← #34018488
Subgroups — #34018488
Order 18688.
682 conjugacy classes of subgroups.
The subgroup lattice has 342 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22626743 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22625570 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22625568 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22625564 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22625481 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22625223 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C8×#11924036 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C4×#14556610 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #17989637 | C22 | 1 | 4 | yes | — |
| 10 | #17989622 | C22 | 1 | 4 | yes | — |
| 11 | #17989619 | — | 2 | 4 | no | — |
| 12 | #17989606 | C22 | 1 | 2 | yes | — |
| 13 | #17989603 | — | 2 | 2 | no | — |
| 14 | C4×#11924037 | — | 2 | 2 | no | — |
| 15 | C4×#11924036 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×#11924036 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17989450 | C22 | 1 | 2 | yes | — |
| 18 | #17989449 | C22 | 1 | 2 | yes | — |
| 19 | #17989437 | C22 | 1 | 4 | yes | — |
| 20 | D4⋊#10596833 | C22 | 1 | 4 | yes | — |
| 21 | C8×#10596833 | C22 | 1 | 2 | yes | — |
| 22 | C8×#10596833 | C22 | 1 | 2 | yes | — |
| 23 | C2×#14556610 | C4 | 1 | 1 | yes | characteristic |
| 24 | C4×#11924027 | C22 | 1 | 2 | yes | — |
| 25 | C4×Dic292 | C4 | 1 | 1 | yes | characteristic |
| 26 | #17988681 | C22 | 1 | 1 | yes | characteristic |
| 27 | #17988678 | C22 | 1 | 2 | yes | — |
| 28 | C4×#11924016 | C4 | 1 | 2 | yes | — |
| 29 | D8×Dic73 | C22 | 1 | 1 | yes | characteristic |
| 30 | #17988624 | C4 | 1 | 1 | yes | characteristic |
| 31 | #17988580 | C4 | 1 | 2 | yes | — |
| 32 | C4×C8×D73 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×D8×C73 | C4 | 1 | 1 | yes | characteristic |
| 34 | C2×#11924037 | — | 2 | 4 | no | — |
| 35 | C2×#11924036 | — | 2 | 1 | no | — |
| 36 | C2×#11924036 | D4 | 1 | 2 | yes | — |
| 37 | C4⋊#10596833 | — | 2 | 4 | no | — |
| 38 | C4⋊#10596833 | C23 | 1 | 4 | yes | — |
| 39 | #14556648 | — | 2 | 2 | no | — |
| 40 | C22⋊#10596833 | — | 2 | 4 | no | — |
| 41 | #14556646 | — | 2 | 4 | no | — |
| 42 | C4×#10596833 | — | 2 | 2 | no | — |
| 43 | C4×#10596833 | — | 2 | 1 | no | — |
| 44 | C4×#10596833 | D4 | 1 | 1 | yes | characteristic |
| 45 | C4×#10596833 | D4 | 1 | 1 | yes | characteristic |
| 46 | C4×#10596833 | C23 | 1 | 2 | yes | — |
| 47 | C4×#10596833 | C23 | 1 | 2 | yes | — |
| 48 | C2×#11924027 | C2×C4 | 1 | 2 | yes | — |
| 49 | #14556610 | — | 2 | 4 | no | — |
| 50 | C2×Dic292 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×#11924016 | C2×C4 | 1 | 2 | yes | — |
| 52 | C2×C8×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C2×C8×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C4×Dic146 | C2×C4 | 1 | 2 | yes | — |
| 55 | #14556556 | C23 | 1 | 2 | yes | — |
| 56 | D4×Dic73 | C23 | 1 | 2 | yes | — |
| 57 | C4×C22⋊D73 | — | 2 | 2 | no | — |
| 58 | #14556551 | — | 2 | 2 | no | — |
| 59 | #14556549 | C2×C4 | 1 | 2 | yes | — |
| 60 | #14556547 | — | 2 | 2 | no | — |
| 61 | C2×C4×Dic73 | — | 2 | 2 | no | — |
| 62 | C42×D73 | C23 | 1 | 1 | yes | characteristic |
| 63 | #14556525 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | #14556522 | C2×C4 | 1 | 2 | yes | — |
| 65 | #14556516 | C2×C4 | 1 | 2 | yes | — |
| 66 | #14556514 | C2×C4 | 1 | 2 | yes | — |
| 67 | #14556512 | C2×C4 | 1 | 2 | yes | — |
| 68 | C4×#10596831 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | C8×Dic73 | C23 | 1 | 1 | yes | characteristic |
| 70 | C8×Dic73 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×D8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | C4×D4×C73 | C2×C4 | 1 | 2 | yes | — |
| 73 | #107×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #102×C73 | C2×C4 | 1 | 2 | yes | — |
| 75 | C4×C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 76 | #11924037 | — | 4 | 8 | no | — |
| 77 | #11924036 | — | 2 | 4 | no | — |
| 78 | #11924036 | — | 2 | 4 | no | — |
| 79 | C2×#10596833 | — | 2 | 2 | no | — |
| 80 | C2×#10596833 | — | 2 | 4 | no | — |
| 81 | C2×#10596833 | C2×D4 | 1 | 2 | yes | — |
| 82 | C2×#10596833 | C2×D4 | 1 | 2 | yes | — |
| 83 | #11924027 | — | 2 | 4 | no | — |
| 84 | #11924027 | — | 2 | 4 | no | — |
| 85 | C2×Dic146 | C22×C4 | 1 | 2 | yes | — |
| 86 | C2×C22⋊D73 | — | 2 | 2 | no | — |
| 87 | C22×Dic73 | — | 2 | 2 | no | — |
| 88 | C22×Dic73 | — | 2 | 2 | no | — |
| 89 | C2×C4×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C4×D73 | #41 | 1 | 1 | yes | characteristic |
| 92 | Dic292 | — | 2 | 2 | no | — |
| 93 | #11924016 | — | 2 | 4 | no | — |
| 94 | C2×#10596831 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C2×#10596831 | C22×C4 | 1 | 1 | yes | characteristic |
| 96 | C8×D73 | — | 2 | 2 | no | — |
| 97 | C8×D73 | M16 | 1 | 4 | yes | complemented |
| 98 | C4⋊Dic73 | C22×C4 | 1 | 2 | yes | — |
| 99 | #11924007 | — | 2 | 2 | no | — |
| 100 | #11924007 | — | 2 | 2 | no | — |
| 101 | C22⋊Dic73 | — | 2 | 2 | no | — |
| 102 | #11924005 | — | 2 | 2 | no | — |
| 103 | C4×Dic73 | — | 2 | 2 | no | — |
| 104 | C4×Dic73 | — | 2 | 2 | no | — |
| 105 | C4×Dic73 | — | 2 | 2 | no | — |
| 106 | C4×Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C4×Dic73 | #41 | 1 | 1 | yes | characteristic |
| 108 | C4×Dic73 | C24 | 1 | 1 | yes | characteristic |
| 109 | C2×D4×C73 | C22×C4 | 1 | 2 | yes | — |
| 110 | C22×C4×C73 | — | 2 | 2 | no | — |
| 111 | D8×C73 | — | 2 | 2 | no | — |
| 112 | C2×C8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 113 | C2×C8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 114 | C4⋊C4×C73 | C22×C4 | 1 | 2 | yes | — |
| 115 | C22⋊C4×C73 | — | 2 | 2 | no | — |
| 116 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 117 | C23×C73 | — | 2 | 2 | no | — |
| 118 | C22×D73 | C4×D4 | 1 | 1 | yes | characteristic |
| 119 | D4×C73 | — | 2 | 2 | no | — |
| 120 | D4×C73 | — | 2 | 2 | no | — |
| 121 | C2×C4×C73 | — | 2 | 2 | no | — |
| 122 | C2×C4×C73 | — | 4 | 4 | no | — |
| 123 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C4×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 126 | C22⋊D73 | — | 4 | 4 | no | — |
| 127 | C2×Dic73 | — | 2 | 2 | no | — |
| 128 | C2×Dic73 | — | 2 | 2 | no | — |
| 129 | C2×Dic73 | — | 4 | 4 | no | — |
| 130 | C2×Dic73 | — | 4 | 4 | no | — |
| 131 | C2×Dic73 | C4×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×Dic73 | C22×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×Dic73 | C2×#41 | 1 | 1 | yes | characteristic |
| 134 | C4×D73 | — | 2 | 2 | no | — |
| 135 | C4×D73 | — | 2 | 2 | no | — |
| 136 | C4×D73 | C2×M16 | 1 | 2 | yes | — |
| 137 | C4×D73 | #131 | 1 | 2 | yes | — |
| 138 | Dic146 | — | 2 | 2 | no | — |
| 139 | Dic146 | — | 2 | 2 | no | — |
| 140 | #10596833 | — | 2 | 4 | no | — |
| 141 | #10596833 | — | 2 | 2 | no | — |
| 142 | #10596833 | — | 4 | 4 | no | — |
| 143 | #10596833 | #135 | 1 | 4 | yes | complemented |
| 144 | C8×C73 | — | 2 | 1 | no | — |
| 145 | C8×C73 | C2×M16 | 1 | 2 | yes | — |
| 146 | #10596831 | — | 2 | 1 | no | — |
| 147 | #10596831 | C2×M16 | 1 | 2 | yes | — |
| 148 | C22×C73 | — | 4 | 2 | no | — |
| 149 | C22×C73 | — | 4 | 2 | no | — |
| 150 | C22×C73 | — | 4 | 2 | no | — |
| 151 | C22×C73 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×D73 | — | 2 | 1 | no | — |
| 153 | C2×D73 | — | 2 | 1 | no | — |
| 154 | C2×D73 | #436 | 1 | 2 | yes | — |
| 155 | C4×C73 | — | 2 | 1 | no | — |
| 156 | C4×C73 | — | 4 | 2 | no | — |
| 157 | C4×C73 | #443 | 1 | 2 | yes | — |
| 158 | C4×C73 | C22×M16 | 1 | 1 | yes | characteristic |
| 159 | C4×C73 | C2×#131 | 1 | 1 | yes | characteristic |
| 160 | Dic73 | — | 2 | 1 | no | — |
| 161 | Dic73 | — | 4 | 2 | no | — |
| 162 | Dic73 | — | 4 | 2 | no | — |
| 163 | Dic73 | #436 | 1 | 2 | yes | — |
| 164 | Dic73 | C2×#135 | 1 | 2 | yes | — |
| 165 | #17886 | — | 73 | 1 | no | maximal, Sylow |
| 166 | C2×C73 | — | 8 | 2 | no | — |
| 167 | C2×C73 | C2×#436 | 1 | 1 | yes | characteristic |
| 168 | C2×C73 | C4×#135 | 1 | 1 | yes | characteristic |
| 169 | C2×C73 | C2×#443 | 1 | 1 | yes | characteristic |
| 170 | D73 | — | 2 | 2 | no | — |
| 171 | #2965 | — | 73 | 2 | no | — |
| 172 | C4×#135 | — | 73 | 1 | no | — |
| 173 | #1591 | — | 73 | 2 | no | — |
| 174 | #1590 | — | 73 | 4 | no | — |
| 175 | #1589 | — | 73 | 2 | no | — |
| 176 | #1564 | — | 73 | 1 | no | — |
| 177 | #1476 | — | 73 | 2 | no | — |
| 178 | C2×C82 | — | 73 | 1 | no | — |
| 179 | C73 | #17886 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 180 | C2×#135 | — | 73 | 1 | no | — |
| 181 | C4×#41 | — | 73 | 2 | no | — |
| 182 | #446 | — | 73 | 4 | no | — |
| 183 | C4×Q16 | — | 73 | 1 | no | — |
| 184 | C4×Q16 | — | 73 | 1 | no | — |
| 185 | C4×SD16 | — | 73 | 2 | no | — |
| 186 | C4×SD16 | — | 73 | 2 | no | — |
| 187 | C4×D8 | — | 73 | 1 | no | — |
| 188 | C4×D8 | #64408 | 1 | 1 | yes | characteristic |
| 189 | #436 | — | 73 | 4 | no | — |
| 190 | #435 | — | 146 | 4 | no | — |
| 191 | #431 | — | 73 | 2 | no | — |
| 192 | #431 | — | 146 | 2 | no | — |
| 193 | #427 | — | 73 | 1 | no | — |
| 194 | #416 | — | 73 | 2 | no | — |
| 195 | C4×M16 | — | 146 | 2 | no | — |
| 196 | C2×C4×C8 | — | 73 | 1 | no | — |
| 197 | C2×C4×C8 | — | 73 | 1 | no | — |
| 198 | C2×C4×C8 | — | 73 | 1 | no | — |
| 199 | #335 | — | 73 | 2 | no | — |
| 200 | #334 | — | 73 | 2 | no | — |
| 201 | Q8⋊C8 | — | 73 | 4 | no | — |
| 202 | D4⋊C8 | — | 73 | 4 | no | — |
| 203 | C82 | — | 73 | 2 | no | — |
| 204 | C82 | — | 73 | 2 | no | — |
| 205 | C2×#41 | — | 73 | 2 | no | — |
| 206 | #135 | — | 146 | 4 | no | — |
| 207 | C2×Q16 | — | 73 | 1 | no | — |
| 208 | C2×SD16 | — | 73 | 2 | no | — |
| 209 | C2×D8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 210 | C2×M16 | — | 146 | 4 | no | — |
| 211 | C22×C8 | — | 73 | 1 | no | — |
| 212 | C22×C8 | — | 73 | 2 | no | — |
| 213 | C22×C8 | — | 73 | 1 | no | — |
| 214 | C22×C8 | — | 146 | 1 | no | — |
| 215 | C4×Q8 | — | 73 | 2 | no | — |
| 216 | C4×Q8 | — | 73 | 2 | no | — |
| 217 | C4×D4 | — | 73 | 2 | no | — |
| 218 | C4×D4 | — | 146 | 2 | no | — |
| 219 | C4×D4 | — | 146 | 2 | no | — |
| 220 | C4×D4 | C2×#64408 | 1 | 2 | yes | — |
| 221 | #117 | — | 73 | 2 | no | — |
| 222 | #117 | — | 146 | 2 | no | — |
| 223 | C2×C42 | — | 73 | 1 | no | — |
| 224 | C2×C42 | — | 146 | 2 | no | — |
| 225 | #107 | — | 73 | 1 | no | — |
| 226 | #107 | C2×#64408 | 1 | 1 | yes | characteristic |
| 227 | #106 | — | 73 | 2 | no | — |
| 228 | C4⋊C8 | — | 73 | 4 | no | — |
| 229 | C4⋊C8 | — | 146 | 4 | no | — |
| 230 | #103 | — | 73 | 2 | no | — |
| 231 | #103 | — | 73 | 2 | no | — |
| 232 | #102 | — | 73 | 2 | no | — |
| 233 | #102 | C2×#64408 | 1 | 2 | yes | — |
| 234 | C22⋊C8 | — | 146 | 4 | no | — |
| 235 | C22⋊C8 | — | 146 | 2 | no | — |
| 236 | #97 | — | 146 | 4 | no | — |
| 237 | C4×C8 | — | 73 | 2 | no | — |
| 238 | C4×C8 | — | 73 | 1 | no | — |
| 239 | C4×C8 | — | 73 | 1 | no | — |
| 240 | C4×C8 | — | 73 | 1 | no | — |
| 241 | C4×C8 | — | 73 | 1 | no | — |
| 242 | C4×C8 | — | 73 | 2 | no | — |
| 243 | C4×C8 | — | 73 | 1 | no | — |
| 244 | C4×C8 | — | 146 | 1 | no | — |
| 245 | C4×C8 | — | 146 | 2 | no | — |
| 246 | C4×C8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 247 | #41 | — | 146 | 4 | no | — |
| 248 | #41 | — | 146 | 4 | no | — |
| 249 | C2×Q8 | — | 73 | 2 | no | — |
| 250 | C2×D4 | — | 146 | 2 | no | — |
| 251 | C2×D4 | C22×#64408 | 1 | 2 | yes | — |
| 252 | C22×C4 | — | 2 | 2 | no | — |
| 253 | C22×C4 | — | 73 | 1 | no | — |
| 254 | C22×C4 | — | 73 | 1 | no | — |
| 255 | C22×C4 | — | 73 | 1 | no | — |
| 256 | C22×C4 | — | 146 | 2 | no | — |
| 257 | C22×C4 | — | 146 | 2 | no | — |
| 258 | Q16 | — | 146 | 2 | no | — |
| 259 | SD16 | — | 146 | 4 | no | — |
| 260 | D8 | — | 2 | 2 | no | — |
| 261 | M16 | — | 292 | 8 | no | — |
| 262 | C2×C8 | — | 73 | 2 | no | — |
| 263 | C2×C8 | — | 73 | 1 | no | — |
| 264 | C2×C8 | — | 73 | 4 | no | — |
| 265 | C2×C8 | — | 73 | 2 | no | — |
| 266 | C2×C8 | — | 73 | 1 | no | — |
| 267 | C2×C8 | — | 146 | 2 | no | — |
| 268 | C2×C8 | — | 146 | 4 | no | — |
| 269 | C2×C8 | — | 146 | 4 | no | — |
| 270 | C2×C8 | — | 146 | 2 | no | — |
| 271 | C2×C8 | — | 146 | 4 | no | — |
| 272 | C2×C8 | C22×#64408 | 1 | 1 | yes | characteristic |
| 273 | C2×C8 | C22×#64408 | 1 | 1 | yes | characteristic |
| 274 | C4⋊C4 | — | 73 | 2 | no | — |
| 275 | C4⋊C4 | — | 146 | 2 | no | — |
| 276 | C4⋊C4 | — | 146 | 2 | no | — |
| 277 | C4⋊C4 | C22×#64408 | 1 | 2 | yes | — |
| 278 | C22⋊C4 | — | 2 | 2 | no | — |
| 279 | C22⋊C4 | — | 146 | 2 | no | — |
| 280 | C22⋊C4 | — | 146 | 2 | no | — |
| 281 | C42 | — | 73 | 1 | no | — |
| 282 | C42 | — | 73 | 1 | no | — |
| 283 | C42 | — | 73 | 1 | no | — |
| 284 | C42 | — | 146 | 2 | no | — |
| 285 | C42 | — | 146 | 2 | no | — |
| 286 | C42 | — | 146 | 2 | no | — |
| 287 | C42 | C22×#64408 | 1 | 1 | yes | characteristic |
| 288 | C23 | — | 2 | 2 | no | — |
| 289 | C23 | — | 73 | 1 | no | — |
| 290 | Q8 | — | 146 | 2 | no | — |
| 291 | Q8 | — | 146 | 2 | no | — |
| 292 | D4 | — | 2 | 2 | no | — |
| 293 | D4 | — | 2 | 2 | no | — |
| 294 | D4 | — | 292 | 4 | no | — |
| 295 | C2×C4 | — | 2 | 2 | no | — |
| 296 | C2×C4 | — | 4 | 4 | no | — |
| 297 | C2×C4 | — | 292 | 4 | no | — |
| 298 | C2×C4 | — | 292 | 4 | no | — |
| 299 | C2×C4 | — | 73 | 1 | no | — |
| 300 | C2×C4 | — | 73 | 1 | no | — |
| 301 | C2×C4 | — | 73 | 2 | no | — |
| 302 | C2×C4 | — | 73 | 2 | no | — |
| 303 | C2×C4 | — | 73 | 1 | no | — |
| 304 | C2×C4 | — | 146 | 2 | no | — |
| 305 | C2×C4 | — | 146 | 2 | no | — |
| 306 | C2×C4 | — | 146 | 2 | no | — |
| 307 | C2×C4 | — | 146 | 2 | no | — |
| 308 | C2×C4 | D4×#64408 | 1 | 1 | yes | characteristic |
| 309 | C2×C4 | D4×#64408 | 1 | 1 | yes | characteristic |
| 310 | C2×C4 | C23×#64408 | 1 | 1 | yes | characteristic |
| 311 | C8 | — | 2 | 1 | no | — |
| 312 | C8 | — | 292 | 4 | no | — |
| 313 | C8 | — | 73 | 4 | no | — |
| 314 | C8 | — | 73 | 2 | no | — |
| 315 | C8 | — | 146 | 2 | no | — |
| 316 | C8 | — | 146 | 4 | no | — |
| 317 | C8 | — | 146 | 1 | no | — |
| 318 | C8 | D73⋊M16 | 1 | 2 | yes | — |
| 319 | C22 | — | 4 | 2 | no | — |
| 320 | C22 | — | 4 | 2 | no | — |
| 321 | C22 | — | 4 | 2 | no | — |
| 322 | C22 | — | 73 | 2 | no | — |
| 323 | C22 | — | 146 | 1 | no | — |
| 324 | C22 | — | 146 | 1 | no | — |
| 325 | C22 | C2×D4×#64408 | 1 | 1 | yes | characteristic |
| 326 | C4 | — | 2 | 1 | no | — |
| 327 | C4 | — | 4 | 2 | no | — |
| 328 | C4 | — | 292 | 2 | no | — |
| 329 | C4 | — | 292 | 2 | no | — |
| 330 | C4 | — | 73 | 2 | no | — |
| 331 | C4 | — | 73 | 2 | no | — |
| 332 | C4 | — | 146 | 1 | no | — |
| 333 | C4 | #17989629 | 1 | 2 | yes | — |
| 334 | C4 | C2×D73⋊M16 | 1 | 1 | yes | characteristic |
| 335 | C4 | D73⋊#131 | 1 | 1 | yes | characteristic |
| 336 | C2 | — | 8 | 2 | no | — |
| 337 | C2 | — | 146 | 2 | no | — |
| 338 | C2 | D73⋊#436 | 1 | 1 | yes | characteristic |
| 339 | C2 | #135×#64408 | 1 | 1 | yes | characteristic |
| 340 | C2 | C2×#17989629 | 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