← #36701211
Subgroups — #36701211
Order 22784.
682 conjugacy classes of subgroups.
The subgroup lattice has 332 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #26025239 | C2 | 1 | 2 | yes | maximal |
| 2 | #26021745 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #26021579 | C2 | 1 | 2 | yes | maximal |
| 4 | #26021578 | C2 | 1 | 2 | yes | maximal |
| 5 | #26021191 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #26020992 | C2 | 1 | 2 | yes | maximal |
| 7 | #26020833 | C2 | 1 | 2 | yes | maximal |
| 8 | #26020828 | C2 | 1 | 2 | yes | maximal |
| 9 | C89×#2087 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×#15668011 | — | 2 | 2 | no | — |
| 11 | C2×#15668011 | C22 | 1 | 2 | yes | — |
| 12 | C2×C4×Dic178 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#15667946 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#15667945 | C22 | 1 | 2 | yes | — |
| 15 | C2×#15667943 | C22 | 1 | 2 | yes | — |
| 16 | C2×#15667923 | C22 | 1 | 1 | yes | characteristic |
| 17 | #19151532 | — | 2 | 2 | no | — |
| 18 | #19151531 | — | 2 | 2 | no | — |
| 19 | #19151502 | — | 2 | 2 | no | — |
| 20 | #19151497 | C22 | 1 | 2 | yes | — |
| 21 | #19151496 | C22 | 1 | 2 | yes | — |
| 22 | #19151494 | C22 | 1 | 2 | yes | — |
| 23 | C4⋊C4×Dic89 | C22 | 1 | 2 | yes | — |
| 24 | #19151361 | C22 | 1 | 2 | yes | — |
| 25 | #19151361 | C22 | 1 | 1 | yes | characteristic |
| 26 | #19151360 | C22 | 1 | 2 | yes | — |
| 27 | #19151360 | C22 | 1 | 2 | yes | — |
| 28 | #19151352 | C22 | 1 | 2 | yes | — |
| 29 | #19151352 | C22 | 1 | 2 | yes | — |
| 30 | C2×#107×C89 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×C4⋊C8×C89 | C22 | 1 | 1 | yes | characteristic |
| 32 | #389×C89 | C22 | 1 | 2 | yes | — |
| 33 | #340×C89 | C22 | 1 | 2 | yes | — |
| 34 | #340×C89 | C22 | 1 | 1 | yes | characteristic |
| 35 | C22×Dic178 | — | 2 | 2 | no | — |
| 36 | C22×Dic178 | D4 | 1 | 1 | yes | characteristic |
| 37 | C22×#10623494 | C23 | 1 | 2 | yes | — |
| 38 | #15668011 | — | 4 | 2 | no | — |
| 39 | #15668011 | — | 4 | 2 | no | — |
| 40 | #15668011 | — | 4 | 8 | no | — |
| 41 | C4×Dic178 | — | 4 | 1 | no | — |
| 42 | C4×Dic178 | — | 4 | 1 | no | — |
| 43 | C2×C4⋊Dic89 | — | 2 | 2 | no | — |
| 44 | C2×C4⋊Dic89 | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×C4⋊Dic89 | C23 | 1 | 2 | yes | — |
| 46 | C2×C4⋊Dic89 | C23 | 1 | 2 | yes | — |
| 47 | C2×#13083553 | — | 2 | 2 | no | — |
| 48 | C2×#13083553 | — | 2 | 2 | no | — |
| 49 | C2×#13083553 | — | 2 | 2 | no | — |
| 50 | C2×#13083553 | D4 | 1 | 2 | yes | — |
| 51 | C2×C4×Dic89 | — | 2 | 2 | no | — |
| 52 | C2×C4×Dic89 | C23 | 1 | 2 | yes | — |
| 53 | #15667946 | — | 4 | 1 | no | — |
| 54 | #15667945 | — | 4 | 2 | no | — |
| 55 | #15667943 | Q8 | 1 | 8 | yes | complemented |
| 56 | #15667923 | — | 4 | 1 | no | — |
| 57 | #15667919 | — | 2 | 2 | no | — |
| 58 | #15667919 | — | 2 | 2 | no | — |
| 59 | #15667919 | — | 2 | 2 | no | — |
| 60 | #15667919 | — | 2 | 2 | no | — |
| 61 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22×C8×C89 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C4⋊C4×C89 | — | 2 | 2 | no | — |
| 64 | C2×C4⋊C4×C89 | C23 | 1 | 2 | yes | — |
| 65 | C2×C4⋊C4×C89 | C23 | 1 | 2 | yes | — |
| 66 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 67 | #107×C89 | — | 4 | 1 | no | — |
| 68 | C4⋊C8×C89 | — | 4 | 1 | no | — |
| 69 | #95×C89 | — | 2 | 2 | no | — |
| 70 | C2×Dic178 | — | 2 | 4 | no | — |
| 71 | C2×Dic178 | — | 4 | 1 | no | — |
| 72 | C2×Dic178 | — | 4 | 4 | no | — |
| 73 | C2×Dic178 | — | 4 | 4 | no | — |
| 74 | C2×Dic178 | — | 4 | 4 | no | — |
| 75 | C22×Dic89 | — | 2 | 2 | no | — |
| 76 | C22×Dic89 | — | 2 | 2 | no | — |
| 77 | C22×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 78 | C22×Dic89 | C2×D4 | 1 | 2 | yes | — |
| 79 | C2×#10623494 | — | 2 | 2 | no | — |
| 80 | C2×#10623494 | — | 2 | 2 | no | — |
| 81 | C2×#10623494 | C2×Q8 | 1 | 4 | yes | — |
| 82 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 83 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 84 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 85 | C4⋊Dic89 | — | 4 | 1 | no | — |
| 86 | C4⋊Dic89 | — | 4 | 4 | no | — |
| 87 | C4⋊Dic89 | C2×Q8 | 1 | 4 | yes | — |
| 88 | #13083553 | — | 4 | 2 | no | — |
| 89 | #13083553 | — | 4 | 4 | no | — |
| 90 | #13083553 | — | 4 | 4 | no | — |
| 91 | #13083553 | — | 4 | 4 | no | — |
| 92 | C4×Dic89 | — | 2 | 2 | no | — |
| 93 | C4×Dic89 | — | 2 | 2 | no | — |
| 94 | C4×Dic89 | — | 4 | 4 | no | — |
| 95 | C22×C4×C89 | — | 2 | 2 | no | — |
| 96 | C22×C4×C89 | — | 2 | 2 | no | — |
| 97 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C22×C4×C89 | C24 | 1 | 1 | yes | characteristic |
| 100 | C2×C8×C89 | — | 2 | 1 | no | — |
| 101 | C2×C8×C89 | — | 2 | 1 | no | — |
| 102 | C2×C8×C89 | — | 2 | 2 | no | — |
| 103 | C2×C8×C89 | — | 2 | 2 | no | — |
| 104 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 105 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 106 | C4⋊C4×C89 | — | 2 | 2 | no | — |
| 107 | C4⋊C4×C89 | — | 4 | 4 | no | — |
| 108 | C4⋊C4×C89 | C2×Q8 | 1 | 4 | yes | — |
| 109 | C42×C89 | — | 2 | 1 | no | — |
| 110 | C42×C89 | — | 2 | 1 | no | — |
| 111 | C23×C89 | C22×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×C89 | — | 2 | 1 | no | — |
| 113 | C2×C4×C89 | — | 2 | 1 | no | — |
| 114 | C2×C4×C89 | — | 2 | 4 | no | — |
| 115 | C2×C4×C89 | — | 2 | 2 | no | — |
| 116 | C2×C4×C89 | — | 2 | 1 | no | — |
| 117 | C2×C4×C89 | — | 2 | 1 | no | — |
| 118 | C2×C4×C89 | — | 4 | 2 | no | — |
| 119 | C2×C4×C89 | — | 4 | 2 | no | — |
| 120 | C2×C4×C89 | — | 4 | 2 | no | — |
| 121 | C2×C4×C89 | — | 4 | 2 | no | — |
| 122 | C2×C4×C89 | — | 4 | 2 | no | — |
| 123 | C2×C4×C89 | C22×Q8 | 1 | 2 | yes | — |
| 124 | C2×C4×C89 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 125 | C2×C4×C89 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C89 | 2−1+4 | 1 | 2 | yes | — |
| 127 | C2×Dic89 | — | 2 | 2 | no | — |
| 128 | C2×Dic89 | — | 2 | 2 | no | — |
| 129 | C2×Dic89 | — | 2 | 2 | no | — |
| 130 | C2×Dic89 | — | 2 | 4 | no | — |
| 131 | C2×Dic89 | — | 2 | 2 | no | — |
| 132 | C2×Dic89 | — | 2 | 2 | no | — |
| 133 | C2×Dic89 | — | 4 | 2 | no | — |
| 134 | C2×Dic89 | — | 4 | 2 | no | — |
| 135 | C2×Dic89 | — | 4 | 2 | no | — |
| 136 | C2×Dic89 | — | 4 | 2 | no | — |
| 137 | C2×Dic89 | — | 4 | 2 | no | — |
| 138 | C2×Dic89 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 139 | Dic178 | — | 4 | 4 | no | — |
| 140 | Dic178 | — | 8 | 8 | no | — |
| 141 | C8×C89 | — | 4 | 1 | no | — |
| 142 | C8×C89 | — | 4 | 1 | no | — |
| 143 | #10623494 | — | 2 | 4 | no | — |
| 144 | C22×C89 | #534 | 1 | 1 | yes | characteristic |
| 145 | C22×C89 | D4×Q8 | 1 | 2 | yes | — |
| 146 | C22×C89 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 147 | C22×C89 | #578 | 1 | 1 | yes | characteristic |
| 148 | C22×C89 | #578 | 1 | 1 | yes | characteristic |
| 149 | C4×C89 | — | 4 | 4 | no | — |
| 150 | C4×C89 | — | 4 | 1 | no | — |
| 151 | C4×C89 | — | 4 | 1 | no | — |
| 152 | C4×C89 | — | 8 | 2 | no | — |
| 153 | C4×C89 | #544 | 1 | 2 | yes | — |
| 154 | C4×C89 | Q82 | 1 | 1 | yes | characteristic |
| 155 | C4×C89 | #563 | 1 | 1 | yes | characteristic |
| 156 | Dic89 | — | 2 | 4 | no | — |
| 157 | Dic89 | — | 4 | 4 | no | — |
| 158 | Dic89 | — | 4 | 2 | no | — |
| 159 | Dic89 | — | 8 | 2 | no | — |
| 160 | #32693 | — | 89 | 1 | no | maximal, Sylow |
| 161 | C2×C89 | #2734 | 1 | 1 | yes | characteristic |
| 162 | C2×C89 | #3192 | 1 | 1 | yes | characteristic |
| 163 | C2×C89 | #3202 | 1 | 1 | yes | characteristic |
| 164 | C2×C89 | #3386 | 1 | 2 | yes | — |
| 165 | C2×C89 | #3386 | 1 | 2 | yes | — |
| 166 | #2546 | — | 89 | 2 | no | — |
| 167 | #2087 | — | 89 | 1 | no | — |
| 168 | #2087 | D89 | 1 | 1 | yes | characteristic |
| 169 | #2057 | — | 89 | 2 | no | — |
| 170 | #2057 | — | 89 | 2 | no | — |
| 171 | #1985 | — | 89 | 1 | no | — |
| 172 | #1944 | — | 89 | 2 | no | — |
| 173 | #1919 | — | 89 | 2 | no | — |
| 174 | #1919 | — | 89 | 2 | no | — |
| 175 | C89 | #32693 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 176 | C2×C4⋊Q8 | — | 89 | 2 | no | — |
| 177 | C2×C4⋊Q8 | — | 178 | 2 | no | — |
| 178 | C2×C4×Q8 | — | 89 | 1 | no | — |
| 179 | C2×#107 | — | 89 | 1 | no | — |
| 180 | C2×#107 | — | 89 | 2 | no | — |
| 181 | C2×#107 | C2×D89 | 1 | 1 | yes | characteristic |
| 182 | C2×#106 | — | 89 | 2 | no | — |
| 183 | C2×C4⋊C8 | C2×D89 | 1 | 1 | yes | characteristic |
| 184 | C2×#97 | — | 89 | 1 | no | — |
| 185 | #398 | — | 178 | 2 | no | — |
| 186 | #398 | — | 178 | 2 | no | — |
| 187 | #391 | — | 178 | 2 | no | — |
| 188 | #389 | — | 89 | 2 | no | — |
| 189 | #389 | — | 89 | 2 | no | — |
| 190 | #389 | — | 89 | 2 | no | — |
| 191 | #389 | C2×D89 | 1 | 2 | yes | — |
| 192 | C4×C4⋊C4 | — | 89 | 2 | no | — |
| 193 | #340 | — | 89 | 2 | no | — |
| 194 | #340 | — | 89 | 1 | no | — |
| 195 | #340 | — | 89 | 2 | no | — |
| 196 | #340 | — | 89 | 2 | no | — |
| 197 | #340 | C2×D89 | 1 | 2 | yes | — |
| 198 | #340 | C2×D89 | 1 | 1 | yes | characteristic |
| 199 | #336 | — | 89 | 2 | no | — |
| 200 | #336 | — | 89 | 2 | no | — |
| 201 | C22×Q8 | — | 89 | 1 | no | — |
| 202 | C22×Q8 | — | 178 | 2 | no | — |
| 203 | C22×C8 | — | 89 | 2 | no | — |
| 204 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 205 | C22×C8 | C22×D89 | 1 | 1 | yes | characteristic |
| 206 | C4⋊Q8 | — | 356 | 8 | no | — |
| 207 | C4⋊Q8 | — | 356 | 2 | no | — |
| 208 | C4⋊Q8 | — | 356 | 2 | no | — |
| 209 | C4×Q8 | — | 356 | 1 | no | — |
| 210 | C4×Q8 | — | 356 | 1 | no | — |
| 211 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 212 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 213 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 214 | C2×C4⋊C4 | — | 89 | 1 | no | — |
| 215 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 216 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 217 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 218 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 219 | C2×C4⋊C4 | — | 178 | 2 | no | — |
| 220 | C2×C4⋊C4 | C22×D89 | 1 | 2 | yes | — |
| 221 | C2×C4⋊C4 | C22×D89 | 1 | 2 | yes | — |
| 222 | C2×C42 | — | 89 | 2 | no | — |
| 223 | C2×C42 | — | 178 | 2 | no | — |
| 224 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 225 | #107 | — | 4 | 1 | no | — |
| 226 | #107 | — | 356 | 2 | no | — |
| 227 | #107 | — | 356 | 1 | no | — |
| 228 | #106 | — | 89 | 8 | no | — |
| 229 | C4⋊C8 | — | 4 | 1 | no | — |
| 230 | #97 | — | 356 | 1 | no | — |
| 231 | #95 | — | 2 | 2 | no | — |
| 232 | #95 | — | 178 | 2 | no | — |
| 233 | #95 | — | 178 | 2 | no | — |
| 234 | #95 | — | 178 | 2 | no | — |
| 235 | #95 | — | 178 | 2 | no | — |
| 236 | C2×Q8 | — | 356 | 1 | no | — |
| 237 | C2×Q8 | — | 356 | 4 | no | — |
| 238 | C2×Q8 | — | 356 | 4 | no | — |
| 239 | C2×Q8 | — | 356 | 4 | no | — |
| 240 | C2×Q8 | — | 178 | 4 | no | — |
| 241 | C22×C4 | — | 2 | 2 | no | — |
| 242 | C22×C4 | — | 2 | 2 | no | — |
| 243 | C22×C4 | — | 89 | 2 | no | — |
| 244 | C22×C4 | — | 89 | 2 | no | — |
| 245 | C22×C4 | — | 178 | 2 | no | — |
| 246 | C22×C4 | — | 178 | 2 | no | — |
| 247 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 248 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 249 | C22×C4 | C23×D89 | 1 | 1 | yes | characteristic |
| 250 | C2×C8 | — | 2 | 1 | no | — |
| 251 | C2×C8 | — | 2 | 1 | no | — |
| 252 | C2×C8 | — | 2 | 2 | no | — |
| 253 | C2×C8 | — | 2 | 2 | no | — |
| 254 | C2×C8 | — | 89 | 4 | no | — |
| 255 | C2×C8 | — | 178 | 2 | no | — |
| 256 | C2×C8 | — | 178 | 2 | no | — |
| 257 | C4⋊C4 | — | 2 | 2 | no | — |
| 258 | C4⋊C4 | — | 2 | 2 | no | — |
| 259 | C4⋊C4 | — | 2 | 2 | no | — |
| 260 | C4⋊C4 | — | 4 | 4 | no | — |
| 261 | C4⋊C4 | — | 89 | 4 | no | — |
| 262 | C4⋊C4 | — | 356 | 4 | no | — |
| 263 | C4⋊C4 | — | 356 | 2 | no | — |
| 264 | C4⋊C4 | — | 356 | 1 | no | — |
| 265 | C4⋊C4 | — | 356 | 4 | no | — |
| 266 | C4⋊C4 | — | 356 | 4 | no | — |
| 267 | C4⋊C4 | — | 356 | 4 | no | — |
| 268 | C4⋊C4 | — | 178 | 2 | no | — |
| 269 | C4⋊C4 | — | 178 | 2 | no | — |
| 270 | C4⋊C4 | — | 178 | 2 | no | — |
| 271 | C4⋊C4 | Q8×D89 | 1 | 4 | yes | — |
| 272 | C42 | — | 2 | 1 | no | — |
| 273 | C42 | — | 2 | 1 | no | — |
| 274 | C42 | — | 356 | 4 | no | — |
| 275 | C42 | — | 178 | 2 | no | — |
| 276 | C42 | — | 178 | 2 | no | — |
| 277 | C23 | C2×D4×D89 | 1 | 1 | yes | characteristic |
| 278 | Q8 | — | 356 | 4 | no | — |
| 279 | Q8 | — | 712 | 8 | no | — |
| 280 | C2×C4 | — | 2 | 1 | no | — |
| 281 | C2×C4 | — | 2 | 1 | no | — |
| 282 | C2×C4 | — | 2 | 1 | no | — |
| 283 | C2×C4 | — | 2 | 1 | no | — |
| 284 | C2×C4 | — | 2 | 4 | no | — |
| 285 | C2×C4 | — | 2 | 2 | no | — |
| 286 | C2×C4 | — | 4 | 2 | no | — |
| 287 | C2×C4 | — | 4 | 2 | no | — |
| 288 | C2×C4 | — | 4 | 2 | no | — |
| 289 | C2×C4 | — | 4 | 2 | no | — |
| 290 | C2×C4 | — | 4 | 2 | no | — |
| 291 | C2×C4 | — | 89 | 4 | no | — |
| 292 | C2×C4 | — | 356 | 2 | no | — |
| 293 | C2×C4 | — | 356 | 2 | no | — |
| 294 | C2×C4 | — | 356 | 2 | no | — |
| 295 | C2×C4 | — | 356 | 2 | no | — |
| 296 | C2×C4 | — | 356 | 2 | no | — |
| 297 | C2×C4 | — | 178 | 2 | no | — |
| 298 | C2×C4 | — | 178 | 2 | no | — |
| 299 | C2×C4 | — | 178 | 2 | no | — |
| 300 | C2×C4 | — | 178 | 4 | no | — |
| 301 | C2×C4 | — | 178 | 2 | no | — |
| 302 | C2×C4 | — | 178 | 2 | no | — |
| 303 | C2×C4 | C2×Q8×D89 | 1 | 2 | yes | — |
| 304 | C2×C4 | #15668057 | 1 | 1 | yes | characteristic |
| 305 | C2×C4 | #15668058 | 1 | 1 | yes | characteristic |
| 306 | C2×C4 | #15668059 | 1 | 2 | yes | — |
| 307 | C8 | — | 4 | 1 | no | — |
| 308 | C8 | — | 4 | 1 | no | — |
| 309 | C8 | — | 178 | 4 | no | — |
| 310 | C22 | #19152156 | 1 | 1 | yes | characteristic |
| 311 | C22 | #19152261 | 1 | 2 | yes | — |
| 312 | C22 | AGL(1,ℤ/8)×D89 | 1 | 2 | yes | — |
| 313 | C22 | #19152411 | 1 | 1 | yes | characteristic |
| 314 | C22 | #19152412 | 1 | 1 | yes | characteristic |
| 315 | C4 | — | 4 | 4 | no | — |
| 316 | C4 | — | 4 | 1 | no | — |
| 317 | C4 | — | 4 | 1 | no | — |
| 318 | C4 | — | 8 | 2 | no | — |
| 319 | C4 | — | 356 | 4 | no | — |
| 320 | C4 | — | 356 | 2 | no | — |
| 321 | C4 | — | 178 | 4 | no | — |
| 322 | C4 | — | 712 | 2 | no | — |
| 323 | C4 | #19152228 | 1 | 2 | yes | — |
| 324 | C4 | #19152328 | 1 | 1 | yes | characteristic |
| 325 | C4 | #19152351 | 1 | 1 | yes | characteristic |
| 326 | C2 | #26027281 | 1 | 1 | yes | characteristic |
| 327 | C2 | #26031048 | 1 | 1 | yes | characteristic |
| 328 | C2 | #26031142 | 1 | 1 | yes | characteristic |
| 329 | C2 | #26033168 | 1 | 2 | yes | — |
| 330 | C2 | #26033176 | 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