← #33239295
Subgroups — #33239295
Order 18688.
682 conjugacy classes of subgroups.
The subgroup lattice has 252 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #135×Dic73 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22611807 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22611802 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22611796 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22611715 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22611638 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#17988362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#508×C73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #41×Dic73 | — | 2 | 2 | no | — |
| 10 | C22×#11924003 | C22 | 1 | 1 | yes | characteristic |
| 11 | Q16×Dic73 | C22 | 1 | 4 | yes | — |
| 12 | SD16×Dic73 | — | 2 | 4 | no | — |
| 13 | D8×Dic73 | C22 | 1 | 4 | yes | — |
| 14 | #17988625 | C22 | 1 | 2 | yes | — |
| 15 | #17988583 | — | 2 | 2 | no | — |
| 16 | C2×C8×Dic73 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17988415 | C22 | 1 | 2 | yes | — |
| 18 | #17988413 | C22 | 1 | 2 | yes | — |
| 19 | #17988391 | C22 | 1 | 4 | yes | — |
| 20 | #17988388 | C22 | 1 | 4 | yes | — |
| 21 | #17988362 | C22 | 1 | 2 | yes | — |
| 22 | #17988362 | C22 | 1 | 2 | yes | — |
| 23 | C2×#135×C73 | C22 | 1 | 2 | yes | — |
| 24 | #508×C73 | C4 | 1 | 8 | yes | complemented |
| 25 | C2×Q32×C73 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×SD32×C73 | C22 | 1 | 2 | yes | — |
| 27 | C2×D16×C73 | C22 | 1 | 1 | yes | characteristic |
| 28 | C22×C16×C73 | C22 | 1 | 1 | yes | characteristic |
| 29 | C22×#10596831 | D4 | 1 | 1 | yes | characteristic |
| 30 | Q8×Dic73 | — | 2 | 4 | no | — |
| 31 | D4×Dic73 | — | 2 | 4 | no | — |
| 32 | D4×Dic73 | — | 4 | 4 | no | — |
| 33 | #14556550 | — | 2 | 2 | no | — |
| 34 | #14556550 | — | 4 | 2 | no | — |
| 35 | C2×C4×Dic73 | — | 4 | 2 | no | — |
| 36 | C2×C4×Dic73 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×#11924003 | — | 2 | 2 | no | — |
| 38 | C2×#11924003 | C23 | 1 | 2 | yes | — |
| 39 | #14556525 | C23 | 1 | 4 | yes | — |
| 40 | #14556523 | — | 2 | 2 | no | — |
| 41 | #14556515 | — | 2 | 4 | no | — |
| 42 | #14556512 | — | 2 | 4 | no | — |
| 43 | C8×Dic73 | D4 | 1 | 2 | yes | — |
| 44 | C8×Dic73 | C23 | 1 | 2 | yes | — |
| 45 | C2×#41×C73 | — | 2 | 2 | no | — |
| 46 | #135×C73 | — | 2 | 4 | no | — |
| 47 | #135×C73 | C2×C4 | 1 | 8 | yes | complemented |
| 48 | C2×Q16×C73 | C23 | 1 | 2 | yes | — |
| 49 | C2×SD16×C73 | — | 2 | 2 | no | — |
| 50 | C2×D8×C73 | C23 | 1 | 2 | yes | — |
| 51 | C22×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 52 | Q32×C73 | C2×C4 | 1 | 4 | yes | complemented |
| 53 | SD32×C73 | C2×C4 | 1 | 8 | yes | complemented |
| 54 | D16×C73 | C2×C4 | 1 | 4 | yes | complemented |
| 55 | C2×C16×C73 | C2×C4 | 1 | 4 | yes | complemented |
| 56 | C2×C16×C73 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×C16×C73 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×Dic73 | — | 4 | 4 | no | — |
| 59 | C22×Dic73 | D8 | 1 | 2 | yes | — |
| 60 | C2×#10596831 | — | 2 | 2 | no | — |
| 61 | C2×#10596831 | C2×D4 | 1 | 2 | yes | — |
| 62 | C4⋊Dic73 | — | 2 | 4 | no | — |
| 63 | C4⋊Dic73 | — | 4 | 4 | no | — |
| 64 | C22⋊Dic73 | — | 4 | 2 | no | — |
| 65 | C22⋊Dic73 | — | 4 | 4 | no | — |
| 66 | C4×Dic73 | — | 4 | 2 | no | — |
| 67 | C4×Dic73 | — | 4 | 4 | no | — |
| 68 | C4×Dic73 | D8 | 1 | 2 | yes | — |
| 69 | C4×Dic73 | C2×D4 | 1 | 2 | yes | — |
| 70 | #11924003 | — | 2 | 2 | no | — |
| 71 | #41×C73 | — | 2 | 8 | no | — |
| 72 | #41×C73 | — | 4 | 4 | no | — |
| 73 | C2×Q8×C73 | — | 2 | 2 | no | — |
| 74 | C2×D4×C73 | — | 2 | 2 | no | — |
| 75 | C2×D4×C73 | — | 4 | 2 | no | — |
| 76 | C22×C4×C73 | — | 4 | 2 | no | — |
| 77 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 78 | Q16×C73 | — | 2 | 2 | no | — |
| 79 | Q16×C73 | C22×C4 | 1 | 4 | yes | — |
| 80 | SD16×C73 | — | 2 | 8 | no | — |
| 81 | D8×C73 | — | 2 | 2 | no | — |
| 82 | D8×C73 | C22×C4 | 1 | 4 | yes | — |
| 83 | C2×C8×C73 | C22×C4 | 1 | 2 | yes | — |
| 84 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C2×C8×C73 | #41 | 1 | 2 | yes | — |
| 86 | C2×C8×C73 | C24 | 1 | 1 | yes | characteristic |
| 87 | C16×C73 | C22×C4 | 1 | 2 | yes | — |
| 88 | C16×C73 | C22×C4 | 1 | 2 | yes | — |
| 89 | C23×C73 | — | 4 | 2 | no | — |
| 90 | C23×C73 | C2×D8 | 1 | 1 | yes | characteristic |
| 91 | Q8×C73 | — | 2 | 4 | no | — |
| 92 | Q8×C73 | — | 4 | 2 | no | — |
| 93 | D4×C73 | — | 2 | 4 | no | — |
| 94 | D4×C73 | — | 4 | 8 | no | — |
| 95 | D4×C73 | — | 4 | 2 | no | — |
| 96 | C2×C4×C73 | — | 4 | 2 | no | — |
| 97 | C2×C4×C73 | — | 4 | 8 | no | — |
| 98 | C2×C4×C73 | C4×D4 | 1 | 2 | yes | — |
| 99 | C2×C4×C73 | C2×D8 | 1 | 1 | yes | characteristic |
| 100 | C2×C4×C73 | #135 | 1 | 2 | yes | — |
| 101 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×Dic73 | — | 4 | 2 | no | — |
| 103 | C2×Dic73 | — | 4 | 4 | no | — |
| 104 | C2×Dic73 | — | 8 | 8 | no | — |
| 105 | C2×Dic73 | C2×D8 | 1 | 4 | yes | — |
| 106 | C8×C73 | C4×D4 | 1 | 2 | yes | — |
| 107 | C8×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 108 | C8×C73 | C2×#41 | 1 | 1 | yes | characteristic |
| 109 | #10596831 | — | 2 | 2 | no | — |
| 110 | C22×C73 | — | 2 | 2 | no | — |
| 111 | C22×C73 | — | 4 | 4 | no | — |
| 112 | C22×C73 | — | 8 | 4 | no | — |
| 113 | C22×C73 | C4×D8 | 1 | 2 | yes | — |
| 114 | C22×C73 | C22×D8 | 1 | 1 | yes | characteristic |
| 115 | C4×C73 | — | 4 | 4 | no | — |
| 116 | C4×C73 | C4×D8 | 1 | 2 | yes | — |
| 117 | C4×C73 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 118 | C4×C73 | C2×#135 | 1 | 1 | yes | characteristic |
| 119 | Dic73 | — | 2 | 4 | no | — |
| 120 | Dic73 | — | 8 | 4 | no | — |
| 121 | #33451 | — | 73 | 1 | no | maximal, Sylow |
| 122 | C2×C73 | — | 2 | 2 | no | — |
| 123 | C2×C73 | — | 8 | 4 | no | — |
| 124 | C2×C73 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 125 | C2×C73 | #3414 | 1 | 2 | yes | — |
| 126 | C2×#508 | D73 | 1 | 1 | yes | characteristic |
| 127 | C4×#135 | — | 73 | 2 | no | — |
| 128 | #2177 | — | 73 | 2 | no | — |
| 129 | #2176 | — | 73 | 2 | no | — |
| 130 | #2175 | — | 73 | 4 | no | — |
| 131 | #2158 | — | 73 | 1 | no | — |
| 132 | #2138 | — | 73 | 2 | no | — |
| 133 | C2×#346 | — | 73 | 1 | no | — |
| 134 | C73 | #33451 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 135 | C2×#135 | C2×D73 | 1 | 2 | yes | — |
| 136 | C4×#41 | — | 146 | 2 | no | — |
| 137 | #508 | Dic73 | 1 | 8 | yes | complemented |
| 138 | C2×Q32 | C2×D73 | 1 | 1 | yes | characteristic |
| 139 | C2×SD32 | C2×D73 | 1 | 2 | yes | — |
| 140 | C2×D16 | C2×D73 | 1 | 1 | yes | characteristic |
| 141 | C22×C16 | — | 73 | 1 | no | — |
| 142 | C22×C16 | C2×D73 | 1 | 1 | yes | characteristic |
| 143 | C4×Q16 | — | 73 | 4 | no | — |
| 144 | C4×SD16 | — | 146 | 4 | no | — |
| 145 | C4×D8 | — | 73 | 4 | no | — |
| 146 | #427 | — | 73 | 2 | no | — |
| 147 | #416 | — | 146 | 2 | no | — |
| 148 | C2×C4×C8 | — | 73 | 1 | no | — |
| 149 | #367 | — | 73 | 2 | no | — |
| 150 | #366 | — | 73 | 2 | no | — |
| 151 | #358 | — | 73 | 4 | no | — |
| 152 | #357 | — | 73 | 4 | no | — |
| 153 | #346 | — | 73 | 2 | no | — |
| 154 | #346 | — | 73 | 2 | no | — |
| 155 | C2×#41 | — | 2 | 2 | no | — |
| 156 | #135 | — | 2 | 4 | no | — |
| 157 | #135 | C2×Dic73 | 1 | 8 | yes | complemented |
| 158 | C2×Q16 | C22×D73 | 1 | 2 | yes | — |
| 159 | C2×SD16 | — | 2 | 2 | no | — |
| 160 | C2×D8 | C22×D73 | 1 | 2 | yes | — |
| 161 | C22×C8 | — | 73 | 1 | no | — |
| 162 | C22×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 163 | C4×Q8 | — | 146 | 4 | no | — |
| 164 | C4×D4 | — | 292 | 4 | no | — |
| 165 | C4×D4 | — | 146 | 4 | no | — |
| 166 | #117 | — | 292 | 2 | no | — |
| 167 | #117 | — | 146 | 2 | no | — |
| 168 | C2×C42 | — | 292 | 2 | no | — |
| 169 | C2×C42 | — | 73 | 1 | no | — |
| 170 | Q32 | C2×Dic73 | 1 | 4 | yes | complemented |
| 171 | SD32 | C2×Dic73 | 1 | 8 | yes | complemented |
| 172 | D16 | C2×Dic73 | 1 | 4 | yes | complemented |
| 173 | C2×C16 | — | 73 | 2 | no | — |
| 174 | C2×C16 | — | 146 | 2 | no | — |
| 175 | C2×C16 | C2×Dic73 | 1 | 4 | yes | complemented |
| 176 | C2×C16 | C22×D73 | 1 | 1 | yes | characteristic |
| 177 | C2×C16 | C22×D73 | 1 | 1 | yes | characteristic |
| 178 | #107 | — | 73 | 4 | no | — |
| 179 | #106 | — | 146 | 2 | no | — |
| 180 | #103 | — | 146 | 4 | no | — |
| 181 | #102 | — | 146 | 4 | no | — |
| 182 | C4×C8 | — | 73 | 2 | no | — |
| 183 | C4×C8 | — | 73 | 2 | no | — |
| 184 | #41 | — | 2 | 8 | no | — |
| 185 | #41 | — | 4 | 4 | no | — |
| 186 | C2×Q8 | — | 2 | 2 | no | — |
| 187 | C2×D4 | — | 2 | 2 | no | — |
| 188 | C2×D4 | — | 4 | 2 | no | — |
| 189 | C22×C4 | — | 4 | 2 | no | — |
| 190 | C22×C4 | — | 292 | 4 | no | — |
| 191 | C22×C4 | — | 73 | 2 | no | — |
| 192 | C22×C4 | D4×D73 | 1 | 1 | yes | characteristic |
| 193 | Q16 | — | 2 | 2 | no | — |
| 194 | Q16 | C22×Dic73 | 1 | 4 | yes | — |
| 195 | SD16 | — | 2 | 8 | no | — |
| 196 | D8 | — | 2 | 2 | no | — |
| 197 | D8 | C22×Dic73 | 1 | 4 | yes | — |
| 198 | C2×C8 | — | 73 | 2 | no | — |
| 199 | C2×C8 | — | 146 | 2 | no | — |
| 200 | C2×C8 | C22×Dic73 | 1 | 2 | yes | — |
| 201 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 202 | C2×C8 | #11924027 | 1 | 2 | yes | — |
| 203 | C2×C8 | C23×D73 | 1 | 1 | yes | characteristic |
| 204 | C4⋊C4 | — | 292 | 4 | no | — |
| 205 | C4⋊C4 | — | 146 | 4 | no | — |
| 206 | C22⋊C4 | — | 292 | 2 | no | — |
| 207 | C22⋊C4 | — | 292 | 4 | no | — |
| 208 | C42 | — | 292 | 4 | no | — |
| 209 | C42 | — | 292 | 2 | no | — |
| 210 | C42 | — | 73 | 2 | no | — |
| 211 | C42 | — | 73 | 2 | no | — |
| 212 | C16 | — | 146 | 2 | no | — |
| 213 | C16 | C22×Dic73 | 1 | 2 | yes | — |
| 214 | C16 | C22×Dic73 | 1 | 2 | yes | — |
| 215 | C23 | — | 4 | 2 | no | — |
| 216 | C23 | D8×D73 | 1 | 1 | yes | characteristic |
| 217 | Q8 | — | 2 | 4 | no | — |
| 218 | Q8 | — | 4 | 2 | no | — |
| 219 | D4 | — | 2 | 4 | no | — |
| 220 | D4 | — | 4 | 8 | no | — |
| 221 | D4 | — | 4 | 2 | no | — |
| 222 | C2×C4 | — | 4 | 2 | no | — |
| 223 | C2×C4 | — | 4 | 8 | no | — |
| 224 | C2×C4 | — | 292 | 4 | no | — |
| 225 | C2×C4 | — | 292 | 2 | no | — |
| 226 | C2×C4 | — | 584 | 8 | no | — |
| 227 | C2×C4 | — | 73 | 4 | no | — |
| 228 | C2×C4 | D4×Dic73 | 1 | 2 | yes | — |
| 229 | C2×C4 | D8×D73 | 1 | 1 | yes | characteristic |
| 230 | C2×C4 | #14556610 | 1 | 2 | yes | — |
| 231 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 232 | C8 | — | 146 | 2 | no | — |
| 233 | C8 | D4×Dic73 | 1 | 2 | yes | — |
| 234 | C8 | C23×Dic73 | 1 | 1 | yes | characteristic |
| 235 | C8 | C2×#11924027 | 1 | 1 | yes | characteristic |
| 236 | C22 | — | 2 | 2 | no | — |
| 237 | C22 | — | 4 | 4 | no | — |
| 238 | C22 | — | 8 | 4 | no | — |
| 239 | C22 | D8×Dic73 | 1 | 2 | yes | — |
| 240 | C22 | C2×D8×D73 | 1 | 1 | yes | characteristic |
| 241 | C4 | — | 4 | 4 | no | — |
| 242 | C4 | — | 584 | 4 | no | — |
| 243 | C4 | — | 146 | 4 | no | — |
| 244 | C4 | D8×Dic73 | 1 | 2 | yes | — |
| 245 | C4 | C2×D4×Dic73 | 1 | 1 | yes | characteristic |
| 246 | C4 | C2×#14556610 | 1 | 1 | yes | characteristic |
| 247 | C2 | — | 2 | 2 | no | — |
| 248 | C2 | — | 8 | 4 | no | — |
| 249 | C2 | C2×D8×Dic73 | 1 | 1 | yes | characteristic |
| 250 | C2 | #22623064 | 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