Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
203 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 31 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, complemented |
| 2 | #10590234 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10590133 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10590025 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10590024 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #63810 | — | 2 | 1 | no | — |
| 7 | #63797 | — | 2 | 1 | no | — |
| 8 | C16×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 9 | C3×#800 | — | 2 | 1 | no | — |
| 10 | C3×D48 | — | 2 | 1 | no | — |
| 11 | #63550 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #63545 | C22 | 1 | 2 | yes | — |
| 13 | #63545 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | #63540 | C22 | 1 | 2 | yes | complemented |
| 15 | #4916 | — | 6 | 1 | no | — |
| 16 | D3×D16 | — | 6 | 1 | no | — |
| 17 | #3802 | — | 4 | 1 | no | — |
| 18 | #3796 | — | 4 | 1 | no | — |
| 19 | C8×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 20 | C3×Dic12 | — | 2 | 1 | no | — |
| 21 | C3×D24 | — | 2 | 2 | no | — |
| 22 | C3×D24 | — | 2 | 1 | no | — |
| 23 | #3715 | — | 4 | 1 | no | — |
| 24 | #3713 | — | 4 | 1 | no | — |
| 25 | C32×C16 | D4 | 1 | 1 | yes | characteristic |
| 26 | C3⋊(C3⋊C16) | C23 | 1 | 1 | yes | characteristic |
| 27 | #2263 | — | 9 | 1 | no | maximal, Sylow |
| 28 | #919 | — | 6 | 1 | no | — |
| 29 | #912 | — | 6 | 1 | no | — |
| 30 | D3×D8 | — | 6 | 2 | no | — |
| 31 | C3×SD32 | — | 6 | 1 | no | — |
| 32 | C3×D16 | — | 6 | 1 | no | — |
| 33 | #829 | — | 6 | 1 | no | — |
| 34 | #826 | — | 6 | 2 | no | — |
| 35 | #826 | — | 6 | 1 | no | — |
| 36 | #800 | — | 2 | 1 | no | — |
| 37 | D48 | — | 2 | 1 | no | — |
| 38 | D3×C16 | — | 6 | 1 | no | — |
| 39 | D3×C16 | — | 6 | 1 | no | — |
| 40 | C2×D32 | — | 8 | 1 | no | — |
| 41 | C4×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 42 | C3×D12 | — | 4 | 2 | no | — |
| 43 | C3×D12 | — | 4 | 1 | no | — |
| 44 | C3×Dic6 | — | 4 | 1 | no | — |
| 45 | #626 | — | 8 | 1 | no | — |
| 46 | #625 | — | 8 | 1 | no | — |
| 47 | D3×Dic3 | — | 8 | 1 | no | — |
| 48 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 49 | C3⋊(C3⋊C8) | D8 | 1 | 1 | yes | characteristic |
| 50 | #508 | — | 9 | 1 | no | — |
| 51 | C2×D16 | — | 9 | 1 | no | — |
| 52 | SD64 | — | 9 | 2 | no | — |
| 53 | D32 | — | 9 | 2 | no | — |
| 54 | M64 | — | 9 | 1 | no | — |
| 55 | #239 | — | 12 | 1 | no | — |
| 56 | #237 | — | 12 | 1 | no | — |
| 57 | D3×D4 | — | 12 | 2 | no | — |
| 58 | C3×Q16 | — | 6 | 1 | no | — |
| 59 | C3×D8 | — | 6 | 2 | no | — |
| 60 | C3×D8 | — | 6 | 1 | no | — |
| 61 | #215 | — | 12 | 1 | no | — |
| 62 | #214 | — | 12 | 1 | no | — |
| 63 | #213 | — | 12 | 2 | no | — |
| 64 | Dic12 | — | 2 | 1 | no | — |
| 65 | D24 | — | 2 | 2 | no | — |
| 66 | D24 | — | 2 | 1 | no | — |
| 67 | D3×C8 | — | 6 | 1 | no | — |
| 68 | D3×C8 | — | 6 | 1 | no | — |
| 69 | C3×C16 | — | 2 | 1 | no | — |
| 70 | C3×C16 | — | 2 | 1 | no | — |
| 71 | C3⋊C16 | — | 6 | 1 | no | — |
| 72 | C3⋊C16 | — | 6 | 1 | no | — |
| 73 | C2×C3⋊D3 | D16 | 1 | 1 | yes | characteristic |
| 74 | C2×C3×D3 | — | 8 | 1 | no | — |
| 75 | C2×C3×D3 | — | 8 | 2 | no | — |
| 76 | D32 | — | 16 | 2 | no | — |
| 77 | C32×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 78 | C3⋊Dic3 | D16 | 1 | 1 | yes | characteristic |
| 79 | C3×Dic3 | — | 8 | 1 | no | — |
| 80 | #135 | — | 18 | 1 | no | — |
| 81 | C2×D8 | — | 18 | 1 | no | — |
| 82 | Q32 | — | 9 | 1 | no | — |
| 83 | SD32 | — | 6 | 1 | no | — |
| 84 | D16 | — | 6 | 1 | no | — |
| 85 | D16 | — | 9 | 1 | no | — |
| 86 | D16 | — | 9 | 2 | no | — |
| 87 | C2×C16 | — | 9 | 1 | no | — |
| 88 | C32 | — | 9 | 2 | no | — |
| 89 | C22×D3 | — | 24 | 2 | no | — |
| 90 | C3×Q8 | — | 12 | 1 | no | — |
| 91 | C3×D4 | — | 12 | 2 | no | — |
| 92 | C3×D4 | — | 12 | 1 | no | — |
| 93 | #67 | — | 24 | 2 | no | — |
| 94 | #67 | — | 24 | 1 | no | — |
| 95 | C2×Dic3 | — | 24 | 1 | no | — |
| 96 | D12 | — | 4 | 2 | no | — |
| 97 | D12 | — | 4 | 1 | no | — |
| 98 | D12 | — | 24 | 1 | no | — |
| 99 | C4×D3 | — | 6 | 1 | no | — |
| 100 | C4×D3 | — | 6 | 1 | no | — |
| 101 | C4×D3 | — | 24 | 1 | no | — |
| 102 | Dic6 | — | 4 | 1 | no | — |
| 103 | C3×C8 | — | 2 | 1 | no | — |
| 104 | C3×C8 | — | 2 | 1 | no | — |
| 105 | C3⋊C8 | — | 6 | 1 | no | — |
| 106 | C3⋊C8 | — | 6 | 1 | no | — |
| 107 | C2×C32 | C2×D16 | 1 | 1 | yes | characteristic |
| 108 | C3⋊D3 | — | 2 | 1 | no | — |
| 109 | C3×D3 | — | 16 | 2 | no | — |
| 110 | C3×D3 | — | 16 | 1 | no | — |
| 111 | #41 | — | 36 | 1 | no | — |
| 112 | C2×D4 | — | 36 | 1 | no | — |
| 113 | Q16 | — | 6 | 1 | no | — |
| 114 | SD16 | — | 36 | 1 | no | — |
| 115 | D8 | — | 6 | 2 | no | — |
| 116 | D8 | — | 6 | 1 | no | — |
| 117 | D8 | — | 36 | 1 | no | — |
| 118 | C2×C8 | — | 9 | 1 | no | — |
| 119 | C16 | — | 9 | 1 | no | — |
| 120 | C16 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 121 | C22×C3 | — | 24 | 1 | no | — |
| 122 | C22×C3 | — | 24 | 2 | no | — |
| 123 | C2×D3 | — | 6 | 1 | no | — |
| 124 | C2×D3 | — | 6 | 1 | no | — |
| 125 | C2×D3 | — | 8 | 1 | no | — |
| 126 | C2×D3 | — | 8 | 2 | no | — |
| 127 | C2×D3 | — | 48 | 4 | no | — |
| 128 | C3×C4 | — | 2 | 1 | no | — |
| 129 | C3×C4 | — | 2 | 1 | no | — |
| 130 | C3×C4 | — | 24 | 1 | no | — |
| 131 | Dic3 | — | 6 | 1 | no | — |
| 132 | Dic3 | — | 6 | 1 | no | — |
| 133 | Dic3 | — | 8 | 1 | no | — |
| 134 | C32 | #2263 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 135 | C23 | — | 72 | 1 | no | — |
| 136 | Q8 | — | 12 | 1 | no | — |
| 137 | D4 | — | 12 | 2 | no | — |
| 138 | D4 | — | 12 | 1 | no | — |
| 139 | D4 | — | 72 | 1 | no | — |
| 140 | D4 | — | 72 | 1 | no | — |
| 141 | C2×C4 | — | 9 | 1 | no | — |
| 142 | C2×C4 | — | 72 | 1 | no | — |
| 143 | C8 | — | 9 | 1 | no | — |
| 144 | C8 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 145 | C2×C3 | — | 2 | 1 | no | — |
| 146 | C2×C3 | — | 2 | 1 | no | — |
| 147 | C2×C3 | — | 48 | 2 | no | — |
| 148 | C2×C3 | — | 48 | 1 | no | — |
| 149 | D3 | — | 6 | 2 | no | — |
| 150 | D3 | — | 12 | 1 | no | — |
| 151 | D3 | — | 16 | 2 | no | — |
| 152 | D3 | — | 16 | 1 | no | — |
| 153 | C22 | — | 9 | 1 | no | — |
| 154 | C22 | — | 24 | 1 | no | — |
| 155 | C22 | — | 24 | 2 | no | — |
| 156 | C22 | — | 144 | 2 | no | — |
| 157 | C4 | — | 9 | 1 | no | — |
| 158 | C4 | — | 24 | 1 | no | — |
| 159 | C4 | #64225 | 1 | 1 | yes | characteristic |
| 160 | C3 | — | 2 | 1 | no | — |
| 161 | C3 | — | 2 | 1 | no | — |
| 162 | C2 | — | 18 | 1 | no | — |
| 163 | C2 | — | 48 | 2 | no | — |
| 164 | C2 | — | 48 | 1 | no | — |
| 165 | C2 | #10593276 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10590245 | C2 | semidirect |
| 2. #10590234 | C2 | semidirect |
| 3. #10590133 | C2 | semidirect |
| 4. #10590025 | C2 | semidirect |
| 5. #10590024 | C2 | semidirect |
| 11. #63550 | C22 | semidirect |
| 13. #63545 | C22 | semidirect |
| 14. #63540 | C22 | semidirect |
| 134. C32 | #2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590245 | 2 |
| #10590234 | 2 |
| #10590133 | 2 |
| #10590025 | 2 |
| #10590024 | 2 |
| #2263 | 9 |