← #27371948
Subgroups — #27371948
Order 13568.
784 conjugacy classes of subgroups.
The subgroup lattice has 430 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20285856 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20285637 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #20285262 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#16811021 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20285175 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #20274350 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20274336 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20274310 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #20274301 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C8×#11719917 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#3167 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×#13133247 | — | 2 | 2 | no | — |
| 13 | C2×#13133217 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#13133217 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16811033 | — | 2 | 2 | no | — |
| 16 | #16811026 | C22 | 1 | 2 | yes | — |
| 17 | #16811021 | — | 2 | 2 | no | — |
| 18 | #16811021 | C22 | 1 | 2 | yes | — |
| 19 | #16811021 | C22 | 1 | 2 | yes | — |
| 20 | #16811019 | C22 | 1 | 2 | yes | — |
| 21 | #16811019 | C22 | 1 | 2 | yes | — |
| 22 | #16811018 | — | 2 | 2 | no | — |
| 23 | #16811002 | C22 | 1 | 2 | yes | — |
| 24 | #16810995 | C22 | 1 | 2 | yes | — |
| 25 | #16810995 | C22 | 1 | 2 | yes | — |
| 26 | #16810975 | C22 | 1 | 2 | yes | — |
| 27 | #16810973 | C22 | 1 | 2 | yes | — |
| 28 | #16810951 | — | 2 | 2 | no | — |
| 29 | #16810908 | — | 2 | 2 | no | — |
| 30 | #16810828 | — | 2 | 2 | no | — |
| 31 | #16810761 | — | 2 | 2 | no | — |
| 32 | #16810676 | C22 | 1 | 1 | yes | characteristic |
| 33 | #16810666 | — | 2 | 2 | no | — |
| 34 | C2×#13133149 | — | 2 | 2 | no | — |
| 35 | C4×#11719917 | C22 | 1 | 1 | yes | characteristic |
| 36 | #16810345 | C22 | 1 | 2 | yes | — |
| 37 | C8×#88322 | C22 | 1 | 2 | yes | — |
| 38 | C53×#533 | C22 | 1 | 1 | yes | characteristic |
| 39 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 40 | C53×#498 | C22 | 1 | 1 | yes | characteristic |
| 41 | C53×#492 | C22 | 1 | 1 | yes | characteristic |
| 42 | C53×#487 | C22 | 1 | 1 | yes | characteristic |
| 43 | C53×#486 | C22 | 1 | 1 | yes | characteristic |
| 44 | C53×#465 | — | 2 | 2 | no | — |
| 45 | C4×SD16×C53 | — | 2 | 2 | no | — |
| 46 | C2×C4×C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 47 | C22×Dic106 | — | 2 | 1 | no | — |
| 48 | C22×Dic106 | — | 2 | 1 | no | — |
| 49 | #13133247 | — | 4 | 8 | no | — |
| 50 | C2×#11719925 | — | 2 | 4 | no | — |
| 51 | C2×#11719923 | — | 2 | 4 | no | — |
| 52 | C2×#11719923 | — | 2 | 4 | no | — |
| 53 | C2×#11719917 | D4 | 1 | 2 | yes | — |
| 54 | #13133217 | — | 2 | 1 | no | — |
| 55 | #13133217 | — | 2 | 1 | no | — |
| 56 | #13133217 | — | 2 | 1 | no | — |
| 57 | #13133217 | — | 2 | 1 | no | — |
| 58 | #13133217 | — | 2 | 1 | no | — |
| 59 | #13133217 | — | 2 | 1 | no | — |
| 60 | #13133217 | C23 | 1 | 2 | yes | — |
| 61 | #13133217 | C23 | 1 | 2 | yes | — |
| 62 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 63 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 64 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 65 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 66 | #13133150 | — | 2 | 4 | no | — |
| 67 | #13133149 | — | 2 | 4 | no | — |
| 68 | #13133149 | — | 2 | 4 | no | — |
| 69 | #13133148 | — | 2 | 4 | no | — |
| 70 | #13133148 | — | 2 | 4 | no | — |
| 71 | C4⋊#88322 | D4 | 1 | 2 | yes | — |
| 72 | #13133141 | — | 2 | 4 | no | — |
| 73 | #13133140 | — | 2 | 4 | no | — |
| 74 | C22⋊#88322 | D4 | 1 | 2 | yes | — |
| 75 | #13133128 | D4 | 1 | 2 | yes | — |
| 76 | C4×#88322 | C23 | 1 | 2 | yes | — |
| 77 | C4×#88322 | C23 | 1 | 2 | yes | — |
| 78 | C2×#41×C53 | — | 2 | 1 | no | — |
| 79 | C2×SD16×C53 | — | 2 | 2 | no | — |
| 80 | C22×C8×C53 | D4 | 1 | 2 | yes | — |
| 81 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 82 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 83 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 84 | #127×C53 | C23 | 1 | 1 | yes | characteristic |
| 85 | #125×C53 | — | 2 | 1 | no | — |
| 86 | #124×C53 | — | 2 | 1 | no | — |
| 87 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 88 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 89 | #121×C53 | — | 2 | 1 | no | — |
| 90 | #121×C53 | — | 2 | 1 | no | — |
| 91 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 92 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 93 | C4×D4×C53 | — | 2 | 1 | no | — |
| 94 | C4×D4×C53 | — | 2 | 1 | no | — |
| 95 | #117×C53 | — | 2 | 1 | no | — |
| 96 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 97 | #106×C53 | — | 2 | 2 | no | — |
| 98 | #103×C53 | — | 2 | 2 | no | — |
| 99 | #102×C53 | — | 2 | 2 | no | — |
| 100 | C4×C8×C53 | D4 | 1 | 2 | yes | — |
| 101 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 102 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 103 | #41×C53 | — | 4 | 4 | no | — |
| 104 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 105 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 106 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 107 | C2×D4×C53 | — | 2 | 1 | no | — |
| 108 | C2×D4×C53 | — | 2 | 1 | no | — |
| 109 | C2×D4×C53 | — | 2 | 1 | no | — |
| 110 | C2×D4×C53 | — | 4 | 1 | no | — |
| 111 | C22×C4×C53 | — | 4 | 1 | no | — |
| 112 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C22×Dic53 | — | 4 | 1 | no | — |
| 116 | C22×Dic53 | — | 4 | 1 | no | — |
| 117 | C2×Dic106 | — | 2 | 2 | no | — |
| 118 | C2×Dic106 | — | 2 | 2 | no | — |
| 119 | C2×Dic106 | — | 4 | 4 | no | — |
| 120 | C2×Dic106 | — | 4 | 1 | no | — |
| 121 | C2×Dic106 | — | 4 | 1 | no | — |
| 122 | C2×Dic106 | — | 8 | 2 | no | — |
| 123 | SD16×C53 | — | 4 | 4 | no | — |
| 124 | C2×C8×C53 | — | 2 | 4 | no | — |
| 125 | C2×C8×C53 | C2×D4 | 1 | 2 | yes | — |
| 126 | C2×C8×C53 | C2×D4 | 1 | 2 | yes | — |
| 127 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 128 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 129 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 130 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 131 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 132 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 133 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 134 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 135 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 136 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 137 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 138 | C42×C53 | — | 4 | 1 | no | — |
| 139 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 143 | #11719925 | — | 4 | 8 | no | — |
| 144 | #11719923 | — | 4 | 8 | no | — |
| 145 | #11719923 | — | 8 | 4 | no | — |
| 146 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 147 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 148 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 149 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 150 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 151 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 152 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 153 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 154 | #11719917 | SD16 | 1 | 8 | yes | complemented |
| 155 | C2×#88322 | C2×D4 | 1 | 4 | yes | — |
| 156 | C2×#88322 | C2×D4 | 1 | 4 | yes | — |
| 157 | C23×C53 | — | 4 | 1 | no | — |
| 158 | C23×C53 | #127 | 1 | 1 | yes | characteristic |
| 159 | Q8×C53 | — | 4 | 2 | no | — |
| 160 | Q8×C53 | — | 4 | 2 | no | — |
| 161 | Q8×C53 | — | 4 | 2 | no | — |
| 162 | D4×C53 | — | 4 | 2 | no | — |
| 163 | D4×C53 | — | 4 | 2 | no | — |
| 164 | D4×C53 | — | 4 | 2 | no | — |
| 165 | D4×C53 | — | 8 | 2 | no | — |
| 166 | C2×C4×C53 | — | 2 | 2 | no | — |
| 167 | C2×C4×C53 | — | 2 | 2 | no | — |
| 168 | C2×C4×C53 | — | 4 | 1 | no | — |
| 169 | C2×C4×C53 | — | 4 | 1 | no | — |
| 170 | C2×C4×C53 | — | 4 | 1 | no | — |
| 171 | C2×C4×C53 | — | 8 | 2 | no | — |
| 172 | C2×C4×C53 | #127 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C53 | #127 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C53 | #127 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C53 | C2×SD16 | 1 | 4 | yes | — |
| 176 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×Dic53 | — | 4 | 2 | no | — |
| 180 | C2×Dic53 | — | 4 | 2 | no | — |
| 181 | C2×Dic53 | — | 8 | 2 | no | — |
| 182 | C2×Dic53 | — | 8 | 2 | no | — |
| 183 | Dic106 | — | 4 | 4 | no | — |
| 184 | Dic106 | — | 4 | 4 | no | — |
| 185 | Dic106 | — | 8 | 2 | no | — |
| 186 | Dic106 | — | 8 | 2 | no | — |
| 187 | C8×C53 | — | 2 | 2 | no | — |
| 188 | C8×C53 | #137 | 1 | 4 | yes | complemented |
| 189 | #88322 | — | 2 | 4 | no | — |
| 190 | #88322 | C2×SD16 | 1 | 8 | yes | — |
| 191 | #19622 | — | 53 | 1 | no | maximal, Sylow |
| 192 | C22×C53 | — | 2 | 1 | no | — |
| 193 | C22×C53 | — | 2 | 1 | no | — |
| 194 | C22×C53 | — | 8 | 1 | no | — |
| 195 | C22×C53 | — | 8 | 1 | no | — |
| 196 | C22×C53 | — | 8 | 1 | no | — |
| 197 | C22×C53 | #492 | 1 | 2 | yes | — |
| 198 | C22×C53 | C2×#127 | 1 | 1 | yes | characteristic |
| 199 | C4×C53 | — | 2 | 1 | no | — |
| 200 | C4×C53 | — | 2 | 1 | no | — |
| 201 | C4×C53 | — | 8 | 1 | no | — |
| 202 | C4×C53 | — | 8 | 1 | no | — |
| 203 | C4×C53 | — | 8 | 1 | no | — |
| 204 | C4×C53 | #492 | 1 | 2 | yes | — |
| 205 | C4×C53 | C22×SD16 | 1 | 2 | yes | — |
| 206 | C4×C53 | C2×#137 | 1 | 2 | yes | — |
| 207 | C4×C53 | #577 | 1 | 2 | yes | — |
| 208 | Dic53 | — | 8 | 2 | no | — |
| 209 | Dic53 | — | 8 | 2 | no | — |
| 210 | #3229 | — | 53 | 1 | no | — |
| 211 | #3206 | — | 53 | 1 | no | — |
| 212 | #3167 | D53 | 1 | 1 | yes | characteristic |
| 213 | #3165 | — | 53 | 1 | no | — |
| 214 | C2×#498 | — | 53 | 1 | no | — |
| 215 | #3152 | — | 53 | 1 | no | — |
| 216 | #1716 | — | 53 | 2 | no | — |
| 217 | #1714 | — | 53 | 2 | no | — |
| 218 | #1707 | — | 53 | 2 | no | — |
| 219 | #1705 | — | 53 | 2 | no | — |
| 220 | C8×M16 | — | 53 | 1 | no | — |
| 221 | C2×C53 | — | 2 | 2 | no | — |
| 222 | C2×C53 | — | 16 | 1 | no | — |
| 223 | C2×C53 | C2×#492 | 1 | 1 | yes | characteristic |
| 224 | C2×C53 | #3152 | 1 | 1 | yes | characteristic |
| 225 | C2×C53 | #3154 | 1 | 1 | yes | characteristic |
| 226 | C2×#137 | — | 106 | 2 | no | — |
| 227 | #533 | C2×D53 | 1 | 1 | yes | characteristic |
| 228 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 229 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 230 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 231 | #501 | — | 106 | 2 | no | — |
| 232 | #500 | — | 53 | 2 | no | — |
| 233 | #498 | — | 53 | 2 | no | — |
| 234 | #498 | — | 53 | 2 | no | — |
| 235 | #498 | — | 53 | 2 | no | — |
| 236 | #498 | — | 53 | 2 | no | — |
| 237 | #498 | — | 106 | 2 | no | — |
| 238 | #498 | C2×D53 | 1 | 1 | yes | characteristic |
| 239 | #497 | — | 106 | 2 | no | — |
| 240 | #494 | — | 53 | 2 | no | — |
| 241 | #492 | — | 53 | 2 | no | — |
| 242 | #492 | — | 53 | 2 | no | — |
| 243 | #492 | C2×D53 | 1 | 1 | yes | characteristic |
| 244 | #487 | — | 53 | 2 | no | — |
| 245 | #487 | — | 53 | 2 | no | — |
| 246 | #487 | C2×D53 | 1 | 1 | yes | characteristic |
| 247 | #486 | C2×D53 | 1 | 1 | yes | characteristic |
| 248 | #483 | — | 106 | 2 | no | — |
| 249 | #475 | — | 106 | 2 | no | — |
| 250 | #465 | — | 2 | 2 | no | — |
| 251 | #461 | — | 106 | 2 | no | — |
| 252 | #448 | — | 106 | 2 | no | — |
| 253 | C4×SD16 | — | 2 | 2 | no | — |
| 254 | #431 | — | 53 | 1 | no | — |
| 255 | #428 | — | 106 | 2 | no | — |
| 256 | C2×#106 | — | 106 | 2 | no | — |
| 257 | C4×M16 | — | 53 | 1 | no | — |
| 258 | C2×C4×C8 | C2×D53 | 1 | 1 | yes | characteristic |
| 259 | #322 | — | 53 | 2 | no | — |
| 260 | C82 | — | 53 | 2 | no | — |
| 261 | C53 | #19622 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 262 | C2×#41 | — | 2 | 1 | no | — |
| 263 | C22×Q8 | — | 106 | 1 | no | — |
| 264 | C22×Q8 | — | 106 | 1 | no | — |
| 265 | #137 | — | 212 | 8 | no | — |
| 266 | C2×Q16 | — | 106 | 4 | no | — |
| 267 | C2×SD16 | — | 2 | 2 | no | — |
| 268 | C2×SD16 | — | 106 | 4 | no | — |
| 269 | C2×SD16 | — | 106 | 4 | no | — |
| 270 | C2×M16 | — | 53 | 2 | no | — |
| 271 | C22×C8 | C22⋊D53 | 1 | 2 | yes | — |
| 272 | C4⋊Q8 | — | 53 | 2 | no | — |
| 273 | C4⋊Q8 | — | 53 | 2 | no | — |
| 274 | C4⋊Q8 | — | 106 | 1 | no | — |
| 275 | C4⋊Q8 | — | 106 | 1 | no | — |
| 276 | C4⋊Q8 | — | 106 | 1 | no | — |
| 277 | C4⋊Q8 | — | 106 | 1 | no | — |
| 278 | C4⋊Q8 | — | 106 | 1 | no | — |
| 279 | C4⋊Q8 | — | 106 | 1 | no | — |
| 280 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 281 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 282 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 283 | #127 | C22×D53 | 1 | 1 | yes | characteristic |
| 284 | #125 | — | 2 | 1 | no | — |
| 285 | #124 | — | 2 | 1 | no | — |
| 286 | C22⋊Q8 | — | 2 | 1 | no | — |
| 287 | C22⋊Q8 | — | 2 | 1 | no | — |
| 288 | #121 | — | 2 | 1 | no | — |
| 289 | #121 | — | 2 | 1 | no | — |
| 290 | C4×Q8 | — | 2 | 1 | no | — |
| 291 | C4×Q8 | — | 2 | 1 | no | — |
| 292 | C4×D4 | — | 2 | 1 | no | — |
| 293 | C4×D4 | — | 2 | 1 | no | — |
| 294 | #117 | — | 2 | 1 | no | — |
| 295 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 296 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 297 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 298 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 299 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 300 | #107 | — | 106 | 4 | no | — |
| 301 | #106 | — | 2 | 2 | no | — |
| 302 | #106 | — | 106 | 4 | no | — |
| 303 | #106 | — | 106 | 4 | no | — |
| 304 | #106 | — | 106 | 4 | no | — |
| 305 | #106 | — | 106 | 4 | no | — |
| 306 | C4⋊C8 | — | 53 | 2 | no | — |
| 307 | #103 | — | 2 | 2 | no | — |
| 308 | #103 | — | 106 | 4 | no | — |
| 309 | #103 | — | 106 | 4 | no | — |
| 310 | #102 | — | 2 | 2 | no | — |
| 311 | C22⋊C8 | — | 53 | 2 | no | — |
| 312 | #97 | — | 53 | 2 | no | — |
| 313 | C4×C8 | — | 53 | 2 | no | — |
| 314 | C4×C8 | — | 53 | 2 | no | — |
| 315 | C4×C8 | C22⋊D53 | 1 | 2 | yes | — |
| 316 | C4×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 317 | C4×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 318 | #41 | — | 4 | 4 | no | — |
| 319 | C2×Q8 | — | 2 | 1 | no | — |
| 320 | C2×Q8 | — | 2 | 1 | no | — |
| 321 | C2×Q8 | — | 2 | 1 | no | — |
| 322 | C2×Q8 | — | 106 | 2 | no | — |
| 323 | C2×Q8 | — | 106 | 2 | no | — |
| 324 | C2×Q8 | — | 424 | 2 | no | — |
| 325 | C2×Q8 | — | 212 | 4 | no | — |
| 326 | C2×Q8 | — | 212 | 1 | no | — |
| 327 | C2×Q8 | — | 212 | 1 | no | — |
| 328 | C2×D4 | — | 2 | 1 | no | — |
| 329 | C2×D4 | — | 2 | 1 | no | — |
| 330 | C2×D4 | — | 2 | 1 | no | — |
| 331 | C2×D4 | — | 4 | 1 | no | — |
| 332 | C22×C4 | — | 4 | 1 | no | — |
| 333 | C22×C4 | — | 212 | 1 | no | — |
| 334 | C22×C4 | — | 212 | 1 | no | — |
| 335 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 336 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 337 | C22×C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 338 | Q16 | — | 212 | 8 | no | — |
| 339 | SD16 | — | 4 | 4 | no | — |
| 340 | SD16 | — | 424 | 4 | no | — |
| 341 | SD16 | — | 212 | 8 | no | — |
| 342 | M16 | — | 53 | 8 | no | — |
| 343 | C2×C8 | — | 2 | 4 | no | — |
| 344 | C2×C8 | — | 53 | 4 | no | — |
| 345 | C2×C8 | — | 53 | 4 | no | — |
| 346 | C2×C8 | C2×C22⋊D53 | 1 | 2 | yes | — |
| 347 | C2×C8 | C2×C22⋊D53 | 1 | 2 | yes | — |
| 348 | C4⋊C4 | — | 2 | 1 | no | — |
| 349 | C4⋊C4 | — | 2 | 1 | no | — |
| 350 | C4⋊C4 | — | 2 | 1 | no | — |
| 351 | C4⋊C4 | — | 2 | 1 | no | — |
| 352 | C4⋊C4 | — | 2 | 1 | no | — |
| 353 | C4⋊C4 | — | 2 | 1 | no | — |
| 354 | C4⋊C4 | — | 4 | 1 | no | — |
| 355 | C4⋊C4 | — | 4 | 1 | no | — |
| 356 | C4⋊C4 | — | 106 | 2 | no | — |
| 357 | C4⋊C4 | — | 106 | 2 | no | — |
| 358 | C4⋊C4 | — | 106 | 2 | no | — |
| 359 | C4⋊C4 | — | 106 | 2 | no | — |
| 360 | C4⋊C4 | — | 212 | 1 | no | — |
| 361 | C4⋊C4 | — | 212 | 1 | no | — |
| 362 | C4⋊C4 | — | 212 | 1 | no | — |
| 363 | C4⋊C4 | — | 212 | 1 | no | — |
| 364 | C22⋊C4 | — | 4 | 1 | no | — |
| 365 | C22⋊C4 | — | 4 | 1 | no | — |
| 366 | C22⋊C4 | — | 4 | 1 | no | — |
| 367 | C42 | — | 4 | 1 | no | — |
| 368 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 369 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 370 | C42 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 371 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 372 | C23 | — | 4 | 1 | no | — |
| 373 | C23 | #13133213 | 1 | 1 | yes | characteristic |
| 374 | Q8 | — | 4 | 2 | no | — |
| 375 | Q8 | — | 4 | 2 | no | — |
| 376 | Q8 | — | 4 | 2 | no | — |
| 377 | Q8 | — | 424 | 2 | no | — |
| 378 | Q8 | — | 424 | 2 | no | — |
| 379 | Q8 | — | 212 | 4 | no | — |
| 380 | Q8 | — | 212 | 4 | no | — |
| 381 | D4 | — | 4 | 2 | no | — |
| 382 | D4 | — | 4 | 2 | no | — |
| 383 | D4 | — | 4 | 2 | no | — |
| 384 | D4 | — | 8 | 2 | no | — |
| 385 | C2×C4 | — | 2 | 2 | no | — |
| 386 | C2×C4 | — | 2 | 2 | no | — |
| 387 | C2×C4 | — | 4 | 1 | no | — |
| 388 | C2×C4 | — | 4 | 1 | no | — |
| 389 | C2×C4 | — | 4 | 1 | no | — |
| 390 | C2×C4 | — | 8 | 2 | no | — |
| 391 | C2×C4 | — | 424 | 2 | no | — |
| 392 | C2×C4 | — | 424 | 2 | no | — |
| 393 | C2×C4 | — | 212 | 2 | no | — |
| 394 | C2×C4 | — | 212 | 2 | no | — |
| 395 | C2×C4 | #13133213 | 1 | 1 | yes | characteristic |
| 396 | C2×C4 | #13133213 | 1 | 1 | yes | characteristic |
| 397 | C2×C4 | #13133213 | 1 | 1 | yes | characteristic |
| 398 | C2×C4 | SD16×D53 | 1 | 4 | yes | — |
| 399 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 400 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 401 | C2×C4 | C22×C22⋊D53 | 1 | 1 | yes | characteristic |
| 402 | C8 | — | 2 | 2 | no | — |
| 403 | C8 | — | 53 | 8 | no | — |
| 404 | C8 | — | 106 | 4 | no | — |
| 405 | C8 | #13133247 | 1 | 4 | yes | complemented |
| 406 | C22 | — | 2 | 1 | no | — |
| 407 | C22 | — | 2 | 1 | no | — |
| 408 | C22 | — | 8 | 1 | no | — |
| 409 | C22 | — | 8 | 1 | no | — |
| 410 | C22 | — | 8 | 1 | no | — |
| 411 | C22 | #16810994 | 1 | 2 | yes | — |
| 412 | C22 | C2×#13133213 | 1 | 1 | yes | characteristic |
| 413 | C4 | — | 2 | 1 | no | — |
| 414 | C4 | — | 2 | 1 | no | — |
| 415 | C4 | — | 8 | 1 | no | — |
| 416 | C4 | — | 8 | 1 | no | — |
| 417 | C4 | — | 8 | 1 | no | — |
| 418 | C4 | — | 424 | 2 | no | — |
| 419 | C4 | — | 424 | 2 | no | — |
| 420 | C4 | #16810994 | 1 | 2 | yes | — |
| 421 | C4 | C2×SD16×D53 | 1 | 2 | yes | — |
| 422 | C4 | C2×#13133247 | 1 | 2 | yes | — |
| 423 | C4 | #16811430 | 1 | 2 | yes | — |
| 424 | C2 | — | 2 | 2 | no | — |
| 425 | C2 | — | 16 | 1 | no | — |
| 426 | C2 | C2×#16810994 | 1 | 1 | yes | characteristic |
| 427 | C2 | #20285175 | 1 | 1 | yes | characteristic |
| 428 | C2 | #20285192 | 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