Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
647 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 647 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #10596187 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10590256 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×#4544 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10589096 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #68382 | — | 3 | 2 | no | maximal |
| 6 | C2×#3830 | C4 | 1 | 2 | yes | — |
| 7 | C32×#127 | C22 | 1 | 1 | yes | characteristic |
| 8 | #64147 | — | 2 | 2 | no | — |
| 9 | #64145 | C4 | 1 | 2 | yes | — |
| 10 | D4×C3⋊Dic3 | — | 2 | 2 | no | — |
| 11 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 12 | #64078 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×C4⋊(C3⋊C8) | C22 | 1 | 4 | yes | — |
| 14 | #63557 | — | 2 | 2 | no | — |
| 15 | #63553 | — | 2 | 2 | no | — |
| 16 | #5716 | — | 3 | 2 | no | — |
| 17 | #5716 | — | 6 | 1 | no | — |
| 18 | #4833 | — | 3 | 4 | no | — |
| 19 | C3×#331 | — | 3 | 2 | no | — |
| 20 | #4544 | D3 | 1 | 2 | yes | complemented |
| 21 | #4481 | — | 3 | 4 | no | — |
| 22 | C2×C32×D4 | — | 2 | 2 | no | — |
| 23 | C2×C32×D4 | C2×C4 | 1 | 2 | yes | — |
| 24 | C2×#638 | — | 2 | 2 | no | — |
| 25 | C22×C3⋊Dic3 | — | 2 | 2 | no | — |
| 26 | #3830 | — | 4 | 4 | no | — |
| 27 | C2×C4×C3⋊D3 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C2×C4×C3⋊D3 | D4 | 1 | 2 | yes | — |
| 29 | C2×#634 | C2×C4 | 1 | 2 | yes | — |
| 30 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 31 | #3757 | — | 2 | 4 | no | — |
| 32 | C4⋊(C3⋊Dic3) | — | 2 | 2 | no | — |
| 33 | C4×C3⋊Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 34 | C4×C3⋊Dic3 | D4 | 1 | 2 | yes | — |
| 35 | C2×C3×C3⋊C8 | — | 2 | 4 | no | — |
| 36 | #1543 | — | 9 | 1 | no | Sylow |
| 37 | C2×#237 | — | 3 | 4 | no | — |
| 38 | C2×#237 | — | 6 | 2 | no | — |
| 39 | C3×#127 | — | 2 | 1 | no | — |
| 40 | C3×#127 | C2×D3 | 1 | 2 | yes | — |
| 41 | #938 | — | 6 | 4 | no | — |
| 42 | #938 | — | 6 | 4 | no | — |
| 43 | #936 | — | 3 | 4 | no | — |
| 44 | #936 | — | 6 | 2 | no | — |
| 45 | D4×Dic3 | — | 6 | 4 | no | — |
| 46 | D4×Dic3 | — | 6 | 4 | no | — |
| 47 | C42×D3 | — | 3 | 2 | no | — |
| 48 | C42×D3 | — | 6 | 1 | no | — |
| 49 | #869 | — | 3 | 2 | no | — |
| 50 | #869 | — | 6 | 1 | no | — |
| 51 | C3×C4⋊C8 | — | 3 | 4 | no | — |
| 52 | (C2×D3)⋊C8 | — | 6 | 4 | no | — |
| 53 | C8×Dic3 | — | 6 | 4 | no | — |
| 54 | C4⋊(C3⋊C8) | C2×D3 | 1 | 4 | yes | — |
| 55 | C23×C32 | — | 2 | 2 | no | — |
| 56 | C22×C3⋊D3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 57 | C32×D4 | — | 4 | 2 | no | — |
| 58 | C32×D4 | — | 4 | 4 | no | — |
| 59 | C2×C32×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 60 | C2×C32×C4 | C2×D4 | 1 | 2 | yes | — |
| 61 | #638 | — | 4 | 4 | no | — |
| 62 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 63 | C2×C3⋊Dic3 | — | 4 | 4 | no | — |
| 64 | C2×C3⋊Dic3 | C22⋊C4 | 1 | 2 | yes | — |
| 65 | C2×C3⋊Dic3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 66 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 67 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 68 | #634 | — | 4 | 2 | no | — |
| 69 | C3×C3⋊C8 | — | 4 | 4 | no | — |
| 70 | #532 | — | 9 | 1 | no | — |
| 71 | #431 | — | 9 | 2 | no | — |
| 72 | #333 | — | 9 | 2 | no | — |
| 73 | #331 | — | 3 | 2 | no | — |
| 74 | C2×C3×D4 | — | 2 | 4 | no | — |
| 75 | C2×C3×D4 | — | 2 | 4 | no | — |
| 76 | C2×C3×D4 | — | 2 | 2 | no | — |
| 77 | C2×C3×D4 | C4×D3 | 1 | 4 | yes | — |
| 78 | C2×#67 | — | 6 | 4 | no | — |
| 79 | C2×#67 | — | 6 | 4 | no | — |
| 80 | C22×Dic3 | — | 6 | 4 | no | — |
| 81 | C22×Dic3 | — | 6 | 4 | no | — |
| 82 | #237 | — | 12 | 8 | no | — |
| 83 | #237 | — | 12 | 8 | no | — |
| 84 | C2×C4×D3 | — | 3 | 2 | no | — |
| 85 | C2×C4×D3 | — | 3 | 4 | no | — |
| 86 | C2×C4×D3 | — | 6 | 1 | no | — |
| 87 | C2×C4×D3 | — | 6 | 2 | no | — |
| 88 | C2×Dic6 | — | 3 | 4 | no | — |
| 89 | C2×Dic6 | — | 6 | 2 | no | — |
| 90 | C2×C3×C8 | — | 6 | 4 | no | — |
| 91 | C3×C42 | — | 2 | 1 | no | — |
| 92 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 93 | #217 | — | 6 | 8 | no | — |
| 94 | #217 | — | 6 | 8 | no | — |
| 95 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 96 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 97 | C4×Dic3 | — | 3 | 2 | no | — |
| 98 | C4×Dic3 | — | 3 | 4 | no | — |
| 99 | C4×Dic3 | — | 6 | 1 | no | — |
| 100 | C4×Dic3 | — | 6 | 2 | no | — |
| 101 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 102 | C22×C32 | — | 4 | 2 | no | — |
| 103 | C22×C32 | — | 4 | 4 | no | — |
| 104 | C22×C32 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 105 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 106 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 107 | C32×C4 | — | 2 | 1 | no | — |
| 108 | C32×C4 | #135 | 1 | 4 | yes | — |
| 109 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 110 | C3⋊Dic3 | — | 4 | 2 | no | — |
| 111 | C3⋊Dic3 | #100 | 1 | 2 | yes | — |
| 112 | C2×#41 | — | 9 | 2 | no | — |
| 113 | C4⋊Q8 | — | 9 | 1 | no | — |
| 114 | #127 | D32 | 1 | 1 | yes | characteristic |
| 115 | #124 | — | 9 | 2 | no | — |
| 116 | #121 | — | 18 | 2 | no | — |
| 117 | C4×D4 | — | 18 | 2 | no | — |
| 118 | C2×C42 | — | 9 | 1 | no | — |
| 119 | C4⋊C8 | — | 3 | 4 | no | — |
| 120 | C22⋊C8 | — | 18 | 2 | no | — |
| 121 | C4×C8 | — | 18 | 2 | no | — |
| 122 | C23×C3 | — | 2 | 4 | no | — |
| 123 | C23×C3 | — | 2 | 4 | no | — |
| 124 | C22×D3 | — | 3 | 2 | no | — |
| 125 | C22×D3 | — | 6 | 1 | no | — |
| 126 | C3×D4 | — | 4 | 4 | no | — |
| 127 | C3×D4 | — | 4 | 4 | no | — |
| 128 | C3×D4 | — | 4 | 8 | no | — |
| 129 | C3×D4 | — | 4 | 4 | no | — |
| 130 | C3×D4 | — | 4 | 4 | no | — |
| 131 | C2×C3×C4 | — | 2 | 1 | no | — |
| 132 | C2×C3×C4 | — | 2 | 2 | no | — |
| 133 | C2×C3×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 134 | C2×C3×C4 | D3×D4 | 1 | 4 | yes | — |
| 135 | #67 | — | 12 | 8 | no | — |
| 136 | #67 | — | 12 | 8 | no | — |
| 137 | C2×Dic3 | — | 3 | 2 | no | — |
| 138 | C2×Dic3 | — | 3 | 4 | no | — |
| 139 | C2×Dic3 | — | 6 | 1 | no | — |
| 140 | C2×Dic3 | — | 6 | 2 | no | — |
| 141 | C2×Dic3 | — | 6 | 4 | no | — |
| 142 | C2×Dic3 | — | 6 | 4 | no | — |
| 143 | C2×Dic3 | — | 12 | 8 | no | — |
| 144 | C2×Dic3 | — | 12 | 8 | no | — |
| 145 | C4×D3 | — | 6 | 4 | no | — |
| 146 | C4×D3 | — | 6 | 4 | no | — |
| 147 | C4×D3 | — | 6 | 4 | no | — |
| 148 | C4×D3 | — | 6 | 4 | no | — |
| 149 | C4×D3 | — | 12 | 4 | no | — |
| 150 | Dic6 | — | 12 | 4 | no | — |
| 151 | Dic6 | — | 12 | 4 | no | — |
| 152 | C3×C8 | — | 12 | 4 | no | — |
| 153 | C3⋊C8 | — | 4 | 4 | no | — |
| 154 | C2×C32 | — | 8 | 2 | no | — |
| 155 | C2×C32 | C2×#100 | 1 | 1 | yes | characteristic |
| 156 | C2×C32 | #416 | 1 | 2 | yes | — |
| 157 | C3⋊D3 | — | 4 | 1 | no | — |
| 158 | #41 | — | 36 | 4 | no | — |
| 159 | C2×Q8 | — | 9 | 2 | no | — |
| 160 | C2×D4 | — | 2 | 2 | no | — |
| 161 | C2×D4 | — | 18 | 2 | no | — |
| 162 | C2×D4 | #624 | 1 | 2 | yes | — |
| 163 | C22×C4 | — | 9 | 1 | no | — |
| 164 | C22×C4 | — | 9 | 2 | no | — |
| 165 | C22×C4 | — | 18 | 2 | no | — |
| 166 | C2×C8 | — | 6 | 4 | no | — |
| 167 | C4⋊C4 | — | 18 | 2 | no | — |
| 168 | C22⋊C4 | — | 18 | 4 | no | — |
| 169 | C42 | — | 9 | 1 | no | — |
| 170 | C42 | — | 9 | 2 | no | — |
| 171 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 172 | C22×C3 | — | 2 | 1 | no | — |
| 173 | C22×C3 | — | 4 | 4 | no | — |
| 174 | C22×C3 | — | 4 | 8 | no | — |
| 175 | C22×C3 | — | 4 | 4 | no | — |
| 176 | C22×C3 | — | 4 | 8 | no | — |
| 177 | C22×C3 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 178 | C2×D3 | — | 6 | 2 | no | — |
| 179 | C2×D3 | — | 6 | 2 | no | — |
| 180 | C2×D3 | — | 6 | 4 | no | — |
| 181 | C2×D3 | — | 12 | 2 | no | — |
| 182 | C3×C4 | — | 2 | 2 | no | — |
| 183 | C3×C4 | — | 2 | 2 | no | — |
| 184 | C3×C4 | — | 2 | 4 | no | — |
| 185 | C3×C4 | #912 | 1 | 4 | yes | — |
| 186 | C3×C4 | #916 | 1 | 4 | yes | — |
| 187 | Dic3 | — | 3 | 4 | no | — |
| 188 | Dic3 | — | 6 | 2 | no | — |
| 189 | Dic3 | — | 6 | 4 | no | — |
| 190 | Dic3 | — | 12 | 2 | no | — |
| 191 | Dic3 | — | 12 | 4 | no | — |
| 192 | Dic3 | — | 12 | 4 | no | — |
| 193 | C32 | #1543 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 194 | C23 | — | 2 | 2 | no | — |
| 195 | C23 | — | 9 | 1 | no | — |
| 196 | Q8 | — | 36 | 2 | no | — |
| 197 | D4 | — | 4 | 2 | no | — |
| 198 | D4 | — | 4 | 4 | no | — |
| 199 | D4 | — | 36 | 4 | no | — |
| 200 | C2×C4 | — | 9 | 1 | no | — |
| 201 | C2×C4 | — | 9 | 2 | no | — |
| 202 | C2×C4 | — | 18 | 2 | no | — |
| 203 | C2×C4 | — | 18 | 4 | no | — |
| 204 | C2×C4 | — | 18 | 2 | no | — |
| 205 | C2×C4 | — | 36 | 4 | no | — |
| 206 | C2×C4 | C2×#624 | 1 | 1 | yes | characteristic |
| 207 | C2×C4 | #3811 | 1 | 2 | yes | — |
| 208 | C8 | — | 12 | 4 | no | — |
| 209 | C2×C3 | — | 2 | 1 | no | — |
| 210 | C2×C3 | — | 2 | 2 | no | — |
| 211 | C2×C3 | — | 8 | 4 | no | — |
| 212 | C2×C3 | — | 8 | 4 | no | — |
| 213 | C2×C3 | D3×#100 | 1 | 2 | yes | — |
| 214 | C2×C3 | #4772 | 1 | 4 | yes | — |
| 215 | D3 | — | 12 | 2 | no | — |
| 216 | D3 | — | 12 | 2 | no | — |
| 217 | C22 | — | 4 | 2 | no | — |
| 218 | C22 | — | 4 | 4 | no | — |
| 219 | C22 | — | 18 | 1 | no | — |
| 220 | C22 | — | 18 | 2 | no | — |
| 221 | C22 | #63974 | 1 | 1 | yes | characteristic |
| 222 | C4 | — | 2 | 1 | no | — |
| 223 | C4 | — | 9 | 2 | no | — |
| 224 | C4 | — | 18 | 2 | no | — |
| 225 | C4 | — | 36 | 2 | no | — |
| 226 | C4 | #63936 | 1 | 4 | yes | — |
| 227 | C3 | — | 2 | 1 | no | — |
| 228 | C3 | #68382 | 1 | 2 | yes | complemented |
| 229 | C2 | — | 8 | 2 | no | — |
| 230 | C2 | — | 36 | 1 | no | — |
| 231 | C2 | #10591424 | 1 | 2 | yes | — |
| 232 | C2 | #10591503 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10590256 | C2 | semidirect |
| 3. C3×#4544 | C2 | semidirect |
| 4. #10589096 | C2 | semidirect |
| 20. #4544 | D3 | semidirect |
| 193. C32 | #1543 | semidirect |
| 228. C3 | #68382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596187 | 2 |
| #10590256 | 2 |
| C3×#4544 | 2 |
| #10589096 | 2 |
| #68382 | 3 |