Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1996 conjugacy classes of subgroups.
The subgroup lattice has 650 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20288499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20288342 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×#11719924 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20287351 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20287350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20287309 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #20287307 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #20287044 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #20287039 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #20286095 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #20285844 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #20284773 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #20284525 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #20283846 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | Q8×SD16×C53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#13133265 | — | 2 | 1 | no | — |
| 17 | #16811339 | — | 2 | 3 | no | — |
| 18 | #16811339 | C22 | 1 | 3 | yes | — |
| 19 | #16811295 | — | 2 | 1 | no | — |
| 20 | #16811295 | C22 | 1 | 3 | yes | — |
| 21 | #16811295 | C22 | 1 | 1 | yes | characteristic |
| 22 | Q8×D212 | C22 | 1 | 1 | yes | characteristic |
| 23 | Q8×C22⋊D53 | — | 2 | 1 | no | — |
| 24 | #16811278 | C22 | 1 | 3 | yes | — |
| 25 | #16811276 | C22 | 1 | 3 | yes | — |
| 26 | #16811275 | — | 2 | 3 | no | — |
| 27 | #16811196 | — | 2 | 3 | no | — |
| 28 | #16811174 | — | 2 | 3 | no | — |
| 29 | #16811174 | C22 | 1 | 3 | yes | — |
| 30 | #16811170 | C22 | 1 | 3 | yes | — |
| 31 | C4⋊Q8×D53 | C22 | 1 | 3 | yes | — |
| 32 | C4×#11719949 | — | 2 | 1 | no | — |
| 33 | C4×#11719949 | C22 | 1 | 3 | yes | — |
| 34 | C4×#11719949 | C22 | 1 | 1 | yes | characteristic |
| 35 | #16811019 | C22 | 1 | 3 | yes | — |
| 36 | #16810971 | C22 | 1 | 3 | yes | — |
| 37 | #16810970 | C22 | 1 | 3 | yes | — |
| 38 | #16810949 | C22 | 1 | 3 | yes | — |
| 39 | #16810945 | C22 | 1 | 3 | yes | — |
| 40 | #16810943 | C22 | 1 | 6 | yes | — |
| 41 | #16810943 | C22 | 1 | 6 | yes | — |
| 42 | #16810916 | C22 | 1 | 3 | yes | — |
| 43 | #16810912 | C22 | 1 | 3 | yes | — |
| 44 | #16810912 | C22 | 1 | 6 | yes | — |
| 45 | #16810910 | C22 | 1 | 3 | yes | — |
| 46 | #16810908 | C22 | 1 | 3 | yes | — |
| 47 | #16810904 | C22 | 1 | 3 | yes | — |
| 48 | #16810900 | C22 | 1 | 3 | yes | — |
| 49 | #16810877 | C22 | 1 | 6 | yes | — |
| 50 | #16810875 | C22 | 1 | 6 | yes | — |
| 51 | #16810821 | C22 | 1 | 1 | yes | characteristic |
| 52 | #16810819 | C22 | 1 | 3 | yes | — |
| 53 | #16810818 | C22 | 1 | 3 | yes | — |
| 54 | #16810817 | C22 | 1 | 3 | yes | — |
| 55 | #16810771 | C22 | 1 | 3 | yes | — |
| 56 | #16810767 | C22 | 1 | 3 | yes | — |
| 57 | Q8×#88322 | C22 | 1 | 1 | yes | characteristic |
| 58 | C4×#11719924 | C22 | 1 | 3 | yes | — |
| 59 | C4×D424 | C22 | 1 | 3 | yes | — |
| 60 | C4×#11719922 | C22 | 1 | 3 | yes | — |
| 61 | #16810702 | C22 | 1 | 3 | yes | — |
| 62 | #16810700 | C22 | 1 | 3 | yes | — |
| 63 | #16810674 | C22 | 1 | 3 | yes | — |
| 64 | #16810662 | C22 | 1 | 6 | yes | — |
| 65 | #16810645 | C22 | 1 | 3 | yes | — |
| 66 | #16810623 | C22 | 1 | 6 | yes | — |
| 67 | Q82×C53 | C22 | 1 | 1 | yes | characteristic |
| 68 | D4×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 69 | C53×#498 | C22 | 1 | 3 | yes | — |
| 70 | C53×#476 | C22 | 1 | 3 | yes | — |
| 71 | C53×#475 | C22 | 1 | 3 | yes | — |
| 72 | C8×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 73 | C4×SD16×C53 | C22 | 1 | 3 | yes | — |
| 74 | #13133265 | — | 4 | 8 | no | — |
| 75 | C2×#11719949 | — | 2 | 1 | no | — |
| 76 | C2×#11719949 | — | 2 | 3 | no | — |
| 77 | C2×#11719949 | — | 2 | 3 | no | — |
| 78 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 79 | C2×#11719949 | C23 | 1 | 3 | yes | — |
| 80 | C2×#11719945 | — | 2 | 3 | no | — |
| 81 | C2×#11719945 | — | 2 | 3 | no | — |
| 82 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 83 | C2×Q8×D53 | — | 2 | 3 | no | — |
| 84 | C2×#11719924 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×D424 | C23 | 1 | 3 | yes | — |
| 86 | C2×#11719922 | C23 | 1 | 3 | yes | — |
| 87 | C2×#11719912 | C23 | 1 | 6 | yes | — |
| 88 | #13133217 | C23 | 1 | 3 | yes | — |
| 89 | #13133216 | — | 2 | 3 | no | — |
| 90 | #13133216 | C23 | 1 | 3 | yes | — |
| 91 | #13133215 | — | 2 | 3 | no | — |
| 92 | #13133214 | — | 2 | 3 | no | — |
| 93 | #13133214 | C23 | 1 | 3 | yes | — |
| 94 | #13133213 | C23 | 1 | 1 | yes | characteristic |
| 95 | #13133206 | — | 2 | 6 | no | — |
| 96 | #13133206 | — | 2 | 3 | no | — |
| 97 | #13133203 | — | 2 | 3 | no | — |
| 98 | #13133202 | — | 2 | 6 | no | — |
| 99 | #13133199 | — | 2 | 6 | no | — |
| 100 | #13133197 | — | 2 | 3 | no | — |
| 101 | #13133196 | — | 2 | 3 | no | — |
| 102 | #13133193 | — | 2 | 3 | no | — |
| 103 | #13133192 | — | 2 | 3 | no | — |
| 104 | #13133192 | — | 2 | 6 | no | — |
| 105 | #13133192 | — | 2 | 3 | no | — |
| 106 | #13133192 | — | 2 | 3 | no | — |
| 107 | #13133192 | C23 | 1 | 3 | yes | — |
| 108 | #13133192 | C23 | 1 | 6 | yes | — |
| 109 | #13133190 | — | 2 | 3 | no | — |
| 110 | #13133188 | C23 | 1 | 3 | yes | — |
| 111 | Q8×Dic53 | D4 | 1 | 1 | yes | characteristic |
| 112 | Q8×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 113 | C4×D212 | — | 2 | 3 | no | — |
| 114 | C4×D212 | — | 2 | 3 | no | — |
| 115 | C4×D212 | C23 | 1 | 3 | yes | — |
| 116 | C4×D212 | C23 | 1 | 3 | yes | — |
| 117 | C4×D212 | C23 | 1 | 3 | yes | — |
| 118 | #13133179 | — | 2 | 3 | no | — |
| 119 | #13133179 | — | 2 | 3 | no | — |
| 120 | #13133179 | D4 | 1 | 3 | yes | — |
| 121 | #13133179 | C23 | 1 | 3 | yes | — |
| 122 | C4×C22⋊D53 | — | 2 | 3 | no | — |
| 123 | #13133175 | — | 2 | 3 | no | — |
| 124 | #13133175 | — | 2 | 3 | no | — |
| 125 | #13133175 | D4 | 1 | 3 | yes | — |
| 126 | #13133175 | C23 | 1 | 3 | yes | — |
| 127 | C4⋊C4×D53 | — | 2 | 3 | no | — |
| 128 | C4⋊C4×D53 | C23 | 1 | 6 | yes | — |
| 129 | C42×D53 | — | 2 | 3 | no | — |
| 130 | C42×D53 | C23 | 1 | 3 | yes | — |
| 131 | #13133151 | C23 | 1 | 3 | yes | — |
| 132 | #13133150 | C23 | 1 | 3 | yes | — |
| 133 | #13133148 | C23 | 1 | 3 | yes | — |
| 134 | #13133148 | C23 | 1 | 6 | yes | — |
| 135 | C4⋊#88322 | C23 | 1 | 3 | yes | — |
| 136 | #13133146 | C23 | 1 | 3 | yes | — |
| 137 | #13133146 | C23 | 1 | 1 | yes | characteristic |
| 138 | #13133141 | C23 | 1 | 3 | yes | — |
| 139 | #13133139 | C23 | 1 | 3 | yes | — |
| 140 | #13133139 | C23 | 1 | 6 | yes | — |
| 141 | #13133139 | C23 | 1 | 1 | yes | characteristic |
| 142 | #13133138 | C23 | 1 | 1 | yes | characteristic |
| 143 | #13133137 | C23 | 1 | 3 | yes | — |
| 144 | #13133137 | C23 | 1 | 3 | yes | — |
| 145 | #13133137 | C23 | 1 | 6 | yes | — |
| 146 | #13133129 | C23 | 1 | 3 | yes | — |
| 147 | #13133129 | C23 | 1 | 3 | yes | — |
| 148 | C4×#88322 | C23 | 1 | 3 | yes | — |
| 149 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 150 | C2×SD16×C53 | C23 | 1 | 1 | yes | characteristic |
| 151 | C4⋊Q8×C53 | — | 2 | 3 | no | — |
| 152 | C4⋊Q8×C53 | C23 | 1 | 3 | yes | — |
| 153 | C4⋊Q8×C53 | C23 | 1 | 3 | yes | — |
| 154 | C22⋊Q8×C53 | — | 2 | 3 | no | — |
| 155 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 156 | C4×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 157 | C4×Q8×C53 | C23 | 1 | 3 | yes | — |
| 158 | C4×D4×C53 | C23 | 1 | 3 | yes | — |
| 159 | #106×C53 | C23 | 1 | 3 | yes | — |
| 160 | #106×C53 | C23 | 1 | 6 | yes | — |
| 161 | C4⋊C8×C53 | C23 | 1 | 3 | yes | — |
| 162 | #103×C53 | C23 | 1 | 3 | yes | — |
| 163 | #102×C53 | C23 | 1 | 3 | yes | — |
| 164 | C4×C8×C53 | C23 | 1 | 3 | yes | — |
| 165 | C2×Q8×C53 | — | 2 | 3 | no | — |
| 166 | C2×Q8×C53 | — | 2 | 3 | no | — |
| 167 | C2×Q8×C53 | — | 4 | 4 | no | — |
| 168 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×Q8×C53 | C24 | 1 | 1 | yes | characteristic |
| 170 | C2×D4×C53 | C24 | 1 | 1 | yes | characteristic |
| 171 | C22×C4×C53 | — | 2 | 3 | no | — |
| 172 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 173 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 174 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 175 | #11719949 | — | 2 | 4 | no | — |
| 176 | #11719949 | — | 2 | 6 | no | — |
| 177 | #11719949 | — | 4 | 3 | no | — |
| 178 | #11719949 | — | 4 | 12 | no | — |
| 179 | #11719949 | — | 4 | 4 | no | — |
| 180 | #11719949 | — | 8 | 6 | no | — |
| 181 | Q8×D53 | — | 4 | 12 | no | — |
| 182 | Q8×D53 | — | 4 | 4 | no | — |
| 183 | #11719945 | — | 4 | 12 | no | — |
| 184 | #11719945 | — | 4 | 12 | no | — |
| 185 | C2×D212 | — | 2 | 3 | no | — |
| 186 | C2×D212 | — | 2 | 3 | no | — |
| 187 | C2×D212 | — | 2 | 3 | no | — |
| 188 | C2×D212 | — | 2 | 6 | no | — |
| 189 | C2×D212 | — | 2 | 3 | no | — |
| 190 | C2×D212 | C2×D4 | 1 | 3 | yes | — |
| 191 | C2×D212 | C24 | 1 | 3 | yes | — |
| 192 | C2×D212 | C24 | 1 | 1 | yes | characteristic |
| 193 | C2×C4×D53 | — | 2 | 6 | no | — |
| 194 | C2×C4×D53 | — | 2 | 3 | no | — |
| 195 | C2×C4×D53 | — | 2 | 3 | no | — |
| 196 | C2×C4×D53 | — | 2 | 3 | no | — |
| 197 | C2×C4×D53 | — | 2 | 3 | no | — |
| 198 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 199 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 200 | C2×C4×D53 | C24 | 1 | 3 | yes | — |
| 201 | C2×Dic106 | — | 2 | 3 | no | — |
| 202 | C2×Dic106 | — | 2 | 3 | no | — |
| 203 | SD16×C53 | — | 2 | 2 | no | — |
| 204 | C2×C8×C53 | C24 | 1 | 1 | yes | characteristic |
| 205 | C2×C8×C53 | C24 | 1 | 3 | yes | — |
| 206 | C4⋊C4×C53 | — | 2 | 3 | no | — |
| 207 | C4⋊C4×C53 | — | 2 | 3 | no | — |
| 208 | C4⋊C4×C53 | — | 2 | 3 | no | — |
| 209 | C4⋊C4×C53 | C2×D4 | 1 | 3 | yes | — |
| 210 | C4⋊C4×C53 | C24 | 1 | 3 | yes | — |
| 211 | C4⋊C4×C53 | C24 | 1 | 3 | yes | — |
| 212 | C22⋊C4×C53 | — | 2 | 3 | no | — |
| 213 | C42×C53 | — | 2 | 3 | no | — |
| 214 | C42×C53 | C24 | 1 | 3 | yes | — |
| 215 | C22⋊Dic53 | — | 2 | 3 | no | — |
| 216 | #11719924 | — | 2 | 2 | no | — |
| 217 | #11719922 | — | 4 | 3 | no | — |
| 218 | #11719921 | — | 2 | 3 | no | — |
| 219 | #11719921 | — | 2 | 3 | no | — |
| 220 | #11719921 | — | 2 | 3 | no | — |
| 221 | #11719921 | — | 2 | 6 | no | — |
| 222 | #11719921 | — | 2 | 3 | no | — |
| 223 | #11719921 | — | 2 | 3 | no | — |
| 224 | #11719921 | C2×D4 | 1 | 6 | yes | — |
| 225 | C4⋊Dic53 | — | 2 | 3 | no | — |
| 226 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 227 | C4⋊Dic53 | C2×D4 | 1 | 3 | yes | — |
| 228 | C4⋊Dic53 | C24 | 1 | 1 | yes | characteristic |
| 229 | C4⋊Dic53 | C24 | 1 | 3 | yes | — |
| 230 | #11719919 | — | 2 | 3 | no | — |
| 231 | #11719919 | — | 2 | 6 | no | — |
| 232 | C4×Dic53 | — | 2 | 1 | no | — |
| 233 | C4×Dic53 | — | 2 | 3 | no | — |
| 234 | C4×Dic53 | C2×D4 | 1 | 3 | yes | — |
| 235 | C4×Dic53 | C2×D4 | 1 | 3 | yes | — |
| 236 | C4×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 237 | C2×#88322 | C24 | 1 | 1 | yes | characteristic |
| 238 | C2×#88322 | C24 | 1 | 3 | yes | — |
| 239 | D424 | — | 4 | 3 | no | — |
| 240 | #11719912 | — | 4 | 6 | no | — |
| 241 | C23×C53 | — | 2 | 1 | no | — |
| 242 | C22×D53 | — | 2 | 3 | no | — |
| 243 | C22×D53 | — | 2 | 1 | no | — |
| 244 | C22×D53 | C22×D4 | 1 | 3 | yes | — |
| 245 | Q8×C53 | — | 2 | 1 | no | — |
| 246 | Q8×C53 | — | 4 | 6 | no | — |
| 247 | Q8×C53 | — | 8 | 3 | no | — |
| 248 | Q8×C53 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 249 | Q8×C53 | 2−1+4 | 1 | 2 | yes | complemented |
| 250 | D4×C53 | — | 2 | 1 | no | — |
| 251 | D4×C53 | — | 2 | 1 | no | — |
| 252 | C2×C4×C53 | — | 2 | 1 | no | — |
| 253 | C2×C4×C53 | — | 2 | 3 | no | — |
| 254 | C2×C4×C53 | — | 2 | 3 | no | — |
| 255 | C2×C4×C53 | — | 4 | 6 | no | — |
| 256 | C2×C4×C53 | C22×D4 | 1 | 3 | yes | — |
| 257 | C2×C4×C53 | C22×D4 | 1 | 3 | yes | — |
| 258 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 259 | C22⋊D53 | — | 4 | 2 | no | — |
| 260 | C22⋊D53 | — | 4 | 6 | no | — |
| 261 | C22⋊D53 | — | 4 | 2 | no | — |
| 262 | C2×Dic53 | — | 2 | 3 | no | — |
| 263 | C2×Dic53 | — | 2 | 1 | no | — |
| 264 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×Dic53 | C22×D4 | 1 | 3 | yes | — |
| 266 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 267 | D212 | — | 2 | 6 | no | — |
| 268 | D212 | — | 2 | 3 | no | — |
| 269 | D212 | — | 2 | 1 | no | — |
| 270 | D212 | — | 2 | 3 | no | — |
| 271 | D212 | — | 2 | 1 | no | — |
| 272 | D212 | — | 4 | 6 | no | — |
| 273 | D212 | — | 4 | 6 | no | — |
| 274 | D212 | — | 4 | 6 | no | — |
| 275 | D212 | — | 8 | 3 | no | — |
| 276 | D212 | — | 8 | 6 | no | — |
| 277 | C4×D53 | — | 2 | 6 | no | — |
| 278 | C4×D53 | — | 2 | 3 | no | — |
| 279 | C4×D53 | — | 2 | 3 | no | — |
| 280 | C4×D53 | — | 2 | 6 | no | — |
| 281 | C4×D53 | — | 4 | 6 | no | — |
| 282 | C4×D53 | — | 4 | 12 | no | — |
| 283 | C4×D53 | — | 4 | 6 | no | — |
| 284 | C4×D53 | — | 4 | 6 | no | — |
| 285 | C4×D53 | — | 4 | 6 | no | — |
| 286 | Dic106 | — | 4 | 6 | no | — |
| 287 | Dic106 | — | 4 | 6 | no | — |
| 288 | C8×C53 | — | 2 | 1 | no | — |
| 289 | C8×C53 | — | 2 | 3 | no | — |
| 290 | #88322 | — | 2 | 1 | no | — |
| 291 | #88322 | — | 2 | 3 | no | — |
| 292 | #62150 | — | 53 | 1 | no | maximal, Sylow |
| 293 | C22×C53 | — | 4 | 1 | no | — |
| 294 | C22×C53 | — | 4 | 1 | no | — |
| 295 | C22×C53 | — | 4 | 1 | no | — |
| 296 | C22×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 297 | C2×D53 | — | 2 | 3 | no | — |
| 298 | C2×D53 | — | 2 | 3 | no | — |
| 299 | C2×D53 | — | 2 | 3 | no | — |
| 300 | C2×D53 | — | 4 | 3 | no | — |
| 301 | C2×D53 | — | 4 | 1 | no | — |
| 302 | C2×D53 | — | 4 | 1 | no | — |
| 303 | C2×D53 | — | 4 | 3 | no | — |
| 304 | C2×D53 | — | 4 | 3 | no | — |
| 305 | C2×D53 | — | 4 | 1 | no | — |
| 306 | C4×C53 | — | 2 | 2 | no | — |
| 307 | C4×C53 | — | 2 | 3 | no | — |
| 308 | C4×C53 | — | 4 | 3 | no | — |
| 309 | C4×C53 | — | 4 | 3 | no | — |
| 310 | C4×C53 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 311 | C4×C53 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 312 | C4×C53 | #585 | 1 | 1 | yes | characteristic |
| 313 | Dic53 | — | 2 | 3 | no | — |
| 314 | Dic53 | — | 2 | 1 | no | — |
| 315 | Dic53 | — | 4 | 3 | no | — |
| 316 | Dic53 | — | 4 | 1 | no | — |
| 317 | Dic53 | #577 | 1 | 2 | yes | — |
| 318 | #3499 | — | 53 | 1 | no | — |
| 319 | #3483 | — | 53 | 1 | no | — |
| 320 | Q8×SD16 | — | 53 | 1 | no | — |
| 321 | Q8×SD16 | D53 | 1 | 1 | yes | characteristic, complemented |
| 322 | #3358 | — | 53 | 1 | no | — |
| 323 | #3358 | — | 53 | 1 | no | — |
| 324 | #3354 | — | 53 | 3 | no | — |
| 325 | #3354 | — | 53 | 3 | no | — |
| 326 | #3332 | — | 53 | 3 | no | — |
| 327 | #3332 | — | 53 | 3 | no | — |
| 328 | #3253 | — | 53 | 3 | no | — |
| 329 | #3227 | — | 53 | 3 | no | — |
| 330 | #3106 | — | 53 | 3 | no | — |
| 331 | #3079 | — | 53 | 3 | no | — |
| 332 | #2991 | — | 53 | 1 | no | — |
| 333 | C2×C53 | — | 8 | 1 | no | — |
| 334 | C2×C53 | #3489 | 1 | 1 | yes | characteristic |
| 335 | C2×C53 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 336 | C2×C53 | C2×#577 | 1 | 1 | yes | characteristic |
| 337 | D53 | — | 4 | 3 | no | — |
| 338 | D53 | — | 8 | 3 | no | — |
| 339 | D53 | — | 8 | 1 | no | — |
| 340 | C2×2−1+4 | — | 106 | 1 | no | — |
| 341 | Q82 | C2×D53 | 1 | 1 | yes | characteristic |
| 342 | #555 | — | 53 | 3 | no | — |
| 343 | #555 | — | 106 | 3 | no | — |
| 344 | #550 | — | 53 | 1 | no | — |
| 345 | #550 | — | 53 | 3 | no | — |
| 346 | #550 | — | 106 | 1 | no | — |
| 347 | D4×Q8 | — | 53 | 1 | no | — |
| 348 | D4×Q8 | — | 106 | 1 | no | — |
| 349 | D4×Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 350 | #547 | — | 53 | 3 | no | — |
| 351 | #547 | — | 53 | 3 | no | — |
| 352 | #547 | — | 106 | 3 | no | — |
| 353 | #536 | — | 106 | 3 | no | — |
| 354 | #532 | — | 53 | 3 | no | — |
| 355 | #532 | — | 53 | 3 | no | — |
| 356 | #532 | — | 106 | 3 | no | — |
| 357 | C2×C4⋊Q8 | — | 53 | 3 | no | — |
| 358 | C4×#41 | — | 53 | 1 | no | — |
| 359 | C4×#41 | — | 53 | 3 | no | — |
| 360 | C4×#41 | — | 106 | 1 | no | — |
| 361 | #498 | — | 53 | 3 | no | — |
| 362 | #498 | C2×D53 | 1 | 3 | yes | — |
| 363 | #486 | — | 53 | 3 | no | — |
| 364 | #486 | — | 53 | 3 | no | — |
| 365 | #482 | — | 53 | 3 | no | — |
| 366 | #482 | — | 53 | 3 | no | — |
| 367 | #481 | — | 53 | 6 | no | — |
| 368 | #481 | — | 53 | 6 | no | — |
| 369 | #477 | — | 53 | 3 | no | — |
| 370 | #476 | — | 53 | 3 | no | — |
| 371 | #476 | — | 53 | 6 | no | — |
| 372 | #476 | — | 53 | 3 | no | — |
| 373 | #476 | C2×D53 | 1 | 3 | yes | — |
| 374 | #475 | — | 53 | 3 | no | — |
| 375 | #475 | C2×D53 | 1 | 3 | yes | — |
| 376 | #474 | — | 53 | 3 | no | — |
| 377 | #474 | — | 53 | 3 | no | — |
| 378 | #469 | — | 53 | 6 | no | — |
| 379 | #469 | — | 53 | 6 | no | — |
| 380 | #460 | — | 53 | 1 | no | — |
| 381 | #459 | — | 53 | 3 | no | — |
| 382 | #459 | — | 53 | 3 | no | — |
| 383 | #459 | — | 53 | 3 | no | — |
| 384 | #449 | — | 53 | 3 | no | — |
| 385 | #449 | — | 53 | 3 | no | — |
| 386 | C8×Q8 | — | 53 | 1 | no | — |
| 387 | C8×Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 388 | C4×SD16 | — | 53 | 3 | no | — |
| 389 | C4×SD16 | C2×D53 | 1 | 3 | yes | — |
| 390 | C4×D8 | — | 53 | 3 | no | — |
| 391 | C4×D8 | — | 53 | 3 | no | — |
| 392 | #436 | — | 53 | 3 | no | — |
| 393 | #436 | — | 53 | 3 | no | — |
| 394 | #431 | — | 53 | 3 | no | — |
| 395 | #428 | — | 53 | 6 | no | — |
| 396 | #423 | — | 53 | 3 | no | — |
| 397 | #417 | — | 53 | 6 | no | — |
| 398 | C53 | #62150 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 399 | 2−1+4 | — | 212 | 8 | no | — |
| 400 | C2×#41 | — | 53 | 1 | no | — |
| 401 | C2×#41 | — | 53 | 3 | no | — |
| 402 | C2×#41 | — | 106 | 3 | no | — |
| 403 | C2×#41 | — | 106 | 3 | no | — |
| 404 | C2×#41 | — | 106 | 3 | no | — |
| 405 | C2×#41 | — | 106 | 3 | no | — |
| 406 | C2×#41 | — | 106 | 1 | no | — |
| 407 | C22×Q8 | — | 2 | 1 | no | — |
| 408 | C22×Q8 | — | 106 | 3 | no | — |
| 409 | C22×Q8 | — | 106 | 1 | no | — |
| 410 | C2×SD16 | — | 53 | 1 | no | — |
| 411 | C2×SD16 | C22×D53 | 1 | 1 | yes | characteristic |
| 412 | C2×D8 | — | 53 | 3 | no | — |
| 413 | C2×D8 | — | 53 | 3 | no | — |
| 414 | C2×M16 | — | 53 | 6 | no | — |
| 415 | C4⋊Q8 | — | 2 | 3 | no | — |
| 416 | C4⋊Q8 | — | 53 | 3 | no | — |
| 417 | C4⋊Q8 | — | 53 | 3 | no | — |
| 418 | C4⋊Q8 | — | 106 | 3 | no | — |
| 419 | C4⋊Q8 | — | 106 | 3 | no | — |
| 420 | C4⋊Q8 | C22×D53 | 1 | 3 | yes | — |
| 421 | C4⋊Q8 | C22×D53 | 1 | 3 | yes | — |
| 422 | #127 | — | 53 | 1 | no | — |
| 423 | #127 | — | 53 | 3 | no | — |
| 424 | #127 | — | 106 | 3 | no | — |
| 425 | #124 | — | 106 | 3 | no | — |
| 426 | #124 | — | 106 | 3 | no | — |
| 427 | #124 | — | 106 | 6 | no | — |
| 428 | #123 | — | 106 | 6 | no | — |
| 429 | #123 | — | 106 | 6 | no | — |
| 430 | C22⋊Q8 | — | 2 | 3 | no | — |
| 431 | C22⋊Q8 | — | 106 | 3 | no | — |
| 432 | C22⋊Q8 | — | 106 | 3 | no | — |
| 433 | C22⋊Q8 | — | 106 | 3 | no | — |
| 434 | #121 | — | 53 | 3 | no | — |
| 435 | #121 | — | 53 | 3 | no | — |
| 436 | #121 | — | 53 | 6 | no | — |
| 437 | #121 | — | 106 | 3 | no | — |
| 438 | #121 | — | 106 | 6 | no | — |
| 439 | #121 | — | 106 | 3 | no | — |
| 440 | #121 | — | 106 | 3 | no | — |
| 441 | #121 | — | 106 | 3 | no | — |
| 442 | C4×Q8 | — | 2 | 1 | no | — |
| 443 | C4×Q8 | — | 53 | 1 | no | — |
| 444 | C4×Q8 | — | 53 | 1 | no | — |
| 445 | C4×Q8 | C22×D53 | 1 | 3 | yes | — |
| 446 | C4×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 447 | C4×D4 | — | 53 | 3 | no | — |
| 448 | C4×D4 | — | 53 | 3 | no | — |
| 449 | C4×D4 | — | 53 | 3 | no | — |
| 450 | C4×D4 | — | 53 | 3 | no | — |
| 451 | C4×D4 | — | 53 | 3 | no | — |
| 452 | C4×D4 | — | 106 | 3 | no | — |
| 453 | C4×D4 | — | 106 | 3 | no | — |
| 454 | C4×D4 | — | 106 | 3 | no | — |
| 455 | C4×D4 | — | 106 | 3 | no | — |
| 456 | C4×D4 | — | 106 | 3 | no | — |
| 457 | C4×D4 | C22×D53 | 1 | 3 | yes | — |
| 458 | #117 | — | 53 | 3 | no | — |
| 459 | #117 | — | 53 | 3 | no | — |
| 460 | #117 | — | 106 | 3 | no | — |
| 461 | #117 | — | 106 | 3 | no | — |
| 462 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 463 | C2×C4⋊C4 | — | 106 | 3 | no | — |
| 464 | C2×C42 | — | 53 | 3 | no | — |
| 465 | C2×C42 | — | 106 | 3 | no | — |
| 466 | #107 | — | 53 | 3 | no | — |
| 467 | #107 | — | 53 | 3 | no | — |
| 468 | #106 | — | 53 | 6 | no | — |
| 469 | #106 | — | 53 | 3 | no | — |
| 470 | #106 | C22×D53 | 1 | 6 | yes | — |
| 471 | #106 | C22×D53 | 1 | 3 | yes | — |
| 472 | C4⋊C8 | — | 53 | 3 | no | — |
| 473 | C4⋊C8 | — | 53 | 1 | no | — |
| 474 | C4⋊C8 | — | 53 | 3 | no | — |
| 475 | C4⋊C8 | C22×D53 | 1 | 3 | yes | — |
| 476 | #103 | — | 53 | 3 | no | — |
| 477 | #103 | C22×D53 | 1 | 3 | yes | — |
| 478 | #102 | — | 53 | 1 | no | — |
| 479 | #102 | — | 53 | 6 | no | — |
| 480 | #102 | — | 53 | 1 | no | — |
| 481 | #102 | — | 53 | 3 | no | — |
| 482 | #102 | — | 53 | 6 | no | — |
| 483 | #102 | — | 53 | 3 | no | — |
| 484 | #102 | — | 53 | 3 | no | — |
| 485 | #102 | C22×D53 | 1 | 3 | yes | — |
| 486 | C22⋊C8 | — | 53 | 3 | no | — |
| 487 | C22⋊C8 | — | 53 | 3 | no | — |
| 488 | C4×C8 | — | 53 | 3 | no | — |
| 489 | C4×C8 | C22×D53 | 1 | 3 | yes | — |
| 490 | #41 | — | 106 | 4 | no | — |
| 491 | #41 | — | 106 | 6 | no | — |
| 492 | #41 | — | 424 | 6 | no | — |
| 493 | #41 | — | 212 | 12 | no | — |
| 494 | #41 | — | 212 | 12 | no | — |
| 495 | #41 | — | 212 | 3 | no | — |
| 496 | #41 | — | 212 | 12 | no | — |
| 497 | #41 | — | 212 | 4 | no | — |
| 498 | C2×Q8 | — | 2 | 3 | no | — |
| 499 | C2×Q8 | — | 2 | 3 | no | — |
| 500 | C2×Q8 | — | 4 | 4 | no | — |
| 501 | C2×Q8 | — | 106 | 3 | no | — |
| 502 | C2×Q8 | — | 106 | 3 | no | — |
| 503 | C2×Q8 | — | 212 | 12 | no | — |
| 504 | C2×Q8 | — | 212 | 4 | no | — |
| 505 | C2×Q8 | D4×D53 | 1 | 1 | yes | characteristic |
| 506 | C2×Q8 | C23×D53 | 1 | 1 | yes | characteristic |
| 507 | C2×D4 | — | 53 | 3 | no | — |
| 508 | C2×D4 | — | 53 | 3 | no | — |
| 509 | C2×D4 | — | 53 | 1 | no | — |
| 510 | C2×D4 | — | 106 | 6 | no | — |
| 511 | C2×D4 | — | 106 | 3 | no | — |
| 512 | C2×D4 | — | 106 | 3 | no | — |
| 513 | C2×D4 | — | 106 | 1 | no | — |
| 514 | C2×D4 | — | 106 | 1 | no | — |
| 515 | C2×D4 | — | 106 | 3 | no | — |
| 516 | C2×D4 | — | 106 | 3 | no | — |
| 517 | C2×D4 | — | 106 | 3 | no | — |
| 518 | C2×D4 | C23×D53 | 1 | 1 | yes | characteristic |
| 519 | C22×C4 | — | 2 | 3 | no | — |
| 520 | C22×C4 | — | 53 | 3 | no | — |
| 521 | C22×C4 | — | 53 | 3 | no | — |
| 522 | C22×C4 | — | 53 | 3 | no | — |
| 523 | C22×C4 | — | 106 | 3 | no | — |
| 524 | C22×C4 | — | 106 | 3 | no | — |
| 525 | C22×C4 | — | 106 | 6 | no | — |
| 526 | C22×C4 | — | 106 | 3 | no | — |
| 527 | C22×C4 | — | 106 | 3 | no | — |
| 528 | SD16 | — | 2 | 2 | no | — |
| 529 | SD16 | — | 106 | 2 | no | — |
| 530 | D8 | — | 212 | 3 | no | — |
| 531 | D8 | — | 212 | 3 | no | — |
| 532 | M16 | — | 212 | 6 | no | — |
| 533 | C2×C8 | — | 53 | 1 | no | — |
| 534 | C2×C8 | — | 53 | 3 | no | — |
| 535 | C2×C8 | C23×D53 | 1 | 1 | yes | characteristic |
| 536 | C2×C8 | C23×D53 | 1 | 3 | yes | — |
| 537 | C4⋊C4 | — | 2 | 3 | no | — |
| 538 | C4⋊C4 | — | 2 | 3 | no | — |
| 539 | C4⋊C4 | — | 2 | 3 | no | — |
| 540 | C4⋊C4 | — | 53 | 3 | no | — |
| 541 | C4⋊C4 | — | 53 | 3 | no | — |
| 542 | C4⋊C4 | — | 53 | 1 | no | — |
| 543 | C4⋊C4 | — | 106 | 6 | no | — |
| 544 | C4⋊C4 | — | 106 | 3 | no | — |
| 545 | C4⋊C4 | — | 106 | 1 | no | — |
| 546 | C4⋊C4 | — | 106 | 3 | no | — |
| 547 | C4⋊C4 | D4×D53 | 1 | 3 | yes | — |
| 548 | C4⋊C4 | C23×D53 | 1 | 3 | yes | — |
| 549 | C4⋊C4 | C23×D53 | 1 | 3 | yes | — |
| 550 | C22⋊C4 | — | 2 | 3 | no | — |
| 551 | C22⋊C4 | — | 53 | 6 | no | — |
| 552 | C22⋊C4 | — | 106 | 3 | no | — |
| 553 | C22⋊C4 | — | 106 | 6 | no | — |
| 554 | C22⋊C4 | — | 106 | 3 | no | — |
| 555 | C22⋊C4 | — | 106 | 3 | no | — |
| 556 | C22⋊C4 | — | 106 | 3 | no | — |
| 557 | C22⋊C4 | — | 106 | 3 | no | — |
| 558 | C22⋊C4 | — | 106 | 3 | no | — |
| 559 | C42 | — | 2 | 3 | no | — |
| 560 | C42 | — | 53 | 3 | no | — |
| 561 | C42 | — | 53 | 3 | no | — |
| 562 | C42 | — | 53 | 1 | no | — |
| 563 | C42 | — | 106 | 1 | no | — |
| 564 | C42 | — | 106 | 3 | no | — |
| 565 | C42 | C23×D53 | 1 | 3 | yes | — |
| 566 | C23 | — | 2 | 1 | no | — |
| 567 | C23 | — | 53 | 3 | no | — |
| 568 | C23 | — | 106 | 1 | no | — |
| 569 | C23 | — | 106 | 3 | no | — |
| 570 | Q8 | — | 2 | 1 | no | — |
| 571 | Q8 | — | 4 | 6 | no | — |
| 572 | Q8 | — | 8 | 3 | no | — |
| 573 | Q8 | — | 212 | 6 | no | — |
| 574 | Q8 | — | 212 | 6 | no | — |
| 575 | Q8 | #13133244 | 1 | 4 | yes | — |
| 576 | Q8 | #13133265 | 1 | 2 | yes | complemented |
| 577 | D4 | — | 2 | 1 | no | — |
| 578 | D4 | — | 2 | 1 | no | — |
| 579 | D4 | — | 106 | 6 | no | — |
| 580 | D4 | — | 106 | 1 | no | — |
| 581 | D4 | — | 106 | 3 | no | — |
| 582 | D4 | — | 106 | 1 | no | — |
| 583 | D4 | — | 106 | 3 | no | — |
| 584 | D4 | — | 424 | 3 | no | — |
| 585 | D4 | — | 424 | 6 | no | — |
| 586 | D4 | — | 212 | 6 | no | — |
| 587 | D4 | — | 212 | 6 | no | — |
| 588 | D4 | — | 212 | 2 | no | — |
| 589 | D4 | — | 212 | 2 | no | — |
| 590 | D4 | — | 212 | 6 | no | — |
| 591 | D4 | — | 212 | 6 | no | — |
| 592 | C2×C4 | — | 2 | 1 | no | — |
| 593 | C2×C4 | — | 2 | 3 | no | — |
| 594 | C2×C4 | — | 2 | 3 | no | — |
| 595 | C2×C4 | — | 4 | 6 | no | — |
| 596 | C2×C4 | — | 53 | 1 | no | — |
| 597 | C2×C4 | — | 53 | 1 | no | — |
| 598 | C2×C4 | — | 53 | 3 | no | — |
| 599 | C2×C4 | — | 106 | 6 | no | — |
| 600 | C2×C4 | — | 106 | 6 | no | — |
| 601 | C2×C4 | — | 106 | 3 | no | — |
| 602 | C2×C4 | — | 106 | 3 | no | — |
| 603 | C2×C4 | — | 106 | 1 | no | — |
| 604 | C2×C4 | — | 106 | 3 | no | — |
| 605 | C2×C4 | — | 212 | 6 | no | — |
| 606 | C2×C4 | — | 212 | 6 | no | — |
| 607 | C2×C4 | — | 212 | 12 | no | — |
| 608 | C2×C4 | — | 212 | 6 | no | — |
| 609 | C2×C4 | — | 212 | 6 | no | — |
| 610 | C2×C4 | C2×D4×D53 | 1 | 3 | yes | — |
| 611 | C2×C4 | C2×D4×D53 | 1 | 3 | yes | — |
| 612 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 613 | C8 | — | 2 | 1 | no | — |
| 614 | C8 | — | 2 | 3 | no | — |
| 615 | C8 | — | 106 | 1 | no | — |
| 616 | C8 | — | 106 | 3 | no | — |
| 617 | C22 | — | 4 | 1 | no | — |
| 618 | C22 | — | 4 | 1 | no | — |
| 619 | C22 | — | 4 | 1 | no | — |
| 620 | C22 | — | 106 | 3 | no | — |
| 621 | C22 | — | 106 | 3 | no | — |
| 622 | C22 | — | 106 | 3 | no | — |
| 623 | C22 | — | 212 | 3 | no | — |
| 624 | C22 | — | 212 | 1 | no | — |
| 625 | C22 | — | 212 | 1 | no | — |
| 626 | C22 | — | 212 | 3 | no | — |
| 627 | C22 | — | 212 | 3 | no | — |
| 628 | C22 | — | 212 | 1 | no | — |
| 629 | C22 | C22×D4×D53 | 1 | 1 | yes | characteristic |
| 630 | C4 | — | 2 | 2 | no | — |
| 631 | C4 | — | 2 | 3 | no | — |
| 632 | C4 | — | 4 | 3 | no | — |
| 633 | C4 | — | 4 | 3 | no | — |
| 634 | C4 | — | 53 | 2 | no | — |
| 635 | C4 | — | 106 | 3 | no | — |
| 636 | C4 | — | 106 | 1 | no | — |
| 637 | C4 | — | 212 | 1 | no | — |
| 638 | C4 | — | 212 | 3 | no | — |
| 639 | C4 | C2×#13133244 | 1 | 6 | yes | — |
| 640 | C4 | C2×#13133265 | 1 | 1 | yes | characteristic |
| 641 | C4 | #16811460 | 1 | 1 | yes | characteristic |
| 642 | C2 | — | 8 | 1 | no | — |
| 643 | C2 | — | 424 | 3 | no | — |
| 644 | C2 | — | 424 | 1 | no | — |
| 645 | C2 | — | 212 | 3 | no | — |
| 646 | C2 | #20288392 | 1 | 1 | yes | characteristic |
| 647 | C2 | C22×#13133244 | 1 | 1 | yes | characteristic |
| 648 | C2 | #577×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20288499 | C2 | semidirect |
| 2. #20288342 | C2 | semidirect |
| 3. Q8×#11719924 | C2 | semidirect |
| 4. #20287351 | C2 | semidirect |
| 5. #20287350 | C2 | semidirect |
| 6. #20287309 | C2 | semidirect |
| 7. #20287307 | C2 | semidirect |
| 8. #20287044 | C2 | semidirect |
| 9. #20287039 | C2 | semidirect |
| 10. #20286095 | C2 | semidirect |
| 11. #20285844 | C2 | semidirect |
| 12. #20284773 | C2 | semidirect |
| 13. #20284525 | C2 | semidirect |
| 14. #20283846 | C2 | semidirect |
| 15. Q8×SD16×C53 | C2 | semidirect |
| 249. Q8×C53 | 2−1+4 | semidirect |
| 321. Q8×SD16 | D53 | semidirect |
| 398. C53 | #62150 | semidirect |
| 576. Q8 | #13133265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288499 | 2 |
| #20288342 | 2 |
| Q8×#11719924 | 2 |
| #20287351 | 2 |
| #20287350 | 2 |
| #20287309 | 2 |
| #20287307 | 2 |
| #20287044 | 2 |
| #20287039 | 2 |
| #20286095 | 2 |
| #20285844 | 2 |
| #20284773 | 2 |
| #20284525 | 2 |
| #20283846 | 2 |
| Q8×SD16×C53 | 2 |
| #62150 | 53 |