← #31985409
Subgroups — #31985409
Order 18176.
750 conjugacy classes of subgroups.
The subgroup lattice has 286 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22599493 | C2 | 1 | 2 | yes | maximal |
| 2 | #22598926 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22598886 | C2 | 1 | 2 | yes | maximal |
| 4 | C2×#17986379 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #22588017 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #22587958 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22587937 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C8×M16×C71 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C22×Dic284 | — | 2 | 2 | no | — |
| 10 | #17986556 | C22 | 1 | 2 | yes | — |
| 11 | C2×#14556128 | C22 | 1 | 2 | yes | — |
| 12 | #17986408 | — | 2 | 4 | no | — |
| 13 | #17986404 | C22 | 1 | 1 | yes | characteristic |
| 14 | #17986404 | C22 | 1 | 4 | yes | — |
| 15 | #17986404 | C22 | 1 | 4 | yes | — |
| 16 | #17986397 | C22 | 1 | 4 | yes | — |
| 17 | #17986379 | — | 2 | 2 | no | — |
| 18 | #17986379 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17986379 | C22 | 1 | 2 | yes | — |
| 20 | #17986379 | C22 | 1 | 2 | yes | — |
| 21 | #17986350 | C22 | 1 | 2 | yes | — |
| 22 | #17986350 | C22 | 1 | 4 | yes | — |
| 23 | #17986335 | — | 2 | 4 | no | — |
| 24 | #17986295 | — | 2 | 4 | no | — |
| 25 | #17986240 | — | 2 | 2 | no | — |
| 26 | C4×Dic284 | — | 2 | 2 | no | — |
| 27 | #17986041 | — | 2 | 4 | no | — |
| 28 | #431×C71 | C22 | 1 | 1 | yes | characteristic |
| 29 | C4×M16×C71 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×C4×C8×C71 | C22 | 1 | 1 | yes | characteristic |
| 31 | #322×C71 | C22 | 1 | 2 | yes | — |
| 32 | C82×C71 | C22 | 1 | 2 | yes | — |
| 33 | C22×Dic142 | — | 2 | 2 | no | — |
| 34 | C2×Dic284 | — | 2 | 2 | no | — |
| 35 | C2×Dic284 | — | 2 | 4 | no | — |
| 36 | C2×Dic284 | — | 2 | 4 | no | — |
| 37 | C2×Dic284 | — | 4 | 8 | no | — |
| 38 | #14556128 | — | 2 | 2 | no | — |
| 39 | #14556128 | — | 2 | 2 | no | — |
| 40 | #14556128 | — | 2 | 2 | no | — |
| 41 | #14556128 | C23 | 1 | 2 | yes | — |
| 42 | #14556128 | C23 | 1 | 4 | yes | — |
| 43 | #14556128 | C23 | 1 | 2 | yes | — |
| 44 | #14556120 | — | 2 | 2 | no | — |
| 45 | #14556107 | — | 2 | 2 | no | — |
| 46 | #14556107 | — | 2 | 2 | no | — |
| 47 | C4×Dic142 | — | 2 | 2 | no | — |
| 48 | C4×Dic142 | — | 2 | 2 | no | — |
| 49 | #14556087 | — | 2 | 2 | no | — |
| 50 | C2×C4⋊Dic71 | — | 2 | 2 | no | — |
| 51 | C2×C4⋊Dic71 | — | 2 | 2 | no | — |
| 52 | #14556062 | — | 2 | 8 | no | — |
| 53 | #14556062 | — | 2 | 2 | no | — |
| 54 | #14556062 | — | 2 | 8 | no | — |
| 55 | #14556060 | — | 2 | 8 | no | — |
| 56 | #14556053 | — | 2 | 8 | no | — |
| 57 | #14556053 | — | 2 | 4 | no | — |
| 58 | C2×M16×C71 | D4 | 1 | 2 | yes | — |
| 59 | C22×C8×C71 | D4 | 1 | 2 | yes | — |
| 60 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 61 | C4⋊C8×C71 | D4 | 1 | 2 | yes | — |
| 62 | C22⋊C8×C71 | D4 | 1 | 2 | yes | — |
| 63 | #97×C71 | D4 | 1 | 2 | yes | — |
| 64 | C4×C8×C71 | D4 | 1 | 2 | yes | — |
| 65 | C4×C8×C71 | C23 | 1 | 2 | yes | — |
| 66 | C4×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 67 | C4×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 68 | C4×C8×C71 | C23 | 1 | 2 | yes | — |
| 69 | C2×Dic142 | — | 2 | 4 | no | — |
| 70 | C2×Dic142 | — | 2 | 2 | no | — |
| 71 | C2×Dic142 | — | 2 | 2 | no | — |
| 72 | C2×Dic142 | — | 4 | 8 | no | — |
| 73 | C2×Dic142 | — | 4 | 2 | no | — |
| 74 | C22×Dic71 | — | 4 | 2 | no | — |
| 75 | Dic284 | — | 4 | 8 | no | — |
| 76 | Dic284 | — | 4 | 4 | no | — |
| 77 | Dic284 | — | 4 | 8 | no | — |
| 78 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 79 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 80 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 81 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 82 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 83 | C4⋊Dic71 | — | 2 | 2 | no | — |
| 84 | C4⋊Dic71 | — | 4 | 2 | no | — |
| 85 | C4⋊Dic71 | — | 4 | 2 | no | — |
| 86 | Dic71⋊C4 | — | 4 | 2 | no | — |
| 87 | Dic71⋊C4 | — | 4 | 2 | no | — |
| 88 | C22⋊Dic71 | — | 4 | 2 | no | — |
| 89 | C4×Dic71 | — | 4 | 2 | no | — |
| 90 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | M16×C71 | Q16 | 1 | 8 | yes | complemented |
| 94 | C2×C8×C71 | — | 2 | 4 | no | — |
| 95 | C2×C8×C71 | C2×D4 | 1 | 2 | yes | — |
| 96 | C2×C8×C71 | C2×D4 | 1 | 4 | yes | — |
| 97 | C2×C8×C71 | C2×D4 | 1 | 4 | yes | — |
| 98 | C2×C8×C71 | C2×D4 | 1 | 2 | yes | — |
| 99 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 103 | C23×C71 | #127 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C71 | — | 2 | 2 | no | — |
| 105 | C2×C4×C71 | — | 2 | 2 | no | — |
| 106 | C2×C4×C71 | #127 | 1 | 1 | yes | characteristic |
| 107 | C2×C4×C71 | #127 | 1 | 1 | yes | characteristic |
| 108 | C2×C4×C71 | #127 | 1 | 1 | yes | characteristic |
| 109 | C2×C4×C71 | C2×Q16 | 1 | 4 | yes | — |
| 110 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×Dic71 | — | 4 | 2 | no | — |
| 114 | C2×Dic71 | — | 4 | 2 | no | — |
| 115 | C2×Dic71 | — | 4 | 4 | no | — |
| 116 | C2×Dic71 | — | 8 | 4 | no | — |
| 117 | Dic142 | — | 4 | 8 | no | — |
| 118 | Dic142 | — | 4 | 4 | no | — |
| 119 | Dic142 | — | 4 | 4 | no | — |
| 120 | Dic142 | — | 8 | 4 | no | — |
| 121 | C8×C71 | — | 2 | 2 | no | — |
| 122 | C8×C71 | — | 2 | 4 | no | — |
| 123 | C8×C71 | C2×Q16 | 1 | 8 | yes | complemented |
| 124 | C8×C71 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 125 | C22×C71 | — | 2 | 1 | no | — |
| 126 | C22×C71 | — | 2 | 1 | no | — |
| 127 | C22×C71 | #494 | 1 | 2 | yes | — |
| 128 | C22×C71 | C2×#127 | 1 | 1 | yes | characteristic |
| 129 | C4×C71 | — | 2 | 1 | no | — |
| 130 | C4×C71 | — | 2 | 1 | no | — |
| 131 | C4×C71 | #494 | 1 | 2 | yes | — |
| 132 | C4×C71 | C22×Q16 | 1 | 2 | yes | — |
| 133 | C4×C71 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 134 | C4×C71 | #578 | 1 | 2 | yes | — |
| 135 | Dic71 | — | 8 | 4 | no | — |
| 136 | Dic71 | — | 8 | 2 | no | — |
| 137 | Dic71 | — | 8 | 2 | no | — |
| 138 | #19632 | — | 71 | 1 | no | maximal, Sylow |
| 139 | C2×C71 | — | 2 | 2 | no | — |
| 140 | C2×C71 | C2×#494 | 1 | 1 | yes | characteristic |
| 141 | C2×C71 | #3151 | 1 | 1 | yes | characteristic |
| 142 | C2×C71 | #3156 | 1 | 1 | yes | characteristic |
| 143 | #3230 | — | 71 | 2 | no | — |
| 144 | #3170 | — | 71 | 1 | no | — |
| 145 | #3165 | — | 71 | 2 | no | — |
| 146 | C2×#494 | — | 71 | 1 | no | — |
| 147 | #1723 | — | 71 | 4 | no | — |
| 148 | #1713 | — | 71 | 2 | no | — |
| 149 | #1707 | — | 71 | 2 | no | — |
| 150 | C8×M16 | D71 | 1 | 1 | yes | characteristic |
| 151 | C71 | #19632 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 152 | C22×Q16 | — | 142 | 2 | no | — |
| 153 | #533 | — | 71 | 2 | no | — |
| 154 | C2×C4⋊Q8 | — | 71 | 2 | no | — |
| 155 | #501 | — | 142 | 4 | no | — |
| 156 | #500 | — | 71 | 4 | no | — |
| 157 | #500 | — | 71 | 1 | no | — |
| 158 | #500 | — | 71 | 4 | no | — |
| 159 | #498 | — | 71 | 4 | no | — |
| 160 | #494 | — | 71 | 2 | no | — |
| 161 | #494 | — | 71 | 2 | no | — |
| 162 | #494 | — | 71 | 1 | no | — |
| 163 | #494 | — | 142 | 2 | no | — |
| 164 | #487 | — | 71 | 2 | no | — |
| 165 | #487 | — | 71 | 4 | no | — |
| 166 | #484 | — | 142 | 4 | no | — |
| 167 | #477 | — | 142 | 4 | no | — |
| 168 | #467 | — | 142 | 2 | no | — |
| 169 | C4×Q16 | — | 142 | 2 | no | — |
| 170 | #431 | C2×D71 | 1 | 1 | yes | characteristic |
| 171 | #428 | — | 142 | 4 | no | — |
| 172 | C4×M16 | C2×D71 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C8 | C2×D71 | 1 | 1 | yes | characteristic |
| 174 | #322 | C2×D71 | 1 | 2 | yes | — |
| 175 | C82 | C2×D71 | 1 | 2 | yes | — |
| 176 | C22×Q8 | — | 142 | 2 | no | — |
| 177 | C2×Q16 | — | 284 | 8 | no | — |
| 178 | C2×Q16 | — | 142 | 4 | no | — |
| 179 | C2×Q16 | — | 142 | 4 | no | — |
| 180 | C2×Q16 | — | 142 | 2 | no | — |
| 181 | C2×M16 | D284 | 1 | 2 | yes | — |
| 182 | C22×C8 | D284 | 1 | 2 | yes | — |
| 183 | C4⋊Q8 | — | 71 | 4 | no | — |
| 184 | C4⋊Q8 | — | 71 | 2 | no | — |
| 185 | C4⋊Q8 | — | 71 | 2 | no | — |
| 186 | C4⋊Q8 | — | 142 | 2 | no | — |
| 187 | C4⋊Q8 | — | 142 | 2 | no | — |
| 188 | C4⋊Q8 | — | 142 | 2 | no | — |
| 189 | #125 | — | 142 | 2 | no | — |
| 190 | C22⋊Q8 | — | 142 | 2 | no | — |
| 191 | C22⋊Q8 | — | 142 | 2 | no | — |
| 192 | C4×Q8 | — | 142 | 2 | no | — |
| 193 | C4×Q8 | — | 142 | 2 | no | — |
| 194 | #117 | — | 142 | 2 | no | — |
| 195 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 196 | C2×C4⋊C4 | — | 142 | 2 | no | — |
| 197 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 198 | #107 | — | 142 | 8 | no | — |
| 199 | #107 | — | 142 | 2 | no | — |
| 200 | #107 | — | 142 | 8 | no | — |
| 201 | #106 | — | 142 | 8 | no | — |
| 202 | C4⋊C8 | D284 | 1 | 2 | yes | — |
| 203 | #103 | — | 142 | 4 | no | — |
| 204 | #103 | — | 142 | 8 | no | — |
| 205 | C22⋊C8 | D284 | 1 | 2 | yes | — |
| 206 | #97 | D284 | 1 | 2 | yes | — |
| 207 | C4×C8 | D284 | 1 | 2 | yes | — |
| 208 | C4×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 209 | C4×C8 | C22×D71 | 1 | 2 | yes | — |
| 210 | C4×C8 | C22×D71 | 1 | 2 | yes | — |
| 211 | C4×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 212 | C2×Q8 | — | 284 | 8 | no | — |
| 213 | C2×Q8 | — | 284 | 2 | no | — |
| 214 | C2×Q8 | — | 142 | 2 | no | — |
| 215 | C2×Q8 | — | 142 | 2 | no | — |
| 216 | C2×Q8 | — | 142 | 4 | no | — |
| 217 | C22×C4 | — | 284 | 2 | no | — |
| 218 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 219 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 220 | C22×C4 | C2×D284 | 1 | 1 | yes | characteristic |
| 221 | Q16 | — | 284 | 8 | no | — |
| 222 | Q16 | — | 284 | 8 | no | — |
| 223 | Q16 | — | 284 | 4 | no | — |
| 224 | M16 | Dic284 | 1 | 8 | yes | complemented |
| 225 | C2×C8 | — | 2 | 4 | no | — |
| 226 | C2×C8 | C2×D284 | 1 | 2 | yes | — |
| 227 | C2×C8 | C2×D284 | 1 | 4 | yes | — |
| 228 | C2×C8 | C2×D284 | 1 | 4 | yes | — |
| 229 | C2×C8 | C2×D284 | 1 | 2 | yes | — |
| 230 | C4⋊C4 | — | 284 | 2 | no | — |
| 231 | C4⋊C4 | — | 284 | 2 | no | — |
| 232 | C4⋊C4 | — | 284 | 2 | no | — |
| 233 | C4⋊C4 | — | 284 | 2 | no | — |
| 234 | C4⋊C4 | — | 142 | 4 | no | — |
| 235 | C4⋊C4 | — | 142 | 2 | no | — |
| 236 | C4⋊C4 | — | 142 | 2 | no | — |
| 237 | C4⋊C4 | — | 142 | 4 | no | — |
| 238 | C4⋊C4 | — | 142 | 2 | no | — |
| 239 | C4⋊C4 | — | 142 | 2 | no | — |
| 240 | C22⋊C4 | — | 284 | 2 | no | — |
| 241 | C42 | — | 284 | 2 | no | — |
| 242 | C42 | C2×D284 | 1 | 1 | yes | characteristic |
| 243 | C42 | C2×D284 | 1 | 1 | yes | characteristic |
| 244 | C42 | C2×D284 | 1 | 1 | yes | characteristic |
| 245 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 246 | C23 | #14556125 | 1 | 1 | yes | characteristic |
| 247 | Q8 | — | 284 | 4 | no | — |
| 248 | Q8 | — | 284 | 8 | no | — |
| 249 | Q8 | — | 284 | 4 | no | — |
| 250 | Q8 | — | 568 | 4 | no | — |
| 251 | C2×C4 | — | 2 | 2 | no | — |
| 252 | C2×C4 | — | 2 | 2 | no | — |
| 253 | C2×C4 | — | 284 | 2 | no | — |
| 254 | C2×C4 | — | 284 | 2 | no | — |
| 255 | C2×C4 | — | 284 | 4 | no | — |
| 256 | C2×C4 | — | 568 | 4 | no | — |
| 257 | C2×C4 | #14556125 | 1 | 1 | yes | characteristic |
| 258 | C2×C4 | #14556125 | 1 | 1 | yes | characteristic |
| 259 | C2×C4 | #14556125 | 1 | 1 | yes | characteristic |
| 260 | C2×C4 | C2×Dic284 | 1 | 4 | yes | — |
| 261 | C2×C4 | C22×D284 | 1 | 1 | yes | characteristic |
| 262 | C2×C4 | C22×D284 | 1 | 1 | yes | characteristic |
| 263 | C2×C4 | C22×D284 | 1 | 1 | yes | characteristic |
| 264 | C8 | — | 2 | 4 | no | — |
| 265 | C8 | — | 2 | 2 | no | — |
| 266 | C8 | C2×Dic284 | 1 | 8 | yes | complemented |
| 267 | C8 | #14556156 | 1 | 4 | yes | — |
| 268 | C22 | — | 2 | 1 | no | — |
| 269 | C22 | — | 2 | 1 | no | — |
| 270 | C22 | #17986379 | 1 | 2 | yes | — |
| 271 | C22 | C2×#14556125 | 1 | 1 | yes | characteristic |
| 272 | C4 | — | 2 | 1 | no | — |
| 273 | C4 | — | 2 | 1 | no | — |
| 274 | C4 | — | 568 | 4 | no | — |
| 275 | C4 | — | 568 | 2 | no | — |
| 276 | C4 | — | 568 | 2 | no | — |
| 277 | C4 | #17986379 | 1 | 2 | yes | — |
| 278 | C4 | C22×Dic284 | 1 | 2 | yes | — |
| 279 | C4 | C2×#14556156 | 1 | 2 | yes | — |
| 280 | C4 | #17986816 | 1 | 2 | yes | — |
| 281 | C2 | — | 2 | 2 | no | — |
| 282 | C2 | C2×#17986379 | 1 | 1 | yes | characteristic |
| 283 | C2 | #22598792 | 1 | 1 | yes | characteristic |
| 284 | C2 | #22598834 | 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