← #33241200
Subgroups — #33241200
Order 18688.
544 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22620581 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22618800 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22612123 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22612096 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22611972 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22611850 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22611797 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C4×#14556536 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C73×#2164 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C22×Dic292 | C22 | 1 | 1 | yes | characteristic |
| 11 | #17989192 | — | 2 | 1 | no | — |
| 12 | #17989064 | — | 2 | 1 | no | — |
| 13 | C2×#14556536 | C22 | 1 | 2 | yes | — |
| 14 | C2×#14556536 | C22 | 1 | 2 | yes | — |
| 15 | #17988989 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17988964 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17988952 | — | 2 | 1 | no | — |
| 18 | #17988840 | — | 2 | 1 | no | — |
| 19 | #17988823 | C22 | 1 | 2 | yes | — |
| 20 | #17988700 | — | 2 | 1 | no | — |
| 21 | #17988695 | — | 2 | 1 | no | — |
| 22 | #17988695 | — | 2 | 1 | no | — |
| 23 | C4×Dic292 | C22 | 1 | 2 | yes | — |
| 24 | C4×Dic292 | C22 | 1 | 2 | yes | — |
| 25 | C4×D584 | C22 | 1 | 2 | yes | — |
| 26 | #17988625 | C22 | 1 | 1 | yes | characteristic |
| 27 | #17988597 | — | 2 | 1 | no | — |
| 28 | #17988415 | C22 | 1 | 2 | yes | — |
| 29 | #17988413 | C22 | 1 | 2 | yes | — |
| 30 | #17988392 | C22 | 1 | 2 | yes | — |
| 31 | #17988392 | C22 | 1 | 2 | yes | — |
| 32 | #17988389 | C22 | 1 | 2 | yes | — |
| 33 | #17988389 | C22 | 1 | 2 | yes | — |
| 34 | #405×C73 | C22 | 1 | 1 | yes | characteristic |
| 35 | C4⋊C16×C73 | C22 | 1 | 2 | yes | — |
| 36 | C22⋊C16×C73 | C22 | 1 | 2 | yes | — |
| 37 | #346×C73 | C22 | 1 | 1 | yes | characteristic |
| 38 | C4×C16×C73 | C22 | 1 | 1 | yes | characteristic |
| 39 | C22×Dic146 | — | 2 | 1 | no | — |
| 40 | C2×Dic292 | — | 2 | 4 | no | — |
| 41 | C2×Dic292 | — | 2 | 1 | no | — |
| 42 | C2×Dic292 | C23 | 1 | 2 | yes | — |
| 43 | C2×D584 | — | 2 | 1 | no | — |
| 44 | C2×D584 | C23 | 1 | 2 | yes | — |
| 45 | #14556588 | — | 2 | 1 | no | — |
| 46 | #14556583 | — | 2 | 1 | no | — |
| 47 | #14556576 | — | 4 | 2 | no | — |
| 48 | #14556565 | — | 2 | 2 | no | — |
| 49 | #14556564 | — | 4 | 2 | no | — |
| 50 | C4×Dic146 | — | 2 | 2 | no | — |
| 51 | C4×Dic146 | — | 2 | 2 | no | — |
| 52 | #14556556 | — | 4 | 2 | no | — |
| 53 | C4×D292 | — | 2 | 2 | no | — |
| 54 | #14556550 | — | 2 | 1 | no | — |
| 55 | #14556547 | — | 4 | 2 | no | — |
| 56 | #14556536 | — | 2 | 4 | no | — |
| 57 | #14556536 | — | 2 | 4 | no | — |
| 58 | #14556525 | C23 | 1 | 2 | yes | — |
| 59 | #14556525 | C23 | 1 | 2 | yes | — |
| 60 | #14556523 | — | 2 | 1 | no | — |
| 61 | #14556523 | — | 2 | 1 | no | — |
| 62 | #14556516 | — | 2 | 2 | no | — |
| 63 | #14556516 | — | 2 | 2 | no | — |
| 64 | #14556513 | — | 2 | 2 | no | — |
| 65 | #14556513 | — | 2 | 2 | no | — |
| 66 | C2×M16×C73 | D4 | 1 | 1 | yes | characteristic |
| 67 | C22×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 68 | #117×C73 | D4 | 1 | 1 | yes | characteristic |
| 69 | C2×C16×C73 | C23 | 1 | 2 | yes | — |
| 70 | C2×C16×C73 | C23 | 1 | 2 | yes | — |
| 71 | #97×C73 | D4 | 1 | 1 | yes | characteristic |
| 72 | #97×C73 | D4 | 1 | 1 | yes | characteristic |
| 73 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×Dic146 | — | 2 | 4 | no | — |
| 76 | C2×Dic146 | — | 2 | 2 | no | — |
| 77 | C2×Dic146 | — | 4 | 2 | no | — |
| 78 | C2×Dic146 | — | 4 | 1 | no | — |
| 79 | C2×D292 | — | 2 | 2 | no | — |
| 80 | C2×D292 | — | 4 | 2 | no | — |
| 81 | C2×C22⋊D73 | — | 4 | 2 | no | — |
| 82 | C22×Dic73 | — | 4 | 1 | no | — |
| 83 | C2×C4×D73 | — | 4 | 2 | no | — |
| 84 | Dic292 | — | 2 | 4 | no | — |
| 85 | Dic292 | — | 2 | 2 | no | — |
| 86 | Dic292 | #41 | 1 | 4 | yes | — |
| 87 | D584 | — | 2 | 2 | no | — |
| 88 | D584 | — | 2 | 2 | no | — |
| 89 | D584 | — | 4 | 2 | no | — |
| 90 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 91 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 92 | #11924007 | — | 4 | 2 | no | — |
| 93 | #11924007 | — | 4 | 2 | no | — |
| 94 | #11924007 | — | 4 | 2 | no | — |
| 95 | C22⋊Dic73 | — | 4 | 1 | no | — |
| 96 | #11924005 | — | 4 | 2 | no | — |
| 97 | #11924005 | — | 4 | 2 | no | — |
| 98 | C4×Dic73 | — | 4 | 2 | no | — |
| 99 | C4×Dic73 | — | 4 | 2 | no | — |
| 100 | C4×Dic73 | — | 4 | 1 | no | — |
| 101 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | M16×C73 | — | 4 | 1 | no | — |
| 103 | C2×C8×C73 | — | 2 | 2 | no | — |
| 104 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C2×C8×C73 | C24 | 1 | 1 | yes | characteristic |
| 108 | C4⋊C4×C73 | D8 | 1 | 2 | yes | — |
| 109 | C22⋊C4×C73 | D8 | 1 | 2 | yes | — |
| 110 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C16×C73 | — | 2 | 2 | no | — |
| 113 | C16×C73 | — | 2 | 2 | no | — |
| 114 | C23×C73 | C2×D8 | 1 | 1 | yes | characteristic |
| 115 | C22×D73 | — | 4 | 2 | no | — |
| 116 | C2×C4×C73 | — | 2 | 1 | no | — |
| 117 | C2×C4×C73 | — | 2 | 1 | no | — |
| 118 | C2×C4×C73 | C2×D8 | 1 | 2 | yes | — |
| 119 | C2×C4×C73 | C2×D8 | 1 | 2 | yes | — |
| 120 | C2×C4×C73 | C2×D8 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 122 | C22⋊D73 | — | 16 | 2 | no | — |
| 123 | C2×Dic73 | — | 4 | 4 | no | — |
| 124 | C2×Dic73 | — | 4 | 2 | no | — |
| 125 | C2×Dic73 | — | 4 | 2 | no | — |
| 126 | C2×Dic73 | — | 4 | 2 | no | — |
| 127 | D292 | — | 4 | 2 | no | — |
| 128 | D292 | — | 4 | 2 | no | — |
| 129 | D292 | — | 16 | 2 | no | — |
| 130 | C4×D73 | — | 16 | 2 | no | — |
| 131 | Dic146 | — | 2 | 4 | no | — |
| 132 | Dic146 | — | 4 | 4 | no | — |
| 133 | Dic146 | — | 4 | 2 | no | — |
| 134 | C8×C73 | — | 2 | 1 | no | — |
| 135 | C8×C73 | — | 2 | 1 | no | — |
| 136 | C8×C73 | — | 2 | 1 | no | — |
| 137 | C8×C73 | C2×#41 | 1 | 2 | yes | — |
| 138 | C22×C73 | — | 2 | 1 | no | — |
| 139 | C22×C73 | — | 2 | 2 | no | — |
| 140 | C22×C73 | C22×D8 | 1 | 1 | yes | characteristic |
| 141 | C2×D73 | — | 8 | 2 | no | — |
| 142 | C2×D73 | — | 8 | 2 | no | — |
| 143 | C2×D73 | — | 8 | 2 | no | — |
| 144 | C4×C73 | — | 2 | 1 | no | — |
| 145 | C4×C73 | — | 2 | 2 | no | — |
| 146 | C4×C73 | — | 2 | 2 | no | — |
| 147 | C4×C73 | #525 | 1 | 1 | yes | characteristic |
| 148 | C4×C73 | #575 | 1 | 1 | yes | characteristic |
| 149 | Dic73 | — | 4 | 4 | no | — |
| 150 | Dic73 | — | 8 | 2 | no | — |
| 151 | Dic73 | — | 8 | 2 | no | — |
| 152 | #33686 | — | 73 | 1 | no | maximal, Sylow |
| 153 | C2×C73 | — | 4 | 1 | no | — |
| 154 | C2×C73 | #3100 | 1 | 1 | yes | characteristic |
| 155 | C2×C73 | #3416 | 1 | 2 | yes | — |
| 156 | D73 | — | 16 | 2 | no | — |
| 157 | #3176 | — | 73 | 1 | no | — |
| 158 | #2950 | — | 73 | 1 | no | — |
| 159 | #2234 | — | 73 | 2 | no | — |
| 160 | #2229 | — | 73 | 2 | no | — |
| 161 | #2207 | — | 73 | 2 | no | — |
| 162 | #2185 | — | 73 | 2 | no | — |
| 163 | #2175 | — | 73 | 2 | no | — |
| 164 | C4×SD32 | — | 73 | 2 | no | — |
| 165 | #2164 | D73 | 1 | 1 | yes | characteristic, complemented |
| 166 | C73 | #33686 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 167 | C22×Q16 | — | 73 | 1 | no | — |
| 168 | #540 | — | 146 | 1 | no | — |
| 169 | #519 | — | 146 | 1 | no | — |
| 170 | C2×SD32 | — | 73 | 2 | no | — |
| 171 | C2×SD32 | — | 73 | 2 | no | — |
| 172 | #499 | — | 73 | 1 | no | — |
| 173 | #493 | — | 73 | 1 | no | — |
| 174 | #490 | — | 146 | 1 | no | — |
| 175 | #469 | — | 146 | 1 | no | — |
| 176 | #466 | — | 73 | 2 | no | — |
| 177 | #442 | — | 146 | 1 | no | — |
| 178 | #441 | — | 146 | 1 | no | — |
| 179 | #441 | — | 146 | 1 | no | — |
| 180 | C4×Q16 | — | 73 | 2 | no | — |
| 181 | C4×Q16 | — | 73 | 2 | no | — |
| 182 | C4×D8 | — | 73 | 2 | no | — |
| 183 | #427 | — | 73 | 1 | no | — |
| 184 | #419 | — | 146 | 1 | no | — |
| 185 | #405 | C2×D73 | 1 | 1 | yes | characteristic |
| 186 | #367 | — | 73 | 2 | no | — |
| 187 | #366 | — | 73 | 2 | no | — |
| 188 | C4⋊C16 | C2×D73 | 1 | 2 | yes | — |
| 189 | #358 | — | 73 | 2 | no | — |
| 190 | #358 | — | 73 | 2 | no | — |
| 191 | #357 | — | 73 | 2 | no | — |
| 192 | #357 | — | 73 | 2 | no | — |
| 193 | C22⋊C16 | C2×D73 | 1 | 2 | yes | — |
| 194 | #346 | C2×D73 | 1 | 1 | yes | characteristic |
| 195 | C4×C16 | C2×D73 | 1 | 1 | yes | characteristic |
| 196 | C22×Q8 | — | 146 | 1 | no | — |
| 197 | C2×Q16 | — | 73 | 2 | no | — |
| 198 | C2×Q16 | — | 146 | 4 | no | — |
| 199 | C2×Q16 | — | 146 | 1 | no | — |
| 200 | C2×D8 | — | 73 | 2 | no | — |
| 201 | C2×D8 | — | 146 | 1 | no | — |
| 202 | C2×M16 | D292 | 1 | 1 | yes | characteristic |
| 203 | C22×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 204 | #127 | — | 146 | 1 | no | — |
| 205 | #125 | — | 146 | 1 | no | — |
| 206 | #123 | — | 292 | 2 | no | — |
| 207 | #121 | — | 292 | 2 | no | — |
| 208 | #121 | — | 146 | 2 | no | — |
| 209 | C4×Q8 | — | 292 | 2 | no | — |
| 210 | C4×Q8 | — | 146 | 2 | no | — |
| 211 | C4×Q8 | — | 146 | 2 | no | — |
| 212 | C4×D4 | — | 146 | 2 | no | — |
| 213 | #117 | — | 292 | 2 | no | — |
| 214 | #117 | — | 146 | 1 | no | — |
| 215 | #117 | D292 | 1 | 1 | yes | characteristic |
| 216 | SD32 | — | 146 | 4 | no | — |
| 217 | SD32 | — | 146 | 4 | no | — |
| 218 | C2×C16 | C22×D73 | 1 | 2 | yes | — |
| 219 | C2×C16 | C22×D73 | 1 | 2 | yes | — |
| 220 | #107 | — | 73 | 2 | no | — |
| 221 | #107 | — | 73 | 2 | no | — |
| 222 | #106 | — | 146 | 1 | no | — |
| 223 | #106 | — | 146 | 1 | no | — |
| 224 | #103 | — | 146 | 2 | no | — |
| 225 | #103 | — | 146 | 2 | no | — |
| 226 | #102 | — | 146 | 2 | no | — |
| 227 | #102 | — | 146 | 2 | no | — |
| 228 | #97 | D292 | 1 | 1 | yes | characteristic |
| 229 | #97 | D292 | 1 | 1 | yes | characteristic |
| 230 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 231 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 232 | C2×Q8 | — | 292 | 2 | no | — |
| 233 | C2×Q8 | — | 292 | 1 | no | — |
| 234 | C2×Q8 | — | 146 | 4 | no | — |
| 235 | C2×Q8 | — | 146 | 2 | no | — |
| 236 | C2×D4 | — | 292 | 2 | no | — |
| 237 | C2×D4 | — | 292 | 2 | no | — |
| 238 | C2×D4 | — | 146 | 2 | no | — |
| 239 | C22×C4 | — | 292 | 1 | no | — |
| 240 | C22×C4 | — | 292 | 2 | no | — |
| 241 | C22×C4 | C2×D292 | 1 | 1 | yes | characteristic |
| 242 | Q16 | — | 73 | 4 | no | — |
| 243 | Q16 | — | 146 | 4 | no | — |
| 244 | Q16 | — | 146 | 2 | no | — |
| 245 | D8 | — | 292 | 2 | no | — |
| 246 | D8 | — | 146 | 2 | no | — |
| 247 | D8 | — | 146 | 2 | no | — |
| 248 | M16 | — | 4 | 1 | no | — |
| 249 | C2×C8 | — | 2 | 2 | no | — |
| 250 | C2×C8 | C2×D292 | 1 | 1 | yes | characteristic |
| 251 | C2×C8 | C2×D292 | 1 | 1 | yes | characteristic |
| 252 | C2×C8 | C2×D292 | 1 | 1 | yes | characteristic |
| 253 | C2×C8 | C23×D73 | 1 | 1 | yes | characteristic |
| 254 | C4⋊C4 | — | 292 | 2 | no | — |
| 255 | C4⋊C4 | — | 292 | 2 | no | — |
| 256 | C4⋊C4 | — | 292 | 2 | no | — |
| 257 | C4⋊C4 | — | 146 | 2 | no | — |
| 258 | C4⋊C4 | — | 146 | 2 | no | — |
| 259 | C4⋊C4 | D584 | 1 | 2 | yes | — |
| 260 | C22⋊C4 | — | 292 | 1 | no | — |
| 261 | C22⋊C4 | — | 292 | 2 | no | — |
| 262 | C22⋊C4 | — | 292 | 2 | no | — |
| 263 | C22⋊C4 | D584 | 1 | 2 | yes | — |
| 264 | C42 | — | 292 | 2 | no | — |
| 265 | C42 | — | 292 | 2 | no | — |
| 266 | C42 | — | 292 | 1 | no | — |
| 267 | C42 | C2×D292 | 1 | 1 | yes | characteristic |
| 268 | C42 | C2×D292 | 1 | 1 | yes | characteristic |
| 269 | C16 | — | 2 | 2 | no | — |
| 270 | C16 | — | 2 | 2 | no | — |
| 271 | C23 | — | 292 | 2 | no | — |
| 272 | C23 | C2×D584 | 1 | 1 | yes | characteristic |
| 273 | Q8 | — | 292 | 4 | no | — |
| 274 | Q8 | — | 292 | 2 | no | — |
| 275 | Q8 | — | 146 | 4 | no | — |
| 276 | D4 | — | 292 | 2 | no | — |
| 277 | D4 | — | 292 | 2 | no | — |
| 278 | D4 | — | 1168 | 2 | no | — |
| 279 | D4 | — | 1168 | 2 | no | — |
| 280 | C2×C4 | — | 2 | 1 | no | — |
| 281 | C2×C4 | — | 2 | 1 | no | — |
| 282 | C2×C4 | — | 292 | 4 | no | — |
| 283 | C2×C4 | — | 292 | 2 | no | — |
| 284 | C2×C4 | — | 292 | 2 | no | — |
| 285 | C2×C4 | — | 292 | 2 | no | — |
| 286 | C2×C4 | — | 1168 | 2 | no | — |
| 287 | C2×C4 | C2×D584 | 1 | 2 | yes | — |
| 288 | C2×C4 | C2×D584 | 1 | 2 | yes | — |
| 289 | C2×C4 | C2×D584 | 1 | 1 | yes | characteristic |
| 290 | C2×C4 | C22×D292 | 1 | 1 | yes | characteristic |
| 291 | C8 | — | 2 | 1 | no | — |
| 292 | C8 | — | 2 | 1 | no | — |
| 293 | C8 | — | 2 | 1 | no | — |
| 294 | C8 | #41×D73 | 1 | 2 | yes | — |
| 295 | C22 | — | 2 | 1 | no | — |
| 296 | C22 | — | 2 | 2 | no | — |
| 297 | C22 | — | 584 | 2 | no | — |
| 298 | C22 | — | 584 | 2 | no | — |
| 299 | C22 | — | 584 | 2 | no | — |
| 300 | C22 | C22×D584 | 1 | 1 | yes | characteristic |
| 301 | C4 | — | 2 | 1 | no | — |
| 302 | C4 | — | 2 | 2 | no | — |
| 303 | C4 | — | 2 | 2 | no | — |
| 304 | C4 | — | 292 | 4 | no | — |
| 305 | C4 | — | 584 | 2 | no | — |
| 306 | C4 | — | 584 | 2 | no | — |
| 307 | C4 | #17989099 | 1 | 1 | yes | characteristic |
| 308 | C4 | #17989387 | 1 | 1 | yes | characteristic |
| 309 | C2 | — | 4 | 1 | no | — |
| 310 | C2 | — | 1168 | 2 | no | — |
| 311 | C2 | #22619932 | 1 | 1 | yes | characteristic |
| 312 | C2 | #22623079 | 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