Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
222 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 20 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 | #10592414 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10590145 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10590143 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#3746 | — | 2 | 1 | no | — |
| 5 | C2×#3744 | — | 2 | 1 | no | — |
| 6 | #64084 | C22 | 1 | 1 | yes | characteristic |
| 7 | #64078 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | #63780 | — | 2 | 1 | no | — |
| 9 | #63774 | — | 2 | 1 | no | — |
| 10 | C32×#97 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | #4715 | — | 6 | 2 | no | — |
| 12 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 13 | C2×#634 | — | 2 | 1 | no | — |
| 14 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 15 | C22⋊#157 | — | 4 | 1 | no | — |
| 16 | #3792 | — | 4 | 1 | no | — |
| 17 | C2×C32×C8 | — | 2 | 1 | no | — |
| 18 | C32×C42 | C2×C4 | 1 | 1 | yes | characteristic |
| 19 | #3752 | — | 4 | 1 | no | — |
| 20 | C4⋊(C3⋊Dic3) | — | 4 | 1 | no | — |
| 21 | #3746 | — | 4 | 2 | no | — |
| 22 | #3744 | — | 4 | 2 | no | — |
| 23 | #1407 | — | 9 | 1 | no | maximal, Sylow |
| 24 | C2×Dic12 | — | 6 | 4 | no | — |
| 25 | C2×#204 | — | 6 | 4 | no | — |
| 26 | #875 | — | 6 | 2 | no | — |
| 27 | #869 | — | 6 | 2 | no | — |
| 28 | C3×#97 | — | 2 | 2 | no | — |
| 29 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 30 | C2×#157 | — | 8 | 1 | no | — |
| 31 | C2×C32×C4 | — | 2 | 1 | no | — |
| 32 | C2×C32×C4 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 33 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 34 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 35 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 36 | #634 | — | 4 | 1 | no | — |
| 37 | #634 | — | 4 | 1 | no | — |
| 38 | #634 | — | 4 | 1 | no | — |
| 39 | #622 | — | 8 | 1 | no | — |
| 40 | C32×C8 | — | 2 | 2 | no | — |
| 41 | #497 | — | 9 | 1 | no | — |
| 42 | #355 | — | 9 | 1 | no | — |
| 43 | #354 | — | 9 | 1 | no | — |
| 44 | C2×D12 | — | 6 | 2 | no | — |
| 45 | C2×Dic6 | — | 6 | 2 | no | — |
| 46 | C2×Dic6 | — | 6 | 4 | no | — |
| 47 | C2×C3×C8 | — | 2 | 4 | no | — |
| 48 | C3×C42 | — | 2 | 2 | no | — |
| 49 | (C2×D3)⋊C4 | — | 12 | 4 | no | — |
| 50 | C4⋊Dic3 | — | 12 | 4 | no | — |
| 51 | Dic12 | — | 12 | 8 | no | — |
| 52 | #204 | — | 12 | 8 | no | — |
| 53 | C22×C32 | #99 | 1 | 1 | yes | characteristic |
| 54 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 55 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 56 | #157 | — | 16 | 1 | no | — |
| 57 | C32×C4 | — | 2 | 1 | no | — |
| 58 | C32×C4 | — | 4 | 1 | no | — |
| 59 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 60 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 61 | C2×Q16 | — | 18 | 1 | no | — |
| 62 | C2×SD16 | — | 18 | 1 | no | — |
| 63 | C4⋊Q8 | — | 9 | 1 | no | — |
| 64 | #124 | — | 9 | 1 | no | — |
| 65 | #101 | — | 18 | 1 | no | — |
| 66 | #99 | — | 18 | 1 | no | — |
| 67 | #97 | #157 | 1 | 1 | yes | characteristic, complemented |
| 68 | C22×D3 | — | 12 | 2 | no | — |
| 69 | C2×C3×C4 | — | 2 | 4 | no | — |
| 70 | C2×C3×C4 | — | 2 | 2 | no | — |
| 71 | C2×Dic3 | — | 12 | 2 | no | — |
| 72 | C2×Dic3 | — | 12 | 4 | no | — |
| 73 | D12 | — | 12 | 4 | no | — |
| 74 | Dic6 | — | 12 | 4 | no | — |
| 75 | Dic6 | — | 12 | 4 | no | — |
| 76 | Dic6 | — | 12 | 4 | no | — |
| 77 | C3×C8 | — | 2 | 8 | no | — |
| 78 | C2×C32 | — | 2 | 1 | no | — |
| 79 | C2×C32 | #353 | 1 | 1 | yes | characteristic |
| 80 | C3⋊D3 | — | 8 | 1 | no | — |
| 81 | C2×Q8 | — | 9 | 1 | no | — |
| 82 | C2×Q8 | — | 18 | 1 | no | — |
| 83 | C2×D4 | — | 9 | 1 | no | — |
| 84 | Q16 | — | 36 | 2 | no | — |
| 85 | SD16 | — | 36 | 2 | no | — |
| 86 | M16 | — | 36 | 1 | no | — |
| 87 | C2×C8 | — | 2 | 1 | no | — |
| 88 | C4⋊C4 | — | 36 | 1 | no | — |
| 89 | C22⋊C4 | — | 36 | 1 | no | — |
| 90 | C22⋊C4 | — | 36 | 1 | no | — |
| 91 | C42 | C2×#157 | 1 | 1 | yes | characteristic |
| 92 | C22×C3 | — | 2 | 2 | no | — |
| 93 | C2×D3 | — | 24 | 2 | no | — |
| 94 | C2×D3 | — | 24 | 4 | no | — |
| 95 | C3×C4 | — | 2 | 4 | no | — |
| 96 | C3×C4 | — | 4 | 4 | no | — |
| 97 | Dic3 | — | 24 | 2 | no | — |
| 98 | Dic3 | — | 24 | 4 | no | — |
| 99 | C32 | #1407 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 100 | C23 | — | 18 | 1 | no | — |
| 101 | Q8 | — | 36 | 1 | no | — |
| 102 | Q8 | — | 36 | 1 | no | — |
| 103 | Q8 | — | 36 | 1 | no | — |
| 104 | D4 | — | 36 | 1 | no | — |
| 105 | C2×C4 | — | 2 | 1 | no | — |
| 106 | C2×C4 | — | 18 | 1 | no | — |
| 107 | C2×C4 | — | 36 | 1 | no | — |
| 108 | C2×C4 | — | 72 | 1 | no | — |
| 109 | C2×C4 | C22⋊#157 | 1 | 1 | yes | characteristic |
| 110 | C8 | — | 2 | 2 | no | — |
| 111 | C8 | — | 72 | 1 | no | — |
| 112 | C2×C3 | — | 2 | 4 | no | — |
| 113 | C2×C3 | — | 2 | 2 | no | — |
| 114 | D3 | — | 48 | 2 | no | — |
| 115 | C22 | — | 36 | 1 | no | — |
| 116 | C22 | — | 72 | 1 | no | — |
| 117 | C22 | #63774 | 1 | 1 | yes | characteristic |
| 118 | C4 | — | 2 | 1 | no | — |
| 119 | C4 | — | 4 | 1 | no | — |
| 120 | C4 | — | 36 | 1 | no | — |
| 121 | C4 | — | 72 | 1 | no | — |
| 122 | C4 | — | 144 | 1 | no | — |
| 123 | C3 | — | 2 | 2 | no | — |
| 124 | C2 | — | 2 | 1 | no | — |
| 125 | C2 | — | 72 | 1 | no | — |
| 126 | C2 | #10590142 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #64078 | C4 | semidirect |
| 10. C32×#97 | C4 | semidirect |
| 67. #97 | #157 | semidirect |
| 99. C32 | #1407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592414 | 2 |
| #10590145 | 2 |
| #10590143 | 2 |
| #1407 | 9 |