← #28274539
Subgroups — #28274539
Order 13568.
1648 conjugacy classes of subgroups.
The subgroup lattice has 702 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20289129 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20288520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20287652 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20287631 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20287598 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20287560 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #20287534 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20287416 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #20285996 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #20285929 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #20284939 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #20284833 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #20284755 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #20283809 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#3228 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #16811373 | — | 2 | 2 | no | — |
| 17 | #16811359 | C22 | 1 | 2 | yes | — |
| 18 | Q8×Dic106 | — | 2 | 1 | no | — |
| 19 | #16811353 | C22 | 1 | 2 | yes | — |
| 20 | #16811353 | C22 | 1 | 2 | yes | — |
| 21 | #16811351 | — | 2 | 1 | no | — |
| 22 | #16811351 | — | 2 | 2 | no | — |
| 23 | #16811350 | C22 | 1 | 4 | yes | — |
| 24 | #16811348 | C22 | 1 | 2 | yes | — |
| 25 | #16811343 | — | 2 | 1 | no | — |
| 26 | #16811343 | C22 | 1 | 2 | yes | — |
| 27 | D4×Dic106 | — | 2 | 1 | no | — |
| 28 | D4×Dic106 | C22 | 1 | 2 | yes | — |
| 29 | #16811252 | — | 2 | 2 | no | — |
| 30 | #16811251 | C22 | 1 | 2 | yes | — |
| 31 | #16811240 | — | 2 | 2 | no | — |
| 32 | #16811240 | C22 | 1 | 4 | yes | — |
| 33 | #16811194 | — | 2 | 2 | no | — |
| 34 | #16811180 | C22 | 1 | 1 | yes | characteristic |
| 35 | #16811180 | C22 | 1 | 1 | yes | characteristic |
| 36 | #16811175 | — | 2 | 2 | no | — |
| 37 | #16811100 | C22 | 1 | 2 | yes | — |
| 38 | C2×C4×Dic106 | C22 | 1 | 1 | yes | characteristic |
| 39 | #16811033 | C22 | 1 | 2 | yes | — |
| 40 | #16811030 | C22 | 1 | 4 | yes | — |
| 41 | #16811027 | C22 | 1 | 4 | yes | — |
| 42 | #16810993 | C22 | 1 | 2 | yes | — |
| 43 | #16810981 | C22 | 1 | 4 | yes | — |
| 44 | #16810976 | C22 | 1 | 4 | yes | — |
| 45 | #16810964 | C22 | 1 | 4 | yes | — |
| 46 | #16810959 | C22 | 1 | 2 | yes | — |
| 47 | #16810934 | C22 | 1 | 2 | yes | — |
| 48 | #16810933 | C22 | 1 | 4 | yes | — |
| 49 | #16810921 | C22 | 1 | 4 | yes | — |
| 50 | #16810919 | C22 | 1 | 2 | yes | — |
| 51 | #16810917 | C22 | 1 | 4 | yes | — |
| 52 | #16810917 | C22 | 1 | 4 | yes | — |
| 53 | #16810915 | C22 | 1 | 2 | yes | — |
| 54 | #16810915 | C22 | 1 | 2 | yes | — |
| 55 | #16810907 | C22 | 1 | 4 | yes | — |
| 56 | #16810905 | C22 | 1 | 2 | yes | — |
| 57 | #16810901 | C22 | 1 | 4 | yes | — |
| 58 | #16810844 | C22 | 1 | 4 | yes | — |
| 59 | #16810844 | C22 | 1 | 4 | yes | — |
| 60 | #16810834 | C22 | 1 | 2 | yes | — |
| 61 | #16810820 | C22 | 1 | 2 | yes | — |
| 62 | #16810781 | C22 | 1 | 2 | yes | — |
| 63 | #16810761 | C22 | 1 | 2 | yes | — |
| 64 | #16810753 | C22 | 1 | 2 | yes | — |
| 65 | #16810752 | C22 | 1 | 4 | yes | — |
| 66 | C8×Dic106 | C22 | 1 | 2 | yes | — |
| 67 | #16810729 | C22 | 1 | 4 | yes | — |
| 68 | #16810723 | C22 | 1 | 4 | yes | — |
| 69 | #16810720 | C22 | 1 | 4 | yes | — |
| 70 | C4×Dic212 | C22 | 1 | 2 | yes | — |
| 71 | C4×Dic212 | C22 | 1 | 2 | yes | — |
| 72 | #16810717 | C22 | 1 | 4 | yes | — |
| 73 | #16810714 | C22 | 1 | 4 | yes | — |
| 74 | #16810681 | C22 | 1 | 4 | yes | — |
| 75 | #16810680 | C22 | 1 | 1 | yes | characteristic |
| 76 | C53×#533 | C22 | 1 | 1 | yes | characteristic |
| 77 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 78 | C53×#500 | C22 | 1 | 1 | yes | characteristic |
| 79 | C53×#498 | C22 | 1 | 1 | yes | characteristic |
| 80 | C53×#486 | C22 | 1 | 1 | yes | characteristic |
| 81 | C53×#486 | C22 | 1 | 1 | yes | characteristic |
| 82 | C53×#482 | C22 | 1 | 4 | yes | — |
| 83 | C53×#478 | C22 | 1 | 4 | yes | — |
| 84 | C53×#431 | C22 | 1 | 1 | yes | characteristic |
| 85 | C22×Dic106 | — | 2 | 2 | no | — |
| 86 | C22×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×Dic212 | C23 | 1 | 2 | yes | — |
| 88 | C2×Dic212 | C23 | 1 | 2 | yes | — |
| 89 | C2×#11719923 | C23 | 1 | 4 | yes | — |
| 90 | #13133217 | — | 2 | 2 | no | — |
| 91 | #13133217 | D4 | 1 | 1 | yes | characteristic |
| 92 | #13133217 | D4 | 1 | 1 | yes | characteristic |
| 93 | #13133217 | C23 | 1 | 1 | yes | characteristic |
| 94 | #13133217 | C23 | 1 | 1 | yes | characteristic |
| 95 | #13133216 | — | 2 | 2 | no | — |
| 96 | #13133216 | — | 2 | 2 | no | — |
| 97 | #13133216 | — | 2 | 4 | no | — |
| 98 | #13133216 | C23 | 1 | 4 | yes | — |
| 99 | #13133216 | C23 | 1 | 4 | yes | — |
| 100 | #13133215 | — | 2 | 4 | no | — |
| 101 | #13133215 | — | 2 | 4 | no | — |
| 102 | #13133215 | — | 2 | 2 | no | — |
| 103 | #13133210 | — | 2 | 4 | no | — |
| 104 | #13133210 | — | 2 | 4 | no | — |
| 105 | #13133209 | — | 2 | 1 | no | — |
| 106 | #13133209 | — | 2 | 2 | no | — |
| 107 | #13133209 | D4 | 1 | 2 | yes | — |
| 108 | #13133208 | C23 | 1 | 4 | yes | — |
| 109 | #13133207 | — | 2 | 4 | no | — |
| 110 | #13133207 | — | 2 | 4 | no | — |
| 111 | #13133207 | — | 2 | 4 | no | — |
| 112 | #13133204 | — | 2 | 4 | no | — |
| 113 | #13133204 | — | 2 | 2 | no | — |
| 114 | #13133204 | C23 | 1 | 4 | yes | — |
| 115 | #13133198 | — | 2 | 4 | no | — |
| 116 | #13133198 | — | 2 | 4 | no | — |
| 117 | #13133196 | — | 2 | 2 | no | — |
| 118 | #13133196 | — | 2 | 1 | no | — |
| 119 | #13133196 | — | 2 | 2 | no | — |
| 120 | #13133196 | D4 | 1 | 2 | yes | — |
| 121 | #13133196 | D4 | 1 | 2 | yes | — |
| 122 | #13133196 | C23 | 1 | 2 | yes | — |
| 123 | #13133194 | — | 2 | 4 | no | — |
| 124 | #13133194 | — | 2 | 4 | no | — |
| 125 | #13133194 | — | 2 | 4 | no | — |
| 126 | Q8×Dic53 | — | 2 | 2 | no | — |
| 127 | C4×Dic106 | — | 2 | 1 | no | — |
| 128 | C4×Dic106 | — | 2 | 1 | no | — |
| 129 | C4×Dic106 | — | 2 | 1 | no | — |
| 130 | C4×Dic106 | — | 2 | 2 | no | — |
| 131 | C4×Dic106 | — | 2 | 2 | no | — |
| 132 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 133 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 134 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 135 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 136 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 137 | #13133182 | — | 2 | 4 | no | — |
| 138 | #13133182 | — | 2 | 2 | no | — |
| 139 | #13133182 | — | 2 | 2 | no | — |
| 140 | #13133182 | C23 | 1 | 4 | yes | — |
| 141 | #13133182 | C23 | 1 | 4 | yes | — |
| 142 | #13133182 | C23 | 1 | 4 | yes | — |
| 143 | D4×Dic53 | — | 2 | 2 | no | — |
| 144 | D4×Dic53 | C23 | 1 | 4 | yes | — |
| 145 | #13133176 | — | 2 | 2 | no | — |
| 146 | #13133176 | — | 2 | 1 | no | — |
| 147 | #13133176 | C23 | 1 | 2 | yes | — |
| 148 | #13133173 | — | 2 | 4 | no | — |
| 149 | C2×C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 150 | C2×#11719919 | — | 2 | 1 | no | — |
| 151 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 152 | #13133151 | C23 | 1 | 2 | yes | — |
| 153 | #13133151 | C23 | 1 | 2 | yes | — |
| 154 | #13133150 | C23 | 1 | 4 | yes | — |
| 155 | #13133150 | C23 | 1 | 4 | yes | — |
| 156 | #13133148 | C23 | 1 | 4 | yes | — |
| 157 | C4⋊#88322 | C23 | 1 | 2 | yes | — |
| 158 | #13133146 | C23 | 1 | 4 | yes | — |
| 159 | #13133146 | C23 | 1 | 4 | yes | — |
| 160 | #13133142 | C23 | 1 | 2 | yes | — |
| 161 | #13133142 | C23 | 1 | 2 | yes | — |
| 162 | #13133142 | C23 | 1 | 2 | yes | — |
| 163 | #13133142 | C23 | 1 | 2 | yes | — |
| 164 | #13133140 | C23 | 1 | 4 | yes | — |
| 165 | #13133140 | C23 | 1 | 4 | yes | — |
| 166 | #13133140 | C23 | 1 | 4 | yes | — |
| 167 | #13133138 | C23 | 1 | 4 | yes | — |
| 168 | C22⋊#88322 | C23 | 1 | 2 | yes | — |
| 169 | #13133128 | C23 | 1 | 2 | yes | — |
| 170 | #13133127 | C23 | 1 | 4 | yes | — |
| 171 | C8×Dic53 | C23 | 1 | 4 | yes | — |
| 172 | C2×#41×C53 | — | 2 | 1 | no | — |
| 173 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 174 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 175 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 176 | #127×C53 | C23 | 1 | 1 | yes | characteristic |
| 177 | #125×C53 | C23 | 1 | 2 | yes | — |
| 178 | #124×C53 | — | 2 | 1 | no | — |
| 179 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 180 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 181 | #121×C53 | — | 2 | 1 | no | — |
| 182 | #121×C53 | C23 | 1 | 2 | yes | — |
| 183 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 184 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 185 | C4×D4×C53 | — | 2 | 1 | no | — |
| 186 | C4×D4×C53 | C23 | 1 | 2 | yes | — |
| 187 | #117×C53 | C23 | 1 | 2 | yes | — |
| 188 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 189 | #107×C53 | C23 | 1 | 4 | yes | — |
| 190 | #106×C53 | C23 | 1 | 4 | yes | — |
| 191 | C4⋊C8×C53 | C23 | 1 | 2 | yes | — |
| 192 | #102×C53 | C23 | 1 | 4 | yes | — |
| 193 | #102×C53 | C23 | 1 | 4 | yes | — |
| 194 | C22⋊C8×C53 | C23 | 1 | 2 | yes | — |
| 195 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 196 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 197 | #41×C53 | — | 8 | 2 | no | — |
| 198 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 199 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 200 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 201 | C2×D4×C53 | — | 2 | 2 | no | — |
| 202 | C2×D4×C53 | — | 2 | 1 | no | — |
| 203 | C2×D4×C53 | — | 2 | 1 | no | — |
| 204 | C2×D4×C53 | C24 | 1 | 2 | yes | — |
| 205 | C22×C4×C53 | — | 2 | 2 | no | — |
| 206 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 209 | C22×Dic53 | — | 2 | 1 | no | — |
| 210 | C22×Dic53 | — | 2 | 1 | no | — |
| 211 | C22×Dic53 | — | 2 | 4 | no | — |
| 212 | C2×Dic106 | — | 2 | 1 | no | — |
| 213 | C2×Dic106 | — | 2 | 4 | no | — |
| 214 | C2×Dic106 | — | 2 | 1 | no | — |
| 215 | C2×Dic106 | — | 2 | 4 | no | — |
| 216 | C2×Dic106 | — | 2 | 4 | no | — |
| 217 | C2×Dic106 | — | 8 | 4 | no | — |
| 218 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 219 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 220 | C2×Dic106 | C24 | 1 | 2 | yes | — |
| 221 | C2×Dic106 | C24 | 1 | 2 | yes | — |
| 222 | C2×C8×C53 | C24 | 1 | 2 | yes | — |
| 223 | C2×C8×C53 | C24 | 1 | 2 | yes | — |
| 224 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 225 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 226 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 227 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 228 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 229 | C4⋊C4×C53 | C24 | 1 | 2 | yes | — |
| 230 | C4⋊C4×C53 | C24 | 1 | 2 | yes | — |
| 231 | C4⋊C4×C53 | C24 | 1 | 2 | yes | — |
| 232 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 233 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 234 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 235 | C42×C53 | — | 2 | 2 | no | — |
| 236 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 239 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 240 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 241 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 242 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 243 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 244 | C22⋊Dic53 | C2×D4 | 1 | 4 | yes | — |
| 245 | #11719923 | — | 2 | 8 | no | — |
| 246 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 247 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 248 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 249 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 250 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 251 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 252 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 253 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 254 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 255 | C4⋊Dic53 | C24 | 1 | 2 | yes | — |
| 256 | C4⋊Dic53 | C24 | 1 | 2 | yes | — |
| 257 | #11719919 | — | 2 | 2 | no | — |
| 258 | #11719919 | — | 2 | 2 | no | — |
| 259 | #11719919 | — | 2 | 2 | no | — |
| 260 | #11719919 | — | 2 | 2 | no | — |
| 261 | #11719919 | — | 2 | 4 | no | — |
| 262 | #11719919 | — | 2 | 4 | no | — |
| 263 | #11719919 | — | 2 | 4 | no | — |
| 264 | #11719919 | — | 2 | 4 | no | — |
| 265 | #11719919 | — | 2 | 4 | no | — |
| 266 | #11719919 | — | 2 | 4 | no | — |
| 267 | #11719919 | C2×D4 | 1 | 4 | yes | — |
| 268 | #11719919 | C2×D4 | 1 | 4 | yes | — |
| 269 | C4×Dic53 | — | 2 | 2 | no | — |
| 270 | C4×Dic53 | — | 2 | 2 | no | — |
| 271 | C4×Dic53 | — | 2 | 2 | no | — |
| 272 | C4×Dic53 | — | 2 | 4 | no | — |
| 273 | C4×Dic53 | — | 2 | 4 | no | — |
| 274 | C4×Dic53 | — | 2 | 4 | no | — |
| 275 | C4×Dic53 | C24 | 1 | 4 | yes | — |
| 276 | C2×#88322 | C24 | 1 | 4 | yes | — |
| 277 | Dic212 | — | 2 | 4 | no | — |
| 278 | Dic212 | — | 2 | 4 | no | — |
| 279 | C23×C53 | — | 2 | 2 | no | — |
| 280 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 281 | Q8×C53 | — | 4 | 2 | no | — |
| 282 | Q8×C53 | — | 8 | 1 | no | — |
| 283 | Q8×C53 | — | 8 | 1 | no | — |
| 284 | D4×C53 | — | 2 | 4 | no | — |
| 285 | D4×C53 | — | 4 | 2 | no | — |
| 286 | D4×C53 | — | 8 | 1 | no | — |
| 287 | D4×C53 | — | 8 | 2 | no | — |
| 288 | C2×C4×C53 | — | 2 | 2 | no | — |
| 289 | C2×C4×C53 | — | 2 | 2 | no | — |
| 290 | C2×C4×C53 | — | 2 | 2 | no | — |
| 291 | C2×C4×C53 | — | 2 | 2 | no | — |
| 292 | C2×C4×C53 | — | 2 | 2 | no | — |
| 293 | C2×C4×C53 | — | 4 | 1 | no | — |
| 294 | C2×C4×C53 | — | 4 | 4 | no | — |
| 295 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 296 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 297 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 298 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 300 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 301 | C2×Dic53 | — | 2 | 4 | no | — |
| 302 | C2×Dic53 | — | 2 | 2 | no | — |
| 303 | C2×Dic53 | — | 2 | 2 | no | — |
| 304 | C2×Dic53 | — | 2 | 2 | no | — |
| 305 | C2×Dic53 | — | 2 | 2 | no | — |
| 306 | C2×Dic53 | — | 8 | 4 | no | — |
| 307 | C2×Dic53 | — | 8 | 1 | no | — |
| 308 | C2×Dic53 | C22×D4 | 1 | 4 | yes | — |
| 309 | C2×Dic53 | C22×D4 | 1 | 4 | yes | — |
| 310 | Dic106 | — | 2 | 4 | no | — |
| 311 | Dic106 | — | 2 | 4 | no | — |
| 312 | Dic106 | — | 2 | 2 | no | — |
| 313 | Dic106 | — | 2 | 2 | no | — |
| 314 | Dic106 | — | 2 | 2 | no | — |
| 315 | Dic106 | — | 4 | 2 | no | — |
| 316 | Dic106 | — | 4 | 2 | no | — |
| 317 | Dic106 | — | 8 | 4 | no | — |
| 318 | Dic106 | — | 8 | 4 | no | — |
| 319 | Dic106 | 2−1+4 | 1 | 4 | yes | — |
| 320 | C8×C53 | — | 2 | 2 | no | — |
| 321 | C8×C53 | — | 2 | 2 | no | — |
| 322 | #88322 | — | 2 | 4 | no | — |
| 323 | #61854 | — | 53 | 1 | no | maximal, Sylow |
| 324 | C22×C53 | — | 2 | 1 | no | — |
| 325 | C22×C53 | — | 2 | 1 | no | — |
| 326 | C22×C53 | — | 2 | 1 | no | — |
| 327 | C22×C53 | — | 4 | 2 | no | — |
| 328 | C22×C53 | — | 4 | 2 | no | — |
| 329 | C22×C53 | — | 4 | 2 | no | — |
| 330 | C22×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 331 | C4×C53 | — | 2 | 1 | no | — |
| 332 | C4×C53 | — | 2 | 1 | no | — |
| 333 | C4×C53 | — | 2 | 1 | no | — |
| 334 | C4×C53 | — | 2 | 1 | no | — |
| 335 | C4×C53 | — | 4 | 2 | no | — |
| 336 | C4×C53 | — | 4 | 2 | no | — |
| 337 | C4×C53 | — | 4 | 2 | no | — |
| 338 | C4×C53 | #578 | 1 | 2 | yes | — |
| 339 | C4×C53 | C2×2−1+4 | 1 | 2 | yes | — |
| 340 | Dic53 | — | 2 | 4 | no | — |
| 341 | Dic53 | — | 2 | 4 | no | — |
| 342 | Dic53 | — | 2 | 4 | no | — |
| 343 | Dic53 | — | 4 | 2 | no | — |
| 344 | Dic53 | — | 4 | 2 | no | — |
| 345 | Dic53 | — | 4 | 2 | no | — |
| 346 | #3550 | — | 53 | 1 | no | — |
| 347 | #3502 | — | 53 | 1 | no | — |
| 348 | #3387 | — | 53 | 2 | no | — |
| 349 | #3386 | — | 53 | 4 | no | — |
| 350 | Q8×Q16 | — | 53 | 2 | no | — |
| 351 | #3377 | — | 53 | 4 | no | — |
| 352 | #3375 | — | 53 | 2 | no | — |
| 353 | #3365 | — | 53 | 2 | no | — |
| 354 | #3243 | — | 53 | 4 | no | — |
| 355 | #3237 | — | 53 | 1 | no | — |
| 356 | #3228 | D53 | 1 | 1 | yes | characteristic |
| 357 | #3121 | — | 53 | 4 | no | — |
| 358 | #3112 | — | 53 | 1 | no | — |
| 359 | #3104 | — | 53 | 1 | no | — |
| 360 | #2985 | — | 53 | 1 | no | — |
| 361 | C2×C53 | — | 4 | 1 | no | — |
| 362 | C2×C53 | — | 8 | 2 | no | — |
| 363 | C2×C53 | #3486 | 1 | 1 | yes | characteristic |
| 364 | C2×C53 | C2×#578 | 1 | 1 | yes | characteristic |
| 365 | C2×C53 | #3585 | 1 | 1 | yes | characteristic |
| 366 | #563 | — | 106 | 2 | no | — |
| 367 | #559 | — | 53 | 2 | no | — |
| 368 | Q82 | — | 53 | 2 | no | — |
| 369 | Q82 | — | 53 | 2 | no | — |
| 370 | Q82 | — | 106 | 1 | no | — |
| 371 | #557 | — | 53 | 2 | no | — |
| 372 | #557 | — | 53 | 4 | no | — |
| 373 | #557 | — | 106 | 2 | no | — |
| 374 | #557 | — | 106 | 1 | no | — |
| 375 | #556 | — | 53 | 2 | no | — |
| 376 | #556 | — | 106 | 1 | no | — |
| 377 | D4×Q8 | — | 53 | 2 | no | — |
| 378 | D4×Q8 | — | 106 | 1 | no | — |
| 379 | #544 | — | 53 | 2 | no | — |
| 380 | #544 | — | 106 | 2 | no | — |
| 381 | #542 | — | 53 | 4 | no | — |
| 382 | #542 | — | 106 | 2 | no | — |
| 383 | #536 | — | 106 | 2 | no | — |
| 384 | #533 | — | 53 | 1 | no | — |
| 385 | #533 | — | 53 | 1 | no | — |
| 386 | #533 | — | 106 | 2 | no | — |
| 387 | #533 | C2×D53 | 1 | 1 | yes | characteristic |
| 388 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 389 | #519 | — | 53 | 2 | no | — |
| 390 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 391 | #501 | — | 53 | 2 | no | — |
| 392 | #501 | — | 53 | 4 | no | — |
| 393 | #500 | — | 53 | 4 | no | — |
| 394 | #500 | C2×D53 | 1 | 1 | yes | characteristic |
| 395 | #498 | C2×D53 | 1 | 1 | yes | characteristic |
| 396 | #491 | — | 53 | 2 | no | — |
| 397 | #489 | — | 53 | 4 | no | — |
| 398 | #488 | — | 53 | 4 | no | — |
| 399 | #486 | C2×D53 | 1 | 1 | yes | characteristic |
| 400 | #486 | C2×D53 | 1 | 1 | yes | characteristic |
| 401 | #485 | — | 53 | 4 | no | — |
| 402 | #484 | — | 53 | 2 | no | — |
| 403 | #482 | C2×D53 | 1 | 4 | yes | — |
| 404 | #480 | — | 53 | 2 | no | — |
| 405 | #479 | — | 53 | 4 | no | — |
| 406 | #478 | — | 53 | 4 | no | — |
| 407 | #478 | C2×D53 | 1 | 4 | yes | — |
| 408 | #477 | — | 53 | 2 | no | — |
| 409 | #477 | — | 53 | 2 | no | — |
| 410 | #477 | — | 53 | 4 | no | — |
| 411 | #477 | — | 53 | 4 | no | — |
| 412 | #477 | — | 53 | 2 | no | — |
| 413 | #475 | — | 53 | 2 | no | — |
| 414 | #475 | — | 53 | 4 | no | — |
| 415 | #474 | — | 53 | 4 | no | — |
| 416 | #464 | — | 53 | 4 | no | — |
| 417 | #464 | — | 53 | 4 | no | — |
| 418 | #462 | — | 53 | 2 | no | — |
| 419 | #460 | — | 53 | 2 | no | — |
| 420 | #451 | — | 53 | 2 | no | — |
| 421 | #448 | — | 53 | 2 | no | — |
| 422 | #446 | — | 53 | 4 | no | — |
| 423 | #446 | — | 53 | 2 | no | — |
| 424 | C8×Q8 | — | 53 | 2 | no | — |
| 425 | #441 | — | 53 | 4 | no | — |
| 426 | #440 | — | 53 | 4 | no | — |
| 427 | #440 | — | 53 | 4 | no | — |
| 428 | C4×Q16 | — | 53 | 4 | no | — |
| 429 | C4×Q16 | — | 53 | 2 | no | — |
| 430 | C4×Q16 | — | 53 | 2 | no | — |
| 431 | C4×SD16 | — | 53 | 4 | no | — |
| 432 | #433 | — | 53 | 4 | no | — |
| 433 | #432 | — | 53 | 1 | no | — |
| 434 | #431 | C2×D53 | 1 | 1 | yes | characteristic |
| 435 | C53 | #61854 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 436 | C2×#41 | — | 2 | 1 | no | — |
| 437 | C22×Q8 | — | 53 | 1 | no | — |
| 438 | C22×Q8 | — | 106 | 2 | no | — |
| 439 | C2×Q16 | — | 53 | 2 | no | — |
| 440 | C2×Q16 | — | 53 | 2 | no | — |
| 441 | C2×SD16 | — | 53 | 4 | no | — |
| 442 | C4⋊Q8 | — | 53 | 4 | no | — |
| 443 | C4⋊Q8 | — | 53 | 4 | no | — |
| 444 | C4⋊Q8 | — | 53 | 1 | no | — |
| 445 | C4⋊Q8 | — | 53 | 1 | no | — |
| 446 | C4⋊Q8 | — | 53 | 1 | no | — |
| 447 | C4⋊Q8 | — | 53 | 1 | no | — |
| 448 | C4⋊Q8 | — | 106 | 2 | no | — |
| 449 | C4⋊Q8 | — | 106 | 2 | no | — |
| 450 | C4⋊Q8 | — | 106 | 2 | no | — |
| 451 | C4⋊Q8 | — | 106 | 4 | no | — |
| 452 | C4⋊Q8 | — | 106 | 4 | no | — |
| 453 | C4⋊Q8 | — | 106 | 4 | no | — |
| 454 | C4⋊Q8 | — | 106 | 2 | no | — |
| 455 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 456 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 457 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 458 | #127 | C22×D53 | 1 | 1 | yes | characteristic |
| 459 | #126 | — | 106 | 4 | no | — |
| 460 | #126 | — | 106 | 4 | no | — |
| 461 | #125 | — | 53 | 4 | no | — |
| 462 | #125 | — | 53 | 2 | no | — |
| 463 | #125 | — | 106 | 2 | no | — |
| 464 | #125 | — | 106 | 4 | no | — |
| 465 | #125 | — | 106 | 4 | no | — |
| 466 | #125 | — | 106 | 4 | no | — |
| 467 | #125 | — | 106 | 1 | no | — |
| 468 | #125 | C22×D53 | 1 | 2 | yes | — |
| 469 | #124 | — | 2 | 1 | no | — |
| 470 | #124 | — | 53 | 4 | no | — |
| 471 | #124 | — | 106 | 4 | no | — |
| 472 | #124 | — | 106 | 2 | no | — |
| 473 | #123 | — | 106 | 4 | no | — |
| 474 | #123 | — | 106 | 4 | no | — |
| 475 | C22⋊Q8 | — | 2 | 1 | no | — |
| 476 | C22⋊Q8 | — | 2 | 1 | no | — |
| 477 | C22⋊Q8 | — | 53 | 2 | no | — |
| 478 | C22⋊Q8 | — | 53 | 2 | no | — |
| 479 | C22⋊Q8 | — | 53 | 2 | no | — |
| 480 | C22⋊Q8 | — | 106 | 4 | no | — |
| 481 | C22⋊Q8 | — | 106 | 4 | no | — |
| 482 | C22⋊Q8 | — | 106 | 4 | no | — |
| 483 | C22⋊Q8 | — | 106 | 2 | no | — |
| 484 | C22⋊Q8 | — | 106 | 2 | no | — |
| 485 | C22⋊Q8 | — | 106 | 1 | no | — |
| 486 | #121 | — | 2 | 1 | no | — |
| 487 | #121 | C22×D53 | 1 | 2 | yes | — |
| 488 | C4×Q8 | — | 2 | 1 | no | — |
| 489 | C4×Q8 | — | 2 | 1 | no | — |
| 490 | C4×Q8 | — | 53 | 2 | no | — |
| 491 | C4×Q8 | — | 53 | 2 | no | — |
| 492 | C4×Q8 | — | 53 | 4 | no | — |
| 493 | C4×Q8 | — | 53 | 4 | no | — |
| 494 | C4×Q8 | — | 53 | 4 | no | — |
| 495 | C4×Q8 | — | 53 | 2 | no | — |
| 496 | C4×Q8 | — | 53 | 2 | no | — |
| 497 | C4×Q8 | — | 53 | 2 | no | — |
| 498 | C4×Q8 | — | 106 | 2 | no | — |
| 499 | C4×Q8 | — | 106 | 2 | no | — |
| 500 | C4×Q8 | — | 106 | 4 | no | — |
| 501 | C4×Q8 | — | 106 | 2 | no | — |
| 502 | C4×Q8 | — | 106 | 2 | no | — |
| 503 | C4×Q8 | — | 106 | 2 | no | — |
| 504 | C4×Q8 | — | 106 | 1 | no | — |
| 505 | C4×Q8 | — | 106 | 1 | no | — |
| 506 | C4×Q8 | — | 106 | 1 | no | — |
| 507 | C4×D4 | — | 2 | 1 | no | — |
| 508 | C4×D4 | — | 53 | 4 | no | — |
| 509 | C4×D4 | — | 106 | 2 | no | — |
| 510 | C4×D4 | C22×D53 | 1 | 2 | yes | — |
| 511 | #117 | — | 53 | 2 | no | — |
| 512 | #117 | — | 106 | 4 | no | — |
| 513 | #117 | — | 106 | 2 | no | — |
| 514 | #117 | — | 106 | 1 | no | — |
| 515 | #117 | C22×D53 | 1 | 2 | yes | — |
| 516 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 517 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 518 | C2×C42 | — | 106 | 1 | no | — |
| 519 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 520 | #107 | — | 53 | 2 | no | — |
| 521 | #107 | — | 53 | 2 | no | — |
| 522 | #107 | — | 53 | 4 | no | — |
| 523 | #107 | — | 53 | 4 | no | — |
| 524 | #107 | C22×D53 | 1 | 4 | yes | — |
| 525 | #106 | — | 53 | 4 | no | — |
| 526 | #106 | C22×D53 | 1 | 4 | yes | — |
| 527 | C4⋊C8 | — | 53 | 4 | no | — |
| 528 | C4⋊C8 | — | 53 | 4 | no | — |
| 529 | C4⋊C8 | — | 53 | 2 | no | — |
| 530 | C4⋊C8 | C22×D53 | 1 | 2 | yes | — |
| 531 | #103 | — | 53 | 2 | no | — |
| 532 | #103 | — | 53 | 2 | no | — |
| 533 | #103 | — | 53 | 2 | no | — |
| 534 | #103 | — | 53 | 2 | no | — |
| 535 | #103 | — | 53 | 4 | no | — |
| 536 | #103 | — | 53 | 4 | no | — |
| 537 | #103 | — | 53 | 4 | no | — |
| 538 | #102 | — | 53 | 4 | no | — |
| 539 | #102 | C22×D53 | 1 | 4 | yes | — |
| 540 | #102 | C22×D53 | 1 | 4 | yes | — |
| 541 | C22⋊C8 | — | 53 | 2 | no | — |
| 542 | C22⋊C8 | C22×D53 | 1 | 2 | yes | — |
| 543 | #97 | — | 53 | 4 | no | — |
| 544 | #97 | — | 53 | 2 | no | — |
| 545 | C4×C8 | — | 53 | 4 | no | — |
| 546 | C4×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 547 | C4×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 548 | #41 | — | 8 | 2 | no | — |
| 549 | C2×Q8 | — | 2 | 1 | no | — |
| 550 | C2×Q8 | — | 2 | 1 | no | — |
| 551 | C2×Q8 | — | 2 | 1 | no | — |
| 552 | C2×Q8 | — | 53 | 2 | no | — |
| 553 | C2×Q8 | — | 53 | 2 | no | — |
| 554 | C2×Q8 | — | 53 | 2 | no | — |
| 555 | C2×Q8 | — | 53 | 2 | no | — |
| 556 | C2×Q8 | — | 106 | 4 | no | — |
| 557 | C2×Q8 | — | 106 | 4 | no | — |
| 558 | C2×Q8 | — | 106 | 4 | no | — |
| 559 | C2×Q8 | — | 106 | 1 | no | — |
| 560 | C2×Q8 | — | 106 | 1 | no | — |
| 561 | C2×Q8 | — | 424 | 4 | no | — |
| 562 | C2×D4 | — | 2 | 2 | no | — |
| 563 | C2×D4 | — | 2 | 1 | no | — |
| 564 | C2×D4 | — | 2 | 1 | no | — |
| 565 | C2×D4 | C23×D53 | 1 | 2 | yes | — |
| 566 | C22×C4 | — | 2 | 2 | no | — |
| 567 | C22×C4 | — | 106 | 4 | no | — |
| 568 | C22×C4 | — | 106 | 1 | no | — |
| 569 | C22×C4 | — | 106 | 1 | no | — |
| 570 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 571 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 572 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 573 | Q16 | — | 106 | 4 | no | — |
| 574 | Q16 | — | 106 | 4 | no | — |
| 575 | SD16 | — | 106 | 8 | no | — |
| 576 | C2×C8 | — | 53 | 4 | no | — |
| 577 | C2×C8 | C23×D53 | 1 | 2 | yes | — |
| 578 | C2×C8 | C23×D53 | 1 | 2 | yes | — |
| 579 | C4⋊C4 | — | 2 | 1 | no | — |
| 580 | C4⋊C4 | — | 2 | 2 | no | — |
| 581 | C4⋊C4 | — | 2 | 1 | no | — |
| 582 | C4⋊C4 | — | 2 | 1 | no | — |
| 583 | C4⋊C4 | — | 2 | 2 | no | — |
| 584 | C4⋊C4 | — | 53 | 2 | no | — |
| 585 | C4⋊C4 | — | 53 | 2 | no | — |
| 586 | C4⋊C4 | — | 53 | 2 | no | — |
| 587 | C4⋊C4 | — | 53 | 2 | no | — |
| 588 | C4⋊C4 | — | 53 | 4 | no | — |
| 589 | C4⋊C4 | — | 53 | 4 | no | — |
| 590 | C4⋊C4 | — | 53 | 2 | no | — |
| 591 | C4⋊C4 | — | 53 | 2 | no | — |
| 592 | C4⋊C4 | — | 106 | 4 | no | — |
| 593 | C4⋊C4 | — | 106 | 4 | no | — |
| 594 | C4⋊C4 | — | 106 | 4 | no | — |
| 595 | C4⋊C4 | — | 106 | 4 | no | — |
| 596 | C4⋊C4 | — | 106 | 4 | no | — |
| 597 | C4⋊C4 | — | 106 | 4 | no | — |
| 598 | C4⋊C4 | — | 106 | 4 | no | — |
| 599 | C4⋊C4 | — | 106 | 1 | no | — |
| 600 | C4⋊C4 | — | 106 | 2 | no | — |
| 601 | C4⋊C4 | — | 106 | 2 | no | — |
| 602 | C4⋊C4 | — | 106 | 1 | no | — |
| 603 | C4⋊C4 | — | 106 | 1 | no | — |
| 604 | C4⋊C4 | — | 106 | 1 | no | — |
| 605 | C4⋊C4 | — | 106 | 2 | no | — |
| 606 | C4⋊C4 | — | 106 | 2 | no | — |
| 607 | C4⋊C4 | C23×D53 | 1 | 2 | yes | — |
| 608 | C4⋊C4 | C23×D53 | 1 | 2 | yes | — |
| 609 | C4⋊C4 | C23×D53 | 1 | 2 | yes | — |
| 610 | C22⋊C4 | — | 2 | 2 | no | — |
| 611 | C22⋊C4 | — | 2 | 2 | no | — |
| 612 | C22⋊C4 | — | 2 | 2 | no | — |
| 613 | C22⋊C4 | — | 53 | 4 | no | — |
| 614 | C22⋊C4 | — | 106 | 4 | no | — |
| 615 | C22⋊C4 | — | 106 | 4 | no | — |
| 616 | C22⋊C4 | — | 106 | 4 | no | — |
| 617 | C22⋊C4 | — | 106 | 2 | no | — |
| 618 | C42 | — | 2 | 2 | no | — |
| 619 | C42 | — | 53 | 4 | no | — |
| 620 | C42 | — | 106 | 4 | no | — |
| 621 | C42 | — | 106 | 4 | no | — |
| 622 | C42 | — | 106 | 4 | no | — |
| 623 | C42 | — | 106 | 2 | no | — |
| 624 | C42 | — | 106 | 2 | no | — |
| 625 | C42 | — | 106 | 2 | no | — |
| 626 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 627 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 628 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 629 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 630 | C23 | — | 2 | 2 | no | — |
| 631 | C23 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 632 | Q8 | — | 4 | 2 | no | — |
| 633 | Q8 | — | 8 | 1 | no | — |
| 634 | Q8 | — | 8 | 1 | no | — |
| 635 | Q8 | — | 53 | 4 | no | — |
| 636 | Q8 | — | 106 | 4 | no | — |
| 637 | Q8 | — | 106 | 4 | no | — |
| 638 | Q8 | — | 106 | 2 | no | — |
| 639 | Q8 | — | 106 | 2 | no | — |
| 640 | Q8 | — | 106 | 2 | no | — |
| 641 | Q8 | — | 424 | 4 | no | — |
| 642 | Q8 | — | 424 | 4 | no | — |
| 643 | Q8 | — | 212 | 2 | no | — |
| 644 | Q8 | — | 212 | 2 | no | — |
| 645 | D4 | — | 2 | 4 | no | — |
| 646 | D4 | — | 4 | 2 | no | — |
| 647 | D4 | — | 8 | 1 | no | — |
| 648 | D4 | — | 8 | 2 | no | — |
| 649 | C2×C4 | — | 2 | 2 | no | — |
| 650 | C2×C4 | — | 2 | 2 | no | — |
| 651 | C2×C4 | — | 2 | 2 | no | — |
| 652 | C2×C4 | — | 2 | 2 | no | — |
| 653 | C2×C4 | — | 2 | 2 | no | — |
| 654 | C2×C4 | — | 4 | 1 | no | — |
| 655 | C2×C4 | — | 4 | 4 | no | — |
| 656 | C2×C4 | — | 53 | 4 | no | — |
| 657 | C2×C4 | — | 53 | 4 | no | — |
| 658 | C2×C4 | — | 106 | 4 | no | — |
| 659 | C2×C4 | — | 106 | 2 | no | — |
| 660 | C2×C4 | — | 106 | 2 | no | — |
| 661 | C2×C4 | — | 106 | 2 | no | — |
| 662 | C2×C4 | — | 106 | 2 | no | — |
| 663 | C2×C4 | — | 424 | 4 | no | — |
| 664 | C2×C4 | — | 424 | 1 | no | — |
| 665 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 666 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 667 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 668 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 669 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 670 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 671 | C8 | — | 2 | 2 | no | — |
| 672 | C8 | — | 2 | 2 | no | — |
| 673 | C8 | — | 106 | 4 | no | — |
| 674 | C22 | — | 2 | 1 | no | — |
| 675 | C22 | — | 2 | 1 | no | — |
| 676 | C22 | — | 2 | 1 | no | — |
| 677 | C22 | — | 4 | 2 | no | — |
| 678 | C22 | — | 4 | 2 | no | — |
| 679 | C22 | — | 4 | 2 | no | — |
| 680 | C22 | C22×D4×D53 | 1 | 1 | yes | characteristic |
| 681 | C4 | — | 2 | 1 | no | — |
| 682 | C4 | — | 2 | 1 | no | — |
| 683 | C4 | — | 2 | 1 | no | — |
| 684 | C4 | — | 2 | 1 | no | — |
| 685 | C4 | — | 4 | 2 | no | — |
| 686 | C4 | — | 4 | 2 | no | — |
| 687 | C4 | — | 4 | 2 | no | — |
| 688 | C4 | — | 106 | 4 | no | — |
| 689 | C4 | — | 106 | 4 | no | — |
| 690 | C4 | — | 106 | 4 | no | — |
| 691 | C4 | — | 212 | 2 | no | — |
| 692 | C4 | — | 212 | 2 | no | — |
| 693 | C4 | — | 212 | 2 | no | — |
| 694 | C4 | #16811437 | 1 | 2 | yes | — |
| 695 | C4 | 2−1+4×D53 | 1 | 2 | yes | — |
| 696 | C2 | — | 4 | 1 | no | — |
| 697 | C2 | — | 8 | 2 | no | — |
| 698 | C2 | #20288364 | 1 | 1 | yes | characteristic |
| 699 | C2 | C2×#16811437 | 1 | 1 | yes | characteristic |
| 700 | C2 | #20289491 | 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