Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
521 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 521 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #10592772 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#5070 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10590373 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10590309 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589079 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71185 | — | 3 | 2 | no | maximal |
| 7 | C32×#127 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×#3753 | — | 2 | 2 | no | — |
| 9 | #64083 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#869 | C22 | 1 | 2 | yes | — |
| 11 | C2×#3717 | — | 2 | 4 | no | — |
| 12 | C4×C3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#832 | — | 2 | 4 | no | — |
| 14 | C3×C4×C3⋊C8 | C22 | 1 | 2 | yes | — |
| 15 | #63574 | — | 2 | 2 | no | — |
| 16 | C3×#486 | — | 3 | 2 | no | — |
| 17 | #5085 | — | 3 | 2 | no | — |
| 18 | #5080 | — | 3 | 2 | no | — |
| 19 | #5073 | — | 3 | 2 | no | — |
| 20 | #5073 | — | 6 | 1 | no | — |
| 21 | #5070 | D3 | 1 | 2 | yes | complemented |
| 22 | #4693 | — | 3 | 2 | no | — |
| 23 | #4454 | — | 3 | 2 | no | — |
| 24 | C2×C32×D4 | — | 2 | 1 | no | — |
| 25 | C2×C32×D4 | — | 2 | 2 | no | — |
| 26 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 27 | C2×C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 28 | C2×C3×Dic6 | — | 2 | 2 | no | — |
| 29 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 30 | #3753 | — | 4 | 4 | no | — |
| 31 | C2×C3⋊(C3⋊C8) | D4 | 1 | 2 | yes | — |
| 32 | C3×C4⋊Dic3 | — | 2 | 2 | no | — |
| 33 | C3×C4⋊Dic3 | — | 2 | 2 | no | — |
| 34 | C2×C3×C3⋊C8 | D4 | 1 | 4 | yes | — |
| 35 | #3717 | — | 4 | 8 | no | — |
| 36 | #1715 | — | 9 | 1 | no | Sylow |
| 37 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 38 | C3×#127 | — | 2 | 1 | no | — |
| 39 | C3×#127 | C2×D3 | 1 | 2 | yes | — |
| 40 | C2×#215 | — | 6 | 4 | no | — |
| 41 | C2×#213 | — | 6 | 4 | no | — |
| 42 | C2×#213 | — | 6 | 4 | no | — |
| 43 | C2×#204 | — | 6 | 4 | no | — |
| 44 | #874 | — | 3 | 2 | no | — |
| 45 | #874 | — | 6 | 1 | no | — |
| 46 | #869 | C2×D3 | 1 | 2 | yes | — |
| 47 | C3×#102 | — | 6 | 4 | no | — |
| 48 | C3×C4×C8 | — | 3 | 2 | no | — |
| 49 | #832 | — | 2 | 4 | no | — |
| 50 | #808 | — | 6 | 4 | no | — |
| 51 | C4×C3⋊C8 | — | 3 | 2 | no | — |
| 52 | C4×C3⋊C8 | — | 6 | 1 | no | — |
| 53 | C4×C3⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 54 | C23×C32 | — | 4 | 1 | no | — |
| 55 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 56 | C32×D4 | — | 4 | 2 | no | — |
| 57 | C32×D4 | — | 4 | 4 | no | — |
| 58 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 59 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 60 | C4⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 61 | C4⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 62 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 63 | C3×Dic6 | — | 4 | 4 | no | — |
| 64 | C3⋊(C3⋊C8) | SD16 | 1 | 4 | yes | complemented |
| 65 | C3×C3⋊C8 | — | 2 | 4 | no | — |
| 66 | #498 | — | 9 | 1 | no | — |
| 67 | #493 | — | 9 | 1 | no | — |
| 68 | #492 | — | 9 | 2 | no | — |
| 69 | #486 | — | 3 | 2 | no | — |
| 70 | #322 | — | 9 | 1 | no | — |
| 71 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 72 | C2×C3×D4 | — | 2 | 2 | no | — |
| 73 | C2×C3×D4 | — | 2 | 2 | no | — |
| 74 | C2×C3×D4 | — | 2 | 2 | no | — |
| 75 | C2×C3×D4 | — | 2 | 2 | no | — |
| 76 | C2×C3×D4 | — | 4 | 2 | no | — |
| 77 | C2×D12 | — | 6 | 2 | no | — |
| 78 | C2×D12 | — | 6 | 2 | no | — |
| 79 | C2×D12 | — | 6 | 2 | no | — |
| 80 | C2×D12 | — | 6 | 2 | no | — |
| 81 | C2×D12 | — | 12 | 2 | no | — |
| 82 | C2×Dic6 | — | 2 | 2 | no | — |
| 83 | C2×C3×C8 | — | 3 | 4 | no | — |
| 84 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 85 | C3×C4⋊C4 | — | 6 | 2 | no | — |
| 86 | C3×C42 | — | 2 | 1 | no | — |
| 87 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 88 | #215 | — | 12 | 8 | no | — |
| 89 | #213 | — | 12 | 8 | no | — |
| 90 | #213 | — | 12 | 8 | no | — |
| 91 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 92 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 93 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 94 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 95 | C2×C3⋊C8 | #67 | 1 | 4 | yes | — |
| 96 | #204 | — | 12 | 8 | no | — |
| 97 | C22×C32 | — | 8 | 1 | no | — |
| 98 | C22×C32 | — | 8 | 2 | no | — |
| 99 | C22×C32 | #127 | 1 | 1 | yes | characteristic |
| 100 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 101 | C2×C3⋊D3 | — | 8 | 2 | no | — |
| 102 | C32×C4 | C2×SD16 | 1 | 2 | yes | — |
| 103 | C32×C4 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 104 | C3×Dic3 | — | 8 | 2 | no | — |
| 105 | C2×SD16 | — | 18 | 4 | no | — |
| 106 | C2×D8 | — | 18 | 2 | no | — |
| 107 | C4⋊Q8 | — | 3 | 2 | no | — |
| 108 | #127 | — | 9 | 1 | no | — |
| 109 | #127 | D32 | 1 | 1 | yes | characteristic |
| 110 | #106 | — | 18 | 2 | no | — |
| 111 | #102 | — | 6 | 4 | no | — |
| 112 | C4×C8 | — | 3 | 2 | no | — |
| 113 | C4×C8 | — | 9 | 1 | no | — |
| 114 | C23×C3 | — | 4 | 2 | no | — |
| 115 | C23×C3 | — | 4 | 2 | no | — |
| 116 | C22×D3 | — | 12 | 2 | no | — |
| 117 | C22×D3 | — | 12 | 2 | no | — |
| 118 | C3×Q8 | — | 12 | 4 | no | — |
| 119 | C3×D4 | — | 4 | 4 | no | — |
| 120 | C3×D4 | — | 4 | 4 | no | — |
| 121 | C3×D4 | — | 4 | 4 | no | — |
| 122 | C3×D4 | — | 4 | 4 | no | — |
| 123 | C3×D4 | — | 8 | 4 | no | — |
| 124 | C2×C3×C4 | — | 2 | 2 | no | — |
| 125 | C2×C3×C4 | — | 2 | 1 | no | — |
| 126 | C2×C3×C4 | — | 12 | 2 | no | — |
| 127 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 128 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 129 | C2×C3×C4 | C2×#67 | 1 | 2 | yes | — |
| 130 | C2×Dic3 | — | 4 | 2 | no | — |
| 131 | D12 | — | 12 | 4 | no | — |
| 132 | D12 | — | 12 | 4 | no | — |
| 133 | D12 | — | 12 | 4 | no | — |
| 134 | D12 | — | 12 | 4 | no | — |
| 135 | D12 | — | 24 | 4 | no | — |
| 136 | Dic6 | — | 4 | 4 | no | — |
| 137 | C3×C8 | — | 6 | 4 | no | — |
| 138 | C3⋊C8 | — | 2 | 4 | no | — |
| 139 | C3⋊C8 | — | 3 | 8 | no | — |
| 140 | C3⋊C8 | — | 6 | 4 | no | — |
| 141 | C2×C32 | — | 16 | 1 | no | — |
| 142 | C2×C32 | #492 | 1 | 1 | yes | characteristic |
| 143 | C2×C32 | #496 | 1 | 2 | yes | — |
| 144 | C3⋊D3 | — | 16 | 1 | no | — |
| 145 | C2×Q8 | — | 6 | 2 | no | — |
| 146 | C2×D4 | — | 2 | 2 | no | — |
| 147 | C2×D4 | — | 2 | 1 | no | — |
| 148 | C2×D4 | — | 18 | 2 | no | — |
| 149 | C2×D4 | — | 18 | 1 | no | — |
| 150 | SD16 | — | 36 | 8 | no | — |
| 151 | D8 | — | 36 | 4 | no | — |
| 152 | C2×C8 | — | 3 | 4 | no | — |
| 153 | C2×C8 | — | 9 | 2 | no | — |
| 154 | C4⋊C4 | — | 6 | 2 | no | — |
| 155 | C4⋊C4 | — | 6 | 2 | no | — |
| 156 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 157 | C22×C3 | — | 2 | 1 | no | — |
| 158 | C22×C3 | — | 8 | 2 | no | — |
| 159 | C22×C3 | — | 8 | 4 | no | — |
| 160 | C22×C3 | — | 8 | 2 | no | — |
| 161 | C22×C3 | — | 8 | 2 | no | — |
| 162 | C22×C3 | — | 8 | 2 | no | — |
| 163 | C22×C3 | #940 | 1 | 2 | yes | — |
| 164 | C2×D3 | — | 24 | 2 | no | — |
| 165 | C2×D3 | — | 24 | 4 | no | — |
| 166 | C2×D3 | — | 24 | 2 | no | — |
| 167 | C2×D3 | — | 24 | 2 | no | — |
| 168 | C2×D3 | — | 24 | 2 | no | — |
| 169 | C3×C4 | — | 2 | 4 | no | — |
| 170 | C3×C4 | — | 2 | 2 | no | — |
| 171 | C3×C4 | — | 24 | 2 | no | — |
| 172 | C3×C4 | #911 | 1 | 4 | yes | — |
| 173 | C3×C4 | D3×SD16 | 1 | 4 | yes | — |
| 174 | C3×C4 | #949 | 1 | 4 | yes | — |
| 175 | Dic3 | — | 8 | 2 | no | — |
| 176 | C32 | #1715 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 177 | C23 | — | 4 | 1 | no | — |
| 178 | C23 | — | 36 | 1 | no | — |
| 179 | Q8 | — | 12 | 4 | no | — |
| 180 | D4 | — | 4 | 4 | no | — |
| 181 | D4 | — | 4 | 2 | no | — |
| 182 | D4 | — | 36 | 4 | no | — |
| 183 | D4 | — | 36 | 2 | no | — |
| 184 | C2×C4 | — | 12 | 2 | no | — |
| 185 | C2×C4 | D3×#67 | 1 | 2 | yes | — |
| 186 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 187 | C8 | — | 6 | 4 | no | — |
| 188 | C8 | — | 9 | 4 | no | — |
| 189 | C2×C3 | — | 2 | 1 | no | — |
| 190 | C2×C3 | — | 2 | 2 | no | — |
| 191 | C2×C3 | — | 16 | 2 | no | — |
| 192 | C2×C3 | — | 16 | 2 | no | — |
| 193 | C2×C3 | #5058 | 1 | 2 | yes | — |
| 194 | C2×C3 | #5154 | 1 | 2 | yes | — |
| 195 | C2×C3 | #5175 | 1 | 2 | yes | — |
| 196 | D3 | — | 48 | 2 | no | — |
| 197 | D3 | — | 48 | 2 | no | — |
| 198 | C22 | — | 8 | 1 | no | — |
| 199 | C22 | — | 8 | 2 | no | — |
| 200 | C22 | — | 72 | 1 | no | — |
| 201 | C22 | — | 72 | 2 | no | — |
| 202 | C22 | #63979 | 1 | 1 | yes | characteristic |
| 203 | C4 | — | 24 | 2 | no | — |
| 204 | C4 | #63925 | 1 | 4 | yes | — |
| 205 | C4 | #63930 | 1 | 2 | yes | — |
| 206 | C3 | — | 2 | 1 | no | — |
| 207 | C3 | #71185 | 1 | 2 | yes | complemented |
| 208 | C2 | — | 16 | 1 | no | — |
| 209 | C2 | — | 144 | 1 | no | — |
| 210 | C2 | #10591483 | 1 | 2 | yes | — |
| 211 | C2 | #10591492 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#5070 | C2 | semidirect |
| 3. #10590373 | C2 | semidirect |
| 4. #10590309 | C2 | semidirect |
| 5. #10589079 | C2 | semidirect |
| 21. #5070 | D3 | semidirect |
| 64. C3⋊(C3⋊C8) | SD16 | semidirect |
| 176. C32 | #1715 | semidirect |
| 207. C3 | #71185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592772 | 2 |
| C3×#5070 | 2 |
| #10590373 | 2 |
| #10590309 | 2 |
| #10589079 | 2 |
| #71185 | 3 |