Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
280 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 43 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 | C3×A4×D8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10593636 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3⋊(A4⋊C16) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #73133 | — | 3 | 3 | no | maximal |
| 5 | #72035 | — | 3 | 1 | no | maximal |
| 6 | C3×D4×A4 | — | 2 | 1 | no | — |
| 7 | C4⋊(C3⋊S4) | — | 2 | 1 | no | — |
| 8 | C3×C8×A4 | C22 | 1 | 1 | yes | characteristic |
| 9 | #63653 | — | 4 | 1 | no | maximal |
| 10 | C22×C3×D8 | D3 | 1 | 1 | yes | characteristic, complemented |
| 11 | A4×D8 | D3 | 1 | 3 | yes | complemented |
| 12 | #5402 | — | 3 | 3 | no | — |
| 13 | C2×#826 | — | 3 | 1 | no | — |
| 14 | C2×#826 | — | 3 | 1 | no | — |
| 15 | #5115 | — | 3 | 1 | no | — |
| 16 | A4⋊C16 | — | 3 | 3 | no | — |
| 17 | #4562 | — | 3 | 1 | no | — |
| 18 | #4562 | — | 3 | 1 | no | — |
| 19 | #4549 | — | 3 | 1 | no | — |
| 20 | C22×C3×A4 | — | 4 | 1 | no | — |
| 21 | C2×C3⋊S4 | — | 4 | 1 | no | — |
| 22 | C3×C4×A4 | D4 | 1 | 1 | yes | characteristic |
| 23 | C32×D8 | — | 4 | 1 | no | — |
| 24 | #3745 | — | 4 | 1 | no | — |
| 25 | C3⋊(C3⋊C16) | — | 4 | 1 | no | — |
| 26 | #2184 | — | 9 | 1 | no | Sylow |
| 27 | C22×C3×D4 | — | 2 | 1 | no | — |
| 28 | D4×A4 | — | 2 | 3 | no | — |
| 29 | C4⋊S4 | — | 6 | 3 | no | — |
| 30 | C2×C3×D8 | — | 3 | 1 | no | — |
| 31 | C2×C3×D8 | — | 3 | 1 | no | — |
| 32 | C2×C3×D8 | — | 6 | 1 | no | — |
| 33 | C22×C3×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 34 | #930 | — | 6 | 1 | no | — |
| 35 | C2×D24 | — | 3 | 1 | no | — |
| 36 | C8×A4 | C2×D3 | 1 | 3 | yes | — |
| 37 | #826 | — | 6 | 2 | no | — |
| 38 | #826 | — | 6 | 1 | no | — |
| 39 | #826 | — | 6 | 1 | no | — |
| 40 | #826 | — | 12 | 3 | no | — |
| 41 | #821 | — | 6 | 1 | no | — |
| 42 | #818 | — | 3 | 1 | no | — |
| 43 | C2×C3⋊C16 | — | 3 | 1 | no | — |
| 44 | C2×C3⋊C16 | — | 3 | 1 | no | — |
| 45 | C2×C3×A4 | — | 8 | 1 | no | — |
| 46 | C2×C3×A4 | D8 | 1 | 1 | yes | characteristic |
| 47 | C3⋊S4 | — | 8 | 1 | no | — |
| 48 | C32×D4 | — | 8 | 1 | no | — |
| 49 | C4⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 50 | C32×C8 | — | 4 | 1 | no | — |
| 51 | C22×D8 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | C2×D16 | — | 9 | 1 | no | — |
| 53 | C2×D16 | — | 9 | 1 | no | — |
| 54 | #466 | — | 9 | 1 | no | — |
| 55 | #357 | — | 9 | 1 | no | — |
| 56 | #357 | — | 9 | 1 | no | — |
| 57 | C22⋊C16 | — | 9 | 1 | no | — |
| 58 | C24×C3 | — | 4 | 1 | no | — |
| 59 | C22×A4 | — | 4 | 3 | no | — |
| 60 | C2×S4 | — | 12 | 3 | no | — |
| 61 | C2×C3×D4 | — | 6 | 1 | no | — |
| 62 | C2×C3×D4 | — | 6 | 1 | no | — |
| 63 | C2×C3×D4 | — | 12 | 1 | no | — |
| 64 | C22×C3×C4 | #67 | 1 | 1 | yes | characteristic |
| 65 | C2×#67 | — | 12 | 1 | no | — |
| 66 | C2×D12 | — | 6 | 1 | no | — |
| 67 | C4×A4 | #67 | 1 | 3 | yes | — |
| 68 | C3×D8 | — | 3 | 2 | no | — |
| 69 | C3×D8 | — | 3 | 1 | no | — |
| 70 | C3×D8 | — | 4 | 3 | no | — |
| 71 | C3×D8 | — | 6 | 1 | no | — |
| 72 | C3×D8 | S4 | 1 | 1 | yes | characteristic, complemented |
| 73 | C2×C3×C8 | — | 3 | 1 | no | — |
| 74 | C2×C3×C8 | — | 3 | 1 | no | — |
| 75 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 76 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 77 | D24 | — | 6 | 1 | no | — |
| 78 | D24 | — | 6 | 1 | no | — |
| 79 | D24 | — | 12 | 3 | no | — |
| 80 | C3⋊C16 | — | 6 | 1 | no | — |
| 81 | C3⋊C16 | — | 6 | 1 | no | — |
| 82 | C3⋊C16 | — | 12 | 3 | no | — |
| 83 | C22×C32 | — | 16 | 1 | no | — |
| 84 | C2×C3⋊D3 | — | 16 | 1 | no | — |
| 85 | C3×A4 | D16 | 1 | 1 | yes | characteristic, complemented |
| 86 | C32×C4 | — | 4 | 1 | no | — |
| 87 | C22×D4 | — | 2 | 1 | no | — |
| 88 | C2×D8 | — | 3 | 1 | no | — |
| 89 | C2×D8 | — | 3 | 1 | no | — |
| 90 | C2×D8 | — | 6 | 1 | no | — |
| 91 | C2×D8 | — | 9 | 1 | no | — |
| 92 | C22×C8 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 93 | #121 | — | 18 | 1 | no | — |
| 94 | D16 | — | 18 | 2 | no | — |
| 95 | D16 | — | 18 | 1 | no | — |
| 96 | D16 | — | 18 | 1 | no | — |
| 97 | C2×C16 | — | 9 | 1 | no | — |
| 98 | C2×C16 | — | 9 | 1 | no | — |
| 99 | #107 | — | 9 | 1 | no | — |
| 100 | #102 | — | 18 | 1 | no | — |
| 101 | C23×C3 | — | 8 | 1 | no | — |
| 102 | C23×C3 | — | 12 | 1 | no | — |
| 103 | C23×C3 | — | 12 | 1 | no | — |
| 104 | C23×C3 | — | 24 | 1 | no | — |
| 105 | C23×C3 | #213 | 1 | 1 | yes | characteristic |
| 106 | C22×D3 | — | 12 | 1 | no | — |
| 107 | C2×A4 | — | 8 | 3 | no | — |
| 108 | C2×A4 | #213 | 1 | 3 | yes | — |
| 109 | S4 | — | 24 | 3 | no | — |
| 110 | C3×D4 | — | 2 | 1 | no | — |
| 111 | C3×D4 | — | 6 | 1 | no | — |
| 112 | C3×D4 | — | 8 | 3 | no | — |
| 113 | C3×D4 | — | 12 | 1 | no | — |
| 114 | C3×D4 | — | 12 | 1 | no | — |
| 115 | C2×C3×C4 | — | 3 | 1 | no | — |
| 116 | C2×C3×C4 | — | 3 | 1 | no | — |
| 117 | #67 | — | 24 | 1 | no | — |
| 118 | #67 | — | 24 | 1 | no | — |
| 119 | C2×Dic3 | — | 12 | 1 | no | — |
| 120 | D12 | — | 12 | 1 | no | — |
| 121 | D12 | — | 12 | 1 | no | — |
| 122 | D12 | — | 24 | 3 | no | — |
| 123 | C3×C8 | — | 3 | 1 | no | — |
| 124 | C3×C8 | — | 4 | 3 | no | — |
| 125 | C3×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 126 | C2×C32 | — | 4 | 1 | no | — |
| 127 | C2×C32 | — | 32 | 1 | no | — |
| 128 | C3⋊D3 | — | 32 | 1 | no | — |
| 129 | C24 | — | 4 | 1 | no | — |
| 130 | C2×D4 | — | 6 | 1 | no | — |
| 131 | C2×D4 | — | 6 | 1 | no | — |
| 132 | C2×D4 | — | 12 | 1 | no | — |
| 133 | C2×D4 | — | 18 | 1 | no | — |
| 134 | C2×D4 | — | 36 | 1 | no | — |
| 135 | C22×C4 | #638 | 1 | 1 | yes | characteristic |
| 136 | D8 | — | 3 | 2 | no | — |
| 137 | D8 | — | 3 | 1 | no | — |
| 138 | D8 | — | 6 | 1 | no | — |
| 139 | D8 | — | 18 | 1 | no | — |
| 140 | D8 | — | 18 | 1 | no | — |
| 141 | D8 | C3⋊S4 | 1 | 1 | yes | characteristic, complemented |
| 142 | C2×C8 | — | 3 | 1 | no | — |
| 143 | C2×C8 | — | 3 | 1 | no | — |
| 144 | C4⋊C4 | — | 18 | 1 | no | — |
| 145 | C22⋊C4 | — | 36 | 1 | no | — |
| 146 | C16 | — | 18 | 1 | no | — |
| 147 | C16 | — | 18 | 1 | no | — |
| 148 | C22×C3 | — | 3 | 1 | no | — |
| 149 | C22×C3 | — | 3 | 1 | no | — |
| 150 | C22×C3 | — | 4 | 1 | no | — |
| 151 | C22×C3 | — | 12 | 1 | no | — |
| 152 | C22×C3 | — | 16 | 3 | no | — |
| 153 | C22×C3 | — | 24 | 1 | no | — |
| 154 | C22×C3 | — | 24 | 1 | no | — |
| 155 | C22×C3 | — | 24 | 1 | no | — |
| 156 | C22×C3 | — | 24 | 1 | no | — |
| 157 | C22×C3 | #826 | 1 | 1 | yes | characteristic, complemented |
| 158 | C2×D3 | — | 24 | 1 | no | — |
| 159 | C2×D3 | — | 24 | 1 | no | — |
| 160 | C2×D3 | — | 24 | 1 | no | — |
| 161 | C2×D3 | — | 48 | 3 | no | — |
| 162 | A4 | #826 | 1 | 3 | yes | complemented |
| 163 | C3×C4 | — | 3 | 1 | no | — |
| 164 | C3×C4 | — | 4 | 3 | no | — |
| 165 | C3×C4 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 166 | Dic3 | — | 24 | 1 | no | — |
| 167 | C32 | — | 4 | 1 | no | Sylow |
| 168 | C23 | — | 8 | 1 | no | — |
| 169 | C23 | — | 12 | 1 | no | — |
| 170 | C23 | — | 12 | 1 | no | — |
| 171 | C23 | — | 24 | 1 | no | — |
| 172 | C23 | — | 36 | 1 | no | — |
| 173 | C23 | #3753 | 1 | 1 | yes | characteristic |
| 174 | D4 | — | 2 | 1 | no | — |
| 175 | D4 | — | 6 | 1 | no | — |
| 176 | D4 | — | 12 | 1 | no | — |
| 177 | D4 | — | 12 | 1 | no | — |
| 178 | D4 | — | 36 | 1 | no | — |
| 179 | D4 | — | 36 | 1 | no | — |
| 180 | D4 | — | 72 | 1 | no | — |
| 181 | D4 | — | 72 | 1 | no | — |
| 182 | C2×C4 | — | 3 | 1 | no | — |
| 183 | C2×C4 | — | 3 | 1 | no | — |
| 184 | C2×C4 | — | 36 | 1 | no | — |
| 185 | C8 | — | 3 | 1 | no | — |
| 186 | C8 | C2×C3⋊S4 | 1 | 1 | yes | characteristic |
| 187 | C2×C3 | — | 3 | 1 | no | — |
| 188 | C2×C3 | — | 3 | 1 | no | — |
| 189 | C2×C3 | — | 4 | 3 | no | — |
| 190 | C2×C3 | — | 8 | 1 | no | — |
| 191 | C2×C3 | — | 24 | 1 | no | — |
| 192 | C2×C3 | — | 32 | 3 | no | — |
| 193 | C2×C3 | #5415 | 1 | 1 | yes | characteristic |
| 194 | D3 | — | 48 | 1 | no | — |
| 195 | D3 | — | 96 | 3 | no | — |
| 196 | C22 | — | 3 | 1 | no | — |
| 197 | C22 | — | 3 | 1 | no | — |
| 198 | C22 | — | 4 | 1 | no | — |
| 199 | C22 | — | 12 | 1 | no | — |
| 200 | C22 | — | 24 | 1 | no | — |
| 201 | C22 | — | 24 | 1 | no | — |
| 202 | C22 | — | 24 | 1 | no | — |
| 203 | C22 | — | 24 | 1 | no | — |
| 204 | C22 | — | 72 | 1 | no | — |
| 205 | C22 | — | 72 | 1 | no | — |
| 206 | C22 | — | 72 | 1 | no | — |
| 207 | C22 | #63653 | 1 | 1 | yes | characteristic, complemented |
| 208 | C4 | — | 3 | 1 | no | — |
| 209 | C4 | — | 72 | 1 | no | — |
| 210 | C4 | #64269 | 1 | 1 | yes | characteristic |
| 211 | C3 | — | 4 | 3 | no | — |
| 212 | C3 | #73133 | 1 | 1 | yes | characteristic, complemented |
| 213 | C2 | — | 3 | 1 | no | — |
| 214 | C2 | — | 3 | 1 | no | — |
| 215 | C2 | — | 8 | 1 | no | — |
| 216 | C2 | — | 24 | 1 | no | — |
| 217 | C2 | — | 144 | 1 | no | — |
| 218 | C2 | #10593649 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×A4×D8 | C2 | semidirect |
| 2. #10593636 | C2 | semidirect |
| 3. C3⋊(A4⋊C16) | C2 | semidirect |
| 10. C22×C3×D8 | D3 | semidirect |
| 11. A4×D8 | D3 | semidirect |
| 51. C22×D8 | C3⋊D3 | semidirect |
| 72. C3×D8 | S4 | semidirect |
| 85. C3×A4 | D16 | semidirect |
| 141. D8 | C3⋊S4 | semidirect |
| 157. C22×C3 | #826 | semidirect |
| 162. A4 | #826 | semidirect |
| 207. C22 | #63653 | semidirect |
| 212. C3 | #73133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×D8 | 2 |
| #10593636 | 2 |
| C3⋊(A4⋊C16) | 2 |
| #73133 | 3 |
| #72035 | 3 |
| #63653 | 4 |