Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
742 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 148 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 | #10594703 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #10592606 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#4909 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×#63550 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10590629 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10590246 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #10590245 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10590240 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #82041 | — | 3 | 2 | no | maximal |
| 10 | #64297 | — | 2 | 2 | no | — |
| 11 | #64110 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×Dic12 | C22 | 1 | 2 | yes | — |
| 13 | C3×#904 | C22 | 1 | 2 | yes | — |
| 14 | #63827 | — | 2 | 2 | no | — |
| 15 | #63811 | — | 2 | 4 | no | — |
| 16 | #63810 | C22 | 1 | 4 | yes | — |
| 17 | #63802 | C22 | 1 | 4 | yes | — |
| 18 | C32×M32 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C3⋊(C3⋊C16) | C22 | 1 | 1 | yes | characteristic |
| 20 | #63625 | C22 | 1 | 2 | yes | — |
| 21 | C16×C3⋊D3 | C22 | 1 | 2 | yes | — |
| 22 | C3×Dic24 | C22 | 1 | 4 | yes | — |
| 23 | C3×#800 | C22 | 1 | 4 | yes | — |
| 24 | #63550 | C22 | 1 | 1 | yes | characteristic |
| 25 | #63550 | C22 | 1 | 2 | yes | — |
| 26 | #63550 | C22 | 1 | 2 | yes | — |
| 27 | #63547 | C22 | 1 | 2 | yes | — |
| 28 | #63545 | C22 | 1 | 1 | yes | characteristic |
| 29 | #5771 | — | 3 | 2 | no | — |
| 30 | #5766 | — | 3 | 2 | no | — |
| 31 | C3×#510 | — | 3 | 2 | no | — |
| 32 | #5194 | — | 3 | 2 | no | — |
| 33 | C2×#829 | — | 3 | 2 | no | — |
| 34 | #4918 | — | 3 | 4 | no | — |
| 35 | D3×Q32 | — | 3 | 4 | no | — |
| 36 | #4916 | — | 3 | 4 | no | — |
| 37 | #4915 | — | 3 | 4 | no | — |
| 38 | #4909 | D3 | 1 | 2 | yes | complemented |
| 39 | #4907 | — | 3 | 2 | no | — |
| 40 | #4907 | — | 6 | 1 | no | — |
| 41 | #3828 | D4 | 1 | 1 | yes | characteristic |
| 42 | C3×#235 | — | 2 | 2 | no | — |
| 43 | C2×C3×Dic6 | — | 2 | 2 | no | — |
| 44 | #3804 | — | 4 | 4 | no | — |
| 45 | #3799 | — | 4 | 2 | no | — |
| 46 | #3797 | — | 2 | 4 | no | — |
| 47 | #3796 | — | 2 | 4 | no | — |
| 48 | D3×Dic6 | — | 4 | 2 | no | — |
| 49 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 50 | #3748 | D4 | 1 | 1 | yes | characteristic |
| 51 | #3743 | D4 | 1 | 2 | yes | — |
| 52 | C8×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 53 | C3×Dic12 | — | 2 | 2 | no | — |
| 54 | C3×Dic12 | C23 | 1 | 2 | yes | — |
| 55 | C3×Dic12 | C23 | 1 | 4 | yes | — |
| 56 | C3×D24 | C23 | 1 | 2 | yes | — |
| 57 | C3×#204 | — | 2 | 2 | no | — |
| 58 | #3718 | — | 2 | 4 | no | — |
| 59 | #3715 | — | 2 | 4 | no | — |
| 60 | C32×C16 | C23 | 1 | 2 | yes | — |
| 61 | C3⋊(C3⋊C16) | C23 | 1 | 1 | yes | characteristic |
| 62 | C3⋊(C3⋊C16) | C23 | 1 | 1 | yes | characteristic |
| 63 | #3417 | — | 9 | 1 | no | Sylow |
| 64 | #1010 | — | 6 | 2 | no | — |
| 65 | #1007 | — | 6 | 2 | no | — |
| 66 | C3×#135 | — | 3 | 2 | no | — |
| 67 | C2×C3×Q16 | — | 3 | 2 | no | — |
| 68 | #951 | — | 6 | 2 | no | — |
| 69 | #942 | — | 6 | 2 | no | — |
| 70 | #919 | — | 3 | 4 | no | — |
| 71 | #918 | — | 6 | 4 | no | — |
| 72 | D3×Q16 | — | 3 | 4 | no | — |
| 73 | D3×Q16 | — | 3 | 4 | no | — |
| 74 | #915 | — | 6 | 4 | no | — |
| 75 | #912 | — | 3 | 4 | no | — |
| 76 | C2×Dic12 | C2×D3 | 1 | 2 | yes | — |
| 77 | #904 | C2×D3 | 1 | 2 | yes | — |
| 78 | #901 | — | 3 | 2 | no | — |
| 79 | #901 | — | 6 | 1 | no | — |
| 80 | C3×Q32 | — | 3 | 4 | no | — |
| 81 | C3×SD32 | — | 3 | 4 | no | — |
| 82 | C3×M32 | — | 2 | 1 | no | — |
| 83 | C3×M32 | C2×D3 | 1 | 2 | yes | — |
| 84 | #829 | — | 3 | 4 | no | — |
| 85 | #829 | — | 3 | 4 | no | — |
| 86 | #829 | — | 3 | 2 | no | — |
| 87 | #828 | — | 3 | 2 | no | — |
| 88 | #827 | — | 3 | 2 | no | — |
| 89 | #826 | — | 3 | 2 | no | — |
| 90 | C2×C3⋊C16 | — | 3 | 2 | no | — |
| 91 | C2×C3⋊C16 | — | 6 | 1 | no | — |
| 92 | Dic24 | C2×D3 | 1 | 4 | yes | — |
| 93 | #800 | C2×D3 | 1 | 4 | yes | — |
| 94 | #798 | — | 3 | 4 | no | — |
| 95 | #798 | — | 6 | 2 | no | — |
| 96 | D3×C16 | — | 3 | 4 | no | — |
| 97 | D3×C16 | — | 6 | 2 | no | — |
| 98 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | #638 | D8 | 1 | 2 | yes | — |
| 100 | C4⋊(C3⋊D3) | D8 | 1 | 1 | yes | characteristic |
| 101 | C4×C3⋊D3 | C2×D4 | 1 | 2 | yes | — |
| 102 | #634 | D8 | 1 | 1 | yes | characteristic |
| 103 | C3×#67 | — | 4 | 2 | no | — |
| 104 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 105 | C3×D12 | — | 2 | 2 | no | — |
| 106 | C3×C4×D3 | — | 4 | 2 | no | — |
| 107 | C3×Dic6 | — | 2 | 4 | no | — |
| 108 | C3×Dic6 | — | 2 | 2 | no | — |
| 109 | C3×Dic6 | — | 4 | 2 | no | — |
| 110 | #627 | — | 4 | 4 | no | — |
| 111 | #626 | — | 4 | 4 | no | — |
| 112 | #624 | — | 4 | 4 | no | — |
| 113 | D3×Dic3 | — | 4 | 4 | no | — |
| 114 | C32×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C32×C8 | C24 | 1 | 1 | yes | characteristic |
| 116 | C3⋊(C3⋊C8) | C2×D4 | 1 | 2 | yes | — |
| 117 | #578 | — | 9 | 2 | no | — |
| 118 | #510 | — | 3 | 2 | no | — |
| 119 | #510 | — | 9 | 4 | no | — |
| 120 | #508 | — | 9 | 2 | no | — |
| 121 | #508 | — | 9 | 1 | no | — |
| 122 | C2×Q32 | — | 9 | 2 | no | — |
| 123 | C2×Q32 | — | 9 | 1 | no | — |
| 124 | #504 | — | 9 | 1 | no | — |
| 125 | C3×#41 | — | 6 | 2 | no | — |
| 126 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 127 | #239 | — | 6 | 4 | no | — |
| 128 | #239 | — | 12 | 2 | no | — |
| 129 | D3×Q8 | — | 6 | 4 | no | — |
| 130 | D3×Q8 | — | 6 | 4 | no | — |
| 131 | D3×Q8 | — | 12 | 2 | no | — |
| 132 | #237 | — | 6 | 4 | no | — |
| 133 | #237 | — | 12 | 4 | no | — |
| 134 | #235 | — | 2 | 2 | no | — |
| 135 | #235 | — | 3 | 2 | no | — |
| 136 | #235 | — | 6 | 1 | no | — |
| 137 | #235 | — | 12 | 2 | no | — |
| 138 | #235 | — | 12 | 4 | no | — |
| 139 | C2×Dic6 | — | 2 | 2 | no | — |
| 140 | C2×Dic6 | — | 12 | 2 | no | — |
| 141 | C3×Q16 | — | 3 | 2 | no | — |
| 142 | C3×Q16 | — | 3 | 4 | no | — |
| 143 | C3×Q16 | — | 6 | 2 | no | — |
| 144 | C3×SD16 | — | 6 | 2 | no | — |
| 145 | C3×D8 | — | 3 | 2 | no | — |
| 146 | C2×C3×C8 | — | 2 | 1 | no | — |
| 147 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 148 | #216 | — | 6 | 4 | no | — |
| 149 | #216 | — | 6 | 4 | no | — |
| 150 | #215 | — | 6 | 4 | no | — |
| 151 | #214 | — | 6 | 4 | no | — |
| 152 | #208 | — | 3 | 2 | no | — |
| 153 | #208 | — | 6 | 1 | no | — |
| 154 | Dic12 | — | 2 | 2 | no | — |
| 155 | Dic12 | C22×D3 | 1 | 4 | yes | — |
| 156 | Dic12 | C22×D3 | 1 | 2 | yes | — |
| 157 | D24 | C22×D3 | 1 | 2 | yes | — |
| 158 | #204 | — | 2 | 2 | no | — |
| 159 | ΓL(1,𝔽25) | — | 3 | 4 | no | — |
| 160 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 161 | D3×C8 | — | 3 | 4 | no | — |
| 162 | D3×C8 | — | 6 | 2 | no | — |
| 163 | C3×C16 | — | 2 | 2 | no | — |
| 164 | C3×C16 | C22×D3 | 1 | 4 | yes | — |
| 165 | C3⋊C16 | — | 3 | 2 | no | — |
| 166 | C3⋊C16 | — | 3 | 2 | no | — |
| 167 | C3⋊C16 | — | 6 | 1 | no | — |
| 168 | C3⋊C16 | — | 6 | 1 | no | — |
| 169 | C22×C32 | C2×D8 | 1 | 1 | yes | characteristic |
| 170 | C2×C3⋊D3 | C2×D8 | 1 | 2 | yes | — |
| 171 | C2×C3×D3 | — | 4 | 2 | no | — |
| 172 | C32×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 173 | C32×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 174 | C3⋊Dic3 | C2×D8 | 1 | 2 | yes | — |
| 175 | C3×Dic3 | — | 4 | 4 | no | — |
| 176 | C3×Dic3 | — | 4 | 2 | no | — |
| 177 | 2−1+4 | — | 18 | 2 | no | — |
| 178 | #137 | — | 18 | 4 | no | — |
| 179 | #137 | — | 18 | 2 | no | — |
| 180 | #135 | — | 3 | 2 | no | — |
| 181 | #135 | — | 9 | 4 | no | — |
| 182 | C2×Q16 | — | 3 | 2 | no | — |
| 183 | C2×Q16 | — | 9 | 4 | no | — |
| 184 | #131 | — | 9 | 1 | no | — |
| 185 | Q32 | — | 3 | 4 | no | — |
| 186 | Q32 | — | 9 | 2 | no | — |
| 187 | Q32 | — | 9 | 1 | no | — |
| 188 | Q32 | — | 9 | 2 | no | — |
| 189 | SD32 | — | 3 | 4 | no | — |
| 190 | SD32 | — | 9 | 2 | no | — |
| 191 | D16 | — | 9 | 1 | no | — |
| 192 | M32 | — | 9 | 2 | no | — |
| 193 | M32 | D32 | 1 | 1 | yes | characteristic |
| 194 | C2×C16 | — | 9 | 1 | no | — |
| 195 | C2×C16 | — | 9 | 2 | no | — |
| 196 | C3×Q8 | — | 6 | 4 | no | — |
| 197 | C3×Q8 | — | 6 | 2 | no | — |
| 198 | C3×Q8 | — | 12 | 2 | no | — |
| 199 | C3×D4 | — | 6 | 2 | no | — |
| 200 | C3×D4 | — | 12 | 2 | no | — |
| 201 | C2×C3×C4 | — | 2 | 1 | no | — |
| 202 | C2×C3×C4 | — | 12 | 2 | no | — |
| 203 | C2×C3×C4 | — | 12 | 2 | no | — |
| 204 | C2×C3×C4 | D3×D4 | 1 | 2 | yes | — |
| 205 | #67 | — | 3 | 4 | no | — |
| 206 | #67 | — | 4 | 2 | no | — |
| 207 | #67 | — | 6 | 2 | no | — |
| 208 | #67 | — | 12 | 4 | no | — |
| 209 | C2×Dic3 | — | 4 | 2 | no | — |
| 210 | C2×Dic3 | — | 12 | 4 | no | — |
| 211 | D12 | — | 2 | 2 | no | — |
| 212 | D12 | — | 3 | 2 | no | — |
| 213 | D12 | — | 6 | 1 | no | — |
| 214 | D12 | — | 12 | 4 | no | — |
| 215 | C4×D3 | — | 3 | 4 | no | — |
| 216 | C4×D3 | — | 4 | 2 | no | — |
| 217 | C4×D3 | — | 6 | 2 | no | — |
| 218 | C4×D3 | — | 12 | 4 | no | — |
| 219 | C4×D3 | — | 12 | 4 | no | — |
| 220 | C4×D3 | — | 12 | 4 | no | — |
| 221 | Dic6 | — | 2 | 2 | no | — |
| 222 | Dic6 | — | 2 | 4 | no | — |
| 223 | Dic6 | — | 3 | 2 | no | — |
| 224 | Dic6 | — | 4 | 2 | no | — |
| 225 | Dic6 | — | 6 | 1 | no | — |
| 226 | Dic6 | — | 12 | 4 | no | — |
| 227 | Dic6 | — | 12 | 4 | no | — |
| 228 | C3×C8 | — | 2 | 1 | no | — |
| 229 | C3×C8 | — | 2 | 1 | no | — |
| 230 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 231 | C3×C8 | C23×D3 | 1 | 2 | yes | — |
| 232 | C3⋊C8 | — | 3 | 4 | no | — |
| 233 | C3⋊C8 | — | 6 | 2 | no | — |
| 234 | C2×C32 | — | 2 | 1 | no | — |
| 235 | C2×C32 | C22×D8 | 1 | 1 | yes | characteristic |
| 236 | C3⋊D3 | — | 2 | 2 | no | — |
| 237 | C3×D3 | — | 8 | 2 | no | — |
| 238 | #41 | — | 6 | 2 | no | — |
| 239 | #41 | — | 9 | 1 | no | — |
| 240 | #41 | — | 18 | 4 | no | — |
| 241 | #41 | — | 36 | 4 | no | — |
| 242 | #41 | — | 36 | 2 | no | — |
| 243 | C2×Q8 | — | 6 | 2 | no | — |
| 244 | C2×Q8 | — | 18 | 4 | no | — |
| 245 | C2×Q8 | — | 36 | 2 | no | — |
| 246 | Q16 | — | 3 | 4 | no | — |
| 247 | Q16 | — | 3 | 2 | no | — |
| 248 | Q16 | — | 6 | 2 | no | — |
| 249 | Q16 | — | 18 | 4 | no | — |
| 250 | SD16 | — | 6 | 2 | no | — |
| 251 | SD16 | — | 18 | 4 | no | — |
| 252 | D8 | — | 3 | 2 | no | — |
| 253 | M16 | — | 9 | 1 | no | — |
| 254 | M16 | — | 9 | 2 | no | — |
| 255 | C2×C8 | — | 9 | 2 | no | — |
| 256 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 257 | C16 | — | 9 | 1 | no | — |
| 258 | C16 | — | 9 | 1 | no | — |
| 259 | C16 | C2×D32 | 1 | 2 | yes | — |
| 260 | C22×C3 | — | 2 | 1 | no | — |
| 261 | C22×C3 | — | 12 | 2 | no | — |
| 262 | C22×C3 | D3×D8 | 1 | 2 | yes | — |
| 263 | C2×D3 | — | 3 | 4 | no | — |
| 264 | C2×D3 | — | 4 | 2 | no | — |
| 265 | C2×D3 | — | 6 | 2 | no | — |
| 266 | C3×C4 | — | 2 | 1 | no | — |
| 267 | C3×C4 | — | 2 | 1 | no | — |
| 268 | C3×C4 | — | 12 | 2 | no | — |
| 269 | C3×C4 | — | 12 | 4 | no | — |
| 270 | C3×C4 | D3×D8 | 1 | 2 | yes | — |
| 271 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 272 | Dic3 | — | 3 | 4 | no | — |
| 273 | Dic3 | — | 4 | 4 | no | — |
| 274 | Dic3 | — | 4 | 2 | no | — |
| 275 | Dic3 | — | 6 | 2 | no | — |
| 276 | C32 | #3417 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 277 | Q8 | — | 6 | 2 | no | — |
| 278 | Q8 | — | 6 | 4 | no | — |
| 279 | Q8 | — | 9 | 1 | no | — |
| 280 | Q8 | — | 12 | 2 | no | — |
| 281 | Q8 | — | 36 | 4 | no | — |
| 282 | D4 | — | 6 | 2 | no | — |
| 283 | D4 | — | 9 | 2 | no | — |
| 284 | D4 | — | 9 | 1 | no | — |
| 285 | D4 | — | 12 | 2 | no | — |
| 286 | D4 | — | 36 | 4 | no | — |
| 287 | C2×C4 | — | 9 | 2 | no | — |
| 288 | C2×C4 | — | 12 | 2 | no | — |
| 289 | C2×C4 | — | 12 | 2 | no | — |
| 290 | C2×C4 | — | 36 | 4 | no | — |
| 291 | C2×C4 | — | 36 | 4 | no | — |
| 292 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 293 | C8 | — | 9 | 2 | no | — |
| 294 | C8 | #3802 | 1 | 1 | yes | characteristic |
| 295 | C8 | C22×D32 | 1 | 1 | yes | characteristic |
| 296 | C2×C3 | — | 2 | 2 | no | — |
| 297 | C2×C3 | — | 2 | 1 | no | — |
| 298 | C2×C3 | — | 4 | 1 | no | — |
| 299 | C2×C3 | — | 24 | 2 | no | — |
| 300 | C2×C3 | C2×D3×D8 | 1 | 2 | yes | — |
| 301 | D3 | — | 6 | 4 | no | — |
| 302 | D3 | — | 8 | 2 | no | — |
| 303 | D3 | — | 12 | 2 | no | — |
| 304 | C22 | — | 9 | 2 | no | — |
| 305 | C22 | — | 12 | 2 | no | — |
| 306 | C22 | #63797 | 1 | 1 | yes | characteristic |
| 307 | C4 | — | 9 | 2 | no | — |
| 308 | C4 | — | 12 | 2 | no | — |
| 309 | C4 | — | 12 | 4 | no | — |
| 310 | C4 | #63797 | 1 | 1 | yes | characteristic |
| 311 | C4 | C2×#3802 | 1 | 1 | yes | characteristic |
| 312 | C3 | — | 2 | 1 | no | — |
| 313 | C3 | #82041 | 1 | 2 | yes | complemented |
| 314 | C2 | — | 2 | 1 | no | — |
| 315 | C2 | — | 18 | 2 | no | — |
| 316 | C2 | — | 24 | 2 | no | — |
| 317 | C2 | C2×#63797 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10594703 | C2 | semidirect |
| 2. #10592606 | C2 | semidirect |
| 3. C3×#4909 | C2 | semidirect |
| 4. C2×#63550 | C2 | semidirect |
| 5. #10590629 | C2 | semidirect |
| 6. #10590246 | C2 | semidirect |
| 7. #10590245 | C2 | semidirect |
| 8. #10590240 | C2 | semidirect |
| 38. #4909 | D3 | semidirect |
| 276. C32 | #3417 | semidirect |
| 313. C3 | #82041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594703 | 2 |
| #10592606 | 2 |
| C3×#4909 | 2 |
| C2×#63550 | 2 |
| #10590629 | 2 |
| #10590246 | 2 |
| #10590245 | 2 |
| #10590240 | 2 |
| #82041 | 3 |