← #11773673
Subgroups — #11773673
Order 1152.
534 conjugacy classes of subgroups.
The subgroup lattice has 195 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C32×#431 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10592624 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10592624 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10589321 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589320 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10589320 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C8×C3⋊(C3⋊C8) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70744 | — | 3 | 4 | no | maximal |
| 9 | C2×C32×C42 | C22 | 1 | 1 | yes | characteristic |
| 10 | C32×C4⋊C8 | C4 | 1 | 2 | yes | — |
| 11 | C32×C22⋊C8 | C4 | 1 | 2 | yes | — |
| 12 | C32×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 13 | C32×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 14 | #63657 | C4 | 1 | 2 | yes | — |
| 15 | #63657 | C4 | 1 | 2 | yes | — |
| 16 | C4⋊(C3⋊(C3⋊C8)) | C4 | 1 | 2 | yes | — |
| 17 | C4⋊(C3⋊(C3⋊C8)) | C4 | 1 | 2 | yes | — |
| 18 | C4×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 21 | C4×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#431 | D3 | 1 | 4 | yes | — |
| 23 | #4925 | — | 3 | 4 | no | — |
| 24 | #4925 | — | 3 | 4 | no | — |
| 25 | #4455 | — | 3 | 4 | no | — |
| 26 | #4454 | — | 3 | 4 | no | — |
| 27 | #4454 | — | 3 | 4 | no | — |
| 28 | C8×C3⋊C8 | — | 3 | 4 | no | — |
| 29 | C22×C32×C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C22×C32×C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C22×C32×C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C2×C32×C8 | C2×C4 | 1 | 2 | yes | — |
| 33 | C2×C32×C8 | C2×C4 | 1 | 2 | yes | — |
| 34 | C32×C42 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C32×C42 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C32×C42 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×C3⋊(C3⋊C8) | C2×C4 | 1 | 2 | yes | — |
| 39 | C2×C3⋊(C3⋊C8) | C2×C4 | 1 | 2 | yes | — |
| 40 | C2×C3⋊(C3⋊C8) | C2×C4 | 1 | 2 | yes | — |
| 41 | C2×C3⋊(C3⋊C8) | C2×C4 | 1 | 2 | yes | — |
| 42 | #1454 | — | 9 | 1 | no | Sylow |
| 43 | C2×C3×C42 | C2×D3 | 1 | 4 | yes | — |
| 44 | C3×C4⋊C8 | Dic3 | 1 | 8 | yes | — |
| 45 | C3×C22⋊C8 | Dic3 | 1 | 8 | yes | — |
| 46 | C3×C4×C8 | C2×D3 | 1 | 4 | yes | — |
| 47 | C3×C4×C8 | C2×D3 | 1 | 4 | yes | — |
| 48 | #830 | — | 3 | 8 | no | — |
| 49 | #830 | — | 3 | 8 | no | — |
| 50 | C4⋊(C3⋊C8) | — | 3 | 8 | no | — |
| 51 | C4⋊(C3⋊C8) | — | 3 | 8 | no | — |
| 52 | C4×C3⋊C8 | — | 3 | 4 | no | — |
| 53 | C4×C3⋊C8 | — | 3 | 4 | no | — |
| 54 | C4×C3⋊C8 | — | 3 | 4 | no | — |
| 55 | C4×C3⋊C8 | — | 3 | 4 | no | — |
| 56 | C23×C32 | C42 | 1 | 1 | yes | characteristic |
| 57 | C2×C32×C4 | — | 2 | 2 | no | — |
| 58 | C2×C32×C4 | — | 2 | 2 | no | — |
| 59 | C2×C32×C4 | — | 2 | 2 | no | — |
| 60 | C2×C32×C4 | C42 | 1 | 1 | yes | characteristic |
| 61 | C2×C32×C4 | C42 | 1 | 1 | yes | characteristic |
| 62 | C2×C32×C4 | C42 | 1 | 1 | yes | characteristic |
| 63 | C2×C32×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 64 | C2×C32×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 65 | C2×C32×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 66 | C32×C8 | — | 2 | 2 | no | — |
| 67 | C32×C8 | — | 2 | 2 | no | — |
| 68 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 69 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 70 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 71 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 72 | #431 | — | 9 | 1 | no | — |
| 73 | #431 | — | 9 | 1 | no | — |
| 74 | #431 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 75 | #322 | — | 9 | 1 | no | — |
| 76 | #322 | — | 9 | 1 | no | — |
| 77 | #322 | — | 9 | 1 | no | — |
| 78 | C82 | — | 9 | 1 | no | — |
| 79 | C22×C3×C4 | C4×D3 | 1 | 4 | yes | — |
| 80 | C22×C3×C4 | C4×D3 | 1 | 4 | yes | — |
| 81 | C22×C3×C4 | C2×Dic3 | 1 | 4 | yes | — |
| 82 | C2×C3×C8 | C2×Dic3 | 1 | 8 | yes | — |
| 83 | C2×C3×C8 | C2×Dic3 | 1 | 8 | yes | — |
| 84 | C3×C42 | C4×D3 | 1 | 4 | yes | — |
| 85 | C3×C42 | C4×D3 | 1 | 4 | yes | — |
| 86 | C3×C42 | C2×Dic3 | 1 | 4 | yes | — |
| 87 | C3×C42 | C22×D3 | 1 | 4 | yes | — |
| 88 | C2×C3⋊C8 | — | 3 | 8 | no | — |
| 89 | C2×C3⋊C8 | — | 3 | 8 | no | — |
| 90 | C2×C3⋊C8 | — | 3 | 8 | no | — |
| 91 | C2×C3⋊C8 | — | 3 | 8 | no | — |
| 92 | C22×C32 | — | 2 | 1 | no | — |
| 93 | C22×C32 | — | 2 | 1 | no | — |
| 94 | C22×C32 | — | 2 | 1 | no | — |
| 95 | C22×C32 | C2×C42 | 1 | 1 | yes | characteristic |
| 96 | C32×C4 | — | 2 | 1 | no | — |
| 97 | C32×C4 | — | 2 | 1 | no | — |
| 98 | C32×C4 | — | 2 | 1 | no | — |
| 99 | C32×C4 | #131 | 1 | 2 | yes | — |
| 100 | C32×C4 | #131 | 1 | 2 | yes | — |
| 101 | C32×C4 | #131 | 1 | 2 | yes | — |
| 102 | C2×C42 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 103 | C4⋊C8 | — | 9 | 2 | no | — |
| 104 | C4⋊C8 | — | 9 | 2 | no | — |
| 105 | C4⋊C8 | C3⋊Dic3 | 1 | 2 | yes | — |
| 106 | C22⋊C8 | — | 9 | 2 | no | — |
| 107 | C22⋊C8 | — | 9 | 2 | no | — |
| 108 | C22⋊C8 | C3⋊Dic3 | 1 | 2 | yes | — |
| 109 | C4×C8 | — | 9 | 1 | no | — |
| 110 | C4×C8 | — | 9 | 1 | no | — |
| 111 | C4×C8 | — | 9 | 1 | no | — |
| 112 | C4×C8 | — | 9 | 1 | no | — |
| 113 | C4×C8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 114 | C4×C8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 115 | C23×C3 | C4×Dic3 | 1 | 4 | yes | — |
| 116 | C2×C3×C4 | — | 2 | 8 | no | — |
| 117 | C2×C3×C4 | — | 2 | 8 | no | — |
| 118 | C2×C3×C4 | — | 2 | 8 | no | — |
| 119 | C2×C3×C4 | C4×Dic3 | 1 | 4 | yes | — |
| 120 | C2×C3×C4 | C4×Dic3 | 1 | 4 | yes | — |
| 121 | C2×C3×C4 | C4×Dic3 | 1 | 4 | yes | — |
| 122 | C2×C3×C4 | C2×C4×D3 | 1 | 4 | yes | — |
| 123 | C2×C3×C4 | C2×C4×D3 | 1 | 4 | yes | — |
| 124 | C2×C3×C4 | C22×Dic3 | 1 | 4 | yes | — |
| 125 | C3×C8 | — | 2 | 8 | no | — |
| 126 | C3×C8 | — | 2 | 8 | no | — |
| 127 | C3⋊C8 | — | 6 | 8 | no | — |
| 128 | C3⋊C8 | — | 6 | 8 | no | — |
| 129 | C3⋊C8 | — | 6 | 8 | no | — |
| 130 | C3⋊C8 | — | 6 | 8 | no | — |
| 131 | C2×C32 | — | 4 | 1 | no | — |
| 132 | C2×C32 | #405 | 1 | 1 | yes | characteristic |
| 133 | C2×C32 | #405 | 1 | 1 | yes | characteristic |
| 134 | C2×C32 | #405 | 1 | 1 | yes | characteristic |
| 135 | C22×C4 | C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 136 | C22×C4 | C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 137 | C22×C4 | C2×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 138 | C2×C8 | — | 9 | 2 | no | — |
| 139 | C2×C8 | — | 9 | 2 | no | — |
| 140 | C2×C8 | — | 9 | 2 | no | — |
| 141 | C2×C8 | — | 9 | 2 | no | — |
| 142 | C2×C8 | C2×C3⋊Dic3 | 1 | 2 | yes | — |
| 143 | C2×C8 | C2×C3⋊Dic3 | 1 | 2 | yes | — |
| 144 | C42 | C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 145 | C42 | C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 146 | C42 | C2×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 147 | C42 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 148 | C22×C3 | — | 2 | 4 | no | — |
| 149 | C22×C3 | — | 2 | 4 | no | — |
| 150 | C22×C3 | — | 2 | 4 | no | — |
| 151 | C22×C3 | C2×C4×Dic3 | 1 | 4 | yes | — |
| 152 | C3×C4 | — | 2 | 4 | no | — |
| 153 | C3×C4 | — | 2 | 4 | no | — |
| 154 | C3×C4 | — | 2 | 4 | no | — |
| 155 | C3×C4 | #901 | 1 | 8 | yes | — |
| 156 | C3×C4 | #907 | 1 | 8 | yes | — |
| 157 | C3×C4 | #948 | 1 | 8 | yes | — |
| 158 | C32 | #1454 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 159 | C23 | C4×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 160 | C2×C4 | — | 2 | 2 | no | — |
| 161 | C2×C4 | — | 2 | 2 | no | — |
| 162 | C2×C4 | — | 2 | 2 | no | — |
| 163 | C2×C4 | C4×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 164 | C2×C4 | C4×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 165 | C2×C4 | C4×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 166 | C2×C4 | C2×C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 167 | C2×C4 | C2×C4×C3⋊D3 | 1 | 1 | yes | characteristic |
| 168 | C2×C4 | C22×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 169 | C8 | — | 2 | 2 | no | — |
| 170 | C8 | — | 2 | 2 | no | — |
| 171 | C8 | — | 18 | 2 | no | — |
| 172 | C8 | — | 18 | 2 | no | — |
| 173 | C8 | — | 18 | 2 | no | — |
| 174 | C8 | — | 18 | 2 | no | — |
| 175 | C2×C3 | — | 4 | 4 | no | — |
| 176 | C2×C3 | #4997 | 1 | 4 | yes | — |
| 177 | C2×C3 | #5101 | 1 | 4 | yes | — |
| 178 | C2×C3 | #5122 | 1 | 4 | yes | — |
| 179 | C22 | — | 2 | 1 | no | — |
| 180 | C22 | — | 2 | 1 | no | — |
| 181 | C22 | — | 2 | 1 | no | — |
| 182 | C22 | C2×C4×C3⋊Dic3 | 1 | 1 | yes | characteristic |
| 183 | C4 | — | 2 | 1 | no | — |
| 184 | C4 | — | 2 | 1 | no | — |
| 185 | C4 | — | 2 | 1 | no | — |
| 186 | C4 | #64110 | 1 | 2 | yes | — |
| 187 | C4 | #64116 | 1 | 2 | yes | — |
| 188 | C4 | #64157 | 1 | 2 | yes | — |
| 189 | C3 | #70744 | 1 | 4 | yes | complemented |
| 190 | C2 | — | 4 | 1 | no | — |
| 191 | C2 | #10592696 | 1 | 1 | yes | characteristic |
| 192 | C2 | #10592800 | 1 | 1 | yes | characteristic |
| 193 | C2 | #10592821 | 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