← #25153228
Subgroups — #25153228
Order 11008.
1218 conjugacy classes of subgroups.
The subgroup lattice has 328 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#14583456 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#14583245 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #19135741 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #19135555 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #19134918 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C4×C22⋊(C43⋊C8) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C43×#2856 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #14583456 | — | 2 | 8 | no | — |
| 9 | C2×#13063325 | C22 | 1 | 2 | yes | — |
| 10 | C2×#13063317 | C22 | 1 | 2 | yes | — |
| 11 | C2×#13063304 | — | 2 | 2 | no | — |
| 12 | C2×C4×Dic86 | — | 2 | 2 | no | — |
| 13 | C2×#13063284 | C22 | 1 | 2 | yes | — |
| 14 | #14583245 | — | 2 | 8 | no | — |
| 15 | C2×#13063246 | C22 | 1 | 8 | yes | — |
| 16 | C2×C22⋊(C43⋊C8) | C22 | 1 | 2 | yes | — |
| 17 | C2×C4×C43⋊C8 | C22 | 1 | 2 | yes | — |
| 18 | #14582661 | C22 | 1 | 8 | yes | — |
| 19 | #14582654 | C22 | 1 | 2 | yes | — |
| 20 | C2×#127×C43 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#121×C43 | — | 2 | 2 | no | — |
| 22 | C2×#121×C43 | C22 | 1 | 2 | yes | — |
| 23 | C22×C42×C43 | C22 | 1 | 1 | yes | characteristic |
| 24 | C43×#390 | — | 2 | 2 | no | — |
| 25 | C43×#390 | C22 | 1 | 2 | yes | — |
| 26 | C43×#384 | C22 | 1 | 1 | yes | characteristic |
| 27 | C22×Dic86 | — | 2 | 2 | no | — |
| 28 | C22×C43⋊C8 | C23 | 1 | 4 | yes | — |
| 29 | #13063325 | — | 2 | 4 | no | — |
| 30 | #13063325 | D4 | 1 | 8 | yes | complemented |
| 31 | #13063317 | — | 2 | 8 | no | — |
| 32 | #13063304 | — | 2 | 16 | no | — |
| 33 | C4×Dic86 | — | 2 | 16 | no | — |
| 34 | #13063284 | — | 2 | 8 | no | — |
| 35 | C2×C4⋊Dic43 | — | 2 | 2 | no | — |
| 36 | C2×C4⋊Dic43 | C23 | 1 | 4 | yes | — |
| 37 | C2×Dic43⋊C4 | — | 2 | 4 | no | — |
| 38 | C2×C22⋊Dic43 | — | 2 | 2 | no | — |
| 39 | C2×C4×Dic43 | — | 2 | 2 | no | — |
| 40 | #13063246 | — | 2 | 16 | no | — |
| 41 | C22⋊(C43⋊C8) | — | 2 | 4 | no | — |
| 42 | C4×C43⋊C8 | — | 2 | 4 | no | — |
| 43 | C22×D4×C43 | — | 2 | 2 | no | — |
| 44 | C22×D4×C43 | — | 2 | 2 | no | — |
| 45 | C22×D4×C43 | C23 | 1 | 2 | yes | — |
| 46 | C23×C4×C43 | D4 | 1 | 2 | yes | — |
| 47 | C23×C4×C43 | C23 | 1 | 1 | yes | characteristic |
| 48 | #127×C43 | — | 2 | 4 | no | — |
| 49 | #121×C43 | — | 2 | 8 | no | — |
| 50 | #121×C43 | — | 4 | 8 | no | — |
| 51 | C2×C4⋊C4×C43 | — | 2 | 2 | no | — |
| 52 | C2×C4⋊C4×C43 | C23 | 1 | 2 | yes | — |
| 53 | C2×C22⋊C4×C43 | — | 2 | 4 | no | — |
| 54 | C2×C22⋊C4×C43 | — | 2 | 2 | no | — |
| 55 | C2×C42×C43 | — | 2 | 4 | no | — |
| 56 | C2×C42×C43 | D4 | 1 | 2 | yes | — |
| 57 | C2×C42×C43 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×C42×C43 | C23 | 1 | 1 | yes | characteristic |
| 59 | C24×C43 | — | 2 | 2 | no | — |
| 60 | C24×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 61 | C2×D4×C43 | — | 2 | 4 | no | — |
| 62 | C2×D4×C43 | — | 2 | 4 | no | — |
| 63 | C2×D4×C43 | — | 2 | 4 | no | — |
| 64 | C2×D4×C43 | — | 4 | 8 | no | — |
| 65 | C2×D4×C43 | — | 4 | 4 | no | — |
| 66 | C2×D4×C43 | — | 4 | 4 | no | — |
| 67 | C2×D4×C43 | — | 4 | 4 | no | — |
| 68 | C2×D4×C43 | — | 4 | 4 | no | — |
| 69 | C22×C4×C43 | — | 2 | 2 | no | — |
| 70 | C22×C4×C43 | — | 2 | 2 | no | — |
| 71 | C22×C4×C43 | — | 2 | 4 | no | — |
| 72 | C22×C4×C43 | — | 2 | 4 | no | — |
| 73 | C22×C4×C43 | — | 2 | 4 | no | — |
| 74 | C22×C4×C43 | — | 2 | 2 | no | — |
| 75 | C22×C4×C43 | C2×D4 | 1 | 2 | yes | — |
| 76 | C22×C4×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C22×C4×C43 | C2×D4 | 1 | 2 | yes | — |
| 78 | C22×C4×C43 | #41 | 1 | 4 | yes | — |
| 79 | C22×C4×C43 | C24 | 1 | 1 | yes | characteristic |
| 80 | C22×Dic43 | — | 2 | 4 | no | — |
| 81 | C2×Dic86 | — | 2 | 8 | no | — |
| 82 | C2×Dic86 | — | 4 | 4 | no | — |
| 83 | C2×Dic86 | — | 4 | 4 | no | — |
| 84 | C4⋊C4×C43 | — | 2 | 4 | no | — |
| 85 | C4⋊C4×C43 | — | 4 | 4 | no | — |
| 86 | C22⋊C4×C43 | — | 4 | 8 | no | — |
| 87 | C22⋊C4×C43 | — | 4 | 4 | no | — |
| 88 | C42×C43 | — | 2 | 4 | no | — |
| 89 | C42×C43 | — | 2 | 2 | no | — |
| 90 | C42×C43 | C2×D4 | 1 | 4 | yes | — |
| 91 | C22⋊Dic43 | — | 2 | 8 | no | — |
| 92 | C4⋊Dic43 | — | 2 | 8 | no | — |
| 93 | C4⋊Dic43 | — | 2 | 4 | no | — |
| 94 | C4⋊Dic43 | C2×D4 | 1 | 8 | yes | — |
| 95 | Dic43⋊C4 | — | 2 | 16 | no | — |
| 96 | C4×Dic43 | — | 2 | 8 | no | — |
| 97 | C2×C43⋊C8 | — | 2 | 4 | no | — |
| 98 | C2×C43⋊C8 | — | 2 | 4 | no | — |
| 99 | C2×C43⋊C8 | — | 2 | 4 | no | — |
| 100 | C23×C43 | — | 2 | 1 | no | — |
| 101 | C23×C43 | — | 2 | 1 | no | — |
| 102 | C23×C43 | — | 2 | 2 | no | — |
| 103 | C23×C43 | — | 2 | 2 | no | — |
| 104 | C23×C43 | — | 4 | 2 | no | — |
| 105 | C23×C43 | — | 4 | 2 | no | — |
| 106 | C23×C43 | — | 4 | 2 | no | — |
| 107 | C23×C43 | — | 4 | 4 | no | — |
| 108 | C23×C43 | — | 4 | 4 | no | — |
| 109 | C23×C43 | #124 | 1 | 2 | yes | — |
| 110 | C23×C43 | C22×D4 | 1 | 1 | yes | characteristic |
| 111 | D4×C43 | — | 4 | 8 | no | — |
| 112 | D4×C43 | — | 8 | 8 | no | — |
| 113 | D4×C43 | — | 8 | 8 | no | — |
| 114 | C2×C4×C43 | — | 2 | 1 | no | — |
| 115 | C2×C4×C43 | — | 2 | 1 | no | — |
| 116 | C2×C4×C43 | — | 2 | 8 | no | — |
| 117 | C2×C4×C43 | — | 2 | 2 | no | — |
| 118 | C2×C4×C43 | — | 2 | 2 | no | — |
| 119 | C2×C4×C43 | — | 2 | 2 | no | — |
| 120 | C2×C4×C43 | — | 4 | 8 | no | — |
| 121 | C2×C4×C43 | — | 4 | 2 | no | — |
| 122 | C2×C4×C43 | — | 4 | 4 | no | — |
| 123 | C2×C4×C43 | #120 | 1 | 4 | yes | — |
| 124 | C2×C4×C43 | #124 | 1 | 2 | yes | — |
| 125 | C2×C4×C43 | #135 | 1 | 4 | yes | — |
| 126 | C2×C4×C43 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 127 | C2×C4×C43 | C22×D4 | 1 | 2 | yes | — |
| 128 | C2×C4×C43 | C2×#41 | 1 | 2 | yes | — |
| 129 | C2×C4×C43 | 2−1+4 | 1 | 2 | yes | — |
| 130 | C2×Dic43 | — | 2 | 8 | no | — |
| 131 | C2×Dic43 | — | 4 | 4 | no | — |
| 132 | C2×Dic43 | — | 4 | 4 | no | — |
| 133 | Dic86 | — | 4 | 16 | no | — |
| 134 | C43⋊C8 | — | 4 | 4 | no | — |
| 135 | #25905 | — | 43 | 1 | no | maximal, Sylow |
| 136 | C22×C43 | — | 2 | 2 | no | — |
| 137 | C22×C43 | — | 2 | 2 | no | — |
| 138 | C22×C43 | — | 2 | 2 | no | — |
| 139 | C22×C43 | — | 4 | 2 | no | — |
| 140 | C22×C43 | — | 4 | 2 | no | — |
| 141 | C22×C43 | — | 8 | 2 | no | — |
| 142 | C22×C43 | — | 8 | 2 | no | — |
| 143 | C22×C43 | — | 8 | 2 | no | — |
| 144 | C22×C43 | — | 8 | 4 | no | — |
| 145 | C22×C43 | — | 8 | 4 | no | — |
| 146 | C22×C43 | C2×#120 | 1 | 1 | yes | characteristic |
| 147 | C22×C43 | C2×#124 | 1 | 1 | yes | characteristic |
| 148 | C22×C43 | #536 | 1 | 1 | yes | characteristic |
| 149 | C22×C43 | C2×#135 | 1 | 2 | yes | — |
| 150 | C22×C43 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 151 | C4×C43 | — | 2 | 2 | no | — |
| 152 | C4×C43 | — | 4 | 2 | no | — |
| 153 | C4×C43 | — | 8 | 2 | no | — |
| 154 | C4×C43 | #449 | 1 | 8 | yes | — |
| 155 | C4×C43 | #548 | 1 | 4 | yes | — |
| 156 | Dic43 | — | 4 | 8 | no | — |
| 157 | C2×#533 | — | 43 | 1 | no | — |
| 158 | C2×#486 | — | 43 | 2 | no | — |
| 159 | #2856 | D43 | 1 | 1 | yes | characteristic |
| 160 | #2025 | — | 43 | 4 | no | — |
| 161 | #1990 | — | 43 | 2 | no | — |
| 162 | #1875 | — | 43 | 4 | no | — |
| 163 | C4×C22⋊C8 | — | 43 | 1 | no | — |
| 164 | C2×C43 | — | 4 | 2 | no | — |
| 165 | C2×C43 | — | 16 | 2 | no | — |
| 166 | C2×C43 | #2436 | 1 | 1 | yes | characteristic |
| 167 | C2×C43 | C2×#449 | 1 | 2 | yes | — |
| 168 | C2×C43 | #3131 | 1 | 1 | yes | characteristic |
| 169 | C2×C43 | #3138 | 1 | 1 | yes | characteristic |
| 170 | C2×C43 | #3228 | 1 | 2 | yes | — |
| 171 | #533 | — | 86 | 8 | no | — |
| 172 | C2×C4⋊Q8 | — | 43 | 2 | no | — |
| 173 | C2×#127 | C2×D43 | 1 | 1 | yes | characteristic |
| 174 | C2×#125 | — | 43 | 2 | no | — |
| 175 | C2×C22⋊Q8 | — | 86 | 2 | no | — |
| 176 | C2×#121 | — | 2 | 2 | no | — |
| 177 | C2×#121 | C2×D43 | 1 | 2 | yes | — |
| 178 | C2×C4×Q8 | — | 86 | 2 | no | — |
| 179 | C2×#117 | — | 43 | 2 | no | — |
| 180 | C22×C42 | C2×D43 | 1 | 1 | yes | characteristic |
| 181 | #486 | — | 86 | 8 | no | — |
| 182 | C2×#102 | — | 43 | 8 | no | — |
| 183 | C2×C22⋊C8 | — | 43 | 2 | no | — |
| 184 | C2×C4×C8 | — | 43 | 2 | no | — |
| 185 | #390 | — | 2 | 2 | no | — |
| 186 | #390 | C2×D43 | 1 | 2 | yes | — |
| 187 | #384 | C2×D43 | 1 | 1 | yes | characteristic |
| 188 | #340 | — | 43 | 8 | no | — |
| 189 | #336 | — | 43 | 2 | no | — |
| 190 | C43 | #25905 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 191 | C22×Q8 | — | 86 | 2 | no | — |
| 192 | C22×D4 | — | 2 | 2 | no | — |
| 193 | C22×D4 | — | 2 | 2 | no | — |
| 194 | C22×D4 | C22×D43 | 1 | 2 | yes | — |
| 195 | C23×C4 | C22⋊D43 | 1 | 2 | yes | — |
| 196 | C23×C4 | C22×D43 | 1 | 1 | yes | characteristic |
| 197 | C22×C8 | — | 43 | 4 | no | — |
| 198 | C4⋊Q8 | — | 43 | 8 | no | — |
| 199 | C4⋊Q8 | — | 86 | 4 | no | — |
| 200 | #127 | — | 2 | 4 | no | — |
| 201 | #125 | — | 86 | 8 | no | — |
| 202 | C22⋊Q8 | — | 86 | 16 | no | — |
| 203 | #121 | — | 2 | 8 | no | — |
| 204 | #121 | — | 4 | 8 | no | — |
| 205 | C4×Q8 | — | 86 | 16 | no | — |
| 206 | #117 | — | 86 | 8 | no | — |
| 207 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 208 | C2×C4⋊C4 | — | 43 | 4 | no | — |
| 209 | C2×C4⋊C4 | — | 86 | 4 | no | — |
| 210 | C2×C4⋊C4 | — | 86 | 2 | no | — |
| 211 | C2×C4⋊C4 | C22×D43 | 1 | 2 | yes | — |
| 212 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 213 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 214 | C2×C22⋊C4 | — | 86 | 2 | no | — |
| 215 | C2×C42 | — | 2 | 4 | no | — |
| 216 | C2×C42 | — | 86 | 2 | no | — |
| 217 | C2×C42 | C22⋊D43 | 1 | 2 | yes | — |
| 218 | C2×C42 | C22×D43 | 1 | 1 | yes | characteristic |
| 219 | C2×C42 | C22×D43 | 1 | 1 | yes | characteristic |
| 220 | #102 | — | 86 | 16 | no | — |
| 221 | C22⋊C8 | — | 86 | 4 | no | — |
| 222 | C4×C8 | — | 86 | 4 | no | — |
| 223 | C24 | — | 2 | 2 | no | — |
| 224 | C24 | C2×C22⋊D43 | 1 | 1 | yes | characteristic |
| 225 | C2×Q8 | — | 86 | 8 | no | — |
| 226 | C2×Q8 | — | 172 | 4 | no | — |
| 227 | C2×Q8 | — | 172 | 4 | no | — |
| 228 | C2×D4 | — | 2 | 4 | no | — |
| 229 | C2×D4 | — | 2 | 4 | no | — |
| 230 | C2×D4 | — | 2 | 4 | no | — |
| 231 | C2×D4 | — | 4 | 8 | no | — |
| 232 | C2×D4 | — | 4 | 4 | no | — |
| 233 | C2×D4 | — | 4 | 4 | no | — |
| 234 | C2×D4 | — | 4 | 4 | no | — |
| 235 | C2×D4 | — | 4 | 4 | no | — |
| 236 | C22×C4 | — | 2 | 2 | no | — |
| 237 | C22×C4 | — | 2 | 2 | no | — |
| 238 | C22×C4 | — | 2 | 4 | no | — |
| 239 | C22×C4 | — | 2 | 4 | no | — |
| 240 | C22×C4 | — | 2 | 4 | no | — |
| 241 | C22×C4 | — | 2 | 2 | no | — |
| 242 | C22×C4 | — | 86 | 4 | no | — |
| 243 | C22×C4 | #10621900 | 1 | 4 | yes | — |
| 244 | C22×C4 | C2×C22⋊D43 | 1 | 2 | yes | — |
| 245 | C22×C4 | C2×C22⋊D43 | 1 | 1 | yes | characteristic |
| 246 | C22×C4 | C2×C22⋊D43 | 1 | 2 | yes | — |
| 247 | C22×C4 | C23×D43 | 1 | 1 | yes | characteristic |
| 248 | C2×C8 | — | 86 | 4 | no | — |
| 249 | C2×C8 | — | 86 | 4 | no | — |
| 250 | C2×C8 | — | 86 | 4 | no | — |
| 251 | C4⋊C4 | — | 2 | 4 | no | — |
| 252 | C4⋊C4 | — | 4 | 4 | no | — |
| 253 | C4⋊C4 | — | 43 | 8 | no | — |
| 254 | C4⋊C4 | — | 86 | 16 | no | — |
| 255 | C4⋊C4 | — | 86 | 8 | no | — |
| 256 | C4⋊C4 | — | 86 | 4 | no | — |
| 257 | C22⋊C4 | — | 4 | 8 | no | — |
| 258 | C22⋊C4 | — | 4 | 4 | no | — |
| 259 | C22⋊C4 | — | 86 | 8 | no | — |
| 260 | C42 | — | 2 | 4 | no | — |
| 261 | C42 | — | 2 | 2 | no | — |
| 262 | C42 | — | 86 | 8 | no | — |
| 263 | C42 | D4×D43 | 1 | 4 | yes | — |
| 264 | C23 | — | 2 | 1 | no | — |
| 265 | C23 | — | 2 | 2 | no | — |
| 266 | C23 | — | 2 | 2 | no | — |
| 267 | C23 | — | 2 | 1 | no | — |
| 268 | C23 | — | 4 | 2 | no | — |
| 269 | C23 | — | 4 | 2 | no | — |
| 270 | C23 | — | 4 | 4 | no | — |
| 271 | C23 | — | 4 | 4 | no | — |
| 272 | C23 | — | 4 | 2 | no | — |
| 273 | C23 | #13063312 | 1 | 2 | yes | — |
| 274 | C23 | C22×C22⋊D43 | 1 | 1 | yes | characteristic |
| 275 | Q8 | — | 172 | 16 | no | — |
| 276 | D4 | — | 4 | 8 | no | — |
| 277 | D4 | — | 8 | 8 | no | — |
| 278 | D4 | — | 8 | 8 | no | — |
| 279 | C2×C4 | — | 2 | 1 | no | — |
| 280 | C2×C4 | — | 2 | 1 | no | — |
| 281 | C2×C4 | — | 2 | 8 | no | — |
| 282 | C2×C4 | — | 2 | 2 | no | — |
| 283 | C2×C4 | — | 2 | 2 | no | — |
| 284 | C2×C4 | — | 2 | 2 | no | — |
| 285 | C2×C4 | — | 4 | 8 | no | — |
| 286 | C2×C4 | — | 4 | 2 | no | — |
| 287 | C2×C4 | — | 4 | 4 | no | — |
| 288 | C2×C4 | — | 86 | 8 | no | — |
| 289 | C2×C4 | — | 172 | 4 | no | — |
| 290 | C2×C4 | — | 172 | 4 | no | — |
| 291 | C2×C4 | #13063293 | 1 | 4 | yes | — |
| 292 | C2×C4 | #13063312 | 1 | 2 | yes | — |
| 293 | C2×C4 | #13063345 | 1 | 4 | yes | — |
| 294 | C2×C4 | #13063351 | 1 | 4 | yes | — |
| 295 | C2×C4 | C2×D4×D43 | 1 | 2 | yes | — |
| 296 | C2×C4 | C2×#10621900 | 1 | 2 | yes | — |
| 297 | C2×C4 | #13063372 | 1 | 2 | yes | — |
| 298 | C8 | — | 172 | 4 | no | — |
| 299 | C22 | — | 2 | 2 | no | — |
| 300 | C22 | — | 2 | 2 | no | — |
| 301 | C22 | — | 2 | 2 | no | — |
| 302 | C22 | — | 4 | 2 | no | — |
| 303 | C22 | — | 4 | 2 | no | — |
| 304 | C22 | — | 8 | 2 | no | — |
| 305 | C22 | — | 8 | 4 | no | — |
| 306 | C22 | — | 8 | 2 | no | — |
| 307 | C22 | — | 8 | 2 | no | — |
| 308 | C22 | — | 8 | 4 | no | — |
| 309 | C22 | C2×#13063293 | 1 | 1 | yes | characteristic |
| 310 | C22 | C2×#13063312 | 1 | 1 | yes | characteristic |
| 311 | C22 | #14583470 | 1 | 1 | yes | characteristic |
| 312 | C22 | C2×#13063345 | 1 | 2 | yes | — |
| 313 | C22 | C2×#13063351 | 1 | 2 | yes | — |
| 314 | C4 | — | 2 | 2 | no | — |
| 315 | C4 | — | 4 | 2 | no | — |
| 316 | C4 | — | 8 | 2 | no | — |
| 317 | C4 | — | 172 | 8 | no | — |
| 318 | C4 | #14583042 | 1 | 8 | yes | — |
| 319 | C4 | #14583555 | 1 | 4 | yes | — |
| 320 | C2 | — | 4 | 2 | no | — |
| 321 | C2 | — | 16 | 2 | no | — |
| 322 | C2 | #19138254 | 1 | 1 | yes | characteristic |
| 323 | C2 | C2×#14583042 | 1 | 2 | yes | — |
| 324 | C2 | #19144917 | 1 | 1 | yes | characteristic |
| 325 | C2 | #19144969 | 1 | 1 | yes | characteristic |
| 326 | C2 | #19145727 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta