← #15622313
Subgroups — #15622313
Order 2816.
2010 conjugacy classes of subgroups.
The subgroup lattice has 564 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#10623049 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13081817 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13078917 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13078869 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #13078832 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #13078565 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13078439 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13078104 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13077878 | C2 | 1 | 2 | yes | maximal |
| 10 | C4×#66962 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | C11×#2921 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×#4339 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C11×#117 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#66979 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#66977 | C22 | 1 | 2 | yes | — |
| 16 | C2×#66962 | C22 | 1 | 4 | yes | — |
| 17 | #10623054 | C22 | 1 | 4 | yes | — |
| 18 | #10623053 | — | 2 | 2 | no | — |
| 19 | #10623052 | C22 | 1 | 2 | yes | — |
| 20 | D11×#117 | — | 2 | 2 | no | — |
| 21 | #10623049 | — | 2 | 2 | no | — |
| 22 | #10623049 | — | 2 | 2 | no | — |
| 23 | #10623049 | C22 | 1 | 4 | yes | — |
| 24 | #10623049 | C22 | 1 | 4 | yes | complemented |
| 25 | #10623047 | C22 | 1 | 2 | yes | — |
| 26 | #10623035 | — | 2 | 2 | no | — |
| 27 | C2×#66942 | — | 2 | 2 | no | — |
| 28 | #10623017 | — | 2 | 2 | no | — |
| 29 | C2×#66932 | — | 2 | 2 | no | — |
| 30 | C4×#4339 | C22 | 1 | 2 | yes | — |
| 31 | C4×#4339 | C22 | 1 | 2 | yes | — |
| 32 | C2×#66923 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | C2×#66922 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C2×C4×Dic22 | C22 | 1 | 2 | yes | complemented |
| 35 | C11×#433 | C22 | 1 | 4 | yes | — |
| 36 | C11×#433 | C22 | 1 | 4 | yes | complemented |
| 37 | C11×#423 | C22 | 1 | 2 | yes | complemented |
| 38 | C11×#407 | C22 | 1 | 2 | yes | — |
| 39 | C4×C11×M16 | C22 | 1 | 2 | yes | complemented |
| 40 | #10622746 | C22 | 1 | 4 | yes | — |
| 41 | #10622734 | C22 | 1 | 4 | yes | complemented |
| 42 | #10622733 | C22 | 1 | 4 | yes | complemented |
| 43 | #10622462 | C22 | 1 | 8 | yes | complemented |
| 44 | #10622460 | C22 | 1 | 8 | yes | complemented |
| 45 | #10622454 | C22 | 1 | 8 | yes | complemented |
| 46 | #10622442 | C22 | 1 | 8 | yes | complemented |
| 47 | #10622352 | C22 | 1 | 4 | yes | — |
| 48 | #10622346 | C22 | 1 | 8 | yes | — |
| 49 | #10622344 | C22 | 1 | 4 | yes | — |
| 50 | #10622336 | C22 | 1 | 8 | yes | — |
| 51 | #10622335 | C22 | 1 | 4 | yes | complemented |
| 52 | #10622334 | C22 | 1 | 4 | yes | complemented |
| 53 | #10622329 | C22 | 1 | 8 | yes | complemented |
| 54 | #10622323 | C22 | 1 | 8 | yes | complemented |
| 55 | C4×Dic44 | C22 | 1 | 8 | yes | complemented |
| 56 | C4×#4314 | C22 | 1 | 8 | yes | complemented |
| 57 | C23×C4×C11 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×C22⋊D11 | — | 2 | 1 | no | — |
| 59 | C2×#4339 | — | 2 | 1 | no | — |
| 60 | C2×#4339 | — | 2 | 1 | no | — |
| 61 | C2×#4339 | — | 2 | 8 | no | — |
| 62 | C2×#4339 | C23 | 1 | 2 | yes | — |
| 63 | C2×#4339 | C23 | 1 | 2 | yes | — |
| 64 | C22×D44 | C23 | 1 | 1 | yes | characteristic |
| 65 | C22×C4×D11 | — | 2 | 1 | no | — |
| 66 | C22×Dic22 | C23 | 1 | 2 | yes | — |
| 67 | C22×Dic22 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×C11×M16 | C23 | 1 | 4 | yes | — |
| 69 | C11×#117 | D4 | 1 | 2 | yes | — |
| 70 | C11×#117 | D4 | 1 | 2 | yes | — |
| 71 | C11×#117 | C23 | 1 | 2 | yes | — |
| 72 | C11×#117 | C23 | 1 | 2 | yes | — |
| 73 | C2×C11×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 74 | C2×C11×C22⋊C4 | D4 | 1 | 2 | yes | — |
| 75 | C2×C42×C11 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×C42×C11 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×C22⋊Dic11 | — | 2 | 2 | no | — |
| 78 | C2×C22⋊Dic11 | — | 2 | 1 | no | — |
| 79 | C4×C22⋊D11 | — | 2 | 4 | no | — |
| 80 | C4×C22⋊D11 | — | 2 | 4 | no | — |
| 81 | #66979 | — | 2 | 1 | no | — |
| 82 | #66979 | — | 2 | 1 | no | — |
| 83 | #66979 | C23 | 1 | 2 | yes | — |
| 84 | #66979 | C23 | 1 | 2 | yes | — |
| 85 | C2×C4⋊Dic11 | — | 2 | 2 | no | — |
| 86 | C2×C4⋊Dic11 | C23 | 1 | 2 | yes | — |
| 87 | C2×C4⋊Dic11 | C23 | 1 | 2 | yes | — |
| 88 | #66977 | — | 2 | 2 | no | — |
| 89 | #66977 | — | 2 | 2 | no | — |
| 90 | #66977 | C23 | 1 | 4 | yes | — |
| 91 | #66977 | C23 | 1 | 4 | yes | — |
| 92 | C2×Dic11⋊C4 | — | 2 | 2 | no | — |
| 93 | C2×Dic11⋊C4 | — | 2 | 2 | no | — |
| 94 | C2×Dic11⋊C4 | — | 2 | 2 | no | — |
| 95 | C2×C4×Dic11 | — | 2 | 2 | no | — |
| 96 | C2×C4×Dic11 | — | 2 | 1 | no | — |
| 97 | #66962 | — | 2 | 16 | no | — |
| 98 | C2×Dic44 | C23 | 1 | 8 | yes | — |
| 99 | C2×#4314 | C23 | 1 | 8 | yes | — |
| 100 | #66946 | — | 2 | 4 | no | — |
| 101 | #66945 | — | 2 | 4 | no | — |
| 102 | C4⋊C4×D11 | — | 2 | 4 | no | — |
| 103 | #66942 | — | 2 | 8 | no | — |
| 104 | #66942 | — | 2 | 8 | no | — |
| 105 | #66940 | — | 2 | 4 | no | — |
| 106 | (C22⋊D11)⋊C4 | — | 2 | 4 | no | — |
| 107 | (C22⋊D11)⋊C4 | — | 2 | 4 | no | — |
| 108 | C22⋊C4×D11 | — | 2 | 4 | no | — |
| 109 | #66932 | — | 2 | 8 | no | — |
| 110 | #66932 | — | 2 | 8 | no | — |
| 111 | #66930 | — | 2 | 4 | no | — |
| 112 | C4×D44 | C23 | 1 | 4 | yes | — |
| 113 | C4×D44 | C23 | 1 | 4 | yes | — |
| 114 | #66925 | — | 2 | 2 | no | — |
| 115 | #66925 | — | 2 | 2 | no | — |
| 116 | C42×D11 | — | 2 | 2 | no | — |
| 117 | C42×D11 | — | 2 | 2 | no | — |
| 118 | #66923 | — | 2 | 2 | no | — |
| 119 | #66923 | C23 | 1 | 4 | yes | — |
| 120 | #66922 | — | 2 | 2 | no | — |
| 121 | #66922 | C23 | 1 | 4 | yes | — |
| 122 | C4×Dic22 | — | 2 | 4 | no | — |
| 123 | C4×Dic22 | C23 | 1 | 8 | yes | — |
| 124 | C4×Dic22 | C23 | 1 | 4 | yes | — |
| 125 | C4×Dic22 | C23 | 1 | 4 | yes | — |
| 126 | C11×C4⋊C8 | C23 | 1 | 8 | yes | — |
| 127 | C11×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 128 | C11×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 129 | C11×#97 | C23 | 1 | 4 | yes | — |
| 130 | C4×C8×C11 | C23 | 1 | 4 | yes | — |
| 131 | #66885 | C23 | 1 | 8 | yes | — |
| 132 | #66882 | C23 | 1 | 8 | yes | — |
| 133 | #66881 | C23 | 1 | 8 | yes | — |
| 134 | #66880 | C23 | 1 | 8 | yes | — |
| 135 | #66880 | C23 | 1 | 8 | yes | — |
| 136 | #66880 | C23 | 1 | 8 | yes | — |
| 137 | #60569 | — | 11 | 1 | no | maximal, Sylow |
| 138 | C24×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C23×D11 | — | 2 | 1 | no | — |
| 140 | C22×C4×C11 | — | 2 | 4 | no | — |
| 141 | C22×C4×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C22×C4×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C22×C4×C11 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C22×C4×C11 | C2×D4 | 1 | 2 | yes | — |
| 145 | C22×C4×C11 | C2×D4 | 1 | 2 | yes | — |
| 146 | C22×C4×C11 | C24 | 1 | 1 | yes | characteristic |
| 147 | C22×C4×C11 | C24 | 1 | 1 | yes | characteristic |
| 148 | C22×C4×C11 | C24 | 1 | 1 | yes | characteristic |
| 149 | C2×C22⋊D11 | — | 2 | 8 | no | — |
| 150 | C2×C22⋊D11 | — | 2 | 2 | no | — |
| 151 | C2×C22⋊D11 | — | 2 | 2 | no | — |
| 152 | C22×Dic11 | — | 2 | 1 | no | — |
| 153 | C22×Dic11 | — | 2 | 2 | no | — |
| 154 | C22×Dic11 | — | 2 | 2 | no | — |
| 155 | C22×Dic11 | — | 2 | 2 | no | — |
| 156 | #4339 | — | 2 | 8 | no | — |
| 157 | #4339 | — | 2 | 8 | no | — |
| 158 | #4339 | — | 2 | 4 | no | — |
| 159 | #4339 | — | 2 | 4 | no | — |
| 160 | #4339 | — | 2 | 4 | no | — |
| 161 | #4339 | #41 | 1 | 8 | yes | — |
| 162 | C2×D44 | — | 2 | 4 | no | — |
| 163 | C2×D44 | — | 2 | 1 | no | — |
| 164 | C2×D44 | C24 | 1 | 2 | yes | — |
| 165 | C2×C4×D11 | — | 2 | 8 | no | — |
| 166 | C2×C4×D11 | — | 2 | 2 | no | — |
| 167 | C2×C4×D11 | — | 2 | 2 | no | — |
| 168 | C2×C4×D11 | — | 2 | 4 | no | — |
| 169 | C2×C4×D11 | — | 2 | 4 | no | — |
| 170 | C2×Dic22 | — | 2 | 4 | no | — |
| 171 | C2×Dic22 | — | 2 | 1 | no | — |
| 172 | C2×Dic22 | — | 2 | 2 | no | — |
| 173 | C2×Dic22 | — | 2 | 8 | no | — |
| 174 | C2×Dic22 | C24 | 1 | 4 | yes | — |
| 175 | C2×Dic22 | C24 | 1 | 2 | yes | — |
| 176 | C11×M16 | — | 2 | 8 | no | — |
| 177 | C2×C8×C11 | C24 | 1 | 8 | yes | — |
| 178 | C11×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 179 | C11×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 180 | C11×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 181 | C11×C22⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 182 | C42×C11 | C2×D4 | 1 | 2 | yes | — |
| 183 | C42×C11 | C2×D4 | 1 | 2 | yes | — |
| 184 | C42×C11 | C24 | 1 | 2 | yes | — |
| 185 | C42×C11 | C24 | 1 | 2 | yes | — |
| 186 | C22⋊Dic11 | — | 2 | 2 | no | — |
| 187 | C22⋊Dic11 | — | 2 | 4 | no | — |
| 188 | C22⋊Dic11 | — | 2 | 4 | no | — |
| 189 | C22⋊Dic11 | — | 2 | 2 | no | — |
| 190 | (C2×D11)⋊C4 | — | 2 | 4 | no | — |
| 191 | (C2×D11)⋊C4 | — | 2 | 4 | no | — |
| 192 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 193 | C4⋊Dic11 | — | 2 | 8 | no | — |
| 194 | C4⋊Dic11 | — | 2 | 2 | no | — |
| 195 | C4⋊Dic11 | C24 | 1 | 4 | yes | — |
| 196 | C4⋊Dic11 | C24 | 1 | 4 | yes | — |
| 197 | Dic11⋊C4 | — | 2 | 8 | no | — |
| 198 | Dic11⋊C4 | — | 2 | 4 | no | — |
| 199 | Dic11⋊C4 | — | 2 | 4 | no | — |
| 200 | Dic11⋊C4 | — | 2 | 8 | no | — |
| 201 | Dic11⋊C4 | — | 2 | 4 | no | — |
| 202 | Dic11⋊C4 | — | 2 | 4 | no | — |
| 203 | C4×Dic11 | — | 2 | 8 | no | — |
| 204 | C4×Dic11 | — | 2 | 4 | no | — |
| 205 | C4×Dic11 | — | 2 | 4 | no | — |
| 206 | C4×Dic11 | — | 2 | 2 | no | — |
| 207 | C4×Dic11 | — | 2 | 2 | no | — |
| 208 | Dic44 | — | 2 | 16 | no | — |
| 209 | #4314 | — | 2 | 16 | no | — |
| 210 | C2×#541 | — | 11 | 1 | no | — |
| 211 | #3428 | — | 11 | 1 | no | — |
| 212 | #3127 | — | 11 | 4 | no | — |
| 213 | #3123 | — | 11 | 4 | no | — |
| 214 | #3120 | — | 11 | 8 | no | — |
| 215 | #3095 | — | 11 | 2 | no | — |
| 216 | #3080 | — | 11 | 2 | no | — |
| 217 | #3039 | — | 11 | 2 | no | — |
| 218 | #3007 | — | 11 | 2 | no | — |
| 219 | C4×#137 | — | 11 | 4 | no | — |
| 220 | #2921 | D11 | 1 | 1 | yes | characteristic, complemented |
| 221 | C23×C11 | — | 2 | 2 | no | — |
| 222 | C23×C11 | — | 4 | 2 | no | — |
| 223 | C23×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 224 | C23×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 225 | C23×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 226 | C22×D11 | — | 2 | 2 | no | — |
| 227 | C22×D11 | — | 2 | 4 | no | — |
| 228 | C22×D11 | — | 8 | 2 | no | — |
| 229 | C2×C4×C11 | — | 2 | 2 | no | — |
| 230 | C2×C4×C11 | — | 2 | 2 | no | — |
| 231 | C2×C4×C11 | — | 2 | 2 | no | — |
| 232 | C2×C4×C11 | — | 2 | 2 | no | — |
| 233 | C2×C4×C11 | — | 2 | 2 | no | — |
| 234 | C2×C4×C11 | — | 4 | 2 | no | — |
| 235 | C2×C4×C11 | — | 4 | 2 | no | — |
| 236 | C2×C4×C11 | C22×D4 | 1 | 4 | yes | — |
| 237 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×C4×C11 | C22×D4 | 1 | 4 | yes | — |
| 239 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 240 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 241 | C2×C4×C11 | C2×#41 | 1 | 4 | yes | — |
| 242 | C2×C4×C11 | C25 | 1 | 1 | yes | characteristic |
| 243 | C22⋊D11 | — | 2 | 8 | no | — |
| 244 | C22⋊D11 | — | 2 | 8 | no | — |
| 245 | C2×Dic11 | — | 2 | 4 | no | — |
| 246 | C2×Dic11 | — | 2 | 2 | no | — |
| 247 | C2×Dic11 | — | 2 | 4 | no | — |
| 248 | C2×Dic11 | — | 2 | 4 | no | — |
| 249 | C2×Dic11 | — | 2 | 4 | no | — |
| 250 | C2×Dic11 | — | 4 | 4 | no | — |
| 251 | C2×Dic11 | — | 4 | 4 | no | — |
| 252 | C2×Dic11 | — | 8 | 2 | no | — |
| 253 | D44 | — | 2 | 4 | no | — |
| 254 | D44 | — | 2 | 2 | no | — |
| 255 | D44 | C2×#41 | 1 | 4 | yes | — |
| 256 | C4×D11 | — | 2 | 8 | no | — |
| 257 | C4×D11 | — | 2 | 8 | no | — |
| 258 | C4×D11 | — | 8 | 4 | no | — |
| 259 | C4×D11 | — | 8 | 4 | no | — |
| 260 | Dic22 | — | 2 | 4 | no | — |
| 261 | Dic22 | — | 2 | 2 | no | — |
| 262 | Dic22 | — | 2 | 8 | no | — |
| 263 | Dic22 | — | 4 | 4 | no | — |
| 264 | Dic22 | C2×#41 | 1 | 4 | yes | — |
| 265 | C8×C11 | — | 2 | 8 | no | — |
| 266 | C22×#41 | — | 11 | 1 | no | — |
| 267 | C2×#137 | — | 11 | 4 | no | — |
| 268 | #541 | — | 11 | 4 | no | — |
| 269 | #541 | — | 11 | 4 | no | — |
| 270 | #541 | — | 22 | 2 | no | — |
| 271 | #541 | — | 22 | 2 | no | — |
| 272 | C2×C4⋊Q8 | — | 11 | 1 | no | — |
| 273 | C2×#126 | — | 22 | 2 | no | — |
| 274 | C2×#125 | — | 11 | 1 | no | — |
| 275 | C2×#125 | — | 22 | 2 | no | — |
| 276 | C2×C22⋊Q8 | — | 11 | 2 | no | — |
| 277 | #520 | — | 11 | 4 | no | — |
| 278 | #520 | — | 22 | 2 | no | — |
| 279 | #519 | — | 11 | 2 | no | — |
| 280 | #518 | — | 11 | 2 | no | — |
| 281 | #518 | — | 22 | 2 | no | — |
| 282 | C4×#41 | — | 11 | 2 | no | — |
| 283 | C4×#41 | — | 11 | 2 | no | — |
| 284 | C4×#41 | — | 22 | 2 | no | — |
| 285 | C2×C4×Q8 | — | 11 | 2 | no | — |
| 286 | C2×#117 | — | 11 | 1 | no | — |
| 287 | C2×#117 | — | 22 | 2 | no | — |
| 288 | C2×#117 | C2×D11 | 1 | 1 | yes | characteristic |
| 289 | #485 | — | 11 | 8 | no | — |
| 290 | #484 | — | 11 | 4 | no | — |
| 291 | #483 | — | 11 | 4 | no | — |
| 292 | #479 | — | 11 | 8 | no | — |
| 293 | #478 | — | 11 | 8 | no | — |
| 294 | #462 | — | 11 | 8 | no | — |
| 295 | #461 | — | 11 | 8 | no | — |
| 296 | #452 | — | 11 | 8 | no | — |
| 297 | #451 | — | 11 | 4 | no | — |
| 298 | #450 | — | 11 | 4 | no | — |
| 299 | #441 | — | 11 | 8 | no | — |
| 300 | #440 | — | 11 | 8 | no | — |
| 301 | C4×Q16 | — | 11 | 8 | no | — |
| 302 | C4×SD16 | — | 11 | 8 | no | — |
| 303 | #433 | C2×D11 | 1 | 4 | yes | — |
| 304 | #433 | C2×D11 | 1 | 4 | yes | complemented |
| 305 | #428 | — | 11 | 4 | no | — |
| 306 | #423 | C2×D11 | 1 | 2 | yes | complemented |
| 307 | #419 | — | 11 | 4 | no | — |
| 308 | #417 | — | 11 | 4 | no | — |
| 309 | #407 | C2×D11 | 1 | 2 | yes | — |
| 310 | C4×M16 | C2×D11 | 1 | 2 | yes | complemented |
| 311 | C22×C11 | — | 2 | 2 | no | — |
| 312 | C22×C11 | — | 2 | 2 | no | — |
| 313 | C22×C11 | — | 2 | 2 | no | — |
| 314 | C22×C11 | — | 2 | 1 | no | — |
| 315 | C22×C11 | — | 2 | 1 | no | — |
| 316 | C22×C11 | — | 8 | 2 | no | — |
| 317 | C22×C11 | #525 | 1 | 2 | yes | — |
| 318 | C22×C11 | C23×D4 | 1 | 1 | yes | characteristic |
| 319 | C2×D11 | — | 2 | 4 | no | — |
| 320 | C2×D11 | — | 4 | 4 | no | — |
| 321 | C2×D11 | — | 8 | 4 | no | — |
| 322 | C4×C11 | — | 2 | 4 | no | — |
| 323 | C4×C11 | — | 2 | 4 | no | — |
| 324 | C4×C11 | — | 2 | 1 | no | — |
| 325 | C4×C11 | — | 2 | 1 | no | — |
| 326 | C4×C11 | #525 | 1 | 2 | yes | — |
| 327 | C4×C11 | C22×#41 | 1 | 2 | yes | — |
| 328 | Dic11 | — | 2 | 4 | no | — |
| 329 | Dic11 | — | 4 | 4 | no | — |
| 330 | Dic11 | — | 4 | 4 | no | — |
| 331 | Dic11 | — | 4 | 4 | no | — |
| 332 | C2×#41 | — | 11 | 2 | no | — |
| 333 | C2×#41 | — | 11 | 2 | no | — |
| 334 | C2×#41 | — | 22 | 8 | no | — |
| 335 | C2×#41 | — | 22 | 1 | no | — |
| 336 | C2×#41 | — | 22 | 1 | no | — |
| 337 | C22×Q8 | — | 11 | 2 | no | — |
| 338 | C22×Q8 | — | 11 | 1 | no | — |
| 339 | C22×D4 | — | 11 | 1 | no | — |
| 340 | C22×D4 | — | 22 | 1 | no | — |
| 341 | C23×C4 | — | 22 | 1 | no | — |
| 342 | C23×C4 | C22×D11 | 1 | 1 | yes | characteristic |
| 343 | #137 | — | 22 | 16 | no | — |
| 344 | C2×Q16 | — | 11 | 8 | no | — |
| 345 | C2×SD16 | — | 11 | 8 | no | — |
| 346 | C2×M16 | C22×D11 | 1 | 4 | yes | — |
| 347 | C4⋊Q8 | — | 11 | 4 | no | — |
| 348 | C4⋊Q8 | — | 22 | 2 | no | — |
| 349 | #126 | — | 22 | 8 | no | — |
| 350 | #126 | — | 22 | 8 | no | — |
| 351 | #125 | — | 11 | 4 | no | — |
| 352 | #125 | — | 22 | 8 | no | — |
| 353 | #125 | — | 22 | 8 | no | — |
| 354 | #125 | — | 22 | 2 | no | — |
| 355 | C22⋊Q8 | — | 11 | 4 | no | — |
| 356 | C22⋊Q8 | — | 11 | 4 | no | — |
| 357 | C22⋊Q8 | — | 22 | 2 | no | — |
| 358 | C22⋊Q8 | — | 22 | 2 | no | — |
| 359 | C4×Q8 | — | 11 | 8 | no | — |
| 360 | C4×Q8 | — | 11 | 4 | no | — |
| 361 | C4×Q8 | — | 11 | 4 | no | — |
| 362 | C4×Q8 | — | 22 | 4 | no | — |
| 363 | C4×Q8 | — | 22 | 4 | no | — |
| 364 | C4×D4 | — | 11 | 4 | no | — |
| 365 | C4×D4 | — | 11 | 4 | no | — |
| 366 | C4×D4 | — | 22 | 4 | no | — |
| 367 | C4×D4 | — | 22 | 4 | no | — |
| 368 | C4×D4 | — | 22 | 4 | no | — |
| 369 | C4×D4 | — | 22 | 4 | no | — |
| 370 | C4×D4 | — | 22 | 4 | no | — |
| 371 | #117 | — | 11 | 2 | no | — |
| 372 | #117 | — | 11 | 2 | no | — |
| 373 | #117 | — | 22 | 1 | no | — |
| 374 | #117 | — | 22 | 1 | no | — |
| 375 | #117 | — | 22 | 4 | no | — |
| 376 | #117 | — | 22 | 4 | no | — |
| 377 | #117 | — | 22 | 2 | no | — |
| 378 | #117 | — | 22 | 2 | no | — |
| 379 | #117 | D44 | 1 | 2 | yes | — |
| 380 | #117 | D44 | 1 | 2 | yes | — |
| 381 | #117 | C22×D11 | 1 | 2 | yes | — |
| 382 | #117 | C22×D11 | 1 | 2 | yes | — |
| 383 | C2×C4⋊C4 | — | 11 | 2 | no | — |
| 384 | C2×C4⋊C4 | — | 11 | 2 | no | — |
| 385 | C2×C4⋊C4 | — | 22 | 2 | no | — |
| 386 | C2×C4⋊C4 | — | 22 | 2 | no | — |
| 387 | C2×C4⋊C4 | — | 22 | 2 | no | — |
| 388 | C2×C4⋊C4 | — | 22 | 2 | no | — |
| 389 | C2×C4⋊C4 | — | 22 | 4 | no | — |
| 390 | C2×C4⋊C4 | D44 | 1 | 2 | yes | — |
| 391 | C2×C22⋊C4 | — | 22 | 1 | no | — |
| 392 | C2×C22⋊C4 | — | 22 | 2 | no | — |
| 393 | C2×C22⋊C4 | — | 22 | 4 | no | — |
| 394 | C2×C22⋊C4 | D44 | 1 | 2 | yes | — |
| 395 | C2×C42 | — | 22 | 1 | no | — |
| 396 | C2×C42 | — | 22 | 2 | no | — |
| 397 | C2×C42 | — | 22 | 2 | no | — |
| 398 | C2×C42 | — | 22 | 2 | no | — |
| 399 | C2×C42 | C22×D11 | 1 | 1 | yes | characteristic |
| 400 | C2×C42 | C22×D11 | 1 | 1 | yes | characteristic |
| 401 | #107 | — | 11 | 8 | no | — |
| 402 | #106 | — | 11 | 8 | no | — |
| 403 | C4⋊C8 | C22×D11 | 1 | 8 | yes | — |
| 404 | #103 | — | 11 | 8 | no | — |
| 405 | #103 | — | 11 | 8 | no | — |
| 406 | #103 | — | 11 | 8 | no | — |
| 407 | #102 | — | 11 | 8 | no | — |
| 408 | C22⋊C8 | C22×D11 | 1 | 4 | yes | — |
| 409 | C22⋊C8 | C22×D11 | 1 | 4 | yes | — |
| 410 | #97 | C22×D11 | 1 | 4 | yes | — |
| 411 | C4×C8 | C22×D11 | 1 | 4 | yes | — |
| 412 | C2×C11 | — | 2 | 2 | no | — |
| 413 | C2×C11 | — | 4 | 1 | no | — |
| 414 | C2×C11 | — | 4 | 1 | no | — |
| 415 | C2×C11 | C2×#525 | 1 | 1 | yes | characteristic |
| 416 | C2×C11 | #3586 | 1 | 2 | yes | — |
| 417 | D11 | — | 4 | 4 | no | — |
| 418 | C24 | — | 22 | 1 | no | — |
| 419 | C24 | C2×D44 | 1 | 1 | yes | characteristic |
| 420 | #41 | — | 11 | 8 | no | — |
| 421 | #41 | — | 22 | 4 | no | — |
| 422 | #41 | — | 22 | 4 | no | — |
| 423 | #41 | — | 22 | 8 | no | — |
| 424 | #41 | — | 22 | 8 | no | — |
| 425 | #41 | — | 22 | 4 | no | — |
| 426 | C2×Q8 | — | 11 | 2 | no | — |
| 427 | C2×Q8 | — | 11 | 4 | no | — |
| 428 | C2×Q8 | — | 22 | 4 | no | — |
| 429 | C2×Q8 | — | 22 | 1 | no | — |
| 430 | C2×Q8 | — | 22 | 2 | no | — |
| 431 | C2×Q8 | — | 22 | 8 | no | — |
| 432 | C2×D4 | — | 11 | 2 | no | — |
| 433 | C2×D4 | — | 22 | 4 | no | — |
| 434 | C2×D4 | — | 22 | 8 | no | — |
| 435 | C2×D4 | — | 22 | 2 | no | — |
| 436 | C2×D4 | — | 22 | 2 | no | — |
| 437 | C2×D4 | — | 22 | 1 | no | — |
| 438 | C22×C4 | — | 2 | 4 | no | — |
| 439 | C22×C4 | — | 22 | 8 | no | — |
| 440 | C22×C4 | — | 22 | 1 | no | — |
| 441 | C22×C4 | — | 22 | 2 | no | — |
| 442 | C22×C4 | — | 22 | 2 | no | — |
| 443 | C22×C4 | — | 22 | 2 | no | — |
| 444 | C22×C4 | — | 22 | 2 | no | — |
| 445 | C22×C4 | — | 22 | 2 | no | — |
| 446 | C22×C4 | — | 22 | 4 | no | — |
| 447 | C22×C4 | — | 22 | 4 | no | — |
| 448 | C22×C4 | C2×D44 | 1 | 1 | yes | characteristic |
| 449 | C22×C4 | C2×D44 | 1 | 1 | yes | characteristic |
| 450 | C22×C4 | C2×D44 | 1 | 1 | yes | characteristic |
| 451 | C22×C4 | C2×D44 | 1 | 2 | yes | — |
| 452 | C22×C4 | C2×D44 | 1 | 2 | yes | — |
| 453 | C22×C4 | C23×D11 | 1 | 1 | yes | characteristic |
| 454 | C22×C4 | C23×D11 | 1 | 1 | yes | characteristic |
| 455 | C22×C4 | C23×D11 | 1 | 1 | yes | characteristic |
| 456 | Q16 | — | 22 | 16 | no | — |
| 457 | SD16 | — | 22 | 16 | no | — |
| 458 | M16 | — | 2 | 8 | no | — |
| 459 | C2×C8 | C23×D11 | 1 | 8 | yes | — |
| 460 | C4⋊C4 | — | 11 | 4 | no | — |
| 461 | C4⋊C4 | — | 11 | 4 | no | — |
| 462 | C4⋊C4 | — | 22 | 2 | no | — |
| 463 | C4⋊C4 | — | 22 | 2 | no | — |
| 464 | C4⋊C4 | — | 22 | 4 | no | — |
| 465 | C4⋊C4 | — | 22 | 4 | no | — |
| 466 | C4⋊C4 | — | 22 | 8 | no | — |
| 467 | C4⋊C4 | — | 22 | 4 | no | — |
| 468 | C4⋊C4 | — | 22 | 4 | no | — |
| 469 | C4⋊C4 | — | 22 | 8 | no | — |
| 470 | C4⋊C4 | — | 22 | 8 | no | — |
| 471 | C4⋊C4 | C2×D44 | 1 | 4 | yes | — |
| 472 | C4⋊C4 | C2×D44 | 1 | 4 | yes | — |
| 473 | C22⋊C4 | — | 22 | 2 | no | — |
| 474 | C22⋊C4 | — | 22 | 2 | no | — |
| 475 | C22⋊C4 | — | 22 | 4 | no | — |
| 476 | C22⋊C4 | — | 22 | 4 | no | — |
| 477 | C22⋊C4 | — | 22 | 4 | no | — |
| 478 | C22⋊C4 | — | 22 | 4 | no | — |
| 479 | C22⋊C4 | C2×D44 | 1 | 4 | yes | — |
| 480 | C22⋊C4 | C2×D44 | 1 | 4 | yes | — |
| 481 | C42 | — | 22 | 2 | no | — |
| 482 | C42 | — | 22 | 2 | no | — |
| 483 | C42 | — | 22 | 4 | no | — |
| 484 | C42 | — | 22 | 4 | no | — |
| 485 | C42 | — | 22 | 8 | no | — |
| 486 | C42 | C2×D44 | 1 | 2 | yes | — |
| 487 | C42 | C2×D44 | 1 | 2 | yes | — |
| 488 | C42 | C23×D11 | 1 | 2 | yes | — |
| 489 | C42 | C23×D11 | 1 | 2 | yes | — |
| 490 | C11 | #60569 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 491 | C23 | — | 2 | 2 | no | — |
| 492 | C23 | — | 4 | 2 | no | — |
| 493 | C23 | — | 22 | 4 | no | — |
| 494 | C23 | — | 22 | 2 | no | — |
| 495 | C23 | — | 88 | 2 | no | — |
| 496 | C23 | C22×D44 | 1 | 1 | yes | characteristic |
| 497 | C23 | C22×D44 | 1 | 1 | yes | characteristic |
| 498 | C23 | C22×D44 | 1 | 1 | yes | characteristic |
| 499 | Q8 | — | 11 | 4 | no | — |
| 500 | Q8 | — | 22 | 4 | no | — |
| 501 | Q8 | — | 22 | 2 | no | — |
| 502 | Q8 | — | 22 | 8 | no | — |
| 503 | Q8 | — | 44 | 4 | no | — |
| 504 | D4 | — | 11 | 4 | no | — |
| 505 | D4 | — | 22 | 4 | no | — |
| 506 | D4 | — | 22 | 8 | no | — |
| 507 | D4 | — | 22 | 8 | no | — |
| 508 | D4 | — | 22 | 2 | no | — |
| 509 | C2×C4 | — | 2 | 2 | no | — |
| 510 | C2×C4 | — | 2 | 2 | no | — |
| 511 | C2×C4 | — | 2 | 2 | no | — |
| 512 | C2×C4 | — | 2 | 2 | no | — |
| 513 | C2×C4 | — | 2 | 2 | no | — |
| 514 | C2×C4 | — | 4 | 2 | no | — |
| 515 | C2×C4 | — | 4 | 2 | no | — |
| 516 | C2×C4 | — | 22 | 8 | no | — |
| 517 | C2×C4 | — | 22 | 4 | no | — |
| 518 | C2×C4 | — | 22 | 2 | no | — |
| 519 | C2×C4 | — | 22 | 8 | no | — |
| 520 | C2×C4 | — | 22 | 4 | no | — |
| 521 | C2×C4 | — | 22 | 4 | no | — |
| 522 | C2×C4 | — | 22 | 4 | no | — |
| 523 | C2×C4 | — | 44 | 4 | no | — |
| 524 | C2×C4 | — | 44 | 4 | no | — |
| 525 | C2×C4 | — | 88 | 4 | no | — |
| 526 | C2×C4 | — | 88 | 4 | no | — |
| 527 | C2×C4 | — | 88 | 2 | no | — |
| 528 | C2×C4 | C22×D44 | 1 | 4 | yes | — |
| 529 | C2×C4 | C22×D44 | 1 | 1 | yes | characteristic |
| 530 | C2×C4 | C22×D44 | 1 | 4 | yes | — |
| 531 | C2×C4 | C22×D44 | 1 | 1 | yes | characteristic |
| 532 | C2×C4 | C22×D44 | 1 | 1 | yes | characteristic |
| 533 | C2×C4 | #41×D11 | 1 | 4 | yes | — |
| 534 | C2×C4 | C24×D11 | 1 | 1 | yes | characteristic |
| 535 | C8 | — | 2 | 8 | no | — |
| 536 | C22 | — | 2 | 2 | no | — |
| 537 | C22 | — | 2 | 1 | no | — |
| 538 | C22 | — | 2 | 1 | no | — |
| 539 | C22 | — | 2 | 2 | no | — |
| 540 | C22 | — | 2 | 2 | no | — |
| 541 | C22 | — | 8 | 2 | no | — |
| 542 | C22 | — | 22 | 4 | no | — |
| 543 | C22 | — | 44 | 4 | no | — |
| 544 | C22 | — | 88 | 4 | no | — |
| 545 | C22 | #10623055 | 1 | 2 | yes | — |
| 546 | C22 | C23×D44 | 1 | 1 | yes | characteristic |
| 547 | C4 | — | 2 | 1 | no | — |
| 548 | C4 | — | 2 | 1 | no | — |
| 549 | C4 | — | 2 | 4 | no | — |
| 550 | C4 | — | 2 | 4 | no | — |
| 551 | C4 | — | 22 | 4 | no | — |
| 552 | C4 | — | 44 | 4 | no | — |
| 553 | C4 | — | 44 | 4 | no | — |
| 554 | C4 | — | 44 | 4 | no | — |
| 555 | C4 | #10623055 | 1 | 2 | yes | — |
| 556 | C4 | C2×#41×D11 | 1 | 2 | yes | — |
| 557 | C2 | — | 2 | 2 | no | — |
| 558 | C2 | — | 4 | 1 | no | — |
| 559 | C2 | — | 4 | 1 | no | — |
| 560 | C2 | — | 44 | 4 | no | — |
| 561 | C2 | C2×#10623055 | 1 | 1 | yes | characteristic |
| 562 | C2 | #13083404 | 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