Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1078 conjugacy classes of subgroups.
The subgroup lattice has 566 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20289120 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20285712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20285710 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20285161 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20274023 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20274005 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #20273349 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #20273325 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C53×#1530 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#13133239 | — | 2 | 2 | no | — |
| 11 | #16811365 | C22 | 1 | 4 | yes | — |
| 12 | #16811339 | — | 2 | 1 | no | — |
| 13 | #16811338 | — | 2 | 1 | no | — |
| 14 | #16811338 | — | 2 | 1 | no | — |
| 15 | D4×D212 | — | 2 | 1 | no | — |
| 16 | D4×D212 | — | 2 | 1 | no | — |
| 17 | #16811258 | — | 2 | 1 | no | — |
| 18 | #16811189 | — | 2 | 2 | no | — |
| 19 | #16811189 | — | 2 | 2 | no | — |
| 20 | #16811187 | — | 2 | 2 | no | — |
| 21 | #16811173 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16811173 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16811173 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #16811017 | — | 2 | 1 | no | — |
| 25 | #16811017 | C22 | 1 | 2 | yes | complemented |
| 26 | #16811013 | C22 | 1 | 2 | yes | complemented |
| 27 | #16811012 | — | 2 | 1 | no | — |
| 28 | #16811012 | C22 | 1 | 2 | yes | complemented |
| 29 | #16811012 | C22 | 1 | 2 | yes | complemented |
| 30 | #16810983 | C22 | 1 | 2 | yes | complemented |
| 31 | #16810982 | C22 | 1 | 2 | yes | complemented |
| 32 | #16810829 | — | 2 | 1 | no | — |
| 33 | #16810825 | — | 2 | 1 | no | — |
| 34 | #16810819 | — | 2 | 1 | no | — |
| 35 | #16810815 | — | 2 | 1 | no | — |
| 36 | #16810770 | — | 2 | 2 | no | — |
| 37 | #16810768 | — | 2 | 2 | no | — |
| 38 | #16810680 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #16810362 | C22 | 1 | 4 | yes | complemented |
| 40 | #16810362 | C22 | 1 | 4 | yes | complemented |
| 41 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 42 | C53×#432 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×#97×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C53×#329 | C22 | 1 | 4 | yes | complemented |
| 45 | C2×#11719945 | — | 2 | 1 | no | — |
| 46 | C2×#11719945 | D4 | 1 | 2 | yes | — |
| 47 | C2×#11719945 | D4 | 1 | 2 | yes | — |
| 48 | C22×D212 | — | 2 | 2 | no | — |
| 49 | C2×D4×D53 | — | 2 | 2 | no | — |
| 50 | C2×D4×D53 | — | 2 | 2 | no | — |
| 51 | #13133239 | — | 4 | 8 | no | — |
| 52 | C2×Dic212 | — | 2 | 2 | no | — |
| 53 | C2×#11719913 | — | 2 | 2 | no | — |
| 54 | C2×#11719913 | — | 2 | 2 | no | — |
| 55 | C2×#11719913 | — | 2 | 2 | no | — |
| 56 | C2×#11719924 | — | 2 | 2 | no | — |
| 57 | C2×D424 | — | 2 | 2 | no | — |
| 58 | C2×D424 | — | 2 | 2 | no | — |
| 59 | C2×#11719922 | — | 2 | 2 | no | — |
| 60 | #13133217 | D4 | 1 | 1 | yes | characteristic |
| 61 | #13133217 | D4 | 1 | 1 | yes | characteristic |
| 62 | #13133217 | C23 | 1 | 1 | yes | characteristic |
| 63 | #13133214 | D4 | 1 | 1 | yes | characteristic |
| 64 | #13133214 | D4 | 1 | 1 | yes | characteristic |
| 65 | #13133214 | C23 | 1 | 1 | yes | characteristic |
| 66 | #13133213 | — | 2 | 4 | no | — |
| 67 | #13133206 | — | 2 | 4 | no | — |
| 68 | #13133205 | — | 2 | 1 | no | — |
| 69 | #13133205 | C23 | 1 | 2 | yes | — |
| 70 | #13133205 | C23 | 1 | 2 | yes | — |
| 71 | #13133203 | — | 2 | 4 | no | — |
| 72 | #13133203 | — | 2 | 4 | no | — |
| 73 | #13133192 | — | 2 | 2 | no | — |
| 74 | #13133192 | — | 2 | 2 | no | — |
| 75 | #13133191 | — | 2 | 2 | no | — |
| 76 | #13133191 | — | 2 | 2 | no | — |
| 77 | #13133191 | — | 2 | 1 | no | — |
| 78 | #13133191 | — | 2 | 1 | no | — |
| 79 | #13133191 | — | 2 | 1 | no | — |
| 80 | #13133191 | — | 2 | 1 | no | — |
| 81 | #13133191 | — | 2 | 1 | no | — |
| 82 | #13133191 | — | 2 | 1 | no | — |
| 83 | #13133188 | — | 2 | 2 | no | — |
| 84 | #13133188 | — | 2 | 2 | no | — |
| 85 | #13133187 | — | 2 | 4 | no | — |
| 86 | #13133187 | — | 2 | 4 | no | — |
| 87 | #13133185 | — | 2 | 4 | no | — |
| 88 | #13133185 | — | 2 | 4 | no | — |
| 89 | C4×D212 | — | 2 | 1 | no | — |
| 90 | C4×D212 | — | 2 | 1 | no | — |
| 91 | C4×D212 | — | 2 | 1 | no | — |
| 92 | C4×D212 | — | 2 | 1 | no | — |
| 93 | C4×D212 | — | 2 | 1 | no | — |
| 94 | C4×D212 | — | 2 | 1 | no | — |
| 95 | #13133176 | — | 2 | 2 | no | — |
| 96 | #13133175 | — | 2 | 2 | no | — |
| 97 | #13133175 | — | 2 | 2 | no | — |
| 98 | C4⋊#88322 | — | 2 | 1 | no | — |
| 99 | #13133142 | — | 2 | 2 | no | — |
| 100 | #13133141 | — | 2 | 2 | no | — |
| 101 | #13133139 | — | 2 | 2 | no | — |
| 102 | #13133138 | — | 2 | 2 | no | — |
| 103 | C22⋊#88322 | — | 2 | 1 | no | — |
| 104 | #13133128 | C23 | 1 | 2 | yes | — |
| 105 | C2×#41×C53 | D4 | 1 | 2 | yes | — |
| 106 | C22×C8×C53 | — | 2 | 1 | no | — |
| 107 | C4⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 108 | #127×C53 | D4 | 1 | 1 | yes | characteristic |
| 109 | #124×C53 | C23 | 1 | 2 | yes | — |
| 110 | #121×C53 | — | 2 | 1 | no | — |
| 111 | #121×C53 | — | 2 | 1 | no | — |
| 112 | C4×D4×C53 | — | 2 | 1 | no | — |
| 113 | C4×D4×C53 | — | 2 | 1 | no | — |
| 114 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 115 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 116 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 117 | #97×C53 | — | 2 | 1 | no | — |
| 118 | #97×C53 | C23 | 1 | 2 | yes | — |
| 119 | #97×C53 | C23 | 1 | 2 | yes | — |
| 120 | C23×D53 | — | 2 | 4 | no | — |
| 121 | #41×C53 | — | 8 | 2 | no | — |
| 122 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 123 | C2×D4×C53 | — | 2 | 2 | no | — |
| 124 | C2×D4×C53 | — | 2 | 1 | no | — |
| 125 | C2×D4×C53 | — | 2 | 1 | no | — |
| 126 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 127 | C22×C4×C53 | — | 2 | 2 | no | — |
| 128 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 132 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 133 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 134 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 135 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 136 | D4×D53 | — | 8 | 4 | no | — |
| 137 | D4×D53 | — | 8 | 4 | no | — |
| 138 | #11719945 | — | 4 | 4 | no | — |
| 139 | #11719945 | — | 4 | 4 | no | — |
| 140 | #11719945 | — | 8 | 2 | no | — |
| 141 | C2×D212 | — | 2 | 1 | no | — |
| 142 | C2×D212 | — | 2 | 1 | no | — |
| 143 | C2×D212 | — | 2 | 1 | no | — |
| 144 | C2×D212 | — | 2 | 1 | no | — |
| 145 | C2×D212 | — | 2 | 1 | no | — |
| 146 | C2×D212 | — | 2 | 1 | no | — |
| 147 | C2×D212 | — | 2 | 1 | no | — |
| 148 | C2×D212 | — | 2 | 4 | no | — |
| 149 | C2×D212 | — | 8 | 4 | no | — |
| 150 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 151 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 152 | C2×C4×D53 | — | 2 | 2 | no | — |
| 153 | C2×C4×D53 | — | 2 | 2 | no | — |
| 154 | C2×C4×D53 | — | 4 | 1 | no | — |
| 155 | C2×Dic106 | — | 2 | 1 | no | — |
| 156 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 157 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 158 | C2×C8×C53 | — | 2 | 4 | no | — |
| 159 | C2×C8×C53 | — | 2 | 2 | no | — |
| 160 | C2×C8×C53 | — | 2 | 2 | no | — |
| 161 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 162 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 163 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 164 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 165 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 169 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 170 | #11719924 | — | 8 | 2 | no | — |
| 171 | #11719922 | — | 8 | 2 | no | — |
| 172 | #11719921 | — | 2 | 4 | no | — |
| 173 | #11719921 | — | 2 | 4 | no | — |
| 174 | #11719921 | — | 2 | 2 | no | — |
| 175 | #11719921 | — | 2 | 2 | no | — |
| 176 | #11719921 | — | 2 | 2 | no | — |
| 177 | #11719921 | — | 2 | 2 | no | — |
| 178 | #11719921 | — | 4 | 1 | no | — |
| 179 | #11719921 | — | 4 | 1 | no | — |
| 180 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 181 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 182 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 183 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 184 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 185 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 186 | C4×Dic53 | — | 2 | 4 | no | — |
| 187 | C2×#88322 | — | 2 | 2 | no | — |
| 188 | Dic212 | — | 4 | 4 | no | — |
| 189 | D424 | — | 4 | 4 | no | — |
| 190 | D424 | — | 8 | 2 | no | — |
| 191 | #11719913 | — | 4 | 4 | no | — |
| 192 | #11719913 | — | 4 | 4 | no | — |
| 193 | #11719913 | — | 8 | 2 | no | — |
| 194 | C23×C53 | — | 2 | 2 | no | — |
| 195 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 196 | C22×D53 | — | 2 | 2 | no | — |
| 197 | C22×D53 | — | 2 | 2 | no | — |
| 198 | C22×D53 | — | 4 | 1 | no | — |
| 199 | C22×D53 | — | 8 | 4 | no | — |
| 200 | C22×D53 | — | 8 | 4 | no | — |
| 201 | C22×D53 | — | 8 | 4 | no | — |
| 202 | Q8×C53 | — | 4 | 2 | no | — |
| 203 | D4×C53 | — | 4 | 2 | no | — |
| 204 | D4×C53 | — | 4 | 2 | no | — |
| 205 | D4×C53 | — | 4 | 2 | no | — |
| 206 | D4×C53 | — | 8 | 2 | no | — |
| 207 | C2×C4×C53 | — | 2 | 2 | no | — |
| 208 | C2×C4×C53 | — | 2 | 2 | no | — |
| 209 | C2×C4×C53 | — | 4 | 1 | no | — |
| 210 | C2×C4×C53 | — | 4 | 1 | no | — |
| 211 | C2×C4×C53 | — | 4 | 4 | no | — |
| 212 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 215 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 218 | C22⋊D53 | — | 8 | 2 | no | — |
| 219 | C22⋊D53 | — | 8 | 2 | no | — |
| 220 | C22⋊D53 | — | 8 | 4 | no | — |
| 221 | C22⋊D53 | — | 8 | 4 | no | — |
| 222 | C22⋊D53 | — | 8 | 2 | no | — |
| 223 | C2×Dic53 | — | 2 | 2 | no | — |
| 224 | C2×Dic53 | — | 2 | 2 | no | — |
| 225 | C2×Dic53 | — | 4 | 1 | no | — |
| 226 | D212 | — | 4 | 2 | no | — |
| 227 | D212 | — | 4 | 2 | no | — |
| 228 | D212 | — | 4 | 2 | no | — |
| 229 | D212 | — | 4 | 2 | no | — |
| 230 | D212 | — | 4 | 2 | no | — |
| 231 | D212 | — | 4 | 2 | no | — |
| 232 | D212 | — | 4 | 1 | no | — |
| 233 | D212 | — | 4 | 1 | no | — |
| 234 | D212 | — | 4 | 1 | no | — |
| 235 | D212 | — | 4 | 1 | no | — |
| 236 | D212 | — | 4 | 2 | no | — |
| 237 | D212 | — | 8 | 4 | no | — |
| 238 | C4×D53 | — | 4 | 4 | no | — |
| 239 | C4×D53 | — | 4 | 4 | no | — |
| 240 | C4×D53 | — | 8 | 2 | no | — |
| 241 | Dic106 | — | 4 | 2 | no | — |
| 242 | Dic106 | — | 4 | 2 | no | — |
| 243 | Dic106 | — | 4 | 2 | no | — |
| 244 | C8×C53 | — | 2 | 4 | no | — |
| 245 | C8×C53 | — | 4 | 2 | no | — |
| 246 | #88322 | — | 4 | 2 | no | — |
| 247 | #19052 | — | 53 | 1 | no | maximal, Sylow |
| 248 | C22×C53 | — | 2 | 1 | no | — |
| 249 | C22×C53 | — | 2 | 1 | no | — |
| 250 | C22×C53 | — | 2 | 1 | no | — |
| 251 | C22×C53 | — | 4 | 2 | no | — |
| 252 | C22×C53 | — | 4 | 2 | no | — |
| 253 | C22×C53 | — | 4 | 2 | no | — |
| 254 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 255 | C2×D53 | — | 4 | 2 | no | — |
| 256 | C2×D53 | — | 4 | 2 | no | — |
| 257 | C2×D53 | — | 4 | 2 | no | — |
| 258 | C2×D53 | — | 4 | 2 | no | — |
| 259 | C2×D53 | — | 4 | 2 | no | — |
| 260 | C2×D53 | — | 4 | 2 | no | — |
| 261 | C2×D53 | — | 8 | 1 | no | — |
| 262 | C2×D53 | — | 8 | 1 | no | — |
| 263 | C2×D53 | — | 8 | 1 | no | — |
| 264 | C2×D53 | — | 16 | 8 | no | — |
| 265 | C4×C53 | — | 2 | 1 | no | — |
| 266 | C4×C53 | — | 2 | 1 | no | — |
| 267 | C4×C53 | — | 2 | 1 | no | — |
| 268 | C4×C53 | — | 2 | 1 | no | — |
| 269 | C4×C53 | — | 2 | 1 | no | — |
| 270 | C4×C53 | — | 4 | 2 | no | — |
| 271 | C4×C53 | #453 | 1 | 2 | yes | — |
| 272 | Dic53 | — | 4 | 2 | no | — |
| 273 | Dic53 | — | 4 | 2 | no | — |
| 274 | Dic53 | — | 8 | 1 | no | — |
| 275 | #3549 | — | 53 | 1 | no | — |
| 276 | #3214 | — | 53 | 1 | no | — |
| 277 | #3214 | — | 53 | 1 | no | — |
| 278 | #3150 | — | 53 | 1 | no | — |
| 279 | #1659 | — | 53 | 4 | no | — |
| 280 | #1655 | — | 53 | 4 | no | — |
| 281 | #1536 | — | 53 | 1 | no | — |
| 282 | #1530 | — | 53 | 1 | no | — |
| 283 | #1530 | D53 | 1 | 1 | yes | characteristic, complemented |
| 284 | C2×C53 | — | 4 | 1 | no | — |
| 285 | C2×C53 | — | 8 | 2 | no | — |
| 286 | C2×C53 | C2×#453 | 1 | 1 | yes | characteristic |
| 287 | C2×C53 | #3019 | 1 | 1 | yes | characteristic |
| 288 | C2×C53 | #3019 | 1 | 1 | yes | characteristic |
| 289 | D53 | — | 8 | 2 | no | — |
| 290 | D53 | — | 8 | 2 | no | — |
| 291 | D53 | — | 16 | 1 | no | — |
| 292 | C2×#135 | — | 106 | 2 | no | — |
| 293 | H(3,𝔽4) | — | 53 | 4 | no | — |
| 294 | #555 | — | 106 | 1 | no | — |
| 295 | #555 | — | 106 | 1 | no | — |
| 296 | #555 | — | 106 | 1 | no | — |
| 297 | D42 | — | 106 | 1 | no | — |
| 298 | D42 | — | 106 | 1 | no | — |
| 299 | D42 | — | 106 | 1 | no | — |
| 300 | #535 | — | 106 | 2 | no | — |
| 301 | #535 | — | 106 | 2 | no | — |
| 302 | #535 | — | 106 | 2 | no | — |
| 303 | #532 | — | 53 | 1 | no | — |
| 304 | #532 | — | 53 | 1 | no | — |
| 305 | #532 | — | 53 | 1 | no | — |
| 306 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 307 | #497 | — | 53 | 2 | no | — |
| 308 | #497 | — | 106 | 1 | no | — |
| 309 | #496 | — | 53 | 2 | no | — |
| 310 | #496 | — | 53 | 2 | no | — |
| 311 | #496 | — | 53 | 2 | no | — |
| 312 | #496 | — | 106 | 1 | no | — |
| 313 | #489 | — | 53 | 2 | no | — |
| 314 | #489 | — | 53 | 2 | no | — |
| 315 | #461 | — | 106 | 1 | no | — |
| 316 | #461 | — | 106 | 1 | no | — |
| 317 | #459 | — | 106 | 1 | no | — |
| 318 | #459 | — | 106 | 1 | no | — |
| 319 | #449 | — | 106 | 2 | no | — |
| 320 | #449 | — | 106 | 2 | no | — |
| 321 | #432 | — | 53 | 1 | no | — |
| 322 | #432 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 323 | C2×#97 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 324 | #329 | — | 53 | 4 | no | — |
| 325 | #329 | — | 53 | 4 | no | — |
| 326 | #329 | C2×D53 | 1 | 4 | yes | complemented |
| 327 | C53 | #19052 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 328 | C2×#41 | — | 53 | 2 | no | — |
| 329 | C2×#41 | — | 53 | 2 | no | — |
| 330 | C2×#41 | — | 106 | 1 | no | — |
| 331 | C2×#41 | D212 | 1 | 2 | yes | — |
| 332 | C22×D4 | — | 106 | 2 | no | — |
| 333 | C22×D4 | — | 106 | 2 | no | — |
| 334 | C22×D4 | — | 106 | 2 | no | — |
| 335 | #135 | — | 212 | 8 | no | — |
| 336 | C2×Q16 | — | 106 | 2 | no | — |
| 337 | C2×SD16 | — | 106 | 2 | no | — |
| 338 | C2×SD16 | — | 106 | 2 | no | — |
| 339 | C2×SD16 | — | 106 | 2 | no | — |
| 340 | C2×SD16 | — | 106 | 2 | no | — |
| 341 | C2×D8 | — | 106 | 2 | no | — |
| 342 | C2×D8 | — | 106 | 2 | no | — |
| 343 | C2×D8 | — | 106 | 2 | no | — |
| 344 | C22×C8 | — | 2 | 1 | no | — |
| 345 | C4⋊Q8 | — | 53 | 1 | no | — |
| 346 | C4⋊Q8 | — | 53 | 1 | no | — |
| 347 | C4⋊Q8 | — | 53 | 1 | no | — |
| 348 | C4⋊Q8 | D212 | 1 | 1 | yes | characteristic |
| 349 | #127 | — | 53 | 1 | no | — |
| 350 | #127 | — | 53 | 1 | no | — |
| 351 | #127 | — | 53 | 1 | no | — |
| 352 | #127 | — | 106 | 4 | no | — |
| 353 | #127 | D212 | 1 | 1 | yes | characteristic |
| 354 | #124 | — | 53 | 2 | no | — |
| 355 | #124 | — | 53 | 2 | no | — |
| 356 | #124 | — | 106 | 4 | no | — |
| 357 | #124 | — | 106 | 4 | no | — |
| 358 | #124 | — | 106 | 4 | no | — |
| 359 | #124 | — | 106 | 1 | no | — |
| 360 | #124 | C22×D53 | 1 | 2 | yes | — |
| 361 | #121 | — | 2 | 1 | no | — |
| 362 | #121 | — | 2 | 1 | no | — |
| 363 | #121 | — | 106 | 2 | no | — |
| 364 | #121 | — | 106 | 2 | no | — |
| 365 | #121 | — | 106 | 2 | no | — |
| 366 | #121 | — | 106 | 2 | no | — |
| 367 | #121 | — | 106 | 2 | no | — |
| 368 | #121 | — | 106 | 2 | no | — |
| 369 | #121 | — | 106 | 1 | no | — |
| 370 | #121 | — | 106 | 1 | no | — |
| 371 | #121 | — | 106 | 1 | no | — |
| 372 | #121 | — | 106 | 1 | no | — |
| 373 | #121 | — | 106 | 1 | no | — |
| 374 | #121 | — | 106 | 1 | no | — |
| 375 | #120 | — | 106 | 4 | no | — |
| 376 | #120 | — | 106 | 4 | no | — |
| 377 | #120 | — | 106 | 4 | no | — |
| 378 | #120 | — | 106 | 4 | no | — |
| 379 | C4×D4 | — | 2 | 1 | no | — |
| 380 | C4×D4 | — | 2 | 1 | no | — |
| 381 | C4×D4 | — | 106 | 1 | no | — |
| 382 | C4×D4 | — | 106 | 1 | no | — |
| 383 | C4×D4 | — | 106 | 1 | no | — |
| 384 | C4×D4 | — | 106 | 1 | no | — |
| 385 | C4×D4 | — | 106 | 1 | no | — |
| 386 | C4×D4 | — | 106 | 1 | no | — |
| 387 | #117 | — | 106 | 2 | no | — |
| 388 | #117 | — | 106 | 2 | no | — |
| 389 | #117 | — | 106 | 2 | no | — |
| 390 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 391 | C4⋊C8 | — | 2 | 1 | no | — |
| 392 | C4⋊C8 | — | 106 | 1 | no | — |
| 393 | #103 | — | 106 | 2 | no | — |
| 394 | #103 | — | 106 | 2 | no | — |
| 395 | #102 | — | 106 | 2 | no | — |
| 396 | #102 | — | 106 | 2 | no | — |
| 397 | C22⋊C8 | — | 2 | 1 | no | — |
| 398 | C22⋊C8 | — | 106 | 1 | no | — |
| 399 | #97 | — | 2 | 1 | no | — |
| 400 | #97 | — | 53 | 2 | no | — |
| 401 | #97 | C22×D53 | 1 | 2 | yes | — |
| 402 | #97 | C22×D53 | 1 | 2 | yes | — |
| 403 | C24 | — | 106 | 4 | no | — |
| 404 | #41 | — | 8 | 2 | no | — |
| 405 | #41 | — | 424 | 2 | no | — |
| 406 | #41 | — | 212 | 4 | no | — |
| 407 | #41 | — | 212 | 4 | no | — |
| 408 | C2×Q8 | — | 53 | 2 | no | — |
| 409 | C2×Q8 | — | 53 | 2 | no | — |
| 410 | C2×Q8 | — | 106 | 1 | no | — |
| 411 | C2×Q8 | C2×D212 | 1 | 2 | yes | — |
| 412 | C2×D4 | — | 2 | 2 | no | — |
| 413 | C2×D4 | — | 2 | 1 | no | — |
| 414 | C2×D4 | — | 2 | 1 | no | — |
| 415 | C2×D4 | — | 53 | 2 | no | — |
| 416 | C2×D4 | — | 53 | 2 | no | — |
| 417 | C2×D4 | — | 106 | 4 | no | — |
| 418 | C2×D4 | — | 106 | 4 | no | — |
| 419 | C2×D4 | — | 106 | 4 | no | — |
| 420 | C2×D4 | — | 106 | 2 | no | — |
| 421 | C2×D4 | — | 106 | 2 | no | — |
| 422 | C2×D4 | — | 106 | 1 | no | — |
| 423 | C2×D4 | — | 106 | 1 | no | — |
| 424 | C2×D4 | — | 106 | 1 | no | — |
| 425 | C2×D4 | — | 106 | 1 | no | — |
| 426 | C2×D4 | — | 106 | 1 | no | — |
| 427 | C2×D4 | — | 106 | 1 | no | — |
| 428 | C2×D4 | — | 106 | 1 | no | — |
| 429 | C2×D4 | — | 424 | 4 | no | — |
| 430 | C2×D4 | — | 424 | 4 | no | — |
| 431 | C2×D4 | — | 424 | 4 | no | — |
| 432 | C2×D4 | — | 212 | 1 | no | — |
| 433 | C2×D4 | C2×D212 | 1 | 2 | yes | — |
| 434 | C22×C4 | — | 2 | 2 | no | — |
| 435 | C22×C4 | — | 106 | 2 | no | — |
| 436 | C22×C4 | — | 106 | 2 | no | — |
| 437 | C22×C4 | — | 212 | 1 | no | — |
| 438 | C22×C4 | C2×D212 | 1 | 1 | yes | characteristic |
| 439 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 440 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 441 | Q16 | — | 212 | 4 | no | — |
| 442 | SD16 | — | 424 | 2 | no | — |
| 443 | SD16 | — | 424 | 2 | no | — |
| 444 | SD16 | — | 212 | 4 | no | — |
| 445 | SD16 | — | 212 | 4 | no | — |
| 446 | D8 | — | 424 | 2 | no | — |
| 447 | D8 | — | 424 | 2 | no | — |
| 448 | D8 | — | 212 | 4 | no | — |
| 449 | C2×C8 | — | 2 | 4 | no | — |
| 450 | C2×C8 | — | 2 | 2 | no | — |
| 451 | C2×C8 | — | 2 | 2 | no | — |
| 452 | C2×C8 | — | 106 | 2 | no | — |
| 453 | C4⋊C4 | — | 2 | 1 | no | — |
| 454 | C4⋊C4 | — | 2 | 1 | no | — |
| 455 | C4⋊C4 | — | 106 | 1 | no | — |
| 456 | C4⋊C4 | — | 106 | 1 | no | — |
| 457 | C4⋊C4 | — | 106 | 1 | no | — |
| 458 | C4⋊C4 | — | 106 | 1 | no | — |
| 459 | C4⋊C4 | — | 106 | 1 | no | — |
| 460 | C4⋊C4 | — | 106 | 1 | no | — |
| 461 | C22⋊C4 | — | 2 | 2 | no | — |
| 462 | C22⋊C4 | — | 2 | 2 | no | — |
| 463 | C22⋊C4 | — | 106 | 4 | no | — |
| 464 | C22⋊C4 | — | 106 | 4 | no | — |
| 465 | C22⋊C4 | — | 106 | 4 | no | — |
| 466 | C22⋊C4 | — | 106 | 2 | no | — |
| 467 | C22⋊C4 | — | 106 | 2 | no | — |
| 468 | C22⋊C4 | — | 106 | 2 | no | — |
| 469 | C22⋊C4 | — | 106 | 2 | no | — |
| 470 | C22⋊C4 | — | 212 | 1 | no | — |
| 471 | C22⋊C4 | — | 212 | 1 | no | — |
| 472 | C42 | — | 106 | 4 | no | — |
| 473 | C42 | C2×D212 | 1 | 1 | yes | characteristic |
| 474 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 475 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 476 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 477 | C23 | — | 2 | 2 | no | — |
| 478 | C23 | — | 106 | 2 | no | — |
| 479 | C23 | — | 106 | 2 | no | — |
| 480 | C23 | — | 424 | 4 | no | — |
| 481 | C23 | — | 424 | 4 | no | — |
| 482 | C23 | — | 424 | 4 | no | — |
| 483 | C23 | — | 212 | 1 | no | — |
| 484 | C23 | #13133187 | 1 | 1 | yes | characteristic |
| 485 | Q8 | — | 4 | 2 | no | — |
| 486 | Q8 | — | 212 | 2 | no | — |
| 487 | Q8 | — | 212 | 2 | no | — |
| 488 | Q8 | — | 212 | 2 | no | — |
| 489 | D4 | — | 4 | 2 | no | — |
| 490 | D4 | — | 4 | 2 | no | — |
| 491 | D4 | — | 4 | 2 | no | — |
| 492 | D4 | — | 8 | 2 | no | — |
| 493 | D4 | — | 424 | 4 | no | — |
| 494 | D4 | — | 424 | 2 | no | — |
| 495 | D4 | — | 424 | 2 | no | — |
| 496 | D4 | — | 424 | 2 | no | — |
| 497 | D4 | — | 424 | 4 | no | — |
| 498 | D4 | — | 424 | 4 | no | — |
| 499 | D4 | — | 212 | 1 | no | — |
| 500 | D4 | — | 212 | 1 | no | — |
| 501 | D4 | — | 212 | 2 | no | — |
| 502 | D4 | — | 212 | 1 | no | — |
| 503 | D4 | — | 212 | 1 | no | — |
| 504 | D4 | — | 212 | 2 | no | — |
| 505 | D4 | — | 212 | 2 | no | — |
| 506 | D4 | — | 212 | 2 | no | — |
| 507 | D4 | — | 212 | 2 | no | — |
| 508 | D4 | — | 212 | 2 | no | — |
| 509 | D4 | — | 212 | 2 | no | — |
| 510 | C2×C4 | — | 2 | 2 | no | — |
| 511 | C2×C4 | — | 2 | 2 | no | — |
| 512 | C2×C4 | — | 4 | 1 | no | — |
| 513 | C2×C4 | — | 4 | 1 | no | — |
| 514 | C2×C4 | — | 4 | 4 | no | — |
| 515 | C2×C4 | — | 106 | 2 | no | — |
| 516 | C2×C4 | — | 106 | 2 | no | — |
| 517 | C2×C4 | — | 424 | 2 | no | — |
| 518 | C2×C4 | — | 212 | 4 | no | — |
| 519 | C2×C4 | — | 212 | 1 | no | — |
| 520 | C2×C4 | — | 212 | 4 | no | — |
| 521 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 522 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 523 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 524 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 526 | C2×C4 | C22×D212 | 1 | 1 | yes | characteristic |
| 527 | C8 | — | 2 | 4 | no | — |
| 528 | C8 | — | 4 | 2 | no | — |
| 529 | C8 | — | 212 | 2 | no | — |
| 530 | C22 | — | 2 | 1 | no | — |
| 531 | C22 | — | 2 | 1 | no | — |
| 532 | C22 | — | 2 | 1 | no | — |
| 533 | C22 | — | 4 | 2 | no | — |
| 534 | C22 | — | 4 | 2 | no | — |
| 535 | C22 | — | 4 | 2 | no | — |
| 536 | C22 | — | 848 | 8 | no | — |
| 537 | C22 | — | 424 | 1 | no | — |
| 538 | C22 | — | 424 | 1 | no | — |
| 539 | C22 | — | 424 | 1 | no | — |
| 540 | C22 | — | 212 | 2 | no | — |
| 541 | C22 | — | 212 | 2 | no | — |
| 542 | C22 | — | 212 | 2 | no | — |
| 543 | C22 | — | 212 | 2 | no | — |
| 544 | C22 | — | 212 | 2 | no | — |
| 545 | C22 | — | 212 | 2 | no | — |
| 546 | C22 | C2×#13133187 | 1 | 1 | yes | characteristic |
| 547 | C4 | — | 2 | 1 | no | — |
| 548 | C4 | — | 2 | 1 | no | — |
| 549 | C4 | — | 2 | 1 | no | — |
| 550 | C4 | — | 2 | 1 | no | — |
| 551 | C4 | — | 2 | 1 | no | — |
| 552 | C4 | — | 4 | 2 | no | — |
| 553 | C4 | — | 424 | 1 | no | — |
| 554 | C4 | — | 212 | 2 | no | — |
| 555 | C4 | — | 212 | 2 | no | — |
| 556 | C4 | #16810792 | 1 | 2 | yes | — |
| 557 | C2 | — | 4 | 1 | no | — |
| 558 | C2 | — | 8 | 2 | no | — |
| 559 | C2 | — | 848 | 1 | no | — |
| 560 | C2 | — | 424 | 2 | no | — |
| 561 | C2 | — | 424 | 2 | no | — |
| 562 | C2 | C2×#16810792 | 1 | 1 | yes | characteristic |
| 563 | C2 | #20284074 | 1 | 1 | yes | characteristic |
| 564 | C2 | #20284075 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289120 | C2 | semidirect |
| 2. #20285712 | C2 | semidirect |
| 3. #20285710 | C2 | semidirect |
| 4. #20285161 | C2 | semidirect |
| 5. #20274023 | C2 | semidirect |
| 6. #20274005 | C2 | semidirect |
| 7. #20273349 | C2 | semidirect |
| 8. #20273325 | C2 | semidirect |
| 9. C53×#1530 | C2 | semidirect |
| 23. #16811173 | C22 | semidirect |
| 25. #16811017 | C22 | semidirect |
| 26. #16811013 | C22 | semidirect |
| 28. #16811012 | C22 | semidirect |
| 29. #16811012 | C22 | semidirect |
| 30. #16810983 | C22 | semidirect |
| 31. #16810982 | C22 | semidirect |
| 38. #16810680 | C22 | semidirect |
| 39. #16810362 | C22 | semidirect |
| 40. #16810362 | C22 | semidirect |
| 42. C53×#432 | C22 | semidirect |
| 43. C2×#97×C53 | C22 | semidirect |
| 44. C53×#329 | C22 | semidirect |
| 283. #1530 | D53 | semidirect |
| 322. #432 | C2×D53 | semidirect |
| 323. C2×#97 | C2×D53 | semidirect |
| 326. #329 | C2×D53 | semidirect |
| 327. C53 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289120 | 2 |
| #20285712 | 2 |
| #20285710 | 2 |
| #20285161 | 2 |
| #20274023 | 2 |
| #20274005 | 2 |
| #20273349 | 2 |
| #20273325 | 2 |
| C53×#1530 | 2 |
| #19052 | 53 |