← #13272056
Subgroups — #13272056
Order 1792.
574 conjugacy classes of subgroups.
The subgroup lattice has 246 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#89467 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×C7×M32 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#89311 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #11727546 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C22×D56 | — | 2 | 1 | no | — |
| 6 | C22×D56 | C22 | 1 | 2 | yes | — |
| 7 | C2×#6437 | — | 2 | 1 | no | — |
| 8 | C2×C7×M32 | C22 | 1 | 2 | yes | — |
| 9 | C2×C4×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#6393 | — | 2 | 1 | no | — |
| 11 | C2×#6393 | C22 | 1 | 2 | yes | — |
| 12 | #89696 | — | 2 | 1 | no | — |
| 13 | #89467 | — | 2 | 1 | no | — |
| 14 | #89467 | — | 2 | 1 | no | — |
| 15 | #89467 | C4 | 1 | 2 | yes | — |
| 16 | #89467 | C4 | 1 | 2 | yes | — |
| 17 | C7×#346 | — | 2 | 1 | no | — |
| 18 | C4×C7×C16 | — | 2 | 1 | no | — |
| 19 | #89311 | — | 2 | 8 | no | — |
| 20 | #13213 | — | 7 | 1 | no | maximal, Sylow |
| 21 | C22×D28 | — | 2 | 2 | no | — |
| 22 | C22×D28 | — | 4 | 2 | no | — |
| 23 | C22×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 24 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 25 | C2×C42×C7 | D4 | 1 | 1 | yes | characteristic |
| 26 | C2×#1136 | — | 2 | 2 | no | — |
| 27 | C2×D56 | — | 2 | 4 | no | — |
| 28 | C2×D56 | — | 2 | 4 | no | — |
| 29 | C2×D56 | — | 2 | 2 | no | — |
| 30 | C2×D56 | — | 2 | 2 | no | — |
| 31 | C2×D56 | — | 2 | 2 | no | — |
| 32 | C2×D56 | — | 4 | 2 | no | — |
| 33 | C2×D56 | — | 4 | 2 | no | — |
| 34 | C2×D56 | C2×C4 | 1 | 4 | yes | — |
| 35 | #6437 | — | 2 | 2 | no | — |
| 36 | #6437 | — | 2 | 2 | no | — |
| 37 | #6437 | — | 4 | 2 | no | — |
| 38 | C7×M32 | — | 2 | 2 | no | — |
| 39 | C7×M32 | D4 | 1 | 4 | yes | complemented |
| 40 | C2×C7×C16 | — | 2 | 2 | no | — |
| 41 | C4×C7×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C4×C7×C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | C4×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 44 | C4×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 45 | #6393 | — | 2 | 4 | no | — |
| 46 | #6393 | — | 4 | 2 | no | — |
| 47 | C4⋊(C7⋊C8) | — | 4 | 2 | no | — |
| 48 | C2×#493 | — | 7 | 1 | no | — |
| 49 | C2×#361 | — | 7 | 4 | no | — |
| 50 | C4×M32 | D7 | 1 | 1 | yes | characteristic, complemented |
| 51 | #1848 | — | 7 | 1 | no | — |
| 52 | C23×D7 | — | 4 | 2 | no | — |
| 53 | C22×C4×C7 | SD16 | 1 | 2 | yes | — |
| 54 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 55 | C2×D28 | — | 2 | 4 | no | — |
| 56 | C2×D28 | — | 4 | 2 | no | — |
| 57 | C2×D28 | — | 4 | 2 | no | — |
| 58 | C2×D28 | — | 4 | 2 | no | — |
| 59 | C2×D28 | — | 4 | 2 | no | — |
| 60 | C2×D28 | — | 4 | 4 | no | — |
| 61 | C2×D28 | — | 4 | 4 | no | — |
| 62 | C2×D28 | — | 4 | 2 | no | — |
| 63 | C2×D28 | — | 8 | 8 | no | — |
| 64 | C2×C7×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 65 | C2×C7×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 66 | C2×C7×C8 | D8 | 1 | 2 | yes | — |
| 67 | C2×C7×C8 | SD16 | 1 | 2 | yes | — |
| 68 | C2×C7×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 69 | C2×C7×C8 | C2×D4 | 1 | 2 | yes | — |
| 70 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C2×C7×C8 | #41 | 1 | 2 | yes | — |
| 72 | C42×C7 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 73 | C42×C7 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 74 | C42×C7 | D8 | 1 | 2 | yes | — |
| 75 | #1136 | — | 4 | 2 | no | — |
| 76 | #1136 | — | 4 | 2 | no | — |
| 77 | C2×C7⋊C8 | — | 4 | 2 | no | — |
| 78 | D56 | — | 2 | 8 | no | — |
| 79 | D56 | — | 4 | 4 | no | — |
| 80 | D56 | — | 4 | 4 | no | — |
| 81 | D56 | — | 4 | 4 | no | — |
| 82 | C7×C16 | — | 2 | 4 | no | — |
| 83 | C22×D8 | — | 7 | 2 | no | — |
| 84 | C22×D8 | — | 14 | 1 | no | — |
| 85 | C2×#127 | — | 14 | 1 | no | — |
| 86 | C2×M32 | C2×D7 | 1 | 2 | yes | — |
| 87 | #493 | — | 7 | 2 | no | — |
| 88 | #493 | — | 7 | 2 | no | — |
| 89 | #493 | — | 14 | 1 | no | — |
| 90 | #493 | — | 14 | 1 | no | — |
| 91 | C2×#108 | — | 7 | 2 | no | — |
| 92 | C2×#108 | — | 14 | 1 | no | — |
| 93 | #423 | — | 14 | 1 | no | — |
| 94 | C2×C4×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 95 | #361 | — | 14 | 8 | no | — |
| 96 | #346 | — | 2 | 1 | no | — |
| 97 | C4×C16 | — | 2 | 1 | no | — |
| 98 | C23×C7 | C2×SD16 | 1 | 1 | yes | characteristic |
| 99 | C22×D7 | — | 4 | 4 | no | — |
| 100 | C22×D7 | — | 8 | 8 | no | — |
| 101 | C22×D7 | — | 8 | 2 | no | — |
| 102 | C22×D7 | — | 8 | 2 | no | — |
| 103 | C2×C4×C7 | — | 2 | 4 | no | — |
| 104 | C2×C4×C7 | #102 | 1 | 2 | yes | — |
| 105 | C2×C4×C7 | #102 | 1 | 2 | yes | — |
| 106 | C2×C4×C7 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 107 | C2×C4×C7 | #124 | 1 | 1 | yes | characteristic |
| 108 | C2×C4×C7 | #127 | 1 | 1 | yes | characteristic |
| 109 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×C7 | C2×SD16 | 1 | 1 | yes | characteristic |
| 112 | D28 | — | 4 | 4 | no | — |
| 113 | D28 | — | 4 | 4 | no | — |
| 114 | D28 | — | 8 | 8 | no | — |
| 115 | D28 | — | 8 | 8 | no | — |
| 116 | D28 | — | 8 | 2 | no | — |
| 117 | D28 | — | 8 | 2 | no | — |
| 118 | C7×C8 | #102 | 1 | 2 | yes | — |
| 119 | C7×C8 | #102 | 1 | 2 | yes | — |
| 120 | C7×C8 | C4×D4 | 1 | 2 | yes | — |
| 121 | C7×C8 | #121 | 1 | 2 | yes | — |
| 122 | C7⋊C8 | — | 8 | 2 | no | — |
| 123 | C22×D4 | — | 14 | 2 | no | — |
| 124 | C22×D4 | — | 28 | 2 | no | — |
| 125 | C2×D8 | — | 7 | 4 | no | — |
| 126 | C2×D8 | — | 14 | 2 | no | — |
| 127 | C2×D8 | — | 14 | 2 | no | — |
| 128 | C2×D8 | — | 14 | 4 | no | — |
| 129 | C2×D8 | — | 14 | 4 | no | — |
| 130 | C2×D8 | — | 14 | 2 | no | — |
| 131 | C2×D8 | — | 28 | 2 | no | — |
| 132 | C2×D8 | — | 28 | 2 | no | — |
| 133 | C2×M16 | — | 14 | 2 | no | — |
| 134 | C22×C8 | D28 | 1 | 1 | yes | characteristic |
| 135 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 136 | #127 | — | 14 | 2 | no | — |
| 137 | #127 | — | 14 | 2 | no | — |
| 138 | #127 | — | 28 | 2 | no | — |
| 139 | C2×C42 | D28 | 1 | 1 | yes | characteristic |
| 140 | M32 | — | 2 | 2 | no | — |
| 141 | M32 | D28 | 1 | 4 | yes | complemented |
| 142 | C2×C16 | — | 2 | 2 | no | — |
| 143 | #108 | — | 14 | 4 | no | — |
| 144 | #108 | — | 28 | 2 | no | — |
| 145 | C4⋊C8 | — | 28 | 2 | no | — |
| 146 | C4×C8 | C4×D7 | 1 | 1 | yes | characteristic |
| 147 | C4×C8 | C4×D7 | 1 | 1 | yes | characteristic |
| 148 | C4×C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 149 | C4×C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 150 | C22×C7 | — | 2 | 2 | no | — |
| 151 | C22×C7 | C2×#102 | 1 | 1 | yes | characteristic |
| 152 | C22×C7 | #486 | 1 | 1 | yes | characteristic |
| 153 | C22×C7 | #492 | 1 | 1 | yes | characteristic |
| 154 | C2×D7 | — | 8 | 8 | no | — |
| 155 | C2×D7 | — | 8 | 4 | no | — |
| 156 | C2×D7 | — | 16 | 4 | no | — |
| 157 | C2×D7 | — | 16 | 4 | no | — |
| 158 | C4×C7 | — | 2 | 2 | no | — |
| 159 | C4×C7 | #361 | 1 | 4 | yes | complemented |
| 160 | C4×C7 | #390 | 1 | 1 | yes | characteristic |
| 161 | C4×C7 | C2×#102 | 1 | 1 | yes | characteristic |
| 162 | C4×C7 | #486 | 1 | 1 | yes | characteristic |
| 163 | C4×C7 | #493 | 1 | 1 | yes | characteristic |
| 164 | C24 | — | 28 | 2 | no | — |
| 165 | C2×D4 | — | 14 | 4 | no | — |
| 166 | C2×D4 | — | 28 | 2 | no | — |
| 167 | C2×D4 | — | 28 | 2 | no | — |
| 168 | C2×D4 | — | 28 | 2 | no | — |
| 169 | C2×D4 | — | 28 | 2 | no | — |
| 170 | C2×D4 | — | 28 | 2 | no | — |
| 171 | C2×D4 | — | 28 | 4 | no | — |
| 172 | C2×D4 | — | 28 | 4 | no | — |
| 173 | C2×D4 | — | 56 | 8 | no | — |
| 174 | C22×C4 | #1132 | 1 | 2 | yes | — |
| 175 | C22×C4 | C2×D28 | 1 | 1 | yes | characteristic |
| 176 | D8 | — | 14 | 8 | no | — |
| 177 | D8 | — | 28 | 4 | no | — |
| 178 | D8 | — | 28 | 4 | no | — |
| 179 | D8 | — | 28 | 4 | no | — |
| 180 | M16 | — | 28 | 2 | no | — |
| 181 | M16 | — | 28 | 2 | no | — |
| 182 | C2×C8 | — | 28 | 2 | no | — |
| 183 | C2×C8 | #1132 | 1 | 2 | yes | — |
| 184 | C2×C8 | D56 | 1 | 2 | yes | — |
| 185 | C2×C8 | (C2×D7)⋊C4 | 1 | 1 | yes | characteristic |
| 186 | C2×C8 | (C2×D7)⋊C4 | 1 | 1 | yes | characteristic |
| 187 | C2×C8 | C2×C4×D7 | 1 | 1 | yes | characteristic |
| 188 | C2×C8 | C2×D28 | 1 | 2 | yes | — |
| 189 | C2×C8 | #1157 | 1 | 2 | yes | — |
| 190 | C2×C8 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 191 | C42 | D56 | 1 | 2 | yes | — |
| 192 | C42 | (C2×D7)⋊C4 | 1 | 1 | yes | characteristic |
| 193 | C42 | (C2×D7)⋊C4 | 1 | 1 | yes | characteristic |
| 194 | C16 | — | 2 | 4 | no | — |
| 195 | C2×C7 | — | 2 | 1 | no | — |
| 196 | C2×C7 | — | 2 | 1 | no | — |
| 197 | C2×C7 | #1957 | 1 | 1 | yes | characteristic |
| 198 | C2×C7 | C2×#361 | 1 | 2 | yes | — |
| 199 | D7 | — | 16 | 4 | no | — |
| 200 | C23 | — | 28 | 4 | no | — |
| 201 | C23 | — | 56 | 8 | no | — |
| 202 | C23 | — | 56 | 2 | no | — |
| 203 | C23 | — | 56 | 2 | no | — |
| 204 | C23 | C2×#1132 | 1 | 1 | yes | characteristic |
| 205 | D4 | — | 28 | 4 | no | — |
| 206 | D4 | — | 28 | 4 | no | — |
| 207 | D4 | — | 56 | 8 | no | — |
| 208 | D4 | — | 56 | 2 | no | — |
| 209 | D4 | — | 56 | 2 | no | — |
| 210 | D4 | — | 56 | 8 | no | — |
| 211 | C2×C4 | — | 2 | 4 | no | — |
| 212 | C2×C4 | #6395 | 1 | 2 | yes | — |
| 213 | C2×C4 | #6395 | 1 | 2 | yes | — |
| 214 | C2×C4 | #6437 | 1 | 1 | yes | characteristic |
| 215 | C2×C4 | #6438 | 1 | 1 | yes | characteristic |
| 216 | C2×C4 | C2×#1132 | 1 | 1 | yes | characteristic |
| 217 | C2×C4 | C2×D56 | 1 | 1 | yes | characteristic |
| 218 | C2×C4 | C2×D56 | 1 | 1 | yes | characteristic |
| 219 | C2×C4 | C2×(C2×D7)⋊C4 | 1 | 1 | yes | characteristic |
| 220 | C8 | — | 56 | 2 | no | — |
| 221 | C8 | #6395 | 1 | 2 | yes | — |
| 222 | C8 | #6395 | 1 | 2 | yes | — |
| 223 | C8 | C4×D28 | 1 | 2 | yes | — |
| 224 | C8 | #6493 | 1 | 2 | yes | — |
| 225 | C7 | #13213 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 226 | C22 | — | 2 | 2 | no | — |
| 227 | C22 | — | 56 | 8 | no | — |
| 228 | C22 | — | 56 | 4 | no | — |
| 229 | C22 | — | 112 | 4 | no | — |
| 230 | C22 | — | 112 | 4 | no | — |
| 231 | C22 | #89465 | 1 | 1 | yes | characteristic |
| 232 | C22 | #89466 | 1 | 1 | yes | characteristic |
| 233 | C22 | C2×#6395 | 1 | 1 | yes | characteristic |
| 234 | C4 | — | 2 | 2 | no | — |
| 235 | C4 | #89311 | 1 | 4 | yes | complemented |
| 236 | C4 | #89466 | 1 | 1 | yes | characteristic |
| 237 | C4 | #89467 | 1 | 1 | yes | characteristic |
| 238 | C4 | #89711 | 1 | 1 | yes | characteristic |
| 239 | C4 | C2×#6395 | 1 | 1 | yes | characteristic |
| 240 | C2 | — | 2 | 1 | no | — |
| 241 | C2 | — | 2 | 1 | no | — |
| 242 | C2 | — | 112 | 4 | no | — |
| 243 | C2 | #11727526 | 1 | 1 | yes | characteristic |
| 244 | C2 | C2×#89311 | 1 | 2 | yes | — |
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