Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
580 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 64 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 | #10596196 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×#3788 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10590216 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C2×#3832 | C4 | 1 | 2 | yes | — |
| 5 | C2×#3788 | — | 2 | 2 | no | — |
| 6 | C32×C4⋊Q8 | C4 | 1 | 1 | yes | characteristic |
| 7 | #64156 | C22 | 1 | 2 | yes | — |
| 8 | #64104 | — | 2 | 2 | no | — |
| 9 | #64102 | — | 2 | 2 | no | — |
| 10 | #64083 | C4 | 1 | 1 | yes | characteristic |
| 11 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 12 | #63777 | C22 | 1 | 4 | yes | — |
| 13 | C4×#622 | — | 2 | 2 | no | — |
| 14 | #5725 | — | 6 | 2 | no | — |
| 15 | C2×C32×Q8 | C2×C4 | 1 | 2 | yes | — |
| 16 | #3832 | — | 4 | 4 | no | — |
| 17 | C2×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 18 | C2×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 19 | C2×C4⋊(C3⋊D3) | C2×C4 | 1 | 2 | yes | — |
| 20 | C2×C4×C3⋊D3 | — | 2 | 2 | no | — |
| 21 | C2×C4×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 22 | C2×C4×C3⋊D3 | D4 | 1 | 2 | yes | — |
| 23 | C2×#622 | — | 2 | 4 | no | — |
| 24 | #3788 | — | 2 | 8 | no | — |
| 25 | C32×C4⋊C4 | — | 2 | 2 | no | — |
| 26 | C32×C42 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | #3752 | — | 2 | 4 | no | — |
| 28 | C4×C3⋊Dic3 | D4 | 1 | 2 | yes | — |
| 29 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 30 | #1525 | — | 9 | 1 | no | maximal, Sylow |
| 31 | C2×#239 | — | 6 | 4 | no | — |
| 32 | C3×C4⋊Q8 | — | 2 | 2 | no | — |
| 33 | #947 | — | 6 | 4 | no | — |
| 34 | #895 | — | 6 | 8 | no | — |
| 35 | #893 | — | 6 | 8 | no | — |
| 36 | #874 | — | 6 | 2 | no | — |
| 37 | C42×D3 | — | 6 | 2 | no | — |
| 38 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 39 | C22×C3⋊D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 40 | C32×Q8 | — | 4 | 2 | no | — |
| 41 | C2×C32×C4 | — | 2 | 2 | no | — |
| 42 | C2×C32×C4 | C22⋊C4 | 1 | 2 | yes | — |
| 43 | C2×C32×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 44 | C2×C3⋊Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 45 | C2×C3⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 46 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 47 | C4⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 48 | C4⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 49 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 50 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 51 | C4×C3⋊D3 | — | 4 | 4 | no | — |
| 52 | #622 | — | 2 | 8 | no | — |
| 53 | #532 | — | 9 | 1 | no | — |
| 54 | C4×M16 | — | 9 | 2 | no | — |
| 55 | #329 | — | 9 | 4 | no | — |
| 56 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 57 | #239 | — | 12 | 16 | no | — |
| 58 | C2×D12 | — | 6 | 4 | no | — |
| 59 | C2×D12 | — | 6 | 8 | no | — |
| 60 | C2×D12 | — | 6 | 8 | no | — |
| 61 | C2×C4×D3 | — | 6 | 2 | no | — |
| 62 | C2×C4×D3 | — | 6 | 4 | no | — |
| 63 | C2×C4×D3 | — | 6 | 8 | no | — |
| 64 | C3×C4⋊C4 | — | 2 | 8 | no | — |
| 65 | C3×C42 | — | 2 | 2 | no | — |
| 66 | (C2×D3)⋊C4 | — | 6 | 16 | no | — |
| 67 | C4×Dic3 | — | 6 | 4 | no | — |
| 68 | C4×Dic3 | — | 6 | 2 | no | — |
| 69 | C22×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 70 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 71 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 72 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 73 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 74 | C32×C4 | — | 2 | 1 | no | — |
| 75 | C32×C4 | — | 4 | 2 | no | — |
| 76 | C32×C4 | #104 | 1 | 4 | yes | — |
| 77 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 78 | C3⋊Dic3 | #100 | 1 | 2 | yes | — |
| 79 | C2×#41 | — | 9 | 2 | no | — |
| 80 | C2×M16 | — | 18 | 2 | no | — |
| 81 | C4⋊Q8 | #157 | 1 | 1 | yes | characteristic |
| 82 | #127 | — | 9 | 1 | no | — |
| 83 | #124 | — | 9 | 2 | no | — |
| 84 | #121 | — | 18 | 2 | no | — |
| 85 | C4×D4 | — | 18 | 2 | no | — |
| 86 | C2×C42 | — | 9 | 1 | no | — |
| 87 | #97 | — | 9 | 4 | no | — |
| 88 | C4×C8 | — | 18 | 2 | no | — |
| 89 | C22×D3 | — | 6 | 2 | no | — |
| 90 | C22×D3 | — | 6 | 8 | no | — |
| 91 | C3×Q8 | — | 4 | 8 | no | — |
| 92 | C2×C3×C4 | — | 2 | 8 | no | — |
| 93 | C2×C3×C4 | — | 2 | 2 | no | — |
| 94 | C2×C3×C4 | — | 2 | 4 | no | — |
| 95 | C2×Dic3 | — | 6 | 2 | no | — |
| 96 | C2×Dic3 | — | 6 | 4 | no | — |
| 97 | D12 | — | 12 | 16 | no | — |
| 98 | D12 | — | 12 | 8 | no | — |
| 99 | D12 | — | 12 | 16 | no | — |
| 100 | C4×D3 | — | 6 | 8 | no | — |
| 101 | C4×D3 | — | 12 | 8 | no | — |
| 102 | C4×D3 | — | 12 | 16 | no | — |
| 103 | C2×C32 | C2×#100 | 1 | 1 | yes | characteristic |
| 104 | C2×C32 | C2×#104 | 1 | 2 | yes | — |
| 105 | C3⋊D3 | — | 4 | 1 | no | — |
| 106 | C3⋊D3 | — | 8 | 2 | no | — |
| 107 | #41 | — | 36 | 4 | no | — |
| 108 | C2×Q8 | C2×#157 | 1 | 2 | yes | — |
| 109 | C2×D4 | — | 9 | 2 | no | — |
| 110 | C2×D4 | — | 18 | 2 | no | — |
| 111 | C2×D4 | — | 18 | 2 | no | — |
| 112 | C22×C4 | — | 9 | 1 | no | — |
| 113 | C22×C4 | — | 9 | 2 | no | — |
| 114 | C22×C4 | — | 18 | 2 | no | — |
| 115 | M16 | — | 18 | 8 | no | — |
| 116 | C2×C8 | — | 18 | 4 | no | — |
| 117 | C4⋊C4 | — | 2 | 2 | no | — |
| 118 | C22⋊C4 | — | 18 | 4 | no | — |
| 119 | C42 | — | 9 | 1 | no | — |
| 120 | C42 | — | 9 | 2 | no | — |
| 121 | C42 | C2×#157 | 1 | 1 | yes | characteristic |
| 122 | C22×C3 | — | 2 | 2 | no | — |
| 123 | C2×D3 | — | 6 | 4 | no | — |
| 124 | C2×D3 | — | 12 | 4 | no | — |
| 125 | C2×D3 | — | 12 | 8 | no | — |
| 126 | C2×D3 | — | 12 | 16 | no | — |
| 127 | C3×C4 | — | 2 | 4 | no | — |
| 128 | C3×C4 | — | 2 | 8 | no | — |
| 129 | C3×C4 | — | 4 | 8 | no | — |
| 130 | Dic3 | — | 6 | 4 | no | — |
| 131 | Dic3 | — | 12 | 4 | no | — |
| 132 | C32 | #1525 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 133 | C23 | — | 9 | 1 | no | — |
| 134 | C23 | — | 18 | 2 | no | — |
| 135 | Q8 | — | 4 | 2 | no | — |
| 136 | D4 | — | 36 | 2 | no | — |
| 137 | D4 | — | 36 | 4 | no | — |
| 138 | D4 | — | 36 | 4 | no | — |
| 139 | C2×C4 | — | 2 | 2 | no | — |
| 140 | C2×C4 | — | 9 | 1 | no | — |
| 141 | C2×C4 | — | 9 | 2 | no | — |
| 142 | C2×C4 | — | 18 | 2 | no | — |
| 143 | C2×C4 | — | 18 | 4 | no | — |
| 144 | C2×C4 | — | 36 | 4 | no | — |
| 145 | C2×C4 | C22⋊#157 | 1 | 2 | yes | — |
| 146 | C2×C4 | C22×#157 | 1 | 1 | yes | characteristic |
| 147 | C8 | — | 18 | 8 | no | — |
| 148 | C2×C3 | — | 2 | 2 | no | — |
| 149 | C2×C3 | — | 2 | 4 | no | — |
| 150 | D3 | — | 12 | 4 | no | — |
| 151 | D3 | — | 24 | 8 | no | — |
| 152 | C22 | — | 18 | 1 | no | — |
| 153 | C22 | — | 18 | 2 | no | — |
| 154 | C22 | — | 36 | 2 | no | — |
| 155 | C22 | — | 36 | 4 | no | — |
| 156 | C22 | C2×C22⋊#157 | 1 | 1 | yes | characteristic |
| 157 | C4 | — | 2 | 1 | no | — |
| 158 | C4 | — | 4 | 2 | no | — |
| 159 | C4 | — | 9 | 2 | no | — |
| 160 | C4 | — | 18 | 2 | no | — |
| 161 | C4 | #63785 | 1 | 4 | yes | — |
| 162 | C3 | — | 2 | 2 | no | — |
| 163 | C2 | — | 36 | 1 | no | — |
| 164 | C2 | — | 72 | 2 | no | — |
| 165 | C2 | #10593825 | 1 | 1 | yes | characteristic |
| 166 | C2 | C2×#63785 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#3788 | C2 | semidirect |
| 3. #10590216 | C2 | semidirect |
| 132. C32 | #1525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596196 | 2 |
| C4×#3788 | 2 |
| #10590216 | 2 |
| #1525 | 9 |