← #20288521
Subgroups — #20288521
Order 6784.
964 conjugacy classes of subgroups.
The subgroup lattice has 178 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | Q8×Dic106 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #16811352 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #16811349 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #16811349 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #16811251 | C2 | 1 | 6 | yes | maximal |
| 6 | #16811176 | C2 | 1 | 6 | yes | maximal |
| 7 | #16811101 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×Q8×Dic53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C53×#519 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #13133217 | C22 | 1 | 12 | yes | — |
| 11 | #13133216 | C22 | 1 | 6 | yes | — |
| 12 | #13133216 | C22 | 1 | 12 | yes | — |
| 13 | #13133216 | C22 | 1 | 6 | yes | — |
| 14 | #13133209 | C22 | 1 | 12 | yes | — |
| 15 | #13133208 | C22 | 1 | 6 | yes | — |
| 16 | #13133208 | C22 | 1 | 12 | yes | — |
| 17 | #13133208 | C22 | 1 | 6 | yes | — |
| 18 | #13133194 | C22 | 1 | 4 | yes | — |
| 19 | #13133194 | C22 | 1 | 12 | yes | — |
| 20 | Q8×Dic53 | C22 | 1 | 4 | yes | — |
| 21 | Q8×Dic53 | C22 | 1 | 4 | yes | — |
| 22 | Q8×Dic53 | C22 | 1 | 4 | yes | — |
| 23 | Q8×Dic53 | C22 | 1 | 4 | yes | — |
| 24 | C4×Dic106 | C22 | 1 | 12 | yes | — |
| 25 | C4×Dic106 | C22 | 1 | 12 | yes | — |
| 26 | #13133176 | C22 | 1 | 6 | yes | — |
| 27 | C2×C4⋊Dic53 | C22 | 1 | 3 | yes | — |
| 28 | C2×C4×Dic53 | C22 | 1 | 3 | yes | — |
| 29 | C22×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 30 | C4×Q8×C53 | C22 | 1 | 4 | yes | — |
| 31 | C4×Q8×C53 | C22 | 1 | 4 | yes | — |
| 32 | #117×C53 | C22 | 1 | 6 | yes | — |
| 33 | C2×Q8×C53 | Q8 | 1 | 8 | yes | complemented |
| 34 | C2×Q8×C53 | C23 | 1 | 4 | yes | — |
| 35 | C22×C4×C53 | C23 | 1 | 3 | yes | — |
| 36 | C22×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 37 | C22×Dic53 | C23 | 1 | 3 | yes | — |
| 38 | C2×Dic106 | C23 | 1 | 4 | yes | — |
| 39 | C2×Dic106 | C23 | 1 | 12 | yes | — |
| 40 | C4⋊C4×C53 | C23 | 1 | 6 | yes | — |
| 41 | C4⋊C4×C53 | C23 | 1 | 6 | yes | — |
| 42 | C22⋊C4×C53 | C23 | 1 | 4 | yes | — |
| 43 | C42×C53 | C23 | 1 | 12 | yes | — |
| 44 | C22⋊Dic53 | C23 | 1 | 4 | yes | — |
| 45 | C4⋊Dic53 | C23 | 1 | 12 | yes | — |
| 46 | C4⋊Dic53 | C23 | 1 | 6 | yes | — |
| 47 | C4⋊Dic53 | C23 | 1 | 6 | yes | — |
| 48 | C4⋊Dic53 | C23 | 1 | 4 | yes | — |
| 49 | C4⋊Dic53 | C23 | 1 | 12 | yes | — |
| 50 | #11719919 | C23 | 1 | 4 | yes | — |
| 51 | #11719919 | C23 | 1 | 4 | yes | — |
| 52 | #11719919 | C23 | 1 | 12 | yes | — |
| 53 | #11719919 | C23 | 1 | 12 | yes | — |
| 54 | C4×Dic53 | C23 | 1 | 6 | yes | — |
| 55 | C4×Dic53 | C23 | 1 | 6 | yes | — |
| 56 | C4×Dic53 | C23 | 1 | 12 | yes | — |
| 57 | C23×C53 | C24 | 1 | 1 | yes | characteristic |
| 58 | Q8×C53 | C2×Q8 | 1 | 16 | yes | — |
| 59 | C2×C4×C53 | C2×Q8 | 1 | 12 | yes | — |
| 60 | C2×C4×C53 | C24 | 1 | 4 | yes | — |
| 61 | C2×C4×C53 | C24 | 1 | 4 | yes | — |
| 62 | C2×C4×C53 | C24 | 1 | 6 | yes | — |
| 63 | C2×Dic53 | — | 2 | 2 | no | — |
| 64 | C2×Dic53 | — | 4 | 3 | no | — |
| 65 | C2×Dic53 | C24 | 1 | 4 | yes | — |
| 66 | C2×Dic53 | C24 | 1 | 6 | yes | — |
| 67 | C2×Dic53 | C24 | 1 | 4 | yes | — |
| 68 | C2×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 69 | C2×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 70 | Dic106 | — | 2 | 8 | no | — |
| 71 | Dic106 | — | 4 | 12 | no | — |
| 72 | C22×C53 | — | 2 | 1 | no | — |
| 73 | C22×C53 | — | 2 | 1 | no | — |
| 74 | C22×C53 | C22×Q8 | 1 | 2 | yes | — |
| 75 | C22×C53 | C25 | 1 | 1 | yes | characteristic |
| 76 | C4×C53 | — | 2 | 4 | no | — |
| 77 | C4×C53 | — | 2 | 4 | no | — |
| 78 | C4×C53 | C22×Q8 | 1 | 12 | yes | — |
| 79 | Dic53 | — | 2 | 4 | no | — |
| 80 | Dic53 | — | 2 | 1 | no | — |
| 81 | Dic53 | — | 2 | 4 | no | — |
| 82 | Dic53 | — | 2 | 6 | no | — |
| 83 | Dic53 | 2−1+4 | 1 | 2 | yes | — |
| 84 | #3502 | — | 53 | 1 | no | maximal, Sylow |
| 85 | C2×C53 | — | 2 | 2 | no | — |
| 86 | C2×C53 | C23×Q8 | 1 | 1 | yes | characteristic |
| 87 | C2×C53 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 88 | C2×C53 | #585 | 1 | 1 | yes | characteristic |
| 89 | Q82 | — | 53 | 4 | no | — |
| 90 | #557 | — | 53 | 4 | no | — |
| 91 | #557 | — | 53 | 4 | no | — |
| 92 | #557 | — | 53 | 4 | no | — |
| 93 | #544 | — | 53 | 6 | no | — |
| 94 | #533 | — | 53 | 6 | no | — |
| 95 | #519 | — | 53 | 1 | no | — |
| 96 | #519 | D53 | 1 | 1 | yes | characteristic |
| 97 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 98 | C53 | #3502 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 99 | C22×Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 100 | C4⋊Q8 | — | 53 | 6 | no | — |
| 101 | C4⋊Q8 | — | 53 | 6 | no | — |
| 102 | C4⋊Q8 | — | 53 | 12 | no | — |
| 103 | C4⋊Q8 | — | 53 | 12 | no | — |
| 104 | #125 | — | 53 | 6 | no | — |
| 105 | #125 | — | 53 | 6 | no | — |
| 106 | #125 | — | 53 | 12 | no | — |
| 107 | #125 | — | 53 | 12 | no | — |
| 108 | C22⋊Q8 | — | 53 | 4 | no | — |
| 109 | C22⋊Q8 | — | 53 | 12 | no | — |
| 110 | C4×Q8 | — | 53 | 4 | no | — |
| 111 | C4×Q8 | — | 53 | 4 | no | — |
| 112 | C4×Q8 | — | 53 | 4 | no | — |
| 113 | C4×Q8 | — | 53 | 4 | no | — |
| 114 | C4×Q8 | — | 53 | 12 | no | — |
| 115 | C4×Q8 | — | 53 | 12 | no | — |
| 116 | C4×Q8 | C2×D53 | 1 | 4 | yes | — |
| 117 | C4×Q8 | C2×D53 | 1 | 4 | yes | — |
| 118 | #117 | — | 53 | 6 | no | — |
| 119 | #117 | C2×D53 | 1 | 6 | yes | — |
| 120 | C2×C4⋊C4 | — | 53 | 3 | no | — |
| 121 | C2×C42 | — | 53 | 3 | no | — |
| 122 | C2×Q8 | — | 53 | 4 | no | — |
| 123 | C2×Q8 | — | 53 | 12 | no | — |
| 124 | C2×Q8 | Dic106 | 1 | 8 | yes | complemented |
| 125 | C2×Q8 | C22×D53 | 1 | 4 | yes | — |
| 126 | C22×C4 | — | 53 | 1 | no | — |
| 127 | C22×C4 | — | 53 | 3 | no | — |
| 128 | C22×C4 | C22×D53 | 1 | 3 | yes | — |
| 129 | C4⋊C4 | — | 53 | 12 | no | — |
| 130 | C4⋊C4 | — | 53 | 6 | no | — |
| 131 | C4⋊C4 | — | 53 | 6 | no | — |
| 132 | C4⋊C4 | — | 53 | 4 | no | — |
| 133 | C4⋊C4 | — | 53 | 4 | no | — |
| 134 | C4⋊C4 | — | 53 | 4 | no | — |
| 135 | C4⋊C4 | — | 53 | 12 | no | — |
| 136 | C4⋊C4 | — | 53 | 12 | no | — |
| 137 | C4⋊C4 | — | 53 | 12 | no | — |
| 138 | C4⋊C4 | C22×D53 | 1 | 6 | yes | — |
| 139 | C4⋊C4 | C22×D53 | 1 | 6 | yes | — |
| 140 | C22⋊C4 | — | 53 | 4 | no | — |
| 141 | C22⋊C4 | C22×D53 | 1 | 4 | yes | — |
| 142 | C42 | — | 53 | 6 | no | — |
| 143 | C42 | — | 53 | 6 | no | — |
| 144 | C42 | — | 53 | 12 | no | — |
| 145 | C42 | C22×D53 | 1 | 12 | yes | — |
| 146 | C23 | C23×D53 | 1 | 1 | yes | characteristic |
| 147 | Q8 | — | 106 | 8 | no | — |
| 148 | Q8 | — | 212 | 12 | no | — |
| 149 | Q8 | C2×Dic106 | 1 | 16 | yes | — |
| 150 | C2×C4 | — | 53 | 1 | no | — |
| 151 | C2×C4 | — | 53 | 1 | no | — |
| 152 | C2×C4 | — | 53 | 4 | no | — |
| 153 | C2×C4 | — | 53 | 4 | no | — |
| 154 | C2×C4 | — | 53 | 6 | no | — |
| 155 | C2×C4 | — | 106 | 2 | no | — |
| 156 | C2×C4 | — | 212 | 3 | no | — |
| 157 | C2×C4 | C2×Dic106 | 1 | 12 | yes | — |
| 158 | C2×C4 | C23×D53 | 1 | 4 | yes | — |
| 159 | C2×C4 | C23×D53 | 1 | 4 | yes | — |
| 160 | C2×C4 | C23×D53 | 1 | 6 | yes | — |
| 161 | C22 | — | 2 | 1 | no | — |
| 162 | C22 | — | 2 | 1 | no | — |
| 163 | C22 | C22×Dic106 | 1 | 2 | yes | — |
| 164 | C22 | C24×D53 | 1 | 1 | yes | characteristic |
| 165 | C4 | — | 2 | 4 | no | — |
| 166 | C4 | — | 2 | 4 | no | — |
| 167 | C4 | — | 53 | 2 | no | — |
| 168 | C4 | — | 106 | 1 | no | — |
| 169 | C4 | — | 106 | 4 | no | — |
| 170 | C4 | — | 106 | 6 | no | — |
| 171 | C4 | — | 106 | 4 | no | — |
| 172 | C4 | C22×Dic106 | 1 | 12 | yes | — |
| 173 | C2 | — | 2 | 2 | no | — |
| 174 | C2 | C23×Dic106 | 1 | 1 | yes | characteristic |
| 175 | C2 | 2−1+4×D53 | 1 | 1 | yes | characteristic |
| 176 | C2 | #16811460 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Finite Group Databasebeta