Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
131 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 131 conjugacy classes of subgroups — too many to draw. Only its 23 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 | #10590245 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10590141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10589067 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #63810 | — | 2 | 1 | no | — |
| 5 | #63771 | — | 2 | 1 | no | — |
| 6 | C16×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 7 | C3×#800 | — | 2 | 1 | no | — |
| 8 | #63550 | C4 | 1 | 1 | yes | characteristic |
| 9 | #63545 | C4 | 1 | 1 | yes | characteristic |
| 10 | C3×C3⋊C32 | — | 2 | 1 | no | — |
| 11 | #4916 | — | 6 | 1 | no | — |
| 12 | D3×C32 | — | 6 | 1 | no | — |
| 13 | #3796 | — | 4 | 1 | no | — |
| 14 | #3788 | — | 4 | 1 | no | — |
| 15 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 16 | C3×Dic12 | — | 2 | 1 | no | — |
| 17 | C3×D24 | — | 2 | 1 | no | — |
| 18 | #3715 | — | 4 | 1 | no | — |
| 19 | C32×C16 | D4 | 1 | 1 | yes | characteristic |
| 20 | C3⋊(C3⋊C16) | C2×C4 | 1 | 1 | yes | characteristic |
| 21 | #1417 | — | 9 | 1 | no | maximal, Sylow |
| 22 | #919 | — | 6 | 1 | no | — |
| 23 | #912 | — | 6 | 1 | no | — |
| 24 | C3×SD32 | — | 6 | 1 | no | — |
| 25 | #829 | — | 6 | 1 | no | — |
| 26 | #826 | — | 6 | 1 | no | — |
| 27 | #800 | — | 2 | 1 | no | — |
| 28 | D3×C16 | — | 6 | 1 | no | — |
| 29 | D3×C16 | — | 6 | 1 | no | — |
| 30 | C3×C32 | — | 6 | 1 | no | — |
| 31 | C3⋊C32 | — | 2 | 1 | no | — |
| 32 | C4×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 33 | C3×D12 | — | 4 | 1 | no | — |
| 34 | C3×Dic6 | — | 4 | 1 | no | — |
| 35 | #626 | — | 8 | 1 | no | — |
| 36 | D3×Dic3 | — | 8 | 1 | no | — |
| 37 | #622 | — | 8 | 1 | no | — |
| 38 | C32×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 39 | C3⋊(C3⋊C8) | SD16 | 1 | 1 | yes | characteristic |
| 40 | #508 | — | 9 | 1 | no | — |
| 41 | C2×C32 | — | 9 | 1 | no | — |
| 42 | #368 | — | 9 | 1 | no | — |
| 43 | #239 | — | 12 | 1 | no | — |
| 44 | #237 | — | 12 | 1 | no | — |
| 45 | C3×Q16 | — | 6 | 1 | no | — |
| 46 | C3×D8 | — | 6 | 1 | no | — |
| 47 | #215 | — | 12 | 1 | no | — |
| 48 | #214 | — | 12 | 1 | no | — |
| 49 | Dic12 | — | 2 | 1 | no | — |
| 50 | D24 | — | 2 | 1 | no | — |
| 51 | D3×C8 | — | 6 | 1 | no | — |
| 52 | D3×C8 | — | 6 | 1 | no | — |
| 53 | C3×C16 | — | 2 | 1 | no | — |
| 54 | C3×C16 | — | 2 | 1 | no | — |
| 55 | C3⋊C16 | — | 6 | 1 | no | — |
| 56 | C3⋊C16 | — | 6 | 1 | no | — |
| 57 | C2×C3⋊D3 | SD32 | 1 | 1 | yes | characteristic |
| 58 | C2×C3×D3 | — | 8 | 1 | no | — |
| 59 | C32×C4 | #102 | 1 | 1 | yes | characteristic |
| 60 | C3⋊Dic3 | D16 | 1 | 1 | yes | characteristic |
| 61 | C3×Dic3 | — | 8 | 1 | no | — |
| 62 | #135 | — | 18 | 1 | no | — |
| 63 | Q32 | — | 9 | 1 | no | — |
| 64 | SD32 | — | 6 | 1 | no | — |
| 65 | D16 | — | 9 | 1 | no | — |
| 66 | C2×C16 | — | 9 | 1 | no | — |
| 67 | #108 | — | 18 | 1 | no | — |
| 68 | C32 | — | 6 | 1 | no | — |
| 69 | C3×Q8 | — | 12 | 1 | no | — |
| 70 | C3×D4 | — | 12 | 1 | no | — |
| 71 | #67 | — | 24 | 1 | no | — |
| 72 | C2×Dic3 | — | 24 | 1 | no | — |
| 73 | D12 | — | 4 | 1 | no | — |
| 74 | D12 | — | 24 | 1 | no | — |
| 75 | C4×D3 | — | 6 | 1 | no | — |
| 76 | C4×D3 | — | 6 | 1 | no | — |
| 77 | C4×D3 | — | 24 | 1 | no | — |
| 78 | Dic6 | — | 4 | 1 | no | — |
| 79 | C3×C8 | — | 2 | 1 | no | — |
| 80 | C3×C8 | — | 2 | 1 | no | — |
| 81 | C3⋊C8 | — | 6 | 1 | no | — |
| 82 | C3⋊C8 | — | 6 | 1 | no | — |
| 83 | C2×C32 | #357 | 1 | 1 | yes | characteristic |
| 84 | C3⋊D3 | — | 2 | 1 | no | — |
| 85 | C3×D3 | — | 16 | 1 | no | — |
| 86 | #41 | — | 36 | 1 | no | — |
| 87 | Q16 | — | 6 | 1 | no | — |
| 88 | SD16 | — | 36 | 1 | no | — |
| 89 | D8 | — | 6 | 1 | no | — |
| 90 | M16 | — | 36 | 1 | no | — |
| 91 | C2×C8 | — | 9 | 1 | no | — |
| 92 | C16 | — | 9 | 1 | no | — |
| 93 | C16 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 94 | C22×C3 | — | 24 | 1 | no | — |
| 95 | C2×D3 | — | 6 | 1 | no | — |
| 96 | C2×D3 | — | 6 | 1 | no | — |
| 97 | C2×D3 | — | 8 | 1 | no | — |
| 98 | C3×C4 | — | 2 | 1 | no | — |
| 99 | C3×C4 | — | 2 | 1 | no | — |
| 100 | C3×C4 | — | 24 | 1 | no | — |
| 101 | Dic3 | — | 6 | 1 | no | — |
| 102 | Dic3 | — | 6 | 1 | no | — |
| 103 | Dic3 | — | 8 | 1 | no | — |
| 104 | C32 | #1417 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 105 | Q8 | — | 12 | 1 | no | — |
| 106 | D4 | — | 12 | 1 | no | — |
| 107 | D4 | — | 72 | 1 | no | — |
| 108 | C2×C4 | — | 9 | 1 | no | — |
| 109 | C2×C4 | — | 72 | 1 | no | — |
| 110 | C8 | — | 9 | 1 | no | — |
| 111 | C8 | — | 72 | 1 | no | — |
| 112 | C8 | D32⋊C4 | 1 | 1 | yes | characteristic |
| 113 | C2×C3 | — | 2 | 1 | no | — |
| 114 | C2×C3 | — | 2 | 1 | no | — |
| 115 | C2×C3 | — | 48 | 1 | no | — |
| 116 | D3 | — | 6 | 2 | no | — |
| 117 | D3 | — | 12 | 1 | no | — |
| 118 | D3 | — | 16 | 1 | no | — |
| 119 | C22 | — | 9 | 1 | no | — |
| 120 | C22 | — | 24 | 1 | no | — |
| 121 | C4 | — | 9 | 1 | no | — |
| 122 | C4 | — | 24 | 1 | no | — |
| 123 | C4 | #63729 | 1 | 1 | yes | characteristic |
| 124 | C3 | — | 2 | 1 | no | — |
| 125 | C3 | — | 2 | 1 | no | — |
| 126 | C2 | — | 18 | 1 | no | — |
| 127 | C2 | — | 48 | 1 | no | — |
| 128 | C2 | #10590016 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10590141 | C2 | semidirect |
| 3. #10589067 | C2 | semidirect |
| 104. C32 | #1417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590245 | 2 |
| #10590141 | 2 |
| #10589067 | 2 |
| #1417 | 9 |