← #25115078
Subgroups — #25115078
Order 11008.
846 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#14583017 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #19143469 | C2 | 1 | 2 | yes | maximal |
| 3 | #19143186 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #19135378 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #19134827 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #19134655 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #19134474 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C43×#1846 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#13063347 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#13063331 | C22 | 1 | 2 | yes | — |
| 11 | #14583380 | C22 | 1 | 4 | yes | — |
| 12 | #14583017 | C4 | 1 | 8 | yes | complemented |
| 13 | #14582998 | — | 2 | 4 | no | — |
| 14 | #14582993 | — | 2 | 2 | no | — |
| 15 | #14582981 | — | 2 | 2 | no | — |
| 16 | C2×#13063261 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#13063261 | C22 | 1 | 1 | yes | characteristic |
| 18 | #14582939 | C22 | 1 | 4 | yes | — |
| 19 | #14582938 | — | 2 | 4 | no | — |
| 20 | #14582937 | C22 | 1 | 1 | yes | characteristic |
| 21 | #14582934 | — | 2 | 2 | no | — |
| 22 | #106×D43 | — | 2 | 2 | no | — |
| 23 | C2×#13063253 | C22 | 1 | 2 | yes | — |
| 24 | #14582898 | C22 | 1 | 4 | yes | — |
| 25 | #14582854 | C22 | 1 | 2 | yes | — |
| 26 | #14582668 | C22 | 1 | 4 | yes | — |
| 27 | #14582659 | C22 | 1 | 2 | yes | — |
| 28 | C2×#107×C43 | C22 | 1 | 2 | yes | — |
| 29 | C2×#106×C43 | C22 | 1 | 2 | yes | — |
| 30 | C2×C4×C8×C43 | C22 | 1 | 1 | yes | characteristic |
| 31 | C43×#382 | C22 | 1 | 2 | yes | — |
| 32 | C2×#10621898 | C23 | 1 | 2 | yes | — |
| 33 | #13063347 | C2×C4 | 1 | 4 | yes | — |
| 34 | #13063347 | Q8 | 1 | 4 | yes | — |
| 35 | C2×Dic172 | D4 | 1 | 1 | yes | characteristic |
| 36 | C2×#10621873 | D4 | 1 | 2 | yes | — |
| 37 | C2×D344 | D4 | 1 | 1 | yes | characteristic |
| 38 | #13063331 | — | 2 | 4 | no | — |
| 39 | #13063331 | C2×C4 | 1 | 8 | yes | complemented |
| 40 | C2×#10621877 | C23 | 1 | 2 | yes | — |
| 41 | C2×#10621877 | C23 | 1 | 2 | yes | — |
| 42 | C2×#10621872 | — | 2 | 2 | no | — |
| 43 | C2×C8×D43 | — | 2 | 2 | no | — |
| 44 | #13063290 | — | 2 | 4 | no | — |
| 45 | #13063287 | — | 2 | 4 | no | — |
| 46 | C4×C22⋊D43 | — | 4 | 4 | no | — |
| 47 | #13063284 | C23 | 1 | 2 | yes | — |
| 48 | #13063283 | — | 2 | 4 | no | — |
| 49 | C4⋊C4×D43 | — | 2 | 4 | no | — |
| 50 | #13063261 | — | 2 | 2 | no | — |
| 51 | #13063261 | C2×C4 | 1 | 4 | yes | complemented |
| 52 | #13063259 | D4 | 1 | 2 | yes | — |
| 53 | #13063258 | — | 2 | 4 | no | — |
| 54 | #13063257 | D4 | 1 | 1 | yes | characteristic |
| 55 | #13063257 | D4 | 1 | 1 | yes | characteristic |
| 56 | #13063256 | — | 2 | 4 | no | — |
| 57 | #13063253 | C2×C4 | 1 | 8 | yes | complemented |
| 58 | #13063248 | — | 2 | 4 | no | — |
| 59 | #13063245 | — | 2 | 4 | no | — |
| 60 | #13063235 | — | 2 | 2 | no | — |
| 61 | C8×Dic43 | — | 2 | 2 | no | — |
| 62 | C22×C8×C43 | C23 | 1 | 1 | yes | characteristic |
| 63 | C22×C8×C43 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C4⋊C4×C43 | C23 | 1 | 4 | yes | — |
| 65 | C2×C42×C43 | C23 | 1 | 1 | yes | characteristic |
| 66 | #107×C43 | — | 2 | 2 | no | — |
| 67 | #107×C43 | — | 2 | 2 | no | — |
| 68 | #106×C43 | — | 2 | 2 | no | — |
| 69 | #106×C43 | — | 2 | 2 | no | — |
| 70 | C4×C8×C43 | C2×C4 | 1 | 4 | yes | complemented |
| 71 | #95×C43 | — | 4 | 2 | no | — |
| 72 | C22×C4×C43 | — | 2 | 1 | no | — |
| 73 | C22×C4×C43 | — | 2 | 4 | no | — |
| 74 | C22×C4×C43 | C24 | 1 | 1 | yes | characteristic |
| 75 | C2×C22⋊D43 | — | 2 | 2 | no | — |
| 76 | #10621898 | — | 2 | 2 | no | — |
| 77 | #10621898 | — | 2 | 2 | no | — |
| 78 | #10621898 | C22×C4 | 1 | 4 | yes | — |
| 79 | #10621898 | C2×Q8 | 1 | 4 | yes | — |
| 80 | C2×D172 | C2×D4 | 1 | 2 | yes | — |
| 81 | C2×C4×D43 | — | 2 | 2 | no | — |
| 82 | C2×C4×D43 | — | 4 | 4 | no | — |
| 83 | C2×Dic86 | C2×D4 | 1 | 2 | yes | — |
| 84 | C2×C8×C43 | C22×C4 | 1 | 2 | yes | — |
| 85 | C2×C8×C43 | C22×C4 | 1 | 2 | yes | — |
| 86 | C2×C8×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C8×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C8×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C2×C8×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C2×C8×C43 | C2×Q8 | 1 | 2 | yes | — |
| 91 | C2×C8×C43 | #41 | 1 | 2 | yes | — |
| 92 | C4⋊C4×C43 | — | 2 | 4 | no | — |
| 93 | C4⋊C4×C43 | — | 2 | 4 | no | — |
| 94 | C42×C43 | — | 2 | 1 | no | — |
| 95 | C42×C43 | C22×C4 | 1 | 2 | yes | — |
| 96 | C22⋊Dic43 | — | 2 | 2 | no | — |
| 97 | (C2×D43)⋊C4 | — | 4 | 4 | no | — |
| 98 | C4⋊Dic43 | C2×D4 | 1 | 2 | yes | — |
| 99 | C4⋊Dic43 | C2×D4 | 1 | 2 | yes | — |
| 100 | Dic43⋊C4 | — | 4 | 4 | no | — |
| 101 | C4×Dic43 | — | 2 | 2 | no | — |
| 102 | C4×Dic43 | — | 4 | 4 | no | — |
| 103 | #10621877 | — | 2 | 2 | no | — |
| 104 | #10621877 | — | 2 | 2 | no | — |
| 105 | #10621877 | — | 2 | 2 | no | — |
| 106 | #10621877 | C22×C4 | 1 | 4 | yes | — |
| 107 | C2×C43⋊C8 | — | 2 | 2 | no | — |
| 108 | C2×C43⋊C8 | — | 2 | 2 | no | — |
| 109 | Dic172 | C4⋊C4 | 1 | 4 | yes | — |
| 110 | D344 | C4⋊C4 | 1 | 4 | yes | — |
| 111 | #10621873 | C4⋊C4 | 1 | 8 | yes | — |
| 112 | #10621872 | — | 2 | 8 | no | — |
| 113 | C8×D43 | — | 2 | 8 | no | — |
| 114 | C23×C43 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 115 | C22×D43 | — | 2 | 2 | no | — |
| 116 | C2×C4×C43 | — | 2 | 2 | no | — |
| 117 | C2×C4×C43 | — | 4 | 2 | no | — |
| 118 | C2×C4×C43 | — | 4 | 4 | no | — |
| 119 | C2×C4×C43 | — | 8 | 4 | no | — |
| 120 | C2×C4×C43 | C23×C4 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×C43 | C22×D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C4×C43 | C22×D4 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×C43 | C22×Q8 | 1 | 1 | yes | characteristic |
| 124 | C2×C4×C43 | C2×#41 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×C43 | 2−1+4 | 1 | 1 | yes | characteristic |
| 126 | C22⋊D43 | — | 2 | 4 | no | — |
| 127 | C22⋊D43 | — | 2 | 4 | no | — |
| 128 | C2×Dic43 | — | 2 | 2 | no | — |
| 129 | C2×Dic43 | — | 2 | 2 | no | — |
| 130 | C2×Dic43 | — | 2 | 2 | no | — |
| 131 | D172 | — | 2 | 2 | no | — |
| 132 | D172 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 133 | C4×D43 | — | 2 | 4 | no | — |
| 134 | C4×D43 | — | 2 | 4 | no | — |
| 135 | C4×D43 | — | 16 | 4 | no | — |
| 136 | Dic86 | — | 2 | 2 | no | — |
| 137 | Dic86 | C2×C4⋊C4 | 1 | 4 | yes | — |
| 138 | C8×C43 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 139 | C8×C43 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 140 | C8×C43 | C4×D4 | 1 | 2 | yes | — |
| 141 | C8×C43 | C4×D4 | 1 | 2 | yes | — |
| 142 | C43⋊C8 | — | 2 | 4 | no | — |
| 143 | C43⋊C8 | — | 4 | 2 | no | — |
| 144 | #22690 | — | 43 | 1 | no | maximal, Sylow |
| 145 | C22×C43 | — | 2 | 2 | no | — |
| 146 | C22×C43 | #520 | 1 | 1 | yes | characteristic |
| 147 | C22×C43 | D42 | 1 | 1 | yes | characteristic |
| 148 | C22×C43 | #554 | 1 | 1 | yes | characteristic |
| 149 | C2×D43 | — | 2 | 4 | no | — |
| 150 | C2×D43 | — | 4 | 4 | no | — |
| 151 | C4×C43 | — | 4 | 2 | no | — |
| 152 | C4×C43 | — | 8 | 4 | no | — |
| 153 | C4×C43 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 154 | C4×C43 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 155 | C4×C43 | #547 | 1 | 1 | yes | characteristic |
| 156 | C4×C43 | D4×Q8 | 1 | 1 | yes | characteristic |
| 157 | Dic43 | — | 2 | 4 | no | — |
| 158 | Dic43 | — | 4 | 2 | no | — |
| 159 | Dic43 | — | 4 | 2 | no | — |
| 160 | C2×#443 | — | 43 | 1 | no | — |
| 161 | #2951 | — | 43 | 2 | no | — |
| 162 | #2912 | — | 43 | 2 | no | — |
| 163 | #1952 | — | 43 | 2 | no | — |
| 164 | #1860 | — | 43 | 4 | no | — |
| 165 | #1846 | D43 | 1 | 1 | yes | characteristic, complemented |
| 166 | #1815 | — | 43 | 2 | no | — |
| 167 | #1772 | — | 43 | 1 | no | — |
| 168 | C2×C43 | — | 2 | 1 | no | — |
| 169 | C2×C43 | — | 2 | 1 | no | — |
| 170 | C2×C43 | D4×C4⋊C4 | 1 | 1 | yes | characteristic |
| 171 | C2×C43 | #3290 | 1 | 2 | yes | — |
| 172 | D43 | — | 4 | 4 | no | — |
| 173 | C2×#135 | — | 43 | 1 | no | — |
| 174 | C2×#131 | — | 43 | 2 | no | — |
| 175 | #520 | — | 43 | 4 | no | — |
| 176 | #443 | — | 43 | 8 | no | — |
| 177 | #440 | — | 86 | 4 | no | — |
| 178 | C4×Q16 | — | 86 | 2 | no | — |
| 179 | C4×D8 | — | 86 | 2 | no | — |
| 180 | C2×#108 | — | 43 | 1 | no | — |
| 181 | C2×#108 | — | 43 | 1 | no | — |
| 182 | #428 | — | 43 | 4 | no | — |
| 183 | #428 | — | 86 | 4 | no | — |
| 184 | #427 | — | 43 | 1 | no | — |
| 185 | #427 | — | 86 | 2 | no | — |
| 186 | C2×#107 | C2×D43 | 1 | 2 | yes | — |
| 187 | C2×#106 | — | 86 | 2 | no | — |
| 188 | C2×#106 | C2×D43 | 1 | 2 | yes | — |
| 189 | C2×#104 | — | 43 | 2 | no | — |
| 190 | #417 | — | 43 | 4 | no | — |
| 191 | #405 | — | 43 | 2 | no | — |
| 192 | C2×C4×C8 | C2×D43 | 1 | 1 | yes | characteristic |
| 193 | #382 | C2×D43 | 1 | 2 | yes | — |
| 194 | #343 | — | 43 | 4 | no | — |
| 195 | #339 | — | 43 | 2 | no | — |
| 196 | C43 | #22690 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 197 | C2×#41 | — | 43 | 2 | no | — |
| 198 | #135 | — | 43 | 4 | no | — |
| 199 | #135 | — | 43 | 4 | no | — |
| 200 | C2×Q16 | — | 43 | 1 | no | — |
| 201 | C2×SD16 | — | 43 | 2 | no | — |
| 202 | C2×D8 | — | 43 | 1 | no | — |
| 203 | #131 | — | 43 | 8 | no | — |
| 204 | #131 | — | 86 | 4 | no | — |
| 205 | C2×M16 | — | 43 | 2 | no | — |
| 206 | C2×M16 | — | 43 | 2 | no | — |
| 207 | C2×M16 | — | 86 | 2 | no | — |
| 208 | C22×C8 | — | 86 | 2 | no | — |
| 209 | C22×C8 | C22×D43 | 1 | 1 | yes | characteristic |
| 210 | C22×C8 | C22×D43 | 1 | 1 | yes | characteristic |
| 211 | C4×Q8 | — | 86 | 4 | no | — |
| 212 | C4×D4 | — | 86 | 4 | no | — |
| 213 | C4×D4 | — | 172 | 4 | no | — |
| 214 | #117 | — | 43 | 2 | no | — |
| 215 | #117 | — | 86 | 4 | no | — |
| 216 | C2×C4⋊C4 | — | 86 | 4 | no | — |
| 217 | C2×C4⋊C4 | C22×D43 | 1 | 4 | yes | — |
| 218 | C2×C42 | C22×D43 | 1 | 1 | yes | characteristic |
| 219 | #108 | — | 43 | 4 | no | — |
| 220 | #108 | — | 86 | 2 | no | — |
| 221 | #107 | — | 2 | 2 | no | — |
| 222 | #107 | — | 2 | 2 | no | — |
| 223 | #107 | — | 43 | 2 | no | — |
| 224 | #107 | — | 86 | 4 | no | — |
| 225 | #106 | — | 2 | 2 | no | — |
| 226 | #106 | — | 2 | 2 | no | — |
| 227 | #106 | — | 43 | 1 | no | — |
| 228 | #106 | — | 43 | 1 | no | — |
| 229 | #106 | — | 86 | 4 | no | — |
| 230 | #104 | — | 43 | 8 | no | — |
| 231 | #103 | — | 86 | 4 | no | — |
| 232 | #102 | — | 86 | 4 | no | — |
| 233 | #97 | — | 86 | 2 | no | — |
| 234 | C4×C8 | — | 86 | 2 | no | — |
| 235 | C4×C8 | C4×D43 | 1 | 4 | yes | complemented |
| 236 | #95 | — | 4 | 2 | no | — |
| 237 | #41 | — | 43 | 4 | no | — |
| 238 | #41 | — | 43 | 4 | no | — |
| 239 | #41 | — | 86 | 2 | no | — |
| 240 | #41 | — | 86 | 2 | no | — |
| 241 | C2×Q8 | — | 43 | 2 | no | — |
| 242 | C2×D4 | — | 43 | 2 | no | — |
| 243 | C2×D4 | — | 86 | 2 | no | — |
| 244 | C22×C4 | — | 2 | 1 | no | — |
| 245 | C22×C4 | — | 2 | 4 | no | — |
| 246 | C22×C4 | — | 86 | 2 | no | — |
| 247 | C22×C4 | — | 172 | 4 | no | — |
| 248 | C22×C4 | C23×D43 | 1 | 1 | yes | characteristic |
| 249 | Q16 | — | 43 | 4 | no | — |
| 250 | SD16 | — | 43 | 8 | no | — |
| 251 | D8 | — | 43 | 4 | no | — |
| 252 | M16 | — | 43 | 4 | no | — |
| 253 | M16 | — | 86 | 2 | no | — |
| 254 | M16 | — | 86 | 8 | no | — |
| 255 | M16 | — | 86 | 2 | no | — |
| 256 | M16 | — | 86 | 2 | no | — |
| 257 | C2×C8 | — | 86 | 2 | no | — |
| 258 | C2×C8 | — | 86 | 8 | no | — |
| 259 | C2×C8 | — | 86 | 2 | no | — |
| 260 | C2×C8 | C2×C4×D43 | 1 | 2 | yes | — |
| 261 | C2×C8 | C2×C4×D43 | 1 | 2 | yes | — |
| 262 | C2×C8 | D4×D43 | 1 | 1 | yes | characteristic |
| 263 | C2×C8 | D4×D43 | 1 | 1 | yes | characteristic |
| 264 | C2×C8 | D4×D43 | 1 | 1 | yes | characteristic |
| 265 | C2×C8 | D4×D43 | 1 | 1 | yes | characteristic |
| 266 | C2×C8 | Q8×D43 | 1 | 2 | yes | — |
| 267 | C2×C8 | #10621902 | 1 | 2 | yes | — |
| 268 | C4⋊C4 | — | 2 | 4 | no | — |
| 269 | C4⋊C4 | — | 2 | 4 | no | — |
| 270 | C4⋊C4 | — | 43 | 2 | no | — |
| 271 | C4⋊C4 | — | 43 | 2 | no | — |
| 272 | C4⋊C4 | — | 172 | 4 | no | — |
| 273 | C22⋊C4 | — | 86 | 2 | no | — |
| 274 | C22⋊C4 | — | 172 | 4 | no | — |
| 275 | C42 | — | 2 | 1 | no | — |
| 276 | C42 | — | 86 | 2 | no | — |
| 277 | C42 | — | 172 | 4 | no | — |
| 278 | C42 | C2×C4×D43 | 1 | 2 | yes | — |
| 279 | C23 | — | 86 | 2 | no | — |
| 280 | C23 | #13063370 | 1 | 1 | yes | characteristic |
| 281 | Q8 | — | 43 | 4 | no | — |
| 282 | Q8 | — | 86 | 2 | no | — |
| 283 | D4 | — | 43 | 4 | no | — |
| 284 | D4 | — | 86 | 4 | no | — |
| 285 | D4 | — | 86 | 4 | no | — |
| 286 | D4 | — | 86 | 2 | no | — |
| 287 | C2×C4 | — | 2 | 2 | no | — |
| 288 | C2×C4 | — | 4 | 2 | no | — |
| 289 | C2×C4 | — | 4 | 4 | no | — |
| 290 | C2×C4 | — | 8 | 4 | no | — |
| 291 | C2×C4 | — | 86 | 2 | no | — |
| 292 | C2×C4 | — | 86 | 4 | no | — |
| 293 | C2×C4 | — | 86 | 4 | no | — |
| 294 | C2×C4 | — | 86 | 2 | no | — |
| 295 | C2×C4 | — | 86 | 2 | no | — |
| 296 | C2×C4 | — | 688 | 4 | no | — |
| 297 | C2×C4 | C22×C4×D43 | 1 | 1 | yes | characteristic |
| 298 | C2×C4 | C2×D4×D43 | 1 | 1 | yes | characteristic |
| 299 | C2×C4 | C2×D4×D43 | 1 | 1 | yes | characteristic |
| 300 | C2×C4 | C2×Q8×D43 | 1 | 1 | yes | characteristic |
| 301 | C2×C4 | C2×#10621902 | 1 | 1 | yes | characteristic |
| 302 | C2×C4 | #13063373 | 1 | 1 | yes | characteristic |
| 303 | C8 | — | 86 | 4 | no | — |
| 304 | C8 | — | 172 | 2 | no | — |
| 305 | C8 | C4⋊C4×D43 | 1 | 2 | yes | — |
| 306 | C8 | C4⋊C4×D43 | 1 | 2 | yes | — |
| 307 | C8 | #13063287 | 1 | 2 | yes | — |
| 308 | C8 | #13063287 | 1 | 2 | yes | — |
| 309 | C22 | — | 2 | 2 | no | — |
| 310 | C22 | — | 86 | 4 | no | — |
| 311 | C22 | — | 172 | 4 | no | — |
| 312 | C22 | #14583380 | 1 | 1 | yes | characteristic |
| 313 | C22 | #14583534 | 1 | 1 | yes | characteristic |
| 314 | C22 | #14583610 | 1 | 1 | yes | characteristic |
| 315 | C4 | — | 4 | 2 | no | — |
| 316 | C4 | — | 8 | 4 | no | — |
| 317 | C4 | — | 86 | 4 | no | — |
| 318 | C4 | — | 172 | 2 | no | — |
| 319 | C4 | — | 172 | 2 | no | — |
| 320 | C4 | C2×C4⋊C4×D43 | 1 | 1 | yes | characteristic |
| 321 | C4 | C2×#13063287 | 1 | 1 | yes | characteristic |
| 322 | C4 | #14583552 | 1 | 1 | yes | characteristic |
| 323 | C4 | #14583564 | 1 | 1 | yes | characteristic |
| 324 | C2 | — | 2 | 1 | no | — |
| 325 | C2 | — | 2 | 1 | no | — |
| 326 | C2 | — | 172 | 4 | no | — |
| 327 | C2 | #19137495 | 1 | 1 | yes | characteristic |
| 328 | C2 | #19146380 | 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