← #33240687
Subgroups — #33240687
Order 18688.
520 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22620471 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22618798 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22612098 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22612094 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22612082 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22612072 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #22611720 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #22611689 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #22611650 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×#17988392 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C73×#2158 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C22×Dic292 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17989215 | — | 2 | 1 | no | — |
| 14 | #17989064 | — | 2 | 1 | no | — |
| 15 | C2×#14556531 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17988994 | — | 2 | 2 | no | — |
| 17 | #17988991 | C22 | 1 | 2 | yes | — |
| 18 | #17988988 | C22 | 1 | 2 | yes | — |
| 19 | #17988693 | — | 2 | 2 | no | — |
| 20 | #17988681 | C22 | 1 | 2 | yes | — |
| 21 | #17988681 | C22 | 1 | 2 | yes | — |
| 22 | #17988630 | — | 2 | 1 | no | — |
| 23 | C2×#14556525 | C22 | 1 | 1 | yes | characteristic |
| 24 | #17988595 | — | 2 | 1 | no | — |
| 25 | #17988542 | C22 | 1 | 1 | yes | characteristic |
| 26 | #17988414 | C22 | 1 | 2 | yes | — |
| 27 | #17988412 | C22 | 1 | 2 | yes | — |
| 28 | #17988405 | C22 | 1 | 2 | yes | — |
| 29 | #17988405 | C22 | 1 | 2 | yes | — |
| 30 | #17988392 | C22 | 1 | 2 | yes | — |
| 31 | #17988392 | C22 | 1 | 2 | yes | — |
| 32 | #17988390 | C22 | 1 | 2 | yes | — |
| 33 | #17988390 | C22 | 1 | 2 | yes | — |
| 34 | C22×C16×C73 | C22 | 1 | 1 | yes | characteristic |
| 35 | #427×C73 | C22 | 1 | 1 | yes | characteristic |
| 36 | #427×C73 | C22 | 1 | 1 | yes | characteristic |
| 37 | #367×C73 | C22 | 1 | 1 | yes | characteristic |
| 38 | #367×C73 | C22 | 1 | 1 | yes | characteristic |
| 39 | #366×C73 | C22 | 1 | 1 | yes | characteristic |
| 40 | #366×C73 | C22 | 1 | 1 | yes | characteristic |
| 41 | C22×Dic146 | — | 2 | 1 | no | — |
| 42 | C2×Dic292 | — | 2 | 1 | no | — |
| 43 | C2×Dic292 | — | 2 | 2 | no | — |
| 44 | C2×Dic292 | Q8 | 1 | 4 | yes | complemented |
| 45 | C2×Dic292 | C23 | 1 | 2 | yes | — |
| 46 | C2×#11924012 | D4 | 1 | 1 | yes | characteristic |
| 47 | #14556591 | — | 4 | 1 | no | — |
| 48 | #14556590 | — | 2 | 2 | no | — |
| 49 | #14556583 | — | 4 | 1 | no | — |
| 50 | #14556582 | — | 2 | 2 | no | — |
| 51 | #14556568 | — | 4 | 2 | no | — |
| 52 | C4×Dic146 | — | 4 | 1 | no | — |
| 53 | C4×Dic146 | — | 4 | 1 | no | — |
| 54 | #14556556 | — | 2 | 2 | no | — |
| 55 | #14556556 | — | 2 | 2 | no | — |
| 56 | #14556550 | D4 | 1 | 1 | yes | characteristic |
| 57 | #14556547 | — | 4 | 2 | no | — |
| 58 | C2×C4⋊Dic73 | — | 2 | 1 | no | — |
| 59 | #14556531 | — | 2 | 2 | no | — |
| 60 | C2×#11924003 | C23 | 1 | 2 | yes | — |
| 61 | #14556525 | — | 2 | 1 | no | — |
| 62 | #14556525 | C23 | 1 | 2 | yes | — |
| 63 | #14556524 | — | 2 | 2 | no | — |
| 64 | #14556522 | — | 2 | 2 | no | — |
| 65 | #14556514 | — | 2 | 2 | no | — |
| 66 | #14556514 | — | 2 | 2 | no | — |
| 67 | #14556501 | D4 | 1 | 2 | yes | — |
| 68 | C8×Dic73 | C23 | 1 | 2 | yes | — |
| 69 | C22×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 70 | #117×C73 | — | 2 | 1 | no | — |
| 71 | #117×C73 | — | 2 | 1 | no | — |
| 72 | C2×C16×C73 | — | 2 | 2 | no | — |
| 73 | C2×C16×C73 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C16×C73 | C23 | 1 | 1 | yes | characteristic |
| 75 | #107×C73 | C23 | 1 | 1 | yes | characteristic |
| 76 | #107×C73 | C23 | 1 | 1 | yes | characteristic |
| 77 | #107×C73 | C23 | 1 | 1 | yes | characteristic |
| 78 | #107×C73 | C23 | 1 | 1 | yes | characteristic |
| 79 | #106×C73 | — | 2 | 1 | no | — |
| 80 | #106×C73 | — | 2 | 1 | no | — |
| 81 | C2×Dic146 | — | 2 | 4 | no | — |
| 82 | C2×Dic146 | — | 2 | 2 | no | — |
| 83 | C2×Dic146 | — | 4 | 1 | no | — |
| 84 | C2×Dic146 | — | 4 | 2 | no | — |
| 85 | C2×Dic146 | — | 4 | 2 | no | — |
| 86 | C22×Dic73 | — | 4 | 1 | no | — |
| 87 | C22×Dic73 | — | 4 | 1 | no | — |
| 88 | Dic292 | — | 2 | 4 | no | — |
| 89 | Dic292 | — | 2 | 2 | no | — |
| 90 | Dic292 | C2×Q8 | 1 | 4 | yes | — |
| 91 | #11924012 | — | 2 | 2 | no | — |
| 92 | C2×#10596831 | C2×D4 | 1 | 2 | yes | — |
| 93 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 94 | C4⋊Dic73 | — | 4 | 1 | no | — |
| 95 | C4⋊Dic73 | — | 4 | 2 | no | — |
| 96 | C4⋊Dic73 | D8 | 1 | 1 | yes | characteristic |
| 97 | C4⋊Dic73 | D8 | 1 | 1 | yes | characteristic |
| 98 | #11924007 | — | 4 | 2 | no | — |
| 99 | #11924007 | — | 4 | 2 | no | — |
| 100 | #11924007 | — | 4 | 2 | no | — |
| 101 | #11924007 | — | 4 | 2 | no | — |
| 102 | C22⋊Dic73 | D8 | 1 | 2 | yes | — |
| 103 | C4×Dic73 | — | 4 | 2 | no | — |
| 104 | C4×Dic73 | — | 4 | 2 | no | — |
| 105 | C4×Dic73 | C2×D4 | 1 | 2 | yes | — |
| 106 | #11924003 | — | 2 | 2 | no | — |
| 107 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×C8×C73 | C2×Q8 | 1 | 2 | yes | — |
| 110 | C2×C8×C73 | #41 | 1 | 2 | yes | — |
| 111 | C2×C8×C73 | C24 | 1 | 1 | yes | characteristic |
| 112 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 113 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 114 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 115 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 116 | C22⋊C4×C73 | — | 4 | 1 | no | — |
| 117 | C22⋊C4×C73 | — | 4 | 1 | no | — |
| 118 | C42×C73 | — | 4 | 1 | no | — |
| 119 | C42×C73 | — | 4 | 1 | no | — |
| 120 | C16×C73 | — | 2 | 1 | no | — |
| 121 | C16×C73 | — | 2 | 1 | no | — |
| 122 | C23×C73 | C2×D8 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×C73 | — | 4 | 1 | no | — |
| 124 | C2×C4×C73 | — | 4 | 1 | no | — |
| 125 | C2×C4×C73 | — | 4 | 1 | no | — |
| 126 | C2×C4×C73 | — | 4 | 1 | no | — |
| 127 | C2×C4×C73 | C22⋊Q8 | 1 | 2 | yes | — |
| 128 | C2×C4×C73 | C2×D8 | 1 | 1 | yes | characteristic |
| 129 | C2×C4×C73 | #137 | 1 | 2 | yes | — |
| 130 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×Dic73 | — | 4 | 2 | no | — |
| 132 | C2×Dic73 | — | 4 | 4 | no | — |
| 133 | C2×Dic73 | — | 4 | 2 | no | — |
| 134 | C2×Dic73 | — | 16 | 1 | no | — |
| 135 | C2×Dic73 | C2×D8 | 1 | 2 | yes | — |
| 136 | C2×Dic73 | C2×D8 | 1 | 2 | yes | — |
| 137 | Dic146 | — | 2 | 4 | no | — |
| 138 | Dic146 | — | 4 | 2 | no | — |
| 139 | Dic146 | — | 4 | 4 | no | — |
| 140 | Dic146 | — | 16 | 2 | no | — |
| 141 | C8×C73 | C22⋊Q8 | 1 | 2 | yes | — |
| 142 | C8×C73 | C22×Q8 | 1 | 1 | yes | characteristic |
| 143 | C8×C73 | C2×#41 | 1 | 1 | yes | characteristic |
| 144 | #10596831 | — | 2 | 2 | no | — |
| 145 | C22×C73 | — | 2 | 1 | no | — |
| 146 | C22×C73 | — | 2 | 1 | no | — |
| 147 | C22×C73 | #474 | 1 | 2 | yes | — |
| 148 | C22×C73 | C22×D8 | 1 | 1 | yes | characteristic |
| 149 | C4×C73 | — | 8 | 1 | no | — |
| 150 | C4×C73 | — | 8 | 1 | no | — |
| 151 | C4×C73 | — | 8 | 1 | no | — |
| 152 | C4×C73 | — | 8 | 1 | no | — |
| 153 | C4×C73 | #474 | 1 | 2 | yes | — |
| 154 | C4×C73 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 155 | C4×C73 | C2×#137 | 1 | 1 | yes | characteristic |
| 156 | Dic73 | — | 2 | 2 | no | — |
| 157 | Dic73 | — | 2 | 2 | no | — |
| 158 | Dic73 | — | 4 | 4 | no | — |
| 159 | Dic73 | — | 8 | 2 | no | — |
| 160 | #33632 | — | 73 | 1 | no | maximal, Sylow |
| 161 | C2×C73 | — | 2 | 2 | no | — |
| 162 | C2×C73 | C2×#474 | 1 | 1 | yes | characteristic |
| 163 | C2×C73 | #3416 | 1 | 1 | yes | characteristic |
| 164 | C2×C73 | #3417 | 1 | 1 | yes | characteristic |
| 165 | #3164 | — | 73 | 1 | no | — |
| 166 | #2950 | — | 73 | 1 | no | — |
| 167 | #2229 | — | 73 | 2 | no | — |
| 168 | #2229 | — | 73 | 2 | no | — |
| 169 | #2227 | — | 73 | 2 | no | — |
| 170 | #2225 | — | 73 | 2 | no | — |
| 171 | #2159 | — | 73 | 1 | no | — |
| 172 | #2158 | D73 | 1 | 1 | yes | characteristic |
| 173 | #2151 | — | 73 | 1 | no | — |
| 174 | #2141 | — | 73 | 1 | no | — |
| 175 | C2×#358 | — | 73 | 1 | no | — |
| 176 | C73 | #33632 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 177 | C22×Q16 | — | 73 | 1 | no | — |
| 178 | #544 | — | 146 | 1 | no | — |
| 179 | #519 | — | 146 | 1 | no | — |
| 180 | C2×M32 | — | 73 | 1 | no | — |
| 181 | C22×C16 | C2×D73 | 1 | 1 | yes | characteristic |
| 182 | #501 | — | 146 | 2 | no | — |
| 183 | #500 | — | 73 | 2 | no | — |
| 184 | #499 | — | 73 | 2 | no | — |
| 185 | #441 | — | 146 | 2 | no | — |
| 186 | C4×Q16 | — | 73 | 2 | no | — |
| 187 | C4×Q16 | — | 73 | 2 | no | — |
| 188 | #428 | — | 146 | 1 | no | — |
| 189 | #427 | C2×D73 | 1 | 1 | yes | characteristic |
| 190 | #427 | C2×D73 | 1 | 1 | yes | characteristic |
| 191 | C2×#107 | — | 73 | 1 | no | — |
| 192 | #419 | — | 146 | 1 | no | — |
| 193 | #405 | — | 73 | 1 | no | — |
| 194 | #367 | — | 73 | 2 | no | — |
| 195 | #367 | C2×D73 | 1 | 1 | yes | characteristic |
| 196 | #367 | C2×D73 | 1 | 1 | yes | characteristic |
| 197 | #366 | — | 73 | 2 | no | — |
| 198 | #366 | C2×D73 | 1 | 1 | yes | characteristic |
| 199 | #366 | C2×D73 | 1 | 1 | yes | characteristic |
| 200 | C4⋊C16 | — | 73 | 2 | no | — |
| 201 | C4⋊C16 | — | 73 | 2 | no | — |
| 202 | #358 | — | 73 | 2 | no | — |
| 203 | #358 | — | 73 | 2 | no | — |
| 204 | #358 | — | 73 | 2 | no | — |
| 205 | #358 | — | 73 | 2 | no | — |
| 206 | C22×Q8 | — | 146 | 1 | no | — |
| 207 | C2×Q16 | — | 73 | 4 | no | — |
| 208 | C2×Q16 | — | 73 | 2 | no | — |
| 209 | C2×Q16 | — | 146 | 1 | no | — |
| 210 | C2×Q16 | — | 146 | 2 | no | — |
| 211 | C2×M16 | — | 73 | 1 | no | — |
| 212 | C22×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 213 | C4⋊Q8 | — | 292 | 1 | no | — |
| 214 | C4⋊Q8 | — | 146 | 2 | no | — |
| 215 | #125 | — | 292 | 1 | no | — |
| 216 | #125 | — | 146 | 2 | no | — |
| 217 | C22⋊Q8 | — | 292 | 2 | no | — |
| 218 | C4×Q8 | — | 292 | 1 | no | — |
| 219 | C4×Q8 | — | 292 | 1 | no | — |
| 220 | C4×Q8 | — | 146 | 2 | no | — |
| 221 | C4×Q8 | — | 146 | 2 | no | — |
| 222 | #117 | — | 2 | 1 | no | — |
| 223 | #117 | — | 2 | 1 | no | — |
| 224 | #117 | — | 292 | 2 | no | — |
| 225 | #117 | — | 73 | 1 | no | — |
| 226 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 227 | M32 | — | 146 | 2 | no | — |
| 228 | C2×C16 | — | 2 | 2 | no | — |
| 229 | C2×C16 | — | 73 | 2 | no | — |
| 230 | C2×C16 | C22×D73 | 1 | 1 | yes | characteristic |
| 231 | C2×C16 | C22×D73 | 1 | 1 | yes | characteristic |
| 232 | #107 | — | 73 | 2 | no | — |
| 233 | #107 | — | 146 | 2 | no | — |
| 234 | #107 | — | 146 | 1 | no | — |
| 235 | #107 | C22×D73 | 1 | 1 | yes | characteristic |
| 236 | #107 | C22×D73 | 1 | 1 | yes | characteristic |
| 237 | #107 | C22×D73 | 1 | 1 | yes | characteristic |
| 238 | #107 | C22×D73 | 1 | 1 | yes | characteristic |
| 239 | #106 | — | 2 | 1 | no | — |
| 240 | #106 | — | 2 | 1 | no | — |
| 241 | #106 | — | 146 | 2 | no | — |
| 242 | #103 | — | 146 | 2 | no | — |
| 243 | #103 | — | 146 | 2 | no | — |
| 244 | #97 | — | 73 | 2 | no | — |
| 245 | C4×C8 | — | 73 | 2 | no | — |
| 246 | C2×Q8 | — | 292 | 2 | no | — |
| 247 | C2×Q8 | — | 292 | 1 | no | — |
| 248 | C2×Q8 | — | 292 | 2 | no | — |
| 249 | C2×Q8 | — | 146 | 4 | no | — |
| 250 | C2×Q8 | — | 146 | 2 | no | — |
| 251 | C22×C4 | — | 292 | 1 | no | — |
| 252 | C22×C4 | — | 292 | 1 | no | — |
| 253 | C22×C4 | D4×D73 | 1 | 1 | yes | characteristic |
| 254 | Q16 | — | 73 | 4 | no | — |
| 255 | Q16 | — | 146 | 4 | no | — |
| 256 | Q16 | — | 146 | 2 | no | — |
| 257 | M16 | — | 146 | 2 | no | — |
| 258 | C2×C8 | — | 73 | 2 | no | — |
| 259 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 260 | C2×C8 | Q8×D73 | 1 | 2 | yes | — |
| 261 | C2×C8 | #11924028 | 1 | 2 | yes | — |
| 262 | C2×C8 | C23×D73 | 1 | 1 | yes | characteristic |
| 263 | C4⋊C4 | — | 2 | 1 | no | — |
| 264 | C4⋊C4 | — | 2 | 1 | no | — |
| 265 | C4⋊C4 | — | 2 | 1 | no | — |
| 266 | C4⋊C4 | — | 2 | 1 | no | — |
| 267 | C4⋊C4 | — | 292 | 2 | no | — |
| 268 | C4⋊C4 | — | 292 | 2 | no | — |
| 269 | C4⋊C4 | — | 292 | 2 | no | — |
| 270 | C4⋊C4 | — | 292 | 2 | no | — |
| 271 | C4⋊C4 | — | 292 | 2 | no | — |
| 272 | C4⋊C4 | — | 292 | 1 | no | — |
| 273 | C4⋊C4 | — | 73 | 1 | no | — |
| 274 | C4⋊C4 | — | 73 | 1 | no | — |
| 275 | C4⋊C4 | — | 146 | 2 | no | — |
| 276 | C22⋊C4 | — | 4 | 1 | no | — |
| 277 | C22⋊C4 | — | 4 | 1 | no | — |
| 278 | C22⋊C4 | — | 73 | 2 | no | — |
| 279 | C42 | — | 4 | 1 | no | — |
| 280 | C42 | — | 4 | 1 | no | — |
| 281 | C42 | — | 292 | 2 | no | — |
| 282 | C42 | — | 292 | 2 | no | — |
| 283 | C42 | — | 73 | 2 | no | — |
| 284 | C16 | — | 2 | 1 | no | — |
| 285 | C16 | — | 2 | 1 | no | — |
| 286 | C16 | — | 146 | 2 | no | — |
| 287 | C23 | D8×D73 | 1 | 1 | yes | characteristic |
| 288 | Q8 | — | 292 | 4 | no | — |
| 289 | Q8 | — | 292 | 2 | no | — |
| 290 | Q8 | — | 1168 | 2 | no | — |
| 291 | Q8 | — | 146 | 4 | no | — |
| 292 | C2×C4 | — | 4 | 1 | no | — |
| 293 | C2×C4 | — | 4 | 1 | no | — |
| 294 | C2×C4 | — | 4 | 1 | no | — |
| 295 | C2×C4 | — | 4 | 1 | no | — |
| 296 | C2×C4 | — | 292 | 4 | no | — |
| 297 | C2×C4 | — | 292 | 2 | no | — |
| 298 | C2×C4 | — | 292 | 2 | no | — |
| 299 | C2×C4 | — | 73 | 2 | no | — |
| 300 | C2×C4 | — | 73 | 2 | no | — |
| 301 | C2×C4 | — | 1168 | 1 | no | — |
| 302 | C2×C4 | #14556569 | 1 | 2 | yes | — |
| 303 | C2×C4 | D8×D73 | 1 | 1 | yes | characteristic |
| 304 | C2×C4 | #14556623 | 1 | 2 | yes | — |
| 305 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 306 | C8 | — | 146 | 2 | no | — |
| 307 | C8 | #14556569 | 1 | 2 | yes | — |
| 308 | C8 | C2×Q8×D73 | 1 | 1 | yes | characteristic |
| 309 | C8 | C2×#11924028 | 1 | 1 | yes | characteristic |
| 310 | C22 | — | 2 | 1 | no | — |
| 311 | C22 | — | 2 | 1 | no | — |
| 312 | C22 | #17988866 | 1 | 2 | yes | — |
| 313 | C22 | C2×D8×D73 | 1 | 1 | yes | characteristic |
| 314 | C4 | — | 8 | 1 | no | — |
| 315 | C4 | — | 8 | 1 | no | — |
| 316 | C4 | — | 8 | 1 | no | — |
| 317 | C4 | — | 8 | 1 | no | — |
| 318 | C4 | — | 292 | 4 | no | — |
| 319 | C4 | — | 584 | 2 | no | — |
| 320 | C4 | — | 146 | 2 | no | — |
| 321 | C4 | — | 146 | 2 | no | — |
| 322 | C4 | #17988866 | 1 | 2 | yes | — |
| 323 | C4 | C2×#14556569 | 1 | 1 | yes | characteristic |
| 324 | C4 | C2×#14556623 | 1 | 1 | yes | characteristic |
| 325 | C2 | — | 2 | 2 | no | — |
| 326 | C2 | C2×#17988866 | 1 | 1 | yes | characteristic |
| 327 | C2 | #22623074 | 1 | 1 | yes | characteristic |
| 328 | C2 | #22623081 | 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