← #14907265
Subgroups — #14907265
Order 2816.
506 conjugacy classes of subgroups.
The subgroup lattice has 244 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13077548 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13070522 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C16×Dic22 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13070376 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13070375 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #13070371 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #13070212 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×C16×Dic11 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C11×#2108 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #10623048 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×C11×M32 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×C11×C16 | C22 | 1 | 1 | yes | characteristic |
| 13 | C11×#405 | C22 | 1 | 1 | yes | characteristic |
| 14 | #10622732 | C4 | 1 | 1 | yes | characteristic |
| 15 | #10622731 | C4 | 1 | 1 | yes | characteristic |
| 16 | #10622714 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C8×Dic11 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#66876 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×C11⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 20 | #10622612 | C4 | 1 | 1 | yes | characteristic |
| 21 | #10622314 | C4 | 1 | 4 | yes | — |
| 22 | C8×Dic22 | C22 | 1 | 4 | yes | — |
| 23 | C11×#346 | C22 | 1 | 2 | yes | — |
| 24 | C4×C11×C16 | C22 | 1 | 2 | yes | — |
| 25 | #10622140 | C22 | 1 | 2 | yes | — |
| 26 | Dic11⋊C16 | C22 | 1 | 4 | yes | — |
| 27 | Dic11⋊C16 | C22 | 1 | 4 | yes | — |
| 28 | C16×Dic11 | C22 | 1 | 2 | yes | — |
| 29 | C16×Dic11 | C22 | 1 | 2 | yes | — |
| 30 | C16×Dic11 | C22 | 1 | 2 | yes | — |
| 31 | C4⋊(C11⋊C16) | C22 | 1 | 4 | yes | — |
| 32 | C2×C11×M16 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C22×C8×C11 | C23 | 1 | 1 | yes | characteristic |
| 34 | C11×#117 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | #66979 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×C4×Dic11 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×#4318 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C22×C11⋊C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | #66943 | C8 | 1 | 2 | yes | — |
| 40 | #66941 | C8 | 1 | 2 | yes | — |
| 41 | #66931 | C8 | 1 | 4 | yes | — |
| 42 | C4×Dic22 | C2×C4 | 1 | 4 | yes | — |
| 43 | C11×M32 | — | 2 | 2 | no | — |
| 44 | C2×C11×C16 | Q8 | 1 | 4 | yes | complemented |
| 45 | C2×C11×C16 | C23 | 1 | 2 | yes | — |
| 46 | C2×C11×C16 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×C11×C16 | C23 | 1 | 1 | yes | characteristic |
| 48 | C11×#97 | C2×C4 | 1 | 2 | yes | — |
| 49 | C4×C8×C11 | C23 | 1 | 2 | yes | — |
| 50 | #66879 | C2×C4 | 1 | 2 | yes | — |
| 51 | Dic11⋊C8 | C2×C4 | 1 | 4 | yes | — |
| 52 | Dic11⋊C8 | C2×C4 | 1 | 4 | yes | — |
| 53 | C8×Dic11 | C2×C4 | 1 | 2 | yes | — |
| 54 | C8×Dic11 | C23 | 1 | 2 | yes | — |
| 55 | C8×Dic11 | C23 | 1 | 2 | yes | — |
| 56 | #66876 | — | 2 | 2 | no | — |
| 57 | C2×C11⋊C16 | — | 2 | 2 | no | — |
| 58 | C2×C11⋊C16 | C23 | 1 | 2 | yes | — |
| 59 | C2×C11⋊C16 | C23 | 1 | 2 | yes | — |
| 60 | C4⋊(C11⋊C8) | C2×C4 | 1 | 4 | yes | — |
| 61 | #33474 | — | 11 | 1 | no | maximal, Sylow |
| 62 | C22×C4×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 63 | C22×Dic11 | C2×C8 | 1 | 2 | yes | — |
| 64 | C2×Dic22 | C2×C8 | 1 | 4 | yes | — |
| 65 | C11×M16 | — | 2 | 2 | no | — |
| 66 | C2×C8×C11 | C22×C4 | 1 | 2 | yes | — |
| 67 | C2×C8×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 68 | C2×C8×C11 | C2×Q8 | 1 | 2 | yes | — |
| 69 | C2×C8×C11 | #41 | 1 | 2 | yes | — |
| 70 | C2×C8×C11 | C24 | 1 | 1 | yes | characteristic |
| 71 | C11×C4⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 72 | C11×C22⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 73 | C42×C11 | C22×C4 | 1 | 2 | yes | — |
| 74 | C22⋊Dic11 | C2×C8 | 1 | 2 | yes | — |
| 75 | C4⋊Dic11 | C2×C8 | 1 | 4 | yes | — |
| 76 | C4⋊Dic11 | C2×C8 | 1 | 2 | yes | — |
| 77 | Dic11⋊C4 | C2×C8 | 1 | 4 | yes | — |
| 78 | Dic11⋊C4 | C2×C8 | 1 | 4 | yes | — |
| 79 | C4×Dic11 | C2×C8 | 1 | 1 | yes | characteristic |
| 80 | C4×Dic11 | C2×C8 | 1 | 1 | yes | characteristic |
| 81 | C4×Dic11 | C22×C4 | 1 | 2 | yes | — |
| 82 | C4×Dic11 | C22×C4 | 1 | 2 | yes | — |
| 83 | #4318 | — | 2 | 2 | no | — |
| 84 | C2×C11⋊C8 | — | 2 | 2 | no | — |
| 85 | C2×C11⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 86 | C2×C11⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 87 | C11×C16 | — | 2 | 2 | no | — |
| 88 | C11×C16 | C2×Q8 | 1 | 2 | yes | — |
| 89 | C11×C16 | C2×Q8 | 1 | 2 | yes | — |
| 90 | C11⋊C16 | — | 2 | 2 | no | — |
| 91 | C11⋊C16 | — | 2 | 2 | no | — |
| 92 | #2960 | — | 11 | 1 | no | — |
| 93 | #2183 | — | 11 | 4 | no | — |
| 94 | Q8×C16 | — | 11 | 4 | no | — |
| 95 | #2151 | — | 11 | 1 | no | — |
| 96 | #2151 | — | 11 | 1 | no | — |
| 97 | #2150 | — | 11 | 1 | no | — |
| 98 | #2108 | — | 11 | 1 | no | — |
| 99 | #2108 | D11 | 1 | 1 | yes | characteristic |
| 100 | C2×C4×C16 | — | 11 | 1 | no | — |
| 101 | C23×C11 | C22×C8 | 1 | 1 | yes | characteristic |
| 102 | C2×C4×C11 | C4×Q8 | 1 | 2 | yes | — |
| 103 | C2×C4×C11 | C22×C8 | 1 | 4 | yes | — |
| 104 | C2×C4×C11 | C22×C8 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C11 | #131 | 1 | 2 | yes | — |
| 106 | C2×C4×C11 | C23×C4 | 1 | 1 | yes | characteristic |
| 107 | C2×Dic11 | — | 2 | 4 | no | — |
| 108 | C2×Dic11 | C22×C8 | 1 | 2 | yes | — |
| 109 | C2×Dic11 | C22×C8 | 1 | 4 | yes | — |
| 110 | C2×Dic11 | C22×C8 | 1 | 2 | yes | — |
| 111 | Dic22 | — | 2 | 8 | no | — |
| 112 | C8×C11 | — | 2 | 2 | no | — |
| 113 | C8×C11 | C4×Q8 | 1 | 2 | yes | — |
| 114 | C8×C11 | C22×Q8 | 1 | 1 | yes | characteristic |
| 115 | C8×C11 | C2×#41 | 1 | 1 | yes | characteristic |
| 116 | C11⋊C8 | — | 2 | 2 | no | — |
| 117 | C11⋊C8 | — | 2 | 2 | no | — |
| 118 | #533 | — | 11 | 1 | no | — |
| 119 | C2×M32 | — | 11 | 1 | no | — |
| 120 | C2×M32 | C2×D11 | 1 | 1 | yes | characteristic |
| 121 | C22×C16 | — | 11 | 1 | no | — |
| 122 | C22×C16 | C2×D11 | 1 | 1 | yes | characteristic |
| 123 | #446 | — | 11 | 4 | no | — |
| 124 | C8×Q8 | — | 11 | 4 | no | — |
| 125 | #424 | — | 11 | 1 | no | — |
| 126 | #424 | — | 11 | 1 | no | — |
| 127 | #423 | — | 11 | 1 | no | — |
| 128 | #405 | — | 11 | 1 | no | — |
| 129 | #405 | C2×D11 | 1 | 1 | yes | characteristic |
| 130 | C2×C4×C8 | — | 11 | 1 | no | — |
| 131 | C4⋊C16 | — | 11 | 4 | no | — |
| 132 | C4⋊C16 | — | 11 | 4 | no | — |
| 133 | C4⋊C16 | — | 11 | 4 | no | — |
| 134 | #346 | — | 11 | 2 | no | — |
| 135 | #346 | C2×D11 | 1 | 2 | yes | — |
| 136 | C4×C16 | — | 11 | 2 | no | — |
| 137 | C4×C16 | — | 11 | 2 | no | — |
| 138 | C4×C16 | — | 11 | 2 | no | — |
| 139 | C4×C16 | C2×D11 | 1 | 2 | yes | — |
| 140 | C22×C11 | — | 2 | 2 | no | — |
| 141 | C22×C11 | C8×Q8 | 1 | 2 | yes | — |
| 142 | C22×C11 | C23×C8 | 1 | 1 | yes | characteristic |
| 143 | C4×C11 | — | 2 | 4 | no | — |
| 144 | C4×C11 | C8×Q8 | 1 | 2 | yes | — |
| 145 | C4×C11 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 146 | C4×C11 | C2×#131 | 1 | 1 | yes | characteristic |
| 147 | Dic11 | — | 2 | 4 | no | — |
| 148 | Dic11 | — | 2 | 2 | no | — |
| 149 | Dic11 | #504 | 1 | 4 | yes | — |
| 150 | C2×M16 | — | 11 | 1 | no | — |
| 151 | C2×M16 | C4×D11 | 1 | 1 | yes | characteristic |
| 152 | C22×C8 | — | 11 | 1 | no | — |
| 153 | C22×C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 154 | C4⋊Q8 | — | 11 | 2 | no | — |
| 155 | #125 | — | 11 | 2 | no | — |
| 156 | C22⋊Q8 | — | 11 | 4 | no | — |
| 157 | C4×Q8 | — | 11 | 4 | no | — |
| 158 | #117 | — | 11 | 1 | no | — |
| 159 | #117 | C4×D11 | 1 | 1 | yes | characteristic |
| 160 | C2×C42 | — | 11 | 1 | no | — |
| 161 | M32 | — | 2 | 2 | no | — |
| 162 | M32 | — | 22 | 2 | no | — |
| 163 | C2×C16 | — | 11 | 2 | no | — |
| 164 | C2×C16 | — | 11 | 2 | no | — |
| 165 | C2×C16 | — | 22 | 2 | no | — |
| 166 | C2×C16 | Dic22 | 1 | 4 | yes | complemented |
| 167 | C2×C16 | C22×D11 | 1 | 2 | yes | — |
| 168 | C2×C16 | C22×D11 | 1 | 1 | yes | characteristic |
| 169 | C2×C16 | C22×D11 | 1 | 1 | yes | characteristic |
| 170 | C4⋊C8 | — | 11 | 4 | no | — |
| 171 | C4⋊C8 | — | 11 | 4 | no | — |
| 172 | C4⋊C8 | — | 11 | 4 | no | — |
| 173 | #97 | — | 11 | 2 | no | — |
| 174 | #97 | C4×D11 | 1 | 2 | yes | — |
| 175 | C4×C8 | — | 11 | 2 | no | — |
| 176 | C4×C8 | — | 11 | 2 | no | — |
| 177 | C4×C8 | — | 11 | 2 | no | — |
| 178 | C4×C8 | C22×D11 | 1 | 2 | yes | — |
| 179 | C2×C11 | — | 2 | 2 | no | — |
| 180 | C2×C11 | C2×C8×Q8 | 1 | 1 | yes | characteristic |
| 181 | C2×C11 | C2×#504 | 1 | 2 | yes | — |
| 182 | C2×Q8 | — | 11 | 4 | no | — |
| 183 | C22×C4 | — | 11 | 2 | no | — |
| 184 | C22×C4 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 185 | M16 | — | 2 | 2 | no | — |
| 186 | M16 | — | 22 | 2 | no | — |
| 187 | C2×C8 | — | 11 | 2 | no | — |
| 188 | C2×C8 | — | 11 | 2 | no | — |
| 189 | C2×C8 | — | 22 | 2 | no | — |
| 190 | C2×C8 | C2×Dic22 | 1 | 2 | yes | — |
| 191 | C2×C8 | C2×C4×D11 | 1 | 2 | yes | — |
| 192 | C2×C8 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 193 | C2×C8 | #4339 | 1 | 2 | yes | — |
| 194 | C2×C8 | C23×D11 | 1 | 1 | yes | characteristic |
| 195 | C4⋊C4 | — | 11 | 2 | no | — |
| 196 | C4⋊C4 | — | 11 | 4 | no | — |
| 197 | C4⋊C4 | — | 11 | 4 | no | — |
| 198 | C4⋊C4 | — | 11 | 4 | no | — |
| 199 | C4⋊C4 | C8×D11 | 1 | 2 | yes | — |
| 200 | C22⋊C4 | — | 11 | 2 | no | — |
| 201 | C22⋊C4 | C8×D11 | 1 | 2 | yes | — |
| 202 | C42 | — | 11 | 1 | no | — |
| 203 | C42 | — | 11 | 1 | no | — |
| 204 | C42 | — | 11 | 2 | no | — |
| 205 | C42 | — | 11 | 2 | no | — |
| 206 | C42 | C2×C4×D11 | 1 | 2 | yes | — |
| 207 | C16 | — | 2 | 2 | no | — |
| 208 | C16 | — | 22 | 2 | no | — |
| 209 | C16 | — | 22 | 2 | no | — |
| 210 | C16 | C2×Dic22 | 1 | 2 | yes | — |
| 211 | C16 | C2×Dic22 | 1 | 2 | yes | — |
| 212 | C11 | #33474 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 213 | C23 | C2×C8×D11 | 1 | 1 | yes | characteristic |
| 214 | Q8 | — | 22 | 8 | no | — |
| 215 | C2×C4 | — | 11 | 2 | no | — |
| 216 | C2×C4 | — | 11 | 2 | no | — |
| 217 | C2×C4 | — | 11 | 4 | no | — |
| 218 | C2×C4 | — | 22 | 4 | no | — |
| 219 | C2×C4 | C4×Dic22 | 1 | 2 | yes | — |
| 220 | C2×C4 | C2×C8×D11 | 1 | 4 | yes | — |
| 221 | C2×C4 | C2×C8×D11 | 1 | 1 | yes | characteristic |
| 222 | C2×C4 | #66954 | 1 | 2 | yes | — |
| 223 | C2×C4 | C22×C4×D11 | 1 | 1 | yes | characteristic |
| 224 | C8 | — | 2 | 2 | no | — |
| 225 | C8 | — | 22 | 2 | no | — |
| 226 | C8 | — | 22 | 2 | no | — |
| 227 | C8 | C4×Dic22 | 1 | 2 | yes | — |
| 228 | C8 | C22×Dic22 | 1 | 1 | yes | characteristic |
| 229 | C8 | C2×#4339 | 1 | 1 | yes | characteristic |
| 230 | C22 | — | 2 | 2 | no | — |
| 231 | C22 | C8×Dic22 | 1 | 2 | yes | — |
| 232 | C22 | C22×C8×D11 | 1 | 1 | yes | characteristic |
| 233 | C4 | — | 2 | 4 | no | — |
| 234 | C4 | — | 11 | 4 | no | — |
| 235 | C4 | — | 22 | 2 | no | — |
| 236 | C4 | — | 22 | 4 | no | — |
| 237 | C4 | C8×Dic22 | 1 | 2 | yes | — |
| 238 | C4 | C2×C4×Dic22 | 1 | 1 | yes | characteristic |
| 239 | C4 | C2×#66954 | 1 | 1 | yes | characteristic |
| 240 | C2 | — | 2 | 2 | no | — |
| 241 | C2 | C2×C8×Dic22 | 1 | 1 | yes | characteristic |
| 242 | C2 | D11×#504 | 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