Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
738 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #21450100 | C2 | 1 | 3 | yes | maximal |
| 2 | #21445891 | C2 | 1 | 3 | yes | maximal |
| 3 | C61×#1304 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C22×C22⋊Dic61 | C22 | 1 | 3 | yes | — |
| 5 | #16839687 | — | 2 | 6 | no | — |
| 6 | #16839637 | — | 2 | 6 | no | — |
| 7 | #16839623 | — | 2 | 6 | no | — |
| 8 | #16839618 | C22 | 1 | 1 | yes | characteristic |
| 9 | #16839528 | — | 2 | 6 | no | — |
| 10 | C61×#379 | C22 | 1 | 3 | yes | — |
| 11 | C23×Dic61 | D4 | 1 | 6 | yes | — |
| 12 | C2×C4⋊Dic61 | — | 2 | 6 | no | — |
| 13 | C2×C22⋊Dic61 | — | 2 | 6 | no | — |
| 14 | C2×C22⋊Dic61 | — | 2 | 3 | no | — |
| 15 | C2×C22⋊Dic61 | — | 2 | 6 | no | — |
| 16 | C2×C22⋊Dic61 | — | 2 | 3 | no | — |
| 17 | C2×C22⋊Dic61 | — | 2 | 3 | no | — |
| 18 | #14519684 | — | 2 | 6 | no | — |
| 19 | #14519684 | — | 2 | 12 | no | — |
| 20 | C25×C61 | C23 | 1 | 1 | yes | characteristic |
| 21 | C2×C22⋊C4×C61 | — | 2 | 6 | no | — |
| 22 | C2×C22⋊C4×C61 | D4 | 1 | 6 | yes | — |
| 23 | C24×C61 | — | 4 | 6 | no | — |
| 24 | C24×C61 | C2×D4 | 1 | 3 | yes | — |
| 25 | C24×C61 | C2×D4 | 1 | 3 | yes | — |
| 26 | C24×C61 | #41 | 1 | 1 | yes | characteristic |
| 27 | C22×C4×C61 | — | 2 | 6 | no | — |
| 28 | C22×Dic61 | — | 2 | 6 | no | — |
| 29 | C22×Dic61 | — | 2 | 6 | no | — |
| 30 | C22×Dic61 | — | 2 | 6 | no | — |
| 31 | C22×Dic61 | — | 4 | 12 | no | — |
| 32 | C22×Dic61 | — | 4 | 1 | no | — |
| 33 | C22⋊C4×C61 | — | 4 | 12 | no | — |
| 34 | C22⋊C4×C61 | — | 4 | 6 | no | — |
| 35 | C22⋊Dic61 | — | 4 | 3 | no | — |
| 36 | C22⋊Dic61 | — | 4 | 6 | no | — |
| 37 | C22⋊Dic61 | — | 4 | 3 | no | — |
| 38 | C22⋊Dic61 | — | 4 | 6 | no | — |
| 39 | C4⋊Dic61 | — | 8 | 6 | no | — |
| 40 | C23×C61 | — | 2 | 12 | no | — |
| 41 | C23×C61 | — | 2 | 6 | no | — |
| 42 | C23×C61 | — | 4 | 3 | no | — |
| 43 | C23×C61 | — | 4 | 6 | no | — |
| 44 | C23×C61 | — | 4 | 3 | no | — |
| 45 | C23×C61 | — | 8 | 8 | no | — |
| 46 | C23×C61 | #120 | 1 | 3 | yes | — |
| 47 | C23×C61 | #121 | 1 | 3 | yes | — |
| 48 | C23×C61 | #127 | 1 | 1 | yes | characteristic |
| 49 | C2×C4×C61 | — | 4 | 12 | no | — |
| 50 | C2×C4×C61 | — | 4 | 6 | no | — |
| 51 | C2×Dic61 | — | 4 | 12 | no | — |
| 52 | C2×Dic61 | — | 4 | 6 | no | — |
| 53 | C2×Dic61 | — | 4 | 12 | no | — |
| 54 | C2×Dic61 | — | 8 | 6 | no | — |
| 55 | C2×Dic61 | — | 8 | 3 | no | — |
| 56 | #10339 | — | 61 | 1 | no | maximal, Sylow |
| 57 | C22×C61 | — | 2 | 6 | no | — |
| 58 | C22×C61 | — | 2 | 6 | no | — |
| 59 | C22×C61 | — | 2 | 3 | no | — |
| 60 | C22×C61 | — | 2 | 3 | no | — |
| 61 | C22×C61 | — | 4 | 12 | no | — |
| 62 | C22×C61 | — | 8 | 6 | no | — |
| 63 | C22×C61 | — | 8 | 2 | no | — |
| 64 | C22×C61 | #392 | 1 | 1 | yes | characteristic |
| 65 | C22×C61 | #458 | 1 | 6 | yes | — |
| 66 | C4×C61 | — | 8 | 6 | no | — |
| 67 | Dic61 | — | 8 | 6 | no | — |
| 68 | Dic61 | — | 16 | 1 | no | — |
| 69 | #2483 | — | 61 | 3 | no | — |
| 70 | #1819 | — | 61 | 3 | no | — |
| 71 | #1304 | D61 | 1 | 1 | yes | characteristic |
| 72 | C2×C61 | — | 2 | 6 | no | — |
| 73 | C2×C61 | — | 4 | 1 | no | — |
| 74 | C2×C61 | — | 4 | 3 | no | — |
| 75 | C2×C61 | #2022 | 1 | 3 | yes | — |
| 76 | C22×C22⋊C4 | — | 61 | 3 | no | — |
| 77 | #397 | — | 122 | 6 | no | — |
| 78 | #385 | — | 122 | 6 | no | — |
| 79 | #381 | — | 122 | 6 | no | — |
| 80 | #379 | — | 61 | 1 | no | — |
| 81 | #379 | C2×D61 | 1 | 3 | yes | — |
| 82 | #342 | — | 122 | 6 | no | — |
| 83 | C61 | #10339 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 84 | C25 | C22×D61 | 1 | 1 | yes | characteristic |
| 85 | C23×C4 | — | 61 | 6 | no | — |
| 86 | C2×C4⋊C4 | — | 122 | 6 | no | — |
| 87 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 88 | C2×C22⋊C4 | — | 122 | 3 | no | — |
| 89 | C2×C22⋊C4 | — | 122 | 6 | no | — |
| 90 | C2×C22⋊C4 | — | 122 | 6 | no | — |
| 91 | C2×C22⋊C4 | — | 122 | 3 | no | — |
| 92 | C2×C22⋊C4 | — | 122 | 3 | no | — |
| 93 | C2×C22⋊C4 | D244 | 1 | 6 | yes | — |
| 94 | #95 | — | 122 | 6 | no | — |
| 95 | #95 | — | 122 | 12 | no | — |
| 96 | C24 | — | 4 | 6 | no | — |
| 97 | C24 | C2×D244 | 1 | 3 | yes | — |
| 98 | C24 | D4×D61 | 1 | 3 | yes | — |
| 99 | C24 | #11758226 | 1 | 1 | yes | characteristic |
| 100 | C22×C4 | — | 2 | 6 | no | — |
| 101 | C22×C4 | — | 122 | 6 | no | — |
| 102 | C22×C4 | — | 122 | 6 | no | — |
| 103 | C22×C4 | — | 122 | 6 | no | — |
| 104 | C22×C4 | — | 244 | 1 | no | — |
| 105 | C22×C4 | — | 244 | 12 | no | — |
| 106 | C4⋊C4 | — | 488 | 6 | no | — |
| 107 | C22⋊C4 | — | 4 | 12 | no | — |
| 108 | C22⋊C4 | — | 4 | 6 | no | — |
| 109 | C22⋊C4 | — | 244 | 6 | no | — |
| 110 | C22⋊C4 | — | 244 | 3 | no | — |
| 111 | C22⋊C4 | — | 244 | 6 | no | — |
| 112 | C22⋊C4 | — | 244 | 3 | no | — |
| 113 | C23 | — | 2 | 12 | no | — |
| 114 | C23 | — | 2 | 6 | no | — |
| 115 | C23 | — | 4 | 3 | no | — |
| 116 | C23 | — | 4 | 6 | no | — |
| 117 | C23 | — | 4 | 3 | no | — |
| 118 | C23 | — | 8 | 8 | no | — |
| 119 | C23 | #14519747 | 1 | 3 | yes | — |
| 120 | C23 | #14519752 | 1 | 3 | yes | — |
| 121 | C23 | #14519774 | 1 | 1 | yes | characteristic |
| 122 | C2×C4 | — | 4 | 12 | no | — |
| 123 | C2×C4 | — | 4 | 6 | no | — |
| 124 | C2×C4 | — | 488 | 3 | no | — |
| 125 | C2×C4 | — | 488 | 6 | no | — |
| 126 | C2×C4 | — | 244 | 12 | no | — |
| 127 | C2×C4 | — | 244 | 12 | no | — |
| 128 | C2×C4 | — | 244 | 6 | no | — |
| 129 | C22 | — | 2 | 6 | no | — |
| 130 | C22 | — | 2 | 6 | no | — |
| 131 | C22 | — | 2 | 3 | no | — |
| 132 | C22 | — | 2 | 3 | no | — |
| 133 | C22 | — | 4 | 12 | no | — |
| 134 | C22 | — | 8 | 6 | no | — |
| 135 | C22 | — | 8 | 2 | no | — |
| 136 | C22 | #16839672 | 1 | 1 | yes | characteristic |
| 137 | C22 | #16839953 | 1 | 6 | yes | — |
| 138 | C4 | — | 8 | 6 | no | — |
| 139 | C4 | — | 976 | 1 | no | — |
| 140 | C4 | — | 488 | 6 | no | — |
| 141 | C2 | — | 2 | 6 | no | — |
| 142 | C2 | — | 4 | 1 | no | — |
| 143 | C2 | — | 4 | 3 | no | — |
| 144 | C2 | #21446951 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 83. C61 | #10339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21450100 | 2 |
| #21445891 | 2 |
| C61×#1304 | 2 |
| #10339 | 61 |