← #13082383
Subgroups — #13082383
Order 1408.
1492 conjugacy classes of subgroups.
The subgroup lattice has 222 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C11×2−1+4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#67040 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10623365 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #10623364 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #10623363 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #10623362 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10623348 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | Q8×C22⋊D11 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C2×Q8×Dic11 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C11×2−1+4 | — | 2 | 8 | no | — |
| 11 | C2×C11×#41 | C22 | 1 | 4 | yes | — |
| 12 | C2×C11×#41 | C22 | 1 | 6 | yes | — |
| 13 | C22×Q8×C11 | C22 | 1 | 4 | yes | — |
| 14 | C22×Q8×C11 | C22 | 1 | 1 | yes | characteristic |
| 15 | #67040 | — | 2 | 8 | no | — |
| 16 | C2×#4343 | C22 | 1 | 4 | yes | — |
| 17 | C2×Q8×D11 | C22 | 1 | 4 | yes | — |
| 18 | C2×#4339 | C22 | 1 | 6 | yes | — |
| 19 | #67000 | C22 | 1 | 6 | yes | — |
| 20 | #66999 | C22 | 1 | 12 | yes | — |
| 21 | Q8×Dic11 | C22 | 1 | 4 | yes | — |
| 22 | Q8×Dic11 | C22 | 1 | 4 | yes | — |
| 23 | #66997 | C22 | 1 | 6 | yes | — |
| 24 | #66993 | C22 | 1 | 6 | yes | — |
| 25 | #66992 | C22 | 1 | 4 | yes | — |
| 26 | #66992 | C22 | 1 | 12 | yes | — |
| 27 | #66991 | C22 | 1 | 12 | yes | — |
| 28 | #66989 | C22 | 1 | 6 | yes | — |
| 29 | #66983 | C22 | 1 | 12 | yes | — |
| 30 | C4×C22⋊D11 | C22 | 1 | 12 | yes | — |
| 31 | C4×C22⋊D11 | C22 | 1 | 12 | yes | — |
| 32 | C2×C4⋊Dic11 | C22 | 1 | 3 | yes | — |
| 33 | #66977 | C22 | 1 | 12 | yes | — |
| 34 | C2×C4×Dic11 | C22 | 1 | 3 | yes | — |
| 35 | C11×#41 | — | 2 | 16 | no | — |
| 36 | C11×#41 | — | 2 | 24 | no | — |
| 37 | C2×Q8×C11 | — | 2 | 16 | no | — |
| 38 | C2×Q8×C11 | D4 | 1 | 8 | yes | complemented |
| 39 | C2×Q8×C11 | C23 | 1 | 6 | yes | — |
| 40 | C2×Q8×C11 | C23 | 1 | 4 | yes | — |
| 41 | C2×D4×C11 | C23 | 1 | 6 | yes | — |
| 42 | C2×D4×C11 | C23 | 1 | 4 | yes | — |
| 43 | C22×C4×C11 | C23 | 1 | 12 | yes | — |
| 44 | C22×C4×C11 | C23 | 1 | 3 | yes | — |
| 45 | C2×C22⋊D11 | C23 | 1 | 4 | yes | — |
| 46 | C2×C22⋊D11 | C23 | 1 | 4 | yes | — |
| 47 | C2×C22⋊D11 | C23 | 1 | 12 | yes | — |
| 48 | C22×Dic11 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×Dic11 | C23 | 1 | 3 | yes | — |
| 50 | #4343 | — | 2 | 16 | no | — |
| 51 | Q8×D11 | — | 2 | 16 | no | — |
| 52 | #4339 | — | 2 | 24 | no | — |
| 53 | C2×D44 | C23 | 1 | 6 | yes | — |
| 54 | C2×C4×D11 | C23 | 1 | 12 | yes | — |
| 55 | C2×Dic22 | C23 | 1 | 6 | yes | — |
| 56 | C22⋊Dic11 | C23 | 1 | 12 | yes | — |
| 57 | C22⋊Dic11 | C23 | 1 | 4 | yes | — |
| 58 | (C2×D11)⋊C4 | C23 | 1 | 4 | yes | — |
| 59 | (C2×D11)⋊C4 | C23 | 1 | 12 | yes | — |
| 60 | C4⋊Dic11 | C23 | 1 | 12 | yes | — |
| 61 | Dic11⋊C4 | C23 | 1 | 12 | yes | — |
| 62 | Dic11⋊C4 | C23 | 1 | 4 | yes | — |
| 63 | C4×Dic11 | C23 | 1 | 6 | yes | — |
| 64 | C4×Dic11 | C23 | 1 | 6 | yes | — |
| 65 | #3497 | — | 11 | 1 | no | maximal, Sylow |
| 66 | C23×C11 | C24 | 1 | 4 | yes | — |
| 67 | C23×C11 | C24 | 1 | 1 | yes | characteristic |
| 68 | C22×D11 | C24 | 1 | 4 | yes | — |
| 69 | Q8×C11 | — | 2 | 12 | no | — |
| 70 | Q8×C11 | C2×D4 | 1 | 16 | yes | — |
| 71 | D4×C11 | — | 2 | 8 | no | — |
| 72 | D4×C11 | — | 2 | 12 | no | — |
| 73 | C2×C4×C11 | — | 2 | 24 | no | — |
| 74 | C2×C4×C11 | C2×D4 | 1 | 12 | yes | — |
| 75 | C2×C4×C11 | C24 | 1 | 4 | yes | — |
| 76 | C2×C4×C11 | C24 | 1 | 6 | yes | — |
| 77 | C22⋊D11 | — | 2 | 8 | no | — |
| 78 | C22⋊D11 | — | 2 | 8 | no | — |
| 79 | C22⋊D11 | — | 4 | 12 | no | — |
| 80 | C2×Dic11 | — | 2 | 2 | no | — |
| 81 | C2×Dic11 | — | 4 | 3 | no | — |
| 82 | C2×Dic11 | C24 | 1 | 1 | yes | characteristic |
| 83 | C2×Dic11 | C24 | 1 | 6 | yes | — |
| 84 | C2×Dic11 | C24 | 1 | 4 | yes | — |
| 85 | C2×Dic11 | C24 | 1 | 1 | yes | characteristic |
| 86 | D44 | — | 2 | 12 | no | — |
| 87 | C4×D11 | — | 2 | 24 | no | — |
| 88 | Dic22 | — | 2 | 12 | no | — |
| 89 | C2×2−1+4 | — | 11 | 1 | no | — |
| 90 | C2×2−1+4 | D11 | 1 | 1 | yes | characteristic, complemented |
| 91 | #550 | — | 11 | 4 | no | — |
| 92 | D4×Q8 | — | 11 | 4 | no | — |
| 93 | #548 | — | 11 | 4 | no | — |
| 94 | #548 | — | 11 | 4 | no | — |
| 95 | #537 | — | 11 | 6 | no | — |
| 96 | #532 | — | 11 | 6 | no | — |
| 97 | C2×C4×Q8 | — | 11 | 1 | no | — |
| 98 | C22×C11 | — | 2 | 1 | no | — |
| 99 | C22×C11 | — | 2 | 1 | no | — |
| 100 | C22×C11 | — | 2 | 4 | no | — |
| 101 | C22×C11 | — | 2 | 4 | no | — |
| 102 | C22×C11 | — | 2 | 4 | no | — |
| 103 | C22×C11 | C22×D4 | 1 | 2 | yes | — |
| 104 | C22×C11 | C25 | 1 | 1 | yes | characteristic |
| 105 | C2×D11 | — | 2 | 4 | no | — |
| 106 | C2×D11 | — | 2 | 4 | no | — |
| 107 | C2×D11 | — | 2 | 4 | no | — |
| 108 | C4×C11 | — | 2 | 4 | no | — |
| 109 | C4×C11 | C22×D4 | 1 | 12 | yes | — |
| 110 | Dic11 | — | 2 | 4 | no | — |
| 111 | Dic11 | — | 2 | 1 | no | — |
| 112 | Dic11 | — | 2 | 6 | no | — |
| 113 | Dic11 | 2−1+4 | 1 | 2 | yes | complemented |
| 114 | 2−1+4 | — | 2 | 8 | no | — |
| 115 | 2−1+4 | — | 22 | 8 | no | — |
| 116 | C2×#41 | — | 11 | 4 | no | — |
| 117 | C2×#41 | — | 11 | 6 | no | — |
| 118 | C2×#41 | C2×D11 | 1 | 6 | yes | — |
| 119 | C2×#41 | C2×D11 | 1 | 4 | yes | — |
| 120 | C22×Q8 | — | 11 | 4 | no | — |
| 121 | C22×Q8 | C2×D11 | 1 | 4 | yes | — |
| 122 | C22×Q8 | C2×D11 | 1 | 1 | yes | characteristic |
| 123 | C4⋊Q8 | — | 11 | 6 | no | — |
| 124 | #127 | — | 11 | 6 | no | — |
| 125 | #124 | — | 11 | 6 | no | — |
| 126 | #124 | — | 11 | 6 | no | — |
| 127 | C22⋊Q8 | — | 11 | 12 | no | — |
| 128 | C22⋊Q8 | — | 11 | 12 | no | — |
| 129 | #121 | — | 11 | 4 | no | — |
| 130 | #121 | — | 11 | 12 | no | — |
| 131 | #121 | — | 11 | 12 | no | — |
| 132 | #121 | — | 11 | 12 | no | — |
| 133 | C4×Q8 | — | 11 | 4 | no | — |
| 134 | C4×Q8 | — | 11 | 4 | no | — |
| 135 | C4×D4 | — | 11 | 12 | no | — |
| 136 | C4×D4 | — | 11 | 12 | no | — |
| 137 | C2×C4⋊C4 | — | 11 | 3 | no | — |
| 138 | C2×C42 | — | 11 | 3 | no | — |
| 139 | C2×C11 | — | 2 | 2 | no | — |
| 140 | C2×C11 | — | 4 | 4 | no | — |
| 141 | C2×C11 | C23×D4 | 1 | 1 | yes | characteristic |
| 142 | C2×C11 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 143 | C2×C11 | #585 | 1 | 1 | yes | characteristic |
| 144 | D11 | — | 4 | 4 | no | — |
| 145 | #41 | — | 2 | 16 | no | — |
| 146 | #41 | — | 2 | 24 | no | — |
| 147 | #41 | — | 22 | 16 | no | — |
| 148 | #41 | — | 22 | 24 | no | — |
| 149 | C2×Q8 | — | 2 | 16 | no | — |
| 150 | C2×Q8 | — | 11 | 6 | no | — |
| 151 | C2×Q8 | — | 22 | 16 | no | — |
| 152 | C2×Q8 | C22⋊D11 | 1 | 8 | yes | complemented |
| 153 | C2×Q8 | C22×D11 | 1 | 6 | yes | — |
| 154 | C2×Q8 | C22×D11 | 1 | 4 | yes | — |
| 155 | C2×D4 | — | 11 | 4 | no | — |
| 156 | C2×D4 | — | 11 | 4 | no | — |
| 157 | C2×D4 | — | 11 | 12 | no | — |
| 158 | C2×D4 | — | 11 | 6 | no | — |
| 159 | C2×D4 | C22×D11 | 1 | 4 | yes | — |
| 160 | C2×D4 | C22×D11 | 1 | 6 | yes | — |
| 161 | C22×C4 | — | 11 | 1 | no | — |
| 162 | C22×C4 | — | 11 | 3 | no | — |
| 163 | C22×C4 | — | 11 | 12 | no | — |
| 164 | C22×C4 | C22×D11 | 1 | 12 | yes | — |
| 165 | C22×C4 | C22×D11 | 1 | 3 | yes | — |
| 166 | C4⋊C4 | — | 11 | 12 | no | — |
| 167 | C4⋊C4 | — | 11 | 4 | no | — |
| 168 | C4⋊C4 | — | 11 | 12 | no | — |
| 169 | C22⋊C4 | — | 11 | 4 | no | — |
| 170 | C22⋊C4 | — | 11 | 12 | no | — |
| 171 | C22⋊C4 | — | 11 | 4 | no | — |
| 172 | C22⋊C4 | — | 11 | 12 | no | — |
| 173 | C42 | — | 11 | 6 | no | — |
| 174 | C42 | — | 11 | 6 | no | — |
| 175 | C11 | #3497 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 176 | C23 | — | 11 | 4 | no | — |
| 177 | C23 | C23×D11 | 1 | 4 | yes | — |
| 178 | C23 | C23×D11 | 1 | 1 | yes | characteristic |
| 179 | Q8 | — | 2 | 12 | no | — |
| 180 | Q8 | — | 22 | 12 | no | — |
| 181 | Q8 | C2×C22⋊D11 | 1 | 16 | yes | — |
| 182 | D4 | — | 2 | 8 | no | — |
| 183 | D4 | — | 2 | 12 | no | — |
| 184 | D4 | — | 22 | 8 | no | — |
| 185 | D4 | — | 22 | 8 | no | — |
| 186 | D4 | — | 22 | 12 | no | — |
| 187 | D4 | — | 44 | 12 | no | — |
| 188 | C2×C4 | — | 2 | 24 | no | — |
| 189 | C2×C4 | — | 11 | 1 | no | — |
| 190 | C2×C4 | — | 11 | 1 | no | — |
| 191 | C2×C4 | — | 11 | 6 | no | — |
| 192 | C2×C4 | — | 11 | 4 | no | — |
| 193 | C2×C4 | — | 22 | 2 | no | — |
| 194 | C2×C4 | — | 22 | 24 | no | — |
| 195 | C2×C4 | — | 44 | 3 | no | — |
| 196 | C2×C4 | C2×C22⋊D11 | 1 | 12 | yes | — |
| 197 | C2×C4 | C23×D11 | 1 | 4 | yes | — |
| 198 | C2×C4 | C23×D11 | 1 | 6 | yes | — |
| 199 | C22 | — | 2 | 1 | no | — |
| 200 | C22 | — | 2 | 1 | no | — |
| 201 | C22 | — | 2 | 4 | no | — |
| 202 | C22 | — | 2 | 4 | no | — |
| 203 | C22 | — | 2 | 4 | no | — |
| 204 | C22 | — | 22 | 4 | no | — |
| 205 | C22 | — | 22 | 4 | no | — |
| 206 | C22 | — | 22 | 4 | no | — |
| 207 | C22 | C22×C22⋊D11 | 1 | 2 | yes | — |
| 208 | C22 | C24×D11 | 1 | 1 | yes | characteristic |
| 209 | C4 | — | 2 | 4 | no | — |
| 210 | C4 | — | 11 | 2 | no | — |
| 211 | C4 | — | 22 | 1 | no | — |
| 212 | C4 | — | 22 | 6 | no | — |
| 213 | C4 | — | 22 | 4 | no | — |
| 214 | C4 | C22×C22⋊D11 | 1 | 12 | yes | — |
| 215 | C2 | — | 2 | 2 | no | — |
| 216 | C2 | — | 4 | 4 | no | — |
| 217 | C2 | — | 44 | 4 | no | — |
| 218 | C2 | D11×2−1+4 | 1 | 1 | yes | characteristic |
| 219 | C2 | #10623457 | 1 | 1 | yes | characteristic |
| 220 | C2 | C23×C22⋊D11 | 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