Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
439 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 439 conjugacy classes of subgroups — too many to draw. Only its 76 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 | #10592571 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10590886 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#63546 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#4491 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10589133 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69202 | — | 3 | 2 | no | maximal |
| 7 | C2×#3745 | C22 | 1 | 1 | yes | characteristic |
| 8 | #64102 | — | 2 | 1 | no | — |
| 9 | C2×C3×D24 | C22 | 1 | 2 | yes | — |
| 10 | #63914 | — | 2 | 1 | no | — |
| 11 | C2×#3713 | — | 2 | 1 | no | — |
| 12 | C32×#107 | C22 | 1 | 1 | yes | characteristic |
| 13 | C8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 14 | #63636 | — | 2 | 1 | no | — |
| 15 | C2×C3×C3⋊C16 | C22 | 1 | 2 | yes | — |
| 16 | #63546 | — | 2 | 4 | no | — |
| 17 | #5151 | — | 3 | 2 | no | — |
| 18 | C2×#826 | — | 3 | 2 | no | — |
| 19 | C2×D48 | — | 3 | 2 | no | — |
| 20 | #4872 | — | 3 | 2 | no | — |
| 21 | #4872 | — | 6 | 1 | no | — |
| 22 | C3×#357 | — | 3 | 2 | no | — |
| 23 | Dic3⋊C16 | — | 3 | 2 | no | — |
| 24 | #4491 | D3 | 1 | 2 | yes | complemented |
| 25 | C2×C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 26 | C2×C4×C3⋊D3 | — | 4 | 1 | no | — |
| 27 | C2×C3×D12 | — | 2 | 2 | no | — |
| 28 | C2×#625 | — | 4 | 1 | no | — |
| 29 | C2×#625 | — | 4 | 1 | no | — |
| 30 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 31 | C32×C4⋊C4 | — | 2 | 1 | no | — |
| 32 | #3752 | — | 4 | 1 | no | — |
| 33 | C4×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 35 | #3745 | — | 2 | 1 | no | — |
| 36 | #3745 | D4 | 1 | 2 | yes | complemented |
| 37 | C3×D24 | — | 2 | 2 | no | — |
| 38 | C3×D24 | — | 2 | 2 | no | — |
| 39 | #3713 | — | 4 | 2 | no | — |
| 40 | C3×C3⋊C16 | — | 2 | 2 | no | — |
| 41 | #2206 | — | 9 | 1 | no | Sylow |
| 42 | C2×C3×D8 | — | 3 | 2 | no | — |
| 43 | #940 | — | 6 | 2 | no | — |
| 44 | C2×#213 | — | 6 | 2 | no | — |
| 45 | C2×D24 | — | 3 | 2 | no | — |
| 46 | C2×D24 | — | 6 | 1 | no | — |
| 47 | C2×D24 | C2×D3 | 1 | 2 | yes | — |
| 48 | #893 | — | 6 | 2 | no | — |
| 49 | #893 | — | 6 | 2 | no | — |
| 50 | C2×C3×C16 | — | 3 | 2 | no | — |
| 51 | C3×#107 | — | 2 | 1 | no | — |
| 52 | C3×#107 | C2×D3 | 1 | 2 | yes | — |
| 53 | #826 | — | 6 | 4 | no | — |
| 54 | C8×Dic3 | — | 3 | 2 | no | — |
| 55 | C8×Dic3 | — | 6 | 1 | no | — |
| 56 | C2×C3⋊C16 | C2×D3 | 1 | 2 | yes | — |
| 57 | #809 | — | 6 | 2 | no | — |
| 58 | #809 | — | 6 | 2 | no | — |
| 59 | D48 | — | 6 | 4 | no | — |
| 60 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 61 | C22×C3×D3 | — | 4 | 2 | no | — |
| 62 | C2×C32×C4 | — | 4 | 1 | no | — |
| 63 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 64 | C2×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 65 | C2×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 66 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 67 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 68 | C4×C3⋊D3 | — | 8 | 2 | no | — |
| 69 | C3×D12 | — | 4 | 2 | no | — |
| 70 | C3×D12 | — | 4 | 2 | no | — |
| 71 | #625 | — | 8 | 2 | no | — |
| 72 | #625 | — | 8 | 2 | no | — |
| 73 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C32×C8 | #41 | 1 | 1 | yes | characteristic |
| 75 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 76 | C2×D16 | — | 9 | 2 | no | — |
| 77 | #493 | — | 9 | 1 | no | — |
| 78 | C4×D8 | — | 9 | 1 | no | — |
| 79 | C4⋊C16 | — | 9 | 1 | no | — |
| 80 | #357 | — | 3 | 2 | no | — |
| 81 | C2×C3×D4 | — | 6 | 2 | no | — |
| 82 | C2×#67 | — | 12 | 2 | no | — |
| 83 | C2×#67 | — | 12 | 2 | no | — |
| 84 | C2×D12 | — | 2 | 2 | no | — |
| 85 | C2×D12 | — | 6 | 2 | no | — |
| 86 | C2×D12 | — | 6 | 2 | no | — |
| 87 | C2×C4×D3 | — | 12 | 2 | no | — |
| 88 | C2×C4×D3 | — | 12 | 2 | no | — |
| 89 | C3×D8 | — | 6 | 2 | no | — |
| 90 | C3×D8 | — | 6 | 2 | no | — |
| 91 | C2×C3×C8 | — | 2 | 1 | no | — |
| 92 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 93 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 94 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 95 | #213 | — | 12 | 4 | no | — |
| 96 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 97 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 98 | C4×Dic3 | — | 3 | 2 | no | — |
| 99 | C4×Dic3 | — | 6 | 1 | no | — |
| 100 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 101 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 102 | D24 | — | 2 | 2 | no | — |
| 103 | D24 | — | 2 | 2 | no | — |
| 104 | D24 | — | 3 | 4 | no | — |
| 105 | D24 | — | 6 | 2 | no | — |
| 106 | D24 | — | 6 | 2 | no | — |
| 107 | D24 | — | 6 | 2 | no | — |
| 108 | C3×C16 | — | 6 | 2 | no | — |
| 109 | C3⋊C16 | — | 2 | 2 | no | — |
| 110 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 111 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 112 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 113 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 114 | C2×C3×D3 | — | 8 | 2 | no | — |
| 115 | C2×C3×D3 | — | 8 | 2 | no | — |
| 116 | C2×C3×D3 | — | 8 | 2 | no | — |
| 117 | C32×C4 | — | 8 | 1 | no | — |
| 118 | C32×C4 | #121 | 1 | 1 | yes | characteristic |
| 119 | C32×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 120 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 121 | C3⋊Dic3 | D16 | 1 | 2 | yes | complemented |
| 122 | C2×D8 | — | 3 | 2 | no | — |
| 123 | C2×D8 | — | 9 | 1 | no | — |
| 124 | C2×D8 | — | 18 | 1 | no | — |
| 125 | #127 | — | 18 | 1 | no | — |
| 126 | C4×D4 | — | 18 | 1 | no | — |
| 127 | D16 | — | 18 | 4 | no | — |
| 128 | C2×C16 | — | 3 | 2 | no | — |
| 129 | #107 | D32 | 1 | 1 | yes | characteristic |
| 130 | #102 | — | 18 | 1 | no | — |
| 131 | C4×C8 | — | 9 | 1 | no | — |
| 132 | C23×C3 | — | 12 | 2 | no | — |
| 133 | C22×D3 | — | 4 | 2 | no | — |
| 134 | C22×D3 | — | 12 | 2 | no | — |
| 135 | C22×D3 | — | 12 | 2 | no | — |
| 136 | C3×D4 | — | 12 | 2 | no | — |
| 137 | C3×D4 | — | 12 | 2 | no | — |
| 138 | C2×C3×C4 | — | 2 | 1 | no | — |
| 139 | C2×C3×C4 | — | 4 | 2 | no | — |
| 140 | C2×C3×C4 | — | 4 | 2 | no | — |
| 141 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 142 | #67 | — | 24 | 4 | no | — |
| 143 | #67 | — | 24 | 4 | no | — |
| 144 | C2×Dic3 | — | 3 | 2 | no | — |
| 145 | C2×Dic3 | — | 3 | 2 | no | — |
| 146 | C2×Dic3 | — | 6 | 1 | no | — |
| 147 | C2×Dic3 | — | 6 | 1 | no | — |
| 148 | D12 | — | 4 | 2 | no | — |
| 149 | D12 | — | 4 | 2 | no | — |
| 150 | D12 | — | 6 | 4 | no | — |
| 151 | D12 | — | 6 | 4 | no | — |
| 152 | D12 | — | 12 | 2 | no | — |
| 153 | D12 | — | 12 | 2 | no | — |
| 154 | C4×D3 | — | 24 | 4 | no | — |
| 155 | C4×D3 | — | 24 | 4 | no | — |
| 156 | C3×C8 | — | 2 | 1 | no | — |
| 157 | C3×C8 | — | 2 | 1 | no | — |
| 158 | C3×C8 | #235 | 1 | 2 | yes | — |
| 159 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 160 | C3⋊C8 | — | 6 | 2 | no | — |
| 161 | C3⋊C8 | — | 12 | 1 | no | — |
| 162 | C2×C32 | #459 | 1 | 1 | yes | characteristic |
| 163 | C2×C32 | C2×D16 | 1 | 1 | yes | characteristic |
| 164 | C2×C32 | #509 | 1 | 1 | yes | characteristic |
| 165 | C3⋊D3 | — | 8 | 2 | no | — |
| 166 | C3×D3 | — | 16 | 2 | no | — |
| 167 | C2×D4 | — | 6 | 2 | no | — |
| 168 | C2×D4 | — | 18 | 1 | no | — |
| 169 | C2×D4 | — | 36 | 1 | no | — |
| 170 | C2×D4 | — | 36 | 1 | no | — |
| 171 | C22×C4 | — | 36 | 1 | no | — |
| 172 | D8 | — | 6 | 2 | no | — |
| 173 | D8 | — | 6 | 2 | no | — |
| 174 | D8 | — | 9 | 2 | no | — |
| 175 | D8 | — | 18 | 1 | no | — |
| 176 | D8 | — | 36 | 2 | no | — |
| 177 | C2×C8 | — | 9 | 1 | no | — |
| 178 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 179 | C4⋊C4 | — | 2 | 1 | no | — |
| 180 | C22⋊C4 | — | 36 | 1 | no | — |
| 181 | C42 | — | 9 | 1 | no | — |
| 182 | C16 | — | 6 | 2 | no | — |
| 183 | C22×C3 | — | 2 | 1 | no | — |
| 184 | C22×C3 | — | 24 | 2 | no | — |
| 185 | C22×C3 | — | 24 | 2 | no | — |
| 186 | C22×C3 | — | 24 | 2 | no | — |
| 187 | C22×C3 | D3×D8 | 1 | 2 | yes | — |
| 188 | C2×D3 | — | 8 | 2 | no | — |
| 189 | C2×D3 | — | 8 | 2 | no | — |
| 190 | C2×D3 | — | 8 | 2 | no | — |
| 191 | C2×D3 | — | 12 | 4 | no | — |
| 192 | C2×D3 | — | 12 | 4 | no | — |
| 193 | C2×D3 | — | 24 | 2 | no | — |
| 194 | C2×D3 | — | 24 | 2 | no | — |
| 195 | C2×D3 | — | 24 | 2 | no | — |
| 196 | C2×D3 | — | 24 | 2 | no | — |
| 197 | C3×C4 | — | 2 | 1 | no | — |
| 198 | C3×C4 | — | 2 | 1 | no | — |
| 199 | C3×C4 | — | 8 | 2 | no | — |
| 200 | C3×C4 | — | 8 | 2 | no | — |
| 201 | C3×C4 | #884 | 1 | 2 | yes | — |
| 202 | C3×C4 | #914 | 1 | 2 | yes | — |
| 203 | Dic3 | — | 3 | 4 | no | — |
| 204 | Dic3 | — | 6 | 2 | no | — |
| 205 | Dic3 | — | 6 | 2 | no | — |
| 206 | Dic3 | — | 12 | 1 | no | — |
| 207 | C32 | #2206 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 208 | C23 | — | 12 | 2 | no | — |
| 209 | C23 | — | 36 | 1 | no | — |
| 210 | D4 | — | 12 | 2 | no | — |
| 211 | D4 | — | 12 | 2 | no | — |
| 212 | D4 | — | 18 | 2 | no | — |
| 213 | D4 | — | 36 | 1 | no | — |
| 214 | D4 | — | 72 | 2 | no | — |
| 215 | D4 | — | 72 | 2 | no | — |
| 216 | C2×C4 | — | 4 | 1 | no | — |
| 217 | C2×C4 | — | 9 | 1 | no | — |
| 218 | C2×C4 | — | 9 | 1 | no | — |
| 219 | C2×C4 | — | 72 | 2 | no | — |
| 220 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 221 | C8 | — | 18 | 1 | no | — |
| 222 | C8 | #3798 | 1 | 1 | yes | characteristic |
| 223 | C8 | #3802 | 1 | 1 | yes | characteristic |
| 224 | C2×C3 | — | 2 | 1 | no | — |
| 225 | C2×C3 | — | 2 | 1 | no | — |
| 226 | C2×C3 | — | 2 | 1 | no | — |
| 227 | C2×C3 | — | 48 | 2 | no | — |
| 228 | C2×C3 | #4786 | 1 | 2 | yes | — |
| 229 | C2×C3 | D3×D16 | 1 | 2 | yes | — |
| 230 | C2×C3 | #4914 | 1 | 2 | yes | — |
| 231 | D3 | — | 16 | 2 | no | — |
| 232 | D3 | — | 24 | 4 | no | — |
| 233 | D3 | — | 24 | 4 | no | — |
| 234 | C22 | — | 24 | 2 | no | — |
| 235 | C22 | — | 24 | 2 | no | — |
| 236 | C22 | — | 24 | 2 | no | — |
| 237 | C22 | — | 36 | 2 | no | — |
| 238 | C22 | — | 72 | 1 | no | — |
| 239 | C22 | — | 72 | 1 | no | — |
| 240 | C22 | #63926 | 1 | 1 | yes | characteristic |
| 241 | C4 | — | 8 | 1 | no | — |
| 242 | C4 | — | 9 | 2 | no | — |
| 243 | C4 | — | 18 | 1 | no | — |
| 244 | C4 | #63912 | 1 | 1 | yes | characteristic |
| 245 | C4 | #63941 | 1 | 1 | yes | characteristic |
| 246 | C3 | — | 2 | 1 | no | — |
| 247 | C3 | #69202 | 1 | 2 | yes | complemented |
| 248 | C2 | — | 48 | 2 | no | — |
| 249 | C2 | — | 72 | 2 | no | — |
| 250 | C2 | #10590551 | 1 | 1 | yes | characteristic |
| 251 | C2 | #10591025 | 1 | 1 | yes | characteristic |
| 252 | C2 | #10591040 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10592571 | C2 | semidirect |
| 2. #10590886 | C2 | semidirect |
| 3. C2×#63546 | C2 | semidirect |
| 4. C3×#4491 | C2 | semidirect |
| 5. #10589133 | C2 | semidirect |
| 24. #4491 | D3 | semidirect |
| 36. #3745 | D4 | semidirect |
| 121. C3⋊Dic3 | D16 | semidirect |
| 207. C32 | #2206 | semidirect |
| 247. C3 | #69202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592571 | 2 |
| #10590886 | 2 |
| C2×#63546 | 2 |
| C3×#4491 | 2 |
| #10589133 | 2 |
| #69202 | 3 |