← #33003003
Subgroups — #33003003
Order 18688.
472 conjugacy classes of subgroups.
The subgroup lattice has 328 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#17988862 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22618542 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#17988404 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#17988404 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22608043 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22608035 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C73×#2117 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#14556621 | — | 2 | 1 | no | — |
| 9 | C22×Dic292 | C22 | 1 | 1 | yes | characteristic |
| 10 | #17989354 | — | 2 | 1 | no | — |
| 11 | #17988862 | — | 2 | 2 | no | — |
| 12 | #17988862 | C4 | 1 | 4 | yes | — |
| 13 | #17988636 | — | 2 | 2 | no | — |
| 14 | #17988636 | — | 2 | 1 | no | — |
| 15 | C2×#14556527 | — | 2 | 2 | no | — |
| 16 | C2×#14556527 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#14556527 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#14556527 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#14556509 | — | 2 | 1 | no | — |
| 20 | #17988404 | — | 2 | 2 | no | — |
| 21 | #17988404 | — | 2 | 2 | no | — |
| 22 | C2×#131×C73 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×M32×C73 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×M32×C73 | C22 | 1 | 1 | yes | characteristic |
| 25 | #350×C73 | — | 2 | 2 | no | — |
| 26 | C22×Dic146 | — | 2 | 1 | no | — |
| 27 | #14556621 | — | 2 | 4 | no | — |
| 28 | #14556621 | — | 4 | 2 | no | — |
| 29 | C2×Dic292 | — | 2 | 1 | no | — |
| 30 | C2×Dic292 | — | 2 | 1 | no | — |
| 31 | C2×Dic292 | — | 2 | 1 | no | — |
| 32 | C2×Dic292 | — | 2 | 1 | no | — |
| 33 | C2×Dic292 | — | 2 | 1 | no | — |
| 34 | C2×Dic292 | C2×C4 | 1 | 2 | yes | — |
| 35 | C2×#11924018 | — | 4 | 1 | no | — |
| 36 | C2×#11924016 | — | 4 | 1 | no | — |
| 37 | #14556598 | — | 4 | 2 | no | — |
| 38 | #14556598 | — | 4 | 2 | no | — |
| 39 | C2×#11924012 | — | 2 | 4 | no | — |
| 40 | C2×#11924012 | — | 2 | 1 | no | — |
| 41 | C2×#11924012 | — | 2 | 1 | no | — |
| 42 | C2×#11924012 | — | 2 | 1 | no | — |
| 43 | #14556527 | — | 2 | 4 | no | — |
| 44 | #14556527 | — | 2 | 1 | no | — |
| 45 | #14556527 | — | 2 | 1 | no | — |
| 46 | #14556527 | — | 2 | 1 | no | — |
| 47 | #14556527 | C2×C4 | 1 | 2 | yes | — |
| 48 | #14556527 | D4 | 1 | 2 | yes | — |
| 49 | #14556527 | D4 | 1 | 2 | yes | — |
| 50 | #14556509 | — | 2 | 4 | no | — |
| 51 | C2×#41×C73 | D4 | 1 | 1 | yes | characteristic |
| 52 | #131×C73 | — | 2 | 1 | no | — |
| 53 | #131×C73 | — | 2 | 1 | no | — |
| 54 | #131×C73 | C2×C4 | 1 | 2 | yes | — |
| 55 | #131×C73 | D4 | 1 | 2 | yes | — |
| 56 | C2×M16×C73 | — | 2 | 1 | no | — |
| 57 | C2×M16×C73 | D4 | 1 | 1 | yes | characteristic |
| 58 | C22×C8×C73 | — | 2 | 1 | no | — |
| 59 | C22×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 60 | M32×C73 | — | 2 | 1 | no | — |
| 61 | M32×C73 | — | 2 | 1 | no | — |
| 62 | M32×C73 | — | 2 | 1 | no | — |
| 63 | M32×C73 | — | 2 | 1 | no | — |
| 64 | C2×C16×C73 | — | 2 | 1 | no | — |
| 65 | C2×C16×C73 | — | 2 | 1 | no | — |
| 66 | C2×Dic146 | — | 2 | 2 | no | — |
| 67 | C2×Dic146 | — | 4 | 1 | no | — |
| 68 | C2×Dic146 | — | 4 | 1 | no | — |
| 69 | C2×Dic146 | — | 4 | 1 | no | — |
| 70 | C2×Dic146 | — | 4 | 1 | no | — |
| 71 | C2×Dic146 | — | 4 | 1 | no | — |
| 72 | C22×Dic73 | — | 4 | 1 | no | — |
| 73 | Dic292 | — | 2 | 2 | no | — |
| 74 | Dic292 | — | 2 | 2 | no | — |
| 75 | Dic292 | — | 4 | 1 | no | — |
| 76 | Dic292 | — | 4 | 1 | no | — |
| 77 | #11924018 | — | 4 | 4 | no | — |
| 78 | #11924016 | — | 4 | 4 | no | — |
| 79 | #11924012 | — | 2 | 2 | no | — |
| 80 | #11924012 | — | 2 | 2 | no | — |
| 81 | #11924012 | — | 2 | 2 | no | — |
| 82 | #11924012 | — | 4 | 4 | no | — |
| 83 | #11924012 | — | 4 | 1 | no | — |
| 84 | #11924012 | — | 4 | 1 | no | — |
| 85 | #11924012 | — | 4 | 1 | no | — |
| 86 | C2×#10596831 | — | 4 | 4 | no | — |
| 87 | C2×#10596831 | — | 4 | 1 | no | — |
| 88 | C2×#10596831 | — | 4 | 1 | no | — |
| 89 | C2×#10596831 | — | 4 | 1 | no | — |
| 90 | #41×C73 | — | 2 | 1 | no | — |
| 91 | #41×C73 | — | 2 | 1 | no | — |
| 92 | #41×C73 | C22⋊C4 | 1 | 2 | yes | — |
| 93 | #41×C73 | D8 | 1 | 2 | yes | — |
| 94 | C2×Q8×C73 | SD16 | 1 | 1 | yes | characteristic |
| 95 | C2×D4×C73 | — | 2 | 1 | no | — |
| 96 | C2×D4×C73 | SD16 | 1 | 1 | yes | characteristic |
| 97 | C22×C4×C73 | — | 2 | 1 | no | — |
| 98 | C22×C4×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | M16×C73 | — | 2 | 1 | no | — |
| 100 | M16×C73 | — | 2 | 2 | no | — |
| 101 | M16×C73 | — | 2 | 2 | no | — |
| 102 | M16×C73 | C22⋊C4 | 1 | 2 | yes | — |
| 103 | C2×C8×C73 | — | 2 | 1 | no | — |
| 104 | C2×C8×C73 | — | 2 | 2 | no | — |
| 105 | C2×C8×C73 | — | 2 | 2 | no | — |
| 106 | C2×C8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 107 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×C8×C73 | #41 | 1 | 1 | yes | characteristic |
| 111 | C2×C8×C73 | #41 | 1 | 1 | yes | characteristic |
| 112 | C16×C73 | — | 4 | 1 | no | — |
| 113 | C16×C73 | — | 4 | 1 | no | — |
| 114 | C23×C73 | — | 2 | 1 | no | — |
| 115 | C23×C73 | #137 | 1 | 1 | yes | characteristic |
| 116 | Q8×C73 | — | 2 | 1 | no | — |
| 117 | Q8×C73 | #102 | 1 | 2 | yes | — |
| 118 | D4×C73 | — | 2 | 2 | no | — |
| 119 | D4×C73 | — | 2 | 2 | no | — |
| 120 | D4×C73 | — | 2 | 1 | no | — |
| 121 | D4×C73 | #102 | 1 | 2 | yes | — |
| 122 | C2×C4×C73 | — | 2 | 1 | no | — |
| 123 | C2×C4×C73 | — | 2 | 2 | no | — |
| 124 | C2×C4×C73 | — | 2 | 2 | no | — |
| 125 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C73 | #120 | 1 | 1 | yes | characteristic |
| 127 | C2×C4×C73 | #123 | 1 | 1 | yes | characteristic |
| 128 | C2×C4×C73 | C2×D8 | 1 | 1 | yes | characteristic |
| 129 | C2×C4×C73 | C2×SD16 | 1 | 1 | yes | characteristic |
| 130 | C2×C4×C73 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 131 | C2×Dic73 | — | 4 | 2 | no | — |
| 132 | C2×Dic73 | — | 8 | 1 | no | — |
| 133 | C2×Dic73 | — | 8 | 1 | no | — |
| 134 | Dic146 | — | 4 | 2 | no | — |
| 135 | Dic146 | — | 4 | 2 | no | — |
| 136 | Dic146 | — | 8 | 1 | no | — |
| 137 | Dic146 | — | 8 | 1 | no | — |
| 138 | C8×C73 | — | 2 | 2 | no | — |
| 139 | C8×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 140 | C8×C73 | C4×D4 | 1 | 1 | yes | characteristic |
| 141 | C8×C73 | #121 | 1 | 1 | yes | characteristic |
| 142 | C8×C73 | #121 | 1 | 1 | yes | characteristic |
| 143 | #10596831 | — | 4 | 2 | no | — |
| 144 | #10596831 | — | 4 | 2 | no | — |
| 145 | #10596831 | — | 4 | 2 | no | — |
| 146 | C22×C73 | — | 2 | 2 | no | — |
| 147 | C22×C73 | — | 4 | 1 | no | — |
| 148 | C22×C73 | — | 8 | 1 | no | — |
| 149 | C22×C73 | #417 | 1 | 1 | yes | characteristic |
| 150 | C22×C73 | #448 | 1 | 1 | yes | characteristic |
| 151 | C22×C73 | #480 | 1 | 1 | yes | characteristic |
| 152 | C4×C73 | — | 2 | 2 | no | — |
| 153 | C4×C73 | #386 | 1 | 1 | yes | characteristic |
| 154 | C4×C73 | C2×#102 | 1 | 1 | yes | characteristic |
| 155 | C4×C73 | #447 | 1 | 1 | yes | characteristic |
| 156 | C4×C73 | #481 | 1 | 1 | yes | characteristic |
| 157 | Dic73 | — | 8 | 2 | no | — |
| 158 | #13006 | — | 73 | 1 | no | maximal, Sylow |
| 159 | C2×C73 | — | 2 | 1 | no | — |
| 160 | C2×C73 | — | 2 | 1 | no | — |
| 161 | C2×C73 | — | 2 | 1 | no | — |
| 162 | C2×C73 | — | 4 | 2 | no | — |
| 163 | C2×C73 | #1874 | 1 | 1 | yes | characteristic |
| 164 | C2×#473 | — | 73 | 1 | no | — |
| 165 | #2916 | — | 73 | 1 | no | — |
| 166 | C2×#362 | — | 73 | 1 | no | — |
| 167 | C2×#362 | — | 73 | 1 | no | — |
| 168 | #2117 | D73 | 1 | 1 | yes | characteristic |
| 169 | #1388 | — | 73 | 1 | no | — |
| 170 | #1385 | — | 73 | 1 | no | — |
| 171 | C73 | #13006 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 172 | C2×#137 | — | 146 | 1 | no | — |
| 173 | C22×Q16 | — | 73 | 1 | no | — |
| 174 | #568 | — | 146 | 1 | no | — |
| 175 | C2×#131 | C2×D73 | 1 | 1 | yes | characteristic |
| 176 | C2×M32 | C2×D73 | 1 | 1 | yes | characteristic |
| 177 | C2×M32 | C2×D73 | 1 | 1 | yes | characteristic |
| 178 | #473 | — | 73 | 4 | no | — |
| 179 | #473 | — | 146 | 2 | no | — |
| 180 | #430 | — | 146 | 2 | no | — |
| 181 | #430 | — | 146 | 1 | no | — |
| 182 | C2×#108 | — | 73 | 1 | no | — |
| 183 | C2×#108 | — | 73 | 1 | no | — |
| 184 | C2×#108 | — | 73 | 1 | no | — |
| 185 | C2×#108 | — | 146 | 2 | no | — |
| 186 | C2×#101 | — | 146 | 1 | no | — |
| 187 | #362 | — | 146 | 2 | no | — |
| 188 | #362 | — | 146 | 2 | no | — |
| 189 | #350 | — | 2 | 2 | no | — |
| 190 | C2×#41 | D292 | 1 | 1 | yes | characteristic |
| 191 | C22×Q8 | — | 146 | 1 | no | — |
| 192 | #137 | — | 292 | 2 | no | — |
| 193 | #137 | — | 146 | 4 | no | — |
| 194 | C2×Q16 | — | 292 | 1 | no | — |
| 195 | C2×Q16 | — | 73 | 2 | no | — |
| 196 | C2×Q16 | — | 146 | 1 | no | — |
| 197 | C2×Q16 | — | 146 | 1 | no | — |
| 198 | C2×Q16 | — | 146 | 1 | no | — |
| 199 | C2×Q16 | — | 146 | 1 | no | — |
| 200 | C2×Q16 | — | 146 | 1 | no | — |
| 201 | C2×SD16 | — | 292 | 1 | no | — |
| 202 | #131 | — | 2 | 1 | no | — |
| 203 | #131 | — | 2 | 1 | no | — |
| 204 | #131 | — | 292 | 2 | no | — |
| 205 | #131 | — | 292 | 2 | no | — |
| 206 | #131 | C4×D73 | 1 | 2 | yes | — |
| 207 | #131 | C22⋊D73 | 1 | 2 | yes | — |
| 208 | C2×M16 | — | 2 | 1 | no | — |
| 209 | C2×M16 | — | 146 | 4 | no | — |
| 210 | C2×M16 | — | 146 | 1 | no | — |
| 211 | C2×M16 | — | 146 | 1 | no | — |
| 212 | C2×M16 | — | 146 | 1 | no | — |
| 213 | C2×M16 | D292 | 1 | 1 | yes | characteristic |
| 214 | C22×C8 | — | 2 | 1 | no | — |
| 215 | C22×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 216 | M32 | — | 2 | 1 | no | — |
| 217 | M32 | — | 2 | 1 | no | — |
| 218 | M32 | — | 2 | 1 | no | — |
| 219 | M32 | — | 2 | 1 | no | — |
| 220 | C2×C16 | — | 2 | 1 | no | — |
| 221 | C2×C16 | — | 2 | 1 | no | — |
| 222 | #108 | — | 73 | 2 | no | — |
| 223 | #108 | — | 73 | 2 | no | — |
| 224 | #108 | — | 73 | 2 | no | — |
| 225 | #108 | — | 146 | 4 | no | — |
| 226 | #108 | — | 146 | 1 | no | — |
| 227 | #108 | — | 146 | 1 | no | — |
| 228 | #108 | — | 146 | 1 | no | — |
| 229 | #101 | — | 146 | 4 | no | — |
| 230 | #41 | — | 2 | 1 | no | — |
| 231 | #41 | — | 2 | 1 | no | — |
| 232 | #41 | #11924005 | 1 | 2 | yes | — |
| 233 | #41 | D584 | 1 | 2 | yes | — |
| 234 | C2×Q8 | — | 292 | 1 | no | — |
| 235 | C2×Q8 | — | 292 | 1 | no | — |
| 236 | C2×Q8 | — | 292 | 1 | no | — |
| 237 | C2×Q8 | — | 292 | 1 | no | — |
| 238 | C2×Q8 | — | 292 | 1 | no | — |
| 239 | C2×Q8 | — | 146 | 2 | no | — |
| 240 | C2×Q8 | #11924017 | 1 | 1 | yes | characteristic |
| 241 | C2×D4 | — | 2 | 1 | no | — |
| 242 | C2×D4 | #11924017 | 1 | 1 | yes | characteristic |
| 243 | C22×C4 | — | 2 | 1 | no | — |
| 244 | C22×C4 | — | 292 | 1 | no | — |
| 245 | C22×C4 | C2×D292 | 1 | 1 | yes | characteristic |
| 246 | Q16 | — | 292 | 4 | no | — |
| 247 | Q16 | — | 292 | 1 | no | — |
| 248 | Q16 | — | 292 | 1 | no | — |
| 249 | Q16 | — | 146 | 2 | no | — |
| 250 | Q16 | — | 146 | 2 | no | — |
| 251 | SD16 | — | 292 | 4 | no | — |
| 252 | M16 | — | 2 | 1 | no | — |
| 253 | M16 | — | 2 | 2 | no | — |
| 254 | M16 | — | 2 | 2 | no | — |
| 255 | M16 | — | 292 | 4 | no | — |
| 256 | M16 | — | 292 | 1 | no | — |
| 257 | M16 | — | 292 | 1 | no | — |
| 258 | M16 | — | 292 | 1 | no | — |
| 259 | M16 | — | 146 | 2 | no | — |
| 260 | M16 | — | 146 | 2 | no | — |
| 261 | M16 | — | 146 | 2 | no | — |
| 262 | M16 | #11924005 | 1 | 2 | yes | — |
| 263 | C2×C8 | — | 2 | 1 | no | — |
| 264 | C2×C8 | — | 2 | 2 | no | — |
| 265 | C2×C8 | — | 2 | 2 | no | — |
| 266 | C2×C8 | — | 292 | 4 | no | — |
| 267 | C2×C8 | — | 292 | 1 | no | — |
| 268 | C2×C8 | — | 292 | 1 | no | — |
| 269 | C2×C8 | — | 292 | 1 | no | — |
| 270 | C2×C8 | C2×C4×D73 | 1 | 1 | yes | characteristic |
| 271 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 272 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 273 | C2×C8 | C2×C22⋊D73 | 1 | 1 | yes | characteristic |
| 274 | C2×C8 | #11924027 | 1 | 1 | yes | characteristic |
| 275 | C2×C8 | #11924027 | 1 | 1 | yes | characteristic |
| 276 | C16 | — | 4 | 1 | no | — |
| 277 | C16 | — | 4 | 1 | no | — |
| 278 | C23 | — | 2 | 1 | no | — |
| 279 | C23 | #14556624 | 1 | 1 | yes | characteristic |
| 280 | Q8 | — | 2 | 1 | no | — |
| 281 | Q8 | — | 292 | 2 | no | — |
| 282 | Q8 | — | 292 | 2 | no | — |
| 283 | Q8 | — | 584 | 1 | no | — |
| 284 | Q8 | — | 584 | 1 | no | — |
| 285 | Q8 | #14556513 | 1 | 2 | yes | — |
| 286 | D4 | — | 2 | 2 | no | — |
| 287 | D4 | — | 2 | 2 | no | — |
| 288 | D4 | — | 2 | 1 | no | — |
| 289 | D4 | #14556513 | 1 | 2 | yes | — |
| 290 | C2×C4 | — | 2 | 1 | no | — |
| 291 | C2×C4 | — | 2 | 2 | no | — |
| 292 | C2×C4 | — | 2 | 2 | no | — |
| 293 | C2×C4 | — | 292 | 2 | no | — |
| 294 | C2×C4 | — | 584 | 1 | no | — |
| 295 | C2×C4 | — | 584 | 1 | no | — |
| 296 | C2×C4 | C2×#11924005 | 1 | 1 | yes | characteristic |
| 297 | C2×C4 | #14556561 | 1 | 1 | yes | characteristic |
| 298 | C2×C4 | #14556575 | 1 | 1 | yes | characteristic |
| 299 | C2×C4 | C2×D584 | 1 | 1 | yes | characteristic |
| 300 | C2×C4 | C2×#11924017 | 1 | 1 | yes | characteristic |
| 301 | C2×C4 | #14556619 | 1 | 1 | yes | characteristic |
| 302 | C8 | — | 2 | 2 | no | — |
| 303 | C8 | — | 292 | 2 | no | — |
| 304 | C8 | — | 292 | 2 | no | — |
| 305 | C8 | — | 292 | 2 | no | — |
| 306 | C8 | #14556551 | 1 | 1 | yes | characteristic |
| 307 | C8 | #14556551 | 1 | 1 | yes | characteristic |
| 308 | C8 | #14556563 | 1 | 1 | yes | characteristic |
| 309 | C8 | #14556563 | 1 | 1 | yes | characteristic |
| 310 | C22 | — | 2 | 2 | no | — |
| 311 | C22 | — | 4 | 1 | no | — |
| 312 | C22 | — | 8 | 1 | no | — |
| 313 | C22 | #17988589 | 1 | 1 | yes | characteristic |
| 314 | C22 | #17988728 | 1 | 1 | yes | characteristic |
| 315 | C22 | #17988901 | 1 | 1 | yes | characteristic |
| 316 | C4 | — | 2 | 2 | no | — |
| 317 | C4 | — | 584 | 2 | no | — |
| 318 | C4 | #17988464 | 1 | 1 | yes | characteristic |
| 319 | C4 | C2×#14556513 | 1 | 1 | yes | characteristic |
| 320 | C4 | #17988723 | 1 | 1 | yes | characteristic |
| 321 | C4 | #17988906 | 1 | 1 | yes | characteristic |
| 322 | C2 | — | 2 | 1 | no | — |
| 323 | C2 | — | 2 | 1 | no | — |
| 324 | C2 | — | 2 | 1 | no | — |
| 325 | C2 | — | 4 | 2 | no | — |
| 326 | C2 | #22610246 | 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