Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
470 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 48 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 | #10593094 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | Q16×C22⋊C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10589519 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10589504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C8×(C22⋊C9)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #83889 | — | 3 | 1 | no | maximal |
| 7 | Q8×C22⋊C9 | C22 | 1 | 2 | yes | — |
| 8 | C4⋊((C22⋊C9)⋊C2) | — | 2 | 2 | no | — |
| 9 | C4⋊((C22⋊C9)⋊C2) | C22 | 1 | 2 | yes | — |
| 10 | C4×(C22⋊C9)⋊C2 | — | 2 | 2 | no | — |
| 11 | C4×(C22⋊C9)⋊C2 | C22 | 1 | 1 | yes | characteristic |
| 12 | #63481 | — | 4 | 1 | no | maximal |
| 13 | C8×C22⋊C9 | C22 | 1 | 1 | yes | characteristic |
| 14 | (C22⋊C9)⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×C3×Q16 | D3 | 1 | 1 | yes | characteristic |
| 16 | #5817 | — | 3 | 2 | no | — |
| 17 | C2×#919 | — | 3 | 1 | no | — |
| 18 | #5227 | — | 3 | 2 | no | — |
| 19 | #5191 | — | 3 | 1 | no | — |
| 20 | #5188 | — | 3 | 1 | no | — |
| 21 | #5187 | — | 3 | 2 | no | — |
| 22 | #5185 | — | 3 | 2 | no | — |
| 23 | Dic3×Q16 | — | 3 | 1 | no | — |
| 24 | #5115 | — | 3 | 1 | no | — |
| 25 | C8×#67 | — | 3 | 1 | no | — |
| 26 | C2×(C22⋊C9)⋊C2 | — | 2 | 2 | no | — |
| 27 | C2×(C22⋊C9)⋊C2 | D4 | 1 | 1 | yes | characteristic |
| 28 | #3701 | — | 4 | 2 | no | — |
| 29 | C4×C22⋊C9 | — | 2 | 2 | no | — |
| 30 | C4×C22⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 31 | (C22⋊C9)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 32 | C9×Q16 | — | 4 | 1 | no | — |
| 33 | #3675 | — | 4 | 2 | no | — |
| 34 | D72 | — | 4 | 1 | no | — |
| 35 | C8×D9 | — | 4 | 1 | no | — |
| 36 | #3285 | — | 9 | 1 | no | Sylow |
| 37 | C22×C3×Q8 | C2×D3 | 1 | 2 | yes | — |
| 38 | C2×#239 | — | 3 | 2 | no | — |
| 39 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 40 | C2×C3×Q16 | — | 3 | 2 | no | — |
| 41 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 42 | C22×C3×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 43 | #947 | — | 3 | 2 | no | — |
| 44 | #947 | — | 6 | 2 | no | — |
| 45 | #946 | — | 3 | 2 | no | — |
| 46 | #946 | — | 6 | 2 | no | — |
| 47 | Q8×Dic3 | — | 3 | 2 | no | — |
| 48 | C2×#215 | — | 3 | 2 | no | — |
| 49 | C2×#215 | — | 3 | 2 | no | — |
| 50 | #930 | — | 3 | 2 | no | — |
| 51 | #930 | — | 6 | 2 | no | — |
| 52 | C4×#67 | — | 3 | 1 | no | — |
| 53 | C4×#67 | — | 6 | 2 | no | — |
| 54 | #919 | — | 6 | 2 | no | — |
| 55 | #919 | — | 6 | 1 | no | — |
| 56 | #919 | — | 6 | 1 | no | — |
| 57 | C2×D24 | — | 3 | 1 | no | — |
| 58 | C2×D3×C8 | — | 3 | 1 | no | — |
| 59 | #835 | — | 3 | 2 | no | — |
| 60 | #835 | — | 3 | 2 | no | — |
| 61 | #830 | — | 3 | 1 | no | — |
| 62 | #821 | — | 3 | 2 | no | — |
| 63 | (C2×D3)⋊C8 | — | 3 | 1 | no | — |
| 64 | #818 | — | 3 | 1 | no | — |
| 65 | Dic3⋊C8 | — | 3 | 1 | no | — |
| 66 | C8×Dic3 | — | 3 | 1 | no | — |
| 67 | C2×C22⋊C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 68 | (C22⋊C9)⋊C2 | — | 2 | 1 | no | — |
| 69 | (C22⋊C9)⋊C2 | — | 4 | 2 | no | — |
| 70 | Q8×C9 | — | 4 | 2 | no | — |
| 71 | D36 | — | 4 | 2 | no | — |
| 72 | D36 | — | 8 | 2 | no | — |
| 73 | C4×D9 | — | 4 | 1 | no | — |
| 74 | C4×D9 | — | 8 | 2 | no | — |
| 75 | C8×C9 | — | 4 | 1 | no | — |
| 76 | C9⋊C8 | — | 4 | 1 | no | — |
| 77 | C2×#135 | — | 9 | 1 | no | — |
| 78 | C22×Q16 | D9 | 1 | 1 | yes | characteristic, complemented |
| 79 | #548 | — | 9 | 2 | no | — |
| 80 | #495 | — | 9 | 1 | no | — |
| 81 | #467 | — | 9 | 1 | no | — |
| 82 | #466 | — | 9 | 1 | no | — |
| 83 | #464 | — | 9 | 2 | no | — |
| 84 | #452 | — | 9 | 2 | no | — |
| 85 | #448 | — | 9 | 2 | no | — |
| 86 | C4×Q16 | — | 9 | 1 | no | — |
| 87 | C8×D4 | — | 9 | 1 | no | — |
| 88 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 89 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 90 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 91 | C22×C3×C4 | — | 2 | 2 | no | — |
| 92 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 93 | C2×#67 | — | 3 | 1 | no | — |
| 94 | C2×#67 | — | 6 | 2 | no | — |
| 95 | #239 | — | 6 | 2 | no | — |
| 96 | #239 | — | 6 | 2 | no | — |
| 97 | #239 | — | 12 | 2 | no | — |
| 98 | C2×D12 | — | 3 | 2 | no | — |
| 99 | C2×D12 | — | 6 | 2 | no | — |
| 100 | C2×C4×D3 | — | 3 | 1 | no | — |
| 101 | C2×C4×D3 | — | 6 | 2 | no | — |
| 102 | C3×Q16 | — | 3 | 2 | no | — |
| 103 | C3×Q16 | — | 3 | 1 | no | — |
| 104 | C3×Q16 | — | 6 | 1 | no | — |
| 105 | C3×Q16 | S4 | 1 | 1 | yes | characteristic |
| 106 | C2×C3×C8 | — | 3 | 1 | no | — |
| 107 | C2×C3×C8 | — | 3 | 1 | no | — |
| 108 | #217 | — | 3 | 1 | no | — |
| 109 | #215 | — | 6 | 2 | no | — |
| 110 | #215 | — | 6 | 2 | no | — |
| 111 | #215 | — | 12 | 2 | no | — |
| 112 | (C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 113 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 114 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 115 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 116 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 117 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 118 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 119 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 120 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 121 | C4×Dic3 | — | 3 | 1 | no | — |
| 122 | C4×Dic3 | — | 6 | 2 | no | — |
| 123 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 124 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 125 | D24 | — | 6 | 1 | no | — |
| 126 | D24 | — | 6 | 1 | no | — |
| 127 | D3×C8 | — | 6 | 1 | no | — |
| 128 | D3×C8 | — | 6 | 1 | no | — |
| 129 | C2×D9 | — | 4 | 1 | no | — |
| 130 | C2×D9 | — | 8 | 2 | no | — |
| 131 | C22⋊C9 | #135 | 1 | 1 | yes | characteristic, complemented |
| 132 | C4×C9 | — | 4 | 1 | no | — |
| 133 | C4×C9 | — | 8 | 2 | no | — |
| 134 | Dic9 | — | 4 | 1 | no | — |
| 135 | C2×#41 | — | 9 | 2 | no | — |
| 136 | C22×Q8 | C2×D9 | 1 | 2 | yes | — |
| 137 | #135 | — | 18 | 2 | no | — |
| 138 | #135 | — | 18 | 1 | no | — |
| 139 | #135 | — | 18 | 1 | no | — |
| 140 | C2×Q16 | — | 3 | 1 | no | — |
| 141 | C2×Q16 | — | 3 | 2 | no | — |
| 142 | C2×Q16 | — | 3 | 1 | no | — |
| 143 | C2×SD16 | — | 9 | 2 | no | — |
| 144 | C2×SD16 | — | 9 | 2 | no | — |
| 145 | C2×D8 | — | 9 | 1 | no | — |
| 146 | C22×C8 | — | 9 | 1 | no | — |
| 147 | C22×C8 | C2×D9 | 1 | 1 | yes | characteristic |
| 148 | #124 | — | 9 | 2 | no | — |
| 149 | #124 | — | 18 | 2 | no | — |
| 150 | C22⋊Q8 | — | 9 | 2 | no | — |
| 151 | C22⋊Q8 | — | 18 | 2 | no | — |
| 152 | #121 | — | 9 | 2 | no | — |
| 153 | #121 | — | 18 | 2 | no | — |
| 154 | C4×Q8 | — | 9 | 2 | no | — |
| 155 | C4×D4 | — | 9 | 1 | no | — |
| 156 | C4×D4 | — | 18 | 2 | no | — |
| 157 | #107 | — | 9 | 1 | no | — |
| 158 | C4⋊C8 | — | 9 | 1 | no | — |
| 159 | #103 | — | 9 | 2 | no | — |
| 160 | #103 | — | 9 | 2 | no | — |
| 161 | #102 | — | 9 | 2 | no | — |
| 162 | C22⋊C8 | — | 9 | 1 | no | — |
| 163 | C22⋊C8 | — | 9 | 1 | no | — |
| 164 | C4×C8 | — | 9 | 1 | no | — |
| 165 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 166 | C22×D3 | — | 3 | 1 | no | — |
| 167 | C22×D3 | — | 6 | 2 | no | — |
| 168 | C3×Q8 | — | 3 | 2 | no | — |
| 169 | C3×Q8 | — | 6 | 2 | no | — |
| 170 | C3×Q8 | — | 6 | 2 | no | — |
| 171 | C3×Q8 | C2×S4 | 1 | 2 | yes | — |
| 172 | C2×C3×C4 | — | 3 | 1 | no | — |
| 173 | C2×C3×C4 | — | 3 | 1 | no | — |
| 174 | C2×C3×C4 | — | 6 | 2 | no | — |
| 175 | C2×C3×C4 | — | 6 | 2 | no | — |
| 176 | #67 | — | 6 | 1 | no | — |
| 177 | #67 | — | 6 | 1 | no | — |
| 178 | #67 | — | 12 | 2 | no | — |
| 179 | #67 | — | 12 | 2 | no | — |
| 180 | C2×Dic3 | — | 3 | 1 | no | — |
| 181 | C2×Dic3 | — | 3 | 1 | no | — |
| 182 | C2×Dic3 | — | 3 | 1 | no | — |
| 183 | C2×Dic3 | — | 6 | 2 | no | — |
| 184 | D12 | — | 6 | 2 | no | — |
| 185 | D12 | — | 6 | 2 | no | — |
| 186 | D12 | — | 12 | 2 | no | — |
| 187 | D12 | — | 12 | 2 | no | — |
| 188 | C4×D3 | — | 6 | 1 | no | — |
| 189 | C4×D3 | — | 6 | 1 | no | — |
| 190 | C4×D3 | — | 12 | 2 | no | — |
| 191 | C4×D3 | — | 12 | 2 | no | — |
| 192 | C3×C8 | — | 3 | 1 | no | — |
| 193 | C3×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 194 | C3⋊C8 | — | 6 | 1 | no | — |
| 195 | C3⋊C8 | — | 6 | 1 | no | — |
| 196 | C2×C9 | — | 4 | 1 | no | — |
| 197 | D9 | — | 8 | 1 | no | — |
| 198 | D9 | — | 16 | 2 | no | — |
| 199 | #41 | — | 18 | 2 | no | — |
| 200 | #41 | — | 18 | 2 | no | — |
| 201 | #41 | — | 36 | 2 | no | — |
| 202 | C2×Q8 | — | 3 | 2 | no | — |
| 203 | C2×Q8 | — | 3 | 2 | no | — |
| 204 | C2×Q8 | — | 6 | 2 | no | — |
| 205 | C2×D4 | — | 9 | 2 | no | — |
| 206 | C2×D4 | — | 9 | 1 | no | — |
| 207 | C2×D4 | — | 18 | 2 | no | — |
| 208 | C2×D4 | — | 18 | 2 | no | — |
| 209 | C22×C4 | — | 2 | 2 | no | — |
| 210 | C22×C4 | — | 9 | 1 | no | — |
| 211 | C22×C4 | — | 18 | 2 | no | — |
| 212 | C22×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 213 | Q16 | — | 3 | 2 | no | — |
| 214 | Q16 | — | 3 | 1 | no | — |
| 215 | Q16 | — | 6 | 1 | no | — |
| 216 | Q16 | (C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 217 | SD16 | — | 18 | 2 | no | — |
| 218 | SD16 | — | 18 | 2 | no | — |
| 219 | SD16 | — | 36 | 2 | no | — |
| 220 | D8 | — | 18 | 1 | no | — |
| 221 | D8 | — | 18 | 1 | no | — |
| 222 | C2×C8 | — | 3 | 1 | no | — |
| 223 | C2×C8 | — | 3 | 1 | no | — |
| 224 | C2×C8 | — | 9 | 1 | no | — |
| 225 | C2×C8 | — | 9 | 1 | no | — |
| 226 | C2×C8 | — | 18 | 1 | no | — |
| 227 | C2×C8 | — | 18 | 1 | no | — |
| 228 | C4⋊C4 | — | 9 | 1 | no | — |
| 229 | C4⋊C4 | — | 9 | 2 | no | — |
| 230 | C4⋊C4 | — | 18 | 2 | no | — |
| 231 | C4⋊C4 | — | 18 | 2 | no | — |
| 232 | C22⋊C4 | — | 9 | 1 | no | — |
| 233 | C22⋊C4 | — | 9 | 1 | no | — |
| 234 | C22⋊C4 | — | 18 | 2 | no | — |
| 235 | C22⋊C4 | — | 18 | 2 | no | — |
| 236 | C22⋊C4 | — | 18 | 2 | no | — |
| 237 | C22⋊C4 | — | 18 | 2 | no | — |
| 238 | C42 | — | 9 | 1 | no | — |
| 239 | C42 | — | 18 | 2 | no | — |
| 240 | C22×C3 | — | 3 | 1 | no | — |
| 241 | C22×C3 | — | 3 | 1 | no | — |
| 242 | C22×C3 | #919 | 1 | 1 | yes | characteristic |
| 243 | C2×D3 | — | 6 | 1 | no | — |
| 244 | C2×D3 | — | 6 | 1 | no | — |
| 245 | C2×D3 | — | 6 | 1 | no | — |
| 246 | C2×D3 | — | 12 | 2 | no | — |
| 247 | C2×D3 | — | 12 | 2 | no | — |
| 248 | C2×D3 | — | 12 | 2 | no | — |
| 249 | C3×C4 | — | 2 | 2 | no | — |
| 250 | C3×C4 | — | 3 | 1 | no | — |
| 251 | C3×C4 | — | 6 | 2 | no | — |
| 252 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 253 | Dic3 | — | 6 | 1 | no | — |
| 254 | Dic3 | — | 6 | 1 | no | — |
| 255 | Dic3 | — | 6 | 1 | no | — |
| 256 | Dic3 | — | 12 | 2 | no | — |
| 257 | C9 | — | 4 | 1 | no | Sylow |
| 258 | C23 | — | 9 | 1 | no | — |
| 259 | C23 | — | 18 | 2 | no | — |
| 260 | C23 | D4×D9 | 1 | 1 | yes | characteristic |
| 261 | Q8 | — | 3 | 2 | no | — |
| 262 | Q8 | — | 6 | 2 | no | — |
| 263 | Q8 | — | 6 | 2 | no | — |
| 264 | Q8 | C2×(C22⋊C9)⋊C2 | 1 | 2 | yes | — |
| 265 | D4 | — | 18 | 2 | no | — |
| 266 | D4 | — | 18 | 1 | no | — |
| 267 | D4 | — | 18 | 1 | no | — |
| 268 | D4 | — | 18 | 2 | no | — |
| 269 | D4 | — | 36 | 2 | no | — |
| 270 | D4 | — | 36 | 2 | no | — |
| 271 | D4 | — | 36 | 2 | no | — |
| 272 | D4 | — | 36 | 2 | no | — |
| 273 | C2×C4 | — | 3 | 1 | no | — |
| 274 | C2×C4 | — | 3 | 1 | no | — |
| 275 | C2×C4 | — | 6 | 2 | no | — |
| 276 | C2×C4 | — | 6 | 2 | no | — |
| 277 | C2×C4 | — | 9 | 1 | no | — |
| 278 | C2×C4 | — | 9 | 1 | no | — |
| 279 | C2×C4 | — | 9 | 1 | no | — |
| 280 | C2×C4 | — | 18 | 1 | no | — |
| 281 | C2×C4 | — | 18 | 1 | no | — |
| 282 | C2×C4 | — | 18 | 2 | no | — |
| 283 | C2×C4 | — | 36 | 2 | no | — |
| 284 | C2×C4 | — | 36 | 2 | no | — |
| 285 | C8 | — | 3 | 1 | no | — |
| 286 | C8 | — | 18 | 1 | no | — |
| 287 | C8 | — | 18 | 1 | no | — |
| 288 | C8 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 289 | C2×C3 | — | 3 | 1 | no | — |
| 290 | C2×C3 | — | 3 | 1 | no | — |
| 291 | C2×C3 | D4×S4 | 1 | 1 | yes | characteristic |
| 292 | D3 | — | 12 | 1 | no | — |
| 293 | D3 | — | 24 | 2 | no | — |
| 294 | C22 | — | 3 | 1 | no | — |
| 295 | C22 | — | 3 | 1 | no | — |
| 296 | C22 | — | 18 | 1 | no | — |
| 297 | C22 | — | 18 | 1 | no | — |
| 298 | C22 | — | 18 | 1 | no | — |
| 299 | C22 | — | 36 | 2 | no | — |
| 300 | C22 | — | 36 | 2 | no | — |
| 301 | C22 | — | 36 | 2 | no | — |
| 302 | C22 | #63481 | 1 | 1 | yes | characteristic, complemented |
| 303 | C4 | — | 2 | 2 | no | — |
| 304 | C4 | — | 3 | 1 | no | — |
| 305 | C4 | — | 6 | 2 | no | — |
| 306 | C4 | — | 18 | 1 | no | — |
| 307 | C4 | — | 18 | 1 | no | — |
| 308 | C4 | — | 18 | 1 | no | — |
| 309 | C4 | — | 36 | 2 | no | — |
| 310 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 311 | C3 | #85465 | 1 | 1 | yes | characteristic |
| 312 | C2 | — | 3 | 1 | no | — |
| 313 | C2 | — | 3 | 1 | no | — |
| 314 | C2 | — | 36 | 1 | no | — |
| 315 | C2 | — | 72 | 2 | no | — |
| 316 | C2 | D4×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10593094 | C2 | semidirect |
| 2. Q16×C22⋊C9 | C2 | semidirect |
| 3. #10589519 | C2 | semidirect |
| 4. #10589504 | C2 | semidirect |
| 5. C8×(C22⋊C9)⋊C2 | C2 | semidirect |
| 78. C22×Q16 | D9 | semidirect |
| 131. C22⋊C9 | #135 | semidirect |
| 216. Q16 | (C22⋊C9)⋊C2 | semidirect |
| 302. C22 | #63481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593094 | 2 |
| Q16×C22⋊C9 | 2 |
| #10589519 | 2 |
| #10589504 | 2 |
| C8×(C22⋊C9)⋊C2 | 2 |
| #83889 | 3 |
| #63481 | 4 |