← #33240880
Subgroups — #33240880
Order 18688.
556 conjugacy classes of subgroups.
The subgroup lattice has 320 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22619540 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22612150 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #22612145 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22611705 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22611678 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#17988369 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#430×C73 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14556613 | C22 | 1 | 1 | yes | characteristic |
| 9 | #17989098 | — | 2 | 1 | no | — |
| 10 | C2×#14556531 | C22 | 1 | 2 | yes | — |
| 11 | #17988845 | C22 | 1 | 2 | yes | — |
| 12 | #17988840 | C22 | 1 | 2 | yes | — |
| 13 | #17988833 | — | 2 | 2 | no | — |
| 14 | #17988625 | C22 | 1 | 1 | yes | characteristic |
| 15 | #17988584 | — | 2 | 1 | no | — |
| 16 | #17988411 | C22 | 1 | 8 | yes | complemented |
| 17 | #17988402 | C22 | 1 | 4 | yes | complemented |
| 18 | #17988399 | C22 | 1 | 4 | yes | complemented |
| 19 | #17988369 | C22 | 1 | 4 | yes | — |
| 20 | C22×M16×C73 | — | 2 | 1 | no | — |
| 21 | C22×M16×C73 | C22 | 1 | 1 | yes | characteristic |
| 22 | #430×C73 | — | 2 | 2 | no | — |
| 23 | #430×C73 | C22 | 1 | 4 | yes | — |
| 24 | C2×#108×C73 | — | 2 | 1 | no | — |
| 25 | C2×#108×C73 | C22 | 1 | 2 | yes | — |
| 26 | C2×#11924028 | — | 2 | 1 | no | — |
| 27 | #14556613 | — | 2 | 2 | no | — |
| 28 | #14556613 | — | 2 | 2 | no | — |
| 29 | C2×Dic292 | C23 | 1 | 1 | yes | characteristic |
| 30 | C2×#11924017 | — | 2 | 1 | no | — |
| 31 | C2×D584 | C23 | 1 | 1 | yes | characteristic |
| 32 | #14556574 | — | 4 | 1 | no | — |
| 33 | #14556570 | — | 2 | 2 | no | — |
| 34 | #14556565 | — | 2 | 2 | no | — |
| 35 | #14556560 | — | 4 | 1 | no | — |
| 36 | C4×C22⋊D73 | — | 4 | 2 | no | — |
| 37 | #14556550 | — | 2 | 1 | no | — |
| 38 | #14556531 | — | 2 | 2 | no | — |
| 39 | #14556531 | C23 | 1 | 4 | yes | — |
| 40 | C2×#11924003 | — | 2 | 2 | no | — |
| 41 | #14556525 | — | 2 | 1 | no | — |
| 42 | #14556523 | C23 | 1 | 2 | yes | — |
| 43 | #14556516 | — | 2 | 2 | no | — |
| 44 | #14556513 | — | 2 | 2 | no | — |
| 45 | C23×C4×C73 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×M16×C73 | — | 2 | 2 | no | — |
| 47 | C2×M16×C73 | — | 2 | 2 | no | — |
| 48 | C2×M16×C73 | — | 2 | 2 | no | — |
| 49 | C2×M16×C73 | — | 2 | 4 | no | — |
| 50 | C2×M16×C73 | — | 4 | 2 | no | — |
| 51 | C2×M16×C73 | — | 4 | 1 | no | — |
| 52 | C2×M16×C73 | D4 | 1 | 2 | yes | — |
| 53 | C2×M16×C73 | C23 | 1 | 2 | yes | — |
| 54 | C22×C8×C73 | — | 4 | 1 | no | — |
| 55 | C22×C8×C73 | D4 | 1 | 1 | yes | characteristic |
| 56 | C22×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 57 | #108×C73 | — | 2 | 4 | no | — |
| 58 | #108×C73 | — | 2 | 2 | no | — |
| 59 | #108×C73 | C23 | 1 | 4 | yes | — |
| 60 | #11924028 | — | 4 | 1 | no | — |
| 61 | #11924028 | — | 4 | 1 | no | — |
| 62 | #11924028 | — | 4 | 1 | no | — |
| 63 | #11924028 | — | 4 | 1 | no | — |
| 64 | C2×Dic146 | — | 2 | 1 | no | — |
| 65 | C2×D292 | — | 2 | 1 | no | — |
| 66 | C2×C22⋊D73 | — | 4 | 2 | no | — |
| 67 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 68 | C2×C4×D73 | — | 4 | 1 | no | — |
| 69 | Dic292 | — | 2 | 2 | no | — |
| 70 | #11924017 | — | 4 | 2 | no | — |
| 71 | D584 | — | 2 | 2 | no | — |
| 72 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 73 | #11924007 | — | 4 | 2 | no | — |
| 74 | C22⋊Dic73 | — | 4 | 1 | no | — |
| 75 | C22⋊Dic73 | — | 4 | 2 | no | — |
| 76 | #11924005 | — | 4 | 2 | no | — |
| 77 | C4×Dic73 | — | 4 | 1 | no | — |
| 78 | #11924003 | — | 2 | 4 | no | — |
| 79 | C24×C73 | SD16 | 1 | 1 | yes | characteristic |
| 80 | C22×C4×C73 | — | 2 | 1 | no | — |
| 81 | C22×C4×C73 | — | 2 | 1 | no | — |
| 82 | C22×C4×C73 | — | 2 | 1 | no | — |
| 83 | C22×C4×C73 | — | 2 | 1 | no | — |
| 84 | C22×C4×C73 | SD16 | 1 | 2 | yes | — |
| 85 | C22×C4×C73 | SD16 | 1 | 1 | yes | characteristic |
| 86 | C22×C4×C73 | C2×D4 | 1 | 2 | yes | — |
| 87 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | M16×C73 | — | 2 | 4 | no | — |
| 89 | M16×C73 | — | 2 | 4 | no | — |
| 90 | M16×C73 | — | 2 | 4 | no | — |
| 91 | M16×C73 | — | 4 | 4 | no | — |
| 92 | M16×C73 | — | 4 | 2 | no | — |
| 93 | C2×C8×C73 | — | 2 | 1 | no | — |
| 94 | C2×C8×C73 | — | 2 | 1 | no | — |
| 95 | C2×C8×C73 | — | 4 | 4 | no | — |
| 96 | C2×C8×C73 | — | 4 | 2 | no | — |
| 97 | C2×C8×C73 | C2×D4 | 1 | 2 | yes | — |
| 98 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C2×C8×C73 | #41 | 1 | 2 | yes | — |
| 100 | C2×C8×C73 | #41 | 1 | 2 | yes | — |
| 101 | C2×C8×C73 | C24 | 1 | 1 | yes | characteristic |
| 102 | C23×C73 | — | 2 | 1 | no | — |
| 103 | C23×C73 | — | 2 | 1 | no | — |
| 104 | C23×C73 | — | 8 | 1 | no | — |
| 105 | C23×C73 | C2×SD16 | 1 | 2 | yes | — |
| 106 | C23×C73 | C2×SD16 | 1 | 1 | yes | characteristic |
| 107 | C22×D73 | — | 4 | 1 | no | — |
| 108 | C2×C4×C73 | — | 2 | 1 | no | — |
| 109 | C2×C4×C73 | — | 2 | 1 | no | — |
| 110 | C2×C4×C73 | — | 2 | 2 | no | — |
| 111 | C2×C4×C73 | — | 2 | 2 | no | — |
| 112 | C2×C4×C73 | — | 2 | 2 | no | — |
| 113 | C2×C4×C73 | — | 2 | 2 | no | — |
| 114 | C2×C4×C73 | #123 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C73 | #123 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C73 | C2×SD16 | 1 | 2 | yes | — |
| 117 | C2×C4×C73 | C2×SD16 | 1 | 1 | yes | characteristic |
| 118 | C2×C4×C73 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 119 | C2×C4×C73 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 120 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 121 | C22⋊D73 | — | 8 | 4 | no | — |
| 122 | C22⋊D73 | — | 8 | 1 | no | — |
| 123 | C22⋊D73 | — | 8 | 1 | no | — |
| 124 | C2×Dic73 | — | 4 | 2 | no | — |
| 125 | C2×Dic73 | — | 4 | 1 | no | — |
| 126 | D292 | — | 4 | 1 | no | — |
| 127 | D292 | — | 4 | 1 | no | — |
| 128 | C4×D73 | — | 8 | 1 | no | — |
| 129 | C4×D73 | — | 8 | 1 | no | — |
| 130 | Dic146 | — | 4 | 1 | no | — |
| 131 | Dic146 | — | 4 | 1 | no | — |
| 132 | C8×C73 | — | 2 | 2 | no | — |
| 133 | C8×C73 | — | 4 | 4 | no | — |
| 134 | C8×C73 | #123 | 1 | 2 | yes | — |
| 135 | C8×C73 | C2×#41 | 1 | 2 | yes | — |
| 136 | C22×C73 | — | 2 | 2 | no | — |
| 137 | C22×C73 | — | 4 | 1 | no | — |
| 138 | C22×C73 | — | 4 | 2 | no | — |
| 139 | C22×C73 | — | 4 | 2 | no | — |
| 140 | C22×C73 | — | 8 | 1 | no | — |
| 141 | C22×C73 | #481 | 1 | 1 | yes | characteristic |
| 142 | C22×C73 | #481 | 1 | 1 | yes | characteristic |
| 143 | C22×C73 | C22×SD16 | 1 | 1 | yes | characteristic |
| 144 | C2×D73 | — | 8 | 2 | no | — |
| 145 | C2×D73 | — | 8 | 1 | no | — |
| 146 | C4×C73 | — | 2 | 2 | no | — |
| 147 | C4×C73 | #481 | 1 | 1 | yes | characteristic |
| 148 | C4×C73 | #481 | 1 | 1 | yes | characteristic |
| 149 | C4×C73 | C2×#123 | 1 | 1 | yes | characteristic |
| 150 | C4×C73 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 151 | Dic73 | — | 8 | 2 | no | — |
| 152 | Dic73 | — | 8 | 1 | no | — |
| 153 | #33656 | — | 73 | 1 | no | maximal, Sylow |
| 154 | C2×C73 | — | 2 | 1 | no | — |
| 155 | C2×C73 | — | 2 | 1 | no | — |
| 156 | C2×C73 | — | 2 | 1 | no | — |
| 157 | C2×C73 | — | 4 | 2 | no | — |
| 158 | C2×C73 | C2×#481 | 1 | 1 | yes | characteristic |
| 159 | D73 | — | 16 | 1 | no | — |
| 160 | #3054 | — | 73 | 1 | no | — |
| 161 | C2×#430 | D73 | 1 | 1 | yes | characteristic, complemented |
| 162 | #2239 | — | 73 | 4 | no | — |
| 163 | #2238 | — | 73 | 4 | no | — |
| 164 | #2155 | — | 73 | 2 | no | — |
| 165 | #2148 | — | 73 | 2 | no | — |
| 166 | C2×#349 | — | 73 | 1 | no | — |
| 167 | C73 | #33656 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 168 | C2×#135 | — | 73 | 1 | no | — |
| 169 | C22×M16 | — | 2 | 1 | no | — |
| 170 | C22×M16 | C2×D73 | 1 | 1 | yes | characteristic |
| 171 | #525 | — | 146 | 1 | no | — |
| 172 | C2×M32 | — | 73 | 2 | no | — |
| 173 | #470 | — | 73 | 2 | no | — |
| 174 | #469 | — | 73 | 2 | no | — |
| 175 | #468 | — | 146 | 2 | no | — |
| 176 | #430 | — | 2 | 2 | no | — |
| 177 | #430 | C2×D73 | 1 | 4 | yes | — |
| 178 | C2×#108 | — | 2 | 1 | no | — |
| 179 | C2×#108 | C2×D73 | 1 | 2 | yes | — |
| 180 | #427 | — | 73 | 1 | no | — |
| 181 | #416 | — | 146 | 1 | no | — |
| 182 | #365 | — | 73 | 8 | no | — |
| 183 | #362 | — | 73 | 4 | no | — |
| 184 | #361 | — | 73 | 4 | no | — |
| 185 | #349 | — | 73 | 4 | no | — |
| 186 | C2×#41 | — | 146 | 1 | no | — |
| 187 | C23×C4 | C22⋊D73 | 1 | 1 | yes | characteristic |
| 188 | #135 | — | 146 | 2 | no | — |
| 189 | #135 | — | 146 | 2 | no | — |
| 190 | C2×Q16 | — | 73 | 1 | no | — |
| 191 | C2×SD16 | — | 146 | 1 | no | — |
| 192 | C2×D8 | — | 73 | 1 | no | — |
| 193 | C2×M16 | — | 2 | 2 | no | — |
| 194 | C2×M16 | — | 2 | 2 | no | — |
| 195 | C2×M16 | — | 2 | 4 | no | — |
| 196 | C2×M16 | — | 2 | 2 | no | — |
| 197 | C2×M16 | — | 4 | 2 | no | — |
| 198 | C2×M16 | — | 4 | 1 | no | — |
| 199 | C2×M16 | C22⋊D73 | 1 | 2 | yes | — |
| 200 | C2×M16 | C22×D73 | 1 | 2 | yes | — |
| 201 | C22×C8 | — | 4 | 1 | no | — |
| 202 | C22×C8 | C22⋊D73 | 1 | 1 | yes | characteristic |
| 203 | C22×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 204 | #123 | — | 292 | 1 | no | — |
| 205 | C22⋊Q8 | — | 146 | 2 | no | — |
| 206 | #121 | — | 146 | 2 | no | — |
| 207 | #120 | — | 292 | 1 | no | — |
| 208 | C4×D4 | — | 292 | 2 | no | — |
| 209 | #117 | — | 146 | 1 | no | — |
| 210 | M32 | — | 73 | 4 | no | — |
| 211 | M32 | — | 146 | 2 | no | — |
| 212 | C2×C16 | — | 146 | 2 | no | — |
| 213 | #108 | — | 2 | 4 | no | — |
| 214 | #108 | — | 2 | 2 | no | — |
| 215 | #108 | C22×D73 | 1 | 4 | yes | — |
| 216 | #107 | — | 146 | 1 | no | — |
| 217 | #106 | — | 73 | 2 | no | — |
| 218 | #103 | — | 146 | 2 | no | — |
| 219 | #102 | — | 146 | 2 | no | — |
| 220 | C24 | #11924015 | 1 | 1 | yes | characteristic |
| 221 | #41 | — | 292 | 1 | no | — |
| 222 | #41 | — | 292 | 1 | no | — |
| 223 | #41 | — | 292 | 1 | no | — |
| 224 | #41 | — | 292 | 1 | no | — |
| 225 | C2×Q8 | — | 146 | 1 | no | — |
| 226 | C2×D4 | — | 292 | 2 | no | — |
| 227 | C2×D4 | — | 292 | 1 | no | — |
| 228 | C2×D4 | — | 146 | 1 | no | — |
| 229 | C22×C4 | — | 2 | 1 | no | — |
| 230 | C22×C4 | — | 2 | 1 | no | — |
| 231 | C22×C4 | — | 2 | 1 | no | — |
| 232 | C22×C4 | — | 2 | 1 | no | — |
| 233 | C22×C4 | — | 292 | 1 | no | — |
| 234 | C22×C4 | #11924015 | 1 | 2 | yes | — |
| 235 | C22×C4 | #11924015 | 1 | 1 | yes | characteristic |
| 236 | C22×C4 | C2×C22⋊D73 | 1 | 2 | yes | — |
| 237 | C22×C4 | C2×C22⋊D73 | 1 | 1 | yes | characteristic |
| 238 | Q16 | — | 146 | 2 | no | — |
| 239 | SD16 | — | 292 | 2 | no | — |
| 240 | D8 | — | 146 | 2 | no | — |
| 241 | M16 | — | 2 | 4 | no | — |
| 242 | M16 | — | 2 | 4 | no | — |
| 243 | M16 | — | 2 | 4 | no | — |
| 244 | M16 | — | 4 | 4 | no | — |
| 245 | M16 | — | 4 | 2 | no | — |
| 246 | C2×C8 | — | 2 | 1 | no | — |
| 247 | C2×C8 | — | 2 | 1 | no | — |
| 248 | C2×C8 | — | 4 | 4 | no | — |
| 249 | C2×C8 | — | 4 | 2 | no | — |
| 250 | C2×C8 | C2×C22⋊D73 | 1 | 2 | yes | — |
| 251 | C2×C8 | C2×C22⋊D73 | 1 | 1 | yes | characteristic |
| 252 | C2×C8 | #11924028 | 1 | 2 | yes | — |
| 253 | C2×C8 | #11924028 | 1 | 2 | yes | — |
| 254 | C2×C8 | C23×D73 | 1 | 1 | yes | characteristic |
| 255 | C4⋊C4 | — | 292 | 2 | no | — |
| 256 | C4⋊C4 | — | 146 | 2 | no | — |
| 257 | C22⋊C4 | — | 292 | 1 | no | — |
| 258 | C22⋊C4 | — | 292 | 2 | no | — |
| 259 | C22⋊C4 | — | 292 | 2 | no | — |
| 260 | C42 | — | 292 | 1 | no | — |
| 261 | C16 | — | 146 | 4 | no | — |
| 262 | C23 | — | 2 | 1 | no | — |
| 263 | C23 | — | 2 | 1 | no | — |
| 264 | C23 | — | 8 | 1 | no | — |
| 265 | C23 | — | 292 | 1 | no | — |
| 266 | C23 | C2×#11924015 | 1 | 2 | yes | — |
| 267 | C23 | C2×#11924015 | 1 | 1 | yes | characteristic |
| 268 | Q8 | — | 292 | 1 | no | — |
| 269 | Q8 | — | 292 | 1 | no | — |
| 270 | D4 | — | 292 | 1 | no | — |
| 271 | D4 | — | 292 | 1 | no | — |
| 272 | D4 | — | 584 | 4 | no | — |
| 273 | D4 | — | 584 | 1 | no | — |
| 274 | D4 | — | 584 | 1 | no | — |
| 275 | C2×C4 | — | 2 | 1 | no | — |
| 276 | C2×C4 | — | 2 | 1 | no | — |
| 277 | C2×C4 | — | 2 | 2 | no | — |
| 278 | C2×C4 | — | 2 | 2 | no | — |
| 279 | C2×C4 | — | 2 | 2 | no | — |
| 280 | C2×C4 | — | 2 | 2 | no | — |
| 281 | C2×C4 | — | 292 | 2 | no | — |
| 282 | C2×C4 | — | 292 | 1 | no | — |
| 283 | C2×C4 | — | 584 | 1 | no | — |
| 284 | C2×C4 | — | 584 | 1 | no | — |
| 285 | C2×C4 | #14556574 | 1 | 1 | yes | characteristic |
| 286 | C2×C4 | #14556574 | 1 | 1 | yes | characteristic |
| 287 | C2×C4 | C2×#11924015 | 1 | 2 | yes | — |
| 288 | C2×C4 | C2×#11924015 | 1 | 1 | yes | characteristic |
| 289 | C2×C4 | #14556617 | 1 | 1 | yes | characteristic |
| 290 | C2×C4 | #14556617 | 1 | 1 | yes | characteristic |
| 291 | C2×C4 | C22×C22⋊D73 | 1 | 1 | yes | characteristic |
| 292 | C8 | — | 2 | 2 | no | — |
| 293 | C8 | — | 4 | 4 | no | — |
| 294 | C8 | #14556574 | 1 | 2 | yes | — |
| 295 | C8 | C2×#11924028 | 1 | 2 | yes | — |
| 296 | C22 | — | 2 | 2 | no | — |
| 297 | C22 | — | 4 | 1 | no | — |
| 298 | C22 | — | 4 | 2 | no | — |
| 299 | C22 | — | 4 | 2 | no | — |
| 300 | C22 | — | 8 | 1 | no | — |
| 301 | C22 | — | 584 | 2 | no | — |
| 302 | C22 | — | 584 | 1 | no | — |
| 303 | C22 | #17988905 | 1 | 1 | yes | characteristic |
| 304 | C22 | #17988905 | 1 | 1 | yes | characteristic |
| 305 | C22 | C22×#11924015 | 1 | 1 | yes | characteristic |
| 306 | C4 | — | 2 | 2 | no | — |
| 307 | C4 | — | 584 | 2 | no | — |
| 308 | C4 | — | 584 | 1 | no | — |
| 309 | C4 | #17988905 | 1 | 1 | yes | characteristic |
| 310 | C4 | #17988905 | 1 | 1 | yes | characteristic |
| 311 | C4 | C2×#14556574 | 1 | 1 | yes | characteristic |
| 312 | C4 | C2×#14556617 | 1 | 1 | yes | characteristic |
| 313 | C2 | — | 2 | 1 | no | — |
| 314 | C2 | — | 2 | 1 | no | — |
| 315 | C2 | — | 2 | 1 | no | — |
| 316 | C2 | — | 4 | 2 | no | — |
| 317 | C2 | — | 1168 | 1 | no | — |
| 318 | C2 | C2×#17988905 | 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