Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
713 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 713 conjugacy classes of subgroups — too many to draw. Only its 140 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 | #10596269 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3×#833 | C2 | 1 | 2 | yes | maximal |
| 3 | #10589171 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #70067 | — | 3 | 2 | no | maximal |
| 5 | C22×C32×D4 | C22 | 1 | 1 | yes | characteristic |
| 6 | C2×#3757 | C4 | 1 | 4 | yes | — |
| 7 | D4×C3⋊Dic3 | — | 2 | 4 | no | — |
| 8 | #64135 | C22 | 1 | 2 | yes | — |
| 9 | C2×C3×#208 | C22 | 1 | 4 | yes | — |
| 10 | C3×#833 | — | 2 | 4 | no | — |
| 11 | #5798 | — | 3 | 2 | no | — |
| 12 | #5798 | — | 6 | 1 | no | — |
| 13 | C2×C3×#100 | — | 3 | 2 | no | — |
| 14 | C2×#833 | D3 | 1 | 2 | yes | — |
| 15 | #4559 | — | 3 | 4 | no | — |
| 16 | #4556 | — | 3 | 4 | no | — |
| 17 | C24×C32 | C2×C4 | 1 | 2 | yes | — |
| 18 | C2×C32×D4 | — | 2 | 4 | no | — |
| 19 | C2×C32×D4 | D4 | 1 | 4 | yes | — |
| 20 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 21 | C22×C3⋊Dic3 | — | 2 | 4 | no | — |
| 22 | #3757 | — | 2 | 4 | no | — |
| 23 | #3757 | C2×C4 | 1 | 4 | yes | — |
| 24 | C4⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 25 | C4×C3⋊Dic3 | — | 2 | 2 | no | — |
| 26 | C3×#208 | — | 2 | 4 | no | — |
| 27 | C3×#208 | — | 2 | 4 | no | — |
| 28 | C2×C3×C3⋊C8 | — | 2 | 4 | no | — |
| 29 | #1829 | — | 9 | 1 | no | Sylow |
| 30 | C22×C3×D4 | — | 2 | 1 | no | — |
| 31 | C22×C3×D4 | C2×D3 | 1 | 2 | yes | — |
| 32 | C2×C3×M16 | — | 3 | 4 | no | — |
| 33 | C2×#217 | — | 3 | 8 | no | — |
| 34 | C2×#217 | — | 6 | 4 | no | — |
| 35 | D4×Dic3 | — | 6 | 8 | no | — |
| 36 | D4×Dic3 | — | 6 | 4 | no | — |
| 37 | D4×Dic3 | — | 6 | 4 | no | — |
| 38 | #926 | — | 3 | 2 | no | — |
| 39 | #926 | — | 3 | 2 | no | — |
| 40 | #926 | — | 6 | 2 | no | — |
| 41 | C2×#208 | C2×D3 | 1 | 4 | yes | — |
| 42 | C3×#100 | — | 6 | 4 | no | — |
| 43 | #833 | — | 2 | 4 | no | — |
| 44 | C23×C32 | — | 2 | 4 | no | — |
| 45 | C23×C32 | — | 8 | 2 | no | — |
| 46 | C23×C32 | C22⋊C4 | 1 | 4 | yes | — |
| 47 | C23×C32 | C22×C4 | 1 | 1 | yes | characteristic |
| 48 | C32×D4 | — | 2 | 8 | no | — |
| 49 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 50 | C2×C32×C4 | #41 | 1 | 4 | yes | — |
| 51 | C2×C3⋊Dic3 | — | 2 | 4 | no | — |
| 52 | C2×C3⋊Dic3 | — | 8 | 4 | no | — |
| 53 | C3×C3⋊C8 | — | 4 | 4 | no | — |
| 54 | #518 | — | 9 | 1 | no | — |
| 55 | C2×#100 | — | 3 | 2 | no | — |
| 56 | #344 | — | 9 | 4 | no | — |
| 57 | C24×C3 | — | 2 | 2 | no | — |
| 58 | C24×C3 | C4×D3 | 1 | 4 | yes | — |
| 59 | C2×C3×D4 | — | 2 | 8 | no | — |
| 60 | C2×C3×D4 | — | 2 | 4 | no | — |
| 61 | C2×C3×D4 | — | 2 | 4 | no | — |
| 62 | C2×C3×D4 | — | 2 | 4 | no | — |
| 63 | C2×C3×D4 | D12 | 1 | 4 | yes | — |
| 64 | C2×C3×D4 | #67 | 1 | 4 | yes | — |
| 65 | C22×C3×C4 | — | 2 | 1 | no | — |
| 66 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 67 | C22×Dic3 | — | 6 | 8 | no | — |
| 68 | C22×Dic3 | — | 6 | 8 | no | — |
| 69 | C3×M16 | — | 6 | 4 | no | — |
| 70 | C3×M16 | — | 6 | 4 | no | — |
| 71 | C2×C3×C8 | — | 6 | 4 | no | — |
| 72 | #217 | — | 3 | 4 | no | — |
| 73 | #217 | — | 3 | 4 | no | — |
| 74 | #217 | — | 6 | 4 | no | — |
| 75 | #217 | — | 6 | 8 | no | — |
| 76 | #217 | — | 6 | 8 | no | — |
| 77 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 78 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 79 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 80 | C4×Dic3 | — | 6 | 4 | no | — |
| 81 | C4×Dic3 | — | 6 | 2 | no | — |
| 82 | C4×Dic3 | — | 6 | 2 | no | — |
| 83 | #208 | — | 2 | 4 | no | — |
| 84 | #208 | — | 2 | 4 | no | — |
| 85 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 86 | C22×C32 | — | 2 | 4 | no | — |
| 87 | C22×C32 | — | 4 | 1 | no | — |
| 88 | C22×C32 | — | 4 | 4 | no | — |
| 89 | C22×C32 | — | 8 | 4 | no | — |
| 90 | C22×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 91 | C22×C32 | #117 | 1 | 2 | yes | — |
| 92 | C32×C4 | #123 | 1 | 4 | yes | — |
| 93 | C3⋊Dic3 | — | 4 | 4 | no | — |
| 94 | C22×D4 | D32 | 1 | 1 | yes | characteristic |
| 95 | C2×M16 | — | 3 | 4 | no | — |
| 96 | C4×D4 | — | 18 | 4 | no | — |
| 97 | #117 | — | 9 | 2 | no | — |
| 98 | C2×C22⋊C4 | — | 9 | 4 | no | — |
| 99 | #100 | — | 6 | 4 | no | — |
| 100 | C23×C3 | — | 2 | 8 | no | — |
| 101 | C23×C3 | — | 2 | 4 | no | — |
| 102 | C23×C3 | — | 2 | 4 | no | — |
| 103 | C23×C3 | — | 2 | 4 | no | — |
| 104 | C23×C3 | — | 2 | 1 | no | — |
| 105 | C23×C3 | — | 8 | 4 | no | — |
| 106 | C23×C3 | — | 8 | 4 | no | — |
| 107 | C23×C3 | (C2×D3)⋊C4 | 1 | 8 | yes | — |
| 108 | C23×C3 | C2×C4×D3 | 1 | 2 | yes | — |
| 109 | C3×D4 | — | 2 | 16 | no | — |
| 110 | C3×D4 | — | 2 | 8 | no | — |
| 111 | C3×D4 | — | 2 | 8 | no | — |
| 112 | C2×C3×C4 | — | 2 | 4 | no | — |
| 113 | C2×C3×C4 | — | 2 | 2 | no | — |
| 114 | C2×C3×C4 | C2×D12 | 1 | 2 | yes | — |
| 115 | C2×C3×C4 | #237 | 1 | 4 | yes | — |
| 116 | C2×C3×C4 | #237 | 1 | 4 | yes | — |
| 117 | C2×C3×C4 | C2×#67 | 1 | 2 | yes | — |
| 118 | C2×Dic3 | — | 6 | 8 | no | — |
| 119 | C2×Dic3 | — | 6 | 4 | no | — |
| 120 | C2×Dic3 | — | 6 | 4 | no | — |
| 121 | C2×Dic3 | — | 24 | 8 | no | — |
| 122 | C2×Dic3 | — | 24 | 8 | no | — |
| 123 | C3×C8 | — | 12 | 4 | no | — |
| 124 | C3⋊C8 | — | 4 | 4 | no | — |
| 125 | C2×C32 | — | 2 | 1 | no | — |
| 126 | C2×C32 | — | 2 | 2 | no | — |
| 127 | C2×C32 | — | 4 | 4 | no | — |
| 128 | C2×C32 | #381 | 1 | 1 | yes | characteristic |
| 129 | C24 | #624 | 1 | 2 | yes | — |
| 130 | C2×D4 | — | 2 | 4 | no | — |
| 131 | C2×D4 | #626 | 1 | 4 | yes | — |
| 132 | C22×C4 | — | 18 | 4 | no | — |
| 133 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 134 | M16 | — | 6 | 4 | no | — |
| 135 | M16 | — | 6 | 4 | no | — |
| 136 | C2×C8 | — | 6 | 4 | no | — |
| 137 | C4⋊C4 | — | 18 | 2 | no | — |
| 138 | C22⋊C4 | — | 9 | 4 | no | — |
| 139 | C22⋊C4 | — | 18 | 4 | no | — |
| 140 | C42 | — | 18 | 2 | no | — |
| 141 | C22×C3 | — | 2 | 8 | no | — |
| 142 | C22×C3 | — | 2 | 8 | no | — |
| 143 | C22×C3 | — | 2 | 2 | no | — |
| 144 | C22×C3 | — | 2 | 1 | no | — |
| 145 | C22×C3 | — | 4 | 2 | no | — |
| 146 | C22×C3 | — | 4 | 8 | no | — |
| 147 | C22×C3 | — | 4 | 8 | no | — |
| 148 | C22×C3 | — | 4 | 2 | no | — |
| 149 | C22×C3 | — | 8 | 4 | no | — |
| 150 | C22×C3 | — | 8 | 4 | no | — |
| 151 | C22×C3 | — | 8 | 8 | no | — |
| 152 | C22×C3 | #877 | 1 | 2 | yes | — |
| 153 | C22×C3 | #877 | 1 | 2 | yes | — |
| 154 | C22×C3 | C2×(C2×D3)⋊C4 | 1 | 2 | yes | — |
| 155 | C3×C4 | — | 2 | 4 | no | — |
| 156 | C3×C4 | #886 | 1 | 4 | yes | — |
| 157 | C3×C4 | #935 | 1 | 4 | yes | — |
| 158 | Dic3 | — | 12 | 8 | no | — |
| 159 | Dic3 | — | 12 | 4 | no | — |
| 160 | Dic3 | — | 12 | 4 | no | — |
| 161 | C32 | #1829 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 162 | C23 | — | 2 | 4 | no | — |
| 163 | C23 | — | 8 | 2 | no | — |
| 164 | C23 | #3722 | 1 | 4 | yes | — |
| 165 | C23 | C2×#624 | 1 | 1 | yes | characteristic |
| 166 | D4 | — | 2 | 8 | no | — |
| 167 | C2×C4 | — | 18 | 4 | no | — |
| 168 | C2×C4 | — | 72 | 4 | no | — |
| 169 | C2×C4 | #3805 | 1 | 4 | yes | — |
| 170 | C2×C4 | C2×#626 | 1 | 2 | yes | — |
| 171 | C8 | — | 12 | 4 | no | — |
| 172 | C2×C3 | — | 2 | 2 | no | — |
| 173 | C2×C3 | — | 2 | 2 | no | — |
| 174 | C2×C3 | — | 2 | 2 | no | — |
| 175 | C2×C3 | — | 2 | 2 | no | — |
| 176 | C2×C3 | — | 2 | 1 | no | — |
| 177 | C2×C3 | — | 4 | 2 | no | — |
| 178 | C2×C3 | — | 4 | 8 | no | — |
| 179 | C2×C3 | — | 4 | 8 | no | — |
| 180 | C2×C3 | #4943 | 1 | 2 | yes | — |
| 181 | C22 | — | 2 | 4 | no | — |
| 182 | C22 | — | 4 | 1 | no | — |
| 183 | C22 | — | 4 | 4 | no | — |
| 184 | C22 | — | 8 | 4 | no | — |
| 185 | C22 | #63957 | 1 | 2 | yes | — |
| 186 | C22 | C2×#3722 | 1 | 1 | yes | characteristic |
| 187 | C4 | — | 36 | 4 | no | — |
| 188 | C4 | #63962 | 1 | 4 | yes | — |
| 189 | C3 | — | 2 | 1 | no | — |
| 190 | C3 | #70067 | 1 | 2 | yes | complemented |
| 191 | C2 | — | 2 | 1 | no | — |
| 192 | C2 | — | 2 | 2 | no | — |
| 193 | C2 | — | 4 | 4 | no | — |
| 194 | C2 | #10591697 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10589171 | C2 | semidirect |
| 161. C32 | #1829 | semidirect |
| 190. C3 | #70067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596269 | 2 |
| C2×C3×#833 | 2 |
| #10589171 | 2 |
| #70067 | 3 |