← #11664739
Subgroups — #11664739
Order 768.
3114 conjugacy classes of subgroups.
The subgroup lattice has 262 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#5753 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #85827 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×C4×#131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #78576 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #78538 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×#4699 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #78467 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #60648 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C2×#1010 | C22 | 1 | 4 | yes | — |
| 10 | C2×C3×#131 | C22 | 1 | 2 | yes | — |
| 11 | C3×C4×#41 | C22 | 1 | 1 | yes | characteristic |
| 12 | #5753 | — | 2 | 32 | no | — |
| 13 | C2×#909 | C22 | 1 | 24 | yes | — |
| 14 | C22×Dic12 | C22 | 1 | 12 | yes | — |
| 15 | C2×#904 | C22 | 1 | 12 | yes | — |
| 16 | Q8×D12 | — | 2 | 4 | no | — |
| 17 | #5555 | — | 2 | 12 | no | — |
| 18 | #5526 | C22 | 1 | 12 | yes | — |
| 19 | #5477 | C22 | 1 | 6 | yes | — |
| 20 | C2×#869 | C22 | 1 | 6 | yes | — |
| 21 | C3×#405 | C22 | 1 | 6 | yes | — |
| 22 | C3×C4×M16 | C22 | 1 | 3 | yes | — |
| 23 | C2×C3×C4×C8 | C22 | 1 | 3 | yes | — |
| 24 | #4715 | C22 | 1 | 24 | yes | — |
| 25 | #4699 | C22 | 1 | 3 | yes | — |
| 26 | #4699 | C22 | 1 | 6 | yes | — |
| 27 | #4699 | C22 | 1 | 12 | yes | — |
| 28 | #4696 | C22 | 1 | 12 | yes | — |
| 29 | #4695 | C22 | 1 | 1 | yes | characteristic |
| 30 | #4693 | C22 | 1 | 6 | yes | — |
| 31 | C2×#578 | — | 3 | 4 | no | — |
| 32 | #3499 | — | 3 | 2 | no | — |
| 33 | #3156 | — | 3 | 12 | no | — |
| 34 | #3152 | — | 3 | 6 | no | — |
| 35 | #3147 | — | 3 | 3 | no | — |
| 36 | C2×#494 | — | 3 | 3 | no | — |
| 37 | C4×#131 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 39 | #1010 | — | 2 | 32 | no | — |
| 40 | C2×D3×Q8 | — | 2 | 4 | no | — |
| 41 | C2×#237 | — | 2 | 12 | no | — |
| 42 | C2×#235 | C23 | 1 | 12 | yes | — |
| 43 | C22×Dic6 | C23 | 1 | 12 | yes | — |
| 44 | C3×#131 | D4 | 1 | 16 | yes | complemented |
| 45 | C2×C3×M16 | C23 | 1 | 6 | yes | — |
| 46 | C22×C3×C8 | C23 | 1 | 6 | yes | — |
| 47 | C3×C4×Q8 | D4 | 1 | 2 | yes | — |
| 48 | C3×C4×D4 | D4 | 1 | 6 | yes | — |
| 49 | C3×#117 | C23 | 1 | 3 | yes | — |
| 50 | C2×C3×C42 | C23 | 1 | 3 | yes | — |
| 51 | #930 | — | 2 | 12 | no | — |
| 52 | C2×C4⋊Dic3 | — | 2 | 12 | no | — |
| 53 | #909 | — | 2 | 96 | no | — |
| 54 | C2×Dic12 | — | 2 | 48 | no | — |
| 55 | C2×Dic12 | C23 | 1 | 12 | yes | — |
| 56 | C2×Dic12 | C23 | 1 | 24 | yes | — |
| 57 | #904 | — | 2 | 48 | no | — |
| 58 | C2×D24 | C23 | 1 | 4 | yes | — |
| 59 | C2×#204 | C23 | 1 | 24 | yes | — |
| 60 | #897 | — | 2 | 24 | no | — |
| 61 | #886 | — | 2 | 24 | no | — |
| 62 | #875 | C23 | 1 | 12 | yes | — |
| 63 | #874 | C23 | 1 | 2 | yes | — |
| 64 | C4×D12 | — | 2 | 12 | no | — |
| 65 | #869 | — | 2 | 12 | no | — |
| 66 | #869 | C23 | 1 | 6 | yes | — |
| 67 | #869 | C23 | 1 | 12 | yes | — |
| 68 | C3×#97 | C23 | 1 | 6 | yes | — |
| 69 | C3×C4×C8 | C23 | 1 | 3 | yes | — |
| 70 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 71 | C3×C4×C8 | C23 | 1 | 6 | yes | — |
| 72 | C2×2−1+4 | — | 3 | 4 | no | — |
| 73 | #578 | — | 6 | 32 | no | — |
| 74 | C2×#137 | — | 3 | 24 | no | — |
| 75 | C2×#135 | — | 3 | 12 | no | — |
| 76 | C22×Q16 | — | 3 | 12 | no | — |
| 77 | C2×#131 | C2×D3 | 1 | 2 | yes | — |
| 78 | D4×Q8 | — | 6 | 4 | no | — |
| 79 | #547 | — | 6 | 12 | no | — |
| 80 | #536 | — | 3 | 12 | no | — |
| 81 | #532 | — | 3 | 6 | no | — |
| 82 | C2×C4⋊Q8 | — | 3 | 6 | no | — |
| 83 | C4×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 84 | #497 | — | 3 | 24 | no | — |
| 85 | #495 | — | 3 | 12 | no | — |
| 86 | #494 | — | 3 | 3 | no | — |
| 87 | #494 | — | 3 | 6 | no | — |
| 88 | #494 | — | 3 | 12 | no | — |
| 89 | #493 | — | 3 | 1 | no | — |
| 90 | #492 | — | 3 | 6 | no | — |
| 91 | #405 | C2×D3 | 1 | 6 | yes | — |
| 92 | C4×M16 | C2×D3 | 1 | 3 | yes | — |
| 93 | C2×C4×C8 | C2×D3 | 1 | 3 | yes | — |
| 94 | C3×#41 | C2×D4 | 1 | 8 | yes | — |
| 95 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 97 | C22×C3×C4 | C2×D4 | 1 | 6 | yes | — |
| 98 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 99 | C2×#67 | — | 2 | 12 | no | — |
| 100 | C22×Dic3 | — | 2 | 12 | no | — |
| 101 | D3×Q8 | — | 4 | 16 | no | — |
| 102 | #237 | — | 4 | 48 | no | — |
| 103 | #235 | — | 2 | 48 | no | — |
| 104 | C2×D12 | — | 2 | 4 | no | — |
| 105 | C2×D12 | C24 | 1 | 4 | yes | — |
| 106 | C2×C4×D3 | — | 2 | 12 | no | — |
| 107 | C2×Dic6 | — | 2 | 48 | no | — |
| 108 | C2×Dic6 | — | 2 | 12 | no | — |
| 109 | C2×Dic6 | C24 | 1 | 12 | yes | — |
| 110 | C3×M16 | C2×D4 | 1 | 24 | yes | — |
| 111 | C2×C3×C8 | C2×D4 | 1 | 24 | yes | — |
| 112 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 113 | C2×C3×C8 | C24 | 1 | 6 | yes | — |
| 114 | C3×C4⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 115 | C3×C22⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 116 | C3×C42 | C2×D4 | 1 | 6 | yes | — |
| 117 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 118 | C3×C42 | C24 | 1 | 3 | yes | — |
| 119 | (C2×D3)⋊C4 | — | 2 | 24 | no | — |
| 120 | C4⋊Dic3 | — | 2 | 12 | no | — |
| 121 | C4⋊Dic3 | — | 2 | 24 | no | — |
| 122 | Dic12 | — | 2 | 24 | no | — |
| 123 | Dic12 | — | 2 | 48 | no | — |
| 124 | D24 | — | 2 | 8 | no | — |
| 125 | #204 | — | 2 | 48 | no | — |
| 126 | 2−1+4 | — | 6 | 32 | no | — |
| 127 | C2×#41 | — | 3 | 12 | no | — |
| 128 | C2×#41 | — | 6 | 12 | no | — |
| 129 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 130 | C22×Q8 | — | 3 | 12 | no | — |
| 131 | C22×Q8 | — | 6 | 4 | no | — |
| 132 | #137 | — | 6 | 96 | no | — |
| 133 | #135 | — | 6 | 48 | no | — |
| 134 | C2×Q16 | — | 3 | 12 | no | — |
| 135 | C2×Q16 | — | 3 | 24 | no | — |
| 136 | C2×Q16 | — | 6 | 48 | no | — |
| 137 | C2×SD16 | — | 3 | 24 | no | — |
| 138 | C2×D8 | — | 3 | 4 | no | — |
| 139 | #131 | D12 | 1 | 16 | yes | complemented |
| 140 | C2×M16 | C22×D3 | 1 | 6 | yes | — |
| 141 | C22×C8 | C22×D3 | 1 | 6 | yes | — |
| 142 | C4⋊Q8 | — | 3 | 6 | no | — |
| 143 | C4⋊Q8 | — | 3 | 12 | no | — |
| 144 | C4⋊Q8 | — | 6 | 12 | no | — |
| 145 | #127 | — | 3 | 2 | no | — |
| 146 | #124 | — | 3 | 12 | no | — |
| 147 | #123 | — | 6 | 24 | no | — |
| 148 | C22⋊Q8 | — | 6 | 24 | no | — |
| 149 | #121 | — | 6 | 12 | no | — |
| 150 | C4×Q8 | D12 | 1 | 2 | yes | — |
| 151 | C4×D4 | — | 6 | 12 | no | — |
| 152 | C4×D4 | D12 | 1 | 6 | yes | — |
| 153 | #117 | C22×D3 | 1 | 3 | yes | — |
| 154 | C2×C4⋊C4 | — | 6 | 12 | no | — |
| 155 | C2×C42 | C22×D3 | 1 | 3 | yes | — |
| 156 | #97 | C22×D3 | 1 | 6 | yes | — |
| 157 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 158 | C4×C8 | C22×D3 | 1 | 3 | yes | — |
| 159 | C4×C8 | C22×D3 | 1 | 6 | yes | — |
| 160 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 161 | C22×D3 | — | 2 | 4 | no | — |
| 162 | C3×Q8 | #127 | 1 | 4 | yes | — |
| 163 | C3×D4 | #127 | 1 | 12 | yes | — |
| 164 | C2×C3×C4 | — | 2 | 12 | no | — |
| 165 | C2×C3×C4 | C22×D4 | 1 | 6 | yes | — |
| 166 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 167 | C2×C3×C4 | C22×D4 | 1 | 12 | yes | — |
| 168 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 169 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 170 | #67 | — | 4 | 24 | no | — |
| 171 | C2×Dic3 | — | 2 | 12 | no | — |
| 172 | C2×Dic3 | — | 4 | 24 | no | — |
| 173 | D12 | — | 2 | 8 | no | — |
| 174 | D12 | — | 4 | 8 | no | — |
| 175 | C4×D3 | — | 4 | 24 | no | — |
| 176 | Dic6 | — | 2 | 24 | no | — |
| 177 | Dic6 | — | 4 | 24 | no | — |
| 178 | C3×C8 | C22×D4 | 1 | 12 | yes | — |
| 179 | C3×C8 | C22×D4 | 1 | 4 | yes | — |
| 180 | #41 | — | 6 | 48 | no | — |
| 181 | #41 | — | 12 | 48 | no | — |
| 182 | #41 | C2×D12 | 1 | 8 | yes | — |
| 183 | C2×Q8 | — | 3 | 12 | no | — |
| 184 | C2×Q8 | — | 6 | 12 | no | — |
| 185 | C2×Q8 | — | 6 | 48 | no | — |
| 186 | C2×Q8 | — | 12 | 16 | no | — |
| 187 | C2×Q8 | C2×D12 | 1 | 1 | yes | characteristic |
| 188 | C2×D4 | — | 3 | 4 | no | — |
| 189 | C2×D4 | — | 6 | 12 | no | — |
| 190 | C2×D4 | — | 6 | 4 | no | — |
| 191 | C2×D4 | C2×D12 | 1 | 3 | yes | — |
| 192 | C22×C4 | — | 6 | 12 | no | — |
| 193 | C22×C4 | — | 6 | 12 | no | — |
| 194 | C22×C4 | C2×D12 | 1 | 6 | yes | — |
| 195 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 196 | Q16 | — | 6 | 24 | no | — |
| 197 | Q16 | — | 6 | 48 | no | — |
| 198 | SD16 | — | 6 | 48 | no | — |
| 199 | D8 | — | 6 | 8 | no | — |
| 200 | M16 | C2×D12 | 1 | 24 | yes | — |
| 201 | C2×C8 | C2×D12 | 1 | 24 | yes | — |
| 202 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 203 | C2×C8 | C23×D3 | 1 | 6 | yes | — |
| 204 | C4⋊C4 | — | 6 | 12 | no | — |
| 205 | C4⋊C4 | — | 6 | 24 | no | — |
| 206 | C4⋊C4 | C2×D12 | 1 | 6 | yes | — |
| 207 | C22⋊C4 | — | 6 | 24 | no | — |
| 208 | C22⋊C4 | C2×D12 | 1 | 6 | yes | — |
| 209 | C42 | C2×D12 | 1 | 6 | yes | — |
| 210 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 211 | C42 | C23×D3 | 1 | 3 | yes | — |
| 212 | C22×C3 | — | 2 | 6 | no | — |
| 213 | C22×C3 | C2×#127 | 1 | 6 | yes | — |
| 214 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 215 | C2×D3 | — | 4 | 4 | no | — |
| 216 | C2×D3 | — | 4 | 8 | no | — |
| 217 | C3×C4 | — | 2 | 6 | no | — |
| 218 | C3×C4 | C2×#127 | 1 | 6 | yes | — |
| 219 | C3×C4 | #578 | 1 | 4 | yes | complemented |
| 220 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 221 | Dic3 | — | 4 | 12 | no | — |
| 222 | C23 | — | 6 | 4 | no | — |
| 223 | C23 | C22×D12 | 1 | 3 | yes | — |
| 224 | Q8 | — | 6 | 24 | no | — |
| 225 | Q8 | — | 12 | 24 | no | — |
| 226 | Q8 | #874 | 1 | 4 | yes | — |
| 227 | D4 | — | 6 | 8 | no | — |
| 228 | D4 | — | 12 | 24 | no | — |
| 229 | D4 | — | 12 | 8 | no | — |
| 230 | D4 | #874 | 1 | 12 | yes | — |
| 231 | C2×C4 | — | 2 | 12 | no | — |
| 232 | C2×C4 | — | 6 | 12 | no | — |
| 233 | C2×C4 | — | 12 | 24 | no | — |
| 234 | C2×C4 | — | 12 | 24 | no | — |
| 235 | C2×C4 | C22×D12 | 1 | 6 | yes | — |
| 236 | C2×C4 | C22×D12 | 1 | 12 | yes | — |
| 237 | C2×C4 | C22×D12 | 1 | 3 | yes | — |
| 238 | C2×C4 | C22×D12 | 1 | 2 | yes | — |
| 239 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 240 | C8 | C22×D12 | 1 | 4 | yes | — |
| 241 | C8 | C22×D12 | 1 | 12 | yes | — |
| 242 | C2×C3 | — | 2 | 6 | no | — |
| 243 | C2×C3 | C22×#127 | 1 | 1 | yes | characteristic |
| 244 | C2×C3 | C2×#578 | 1 | 2 | yes | — |
| 245 | D3 | — | 8 | 4 | no | — |
| 246 | C22 | — | 2 | 6 | no | — |
| 247 | C22 | — | 12 | 8 | no | — |
| 248 | C22 | — | 12 | 4 | no | — |
| 249 | C22 | C2×#874 | 1 | 6 | yes | — |
| 250 | C22 | C23×D12 | 1 | 1 | yes | characteristic |
| 251 | C4 | — | 2 | 6 | no | — |
| 252 | C4 | — | 12 | 12 | no | — |
| 253 | C4 | C2×#874 | 1 | 6 | yes | — |
| 254 | C4 | #5753 | 1 | 4 | yes | complemented |
| 255 | C4 | C23×D12 | 1 | 2 | yes | — |
| 256 | C3 | #60648 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 257 | C2 | — | 2 | 6 | no | — |
| 258 | C2 | — | 24 | 4 | no | — |
| 259 | C2 | C22×#874 | 1 | 1 | yes | characteristic |
| 260 | C2 | C2×#5753 | 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