← #33004480
Subgroups — #33004480
Order 18688.
472 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 | #22620359 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22611668 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22611660 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22609810 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#364×C73 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#14556613 | — | 2 | 1 | no | — |
| 7 | C2×#14556613 | C22 | 1 | 2 | yes | — |
| 8 | #17989137 | — | 2 | 1 | no | — |
| 9 | #17988971 | — | 2 | 1 | no | — |
| 10 | #17988971 | C4 | 1 | 2 | yes | complemented |
| 11 | #17988967 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | #17988964 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | #17988960 | — | 2 | 1 | no | — |
| 14 | C2×#14556527 | C22 | 1 | 1 | yes | characteristic |
| 15 | #17988625 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17988542 | — | 2 | 1 | no | — |
| 17 | #17988398 | — | 2 | 4 | no | — |
| 18 | #17988395 | — | 2 | 4 | no | — |
| 19 | #17988347 | — | 2 | 1 | no | — |
| 20 | C2×M32×C73 | C22 | 1 | 2 | yes | — |
| 21 | C2×C4×C8×C73 | C22 | 1 | 1 | yes | characteristic |
| 22 | #364×C73 | — | 2 | 1 | no | — |
| 23 | #364×C73 | — | 2 | 1 | no | — |
| 24 | C2×#11924028 | — | 2 | 2 | no | — |
| 25 | #14556613 | — | 2 | 2 | no | — |
| 26 | #14556613 | — | 2 | 2 | no | — |
| 27 | #14556613 | — | 2 | 2 | no | — |
| 28 | #14556613 | — | 2 | 2 | no | — |
| 29 | #14556613 | — | 4 | 1 | no | — |
| 30 | #14556613 | — | 4 | 1 | no | — |
| 31 | #14556613 | — | 4 | 1 | no | — |
| 32 | #14556613 | — | 4 | 1 | no | — |
| 33 | C2×Dic292 | — | 2 | 1 | no | — |
| 34 | C2×Dic292 | C2×C4 | 1 | 2 | yes | — |
| 35 | C2×#11924017 | — | 2 | 2 | no | — |
| 36 | C2×#11924017 | — | 2 | 2 | no | — |
| 37 | C2×D584 | — | 2 | 1 | no | — |
| 38 | C2×D584 | C2×C4 | 1 | 2 | yes | — |
| 39 | C2×#11924012 | — | 2 | 1 | no | — |
| 40 | #14556591 | — | 2 | 1 | no | — |
| 41 | #14556588 | — | 2 | 1 | no | — |
| 42 | #14556579 | — | 2 | 2 | no | — |
| 43 | #14556565 | — | 4 | 2 | no | — |
| 44 | C4×D292 | — | 4 | 2 | no | — |
| 45 | #14556550 | — | 2 | 1 | no | — |
| 46 | #14556527 | — | 2 | 1 | no | — |
| 47 | #14556527 | D4 | 1 | 2 | yes | complemented |
| 48 | #14556525 | — | 2 | 1 | no | — |
| 49 | #14556523 | D4 | 1 | 2 | yes | complemented |
| 50 | #14556501 | — | 4 | 1 | no | — |
| 51 | C8×Dic73 | — | 4 | 1 | no | — |
| 52 | C22×C8×C73 | D4 | 1 | 1 | yes | characteristic |
| 53 | C22×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 54 | C2×C42×C73 | D4 | 1 | 1 | yes | characteristic |
| 55 | M32×C73 | — | 2 | 2 | no | — |
| 56 | M32×C73 | — | 2 | 2 | no | — |
| 57 | C2×C16×C73 | — | 2 | 2 | no | — |
| 58 | C4×C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C4×C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C4×C8×C73 | D4 | 1 | 1 | yes | characteristic |
| 61 | C4×C8×C73 | D4 | 1 | 1 | yes | characteristic |
| 62 | #11924028 | — | 4 | 2 | no | — |
| 63 | #11924028 | — | 4 | 2 | no | — |
| 64 | #11924028 | — | 4 | 2 | no | — |
| 65 | #11924028 | — | 4 | 2 | no | — |
| 66 | C2×Dic146 | — | 2 | 2 | no | — |
| 67 | C2×D292 | — | 2 | 2 | no | — |
| 68 | C2×D292 | — | 4 | 2 | no | — |
| 69 | C2×C22⋊D73 | — | 4 | 2 | no | — |
| 70 | C2×C4×D73 | — | 4 | 2 | no | — |
| 71 | Dic292 | — | 2 | 2 | no | — |
| 72 | Dic292 | — | 2 | 2 | no | — |
| 73 | Dic292 | — | 4 | 1 | no | — |
| 74 | Dic292 | — | 4 | 1 | no | — |
| 75 | #11924017 | — | 4 | 2 | no | — |
| 76 | #11924017 | — | 4 | 2 | no | — |
| 77 | #11924017 | — | 4 | 2 | no | — |
| 78 | #11924017 | — | 4 | 2 | no | — |
| 79 | D584 | — | 2 | 2 | no | — |
| 80 | D584 | — | 2 | 2 | no | — |
| 81 | D584 | — | 4 | 1 | no | — |
| 82 | D584 | — | 4 | 1 | no | — |
| 83 | #11924012 | — | 2 | 2 | no | — |
| 84 | #11924012 | — | 4 | 1 | no | — |
| 85 | C2×#10596831 | — | 4 | 1 | no | — |
| 86 | C4⋊Dic73 | — | 2 | 2 | no | — |
| 87 | C4⋊Dic73 | — | 4 | 2 | no | — |
| 88 | C22⋊Dic73 | — | 4 | 1 | no | — |
| 89 | #11924005 | — | 4 | 4 | no | — |
| 90 | C4×Dic73 | — | 4 | 1 | no | — |
| 91 | C22×C4×C73 | — | 2 | 1 | no | — |
| 92 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C2×C8×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 95 | C2×C8×C73 | D8 | 1 | 1 | yes | characteristic |
| 96 | C2×C8×C73 | D8 | 1 | 1 | yes | characteristic |
| 97 | C2×C8×C73 | SD16 | 1 | 1 | yes | characteristic |
| 98 | C2×C8×C73 | SD16 | 1 | 1 | yes | characteristic |
| 99 | C2×C8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×C8×C73 | #41 | 1 | 1 | yes | characteristic |
| 104 | C2×C8×C73 | #41 | 1 | 1 | yes | characteristic |
| 105 | C42×C73 | — | 2 | 1 | no | — |
| 106 | C42×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 107 | C42×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 108 | C16×C73 | — | 4 | 2 | no | — |
| 109 | C23×C73 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 110 | C22×D73 | — | 4 | 2 | no | — |
| 111 | C2×C4×C73 | — | 2 | 1 | no | — |
| 112 | C2×C4×C73 | — | 2 | 1 | no | — |
| 113 | C2×C4×C73 | — | 4 | 2 | no | — |
| 114 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C73 | #121 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C73 | #121 | 1 | 1 | yes | characteristic |
| 117 | C2×C4×C73 | C2×D8 | 1 | 1 | yes | characteristic |
| 118 | C2×C4×C73 | C2×SD16 | 1 | 1 | yes | characteristic |
| 119 | C2×C4×C73 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 120 | C22⋊D73 | — | 8 | 2 | no | — |
| 121 | C22⋊D73 | — | 8 | 2 | no | — |
| 122 | C2×Dic73 | — | 4 | 2 | no | — |
| 123 | C2×Dic73 | — | 4 | 2 | no | — |
| 124 | D292 | — | 4 | 2 | no | — |
| 125 | D292 | — | 4 | 2 | no | — |
| 126 | D292 | — | 8 | 4 | no | — |
| 127 | C4×D73 | — | 8 | 2 | no | — |
| 128 | C4×D73 | — | 8 | 2 | no | — |
| 129 | Dic146 | — | 4 | 2 | no | — |
| 130 | Dic146 | — | 4 | 2 | no | — |
| 131 | C8×C73 | #102 | 1 | 1 | yes | characteristic |
| 132 | C8×C73 | #102 | 1 | 1 | yes | characteristic |
| 133 | C8×C73 | #102 | 1 | 1 | yes | characteristic |
| 134 | C8×C73 | #102 | 1 | 1 | yes | characteristic |
| 135 | C8×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 136 | C8×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 137 | C8×C73 | #124 | 1 | 1 | yes | characteristic |
| 138 | C8×C73 | #127 | 1 | 1 | yes | characteristic |
| 139 | #10596831 | — | 4 | 2 | no | — |
| 140 | C22×C73 | — | 4 | 1 | no | — |
| 141 | C22×C73 | #418 | 1 | 1 | yes | characteristic |
| 142 | C22×C73 | #459 | 1 | 1 | yes | characteristic |
| 143 | C22×C73 | #460 | 1 | 1 | yes | characteristic |
| 144 | C2×D73 | — | 8 | 4 | no | — |
| 145 | C2×D73 | — | 8 | 2 | no | — |
| 146 | C4×C73 | — | 2 | 2 | no | — |
| 147 | C4×C73 | — | 4 | 1 | no | — |
| 148 | C4×C73 | #390 | 1 | 1 | yes | characteristic |
| 149 | C4×C73 | C2×#102 | 1 | 1 | yes | characteristic |
| 150 | C4×C73 | #459 | 1 | 1 | yes | characteristic |
| 151 | C4×C73 | #460 | 1 | 1 | yes | characteristic |
| 152 | Dic73 | — | 8 | 2 | no | — |
| 153 | Dic73 | — | 8 | 2 | no | — |
| 154 | #13259 | — | 73 | 1 | no | maximal, Sylow |
| 155 | C2×C73 | — | 2 | 1 | no | — |
| 156 | C2×C73 | — | 2 | 1 | no | — |
| 157 | C2×C73 | — | 2 | 1 | no | — |
| 158 | C2×C73 | #1982 | 1 | 1 | yes | characteristic |
| 159 | D73 | — | 16 | 2 | no | — |
| 160 | #3147 | — | 73 | 1 | no | — |
| 161 | C2×#364 | D73 | 1 | 1 | yes | characteristic, complemented |
| 162 | #2145 | — | 73 | 2 | no | — |
| 163 | #2143 | — | 73 | 2 | no | — |
| 164 | #1772 | — | 73 | 1 | no | — |
| 165 | C73 | #13259 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 166 | C2×#135 | — | 73 | 2 | no | — |
| 167 | C2×#135 | — | 146 | 1 | no | — |
| 168 | #532 | — | 146 | 1 | no | — |
| 169 | C2×M32 | C2×D73 | 1 | 2 | yes | — |
| 170 | #495 | — | 73 | 2 | no | — |
| 171 | #495 | — | 146 | 1 | no | — |
| 172 | #494 | — | 73 | 1 | no | — |
| 173 | #493 | — | 73 | 1 | no | — |
| 174 | #492 | — | 146 | 1 | no | — |
| 175 | C2×#108 | — | 73 | 1 | no | — |
| 176 | #427 | — | 73 | 1 | no | — |
| 177 | #405 | — | 146 | 1 | no | — |
| 178 | C2×C4×C8 | C2×D73 | 1 | 1 | yes | characteristic |
| 179 | #364 | — | 2 | 1 | no | — |
| 180 | #364 | — | 2 | 1 | no | — |
| 181 | #360 | — | 146 | 4 | no | — |
| 182 | #359 | — | 146 | 4 | no | — |
| 183 | #339 | — | 146 | 1 | no | — |
| 184 | C2×#41 | — | 146 | 2 | no | — |
| 185 | #135 | — | 292 | 1 | no | — |
| 186 | #135 | — | 292 | 1 | no | — |
| 187 | #135 | — | 292 | 1 | no | — |
| 188 | #135 | — | 292 | 1 | no | — |
| 189 | #135 | — | 146 | 2 | no | — |
| 190 | #135 | — | 146 | 2 | no | — |
| 191 | #135 | — | 146 | 2 | no | — |
| 192 | #135 | — | 146 | 2 | no | — |
| 193 | C2×Q16 | — | 73 | 2 | no | — |
| 194 | C2×Q16 | — | 146 | 1 | no | — |
| 195 | C2×SD16 | — | 146 | 2 | no | — |
| 196 | C2×SD16 | — | 146 | 2 | no | — |
| 197 | C2×D8 | — | 73 | 2 | no | — |
| 198 | C2×D8 | — | 146 | 1 | no | — |
| 199 | C2×M16 | — | 146 | 1 | no | — |
| 200 | C22×C8 | D292 | 1 | 1 | yes | characteristic |
| 201 | C22×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 202 | C4⋊Q8 | — | 146 | 1 | no | — |
| 203 | #127 | — | 146 | 1 | no | — |
| 204 | #124 | — | 146 | 2 | no | — |
| 205 | #121 | — | 292 | 2 | no | — |
| 206 | C4×D4 | — | 292 | 2 | no | — |
| 207 | #117 | — | 146 | 1 | no | — |
| 208 | C2×C42 | D292 | 1 | 1 | yes | characteristic |
| 209 | M32 | — | 2 | 2 | no | — |
| 210 | M32 | — | 2 | 2 | no | — |
| 211 | C2×C16 | — | 2 | 2 | no | — |
| 212 | #108 | — | 73 | 2 | no | — |
| 213 | #108 | — | 146 | 1 | no | — |
| 214 | #107 | — | 146 | 1 | no | — |
| 215 | #106 | — | 73 | 2 | no | — |
| 216 | #97 | — | 292 | 1 | no | — |
| 217 | C4×C8 | — | 292 | 1 | no | — |
| 218 | C4×C8 | C4×D73 | 1 | 1 | yes | characteristic |
| 219 | C4×C8 | C4×D73 | 1 | 1 | yes | characteristic |
| 220 | C4×C8 | C22⋊D73 | 1 | 1 | yes | characteristic |
| 221 | C4×C8 | C22⋊D73 | 1 | 1 | yes | characteristic |
| 222 | #41 | — | 292 | 2 | no | — |
| 223 | #41 | — | 292 | 2 | no | — |
| 224 | #41 | — | 292 | 2 | no | — |
| 225 | #41 | — | 292 | 2 | no | — |
| 226 | C2×Q8 | — | 146 | 2 | no | — |
| 227 | C2×D4 | — | 292 | 2 | no | — |
| 228 | C2×D4 | — | 292 | 2 | no | — |
| 229 | C2×D4 | — | 146 | 2 | no | — |
| 230 | C22×C4 | — | 2 | 1 | no | — |
| 231 | C22×C4 | — | 292 | 2 | no | — |
| 232 | C22×C4 | C2×D292 | 1 | 1 | yes | characteristic |
| 233 | Q16 | — | 292 | 1 | no | — |
| 234 | Q16 | — | 292 | 1 | no | — |
| 235 | Q16 | — | 146 | 2 | no | — |
| 236 | Q16 | — | 146 | 2 | no | — |
| 237 | SD16 | — | 292 | 2 | no | — |
| 238 | SD16 | — | 292 | 2 | no | — |
| 239 | SD16 | — | 292 | 2 | no | — |
| 240 | SD16 | — | 292 | 2 | no | — |
| 241 | D8 | — | 292 | 1 | no | — |
| 242 | D8 | — | 292 | 1 | no | — |
| 243 | D8 | — | 146 | 2 | no | — |
| 244 | D8 | — | 146 | 2 | no | — |
| 245 | M16 | — | 292 | 1 | no | — |
| 246 | M16 | — | 146 | 2 | no | — |
| 247 | C2×C8 | — | 292 | 1 | no | — |
| 248 | C2×C8 | #11924005 | 1 | 1 | yes | characteristic |
| 249 | C2×C8 | #11924005 | 1 | 1 | yes | characteristic |
| 250 | C2×C8 | D584 | 1 | 1 | yes | characteristic |
| 251 | C2×C8 | D584 | 1 | 1 | yes | characteristic |
| 252 | C2×C8 | #11924017 | 1 | 1 | yes | characteristic |
| 253 | C2×C8 | #11924017 | 1 | 1 | yes | characteristic |
| 254 | C2×C8 | C2×C4×D73 | 1 | 1 | yes | characteristic |
| 255 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 256 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 257 | C2×C8 | C2×C22⋊D73 | 1 | 1 | yes | characteristic |
| 258 | C2×C8 | #11924029 | 1 | 1 | yes | characteristic |
| 259 | C2×C8 | #11924029 | 1 | 1 | yes | characteristic |
| 260 | C4⋊C4 | — | 292 | 2 | no | — |
| 261 | C4⋊C4 | — | 146 | 2 | no | — |
| 262 | C22⋊C4 | — | 292 | 4 | no | — |
| 263 | C22⋊C4 | — | 292 | 1 | no | — |
| 264 | C42 | — | 2 | 1 | no | — |
| 265 | C42 | — | 292 | 1 | no | — |
| 266 | C42 | #11924005 | 1 | 1 | yes | characteristic |
| 267 | C42 | #11924005 | 1 | 1 | yes | characteristic |
| 268 | C16 | — | 4 | 2 | no | — |
| 269 | C23 | — | 292 | 2 | no | — |
| 270 | C23 | #14556619 | 1 | 1 | yes | characteristic |
| 271 | Q8 | — | 292 | 2 | no | — |
| 272 | Q8 | — | 292 | 2 | no | — |
| 273 | D4 | — | 292 | 2 | no | — |
| 274 | D4 | — | 292 | 2 | no | — |
| 275 | D4 | — | 584 | 4 | no | — |
| 276 | D4 | — | 584 | 2 | no | — |
| 277 | D4 | — | 584 | 2 | no | — |
| 278 | C2×C4 | — | 2 | 1 | no | — |
| 279 | C2×C4 | — | 2 | 1 | no | — |
| 280 | C2×C4 | — | 4 | 2 | no | — |
| 281 | C2×C4 | — | 292 | 2 | no | — |
| 282 | C2×C4 | — | 292 | 2 | no | — |
| 283 | C2×C4 | — | 584 | 2 | no | — |
| 284 | C2×C4 | — | 584 | 2 | no | — |
| 285 | C2×C4 | C2×#11924005 | 1 | 1 | yes | characteristic |
| 286 | C2×C4 | #14556566 | 1 | 1 | yes | characteristic |
| 287 | C2×C4 | #14556566 | 1 | 1 | yes | characteristic |
| 288 | C2×C4 | C2×D584 | 1 | 1 | yes | characteristic |
| 289 | C2×C4 | C2×#11924017 | 1 | 1 | yes | characteristic |
| 290 | C2×C4 | #14556619 | 1 | 1 | yes | characteristic |
| 291 | C8 | — | 292 | 2 | no | — |
| 292 | C8 | #14556513 | 1 | 1 | yes | characteristic |
| 293 | C8 | #14556513 | 1 | 1 | yes | characteristic |
| 294 | C8 | #14556513 | 1 | 1 | yes | characteristic |
| 295 | C8 | #14556513 | 1 | 1 | yes | characteristic |
| 296 | C8 | #14556553 | 1 | 1 | yes | characteristic |
| 297 | C8 | #14556553 | 1 | 1 | yes | characteristic |
| 298 | C8 | #14556580 | 1 | 1 | yes | characteristic |
| 299 | C8 | #14556587 | 1 | 1 | yes | characteristic |
| 300 | C22 | — | 4 | 1 | no | — |
| 301 | C22 | — | 584 | 4 | no | — |
| 302 | C22 | — | 584 | 2 | no | — |
| 303 | C22 | #17988593 | 1 | 1 | yes | characteristic |
| 304 | C22 | #17988783 | 1 | 1 | yes | characteristic |
| 305 | C22 | #17988788 | 1 | 1 | yes | characteristic |
| 306 | C4 | — | 2 | 2 | no | — |
| 307 | C4 | — | 4 | 1 | no | — |
| 308 | C4 | — | 584 | 2 | no | — |
| 309 | C4 | — | 584 | 2 | no | — |
| 310 | C4 | #17988488 | 1 | 1 | yes | characteristic |
| 311 | C4 | C2×#14556513 | 1 | 1 | yes | characteristic |
| 312 | C4 | #17988783 | 1 | 1 | yes | characteristic |
| 313 | C4 | #17988788 | 1 | 1 | yes | characteristic |
| 314 | C2 | — | 2 | 1 | no | — |
| 315 | C2 | — | 2 | 1 | no | — |
| 316 | C2 | — | 2 | 1 | no | — |
| 317 | C2 | — | 1168 | 2 | no | — |
| 318 | C2 | #22610857 | 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