← #25079812
Subgroups — #25079812
Order 11008.
646 conjugacy classes of subgroups.
The subgroup lattice has 312 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #19145741 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×#14583279 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #19143529 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #19134090 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #19133966 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #19133266 | C2 | 1 | 2 | yes | maximal |
| 7 | C43×#1564 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C22×Dic172 | — | 2 | 1 | no | — |
| 9 | C22×Dic172 | — | 2 | 1 | no | — |
| 10 | #14583456 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#13063325 | C22 | 1 | 2 | yes | — |
| 12 | #14583297 | — | 2 | 2 | no | — |
| 13 | #14583279 | — | 2 | 1 | no | — |
| 14 | #14583279 | — | 2 | 1 | no | — |
| 15 | #14583279 | C22 | 1 | 2 | yes | — |
| 16 | #14583279 | C22 | 1 | 2 | yes | — |
| 17 | #14583250 | — | 2 | 2 | no | — |
| 18 | #14583230 | — | 2 | 4 | no | — |
| 19 | #14583185 | C22 | 1 | 8 | yes | — |
| 20 | #14583029 | — | 2 | 1 | no | — |
| 21 | #14583029 | C22 | 1 | 2 | yes | — |
| 22 | C8×Dic86 | — | 2 | 1 | no | — |
| 23 | C8×Dic86 | C22 | 1 | 2 | yes | — |
| 24 | #14582925 | — | 2 | 1 | no | — |
| 25 | #14582923 | C22 | 1 | 1 | yes | characteristic |
| 26 | #14582854 | — | 2 | 1 | no | — |
| 27 | #14582644 | C22 | 1 | 8 | yes | — |
| 28 | C43×#431 | C22 | 1 | 2 | yes | — |
| 29 | C2×C4×C8×C43 | C22 | 1 | 1 | yes | characteristic |
| 30 | C43×#335 | C22 | 1 | 2 | yes | — |
| 31 | C43×#334 | C22 | 1 | 2 | yes | — |
| 32 | C22×Dic86 | — | 2 | 2 | no | — |
| 33 | C2×Dic172 | — | 2 | 2 | no | — |
| 34 | C2×Dic172 | — | 2 | 2 | no | — |
| 35 | C2×Dic172 | — | 2 | 2 | no | — |
| 36 | C2×Dic172 | — | 2 | 2 | no | — |
| 37 | C2×Dic172 | — | 4 | 4 | no | — |
| 38 | C2×Dic172 | — | 4 | 4 | no | — |
| 39 | C2×#10621877 | — | 2 | 1 | no | — |
| 40 | #13063325 | — | 2 | 2 | no | — |
| 41 | #13063325 | — | 2 | 2 | no | — |
| 42 | #13063325 | — | 2 | 2 | no | — |
| 43 | #13063325 | D4 | 1 | 1 | yes | characteristic |
| 44 | #13063325 | D4 | 1 | 1 | yes | characteristic |
| 45 | #13063325 | C23 | 1 | 4 | yes | — |
| 46 | #13063317 | — | 2 | 1 | no | — |
| 47 | #13063304 | — | 2 | 1 | no | — |
| 48 | #13063304 | D4 | 1 | 2 | yes | — |
| 49 | C4×Dic86 | — | 2 | 1 | no | — |
| 50 | C4×Dic86 | C23 | 1 | 2 | yes | — |
| 51 | #13063284 | — | 2 | 1 | no | — |
| 52 | C2×C4⋊Dic43 | — | 2 | 2 | no | — |
| 53 | C2×C4⋊Dic43 | — | 2 | 2 | no | — |
| 54 | #13063257 | — | 2 | 8 | no | — |
| 55 | C4⋊(C43⋊C8) | — | 2 | 1 | no | — |
| 56 | C4⋊(C43⋊C8) | C23 | 1 | 2 | yes | — |
| 57 | Dic43⋊C8 | — | 2 | 2 | no | — |
| 58 | Dic43⋊C8 | — | 2 | 2 | no | — |
| 59 | #13063250 | — | 2 | 8 | no | — |
| 60 | #13063235 | — | 2 | 2 | no | — |
| 61 | C8×Dic43 | — | 2 | 2 | no | — |
| 62 | C22×C8×C43 | D4 | 1 | 1 | yes | characteristic |
| 63 | C22×C8×C43 | D4 | 1 | 1 | yes | characteristic |
| 64 | C2×C42×C43 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4⋊C8×C43 | C23 | 1 | 4 | yes | — |
| 66 | C22⋊C8×C43 | — | 2 | 2 | no | — |
| 67 | C4×C8×C43 | — | 2 | 2 | no | — |
| 68 | C4×C8×C43 | D4 | 1 | 1 | yes | characteristic |
| 69 | C4×C8×C43 | D4 | 1 | 1 | yes | characteristic |
| 70 | C4×C8×C43 | C23 | 1 | 1 | yes | characteristic |
| 71 | C4×C8×C43 | C23 | 1 | 1 | yes | characteristic |
| 72 | C22×C4×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C22×C4×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C22×C4×C43 | #41 | 1 | 1 | yes | characteristic |
| 75 | C22×Dic43 | — | 4 | 2 | no | — |
| 76 | C2×Dic86 | — | 2 | 1 | no | — |
| 77 | C2×Dic86 | — | 2 | 4 | no | — |
| 78 | C2×Dic86 | — | 4 | 4 | no | — |
| 79 | C2×Dic86 | — | 4 | 4 | no | — |
| 80 | C2×Dic86 | — | 4 | 2 | no | — |
| 81 | C2×Dic86 | C2×D4 | 1 | 2 | yes | — |
| 82 | C2×C8×C43 | — | 2 | 2 | no | — |
| 83 | C2×C8×C43 | — | 2 | 4 | no | — |
| 84 | C2×C8×C43 | SD16 | 1 | 4 | yes | — |
| 85 | C2×C8×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 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 | C42×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C42×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C42×C43 | #41 | 1 | 1 | yes | characteristic |
| 92 | C42×C43 | C24 | 1 | 1 | yes | characteristic |
| 93 | C22⋊Dic43 | — | 2 | 2 | no | — |
| 94 | C4⋊Dic43 | — | 2 | 1 | no | — |
| 95 | C4⋊Dic43 | — | 2 | 1 | no | — |
| 96 | C4⋊Dic43 | — | 2 | 1 | no | — |
| 97 | C4⋊Dic43 | — | 2 | 4 | no | — |
| 98 | C4⋊Dic43 | — | 2 | 4 | no | — |
| 99 | C4⋊Dic43 | — | 4 | 2 | no | — |
| 100 | C4⋊Dic43 | — | 4 | 2 | no | — |
| 101 | C4⋊Dic43 | C2×D4 | 1 | 2 | yes | — |
| 102 | Dic43⋊C4 | — | 2 | 2 | no | — |
| 103 | Dic43⋊C4 | — | 2 | 2 | no | — |
| 104 | C4×Dic43 | — | 2 | 2 | no | — |
| 105 | #10621877 | — | 4 | 2 | no | — |
| 106 | C2×C43⋊C8 | — | 2 | 2 | no | — |
| 107 | Dic172 | — | 4 | 4 | no | — |
| 108 | Dic172 | — | 4 | 4 | no | — |
| 109 | Dic172 | — | 4 | 4 | no | — |
| 110 | Dic172 | — | 4 | 4 | no | — |
| 111 | C23×C43 | #121 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C43 | — | 2 | 2 | no | — |
| 113 | C2×C4×C43 | — | 2 | 2 | no | — |
| 114 | C2×C4×C43 | #121 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C43 | #121 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C43 | #121 | 1 | 1 | yes | characteristic |
| 117 | C2×C4×C43 | C2×SD16 | 1 | 2 | yes | — |
| 118 | C2×C4×C43 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 119 | C2×C4×C43 | C22×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×C4×C43 | C22×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×C43 | C2×#41 | 1 | 1 | yes | characteristic |
| 122 | C2×Dic43 | — | 2 | 2 | no | — |
| 123 | C2×Dic43 | — | 2 | 2 | no | — |
| 124 | C2×Dic43 | — | 4 | 4 | no | — |
| 125 | C2×Dic43 | — | 8 | 4 | no | — |
| 126 | Dic86 | — | 2 | 4 | no | — |
| 127 | Dic86 | — | 4 | 2 | no | — |
| 128 | Dic86 | — | 4 | 4 | no | — |
| 129 | Dic86 | — | 4 | 4 | no | — |
| 130 | Dic86 | — | 8 | 4 | no | — |
| 131 | C8×C43 | — | 2 | 1 | no | — |
| 132 | C8×C43 | — | 2 | 1 | no | — |
| 133 | C8×C43 | — | 4 | 4 | no | — |
| 134 | C8×C43 | C2×SD16 | 1 | 2 | yes | — |
| 135 | C8×C43 | C2×SD16 | 1 | 2 | yes | — |
| 136 | C43⋊C8 | — | 4 | 2 | no | — |
| 137 | #19204 | — | 43 | 1 | no | maximal, Sylow |
| 138 | C22×C43 | — | 2 | 1 | no | — |
| 139 | C22×C43 | — | 2 | 1 | no | — |
| 140 | C22×C43 | #460 | 1 | 2 | yes | — |
| 141 | C22×C43 | C2×#121 | 1 | 1 | yes | characteristic |
| 142 | C4×C43 | — | 2 | 1 | no | — |
| 143 | C4×C43 | — | 2 | 1 | no | — |
| 144 | C4×C43 | #460 | 1 | 2 | yes | — |
| 145 | C4×C43 | #473 | 1 | 2 | yes | — |
| 146 | C4×C43 | C22×SD16 | 1 | 1 | yes | characteristic |
| 147 | C4×C43 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 148 | C4×C43 | #578 | 1 | 2 | yes | — |
| 149 | Dic43 | — | 4 | 2 | no | — |
| 150 | Dic43 | — | 4 | 2 | no | — |
| 151 | Dic43 | — | 8 | 4 | no | — |
| 152 | #3229 | — | 43 | 2 | no | — |
| 153 | C2×#494 | — | 43 | 1 | no | — |
| 154 | #2960 | — | 43 | 1 | no | — |
| 155 | #1690 | — | 43 | 4 | no | — |
| 156 | #1670 | — | 43 | 4 | no | — |
| 157 | #1564 | D43 | 1 | 1 | yes | characteristic |
| 158 | #1546 | — | 43 | 2 | no | — |
| 159 | C2×C43 | — | 2 | 2 | no | — |
| 160 | C2×C43 | C2×#460 | 1 | 1 | yes | characteristic |
| 161 | C2×C43 | #3059 | 1 | 1 | yes | characteristic |
| 162 | C2×C43 | C2×#473 | 1 | 1 | yes | characteristic |
| 163 | C22×Q16 | — | 86 | 1 | no | — |
| 164 | C22×Q16 | — | 86 | 1 | no | — |
| 165 | #533 | — | 43 | 1 | no | — |
| 166 | C2×C4⋊Q8 | — | 43 | 2 | no | — |
| 167 | #498 | — | 86 | 2 | no | — |
| 168 | #494 | — | 43 | 2 | no | — |
| 169 | #494 | — | 43 | 2 | no | — |
| 170 | #494 | — | 86 | 1 | no | — |
| 171 | #494 | — | 86 | 1 | no | — |
| 172 | #487 | — | 86 | 2 | no | — |
| 173 | #483 | — | 86 | 4 | no | — |
| 174 | #475 | — | 43 | 8 | no | — |
| 175 | #446 | — | 43 | 2 | no | — |
| 176 | #446 | — | 86 | 1 | no | — |
| 177 | C8×Q8 | — | 43 | 2 | no | — |
| 178 | C8×Q8 | — | 86 | 1 | no | — |
| 179 | #431 | C2×D43 | 1 | 2 | yes | — |
| 180 | #424 | — | 86 | 1 | no | — |
| 181 | #423 | — | 43 | 1 | no | — |
| 182 | #405 | — | 86 | 1 | no | — |
| 183 | C2×C4×C8 | C2×D43 | 1 | 1 | yes | characteristic |
| 184 | #335 | C2×D43 | 1 | 2 | yes | — |
| 185 | #334 | C2×D43 | 1 | 2 | yes | — |
| 186 | #332 | — | 43 | 8 | no | — |
| 187 | C43 | #19204 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 188 | C22×Q8 | — | 86 | 2 | no | — |
| 189 | C2×Q16 | — | 86 | 2 | no | — |
| 190 | C2×Q16 | — | 86 | 2 | no | — |
| 191 | C2×Q16 | — | 86 | 2 | no | — |
| 192 | C2×Q16 | — | 86 | 2 | no | — |
| 193 | C2×Q16 | — | 172 | 4 | no | — |
| 194 | C2×Q16 | — | 172 | 4 | no | — |
| 195 | C2×M16 | — | 86 | 1 | no | — |
| 196 | C22×C8 | D172 | 1 | 1 | yes | characteristic |
| 197 | C22×C8 | D172 | 1 | 1 | yes | characteristic |
| 198 | C4⋊Q8 | — | 43 | 1 | no | — |
| 199 | C4⋊Q8 | — | 43 | 1 | no | — |
| 200 | C4⋊Q8 | — | 43 | 4 | no | — |
| 201 | C4⋊Q8 | — | 86 | 2 | no | — |
| 202 | C4⋊Q8 | — | 86 | 2 | no | — |
| 203 | C4⋊Q8 | — | 86 | 2 | no | — |
| 204 | #125 | — | 86 | 1 | no | — |
| 205 | C22⋊Q8 | — | 43 | 2 | no | — |
| 206 | C22⋊Q8 | — | 86 | 1 | no | — |
| 207 | C4×Q8 | — | 43 | 2 | no | — |
| 208 | C4×Q8 | — | 86 | 1 | no | — |
| 209 | #117 | — | 86 | 1 | no | — |
| 210 | C2×C4⋊C4 | — | 86 | 2 | no | — |
| 211 | C2×C4⋊C4 | — | 86 | 2 | no | — |
| 212 | C2×C42 | C22×D43 | 1 | 1 | yes | characteristic |
| 213 | #106 | — | 86 | 8 | no | — |
| 214 | C4⋊C8 | — | 43 | 2 | no | — |
| 215 | C4⋊C8 | — | 86 | 2 | no | — |
| 216 | C4⋊C8 | — | 86 | 2 | no | — |
| 217 | C4⋊C8 | — | 86 | 1 | no | — |
| 218 | C4⋊C8 | C22×D43 | 1 | 4 | yes | — |
| 219 | #103 | — | 86 | 8 | no | — |
| 220 | C22⋊C8 | — | 2 | 2 | no | — |
| 221 | #97 | — | 86 | 2 | no | — |
| 222 | C4×C8 | — | 2 | 2 | no | — |
| 223 | C4×C8 | — | 86 | 2 | no | — |
| 224 | C4×C8 | D172 | 1 | 1 | yes | characteristic |
| 225 | C4×C8 | D172 | 1 | 1 | yes | characteristic |
| 226 | C4×C8 | C22×D43 | 1 | 1 | yes | characteristic |
| 227 | C4×C8 | C22×D43 | 1 | 1 | yes | characteristic |
| 228 | C2×Q8 | — | 43 | 2 | no | — |
| 229 | C2×Q8 | — | 86 | 1 | no | — |
| 230 | C2×Q8 | — | 86 | 4 | no | — |
| 231 | C2×Q8 | — | 172 | 4 | no | — |
| 232 | C2×Q8 | — | 172 | 4 | no | — |
| 233 | C2×Q8 | — | 172 | 2 | no | — |
| 234 | C22×C4 | — | 172 | 2 | no | — |
| 235 | C22×C4 | C2×D172 | 1 | 1 | yes | characteristic |
| 236 | C22×C4 | D4×D43 | 1 | 1 | yes | characteristic |
| 237 | C22×C4 | #10621902 | 1 | 1 | yes | characteristic |
| 238 | Q16 | — | 172 | 4 | no | — |
| 239 | Q16 | — | 172 | 4 | no | — |
| 240 | Q16 | — | 172 | 4 | no | — |
| 241 | Q16 | — | 172 | 4 | no | — |
| 242 | M16 | — | 172 | 2 | no | — |
| 243 | C2×C8 | — | 2 | 2 | no | — |
| 244 | C2×C8 | — | 2 | 4 | no | — |
| 245 | C2×C8 | — | 86 | 2 | no | — |
| 246 | C2×C8 | #10621873 | 1 | 4 | yes | — |
| 247 | C2×C8 | C2×D172 | 1 | 1 | yes | characteristic |
| 248 | C2×C8 | C2×D172 | 1 | 1 | yes | characteristic |
| 249 | C2×C8 | C2×D172 | 1 | 1 | yes | characteristic |
| 250 | C2×C8 | C2×D172 | 1 | 1 | yes | characteristic |
| 251 | C4⋊C4 | — | 43 | 2 | no | — |
| 252 | C4⋊C4 | — | 86 | 1 | no | — |
| 253 | C4⋊C4 | — | 86 | 1 | no | — |
| 254 | C4⋊C4 | — | 86 | 2 | no | — |
| 255 | C4⋊C4 | — | 86 | 1 | no | — |
| 256 | C4⋊C4 | — | 86 | 2 | no | — |
| 257 | C4⋊C4 | — | 86 | 4 | no | — |
| 258 | C4⋊C4 | — | 86 | 4 | no | — |
| 259 | C4⋊C4 | — | 172 | 2 | no | — |
| 260 | C4⋊C4 | — | 172 | 2 | no | — |
| 261 | C22⋊C4 | — | 86 | 2 | no | — |
| 262 | C42 | — | 86 | 2 | no | — |
| 263 | C42 | C2×D172 | 1 | 1 | yes | characteristic |
| 264 | C42 | D4×D43 | 1 | 1 | yes | characteristic |
| 265 | C42 | #10621902 | 1 | 1 | yes | characteristic |
| 266 | C42 | C23×D43 | 1 | 1 | yes | characteristic |
| 267 | C23 | #13063300 | 1 | 1 | yes | characteristic |
| 268 | Q8 | — | 86 | 4 | no | — |
| 269 | Q8 | — | 344 | 4 | no | — |
| 270 | Q8 | — | 172 | 4 | no | — |
| 271 | Q8 | — | 172 | 4 | no | — |
| 272 | Q8 | — | 172 | 2 | no | — |
| 273 | C2×C4 | — | 2 | 2 | no | — |
| 274 | C2×C4 | — | 2 | 2 | no | — |
| 275 | C2×C4 | — | 86 | 2 | no | — |
| 276 | C2×C4 | — | 86 | 2 | no | — |
| 277 | C2×C4 | — | 344 | 4 | no | — |
| 278 | C2×C4 | — | 172 | 4 | no | — |
| 279 | C2×C4 | #13063300 | 1 | 1 | yes | characteristic |
| 280 | C2×C4 | #13063300 | 1 | 1 | yes | characteristic |
| 281 | C2×C4 | #13063300 | 1 | 1 | yes | characteristic |
| 282 | C2×C4 | C2×#10621873 | 1 | 2 | yes | — |
| 283 | C2×C4 | #13063353 | 1 | 2 | yes | — |
| 284 | C2×C4 | C2×D4×D43 | 1 | 1 | yes | characteristic |
| 285 | C2×C4 | C22×D172 | 1 | 1 | yes | characteristic |
| 286 | C2×C4 | C2×#10621902 | 1 | 1 | yes | characteristic |
| 287 | C8 | — | 2 | 1 | no | — |
| 288 | C8 | — | 2 | 1 | no | — |
| 289 | C8 | — | 4 | 4 | no | — |
| 290 | C8 | — | 172 | 2 | no | — |
| 291 | C8 | C2×#10621873 | 1 | 2 | yes | — |
| 292 | C8 | C2×#10621873 | 1 | 2 | yes | — |
| 293 | C22 | — | 2 | 1 | no | — |
| 294 | C22 | — | 2 | 1 | no | — |
| 295 | C22 | #14583100 | 1 | 2 | yes | — |
| 296 | C22 | C2×#13063300 | 1 | 1 | yes | characteristic |
| 297 | C4 | — | 2 | 1 | no | — |
| 298 | C4 | — | 2 | 1 | no | — |
| 299 | C4 | — | 344 | 4 | no | — |
| 300 | C4 | — | 172 | 2 | no | — |
| 301 | C4 | — | 172 | 2 | no | — |
| 302 | C4 | #14583100 | 1 | 2 | yes | — |
| 303 | C4 | #14583175 | 1 | 2 | yes | — |
| 304 | C4 | C22×#10621873 | 1 | 1 | yes | characteristic |
| 305 | C4 | C2×#13063353 | 1 | 1 | yes | characteristic |
| 306 | C4 | #14583713 | 1 | 2 | yes | — |
| 307 | C2 | — | 2 | 2 | no | — |
| 308 | C2 | C2×#14583100 | 1 | 1 | yes | characteristic |
| 309 | C2 | #19144251 | 1 | 1 | yes | characteristic |
| 310 | C2 | C2×#14583175 | 1 | 1 | yes | characteristic |
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