← #13128642
Subgroups — #13128642
Order 1664.
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 | C13×#519 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11719517 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×Q8×Dic13 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11719275 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #11719274 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #11719274 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | Q8×Dic26 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #11719224 | C2 | 1 | 6 | yes | maximal |
| 9 | #11719222 | C2 | 1 | 6 | yes | maximal |
| 10 | C22×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 11 | C4×Q8×C13 | C22 | 1 | 4 | yes | — |
| 12 | C4×Q8×C13 | C22 | 1 | 4 | yes | — |
| 13 | C13×#117 | C22 | 1 | 6 | yes | — |
| 14 | Q8×Dic13 | C22 | 1 | 4 | yes | — |
| 15 | Q8×Dic13 | C22 | 1 | 4 | yes | — |
| 16 | Q8×Dic13 | C22 | 1 | 4 | yes | — |
| 17 | Q8×Dic13 | C22 | 1 | 4 | yes | — |
| 18 | #88180 | C22 | 1 | 6 | yes | — |
| 19 | C2×C4⋊Dic13 | C22 | 1 | 3 | yes | — |
| 20 | C2×C4×Dic13 | C22 | 1 | 3 | yes | — |
| 21 | #88144 | C22 | 1 | 6 | yes | — |
| 22 | #88144 | C22 | 1 | 6 | yes | — |
| 23 | #88144 | C22 | 1 | 12 | yes | — |
| 24 | #88142 | C22 | 1 | 6 | yes | — |
| 25 | #88142 | C22 | 1 | 6 | yes | — |
| 26 | #88142 | C22 | 1 | 12 | yes | — |
| 27 | #88132 | C22 | 1 | 4 | yes | — |
| 28 | #88132 | C22 | 1 | 12 | yes | — |
| 29 | #88124 | C22 | 1 | 12 | yes | — |
| 30 | #88123 | C22 | 1 | 12 | yes | — |
| 31 | C4×Dic26 | C22 | 1 | 12 | yes | — |
| 32 | C4×Dic26 | C22 | 1 | 12 | yes | — |
| 33 | C2×Q8×C13 | Q8 | 1 | 8 | yes | complemented |
| 34 | C2×Q8×C13 | C23 | 1 | 4 | yes | — |
| 35 | C22×C4×C13 | C23 | 1 | 3 | yes | — |
| 36 | C22×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 37 | C22×Dic13 | C23 | 1 | 3 | yes | — |
| 38 | C2×Dic26 | C23 | 1 | 4 | yes | — |
| 39 | C2×Dic26 | C23 | 1 | 12 | yes | — |
| 40 | C13×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 41 | C13×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 42 | C13×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 43 | C42×C13 | C23 | 1 | 12 | yes | — |
| 44 | C22⋊Dic13 | C23 | 1 | 4 | yes | — |
| 45 | C4⋊Dic13 | C23 | 1 | 4 | yes | — |
| 46 | C4⋊Dic13 | C23 | 1 | 12 | yes | — |
| 47 | C4⋊Dic13 | C23 | 1 | 6 | yes | — |
| 48 | C4⋊Dic13 | C23 | 1 | 12 | yes | — |
| 49 | C4⋊Dic13 | C23 | 1 | 6 | yes | — |
| 50 | #6101 | C23 | 1 | 4 | yes | — |
| 51 | #6101 | C23 | 1 | 4 | yes | — |
| 52 | #6101 | C23 | 1 | 12 | yes | — |
| 53 | #6101 | C23 | 1 | 12 | yes | — |
| 54 | C4×Dic13 | C23 | 1 | 6 | yes | — |
| 55 | C4×Dic13 | C23 | 1 | 12 | yes | — |
| 56 | C4×Dic13 | C23 | 1 | 6 | yes | — |
| 57 | #3502 | — | 13 | 1 | no | maximal, Sylow |
| 58 | C23×C13 | C24 | 1 | 1 | yes | characteristic |
| 59 | Q8×C13 | C2×Q8 | 1 | 16 | yes | — |
| 60 | C2×C4×C13 | C2×Q8 | 1 | 12 | yes | — |
| 61 | C2×C4×C13 | C24 | 1 | 4 | yes | — |
| 62 | C2×C4×C13 | C24 | 1 | 4 | yes | — |
| 63 | C2×C4×C13 | C24 | 1 | 6 | yes | — |
| 64 | C2×Dic13 | — | 2 | 2 | no | — |
| 65 | C2×Dic13 | — | 4 | 3 | no | — |
| 66 | C2×Dic13 | C24 | 1 | 1 | yes | characteristic |
| 67 | C2×Dic13 | C24 | 1 | 4 | yes | — |
| 68 | C2×Dic13 | C24 | 1 | 4 | yes | — |
| 69 | C2×Dic13 | C24 | 1 | 6 | yes | — |
| 70 | C2×Dic13 | C24 | 1 | 1 | yes | characteristic |
| 71 | Dic26 | — | 2 | 8 | no | — |
| 72 | Dic26 | — | 4 | 12 | no | — |
| 73 | Q82 | — | 13 | 4 | no | — |
| 74 | #557 | — | 13 | 4 | no | — |
| 75 | #557 | — | 13 | 4 | no | — |
| 76 | #557 | — | 13 | 4 | no | — |
| 77 | #544 | — | 13 | 6 | no | — |
| 78 | #533 | — | 13 | 6 | no | — |
| 79 | #519 | — | 13 | 1 | no | — |
| 80 | #519 | D13 | 1 | 1 | yes | characteristic |
| 81 | C2×C4×Q8 | — | 13 | 1 | no | — |
| 82 | C22×C13 | — | 2 | 1 | no | — |
| 83 | C22×C13 | — | 2 | 1 | no | — |
| 84 | C22×C13 | C22×Q8 | 1 | 2 | yes | — |
| 85 | C22×C13 | C25 | 1 | 1 | yes | characteristic |
| 86 | C4×C13 | — | 2 | 4 | no | — |
| 87 | C4×C13 | — | 2 | 4 | no | — |
| 88 | C4×C13 | C22×Q8 | 1 | 12 | yes | — |
| 89 | Dic13 | — | 2 | 4 | no | — |
| 90 | Dic13 | — | 2 | 1 | no | — |
| 91 | Dic13 | — | 2 | 4 | no | — |
| 92 | Dic13 | — | 2 | 6 | no | — |
| 93 | Dic13 | 2−1+4 | 1 | 2 | yes | — |
| 94 | C22×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 95 | C4⋊Q8 | — | 13 | 6 | no | — |
| 96 | C4⋊Q8 | — | 13 | 6 | no | — |
| 97 | C4⋊Q8 | — | 13 | 12 | no | — |
| 98 | C4⋊Q8 | — | 13 | 12 | no | — |
| 99 | #125 | — | 13 | 6 | no | — |
| 100 | #125 | — | 13 | 6 | no | — |
| 101 | #125 | — | 13 | 12 | no | — |
| 102 | #125 | — | 13 | 12 | no | — |
| 103 | C22⋊Q8 | — | 13 | 4 | no | — |
| 104 | C22⋊Q8 | — | 13 | 12 | no | — |
| 105 | C4×Q8 | — | 13 | 4 | no | — |
| 106 | C4×Q8 | — | 13 | 4 | no | — |
| 107 | C4×Q8 | — | 13 | 4 | no | — |
| 108 | C4×Q8 | — | 13 | 4 | no | — |
| 109 | C4×Q8 | — | 13 | 12 | no | — |
| 110 | C4×Q8 | — | 13 | 12 | no | — |
| 111 | C4×Q8 | C2×D13 | 1 | 4 | yes | — |
| 112 | C4×Q8 | C2×D13 | 1 | 4 | yes | — |
| 113 | #117 | — | 13 | 6 | no | — |
| 114 | #117 | C2×D13 | 1 | 6 | yes | — |
| 115 | C2×C4⋊C4 | — | 13 | 3 | no | — |
| 116 | C2×C42 | — | 13 | 3 | no | — |
| 117 | C2×C13 | — | 2 | 2 | no | — |
| 118 | C2×C13 | C23×Q8 | 1 | 1 | yes | characteristic |
| 119 | C2×C13 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 120 | C2×C13 | #585 | 1 | 1 | yes | characteristic |
| 121 | C2×Q8 | — | 13 | 4 | no | — |
| 122 | C2×Q8 | — | 13 | 12 | no | — |
| 123 | C2×Q8 | Dic26 | 1 | 8 | yes | complemented |
| 124 | C2×Q8 | C22×D13 | 1 | 4 | yes | — |
| 125 | C22×C4 | — | 13 | 1 | no | — |
| 126 | C22×C4 | — | 13 | 3 | no | — |
| 127 | C22×C4 | C22×D13 | 1 | 3 | yes | — |
| 128 | C4⋊C4 | — | 13 | 12 | no | — |
| 129 | C4⋊C4 | — | 13 | 6 | no | — |
| 130 | C4⋊C4 | — | 13 | 6 | no | — |
| 131 | C4⋊C4 | — | 13 | 4 | no | — |
| 132 | C4⋊C4 | — | 13 | 4 | no | — |
| 133 | C4⋊C4 | — | 13 | 4 | no | — |
| 134 | C4⋊C4 | — | 13 | 12 | no | — |
| 135 | C4⋊C4 | — | 13 | 12 | no | — |
| 136 | C4⋊C4 | — | 13 | 12 | no | — |
| 137 | C4⋊C4 | C22×D13 | 1 | 6 | yes | — |
| 138 | C4⋊C4 | C22×D13 | 1 | 6 | yes | — |
| 139 | C22⋊C4 | — | 13 | 4 | no | — |
| 140 | C22⋊C4 | C22×D13 | 1 | 4 | yes | — |
| 141 | C42 | — | 13 | 6 | no | — |
| 142 | C42 | — | 13 | 6 | no | — |
| 143 | C42 | — | 13 | 12 | no | — |
| 144 | C42 | C22×D13 | 1 | 12 | yes | — |
| 145 | C13 | #3502 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 146 | C23 | C23×D13 | 1 | 1 | yes | characteristic |
| 147 | Q8 | — | 26 | 8 | no | — |
| 148 | Q8 | — | 52 | 12 | no | — |
| 149 | Q8 | C2×Dic26 | 1 | 16 | yes | — |
| 150 | C2×C4 | — | 13 | 1 | no | — |
| 151 | C2×C4 | — | 13 | 1 | no | — |
| 152 | C2×C4 | — | 13 | 4 | no | — |
| 153 | C2×C4 | — | 13 | 4 | no | — |
| 154 | C2×C4 | — | 13 | 6 | no | — |
| 155 | C2×C4 | — | 26 | 2 | no | — |
| 156 | C2×C4 | — | 52 | 3 | no | — |
| 157 | C2×C4 | C2×Dic26 | 1 | 12 | yes | — |
| 158 | C2×C4 | C23×D13 | 1 | 4 | yes | — |
| 159 | C2×C4 | C23×D13 | 1 | 4 | yes | — |
| 160 | C2×C4 | C23×D13 | 1 | 6 | yes | — |
| 161 | C22 | — | 2 | 1 | no | — |
| 162 | C22 | — | 2 | 1 | no | — |
| 163 | C22 | C22×Dic26 | 1 | 2 | yes | — |
| 164 | C22 | C24×D13 | 1 | 1 | yes | characteristic |
| 165 | C4 | — | 2 | 4 | no | — |
| 166 | C4 | — | 2 | 4 | no | — |
| 167 | C4 | — | 13 | 2 | no | — |
| 168 | C4 | — | 26 | 1 | no | — |
| 169 | C4 | — | 26 | 4 | no | — |
| 170 | C4 | — | 26 | 6 | no | — |
| 171 | C4 | — | 26 | 4 | no | — |
| 172 | C4 | C22×Dic26 | 1 | 12 | yes | — |
| 173 | C2 | — | 2 | 2 | no | — |
| 174 | C2 | C23×Dic26 | 1 | 1 | yes | characteristic |
| 175 | C2 | D13×2−1+4 | 1 | 1 | yes | characteristic |
| 176 | C2 | #11719652 | 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