Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
6640 conjugacy classes of subgroups.
The subgroup lattice has 528 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13082764 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13082763 | C2 | 1 | 5 | yes | maximal, complemented |
| 3 | #13082762 | C2 | 1 | 10 | yes | maximal, complemented |
| 4 | #13082757 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | #13082755 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | #13082753 | C2 | 1 | 10 | yes | maximal, complemented |
| 7 | #13081913 | C2 | 1 | 5 | yes | maximal, complemented |
| 8 | #13081910 | C2 | 1 | 10 | yes | maximal, complemented |
| 9 | C11×#3531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C11×#564 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C11×#563 | C22 | 1 | 10 | yes | complemented |
| 12 | C11×#562 | C22 | 1 | 5 | yes | complemented |
| 13 | C11×#533 | C22 | 1 | 5 | yes | complemented |
| 14 | C11×#529 | C22 | 1 | 10 | yes | complemented |
| 15 | #10623266 | C22 | 1 | 20 | yes | complemented |
| 16 | #10623259 | C22 | 1 | 10 | yes | complemented |
| 17 | #10623256 | C22 | 1 | 10 | yes | — |
| 18 | #10623243 | C22 | 1 | 20 | yes | complemented |
| 19 | #10623242 | C22 | 1 | 20 | yes | complemented |
| 20 | #10623237 | C22 | 1 | 20 | yes | complemented |
| 21 | #10623237 | C22 | 1 | 20 | yes | complemented |
| 22 | #10623231 | C22 | 1 | 10 | yes | complemented |
| 23 | #10623231 | C22 | 1 | 5 | yes | complemented |
| 24 | #10623230 | C22 | 1 | 10 | yes | complemented |
| 25 | #10623230 | C22 | 1 | 10 | yes | complemented |
| 26 | #10623222 | C22 | 1 | 10 | yes | complemented |
| 27 | #10623222 | C22 | 1 | 10 | yes | complemented |
| 28 | #10623222 | C22 | 1 | 10 | yes | complemented |
| 29 | #10623219 | C22 | 1 | 10 | yes | complemented |
| 30 | C11⋊#564 | C22 | 1 | 5 | yes | complemented |
| 31 | #10623215 | C22 | 1 | 10 | yes | complemented |
| 32 | #10623214 | C22 | 1 | 10 | yes | complemented |
| 33 | #10623211 | C22 | 1 | 10 | yes | complemented |
| 34 | #10623199 | C22 | 1 | 10 | yes | — |
| 35 | #10623198 | C22 | 1 | 20 | yes | complemented |
| 36 | #10623197 | C22 | 1 | 20 | yes | complemented |
| 37 | #10623187 | C22 | 1 | 20 | yes | complemented |
| 38 | #10623180 | C22 | 1 | 20 | yes | complemented |
| 39 | #10623178 | C22 | 1 | 20 | yes | complemented |
| 40 | #10623178 | C22 | 1 | 20 | yes | complemented |
| 41 | #10623177 | C22 | 1 | 20 | yes | complemented |
| 42 | #10623158 | C22 | 1 | 10 | yes | complemented |
| 43 | #10623158 | C22 | 1 | 20 | yes | complemented |
| 44 | #10623155 | C22 | 1 | 20 | yes | complemented |
| 45 | #10623153 | C22 | 1 | 10 | yes | complemented |
| 46 | #10623151 | C22 | 1 | 20 | yes | complemented |
| 47 | #10623137 | C22 | 1 | 10 | yes | complemented |
| 48 | #10623127 | C22 | 1 | 10 | yes | — |
| 49 | #10623111 | C22 | 1 | 20 | yes | complemented |
| 50 | #10623109 | C22 | 1 | 10 | yes | complemented |
| 51 | C4×#4343 | C22 | 1 | 10 | yes | complemented |
| 52 | #10623079 | C22 | 1 | 10 | yes | — |
| 53 | #10623078 | C22 | 1 | 20 | yes | complemented |
| 54 | C4×#4341 | C22 | 1 | 10 | yes | complemented |
| 55 | #10623059 | C22 | 1 | 20 | yes | complemented |
| 56 | #10623055 | C22 | 1 | 10 | yes | complemented |
| 57 | #10623053 | C22 | 1 | 10 | yes | complemented |
| 58 | #10623010 | C22 | 1 | 10 | yes | complemented |
| 59 | #10623008 | C22 | 1 | 5 | yes | — |
| 60 | C2×C42×D11 | C22 | 1 | 5 | yes | complemented |
| 61 | C2×#4343 | C23 | 1 | 10 | yes | — |
| 62 | C2×#4341 | C23 | 1 | 10 | yes | — |
| 63 | C2×#4339 | C23 | 1 | 10 | yes | — |
| 64 | C22×C4×D11 | C23 | 1 | 5 | yes | — |
| 65 | C22×C4×D11 | C23 | 1 | 10 | yes | — |
| 66 | C11×C4⋊Q8 | C23 | 1 | 10 | yes | — |
| 67 | C11×#126 | C23 | 1 | 20 | yes | — |
| 68 | C11×#125 | C23 | 1 | 10 | yes | — |
| 69 | C11×#125 | C23 | 1 | 5 | yes | — |
| 70 | C11×#125 | C23 | 1 | 5 | yes | — |
| 71 | C11×#124 | C23 | 1 | 10 | yes | — |
| 72 | C11×#123 | C23 | 1 | 20 | yes | — |
| 73 | C11×C22⋊Q8 | C23 | 1 | 10 | yes | — |
| 74 | C11×C22⋊Q8 | C23 | 1 | 20 | yes | — |
| 75 | C11×#121 | C23 | 1 | 10 | yes | — |
| 76 | C4×Q8×C11 | C23 | 1 | 10 | yes | — |
| 77 | C4×D4×C11 | C23 | 1 | 10 | yes | — |
| 78 | C11×#117 | C23 | 1 | 10 | yes | — |
| 79 | C2×C42×C11 | C23 | 1 | 5 | yes | — |
| 80 | #67000 | C23 | 1 | 20 | yes | — |
| 81 | #66999 | C23 | 1 | 20 | yes | — |
| 82 | #66999 | C23 | 1 | 10 | yes | — |
| 83 | Q8×Dic11 | C23 | 1 | 10 | yes | — |
| 84 | #66997 | C23 | 1 | 10 | yes | — |
| 85 | #66993 | C23 | 1 | 10 | yes | — |
| 86 | #66992 | C23 | 1 | 20 | yes | — |
| 87 | #66991 | C23 | 1 | 10 | yes | — |
| 88 | #66990 | C23 | 1 | 20 | yes | — |
| 89 | D4×Dic11 | C23 | 1 | 10 | yes | — |
| 90 | #66983 | C23 | 1 | 20 | yes | — |
| 91 | #66983 | C23 | 1 | 10 | yes | — |
| 92 | #66982 | C23 | 1 | 20 | yes | — |
| 93 | C4×C22⋊D11 | C23 | 1 | 20 | yes | — |
| 94 | #66977 | C23 | 1 | 10 | yes | — |
| 95 | C2×C4×Dic11 | C23 | 1 | 5 | yes | — |
| 96 | C2×C4×Dic11 | C23 | 1 | 10 | yes | — |
| 97 | #66951 | C23 | 1 | 20 | yes | — |
| 98 | #66951 | C23 | 1 | 20 | yes | — |
| 99 | #66951 | C23 | 1 | 20 | yes | — |
| 100 | #66950 | C23 | 1 | 10 | yes | — |
| 101 | #66950 | C23 | 1 | 10 | yes | — |
| 102 | #66950 | C23 | 1 | 10 | yes | — |
| 103 | #66949 | C23 | 1 | 20 | yes | — |
| 104 | #66949 | C23 | 1 | 20 | yes | — |
| 105 | #66949 | C23 | 1 | 20 | yes | — |
| 106 | #66948 | C23 | 1 | 10 | yes | — |
| 107 | #66948 | C23 | 1 | 10 | yes | — |
| 108 | #66948 | C23 | 1 | 20 | yes | — |
| 109 | #66948 | C23 | 1 | 10 | yes | — |
| 110 | #66947 | C23 | 1 | 20 | yes | — |
| 111 | #66947 | C23 | 1 | 20 | yes | — |
| 112 | #66947 | C23 | 1 | 20 | yes | — |
| 113 | #66947 | C23 | 1 | 20 | yes | — |
| 114 | #66946 | C23 | 1 | 10 | yes | — |
| 115 | #66946 | C23 | 1 | 20 | yes | — |
| 116 | #66946 | C23 | 1 | 10 | yes | — |
| 117 | #66946 | C23 | 1 | 10 | yes | — |
| 118 | #66945 | C23 | 1 | 10 | yes | — |
| 119 | #66945 | C23 | 1 | 20 | yes | — |
| 120 | #66945 | C23 | 1 | 10 | yes | — |
| 121 | #66943 | C23 | 1 | 20 | yes | — |
| 122 | #66942 | C23 | 1 | 20 | yes | — |
| 123 | #66942 | C23 | 1 | 20 | yes | — |
| 124 | #66941 | C23 | 1 | 10 | yes | — |
| 125 | #66941 | C23 | 1 | 10 | yes | — |
| 126 | #66940 | C23 | 1 | 10 | yes | — |
| 127 | #66940 | C23 | 1 | 10 | yes | — |
| 128 | #66940 | C23 | 1 | 10 | yes | — |
| 129 | #66939 | C23 | 1 | 20 | yes | — |
| 130 | #66938 | C23 | 1 | 20 | yes | — |
| 131 | #66938 | C23 | 1 | 20 | yes | — |
| 132 | #66937 | C23 | 1 | 20 | yes | — |
| 133 | #66937 | C23 | 1 | 20 | yes | — |
| 134 | #66937 | C23 | 1 | 20 | yes | — |
| 135 | #66936 | C23 | 1 | 20 | yes | — |
| 136 | #66936 | C23 | 1 | 20 | yes | — |
| 137 | #66935 | C23 | 1 | 20 | yes | — |
| 138 | #66935 | C23 | 1 | 20 | yes | — |
| 139 | (C22⋊D11)⋊C4 | C23 | 1 | 20 | yes | — |
| 140 | (C22⋊D11)⋊C4 | C23 | 1 | 20 | yes | — |
| 141 | (C22⋊D11)⋊C4 | C23 | 1 | 20 | yes | — |
| 142 | #66932 | C23 | 1 | 20 | yes | — |
| 143 | #66931 | C23 | 1 | 20 | yes | — |
| 144 | #66930 | C23 | 1 | 20 | yes | — |
| 145 | #66929 | C23 | 1 | 20 | yes | — |
| 146 | #66928 | C23 | 1 | 10 | yes | — |
| 147 | #66928 | C23 | 1 | 10 | yes | — |
| 148 | #66927 | C23 | 1 | 5 | yes | — |
| 149 | C4×D44 | C23 | 1 | 20 | yes | — |
| 150 | C4×D44 | C23 | 1 | 10 | yes | — |
| 151 | #66925 | C23 | 1 | 20 | yes | — |
| 152 | C42×D11 | C23 | 1 | 10 | yes | — |
| 153 | C42×D11 | C23 | 1 | 10 | yes | — |
| 154 | C42×D11 | C23 | 1 | 10 | yes | — |
| 155 | C42×D11 | C23 | 1 | 10 | yes | — |
| 156 | #66923 | C23 | 1 | 10 | yes | — |
| 157 | #66922 | C23 | 1 | 5 | yes | — |
| 158 | C4×Dic22 | C23 | 1 | 10 | yes | — |
| 159 | #62694 | — | 11 | 1 | no | maximal, Sylow |
| 160 | C23×D11 | C24 | 1 | 5 | yes | — |
| 161 | C2×Q8×C11 | C24 | 1 | 10 | yes | — |
| 162 | C2×D4×C11 | C24 | 1 | 10 | yes | — |
| 163 | C22×C4×C11 | C24 | 1 | 5 | yes | — |
| 164 | C22×C4×C11 | C24 | 1 | 10 | yes | — |
| 165 | C2×C22⋊D11 | C24 | 1 | 20 | yes | — |
| 166 | C2×C22⋊D11 | C24 | 1 | 20 | yes | — |
| 167 | C22×Dic11 | C24 | 1 | 10 | yes | — |
| 168 | C22×Dic11 | C24 | 1 | 5 | yes | — |
| 169 | #4343 | — | 4 | 20 | no | — |
| 170 | #4341 | — | 4 | 20 | no | — |
| 171 | #4339 | — | 4 | 20 | no | — |
| 172 | C2×D44 | C24 | 1 | 20 | yes | — |
| 173 | C2×D44 | C24 | 1 | 10 | yes | — |
| 174 | C2×D44 | C24 | 1 | 10 | yes | — |
| 175 | C2×C4×D11 | — | 4 | 10 | no | — |
| 176 | C2×C4×D11 | — | 4 | 20 | no | — |
| 177 | C2×C4×D11 | C24 | 1 | 10 | yes | — |
| 178 | C2×C4×D11 | C24 | 1 | 10 | yes | — |
| 179 | C2×C4×D11 | C24 | 1 | 10 | yes | — |
| 180 | C2×C4×D11 | C24 | 1 | 10 | yes | — |
| 181 | C2×C4×D11 | C24 | 1 | 10 | yes | — |
| 182 | C2×C4×D11 | C24 | 1 | 10 | yes | — |
| 183 | C2×Dic22 | C24 | 1 | 10 | yes | — |
| 184 | C2×Dic22 | C24 | 1 | 10 | yes | — |
| 185 | C11×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 186 | C11×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 187 | C11×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 188 | C11×C4⋊C4 | C24 | 1 | 10 | yes | — |
| 189 | C11×C4⋊C4 | C24 | 1 | 20 | yes | — |
| 190 | C11×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 191 | C11×C22⋊C4 | C24 | 1 | 20 | yes | — |
| 192 | C42×C11 | C24 | 1 | 10 | yes | — |
| 193 | C42×C11 | C24 | 1 | 5 | yes | — |
| 194 | C42×C11 | C24 | 1 | 5 | yes | — |
| 195 | C22⋊Dic11 | C24 | 1 | 20 | yes | — |
| 196 | (C2×D11)⋊C4 | C24 | 1 | 20 | yes | — |
| 197 | (C2×D11)⋊C4 | C24 | 1 | 20 | yes | — |
| 198 | (C2×D11)⋊C4 | C24 | 1 | 20 | yes | — |
| 199 | (C2×D11)⋊C4 | C24 | 1 | 20 | yes | — |
| 200 | (C2×D11)⋊C4 | C24 | 1 | 20 | yes | — |
| 201 | (C2×D11)⋊C4 | C24 | 1 | 20 | yes | — |
| 202 | C4⋊Dic11 | C24 | 1 | 10 | yes | — |
| 203 | C4⋊Dic11 | C24 | 1 | 20 | yes | — |
| 204 | C4⋊Dic11 | C24 | 1 | 10 | yes | — |
| 205 | Dic11⋊C4 | C24 | 1 | 20 | yes | — |
| 206 | Dic11⋊C4 | C24 | 1 | 20 | yes | — |
| 207 | Dic11⋊C4 | C24 | 1 | 20 | yes | — |
| 208 | Dic11⋊C4 | C24 | 1 | 20 | yes | — |
| 209 | C4×Dic11 | C24 | 1 | 5 | yes | — |
| 210 | C4×Dic11 | C24 | 1 | 1 | yes | characteristic |
| 211 | C4×Dic11 | C24 | 1 | 10 | yes | — |
| 212 | C4×Dic11 | C24 | 1 | 10 | yes | — |
| 213 | C4×Dic11 | C24 | 1 | 10 | yes | — |
| 214 | C4×Dic11 | C24 | 1 | 10 | yes | — |
| 215 | C4×Dic11 | C24 | 1 | 10 | yes | — |
| 216 | #3531 | — | 11 | 2 | no | — |
| 217 | #3531 | — | 11 | 10 | no | — |
| 218 | #3531 | — | 11 | 5 | no | — |
| 219 | #3531 | D11 | 1 | 1 | yes | characteristic, complemented |
| 220 | #3529 | — | 11 | 10 | no | — |
| 221 | #3529 | — | 11 | 10 | no | — |
| 222 | #3529 | — | 11 | 10 | no | — |
| 223 | #3444 | — | 11 | 5 | no | — |
| 224 | #3444 | — | 11 | 10 | no | — |
| 225 | C23×C11 | C25 | 1 | 5 | yes | — |
| 226 | C22×D11 | — | 4 | 10 | no | — |
| 227 | C22×D11 | — | 4 | 5 | no | — |
| 228 | C22×D11 | C25 | 1 | 10 | yes | — |
| 229 | Q8×C11 | — | 4 | 10 | no | — |
| 230 | D4×C11 | — | 4 | 10 | no | — |
| 231 | C2×C4×C11 | — | 2 | 10 | no | — |
| 232 | C2×C4×C11 | — | 4 | 10 | no | — |
| 233 | C2×C4×C11 | C25 | 1 | 10 | yes | — |
| 234 | C2×C4×C11 | C25 | 1 | 5 | yes | — |
| 235 | C2×C4×C11 | C25 | 1 | 10 | yes | — |
| 236 | C2×C4×C11 | C25 | 1 | 1 | yes | characteristic |
| 237 | C22⋊D11 | — | 4 | 20 | no | — |
| 238 | C22⋊D11 | — | 4 | 20 | no | — |
| 239 | C2×Dic11 | — | 2 | 20 | no | — |
| 240 | C2×Dic11 | — | 4 | 5 | no | — |
| 241 | C2×Dic11 | C25 | 1 | 10 | yes | — |
| 242 | C2×Dic11 | C25 | 1 | 10 | yes | — |
| 243 | C2×Dic11 | C25 | 1 | 2 | yes | — |
| 244 | D44 | — | 4 | 10 | no | — |
| 245 | D44 | — | 4 | 10 | no | — |
| 246 | D44 | — | 4 | 20 | no | — |
| 247 | C4×D11 | — | 2 | 20 | no | — |
| 248 | C4×D11 | — | 2 | 20 | no | — |
| 249 | C4×D11 | — | 2 | 20 | no | — |
| 250 | C4×D11 | — | 4 | 10 | no | — |
| 251 | C4×D11 | — | 4 | 10 | no | — |
| 252 | C4×D11 | — | 4 | 10 | no | — |
| 253 | Dic22 | — | 4 | 10 | no | — |
| 254 | Dic22 | — | 4 | 10 | no | — |
| 255 | #564 | — | 11 | 5 | no | — |
| 256 | #564 | C2×D11 | 1 | 1 | yes | characteristic, complemented |
| 257 | #563 | — | 11 | 20 | no | — |
| 258 | #563 | — | 11 | 20 | no | — |
| 259 | #563 | — | 11 | 10 | no | — |
| 260 | #563 | — | 11 | 10 | no | — |
| 261 | #563 | — | 11 | 20 | no | — |
| 262 | #563 | C2×D11 | 1 | 10 | yes | complemented |
| 263 | #562 | — | 11 | 5 | no | — |
| 264 | #562 | — | 11 | 10 | no | — |
| 265 | #562 | — | 11 | 10 | no | — |
| 266 | #562 | — | 11 | 20 | no | — |
| 267 | #562 | — | 11 | 20 | no | — |
| 268 | #562 | — | 11 | 20 | no | — |
| 269 | #562 | C2×D11 | 1 | 5 | yes | complemented |
| 270 | H(3,𝔽4) | — | 11 | 10 | no | — |
| 271 | #560 | — | 11 | 20 | no | — |
| 272 | #560 | — | 11 | 20 | no | — |
| 273 | #560 | — | 11 | 20 | no | — |
| 274 | #533 | — | 11 | 10 | no | — |
| 275 | #533 | — | 11 | 10 | no | — |
| 276 | #533 | — | 11 | 10 | no | — |
| 277 | #533 | — | 11 | 10 | no | — |
| 278 | #533 | C2×D11 | 1 | 5 | yes | complemented |
| 279 | #532 | — | 11 | 10 | no | — |
| 280 | #532 | — | 11 | 10 | no | — |
| 281 | #532 | — | 11 | 10 | no | — |
| 282 | #532 | — | 11 | 10 | no | — |
| 283 | #532 | — | 11 | 5 | no | — |
| 284 | #529 | — | 11 | 20 | no | — |
| 285 | #529 | — | 11 | 20 | no | — |
| 286 | #529 | — | 11 | 10 | no | — |
| 287 | #529 | — | 11 | 10 | no | — |
| 288 | #529 | — | 11 | 10 | no | — |
| 289 | #529 | — | 11 | 10 | no | — |
| 290 | #529 | — | 11 | 20 | no | — |
| 291 | #529 | — | 11 | 20 | no | — |
| 292 | #529 | — | 11 | 20 | no | — |
| 293 | #529 | — | 11 | 20 | no | — |
| 294 | #529 | — | 11 | 10 | no | — |
| 295 | #529 | C2×D11 | 1 | 10 | yes | complemented |
| 296 | #525 | — | 11 | 20 | no | — |
| 297 | #525 | — | 11 | 20 | no | — |
| 298 | #525 | — | 11 | 10 | no | — |
| 299 | #525 | — | 11 | 10 | no | — |
| 300 | #525 | — | 11 | 20 | no | — |
| 301 | #525 | — | 11 | 10 | no | — |
| 302 | C4×#41 | — | 11 | 10 | no | — |
| 303 | C4×#41 | — | 11 | 10 | no | — |
| 304 | C4×#41 | — | 11 | 10 | no | — |
| 305 | C22×C42 | — | 11 | 5 | no | — |
| 306 | C22×C11 | — | 2 | 5 | no | — |
| 307 | C22×C11 | — | 2 | 10 | no | — |
| 308 | C22×C11 | C26 | 1 | 1 | yes | characteristic |
| 309 | C2×D11 | — | 2 | 10 | no | — |
| 310 | C2×D11 | — | 2 | 10 | no | — |
| 311 | C2×D11 | — | 2 | 10 | no | — |
| 312 | C2×D11 | — | 4 | 20 | no | — |
| 313 | C4×C11 | — | 2 | 5 | no | — |
| 314 | C4×C11 | — | 2 | 10 | no | — |
| 315 | C4×C11 | — | 2 | 10 | no | — |
| 316 | C4×C11 | #585 | 1 | 2 | yes | — |
| 317 | Dic11 | — | 2 | 10 | no | — |
| 318 | Dic11 | — | 2 | 10 | no | — |
| 319 | Dic11 | #585 | 1 | 4 | yes | — |
| 320 | C2×#41 | — | 11 | 10 | no | — |
| 321 | C2×#41 | — | 11 | 10 | no | — |
| 322 | C2×#41 | — | 11 | 10 | no | — |
| 323 | C23×C4 | — | 11 | 10 | no | — |
| 324 | C23×C4 | — | 11 | 5 | no | — |
| 325 | C4⋊Q8 | — | 11 | 10 | no | — |
| 326 | C4⋊Q8 | — | 11 | 10 | no | — |
| 327 | C4⋊Q8 | — | 11 | 10 | no | — |
| 328 | C4⋊Q8 | — | 11 | 5 | no | — |
| 329 | C4⋊Q8 | C22×D11 | 1 | 10 | yes | — |
| 330 | #127 | — | 11 | 10 | no | — |
| 331 | #127 | — | 11 | 5 | no | — |
| 332 | #126 | — | 11 | 20 | no | — |
| 333 | #126 | — | 11 | 20 | no | — |
| 334 | #126 | — | 11 | 20 | no | — |
| 335 | #126 | — | 11 | 20 | no | — |
| 336 | #126 | — | 11 | 20 | no | — |
| 337 | #126 | C22×D11 | 1 | 20 | yes | — |
| 338 | #125 | — | 11 | 20 | no | — |
| 339 | #125 | — | 11 | 20 | no | — |
| 340 | #125 | — | 11 | 20 | no | — |
| 341 | #125 | — | 11 | 10 | no | — |
| 342 | #125 | C22×D11 | 1 | 5 | yes | — |
| 343 | #125 | C22×D11 | 1 | 5 | yes | — |
| 344 | #125 | C22×D11 | 1 | 10 | yes | — |
| 345 | #124 | — | 11 | 20 | no | — |
| 346 | #124 | — | 11 | 20 | no | — |
| 347 | #124 | — | 11 | 20 | no | — |
| 348 | #124 | — | 11 | 10 | no | — |
| 349 | #124 | — | 11 | 10 | no | — |
| 350 | #124 | C22×D11 | 1 | 10 | yes | — |
| 351 | #123 | — | 11 | 20 | no | — |
| 352 | #123 | — | 11 | 20 | no | — |
| 353 | #123 | — | 11 | 20 | no | — |
| 354 | #123 | — | 11 | 20 | no | — |
| 355 | #123 | — | 11 | 20 | no | — |
| 356 | #123 | — | 11 | 20 | no | — |
| 357 | #123 | — | 11 | 20 | no | — |
| 358 | #123 | — | 11 | 20 | no | — |
| 359 | #123 | C22×D11 | 1 | 20 | yes | — |
| 360 | C22⋊Q8 | — | 11 | 10 | no | — |
| 361 | C22⋊Q8 | — | 11 | 20 | no | — |
| 362 | C22⋊Q8 | — | 11 | 10 | no | — |
| 363 | C22⋊Q8 | — | 11 | 20 | no | — |
| 364 | C22⋊Q8 | — | 11 | 20 | no | — |
| 365 | C22⋊Q8 | — | 11 | 20 | no | — |
| 366 | C22⋊Q8 | — | 11 | 10 | no | — |
| 367 | C22⋊Q8 | — | 11 | 10 | no | — |
| 368 | C22⋊Q8 | — | 11 | 10 | no | — |
| 369 | C22⋊Q8 | — | 11 | 20 | no | — |
| 370 | C22⋊Q8 | C22×D11 | 1 | 20 | yes | — |
| 371 | C22⋊Q8 | C22×D11 | 1 | 10 | yes | — |
| 372 | #121 | — | 11 | 10 | no | — |
| 373 | #121 | — | 11 | 20 | no | — |
| 374 | #121 | — | 11 | 20 | no | — |
| 375 | #121 | — | 11 | 10 | no | — |
| 376 | #121 | — | 11 | 20 | no | — |
| 377 | #121 | — | 11 | 10 | no | — |
| 378 | #121 | — | 11 | 10 | no | — |
| 379 | #121 | — | 11 | 10 | no | — |
| 380 | #121 | — | 11 | 20 | no | — |
| 381 | #121 | — | 11 | 20 | no | — |
| 382 | #121 | — | 11 | 20 | no | — |
| 383 | #121 | C22×D11 | 1 | 10 | yes | — |
| 384 | #120 | — | 11 | 20 | no | — |
| 385 | #120 | — | 11 | 20 | no | — |
| 386 | #120 | — | 11 | 20 | no | — |
| 387 | C4×Q8 | — | 11 | 10 | no | — |
| 388 | C4×Q8 | — | 11 | 10 | no | — |
| 389 | C4×Q8 | — | 11 | 10 | no | — |
| 390 | C4×Q8 | — | 11 | 10 | no | — |
| 391 | C4×Q8 | — | 11 | 10 | no | — |
| 392 | C4×Q8 | C22×D11 | 1 | 10 | yes | — |
| 393 | C4×D4 | — | 11 | 10 | no | — |
| 394 | C4×D4 | — | 11 | 20 | no | — |
| 395 | C4×D4 | — | 11 | 20 | no | — |
| 396 | C4×D4 | — | 11 | 10 | no | — |
| 397 | C4×D4 | — | 11 | 10 | no | — |
| 398 | C4×D4 | — | 11 | 10 | no | — |
| 399 | C4×D4 | — | 11 | 20 | no | — |
| 400 | C4×D4 | — | 11 | 20 | no | — |
| 401 | C4×D4 | — | 11 | 20 | no | — |
| 402 | C4×D4 | — | 11 | 20 | no | — |
| 403 | C4×D4 | — | 11 | 10 | no | — |
| 404 | C4×D4 | C22×D11 | 1 | 10 | yes | — |
| 405 | #117 | — | 11 | 20 | no | — |
| 406 | #117 | — | 11 | 10 | no | — |
| 407 | #117 | — | 11 | 10 | no | — |
| 408 | #117 | — | 11 | 20 | no | — |
| 409 | #117 | — | 11 | 20 | no | — |
| 410 | #117 | C22×D11 | 1 | 10 | yes | — |
| 411 | C2×C42 | — | 11 | 5 | no | — |
| 412 | C2×C42 | — | 11 | 10 | no | — |
| 413 | C2×C42 | — | 11 | 10 | no | — |
| 414 | C2×C42 | — | 11 | 10 | no | — |
| 415 | C2×C42 | — | 11 | 10 | no | — |
| 416 | C2×C42 | — | 11 | 10 | no | — |
| 417 | C2×C42 | C22×D11 | 1 | 5 | yes | — |
| 418 | C2×C11 | — | 4 | 5 | no | — |
| 419 | C2×C11 | C2×#585 | 1 | 2 | yes | — |
| 420 | C2×C11 | C2×#585 | 1 | 1 | yes | characteristic |
| 421 | D11 | — | 4 | 10 | no | — |
| 422 | C24 | — | 11 | 5 | no | — |
| 423 | #41 | — | 44 | 20 | no | — |
| 424 | #41 | — | 44 | 20 | no | — |
| 425 | #41 | — | 44 | 20 | no | — |
| 426 | C2×Q8 | — | 11 | 10 | no | — |
| 427 | C2×Q8 | — | 11 | 10 | no | — |
| 428 | C2×Q8 | C23×D11 | 1 | 10 | yes | — |
| 429 | C2×D4 | — | 11 | 20 | no | — |
| 430 | C2×D4 | — | 11 | 20 | no | — |
| 431 | C2×D4 | — | 11 | 10 | no | — |
| 432 | C2×D4 | — | 11 | 20 | no | — |
| 433 | C2×D4 | — | 11 | 10 | no | — |
| 434 | C2×D4 | C23×D11 | 1 | 10 | yes | — |
| 435 | C22×C4 | — | 11 | 10 | no | — |
| 436 | C22×C4 | — | 11 | 5 | no | — |
| 437 | C22×C4 | — | 11 | 10 | no | — |
| 438 | C22×C4 | — | 11 | 10 | no | — |
| 439 | C22×C4 | — | 11 | 10 | no | — |
| 440 | C22×C4 | — | 11 | 10 | no | — |
| 441 | C22×C4 | — | 11 | 10 | no | — |
| 442 | C22×C4 | — | 11 | 10 | no | — |
| 443 | C22×C4 | — | 44 | 10 | no | — |
| 444 | C22×C4 | — | 44 | 20 | no | — |
| 445 | C22×C4 | C23×D11 | 1 | 5 | yes | — |
| 446 | C22×C4 | C23×D11 | 1 | 10 | yes | — |
| 447 | C4⋊C4 | — | 11 | 20 | no | — |
| 448 | C4⋊C4 | — | 11 | 20 | no | — |
| 449 | C4⋊C4 | — | 11 | 20 | no | — |
| 450 | C4⋊C4 | — | 11 | 20 | no | — |
| 451 | C4⋊C4 | — | 11 | 10 | no | — |
| 452 | C4⋊C4 | — | 11 | 10 | no | — |
| 453 | C4⋊C4 | — | 11 | 20 | no | — |
| 454 | C4⋊C4 | C23×D11 | 1 | 20 | yes | — |
| 455 | C4⋊C4 | C23×D11 | 1 | 10 | yes | — |
| 456 | C4⋊C4 | C23×D11 | 1 | 10 | yes | — |
| 457 | C4⋊C4 | C23×D11 | 1 | 10 | yes | — |
| 458 | C4⋊C4 | C23×D11 | 1 | 10 | yes | — |
| 459 | C22⋊C4 | — | 11 | 20 | no | — |
| 460 | C22⋊C4 | — | 11 | 20 | no | — |
| 461 | C22⋊C4 | — | 11 | 20 | no | — |
| 462 | C22⋊C4 | — | 11 | 20 | no | — |
| 463 | C22⋊C4 | — | 11 | 20 | no | — |
| 464 | C22⋊C4 | — | 11 | 20 | no | — |
| 465 | C22⋊C4 | — | 11 | 20 | no | — |
| 466 | C22⋊C4 | C23×D11 | 1 | 20 | yes | — |
| 467 | C22⋊C4 | C23×D11 | 1 | 20 | yes | — |
| 468 | C42 | — | 11 | 10 | no | — |
| 469 | C42 | — | 11 | 10 | no | — |
| 470 | C42 | — | 11 | 10 | no | — |
| 471 | C42 | — | 11 | 10 | no | — |
| 472 | C42 | — | 11 | 10 | no | — |
| 473 | C42 | — | 11 | 1 | no | — |
| 474 | C42 | — | 11 | 5 | no | — |
| 475 | C42 | C23×D11 | 1 | 5 | yes | — |
| 476 | C42 | C23×D11 | 1 | 5 | yes | — |
| 477 | C42 | C23×D11 | 1 | 10 | yes | — |
| 478 | C11 | #62694 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 479 | C23 | — | 11 | 10 | no | — |
| 480 | C23 | — | 44 | 10 | no | — |
| 481 | C23 | — | 44 | 5 | no | — |
| 482 | C23 | C24×D11 | 1 | 5 | yes | — |
| 483 | Q8 | — | 4 | 10 | no | — |
| 484 | Q8 | — | 44 | 10 | no | — |
| 485 | Q8 | — | 44 | 10 | no | — |
| 486 | D4 | — | 4 | 10 | no | — |
| 487 | D4 | — | 44 | 10 | no | — |
| 488 | D4 | — | 44 | 20 | no | — |
| 489 | D4 | — | 44 | 10 | no | — |
| 490 | D4 | — | 44 | 20 | no | — |
| 491 | D4 | — | 44 | 20 | no | — |
| 492 | C2×C4 | — | 2 | 10 | no | — |
| 493 | C2×C4 | — | 4 | 10 | no | — |
| 494 | C2×C4 | — | 11 | 2 | no | — |
| 495 | C2×C4 | — | 11 | 10 | no | — |
| 496 | C2×C4 | — | 11 | 10 | no | — |
| 497 | C2×C4 | — | 22 | 20 | no | — |
| 498 | C2×C4 | — | 22 | 20 | no | — |
| 499 | C2×C4 | — | 22 | 20 | no | — |
| 500 | C2×C4 | — | 22 | 20 | no | — |
| 501 | C2×C4 | — | 44 | 10 | no | — |
| 502 | C2×C4 | — | 44 | 10 | no | — |
| 503 | C2×C4 | — | 44 | 10 | no | — |
| 504 | C2×C4 | — | 44 | 5 | no | — |
| 505 | C2×C4 | C24×D11 | 1 | 10 | yes | — |
| 506 | C2×C4 | C24×D11 | 1 | 10 | yes | — |
| 507 | C2×C4 | C24×D11 | 1 | 5 | yes | — |
| 508 | C2×C4 | C24×D11 | 1 | 1 | yes | characteristic |
| 509 | C22 | — | 2 | 10 | no | — |
| 510 | C22 | — | 2 | 5 | no | — |
| 511 | C22 | — | 22 | 10 | no | — |
| 512 | C22 | — | 22 | 10 | no | — |
| 513 | C22 | — | 22 | 10 | no | — |
| 514 | C22 | — | 44 | 20 | no | — |
| 515 | C22 | C25×D11 | 1 | 1 | yes | characteristic |
| 516 | C4 | — | 2 | 10 | no | — |
| 517 | C4 | — | 2 | 10 | no | — |
| 518 | C4 | — | 2 | 5 | no | — |
| 519 | C4 | — | 11 | 4 | no | — |
| 520 | C4 | — | 22 | 10 | no | — |
| 521 | C4 | — | 22 | 10 | no | — |
| 522 | C4 | #10623457 | 1 | 2 | yes | — |
| 523 | C2 | — | 4 | 5 | no | — |
| 524 | C2 | — | 44 | 10 | no | — |
| 525 | C2 | D11×#585 | 1 | 2 | yes | — |
| 526 | C2 | C2×#10623457 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D11 |
| commutator, socle, cosocle | C22×C11 | C26 |
| Frattini | C22 | C25×D11 |
| Fitting | C11×#3531 | C2 |
| hypercenter | #3531 | D11 |
| hypocenter | C11 | #62694 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C2×C4 ◁ #3531 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13082764 | C2 | semidirect |
| 2. #13082763 | C2 | semidirect |
| 3. #13082762 | C2 | semidirect |
| 4. #13082757 | C2 | semidirect |
| 5. #13082755 | C2 | semidirect |
| 6. #13082753 | C2 | semidirect |
| 7. #13081913 | C2 | semidirect |
| 8. #13081910 | C2 | semidirect |
| 9. C11×#3531 | C2 | semidirect |
| 10. C11×#564 | C22 | semidirect |
| 11. C11×#563 | C22 | semidirect |
| 12. C11×#562 | C22 | semidirect |
| 13. C11×#533 | C22 | semidirect |
| 14. C11×#529 | C22 | semidirect |
| 15. #10623266 | C22 | semidirect |
| 16. #10623259 | C22 | semidirect |
| 18. #10623243 | C22 | semidirect |
| 19. #10623242 | C22 | semidirect |
| 20. #10623237 | C22 | semidirect |
| 21. #10623237 | C22 | semidirect |
| 22. #10623231 | C22 | semidirect |
| 23. #10623231 | C22 | semidirect |
| 24. #10623230 | C22 | semidirect |
| 25. #10623230 | C22 | semidirect |
| 26. #10623222 | C22 | semidirect |
| 27. #10623222 | C22 | semidirect |
| 28. #10623222 | C22 | semidirect |
| 29. #10623219 | C22 | semidirect |
| 30. C11⋊#564 | C22 | semidirect |
| 31. #10623215 | C22 | semidirect |
| 32. #10623214 | C22 | semidirect |
| 33. #10623211 | C22 | semidirect |
| 35. #10623198 | C22 | semidirect |
| 36. #10623197 | C22 | semidirect |
| 37. #10623187 | C22 | semidirect |
| 38. #10623180 | C22 | semidirect |
| 39. #10623178 | C22 | semidirect |
| 40. #10623178 | C22 | semidirect |
| 41. #10623177 | C22 | semidirect |
| 42. #10623158 | C22 | semidirect |
| 43. #10623158 | C22 | semidirect |
| 44. #10623155 | C22 | semidirect |
| 45. #10623153 | C22 | semidirect |
| 46. #10623151 | C22 | semidirect |
| 47. #10623137 | C22 | semidirect |
| 49. #10623111 | C22 | semidirect |
| 50. #10623109 | C22 | semidirect |
| 51. C4×#4343 | C22 | semidirect |
| 53. #10623078 | C22 | semidirect |
| 54. C4×#4341 | C22 | semidirect |
| 55. #10623059 | C22 | semidirect |
| 56. #10623055 | C22 | semidirect |
| 57. #10623053 | C22 | semidirect |
| 58. #10623010 | C22 | semidirect |
| 60. C2×C42×D11 | C22 | semidirect |
| 219. #3531 | D11 | semidirect |
| 256. #564 | C2×D11 | semidirect |
| 262. #563 | C2×D11 | semidirect |
| 269. #562 | C2×D11 | semidirect |
| 278. #533 | C2×D11 | semidirect |
| 295. #529 | C2×D11 | semidirect |
| 478. C11 | #62694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13082764 | 2 |
| #13082763 | 2 |
| #13082762 | 2 |
| #13082757 | 2 |
| #13082755 | 2 |
| #13082753 | 2 |
| #13081913 | 2 |
| #13081910 | 2 |
| C11×#3531 | 2 |
| #62694 | 11 |