← #35560734
Subgroups — #35560734
Order 21248.
502 conjugacy classes of subgroups.
The subgroup lattice has 294 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #24918033 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #24909628 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #24909621 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #24909559 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #24909554 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #24909549 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #24909526 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #24909519 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×C4⋊C16×C83 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #19128235 | — | 2 | 2 | no | — |
| 11 | C2×Dic664 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#14581737 | C22 | 1 | 2 | yes | — |
| 13 | C2×D1328 | C22 | 1 | 1 | yes | characteristic |
| 14 | #19128103 | C22 | 1 | 2 | yes | — |
| 15 | #19128085 | C22 | 1 | 2 | yes | — |
| 16 | #19128056 | — | 2 | 2 | no | — |
| 17 | #19127942 | C22 | 1 | 2 | yes | — |
| 18 | #19127937 | C22 | 1 | 2 | yes | — |
| 19 | #19127930 | — | 2 | 2 | no | — |
| 20 | C4×Dic332 | C22 | 1 | 2 | yes | — |
| 21 | C4×#13050579 | — | 2 | 2 | no | — |
| 22 | C4×D664 | C22 | 1 | 2 | yes | — |
| 23 | #19127529 | C22 | 1 | 2 | yes | — |
| 24 | #19127527 | C22 | 1 | 1 | yes | characteristic |
| 25 | #19127527 | C22 | 1 | 1 | yes | characteristic |
| 26 | #19127506 | C22 | 1 | 2 | yes | — |
| 27 | #19127506 | C22 | 1 | 2 | yes | — |
| 28 | #19127503 | C22 | 1 | 2 | yes | — |
| 29 | #19127503 | C22 | 1 | 2 | yes | — |
| 30 | C22×C16×C83 | C22 | 1 | 1 | yes | characteristic |
| 31 | C22×C16×C83 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×C4×C8×C83 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4⋊C16×C83 | C22 | 1 | 2 | yes | — |
| 34 | C4⋊C16×C83 | C22 | 1 | 2 | yes | — |
| 35 | C2×Dic332 | C23 | 1 | 2 | yes | — |
| 36 | C2×#13050579 | — | 2 | 2 | no | — |
| 37 | C2×D664 | C23 | 1 | 2 | yes | — |
| 38 | #14581786 | — | 4 | 2 | no | — |
| 39 | #14581784 | — | 2 | 2 | no | — |
| 40 | #14581780 | — | 2 | 2 | no | — |
| 41 | #14581775 | — | 4 | 2 | no | — |
| 42 | #14581771 | — | 2 | 2 | no | — |
| 43 | #14581766 | — | 2 | 2 | no | — |
| 44 | C4×Dic166 | — | 2 | 2 | no | — |
| 45 | C4×D332 | — | 2 | 2 | no | — |
| 46 | C4×C22⋊D83 | — | 4 | 2 | no | — |
| 47 | #14581749 | — | 4 | 2 | no | — |
| 48 | Dic664 | — | 4 | 1 | no | — |
| 49 | #14581737 | — | 4 | 2 | no | — |
| 50 | D1328 | — | 4 | 1 | no | — |
| 51 | #14581726 | C23 | 1 | 2 | yes | — |
| 52 | #14581726 | C23 | 1 | 2 | yes | — |
| 53 | #14581724 | — | 2 | 2 | no | — |
| 54 | #14581717 | — | 2 | 2 | no | — |
| 55 | #14581717 | — | 2 | 2 | no | — |
| 56 | #14581714 | — | 2 | 2 | no | — |
| 57 | #14581714 | — | 2 | 2 | no | — |
| 58 | C22×C8×C83 | D4 | 1 | 1 | yes | characteristic |
| 59 | C22×C8×C83 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C42×C83 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×C16×C83 | — | 4 | 1 | no | — |
| 62 | C2×C16×C83 | — | 4 | 1 | no | — |
| 63 | C2×C16×C83 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C16×C83 | C23 | 1 | 2 | yes | — |
| 65 | C2×C16×C83 | C23 | 1 | 1 | yes | characteristic |
| 66 | C4×C8×C83 | D4 | 1 | 2 | yes | — |
| 67 | C4×C8×C83 | C23 | 1 | 2 | yes | — |
| 68 | C2×Dic166 | — | 2 | 2 | no | — |
| 69 | C2×D332 | — | 2 | 2 | no | — |
| 70 | C2×C22⋊D83 | — | 4 | 2 | no | — |
| 71 | C2×C4×D83 | — | 4 | 2 | no | — |
| 72 | Dic332 | — | 2 | 2 | no | — |
| 73 | Dic332 | — | 2 | 2 | no | — |
| 74 | #13050579 | — | 4 | 4 | no | — |
| 75 | D664 | — | 2 | 2 | no | — |
| 76 | D664 | — | 2 | 2 | no | — |
| 77 | C4⋊Dic83 | — | 2 | 2 | no | — |
| 78 | C4⋊Dic83 | — | 2 | 2 | no | — |
| 79 | Dic83⋊C4 | — | 4 | 2 | no | — |
| 80 | Dic83⋊C4 | — | 4 | 2 | no | — |
| 81 | Dic83⋊C4 | — | 4 | 2 | no | — |
| 82 | Dic83⋊C4 | — | 4 | 2 | no | — |
| 83 | C22⋊Dic83 | — | 4 | 2 | no | — |
| 84 | (C2×D83)⋊C4 | — | 4 | 2 | no | — |
| 85 | (C2×D83)⋊C4 | — | 4 | 2 | no | — |
| 86 | (C2×D83)⋊C4 | — | 4 | 2 | no | — |
| 87 | (C2×D83)⋊C4 | — | 4 | 2 | no | — |
| 88 | C4×Dic83 | — | 4 | 2 | no | — |
| 89 | C22×C4×C83 | D8 | 1 | 1 | yes | characteristic |
| 90 | C22×C4×C83 | D8 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×C83 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C2×C8×C83 | — | 2 | 1 | no | — |
| 93 | C2×C8×C83 | — | 2 | 1 | no | — |
| 94 | C2×C8×C83 | — | 4 | 1 | no | — |
| 95 | C2×C8×C83 | C2×D4 | 1 | 2 | yes | — |
| 96 | C2×C8×C83 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×C8×C83 | C24 | 1 | 1 | yes | characteristic |
| 98 | C42×C83 | D8 | 1 | 2 | yes | — |
| 99 | C42×C83 | C2×D4 | 1 | 2 | yes | — |
| 100 | C16×C83 | — | 2 | 1 | no | — |
| 101 | C16×C83 | — | 2 | 2 | no | — |
| 102 | C16×C83 | — | 2 | 1 | no | — |
| 103 | C23×C83 | C2×D8 | 1 | 1 | yes | characteristic |
| 104 | C22×D83 | — | 4 | 2 | no | — |
| 105 | C2×C4×C83 | — | 2 | 2 | no | — |
| 106 | C2×C4×C83 | — | 2 | 1 | no | — |
| 107 | C2×C4×C83 | — | 2 | 1 | no | — |
| 108 | C2×C4×C83 | — | 4 | 1 | no | — |
| 109 | C2×C4×C83 | C2×D8 | 1 | 1 | yes | characteristic |
| 110 | C2×C4×C83 | C2×D8 | 1 | 2 | yes | — |
| 111 | C2×C4×C83 | C2×D8 | 1 | 2 | yes | — |
| 112 | C2×C4×C83 | C22×D4 | 1 | 1 | yes | characteristic |
| 113 | C22⋊D83 | — | 8 | 4 | no | — |
| 114 | C2×Dic83 | — | 4 | 2 | no | — |
| 115 | C2×Dic83 | — | 4 | 2 | no | — |
| 116 | C2×Dic83 | — | 4 | 2 | no | — |
| 117 | D332 | — | 4 | 2 | no | — |
| 118 | D332 | — | 4 | 2 | no | — |
| 119 | C4×D83 | — | 8 | 4 | no | — |
| 120 | Dic166 | — | 4 | 2 | no | — |
| 121 | Dic166 | — | 4 | 2 | no | — |
| 122 | C8×C83 | — | 2 | 1 | no | — |
| 123 | C8×C83 | — | 2 | 2 | no | — |
| 124 | C8×C83 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 125 | C8×C83 | 2−1+4 | 1 | 1 | yes | characteristic |
| 126 | C22×C83 | — | 2 | 1 | no | — |
| 127 | C22×C83 | — | 2 | 1 | no | — |
| 128 | C22×C83 | #508 | 1 | 2 | yes | — |
| 129 | C22×C83 | C22×D8 | 1 | 1 | yes | characteristic |
| 130 | C2×D83 | — | 8 | 2 | no | — |
| 131 | C2×D83 | — | 8 | 2 | no | — |
| 132 | C2×D83 | — | 8 | 2 | no | — |
| 133 | C4×C83 | — | 2 | 2 | no | — |
| 134 | C4×C83 | — | 2 | 2 | no | — |
| 135 | C4×C83 | — | 2 | 1 | no | — |
| 136 | C4×C83 | #537 | 1 | 1 | yes | characteristic |
| 137 | C4×C83 | #575 | 1 | 1 | yes | characteristic |
| 138 | Dic83 | — | 8 | 2 | no | — |
| 139 | Dic83 | — | 8 | 2 | no | — |
| 140 | Dic83 | — | 8 | 2 | no | — |
| 141 | #33816 | — | 83 | 1 | no | maximal, Sylow |
| 142 | C2×C83 | — | 2 | 2 | no | — |
| 143 | C2×C83 | #3245 | 1 | 1 | yes | characteristic |
| 144 | C2×C83 | C2×#508 | 1 | 1 | yes | characteristic |
| 145 | C2×C83 | #3414 | 1 | 1 | yes | characteristic |
| 146 | D83 | — | 16 | 2 | no | — |
| 147 | #3168 | — | 83 | 2 | no | — |
| 148 | #2229 | — | 83 | 2 | no | — |
| 149 | #2228 | — | 83 | 2 | no | — |
| 150 | #2217 | — | 83 | 2 | no | — |
| 151 | #2216 | — | 83 | 1 | no | — |
| 152 | #2215 | — | 83 | 1 | no | — |
| 153 | #2211 | — | 83 | 2 | no | — |
| 154 | #2210 | — | 83 | 2 | no | — |
| 155 | C2×C4⋊C16 | D83 | 1 | 1 | yes | characteristic, complemented |
| 156 | C83 | #33816 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 157 | #529 | — | 166 | 2 | no | — |
| 158 | C2×Q32 | — | 83 | 1 | no | — |
| 159 | C2×SD32 | — | 83 | 2 | no | — |
| 160 | C2×D16 | — | 83 | 1 | no | — |
| 161 | C22×C16 | C2×D83 | 1 | 1 | yes | characteristic |
| 162 | C22×C16 | C2×D83 | 1 | 1 | yes | characteristic |
| 163 | #499 | — | 83 | 2 | no | — |
| 164 | #495 | — | 83 | 2 | no | — |
| 165 | #488 | — | 166 | 2 | no | — |
| 166 | #467 | — | 83 | 2 | no | — |
| 167 | #466 | — | 83 | 2 | no | — |
| 168 | #465 | — | 166 | 2 | no | — |
| 169 | C4×Q16 | — | 83 | 2 | no | — |
| 170 | C4×SD16 | — | 166 | 2 | no | — |
| 171 | C4×D8 | — | 83 | 2 | no | — |
| 172 | C2×C4×C8 | C2×D83 | 1 | 1 | yes | characteristic |
| 173 | #367 | — | 83 | 2 | no | — |
| 174 | #366 | — | 83 | 1 | no | — |
| 175 | #366 | — | 83 | 1 | no | — |
| 176 | C4⋊C16 | C2×D83 | 1 | 2 | yes | — |
| 177 | C4⋊C16 | C2×D83 | 1 | 2 | yes | — |
| 178 | #358 | — | 83 | 2 | no | — |
| 179 | #358 | — | 83 | 2 | no | — |
| 180 | #357 | — | 83 | 2 | no | — |
| 181 | #357 | — | 83 | 2 | no | — |
| 182 | C2×Q16 | — | 83 | 2 | no | — |
| 183 | C2×SD16 | — | 166 | 2 | no | — |
| 184 | C2×D8 | — | 83 | 2 | no | — |
| 185 | C22×C8 | D332 | 1 | 1 | yes | characteristic |
| 186 | C22×C8 | C22×D83 | 1 | 1 | yes | characteristic |
| 187 | #126 | — | 332 | 2 | no | — |
| 188 | #125 | — | 166 | 2 | no | — |
| 189 | #124 | — | 166 | 2 | no | — |
| 190 | #123 | — | 332 | 2 | no | — |
| 191 | C22⋊Q8 | — | 166 | 2 | no | — |
| 192 | #121 | — | 166 | 2 | no | — |
| 193 | C4×Q8 | — | 166 | 2 | no | — |
| 194 | C4×D4 | — | 332 | 2 | no | — |
| 195 | C4×D4 | — | 166 | 2 | no | — |
| 196 | #117 | — | 332 | 2 | no | — |
| 197 | C2×C42 | D332 | 1 | 1 | yes | characteristic |
| 198 | Q32 | — | 332 | 1 | no | — |
| 199 | SD32 | — | 332 | 2 | no | — |
| 200 | D16 | — | 332 | 1 | no | — |
| 201 | C2×C16 | — | 4 | 1 | no | — |
| 202 | C2×C16 | — | 4 | 1 | no | — |
| 203 | C2×C16 | C22×D83 | 1 | 1 | yes | characteristic |
| 204 | C2×C16 | C22×D83 | 1 | 2 | yes | — |
| 205 | C2×C16 | C22×D83 | 1 | 1 | yes | characteristic |
| 206 | #107 | — | 83 | 2 | no | — |
| 207 | #107 | — | 83 | 2 | no | — |
| 208 | #106 | — | 166 | 2 | no | — |
| 209 | #103 | — | 166 | 2 | no | — |
| 210 | #103 | — | 166 | 2 | no | — |
| 211 | #102 | — | 166 | 2 | no | — |
| 212 | #102 | — | 166 | 2 | no | — |
| 213 | C4×C8 | D332 | 1 | 2 | yes | — |
| 214 | C4×C8 | C22×D83 | 1 | 2 | yes | — |
| 215 | C2×Q8 | — | 166 | 2 | no | — |
| 216 | C2×D4 | — | 332 | 2 | no | — |
| 217 | C2×D4 | — | 166 | 2 | no | — |
| 218 | C22×C4 | — | 332 | 2 | no | — |
| 219 | C22×C4 | D664 | 1 | 1 | yes | characteristic |
| 220 | C22×C4 | D664 | 1 | 1 | yes | characteristic |
| 221 | C22×C4 | C2×D332 | 1 | 1 | yes | characteristic |
| 222 | Q16 | — | 166 | 2 | no | — |
| 223 | Q16 | — | 166 | 2 | no | — |
| 224 | SD16 | — | 332 | 4 | no | — |
| 225 | D8 | — | 166 | 2 | no | — |
| 226 | D8 | — | 166 | 2 | no | — |
| 227 | C2×C8 | — | 2 | 1 | no | — |
| 228 | C2×C8 | — | 2 | 1 | no | — |
| 229 | C2×C8 | — | 4 | 1 | no | — |
| 230 | C2×C8 | C2×D332 | 1 | 1 | yes | characteristic |
| 231 | C2×C8 | C2×D332 | 1 | 2 | yes | — |
| 232 | C2×C8 | C23×D83 | 1 | 1 | yes | characteristic |
| 233 | C4⋊C4 | — | 332 | 2 | no | — |
| 234 | C4⋊C4 | — | 332 | 2 | no | — |
| 235 | C4⋊C4 | — | 332 | 2 | no | — |
| 236 | C4⋊C4 | — | 332 | 2 | no | — |
| 237 | C4⋊C4 | — | 166 | 2 | no | — |
| 238 | C4⋊C4 | — | 166 | 2 | no | — |
| 239 | C22⋊C4 | — | 332 | 2 | no | — |
| 240 | C22⋊C4 | — | 332 | 2 | no | — |
| 241 | C22⋊C4 | — | 332 | 2 | no | — |
| 242 | C22⋊C4 | — | 332 | 2 | no | — |
| 243 | C22⋊C4 | — | 332 | 2 | no | — |
| 244 | C42 | — | 332 | 2 | no | — |
| 245 | C42 | D664 | 1 | 2 | yes | — |
| 246 | C42 | C2×D332 | 1 | 2 | yes | — |
| 247 | C16 | — | 2 | 1 | no | — |
| 248 | C16 | — | 2 | 2 | no | — |
| 249 | C16 | — | 2 | 1 | no | — |
| 250 | C23 | — | 332 | 2 | no | — |
| 251 | C23 | C2×D664 | 1 | 1 | yes | characteristic |
| 252 | Q8 | — | 332 | 2 | no | — |
| 253 | Q8 | — | 332 | 2 | no | — |
| 254 | D4 | — | 332 | 2 | no | — |
| 255 | D4 | — | 332 | 2 | no | — |
| 256 | D4 | — | 664 | 4 | no | — |
| 257 | C2×C4 | — | 2 | 2 | no | — |
| 258 | C2×C4 | — | 2 | 1 | no | — |
| 259 | C2×C4 | — | 2 | 1 | no | — |
| 260 | C2×C4 | — | 4 | 1 | no | — |
| 261 | C2×C4 | — | 332 | 2 | no | — |
| 262 | C2×C4 | — | 332 | 2 | no | — |
| 263 | C2×C4 | — | 332 | 2 | no | — |
| 264 | C2×C4 | — | 664 | 4 | no | — |
| 265 | C2×C4 | C2×D664 | 1 | 2 | yes | — |
| 266 | C2×C4 | C2×D664 | 1 | 1 | yes | characteristic |
| 267 | C2×C4 | C2×D664 | 1 | 2 | yes | — |
| 268 | C2×C4 | C22×D332 | 1 | 1 | yes | characteristic |
| 269 | C8 | — | 2 | 2 | no | — |
| 270 | C8 | — | 2 | 1 | no | — |
| 271 | C8 | #14581837 | 1 | 1 | yes | characteristic |
| 272 | C8 | #14581840 | 1 | 1 | yes | characteristic |
| 273 | C22 | — | 2 | 1 | no | — |
| 274 | C22 | — | 2 | 1 | no | — |
| 275 | C22 | — | 664 | 2 | no | — |
| 276 | C22 | — | 664 | 2 | no | — |
| 277 | C22 | — | 664 | 2 | no | — |
| 278 | C22 | #19128133 | 1 | 2 | yes | — |
| 279 | C22 | C22×D664 | 1 | 1 | yes | characteristic |
| 280 | C4 | — | 2 | 2 | no | — |
| 281 | C4 | — | 2 | 2 | no | — |
| 282 | C4 | — | 2 | 1 | no | — |
| 283 | C4 | — | 664 | 2 | no | — |
| 284 | C4 | — | 664 | 2 | no | — |
| 285 | C4 | — | 664 | 2 | no | — |
| 286 | C4 | #19128282 | 1 | 1 | yes | characteristic |
| 287 | C4 | #19128501 | 1 | 1 | yes | characteristic |
| 288 | C2 | — | 2 | 2 | no | — |
| 289 | C2 | — | 1328 | 2 | no | — |
| 290 | C2 | #24918773 | 1 | 1 | yes | characteristic |
| 291 | C2 | C2×#19128133 | 1 | 1 | yes | characteristic |
| 292 | C2 | #24920599 | 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