1 | 1 | yes | characteristic |
| 195 | C22×C4 | — | 28 | 2 | no | — |
| 196 | C22×C4 | C2×D28 | 1 | 2 | yes | — |
| 197 | Q16 | — | 14 | 2 | no | — |
| 198 | Q16 | — | 14 | 2 | no | — |
| 199 | C2×C8 | — | 2 | 2 | no | — |
| 200 | C2×C8 | — | 2 | 2 | no | — |
| 201 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 202 | C2×C8 | C2×D28 | 1 | 2 | yes | — |
| 203 | C2×C8 | C23×D7 | 1 | 1 | yes | characteristic |
| 204 | C4⋊C4 | — | 14 | 2 | no | — |
| 205 | C4⋊C4 | — | 14 | 2 | no | — |
| 206 | C4⋊C4 | — | 14 | 2 | no | — |
| 207 | C4⋊C4 | — | 28 | 2 | no | — |
| 208 | C4⋊C4 | — | 28 | 2 | no | — |
| 209 | C4⋊C4 | — | 28 | 2 | no | — |
| 210 | C4⋊C4 | — | 28 | 2 | no | — |
| 211 | C4⋊C4 | — | 28 | 2 | no | — |
| 212 | C4⋊C4 | — | 28 | 2 | no | — |
| 213 | C4⋊C4 | D56 | 1 | 1 | yes | characteristic |
| 214 | C22⋊C4 | — | 28 | 2 | no | — |
| 215 | C22⋊C4 | — | 28 | 2 | no | — |
| 216 | C22⋊C4 | — | 28 | 2 | no | — |
| 217 | C22⋊C4 | D56 | 1 | 2 | yes | — |
| 218 | C42 | — | 28 | 2 | no | — |
| 219 | C42 | — | 28 | 2 | no | — |
| 220 | C42 | C2×D28 | 1 | 1 | yes | characteristic |
| 221 | C16 | — | 2 | 2 | no | — |
| 222 | C16 | — | 2 | 1 | no | — |
| 223 | C16 | #1159 | 1 | 2 | yes | — |
| 224 | C2×C7 | — | 4 | 2 | no | — |
| 225 | C2×C7 | #3334 | 1 | 1 | yes | characteristic |
| 226 | C2×C7 | #3414 | 1 | 1 | yes | characteristic |
| 227 | C2×C7 | #3417 | 1 | 1 | yes | characteristic |
| 228 | C23 | C2×D56 | 1 | 2 | yes | — |
| 229 | Q8 | — | 28 | 2 | no | — |
| 230 | Q8 | — | 28 | 2 | no | — |
| 231 | D4 | — | 4 | 1 | no | — |
| 232 | C2×C4 | — | 2 | 2 | no | — |
| 233 | C2×C4 | — | 2 | 2 | no | — |
| 234 | C2×C4 | — | 28 | 2 | no | — |
| 235 | C2×C4 | — | 28 | 2 | no | — |
| 236 | C2×C4 | — | 28 | 2 | no | — |
| 237 | C2×C4 | — | 28 | 2 | no | — |
| 238 | C2×C4 | — | 56 | 4 | no | — |
| 239 | C2×C4 | C2×D56 | 1 | 1 | yes | characteristic |
| 240 | C2×C4 | C2×D56 | 1 | 2 | yes | — |
| 241 | C2×C4 | C2×D56 | 1 | 1 | yes | characteristic |
| 242 | C2×C4 | C22×D28 | 1 | 1 | yes | characteristic |
| 243 | C8 | — | 2 | 1 | no | — |
| 244 | C8 | — | 2 | 2 | no | — |
| 245 | C8 | C2×#1159 | 1 | 1 | yes | characteristic |
| 246 | C8 | #6554 | 1 | 1 | yes | characteristic |
| 247 | C7 | #33919 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 248 | C22 | — | 2 | 2 | no | — |
| 249 | C22 | — | 2 | 2 | no | — |
| 250 | C22 | — | 2 | 2 | no | — |
| 251 | C22 | C22×D56 | 1 | 1 | yes | characteristic |
| 252 | C4 | — | 2 | 2 | no | — |
| 253 | C4 | — | 2 | 1 | no | — |
| 254 | C4 | — | 2 | 1 | no | — |
| 255 | C4 | — | 56 | 2 | no | — |
| 256 | C4 | — | 56 | 2 | no | — |
| 257 | C4 | — | 56 | 2 | no | — |
| 258 | C4 | — | 56 | 2 | no | — |
| 259 | C4 | #90246 | 1 | 1 | yes | characteristic |
| 260 | C4 | #90444 | 1 | 1 | yes | characteristic |
| 261 | C2 | — | 4 | 2 | no | — |
| 262 | C2 | #11736856 | 1 | 1 | yes | characteristic |
| 263 | C2 | #11739454 | 1 | 1 | yes | characteristic |
| 264 | C2 | #11739460 | 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