Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
569 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 569 conjugacy classes of subgroups — too many to draw. Only its 82 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 | C2×#63797 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10592586 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#63548 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#4491 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10589108 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69193 | — | 3 | 2 | no | maximal |
| 7 | C2×#3802 | — | 2 | 1 | no | — |
| 8 | C2×#3746 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×C8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 10 | #64106 | — | 2 | 1 | no | — |
| 11 | C2×C3×D24 | C22 | 1 | 2 | yes | — |
| 12 | C2×#3713 | — | 2 | 1 | no | — |
| 13 | #63797 | — | 2 | 4 | no | — |
| 14 | C32×#107 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #63637 | — | 2 | 1 | no | — |
| 16 | C2×C3×C3⋊C16 | C22 | 1 | 2 | yes | complemented |
| 17 | #63548 | — | 2 | 4 | no | — |
| 18 | C2×D3×D8 | — | 3 | 2 | no | — |
| 19 | C2×#827 | — | 3 | 2 | no | — |
| 20 | C2×#800 | — | 3 | 2 | no | — |
| 21 | #4887 | — | 3 | 2 | no | — |
| 22 | #4887 | — | 6 | 1 | no | — |
| 23 | C3×#357 | — | 3 | 2 | no | — |
| 24 | (C2×D3)⋊C16 | — | 3 | 2 | no | — |
| 25 | #4491 | D3 | 1 | 2 | yes | complemented |
| 26 | C22×D32 | — | 4 | 1 | no | — |
| 27 | C2×C4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×#634 | — | 2 | 1 | no | — |
| 29 | C2×C3×D12 | — | 2 | 2 | no | — |
| 30 | C2×#625 | — | 4 | 1 | no | — |
| 31 | #3802 | — | 2 | 4 | no | — |
| 32 | #3802 | — | 4 | 2 | no | — |
| 33 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 34 | C32×C4⋊C4 | — | 2 | 1 | no | — |
| 35 | #3752 | — | 4 | 1 | no | — |
| 36 | C4⋊(C3⋊Dic3) | — | 4 | 1 | no | — |
| 37 | C2×C3⋊(C3⋊C8) | D4 | 1 | 1 | yes | characteristic |
| 38 | #3746 | — | 2 | 2 | no | — |
| 39 | C8×C3⋊D3 | — | 2 | 2 | no | — |
| 40 | C3×D24 | — | 2 | 2 | no | — |
| 41 | C3×D24 | D4 | 1 | 4 | yes | — |
| 42 | #3713 | — | 2 | 4 | no | — |
| 43 | C3×C3⋊C16 | — | 2 | 2 | no | — |
| 44 | #2187 | — | 9 | 1 | no | Sylow |
| 45 | C2×D3×D4 | — | 6 | 2 | no | — |
| 46 | C2×C3×D8 | — | 3 | 2 | no | — |
| 47 | C2×#213 | — | 6 | 2 | no | — |
| 48 | D3×D8 | — | 6 | 4 | no | — |
| 49 | D3×D8 | — | 6 | 4 | no | — |
| 50 | C2×Dic12 | — | 3 | 2 | no | — |
| 51 | C2×Dic12 | — | 6 | 1 | no | — |
| 52 | C2×D24 | C2×D3 | 1 | 2 | yes | — |
| 53 | C2×D3×C8 | — | 3 | 2 | no | — |
| 54 | C2×D3×C8 | — | 6 | 1 | no | — |
| 55 | #897 | — | 6 | 2 | no | — |
| 56 | #897 | — | 6 | 2 | no | — |
| 57 | C2×C3×C16 | — | 3 | 2 | no | — |
| 58 | C3×#107 | — | 2 | 1 | no | — |
| 59 | C3×#107 | C2×D3 | 1 | 2 | yes | complemented |
| 60 | #827 | — | 6 | 4 | no | — |
| 61 | C2×C3⋊C16 | C2×D3 | 1 | 2 | yes | complemented |
| 62 | #810 | — | 6 | 2 | no | — |
| 63 | #810 | — | 6 | 2 | no | — |
| 64 | #800 | — | 6 | 4 | no | — |
| 65 | C22×C3⋊D3 | D8 | 1 | 1 | yes | characteristic |
| 66 | C22×C3×D3 | — | 4 | 2 | no | — |
| 67 | C2×D32 | — | 4 | 4 | no | — |
| 68 | C2×D32 | — | 8 | 2 | no | — |
| 69 | C2×D32 | — | 8 | 2 | no | — |
| 70 | C2×C32×C4 | — | 4 | 1 | no | — |
| 71 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 72 | C2×C3⋊Dic3 | — | 4 | 1 | no | — |
| 73 | C2×C3⋊Dic3 | D8 | 1 | 1 | yes | characteristic |
| 74 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 75 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 76 | #634 | — | 4 | 1 | no | — |
| 77 | #634 | — | 4 | 1 | no | — |
| 78 | C3×D12 | — | 2 | 4 | no | — |
| 79 | C3×D12 | — | 4 | 2 | no | — |
| 80 | #625 | — | 4 | 4 | no | — |
| 81 | C32×C8 | C2×D4 | 1 | 2 | yes | — |
| 82 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 83 | C22×D8 | — | 9 | 1 | no | — |
| 84 | C2×SD32 | — | 9 | 2 | no | — |
| 85 | #467 | — | 9 | 1 | no | — |
| 86 | #357 | — | 3 | 2 | no | — |
| 87 | C22⋊C16 | — | 9 | 1 | no | — |
| 88 | C23×D3 | — | 12 | 2 | no | — |
| 89 | C2×C3×D4 | — | 6 | 2 | no | — |
| 90 | C2×#67 | — | 12 | 2 | no | — |
| 91 | D3×D4 | — | 6 | 8 | no | — |
| 92 | D3×D4 | — | 12 | 4 | no | — |
| 93 | C2×D12 | — | 2 | 2 | no | — |
| 94 | C2×C4×D3 | — | 3 | 2 | no | — |
| 95 | C2×C4×D3 | — | 6 | 1 | no | — |
| 96 | C2×Dic6 | — | 6 | 2 | no | — |
| 97 | C2×Dic6 | — | 6 | 2 | no | — |
| 98 | C3×D8 | — | 3 | 4 | no | — |
| 99 | C3×D8 | — | 6 | 2 | no | — |
| 100 | C2×C3×C8 | — | 2 | 1 | no | — |
| 101 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 102 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 103 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 104 | #213 | — | 6 | 8 | no | — |
| 105 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 106 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 107 | C4⋊Dic3 | — | 12 | 2 | no | — |
| 108 | C4⋊Dic3 | — | 12 | 2 | no | — |
| 109 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 110 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 111 | Dic12 | — | 6 | 2 | no | — |
| 112 | Dic12 | — | 6 | 2 | no | — |
| 113 | Dic12 | — | 12 | 2 | no | — |
| 114 | D24 | — | 2 | 2 | no | — |
| 115 | D24 | D12 | 1 | 4 | yes | — |
| 116 | D3×C8 | — | 6 | 2 | no | — |
| 117 | D3×C8 | — | 6 | 2 | no | — |
| 118 | D3×C8 | — | 12 | 2 | no | — |
| 119 | C3×C16 | — | 6 | 2 | no | — |
| 120 | C3⋊C16 | — | 2 | 2 | no | — |
| 121 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 122 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 123 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 124 | C2×C3⋊D3 | SD32 | 1 | 2 | yes | complemented |
| 125 | C2×C3×D3 | — | 4 | 4 | no | — |
| 126 | C2×C3×D3 | — | 8 | 2 | no | — |
| 127 | C2×C3×D3 | — | 8 | 2 | no | — |
| 128 | D32 | — | 8 | 8 | no | — |
| 129 | C32×C4 | — | 8 | 1 | no | — |
| 130 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 131 | C32×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 132 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 133 | C3⋊Dic3 | — | 8 | 1 | no | — |
| 134 | C22×D4 | — | 18 | 1 | no | — |
| 135 | C2×Q16 | — | 9 | 1 | no | — |
| 136 | C2×D8 | — | 3 | 2 | no | — |
| 137 | C2×D8 | — | 18 | 1 | no | — |
| 138 | C2×D8 | — | 18 | 4 | no | — |
| 139 | C22×C8 | — | 9 | 1 | no | — |
| 140 | C22⋊Q8 | — | 18 | 1 | no | — |
| 141 | SD32 | — | 18 | 4 | no | — |
| 142 | C2×C16 | — | 3 | 2 | no | — |
| 143 | #107 | D32 | 1 | 1 | yes | characteristic, complemented |
| 144 | #103 | — | 18 | 1 | no | — |
| 145 | C23×C3 | — | 12 | 2 | no | — |
| 146 | C22×D3 | — | 3 | 2 | no | — |
| 147 | C22×D3 | — | 4 | 2 | no | — |
| 148 | C22×D3 | — | 6 | 1 | no | — |
| 149 | C22×D3 | — | 12 | 8 | no | — |
| 150 | C22×D3 | — | 24 | 4 | no | — |
| 151 | C22×D3 | — | 24 | 4 | no | — |
| 152 | C3×D4 | — | 6 | 4 | no | — |
| 153 | C3×D4 | — | 12 | 2 | no | — |
| 154 | C2×C3×C4 | — | 2 | 1 | no | — |
| 155 | C2×C3×C4 | — | 4 | 2 | no | — |
| 156 | C2×C3×C4 | — | 4 | 2 | no | — |
| 157 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 158 | #67 | — | 12 | 8 | no | — |
| 159 | C2×Dic3 | — | 3 | 2 | no | — |
| 160 | C2×Dic3 | — | 6 | 1 | no | — |
| 161 | C2×Dic3 | — | 12 | 2 | no | — |
| 162 | C2×Dic3 | — | 12 | 2 | no | — |
| 163 | D12 | — | 2 | 4 | no | — |
| 164 | D12 | — | 4 | 2 | no | — |
| 165 | C4×D3 | — | 6 | 2 | no | — |
| 166 | C4×D3 | — | 6 | 2 | no | — |
| 167 | C4×D3 | — | 12 | 1 | no | — |
| 168 | C4×D3 | — | 12 | 1 | no | — |
| 169 | Dic6 | — | 12 | 2 | no | — |
| 170 | Dic6 | — | 12 | 2 | no | — |
| 171 | Dic6 | — | 12 | 2 | no | — |
| 172 | Dic6 | — | 12 | 2 | no | — |
| 173 | C3×C8 | — | 2 | 2 | no | — |
| 174 | C3×C8 | C2×D12 | 1 | 2 | yes | — |
| 175 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 176 | C3⋊C8 | — | 6 | 2 | no | — |
| 177 | C3⋊C8 | — | 12 | 1 | no | — |
| 178 | C2×C32 | #447 | 1 | 1 | yes | characteristic |
| 179 | C2×C32 | C2×SD32 | 1 | 1 | yes | characteristic |
| 180 | C2×C32 | #509 | 1 | 1 | yes | characteristic |
| 181 | C3⋊D3 | — | 2 | 2 | no | — |
| 182 | C3×D3 | — | 8 | 4 | no | — |
| 183 | C24 | — | 36 | 1 | no | — |
| 184 | C2×Q8 | — | 18 | 1 | no | — |
| 185 | C2×D4 | — | 6 | 2 | no | — |
| 186 | C2×D4 | — | 18 | 4 | no | — |
| 187 | C2×D4 | — | 36 | 1 | no | — |
| 188 | C2×D4 | — | 36 | 2 | no | — |
| 189 | C22×C4 | — | 9 | 1 | no | — |
| 190 | Q16 | — | 18 | 2 | no | — |
| 191 | D8 | — | 3 | 4 | no | — |
| 192 | D8 | — | 6 | 2 | no | — |
| 193 | D8 | — | 18 | 4 | no | — |
| 194 | C2×C8 | — | 9 | 1 | no | — |
| 195 | C2×C8 | — | 18 | 2 | no | — |
| 196 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 197 | C4⋊C4 | — | 2 | 1 | no | — |
| 198 | C4⋊C4 | — | 36 | 1 | no | — |
| 199 | C22⋊C4 | — | 36 | 1 | no | — |
| 200 | C16 | — | 6 | 2 | no | — |
| 201 | C22×C3 | — | 2 | 1 | no | — |
| 202 | C22×C3 | — | 12 | 4 | no | — |
| 203 | C22×C3 | — | 24 | 2 | no | — |
| 204 | C22×C3 | — | 24 | 2 | no | — |
| 205 | C22×C3 | D3×D8 | 1 | 2 | yes | — |
| 206 | C2×D3 | — | 3 | 4 | no | — |
| 207 | C2×D3 | — | 4 | 4 | no | — |
| 208 | C2×D3 | — | 6 | 2 | no | — |
| 209 | C2×D3 | — | 6 | 2 | no | — |
| 210 | C2×D3 | — | 6 | 2 | no | — |
| 211 | C2×D3 | — | 8 | 2 | no | — |
| 212 | C2×D3 | — | 8 | 2 | no | — |
| 213 | C2×D3 | — | 12 | 1 | no | — |
| 214 | C2×D3 | — | 12 | 1 | no | — |
| 215 | C2×D3 | — | 24 | 16 | no | — |
| 216 | C3×C4 | — | 2 | 1 | no | — |
| 217 | C3×C4 | — | 2 | 1 | no | — |
| 218 | C3×C4 | — | 8 | 2 | no | — |
| 219 | C3×C4 | — | 8 | 2 | no | — |
| 220 | C3×C4 | #882 | 1 | 2 | yes | — |
| 221 | C3×C4 | #914 | 1 | 2 | yes | — |
| 222 | Dic3 | — | 6 | 2 | no | — |
| 223 | Dic3 | — | 12 | 1 | no | — |
| 224 | Dic3 | — | 24 | 2 | no | — |
| 225 | Dic3 | — | 24 | 2 | no | — |
| 226 | C32 | #2187 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 227 | C23 | — | 9 | 1 | no | — |
| 228 | C23 | — | 12 | 2 | no | — |
| 229 | C23 | — | 36 | 4 | no | — |
| 230 | C23 | — | 72 | 2 | no | — |
| 231 | C23 | — | 72 | 2 | no | — |
| 232 | Q8 | — | 36 | 1 | no | — |
| 233 | Q8 | — | 36 | 1 | no | — |
| 234 | D4 | — | 6 | 4 | no | — |
| 235 | D4 | — | 12 | 2 | no | — |
| 236 | D4 | — | 36 | 4 | no | — |
| 237 | C2×C4 | — | 4 | 1 | no | — |
| 238 | C2×C4 | — | 9 | 1 | no | — |
| 239 | C2×C4 | — | 18 | 1 | no | — |
| 240 | C2×C4 | — | 18 | 1 | no | — |
| 241 | C2×C4 | — | 36 | 1 | no | — |
| 242 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 243 | C8 | — | 18 | 1 | no | — |
| 244 | C8 | D3×D12 | 1 | 2 | yes | — |
| 245 | C2×C3 | — | 2 | 1 | no | — |
| 246 | C2×C3 | — | 2 | 1 | no | — |
| 247 | C2×C3 | — | 2 | 1 | no | — |
| 248 | C2×C3 | — | 24 | 4 | no | — |
| 249 | C2×C3 | #4773 | 1 | 2 | yes | — |
| 250 | C2×C3 | #4911 | 1 | 2 | yes | — |
| 251 | C2×C3 | D3×SD32 | 1 | 2 | yes | — |
| 252 | D3 | — | 6 | 4 | no | — |
| 253 | D3 | — | 8 | 4 | no | — |
| 254 | D3 | — | 12 | 2 | no | — |
| 255 | C22 | — | 9 | 2 | no | — |
| 256 | C22 | — | 12 | 4 | no | — |
| 257 | C22 | — | 18 | 1 | no | — |
| 258 | C22 | — | 18 | 1 | no | — |
| 259 | C22 | — | 24 | 2 | no | — |
| 260 | C22 | — | 24 | 2 | no | — |
| 261 | C22 | — | 72 | 8 | no | — |
| 262 | C22 | #63926 | 1 | 1 | yes | characteristic |
| 263 | C4 | — | 8 | 1 | no | — |
| 264 | C4 | — | 18 | 1 | no | — |
| 265 | C4 | — | 72 | 1 | no | — |
| 266 | C4 | #63923 | 1 | 1 | yes | characteristic |
| 267 | C4 | #63941 | 1 | 1 | yes | characteristic |
| 268 | C3 | — | 2 | 1 | no | — |
| 269 | C3 | #69193 | 1 | 2 | yes | complemented |
| 270 | C2 | — | 18 | 2 | no | — |
| 271 | C2 | — | 24 | 4 | no | — |
| 272 | C2 | #10590598 | 1 | 1 | yes | characteristic |
| 273 | C2 | #10591026 | 1 | 1 | yes | characteristic |
| 274 | C2 | #10591039 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10592586 | C2 | semidirect |
| 3. C2×#63548 | C2 | semidirect |
| 4. C3×#4491 | C2 | semidirect |
| 5. #10589108 | C2 | semidirect |
| 8. C2×#3746 | C22 | semidirect |
| 14. C32×#107 | C22 | semidirect |
| 16. C2×C3×C3⋊C16 | C22 | semidirect |
| 25. #4491 | D3 | semidirect |
| 59. C3×#107 | C2×D3 | semidirect |
| 61. C2×C3⋊C16 | C2×D3 | semidirect |
| 124. C2×C3⋊D3 | SD32 | semidirect |
| 143. #107 | D32 | semidirect |
| 226. C32 | #2187 | semidirect |
| 269. C3 | #69193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63797 | 2 |
| #10592586 | 2 |
| C2×#63548 | 2 |
| C3×#4491 | 2 |
| #10589108 | 2 |
| #69193 | 3 |