Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
264 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 39 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 | Q16×#157 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10593293 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10591039 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10590022 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10590016 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | Q8×#157 | — | 2 | 1 | no | — |
| 7 | #64231 | — | 2 | 1 | no | — |
| 8 | #64225 | — | 2 | 1 | no | — |
| 9 | Q16×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 10 | #63797 | C22 | 1 | 2 | yes | — |
| 11 | #63784 | — | 2 | 1 | no | — |
| 12 | #63769 | C22 | 1 | 1 | yes | characteristic |
| 13 | C8×#157 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#828 | — | 2 | 2 | no | — |
| 15 | #63548 | — | 2 | 2 | no | — |
| 16 | #63542 | C22 | 1 | 2 | yes | — |
| 17 | D3×SD32 | — | 6 | 2 | no | — |
| 18 | C2×GO+(4,𝔽2) | — | 4 | 1 | no | — |
| 19 | C2×GO+(4,𝔽2) | — | 4 | 1 | no | — |
| 20 | Q8×C3⋊D3 | — | 2 | 1 | no | — |
| 21 | #3802 | — | 2 | 2 | no | — |
| 22 | C4⋊#157 | — | 2 | 1 | no | — |
| 23 | C4⋊#157 | — | 4 | 1 | no | — |
| 24 | C4×#157 | — | 4 | 1 | no | — |
| 25 | C4×#157 | D4 | 1 | 1 | yes | characteristic |
| 26 | #3787 | D4 | 1 | 1 | yes | characteristic |
| 27 | #3774 | — | 4 | 2 | no | — |
| 28 | C32×Q16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 29 | #3756 | — | 2 | 1 | no | — |
| 30 | #3746 | D4 | 1 | 1 | yes | characteristic, complemented |
| 31 | C8×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 32 | C3×D24 | — | 2 | 2 | no | — |
| 33 | #3713 | — | 2 | 2 | no | — |
| 34 | C3×C3⋊C16 | — | 2 | 2 | no | — |
| 35 | #2207 | — | 9 | 1 | no | maximal, Sylow |
| 36 | D3×Q16 | — | 6 | 2 | no | — |
| 37 | D3×D8 | — | 6 | 2 | no | — |
| 38 | C3×SD32 | — | 6 | 2 | no | — |
| 39 | #828 | — | 2 | 2 | no | — |
| 40 | #827 | — | 6 | 2 | no | — |
| 41 | #800 | — | 6 | 2 | no | — |
| 42 | D3×C16 | — | 6 | 2 | no | — |
| 43 | C2×D32 | — | 4 | 2 | no | — |
| 44 | C2×#157 | — | 4 | 1 | no | — |
| 45 | C2×#157 | D8 | 1 | 1 | yes | characteristic |
| 46 | C2×#157 | D8 | 1 | 1 | yes | characteristic |
| 47 | GO+(4,𝔽2) | — | 8 | 2 | no | — |
| 48 | GO+(4,𝔽2) | — | 8 | 2 | no | — |
| 49 | C32×Q8 | — | 2 | 1 | no | — |
| 50 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 51 | C4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 52 | #634 | — | 2 | 1 | no | — |
| 53 | #634 | — | 4 | 1 | no | — |
| 54 | C3×D12 | — | 4 | 2 | no | — |
| 55 | #625 | — | 4 | 2 | no | — |
| 56 | #622 | — | 2 | 1 | no | — |
| 57 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 58 | C3⋊(C3⋊C8) | #41 | 1 | 1 | yes | characteristic |
| 59 | C2×SD32 | — | 9 | 2 | no | — |
| 60 | #493 | — | 9 | 1 | no | — |
| 61 | C4×Q16 | — | 9 | 1 | no | — |
| 62 | C4⋊C16 | — | 9 | 1 | no | — |
| 63 | #357 | — | 9 | 2 | no | — |
| 64 | D3×Q8 | — | 12 | 2 | no | — |
| 65 | D3×D4 | — | 12 | 2 | no | — |
| 66 | C3×Q16 | — | 2 | 2 | no | — |
| 67 | C3×D8 | — | 6 | 2 | no | — |
| 68 | #216 | — | 12 | 2 | no | — |
| 69 | #213 | — | 12 | 2 | no | — |
| 70 | Dic12 | — | 6 | 2 | no | — |
| 71 | D24 | — | 2 | 2 | no | — |
| 72 | D3×C8 | — | 6 | 2 | no | — |
| 73 | C3×C16 | — | 6 | 2 | no | — |
| 74 | C3⋊C16 | — | 2 | 2 | no | — |
| 75 | C2×C3⋊D3 | C2×D8 | 1 | 1 | yes | characteristic |
| 76 | C2×C3×D3 | — | 8 | 2 | no | — |
| 77 | D32 | — | 8 | 2 | no | — |
| 78 | D32 | — | 8 | 2 | no | — |
| 79 | #157 | — | 2 | 1 | no | — |
| 80 | #157 | — | 8 | 1 | no | — |
| 81 | #157 | SD32 | 1 | 2 | yes | complemented |
| 82 | C32×C4 | — | 4 | 1 | no | — |
| 83 | C32×C4 | #121 | 1 | 1 | yes | characteristic |
| 84 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 85 | C3⋊Dic3 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 86 | C2×Q16 | — | 9 | 1 | no | — |
| 87 | C2×D8 | — | 9 | 2 | no | — |
| 88 | C2×D8 | — | 18 | 1 | no | — |
| 89 | #127 | — | 18 | 1 | no | — |
| 90 | C4×Q8 | — | 18 | 1 | no | — |
| 91 | SD32 | — | 6 | 2 | no | — |
| 92 | SD32 | — | 18 | 2 | no | — |
| 93 | C2×C16 | — | 9 | 2 | no | — |
| 94 | #107 | — | 9 | 1 | no | — |
| 95 | #103 | — | 18 | 1 | no | — |
| 96 | C4×C8 | — | 9 | 1 | no | — |
| 97 | C22×D3 | — | 24 | 2 | no | — |
| 98 | C3×Q8 | — | 4 | 2 | no | — |
| 99 | C3×D4 | — | 12 | 2 | no | — |
| 100 | #67 | — | 24 | 2 | no | — |
| 101 | D12 | — | 4 | 2 | no | — |
| 102 | C4×D3 | — | 6 | 2 | no | — |
| 103 | C4×D3 | — | 24 | 2 | no | — |
| 104 | Dic6 | — | 12 | 2 | no | — |
| 105 | Dic6 | — | 24 | 2 | no | — |
| 106 | C3×C8 | — | 2 | 2 | no | — |
| 107 | C3⋊C8 | — | 6 | 2 | no | — |
| 108 | C2×C32 | #459 | 1 | 1 | yes | characteristic |
| 109 | C3⋊D3 | C2×SD32 | 1 | 1 | yes | characteristic |
| 110 | C3⋊D3 | #509 | 1 | 1 | yes | characteristic |
| 111 | C3×D3 | — | 16 | 2 | no | — |
| 112 | C2×Q8 | — | 18 | 1 | no | — |
| 113 | C2×D4 | — | 18 | 2 | no | — |
| 114 | C2×D4 | — | 36 | 1 | no | — |
| 115 | C2×D4 | — | 36 | 1 | no | — |
| 116 | Q16 | — | 9 | 1 | no | — |
| 117 | Q16 | — | 18 | 1 | no | — |
| 118 | Q16 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 119 | D8 | — | 6 | 2 | no | — |
| 120 | D8 | — | 18 | 2 | no | — |
| 121 | D8 | — | 36 | 2 | no | — |
| 122 | C2×C8 | — | 9 | 1 | no | — |
| 123 | C2×C8 | — | 9 | 1 | no | — |
| 124 | C4⋊C4 | — | 18 | 1 | no | — |
| 125 | C4⋊C4 | — | 36 | 1 | no | — |
| 126 | C42 | — | 9 | 1 | no | — |
| 127 | C42 | — | 36 | 1 | no | — |
| 128 | C16 | — | 6 | 2 | no | — |
| 129 | C22×C3 | — | 24 | 2 | no | — |
| 130 | C2×D3 | — | 6 | 2 | no | — |
| 131 | C2×D3 | — | 8 | 2 | no | — |
| 132 | C2×D3 | — | 48 | 2 | no | — |
| 133 | C2×D3 | — | 48 | 2 | no | — |
| 134 | C3×C4 | — | 2 | 2 | no | — |
| 135 | C3×C4 | — | 8 | 2 | no | — |
| 136 | Dic3 | — | 6 | 2 | no | — |
| 137 | Dic3 | — | 24 | 2 | no | — |
| 138 | C32 | #2207 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 139 | C23 | — | 36 | 2 | no | — |
| 140 | Q8 | — | 2 | 1 | no | — |
| 141 | Q8 | — | 18 | 1 | no | — |
| 142 | Q8 | — | 36 | 1 | no | — |
| 143 | D4 | — | 12 | 2 | no | — |
| 144 | D4 | — | 36 | 2 | no | — |
| 145 | D4 | — | 72 | 2 | no | — |
| 146 | D4 | — | 72 | 2 | no | — |
| 147 | C2×C4 | — | 9 | 1 | no | — |
| 148 | C2×C4 | — | 9 | 1 | no | — |
| 149 | C2×C4 | — | 9 | 1 | no | — |
| 150 | C2×C4 | — | 36 | 1 | no | — |
| 151 | C2×C4 | — | 36 | 1 | no | — |
| 152 | C8 | — | 9 | 1 | no | — |
| 153 | C8 | — | 18 | 1 | no | — |
| 154 | C8 | C2×GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 155 | C2×C3 | — | 2 | 2 | no | — |
| 156 | C2×C3 | — | 48 | 2 | no | — |
| 157 | D3 | — | 6 | 2 | no | — |
| 158 | D3 | — | 6 | 2 | no | — |
| 159 | D3 | — | 16 | 2 | no | — |
| 160 | C22 | — | 9 | 1 | no | — |
| 161 | C22 | — | 24 | 2 | no | — |
| 162 | C22 | — | 72 | 2 | no | — |
| 163 | C22 | — | 72 | 2 | no | — |
| 164 | C4 | — | 4 | 1 | no | — |
| 165 | C4 | — | 9 | 2 | no | — |
| 166 | C4 | — | 9 | 1 | no | — |
| 167 | C4 | — | 18 | 1 | no | — |
| 168 | C4 | — | 36 | 1 | no | — |
| 169 | C4 | — | 72 | 1 | no | — |
| 170 | C4 | #64242 | 1 | 1 | yes | characteristic |
| 171 | C3 | — | 2 | 2 | no | — |
| 172 | C2 | — | 9 | 1 | no | — |
| 173 | C2 | — | 9 | 1 | no | — |
| 174 | C2 | — | 48 | 2 | no | — |
| 175 | C2 | #10593464 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q16×#157 | C2 | semidirect |
| 3. #10591039 | C2 | semidirect |
| 4. #10590022 | C2 | semidirect |
| 5. #10590016 | C2 | semidirect |
| 28. C32×Q16 | D4 | semidirect |
| 30. #3746 | D4 | semidirect |
| 81. #157 | SD32 | semidirect |
| 118. Q16 | GO+(4,𝔽2) | semidirect |
| 138. C32 | #2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#157 | 2 |
| #10593293 | 2 |
| #10591039 | 2 |
| #10590022 | 2 |
| #10590016 | 2 |
| #2207 | 9 |