← #36450965
Subgroups — #36450965
Order 22784.
428 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 | #26031398 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #26029199 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #26021096 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #26018940 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C2×#19151343 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #26018148 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C89×#1283 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #19152155 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#15668012 | C22 | 1 | 1 | yes | characteristic |
| 10 | #19151996 | — | 2 | 1 | no | — |
| 11 | #19151949 | — | 2 | 1 | no | — |
| 12 | #19151929 | C4 | 1 | 4 | yes | — |
| 13 | #19151884 | — | 2 | 2 | no | — |
| 14 | #19151728 | — | 2 | 1 | no | — |
| 15 | #19151726 | — | 2 | 2 | no | — |
| 16 | C8×Dic178 | — | 2 | 1 | no | — |
| 17 | #19151626 | — | 2 | 1 | no | — |
| 18 | #19151622 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4⋊#10623494 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#15667930 | — | 2 | 1 | no | — |
| 21 | C2×#15667930 | — | 2 | 1 | no | — |
| 22 | #19151556 | — | 2 | 1 | no | — |
| 23 | #19151346 | — | 2 | 1 | no | — |
| 24 | #19151345 | — | 2 | 1 | no | — |
| 25 | #19151343 | — | 2 | 1 | no | — |
| 26 | #19151343 | — | 2 | 1 | no | — |
| 27 | #431×C89 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C4⋊C8×C89 | C22 | 1 | 1 | yes | characteristic |
| 29 | C4×M16×C89 | C22 | 1 | 1 | yes | characteristic |
| 30 | C22×Dic178 | — | 2 | 1 | no | — |
| 31 | C2×#13083558 | — | 2 | 1 | no | — |
| 32 | C22×#10623494 | — | 2 | 1 | no | — |
| 33 | #15668012 | — | 2 | 1 | no | — |
| 34 | #15668012 | — | 2 | 1 | no | — |
| 35 | #15668012 | — | 2 | 1 | no | — |
| 36 | #15668012 | — | 2 | 1 | no | — |
| 37 | #15668012 | D4 | 1 | 1 | yes | characteristic |
| 38 | #15668012 | D4 | 1 | 1 | yes | characteristic |
| 39 | #15668004 | — | 2 | 1 | no | — |
| 40 | #15667991 | — | 2 | 1 | no | — |
| 41 | #15667991 | C2×C4 | 1 | 2 | yes | — |
| 42 | C4×Dic178 | — | 2 | 1 | no | — |
| 43 | C4×Dic178 | D4 | 1 | 2 | yes | — |
| 44 | #15667971 | — | 2 | 1 | no | — |
| 45 | C2×C4⋊Dic89 | — | 2 | 1 | no | — |
| 46 | C2×C4⋊Dic89 | C2×C4 | 1 | 2 | yes | — |
| 47 | #15667944 | — | 2 | 4 | no | — |
| 48 | C4⋊#10623494 | — | 2 | 1 | no | — |
| 49 | C4⋊#10623494 | — | 2 | 1 | no | — |
| 50 | C4⋊#10623494 | — | 2 | 1 | no | — |
| 51 | C4⋊#10623494 | D4 | 1 | 1 | yes | characteristic |
| 52 | C4⋊#10623494 | D4 | 1 | 1 | yes | characteristic |
| 53 | #15667941 | — | 2 | 2 | no | — |
| 54 | #15667941 | — | 2 | 2 | no | — |
| 55 | #15667937 | — | 2 | 4 | no | — |
| 56 | #15667930 | — | 4 | 2 | no | — |
| 57 | #15667930 | — | 4 | 2 | no | — |
| 58 | #15667922 | — | 2 | 2 | no | — |
| 59 | C8×Dic89 | — | 2 | 2 | no | — |
| 60 | C2×M16×C89 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×M16×C89 | D4 | 1 | 1 | yes | characteristic |
| 62 | C22×C8×C89 | — | 2 | 1 | no | — |
| 63 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 65 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 66 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 67 | C22⋊C8×C89 | C2×C4 | 1 | 2 | yes | — |
| 68 | #97×C89 | — | 2 | 1 | no | — |
| 69 | C4×C8×C89 | — | 2 | 1 | no | — |
| 70 | C4×C8×C89 | — | 2 | 1 | no | — |
| 71 | C2×Dic178 | — | 2 | 1 | no | — |
| 72 | C2×Dic178 | — | 4 | 1 | no | — |
| 73 | C2×Dic178 | — | 4 | 1 | no | — |
| 74 | C2×Dic178 | — | 4 | 1 | no | — |
| 75 | C2×Dic178 | — | 4 | 1 | no | — |
| 76 | C2×Dic178 | — | 4 | 1 | no | — |
| 77 | C2×Dic178 | — | 4 | 1 | no | — |
| 78 | C2×Dic178 | C22⋊C4 | 1 | 2 | yes | — |
| 79 | C22×Dic89 | — | 2 | 2 | no | — |
| 80 | #13083558 | — | 4 | 1 | no | — |
| 81 | #13083558 | — | 4 | 1 | no | — |
| 82 | C2×#10623494 | — | 2 | 1 | no | — |
| 83 | C2×#10623494 | — | 2 | 1 | no | — |
| 84 | C2×#10623494 | — | 4 | 1 | no | — |
| 85 | C2×#10623494 | — | 4 | 1 | no | — |
| 86 | C2×#10623494 | — | 4 | 1 | no | — |
| 87 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 88 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 89 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 90 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 91 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 92 | C4⋊Dic89 | — | 4 | 1 | no | — |
| 93 | C4⋊Dic89 | — | 4 | 1 | no | — |
| 94 | C4⋊Dic89 | C22⋊C4 | 1 | 2 | yes | — |
| 95 | #13083553 | — | 2 | 2 | no | — |
| 96 | #13083553 | — | 2 | 2 | no | — |
| 97 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 98 | C4×Dic89 | — | 2 | 2 | no | — |
| 99 | C22×C4×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C22×C4×C89 | #41 | 1 | 1 | yes | characteristic |
| 102 | M16×C89 | — | 2 | 1 | no | — |
| 103 | M16×C89 | — | 2 | 1 | no | — |
| 104 | M16×C89 | — | 2 | 1 | no | — |
| 105 | M16×C89 | SD16 | 1 | 2 | yes | — |
| 106 | C2×C8×C89 | — | 2 | 1 | no | — |
| 107 | C2×C8×C89 | — | 2 | 2 | no | — |
| 108 | C2×C8×C89 | — | 2 | 1 | no | — |
| 109 | C2×C8×C89 | — | 4 | 1 | no | — |
| 110 | C2×C8×C89 | — | 8 | 1 | no | — |
| 111 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C42×C89 | #41 | 1 | 1 | yes | characteristic |
| 115 | C23×C89 | C4×D4 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C89 | — | 2 | 1 | no | — |
| 117 | C2×C4×C89 | — | 2 | 1 | no | — |
| 118 | C2×C4×C89 | — | 4 | 1 | no | — |
| 119 | C2×C4×C89 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 120 | C2×C4×C89 | C4×D4 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 122 | C2×C4×C89 | #121 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×C89 | #121 | 1 | 1 | yes | characteristic |
| 124 | C2×C4×C89 | #123 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×C89 | C2×SD16 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C89 | #135 | 1 | 1 | yes | characteristic |
| 127 | C2×C4×C89 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 128 | C2×C4×C89 | #137 | 1 | 1 | yes | characteristic |
| 129 | C2×Dic89 | — | 2 | 2 | no | — |
| 130 | C2×Dic89 | — | 2 | 2 | no | — |
| 131 | C2×Dic89 | — | 4 | 2 | no | — |
| 132 | C2×Dic89 | — | 4 | 2 | no | — |
| 133 | C2×Dic89 | — | 4 | 2 | no | — |
| 134 | Dic178 | — | 4 | 1 | no | — |
| 135 | Dic178 | — | 4 | 1 | no | — |
| 136 | Dic178 | — | 4 | 2 | no | — |
| 137 | Dic178 | — | 8 | 1 | no | — |
| 138 | Dic178 | — | 8 | 1 | no | — |
| 139 | Dic178 | — | 8 | 1 | no | — |
| 140 | Dic178 | — | 8 | 1 | no | — |
| 141 | C8×C89 | — | 2 | 2 | no | — |
| 142 | C8×C89 | — | 4 | 2 | no | — |
| 143 | C8×C89 | — | 4 | 1 | no | — |
| 144 | C8×C89 | — | 8 | 1 | no | — |
| 145 | #10623494 | — | 4 | 1 | no | — |
| 146 | #10623494 | — | 4 | 1 | no | — |
| 147 | #10623494 | — | 8 | 1 | no | — |
| 148 | C22×C89 | — | 2 | 1 | no | — |
| 149 | C22×C89 | — | 2 | 1 | no | — |
| 150 | C22×C89 | #386 | 1 | 1 | yes | characteristic |
| 151 | C22×C89 | C4×SD16 | 1 | 1 | yes | characteristic |
| 152 | C22×C89 | #440 | 1 | 1 | yes | characteristic |
| 153 | C4×C89 | — | 2 | 1 | no | — |
| 154 | C4×C89 | — | 2 | 1 | no | — |
| 155 | C4×C89 | — | 2 | 1 | no | — |
| 156 | C4×C89 | #448 | 1 | 1 | yes | characteristic |
| 157 | C4×C89 | #449 | 1 | 1 | yes | characteristic |
| 158 | C4×C89 | #460 | 1 | 1 | yes | characteristic |
| 159 | C4×C89 | #464 | 1 | 1 | yes | characteristic |
| 160 | C4×C89 | #471 | 1 | 1 | yes | characteristic |
| 161 | C4×C89 | #473 | 1 | 1 | yes | characteristic |
| 162 | Dic89 | — | 4 | 2 | no | — |
| 163 | Dic89 | — | 4 | 2 | no | — |
| 164 | Dic89 | — | 8 | 2 | no | — |
| 165 | #9272 | — | 89 | 1 | no | maximal, Sylow |
| 166 | C2×C89 | — | 2 | 1 | no | — |
| 167 | C2×C89 | — | 2 | 1 | no | — |
| 168 | C2×C89 | #1880 | 1 | 1 | yes | characteristic |
| 169 | C2×C89 | #1908 | 1 | 1 | yes | characteristic |
| 170 | C2×C89 | #1915 | 1 | 1 | yes | characteristic |
| 171 | #3229 | — | 89 | 1 | no | — |
| 172 | #2962 | — | 89 | 1 | no | — |
| 173 | #1966 | — | 89 | 1 | no | — |
| 174 | #1550 | — | 89 | 1 | no | — |
| 175 | C2×#332 | — | 89 | 1 | no | — |
| 176 | #1301 | — | 89 | 1 | no | — |
| 177 | #1283 | D89 | 1 | 1 | yes | characteristic |
| 178 | C89 | #9272 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 179 | #533 | — | 89 | 1 | no | — |
| 180 | C2×C4⋊Q8 | — | 89 | 1 | no | — |
| 181 | #498 | — | 178 | 1 | no | — |
| 182 | #487 | — | 178 | 1 | no | — |
| 183 | #483 | — | 89 | 4 | no | — |
| 184 | #475 | — | 178 | 2 | no | — |
| 185 | #446 | — | 178 | 1 | no | — |
| 186 | #446 | — | 178 | 2 | no | — |
| 187 | C8×Q8 | — | 178 | 1 | no | — |
| 188 | #431 | C2×D89 | 1 | 1 | yes | characteristic |
| 189 | #424 | — | 178 | 1 | no | — |
| 190 | #423 | — | 89 | 1 | no | — |
| 191 | C2×C4⋊C8 | — | 89 | 1 | no | — |
| 192 | C2×C4⋊C8 | C2×D89 | 1 | 1 | yes | characteristic |
| 193 | C2×#101 | — | 178 | 1 | no | — |
| 194 | C2×#101 | — | 178 | 1 | no | — |
| 195 | #405 | — | 178 | 1 | no | — |
| 196 | C4×M16 | C2×D89 | 1 | 1 | yes | characteristic |
| 197 | #333 | — | 178 | 1 | no | — |
| 198 | #332 | — | 178 | 1 | no | — |
| 199 | #332 | — | 178 | 1 | no | — |
| 200 | #332 | — | 178 | 1 | no | — |
| 201 | C22×Q8 | — | 178 | 1 | no | — |
| 202 | C2×M16 | — | 178 | 1 | no | — |
| 203 | C2×M16 | D356 | 1 | 1 | yes | characteristic |
| 204 | C2×M16 | D356 | 1 | 1 | yes | characteristic |
| 205 | C22×C8 | — | 2 | 1 | no | — |
| 206 | C22×C8 | — | 178 | 1 | no | — |
| 207 | C4⋊Q8 | — | 89 | 1 | no | — |
| 208 | C4⋊Q8 | — | 89 | 1 | no | — |
| 209 | C4⋊Q8 | — | 178 | 1 | no | — |
| 210 | C4⋊Q8 | — | 178 | 1 | no | — |
| 211 | C4⋊Q8 | — | 178 | 1 | no | — |
| 212 | C4⋊Q8 | — | 178 | 1 | no | — |
| 213 | #125 | — | 178 | 1 | no | — |
| 214 | C22⋊Q8 | — | 89 | 2 | no | — |
| 215 | C22⋊Q8 | — | 178 | 1 | no | — |
| 216 | C4×Q8 | — | 89 | 2 | no | — |
| 217 | C4×Q8 | — | 178 | 1 | no | — |
| 218 | #117 | — | 178 | 1 | no | — |
| 219 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 220 | C2×C4⋊C4 | — | 178 | 1 | no | — |
| 221 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 222 | #106 | — | 178 | 4 | no | — |
| 223 | C4⋊C8 | — | 2 | 1 | no | — |
| 224 | C4⋊C8 | — | 2 | 1 | no | — |
| 225 | C4⋊C8 | — | 2 | 1 | no | — |
| 226 | C4⋊C8 | — | 89 | 1 | no | — |
| 227 | C4⋊C8 | — | 89 | 1 | no | — |
| 228 | C4⋊C8 | — | 178 | 2 | no | — |
| 229 | C4⋊C8 | — | 178 | 2 | no | — |
| 230 | C4⋊C8 | — | 178 | 1 | no | — |
| 231 | C4⋊C8 | — | 178 | 1 | no | — |
| 232 | C4⋊C8 | — | 178 | 1 | no | — |
| 233 | #103 | — | 178 | 4 | no | — |
| 234 | #101 | — | 356 | 2 | no | — |
| 235 | #101 | — | 356 | 2 | no | — |
| 236 | C22⋊C8 | C4×D89 | 1 | 2 | yes | — |
| 237 | #97 | — | 2 | 1 | no | — |
| 238 | #97 | — | 178 | 2 | no | — |
| 239 | C4×C8 | — | 2 | 1 | no | — |
| 240 | C4×C8 | — | 2 | 1 | no | — |
| 241 | C4×C8 | — | 178 | 2 | no | — |
| 242 | C2×Q8 | — | 89 | 2 | no | — |
| 243 | C2×Q8 | — | 356 | 1 | no | — |
| 244 | C2×Q8 | — | 356 | 1 | no | — |
| 245 | C2×Q8 | — | 356 | 1 | no | — |
| 246 | C2×Q8 | — | 356 | 1 | no | — |
| 247 | C2×Q8 | — | 356 | 1 | no | — |
| 248 | C2×Q8 | — | 356 | 1 | no | — |
| 249 | C2×Q8 | — | 178 | 1 | no | — |
| 250 | C22×C4 | — | 178 | 2 | no | — |
| 251 | C22×C4 | C2×C4×D89 | 1 | 1 | yes | characteristic |
| 252 | C22×C4 | C2×D356 | 1 | 1 | yes | characteristic |
| 253 | C22×C4 | #13083574 | 1 | 1 | yes | characteristic |
| 254 | M16 | — | 2 | 1 | no | — |
| 255 | M16 | — | 2 | 1 | no | — |
| 256 | M16 | — | 2 | 1 | no | — |
| 257 | M16 | — | 356 | 1 | no | — |
| 258 | M16 | — | 356 | 1 | no | — |
| 259 | M16 | #13083563 | 1 | 2 | yes | — |
| 260 | C2×C8 | — | 2 | 1 | no | — |
| 261 | C2×C8 | — | 2 | 1 | no | — |
| 262 | C2×C8 | — | 2 | 2 | no | — |
| 263 | C2×C8 | — | 4 | 1 | no | — |
| 264 | C2×C8 | — | 8 | 1 | no | — |
| 265 | C2×C8 | — | 356 | 1 | no | — |
| 266 | C2×C8 | — | 356 | 1 | no | — |
| 267 | C2×C8 | — | 356 | 1 | no | — |
| 268 | C2×C8 | — | 178 | 1 | no | — |
| 269 | C2×C8 | — | 178 | 1 | no | — |
| 270 | C4⋊C4 | — | 89 | 2 | no | — |
| 271 | C4⋊C4 | — | 356 | 1 | no | — |
| 272 | C4⋊C4 | — | 356 | 1 | no | — |
| 273 | C4⋊C4 | — | 178 | 2 | no | — |
| 274 | C4⋊C4 | — | 178 | 2 | no | — |
| 275 | C4⋊C4 | — | 178 | 2 | no | — |
| 276 | C4⋊C4 | — | 178 | 1 | no | — |
| 277 | C4⋊C4 | — | 178 | 1 | no | — |
| 278 | C4⋊C4 | — | 178 | 1 | no | — |
| 279 | C4⋊C4 | — | 178 | 2 | no | — |
| 280 | C22⋊C4 | — | 178 | 2 | no | — |
| 281 | C42 | — | 178 | 2 | no | — |
| 282 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 283 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 284 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 285 | C42 | #13083575 | 1 | 1 | yes | characteristic |
| 286 | C23 | C4×D356 | 1 | 1 | yes | characteristic |
| 287 | Q8 | — | 356 | 2 | no | — |
| 288 | Q8 | — | 356 | 1 | no | — |
| 289 | Q8 | — | 356 | 1 | no | — |
| 290 | Q8 | — | 712 | 1 | no | — |
| 291 | Q8 | — | 712 | 1 | no | — |
| 292 | Q8 | — | 712 | 1 | no | — |
| 293 | Q8 | — | 712 | 1 | no | — |
| 294 | C2×C4 | — | 2 | 1 | no | — |
| 295 | C2×C4 | — | 2 | 1 | no | — |
| 296 | C2×C4 | — | 4 | 1 | no | — |
| 297 | C2×C4 | — | 356 | 2 | no | — |
| 298 | C2×C4 | — | 356 | 2 | no | — |
| 299 | C2×C4 | — | 356 | 2 | no | — |
| 300 | C2×C4 | — | 178 | 2 | no | — |
| 301 | C2×C4 | — | 178 | 2 | no | — |
| 302 | C2×C4 | C22⋊C4×D89 | 1 | 1 | yes | characteristic |
| 303 | C2×C4 | #15667974 | 1 | 1 | yes | characteristic |
| 304 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 305 | C2×C4 | #15667985 | 1 | 1 | yes | characteristic |
| 306 | C2×C4 | #15667987 | 1 | 1 | yes | characteristic |
| 307 | C2×C4 | #15667997 | 1 | 1 | yes | characteristic |
| 308 | C2×C4 | C2×#13083563 | 1 | 1 | yes | characteristic |
| 309 | C2×C4 | #15668034 | 1 | 1 | yes | characteristic |
| 310 | C2×C4 | #15668040 | 1 | 1 | yes | characteristic |
| 311 | C2×C4 | #15668045 | 1 | 1 | yes | characteristic |
| 312 | C8 | — | 2 | 2 | no | — |
| 313 | C8 | — | 4 | 2 | no | — |
| 314 | C8 | — | 4 | 1 | no | — |
| 315 | C8 | — | 8 | 1 | no | — |
| 316 | C8 | — | 356 | 1 | no | — |
| 317 | C8 | — | 356 | 1 | no | — |
| 318 | C8 | — | 712 | 1 | no | — |
| 319 | C22 | — | 2 | 1 | no | — |
| 320 | C22 | — | 2 | 1 | no | — |
| 321 | C22 | #19151476 | 1 | 1 | yes | characteristic |
| 322 | C22 | C4×#13083563 | 1 | 1 | yes | characteristic |
| 323 | C22 | #19151700 | 1 | 1 | yes | characteristic |
| 324 | C4 | — | 2 | 1 | no | — |
| 325 | C4 | — | 2 | 1 | no | — |
| 326 | C4 | — | 2 | 1 | no | — |
| 327 | C4 | — | 356 | 2 | no | — |
| 328 | C4 | — | 356 | 2 | no | — |
| 329 | C4 | — | 712 | 2 | no | — |
| 330 | C4 | #19151739 | 1 | 1 | yes | characteristic |
| 331 | C4 | #19151745 | 1 | 1 | yes | characteristic |
| 332 | C4 | #19151799 | 1 | 1 | yes | characteristic |
| 333 | C4 | #19151821 | 1 | 1 | yes | characteristic |
| 334 | C4 | #19151860 | 1 | 1 | yes | characteristic |
| 335 | C4 | #19151872 | 1 | 1 | yes | characteristic |
| 336 | C2 | — | 2 | 1 | no | — |
| 337 | C2 | — | 2 | 1 | no | — |
| 338 | C2 | #26020606 | 1 | 1 | yes | characteristic |
| 339 | C2 | #26020768 | 1 | 1 | yes | characteristic |
| 340 | C2 | #26020803 | 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