← #36707798
Subgroups — #36707798
Order 22784.
682 conjugacy classes of subgroups.
The subgroup lattice has 302 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #26029120 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #26029104 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #26022117 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | SD32×Dic89 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #26022036 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #26021972 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #26021968 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #26021848 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C22×SD32×C89 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #19152076 | — | 2 | 1 | no | — |
| 11 | #19152073 | — | 2 | 1 | no | — |
| 12 | C2×#15667952 | C22 | 1 | 1 | yes | characteristic |
| 13 | #19151710 | — | 2 | 2 | no | — |
| 14 | #19151705 | — | 2 | 2 | no | — |
| 15 | Q16×Dic89 | C22 | 1 | 4 | yes | complemented |
| 16 | D8×Dic89 | C22 | 1 | 4 | yes | — |
| 17 | #19151636 | C22 | 1 | 1 | yes | characteristic |
| 18 | #19151636 | C22 | 1 | 1 | yes | characteristic |
| 19 | #19151607 | — | 2 | 1 | no | — |
| 20 | #19151603 | — | 2 | 1 | no | — |
| 21 | #19151553 | C22 | 1 | 1 | yes | characteristic |
| 22 | #19151426 | C22 | 1 | 2 | yes | complemented |
| 23 | #19151424 | C22 | 1 | 2 | yes | complemented |
| 24 | #19151402 | C22 | 1 | 4 | yes | complemented |
| 25 | #19151399 | C22 | 1 | 4 | yes | — |
| 26 | #19151373 | C22 | 1 | 2 | yes | complemented |
| 27 | C16×Dic89 | C22 | 1 | 2 | yes | complemented |
| 28 | C22×Q16×C89 | C22 | 1 | 1 | yes | characteristic |
| 29 | C22×D8×C89 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×SD32×C89 | C4 | 1 | 8 | yes | complemented |
| 31 | C2×SD32×C89 | C22 | 1 | 2 | yes | — |
| 32 | C2×SD32×C89 | C22 | 1 | 2 | yes | — |
| 33 | C22×C16×C89 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#13083558 | D4 | 1 | 1 | yes | characteristic |
| 35 | Q8×Dic89 | — | 2 | 4 | no | — |
| 36 | Q8×Dic89 | — | 4 | 2 | no | — |
| 37 | D4×Dic89 | — | 2 | 4 | no | — |
| 38 | D4×Dic89 | — | 4 | 2 | no | — |
| 39 | #15667971 | — | 2 | 1 | no | — |
| 40 | #15667971 | — | 2 | 1 | no | — |
| 41 | #15667971 | — | 4 | 2 | no | — |
| 42 | #15667971 | D4 | 1 | 1 | yes | characteristic |
| 43 | C2×C22⋊Dic89 | — | 4 | 2 | no | — |
| 44 | #15667952 | — | 2 | 2 | no | — |
| 45 | C2×#13083549 | C23 | 1 | 2 | yes | — |
| 46 | #15667946 | C23 | 1 | 2 | yes | — |
| 47 | #15667946 | C23 | 1 | 2 | yes | — |
| 48 | #15667944 | — | 2 | 1 | no | — |
| 49 | #15667944 | — | 2 | 1 | no | — |
| 50 | #15667936 | — | 2 | 4 | no | — |
| 51 | #15667933 | — | 2 | 4 | no | — |
| 52 | #15667922 | D4 | 1 | 2 | yes | — |
| 53 | C8×Dic89 | C23 | 1 | 2 | yes | — |
| 54 | C22×Q8×C89 | — | 2 | 1 | no | — |
| 55 | C22×D4×C89 | — | 2 | 1 | no | — |
| 56 | C2×Q16×C89 | — | 2 | 1 | no | — |
| 57 | C2×Q16×C89 | — | 2 | 2 | no | — |
| 58 | C2×Q16×C89 | C2×C4 | 1 | 4 | yes | complemented |
| 59 | C2×Q16×C89 | C23 | 1 | 2 | yes | — |
| 60 | C2×D8×C89 | — | 2 | 1 | no | — |
| 61 | C2×D8×C89 | — | 2 | 2 | no | — |
| 62 | C2×D8×C89 | C2×C4 | 1 | 4 | yes | — |
| 63 | C2×D8×C89 | C23 | 1 | 2 | yes | — |
| 64 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 65 | SD32×C89 | C2×C4 | 1 | 8 | yes | complemented |
| 66 | SD32×C89 | C2×C4 | 1 | 8 | yes | complemented |
| 67 | C2×C16×C89 | C2×C4 | 1 | 4 | yes | complemented |
| 68 | C2×C16×C89 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C16×C89 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×Dic89 | — | 4 | 4 | no | — |
| 71 | #13083558 | — | 2 | 2 | no | — |
| 72 | C2×#10623494 | C2×D4 | 1 | 2 | yes | — |
| 73 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 74 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 75 | C4⋊Dic89 | — | 4 | 4 | no | — |
| 76 | C4⋊Dic89 | D8 | 1 | 2 | yes | — |
| 77 | C22⋊Dic89 | — | 4 | 1 | no | — |
| 78 | C22⋊Dic89 | — | 4 | 1 | no | — |
| 79 | C22⋊Dic89 | — | 4 | 4 | no | — |
| 80 | C22⋊Dic89 | D8 | 1 | 2 | yes | — |
| 81 | C4×Dic89 | — | 4 | 1 | no | — |
| 82 | C4×Dic89 | — | 4 | 1 | no | — |
| 83 | C4×Dic89 | — | 4 | 4 | no | — |
| 84 | C4×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 85 | #13083549 | — | 2 | 2 | no | — |
| 86 | C24×C89 | — | 4 | 1 | no | — |
| 87 | C2×Q8×C89 | — | 2 | 4 | no | — |
| 88 | C2×Q8×C89 | — | 2 | 2 | no | — |
| 89 | C2×Q8×C89 | — | 4 | 1 | no | — |
| 90 | C2×Q8×C89 | — | 4 | 2 | no | — |
| 91 | C2×D4×C89 | — | 2 | 4 | no | — |
| 92 | C2×D4×C89 | — | 2 | 2 | no | — |
| 93 | C2×D4×C89 | — | 4 | 1 | no | — |
| 94 | C2×D4×C89 | — | 4 | 2 | no | — |
| 95 | C22×C4×C89 | — | 4 | 1 | no | — |
| 96 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | Q16×C89 | — | 2 | 4 | no | — |
| 98 | Q16×C89 | — | 2 | 2 | no | — |
| 99 | Q16×C89 | C22×C4 | 1 | 4 | yes | — |
| 100 | D8×C89 | — | 2 | 4 | no | — |
| 101 | D8×C89 | — | 2 | 2 | no | — |
| 102 | D8×C89 | C22×C4 | 1 | 4 | yes | — |
| 103 | C2×C8×C89 | C22×C4 | 1 | 2 | yes | — |
| 104 | C2×C8×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C8×C89 | #41 | 1 | 2 | yes | — |
| 106 | C2×C8×C89 | C24 | 1 | 1 | yes | characteristic |
| 107 | C16×C89 | C22×C4 | 1 | 2 | yes | — |
| 108 | C16×C89 | C22×C4 | 1 | 2 | yes | — |
| 109 | C23×C89 | — | 4 | 2 | no | — |
| 110 | C23×C89 | — | 4 | 4 | no | — |
| 111 | C23×C89 | — | 16 | 2 | no | — |
| 112 | C23×C89 | C2×D8 | 1 | 1 | yes | characteristic |
| 113 | Q8×C89 | — | 2 | 4 | no | — |
| 114 | Q8×C89 | — | 4 | 2 | no | — |
| 115 | Q8×C89 | — | 4 | 4 | no | — |
| 116 | D4×C89 | — | 2 | 4 | no | — |
| 117 | D4×C89 | — | 4 | 2 | no | — |
| 118 | D4×C89 | — | 4 | 4 | no | — |
| 119 | C2×C4×C89 | — | 4 | 2 | no | — |
| 120 | C2×C4×C89 | — | 4 | 4 | no | — |
| 121 | C2×C4×C89 | C4×D4 | 1 | 2 | yes | — |
| 122 | C2×C4×C89 | C2×D8 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×C89 | #135 | 1 | 2 | yes | — |
| 124 | C2×C4×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×Dic89 | — | 4 | 2 | no | — |
| 126 | C2×Dic89 | — | 4 | 2 | no | — |
| 127 | C2×Dic89 | — | 16 | 4 | no | — |
| 128 | C2×Dic89 | C2×D8 | 1 | 4 | yes | — |
| 129 | C8×C89 | C4×D4 | 1 | 2 | yes | — |
| 130 | C8×C89 | C23×C4 | 1 | 1 | yes | characteristic |
| 131 | C8×C89 | C2×#41 | 1 | 1 | yes | characteristic |
| 132 | #10623494 | — | 2 | 2 | no | — |
| 133 | C22×C89 | — | 2 | 2 | no | — |
| 134 | C22×C89 | — | 4 | 4 | no | — |
| 135 | C22×C89 | — | 8 | 4 | no | — |
| 136 | C22×C89 | — | 16 | 4 | no | — |
| 137 | C22×C89 | C4×D8 | 1 | 2 | yes | — |
| 138 | C22×C89 | C22×D8 | 1 | 1 | yes | characteristic |
| 139 | C4×C89 | — | 4 | 4 | no | — |
| 140 | C4×C89 | C4×D8 | 1 | 2 | yes | — |
| 141 | C4×C89 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 142 | C4×C89 | C2×#135 | 1 | 1 | yes | characteristic |
| 143 | Dic89 | — | 2 | 4 | no | — |
| 144 | Dic89 | — | 8 | 2 | no | — |
| 145 | Dic89 | — | 8 | 2 | no | — |
| 146 | #33457 | — | 89 | 1 | no | maximal, Sylow |
| 147 | C2×C89 | — | 2 | 2 | no | — |
| 148 | C2×C89 | — | 8 | 4 | no | — |
| 149 | C2×C89 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 150 | C2×C89 | #3416 | 1 | 2 | yes | — |
| 151 | C22×SD32 | D89 | 1 | 1 | yes | characteristic |
| 152 | #2950 | — | 89 | 1 | no | — |
| 153 | #2948 | — | 89 | 1 | no | — |
| 154 | #2175 | — | 89 | 4 | no | — |
| 155 | C4×SD32 | — | 89 | 4 | no | — |
| 156 | #2158 | — | 89 | 1 | no | — |
| 157 | #2141 | — | 89 | 1 | no | — |
| 158 | #2140 | — | 89 | 1 | no | — |
| 159 | #2108 | — | 89 | 1 | no | — |
| 160 | C89 | #33457 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 161 | C22×Q16 | C2×D89 | 1 | 1 | yes | characteristic |
| 162 | C22×D8 | C2×D89 | 1 | 1 | yes | characteristic |
| 163 | #519 | — | 178 | 1 | no | — |
| 164 | #518 | — | 178 | 1 | no | — |
| 165 | C2×SD32 | Dic89 | 1 | 8 | yes | complemented |
| 166 | C2×SD32 | C2×D89 | 1 | 2 | yes | — |
| 167 | C2×SD32 | C2×D89 | 1 | 2 | yes | — |
| 168 | C2×M32 | — | 89 | 1 | no | — |
| 169 | C22×C16 | C2×D89 | 1 | 1 | yes | characteristic |
| 170 | #442 | — | 178 | 2 | no | — |
| 171 | #441 | — | 178 | 2 | no | — |
| 172 | C4×Q16 | — | 89 | 4 | no | — |
| 173 | C4×D8 | — | 89 | 4 | no | — |
| 174 | #427 | — | 89 | 1 | no | — |
| 175 | #427 | — | 89 | 1 | no | — |
| 176 | #419 | — | 178 | 1 | no | — |
| 177 | #418 | — | 178 | 1 | no | — |
| 178 | #405 | — | 89 | 1 | no | — |
| 179 | #367 | — | 89 | 2 | no | — |
| 180 | #366 | — | 89 | 2 | no | — |
| 181 | #358 | — | 89 | 4 | no | — |
| 182 | #357 | — | 89 | 4 | no | — |
| 183 | #346 | — | 89 | 2 | no | — |
| 184 | C4×C16 | — | 89 | 2 | no | — |
| 185 | C22×Q8 | — | 2 | 1 | no | — |
| 186 | C22×D4 | — | 2 | 1 | no | — |
| 187 | C2×Q16 | — | 2 | 1 | no | — |
| 188 | C2×Q16 | — | 2 | 2 | no | — |
| 189 | C2×Q16 | C2×Dic89 | 1 | 4 | yes | complemented |
| 190 | C2×Q16 | C22×D89 | 1 | 2 | yes | — |
| 191 | C2×D8 | — | 2 | 1 | no | — |
| 192 | C2×D8 | — | 2 | 2 | no | — |
| 193 | C2×D8 | C2×Dic89 | 1 | 4 | yes | — |
| 194 | C2×D8 | C22×D89 | 1 | 2 | yes | — |
| 195 | C2×M16 | — | 89 | 1 | no | — |
| 196 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 197 | C4×Q8 | — | 356 | 2 | no | — |
| 198 | C4×Q8 | — | 178 | 4 | no | — |
| 199 | C4×D4 | — | 356 | 2 | no | — |
| 200 | C4×D4 | — | 178 | 4 | no | — |
| 201 | #117 | — | 89 | 1 | no | — |
| 202 | #117 | — | 356 | 2 | no | — |
| 203 | #117 | — | 178 | 1 | no | — |
| 204 | #117 | — | 178 | 1 | no | — |
| 205 | C2×C22⋊C4 | — | 356 | 2 | no | — |
| 206 | SD32 | C2×Dic89 | 1 | 8 | yes | complemented |
| 207 | SD32 | C2×Dic89 | 1 | 8 | yes | complemented |
| 208 | M32 | — | 178 | 2 | no | — |
| 209 | C2×C16 | — | 89 | 2 | no | — |
| 210 | C2×C16 | C2×Dic89 | 1 | 4 | yes | complemented |
| 211 | C2×C16 | C22×D89 | 1 | 1 | yes | characteristic |
| 212 | C2×C16 | C22×D89 | 1 | 1 | yes | characteristic |
| 213 | #107 | — | 89 | 2 | no | — |
| 214 | #107 | — | 89 | 2 | no | — |
| 215 | #106 | — | 178 | 1 | no | — |
| 216 | #106 | — | 178 | 1 | no | — |
| 217 | #103 | — | 178 | 4 | no | — |
| 218 | #102 | — | 178 | 4 | no | — |
| 219 | #97 | — | 89 | 2 | no | — |
| 220 | C4×C8 | — | 89 | 2 | no | — |
| 221 | C24 | — | 4 | 1 | no | — |
| 222 | C2×Q8 | — | 2 | 4 | no | — |
| 223 | C2×Q8 | — | 2 | 2 | no | — |
| 224 | C2×Q8 | — | 4 | 1 | no | — |
| 225 | C2×Q8 | — | 4 | 2 | no | — |
| 226 | C2×D4 | — | 2 | 4 | no | — |
| 227 | C2×D4 | — | 2 | 2 | no | — |
| 228 | C2×D4 | — | 4 | 1 | no | — |
| 229 | C2×D4 | — | 4 | 2 | no | — |
| 230 | C22×C4 | — | 4 | 1 | no | — |
| 231 | C22×C4 | — | 356 | 4 | no | — |
| 232 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 233 | Q16 | — | 2 | 4 | no | — |
| 234 | Q16 | — | 2 | 2 | no | — |
| 235 | Q16 | C22×Dic89 | 1 | 4 | yes | — |
| 236 | D8 | — | 2 | 4 | no | — |
| 237 | D8 | — | 2 | 2 | no | — |
| 238 | D8 | C22×Dic89 | 1 | 4 | yes | — |
| 239 | M16 | — | 178 | 2 | no | — |
| 240 | C2×C8 | — | 89 | 2 | no | — |
| 241 | C2×C8 | C22×Dic89 | 1 | 2 | yes | — |
| 242 | C2×C8 | D4×D89 | 1 | 1 | yes | characteristic |
| 243 | C2×C8 | #13083573 | 1 | 2 | yes | — |
| 244 | C2×C8 | C23×D89 | 1 | 1 | yes | characteristic |
| 245 | C4⋊C4 | — | 89 | 2 | no | — |
| 246 | C4⋊C4 | — | 356 | 4 | no | — |
| 247 | C4⋊C4 | — | 178 | 2 | no | — |
| 248 | C4⋊C4 | — | 178 | 2 | no | — |
| 249 | C22⋊C4 | — | 89 | 2 | no | — |
| 250 | C22⋊C4 | — | 356 | 4 | no | — |
| 251 | C22⋊C4 | — | 356 | 1 | no | — |
| 252 | C22⋊C4 | — | 356 | 1 | no | — |
| 253 | C42 | — | 89 | 2 | no | — |
| 254 | C42 | — | 356 | 4 | no | — |
| 255 | C42 | — | 356 | 1 | no | — |
| 256 | C42 | — | 356 | 1 | no | — |
| 257 | C16 | — | 178 | 2 | no | — |
| 258 | C16 | C22×Dic89 | 1 | 2 | yes | — |
| 259 | C16 | C22×Dic89 | 1 | 2 | yes | — |
| 260 | C23 | — | 4 | 2 | no | — |
| 261 | C23 | — | 4 | 4 | no | — |
| 262 | C23 | — | 16 | 2 | no | — |
| 263 | C23 | D8×D89 | 1 | 1 | yes | characteristic |
| 264 | Q8 | — | 2 | 4 | no | — |
| 265 | Q8 | — | 4 | 4 | no | — |
| 266 | Q8 | — | 4 | 2 | no | — |
| 267 | D4 | — | 2 | 4 | no | — |
| 268 | D4 | — | 4 | 4 | no | — |
| 269 | D4 | — | 4 | 2 | no | — |
| 270 | C2×C4 | — | 4 | 4 | no | — |
| 271 | C2×C4 | — | 4 | 2 | no | — |
| 272 | C2×C4 | — | 89 | 4 | no | — |
| 273 | C2×C4 | — | 356 | 2 | no | — |
| 274 | C2×C4 | — | 356 | 2 | no | — |
| 275 | C2×C4 | — | 1424 | 4 | no | — |
| 276 | C2×C4 | D4×Dic89 | 1 | 2 | yes | — |
| 277 | C2×C4 | D8×D89 | 1 | 1 | yes | characteristic |
| 278 | C2×C4 | #15668031 | 1 | 2 | yes | — |
| 279 | C2×C4 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 280 | C8 | — | 178 | 2 | no | — |
| 281 | C8 | D4×Dic89 | 1 | 2 | yes | — |
| 282 | C8 | C23×Dic89 | 1 | 1 | yes | characteristic |
| 283 | C8 | C2×#13083573 | 1 | 1 | yes | characteristic |
| 284 | C22 | — | 2 | 2 | no | — |
| 285 | C22 | — | 4 | 4 | no | — |
| 286 | C22 | — | 8 | 4 | no | — |
| 287 | C22 | — | 16 | 4 | no | — |
| 288 | C22 | D8×Dic89 | 1 | 2 | yes | — |
| 289 | C22 | C2×D8×D89 | 1 | 1 | yes | characteristic |
| 290 | C4 | — | 4 | 4 | no | — |
| 291 | C4 | — | 178 | 4 | no | — |
| 292 | C4 | — | 712 | 2 | no | — |
| 293 | C4 | — | 712 | 2 | no | — |
| 294 | C4 | D8×Dic89 | 1 | 2 | yes | — |
| 295 | C4 | C2×D4×Dic89 | 1 | 1 | yes | characteristic |
| 296 | C4 | C2×#15668031 | 1 | 1 | yes | characteristic |
| 297 | C2 | — | 2 | 2 | no | — |
| 298 | C2 | — | 8 | 4 | no | — |
| 299 | C2 | C2×D8×Dic89 | 1 | 1 | yes | characteristic |
| 300 | C2 | #26033394 | 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