← #33073642
Subgroups — #33073642
Order 18688.
814 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 | #22620486 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #22620445 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22609530 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #22609525 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #22609520 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #22609517 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×C8×#10596831 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C73×#3147 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #17989144 | C22 | 1 | 2 | yes | — |
| 10 | #17988992 | C22 | 1 | 2 | yes | — |
| 11 | #17988989 | — | 2 | 2 | no | — |
| 12 | #17988985 | C22 | 1 | 2 | yes | — |
| 13 | #17988983 | C22 | 1 | 4 | yes | — |
| 14 | #17988959 | C22 | 1 | 4 | yes | — |
| 15 | #17988939 | C22 | 1 | 4 | yes | — |
| 16 | #17988933 | C22 | 1 | 4 | yes | — |
| 17 | #17988814 | — | 2 | 8 | no | — |
| 18 | C4×#11924016 | — | 2 | 8 | no | — |
| 19 | #17988625 | — | 2 | 2 | no | — |
| 20 | C2×C4×#10596831 | C22 | 1 | 2 | yes | — |
| 21 | C8×#10596831 | C22 | 1 | 1 | yes | characteristic |
| 22 | C8×#10596831 | C22 | 1 | 2 | yes | — |
| 23 | C8×#10596831 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#135×C73 | — | 2 | 2 | no | — |
| 25 | #532×C73 | C22 | 1 | 2 | yes | — |
| 26 | #495×C73 | — | 2 | 2 | no | — |
| 27 | #494×C73 | C22 | 1 | 1 | yes | characteristic |
| 28 | #493×C73 | C22 | 1 | 1 | yes | characteristic |
| 29 | #492×C73 | C22 | 1 | 2 | yes | — |
| 30 | C2×C4×C8×C73 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#11924016 | — | 2 | 8 | no | — |
| 32 | C22×#10596831 | D4 | 1 | 4 | yes | — |
| 33 | #14556591 | C23 | 1 | 4 | yes | — |
| 34 | #14556583 | — | 2 | 2 | no | — |
| 35 | #14556570 | — | 2 | 4 | no | — |
| 36 | C4×Dic146 | — | 2 | 4 | no | — |
| 37 | #14556550 | — | 2 | 2 | no | — |
| 38 | #14556525 | — | 2 | 4 | no | — |
| 39 | #14556523 | — | 2 | 4 | no | — |
| 40 | #14556522 | — | 2 | 8 | no | — |
| 41 | #14556514 | — | 2 | 8 | no | — |
| 42 | #14556512 | — | 2 | 8 | no | — |
| 43 | C4×#10596831 | D4 | 1 | 4 | yes | — |
| 44 | C4×#10596831 | C23 | 1 | 2 | yes | — |
| 45 | C4×#10596831 | C23 | 1 | 2 | yes | — |
| 46 | C2×#41×C73 | — | 2 | 2 | no | — |
| 47 | #135×C73 | — | 4 | 8 | no | — |
| 48 | C2×Q16×C73 | — | 2 | 2 | no | — |
| 49 | C2×SD16×C73 | — | 2 | 4 | no | — |
| 50 | C2×D8×C73 | — | 2 | 2 | no | — |
| 51 | C22×C8×C73 | D4 | 1 | 2 | yes | — |
| 52 | C4⋊Q8×C73 | C23 | 1 | 2 | yes | — |
| 53 | #127×C73 | C23 | 1 | 2 | yes | — |
| 54 | #124×C73 | — | 2 | 2 | no | — |
| 55 | #121×C73 | — | 2 | 4 | no | — |
| 56 | C4×D4×C73 | — | 2 | 4 | no | — |
| 57 | C2×C42×C73 | C23 | 1 | 1 | yes | characteristic |
| 58 | C4×C8×C73 | D4 | 1 | 2 | yes | — |
| 59 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 60 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×Dic146 | — | 2 | 4 | no | — |
| 62 | #11924016 | — | 4 | 16 | no | — |
| 63 | C2×#10596831 | — | 2 | 8 | no | — |
| 64 | C2×#10596831 | C2×D4 | 1 | 4 | yes | — |
| 65 | C2×#10596831 | C2×D4 | 1 | 4 | yes | — |
| 66 | C4⋊Dic73 | — | 2 | 4 | no | — |
| 67 | C4⋊Dic73 | — | 2 | 4 | no | — |
| 68 | #11924007 | — | 4 | 4 | no | — |
| 69 | C22⋊Dic73 | — | 4 | 2 | no | — |
| 70 | C4×Dic73 | — | 4 | 2 | no | — |
| 71 | #41×C73 | — | 4 | 8 | no | — |
| 72 | C2×Q8×C73 | — | 2 | 2 | no | — |
| 73 | C2×D4×C73 | — | 2 | 4 | 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 | 2 | yes | — |
| 78 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 79 | Q16×C73 | — | 4 | 4 | no | — |
| 80 | SD16×C73 | — | 4 | 8 | no | — |
| 81 | D8×C73 | — | 4 | 4 | no | — |
| 82 | C2×C8×C73 | SD16 | 1 | 8 | yes | complemented |
| 83 | C2×C8×C73 | C2×D4 | 1 | 2 | yes | — |
| 84 | C2×C8×C73 | C2×D4 | 1 | 2 | yes | — |
| 85 | C4⋊C4×C73 | — | 2 | 4 | no | — |
| 86 | C22⋊C4×C73 | — | 4 | 4 | no | — |
| 87 | C42×C73 | C2×D4 | 1 | 2 | yes | — |
| 88 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 90 | C23×C73 | — | 4 | 2 | no | — |
| 91 | C23×C73 | #127 | 1 | 1 | yes | characteristic |
| 92 | Q8×C73 | — | 4 | 4 | no | — |
| 93 | D4×C73 | — | 4 | 4 | no | — |
| 94 | D4×C73 | — | 4 | 8 | no | — |
| 95 | D4×C73 | — | 8 | 4 | no | — |
| 96 | C2×C4×C73 | — | 2 | 4 | no | — |
| 97 | C2×C4×C73 | — | 4 | 2 | no | — |
| 98 | C2×C4×C73 | — | 8 | 4 | no | — |
| 99 | C2×C4×C73 | #127 | 1 | 2 | yes | — |
| 100 | C2×C4×C73 | #127 | 1 | 1 | yes | characteristic |
| 101 | C2×C4×C73 | C2×SD16 | 1 | 4 | yes | — |
| 102 | C2×C4×C73 | C22×D4 | 1 | 2 | yes | — |
| 103 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×Dic73 | — | 4 | 4 | no | — |
| 105 | Dic146 | — | 4 | 8 | no | — |
| 106 | C8×C73 | C2×SD16 | 1 | 4 | yes | — |
| 107 | C8×C73 | C2×SD16 | 1 | 4 | yes | — |
| 108 | #10596831 | — | 2 | 4 | no | — |
| 109 | #10596831 | #135 | 1 | 8 | yes | complemented |
| 110 | C22×C73 | — | 2 | 2 | no | — |
| 111 | C22×C73 | — | 8 | 2 | no | — |
| 112 | C22×C73 | — | 8 | 4 | no | — |
| 113 | C22×C73 | #492 | 1 | 2 | yes | — |
| 114 | C22×C73 | C2×#127 | 1 | 1 | yes | characteristic |
| 115 | C4×C73 | — | 2 | 2 | no | — |
| 116 | C4×C73 | — | 8 | 2 | no | — |
| 117 | C4×C73 | #492 | 1 | 2 | yes | — |
| 118 | C4×C73 | C22×SD16 | 1 | 2 | yes | — |
| 119 | C4×C73 | C2×#135 | 1 | 4 | yes | — |
| 120 | Dic73 | — | 8 | 4 | no | — |
| 121 | #19596 | — | 73 | 1 | no | maximal, Sylow |
| 122 | C2×C73 | — | 2 | 2 | no | — |
| 123 | C2×C73 | — | 16 | 2 | no | — |
| 124 | C2×C73 | C2×#492 | 1 | 1 | yes | characteristic |
| 125 | C2×C73 | #3147 | 1 | 2 | yes | — |
| 126 | #3167 | — | 73 | 4 | no | — |
| 127 | #3160 | — | 73 | 1 | no | — |
| 128 | #3147 | D73 | 1 | 1 | yes | characteristic |
| 129 | #1708 | — | 73 | 2 | no | — |
| 130 | #1707 | — | 73 | 2 | no | — |
| 131 | #1706 | — | 73 | 2 | no | — |
| 132 | #1705 | — | 73 | 2 | no | — |
| 133 | C2×C82 | — | 73 | 1 | no | — |
| 134 | C73 | #19596 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 135 | C2×#135 | — | 2 | 2 | no | — |
| 136 | #533 | — | 73 | 2 | no | — |
| 137 | #532 | C2×D73 | 1 | 2 | yes | — |
| 138 | #500 | — | 73 | 2 | no | — |
| 139 | #499 | — | 146 | 2 | no | — |
| 140 | #498 | — | 73 | 4 | no | — |
| 141 | #498 | — | 73 | 2 | no | — |
| 142 | #495 | — | 2 | 2 | no | — |
| 143 | #494 | C2×D73 | 1 | 1 | yes | characteristic |
| 144 | #493 | C2×D73 | 1 | 1 | yes | characteristic |
| 145 | #492 | — | 73 | 4 | no | — |
| 146 | #492 | C2×D73 | 1 | 2 | yes | — |
| 147 | #487 | — | 73 | 4 | no | — |
| 148 | #486 | — | 73 | 4 | no | — |
| 149 | #465 | — | 146 | 8 | no | — |
| 150 | C4×SD16 | — | 146 | 8 | no | — |
| 151 | #427 | — | 146 | 2 | no | — |
| 152 | C2×C4×C8 | — | 73 | 2 | no | — |
| 153 | C2×C4×C8 | C2×D73 | 1 | 1 | yes | characteristic |
| 154 | C82 | — | 73 | 1 | no | — |
| 155 | C82 | — | 73 | 2 | no | — |
| 156 | C82 | — | 73 | 1 | no | — |
| 157 | C2×#41 | — | 2 | 2 | no | — |
| 158 | #135 | — | 4 | 8 | no | — |
| 159 | C2×Q16 | — | 2 | 2 | no | — |
| 160 | C2×SD16 | — | 2 | 4 | no | — |
| 161 | C2×SD16 | — | 146 | 8 | no | — |
| 162 | C2×D8 | — | 2 | 2 | no | — |
| 163 | C22×C8 | — | 73 | 4 | no | — |
| 164 | C22×C8 | C22⋊D73 | 1 | 2 | yes | — |
| 165 | C4⋊Q8 | — | 73 | 4 | no | — |
| 166 | C4⋊Q8 | C22×D73 | 1 | 2 | yes | — |
| 167 | #127 | C22×D73 | 1 | 2 | yes | — |
| 168 | #125 | — | 146 | 2 | no | — |
| 169 | #124 | — | 2 | 2 | no | — |
| 170 | C22⋊Q8 | — | 146 | 4 | no | — |
| 171 | #121 | — | 2 | 4 | no | — |
| 172 | C4×Q8 | — | 146 | 4 | no | — |
| 173 | C4×D4 | — | 2 | 4 | no | — |
| 174 | #117 | — | 146 | 2 | no | — |
| 175 | C2×C42 | C22×D73 | 1 | 1 | yes | characteristic |
| 176 | #107 | — | 146 | 4 | no | — |
| 177 | #106 | — | 146 | 8 | no | — |
| 178 | #106 | — | 146 | 4 | no | — |
| 179 | #103 | — | 146 | 8 | no | — |
| 180 | #102 | — | 146 | 8 | no | — |
| 181 | C4×C8 | — | 73 | 4 | no | — |
| 182 | C4×C8 | — | 73 | 2 | no | — |
| 183 | C4×C8 | — | 73 | 2 | no | — |
| 184 | C4×C8 | C22⋊D73 | 1 | 2 | yes | — |
| 185 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 186 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 187 | #41 | — | 4 | 8 | no | — |
| 188 | C2×Q8 | — | 2 | 2 | no | — |
| 189 | C2×Q8 | — | 146 | 4 | no | — |
| 190 | C2×D4 | — | 2 | 4 | no | — |
| 191 | C2×D4 | — | 2 | 2 | no | — |
| 192 | C2×D4 | — | 4 | 2 | no | — |
| 193 | C22×C4 | — | 4 | 2 | no | — |
| 194 | C22×C4 | D4×D73 | 1 | 2 | yes | — |
| 195 | C22×C4 | C2×C22⋊D73 | 1 | 1 | yes | characteristic |
| 196 | Q16 | — | 4 | 4 | no | — |
| 197 | SD16 | — | 4 | 8 | no | — |
| 198 | SD16 | — | 292 | 16 | no | — |
| 199 | D8 | — | 4 | 4 | no | — |
| 200 | C2×C8 | — | 73 | 4 | no | — |
| 201 | C2×C8 | — | 73 | 4 | no | — |
| 202 | C2×C8 | — | 146 | 8 | no | — |
| 203 | C2×C8 | #11924016 | 1 | 8 | yes | complemented |
| 204 | C2×C8 | C2×C22⋊D73 | 1 | 2 | yes | — |
| 205 | C2×C8 | C2×C22⋊D73 | 1 | 2 | yes | — |
| 206 | C4⋊C4 | — | 2 | 4 | no | — |
| 207 | C4⋊C4 | — | 292 | 4 | no | — |
| 208 | C4⋊C4 | — | 146 | 4 | no | — |
| 209 | C4⋊C4 | — | 146 | 4 | no | — |
| 210 | C22⋊C4 | — | 4 | 4 | no | — |
| 211 | C22⋊C4 | — | 292 | 2 | no | — |
| 212 | C42 | — | 292 | 2 | no | — |
| 213 | C42 | D4×D73 | 1 | 2 | yes | — |
| 214 | C42 | C2×C22⋊D73 | 1 | 1 | yes | characteristic |
| 215 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 216 | C23 | — | 4 | 2 | no | — |
| 217 | C23 | #14556587 | 1 | 1 | yes | characteristic |
| 218 | Q8 | — | 4 | 4 | no | — |
| 219 | Q8 | — | 292 | 8 | no | — |
| 220 | D4 | — | 4 | 4 | no | — |
| 221 | D4 | — | 4 | 8 | no | — |
| 222 | D4 | — | 8 | 4 | no | — |
| 223 | C2×C4 | — | 2 | 4 | no | — |
| 224 | C2×C4 | — | 4 | 2 | no | — |
| 225 | C2×C4 | — | 8 | 4 | no | — |
| 226 | C2×C4 | — | 292 | 4 | no | — |
| 227 | C2×C4 | #14556587 | 1 | 2 | yes | — |
| 228 | C2×C4 | #14556587 | 1 | 1 | yes | characteristic |
| 229 | C2×C4 | C2×#11924016 | 1 | 4 | yes | — |
| 230 | C2×C4 | C2×D4×D73 | 1 | 2 | yes | — |
| 231 | C2×C4 | C22×C22⋊D73 | 1 | 1 | yes | characteristic |
| 232 | C8 | — | 73 | 8 | no | — |
| 233 | C8 | — | 146 | 4 | no | — |
| 234 | C8 | C2×#11924016 | 1 | 4 | yes | — |
| 235 | C8 | C2×#11924016 | 1 | 4 | yes | — |
| 236 | C22 | — | 2 | 2 | no | — |
| 237 | C22 | — | 8 | 2 | no | — |
| 238 | C22 | — | 8 | 4 | no | — |
| 239 | C22 | #17988959 | 1 | 2 | yes | — |
| 240 | C22 | C2×#14556587 | 1 | 1 | yes | characteristic |
| 241 | C4 | — | 2 | 2 | no | — |
| 242 | C4 | — | 8 | 2 | no | — |
| 243 | C4 | — | 584 | 4 | no | — |
| 244 | C4 | #17988959 | 1 | 2 | yes | — |
| 245 | C4 | C22×#11924016 | 1 | 2 | yes | — |
| 246 | C4 | #135×D73 | 1 | 4 | yes | — |
| 247 | C2 | — | 2 | 2 | no | — |
| 248 | C2 | — | 16 | 2 | no | — |
| 249 | C2 | C2×#17988959 | 1 | 1 | yes | characteristic |
| 250 | C2 | #22620355 | 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