← #15898159
Subgroups — #15898159
Order 3328.
1378 conjugacy classes of subgroups.
The subgroup lattice has 488 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13128607 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13124300 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×#11718723 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13116060 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13115877 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13115668 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13114832 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13114794 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C13×#2326 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#88254 | C22 | 1 | 2 | yes | — |
| 11 | C2×C13×#124 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C4×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C4×D4×C13 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#88186 | C22 | 1 | 4 | yes | — |
| 15 | #11719282 | — | 2 | 2 | no | — |
| 16 | #11719281 | — | 2 | 4 | no | — |
| 17 | Q8×D52 | — | 2 | 2 | no | — |
| 18 | #11719215 | — | 2 | 2 | no | — |
| 19 | #11719215 | C22 | 1 | 2 | yes | — |
| 20 | #11719182 | — | 2 | 2 | no | — |
| 21 | #11719182 | C22 | 1 | 2 | yes | — |
| 22 | C13×#391 | C22 | 1 | 1 | yes | characteristic |
| 23 | C13×#390 | C22 | 1 | 1 | yes | characteristic |
| 24 | C13×#388 | — | 2 | 2 | no | — |
| 25 | C13×#385 | — | 2 | 2 | no | — |
| 26 | C13×#384 | C22 | 1 | 1 | yes | characteristic |
| 27 | C13×#376 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#88076 | C22 | 1 | 2 | yes | — |
| 29 | #11718723 | — | 2 | 8 | no | — |
| 30 | #11718680 | — | 2 | 2 | no | — |
| 31 | #11718677 | — | 2 | 4 | no | — |
| 32 | #11718676 | — | 2 | 2 | no | — |
| 33 | #11718627 | C22 | 1 | 4 | yes | — |
| 34 | C2×#88045 | C22 | 1 | 4 | yes | — |
| 35 | C2×#88045 | C22 | 1 | 4 | yes | — |
| 36 | #11718585 | C22 | 1 | 2 | yes | — |
| 37 | #11718122 | C22 | 1 | 2 | yes | — |
| 38 | C22×Q8×C13 | C23 | 1 | 1 | yes | characteristic |
| 39 | C22×D4×C13 | C23 | 1 | 1 | yes | characteristic |
| 40 | C23×C4×C13 | — | 2 | 1 | no | — |
| 41 | #88254 | — | 2 | 4 | no | — |
| 42 | #88254 | — | 2 | 4 | no | — |
| 43 | #88254 | — | 4 | 4 | no | — |
| 44 | C2×#6131 | — | 2 | 4 | no | — |
| 45 | C2×Q8×D13 | — | 2 | 4 | no | — |
| 46 | C2×#6127 | — | 2 | 4 | no | — |
| 47 | C2×#6127 | C23 | 1 | 4 | yes | — |
| 48 | C13×#124 | — | 2 | 2 | no | — |
| 49 | C13×#124 | D4 | 1 | 4 | yes | complemented |
| 50 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 51 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 52 | C4×D4×C13 | — | 2 | 2 | no | — |
| 53 | C4×D4×C13 | — | 2 | 2 | no | — |
| 54 | C2×C13×C4⋊C4 | — | 2 | 2 | no | — |
| 55 | C2×C13×C4⋊C4 | D4 | 1 | 2 | yes | — |
| 56 | C2×C13×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×C13×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×C13×C22⋊C4 | — | 2 | 2 | no | — |
| 59 | C2×C13×C22⋊C4 | — | 2 | 1 | no | — |
| 60 | C2×C13×C22⋊C4 | — | 2 | 2 | no | — |
| 61 | C2×C42×C13 | D4 | 1 | 2 | yes | — |
| 62 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×#6105 | — | 2 | 4 | no | — |
| 66 | #88186 | — | 2 | 8 | no | — |
| 67 | #88186 | — | 4 | 4 | no | — |
| 68 | C2×#6104 | — | 2 | 4 | no | — |
| 69 | #88184 | — | 2 | 2 | no | — |
| 70 | #88184 | — | 2 | 4 | no | — |
| 71 | #88184 | — | 2 | 2 | no | — |
| 72 | C2×#6099 | C23 | 1 | 4 | yes | — |
| 73 | #88151 | — | 2 | 8 | no | — |
| 74 | #88151 | — | 2 | 4 | no | — |
| 75 | #88149 | — | 2 | 8 | no | — |
| 76 | #88149 | — | 2 | 4 | no | — |
| 77 | #88129 | — | 2 | 4 | no | — |
| 78 | #88129 | D4 | 1 | 4 | yes | — |
| 79 | #88128 | — | 2 | 2 | no | — |
| 80 | #88128 | D4 | 1 | 2 | yes | — |
| 81 | C4×D52 | — | 2 | 4 | no | — |
| 82 | C4×D52 | — | 2 | 4 | no | — |
| 83 | C4×D52 | — | 2 | 2 | no | — |
| 84 | C4×D52 | — | 2 | 2 | no | — |
| 85 | #88123 | — | 2 | 2 | no | — |
| 86 | #88123 | D4 | 1 | 2 | yes | — |
| 87 | C13×#95 | — | 2 | 1 | no | — |
| 88 | C13×#95 | — | 2 | 2 | no | — |
| 89 | C13×#95 | — | 2 | 1 | no | — |
| 90 | #88076 | — | 2 | 4 | no | — |
| 91 | #88050 | — | 2 | 4 | no | — |
| 92 | #88049 | — | 2 | 4 | no | — |
| 93 | #88045 | — | 2 | 8 | no | — |
| 94 | #88045 | — | 4 | 4 | no | — |
| 95 | C4⋊#1055 | — | 2 | 2 | no | — |
| 96 | C4⋊#1055 | — | 2 | 2 | no | — |
| 97 | #24227 | — | 13 | 1 | no | maximal, Sylow |
| 98 | C24×C13 | — | 2 | 1 | no | — |
| 99 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 100 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 101 | C2×Q8×C13 | C2×D4 | 1 | 2 | yes | — |
| 102 | C2×Q8×C13 | #41 | 1 | 2 | yes | — |
| 103 | C2×D4×C13 | — | 2 | 2 | no | — |
| 104 | C2×D4×C13 | — | 2 | 1 | no | — |
| 105 | C2×D4×C13 | — | 2 | 2 | no | — |
| 106 | C2×D4×C13 | C2×D4 | 1 | 2 | yes | — |
| 107 | C22×C4×C13 | — | 2 | 1 | no | — |
| 108 | C22×C4×C13 | — | 2 | 1 | no | — |
| 109 | C22×C4×C13 | — | 2 | 1 | no | — |
| 110 | C22×C4×C13 | — | 4 | 2 | no | — |
| 111 | C22×C4×C13 | — | 8 | 2 | no | — |
| 112 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 113 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 114 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 117 | C2×C22⋊D13 | — | 2 | 4 | no | — |
| 118 | #6131 | — | 4 | 8 | no | — |
| 119 | #6131 | — | 4 | 8 | no | — |
| 120 | Q8×D13 | — | 4 | 8 | no | — |
| 121 | Q8×D13 | — | 4 | 8 | no | — |
| 122 | #6127 | — | 2 | 4 | no | — |
| 123 | #6127 | — | 2 | 4 | no | — |
| 124 | #6127 | — | 2 | 4 | no | — |
| 125 | #6127 | — | 2 | 4 | no | — |
| 126 | #6127 | — | 4 | 8 | no | — |
| 127 | #6127 | — | 4 | 8 | no | — |
| 128 | C2×D52 | — | 2 | 4 | no | — |
| 129 | C2×D52 | — | 2 | 2 | no | — |
| 130 | C2×D52 | — | 2 | 4 | no | — |
| 131 | C2×D52 | — | 2 | 2 | no | — |
| 132 | C2×D52 | C2×D4 | 1 | 4 | yes | — |
| 133 | C2×C4×D13 | — | 2 | 8 | no | — |
| 134 | C2×C4×D13 | — | 2 | 4 | no | — |
| 135 | C2×Dic26 | — | 2 | 4 | no | — |
| 136 | C2×Dic26 | C2×D4 | 1 | 4 | yes | — |
| 137 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 138 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 139 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 140 | C13×C4⋊C4 | — | 8 | 2 | no | — |
| 141 | C13×C22⋊C4 | — | 2 | 8 | no | — |
| 142 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 143 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 144 | C13×C22⋊C4 | — | 8 | 2 | no | — |
| 145 | C42×C13 | — | 2 | 2 | no | — |
| 146 | C42×C13 | — | 2 | 2 | no | — |
| 147 | C42×C13 | — | 2 | 1 | no | — |
| 148 | C42×C13 | — | 2 | 2 | no | — |
| 149 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 150 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 151 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 152 | #6105 | — | 4 | 8 | no | — |
| 153 | #6104 | — | 4 | 8 | no | — |
| 154 | #6103 | — | 2 | 8 | no | — |
| 155 | #6103 | — | 2 | 4 | no | — |
| 156 | #6103 | — | 2 | 4 | no | — |
| 157 | C4⋊Dic13 | — | 2 | 4 | no | — |
| 158 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 159 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 160 | #6099 | — | 2 | 4 | no | — |
| 161 | #6099 | — | 2 | 4 | no | — |
| 162 | C2×#1055 | — | 2 | 4 | no | — |
| 163 | #3497 | — | 13 | 1 | no | — |
| 164 | #3036 | — | 13 | 2 | no | — |
| 165 | C2×#454 | — | 13 | 2 | no | — |
| 166 | #2326 | D13 | 1 | 1 | yes | characteristic, complemented |
| 167 | #2039 | — | 13 | 2 | no | — |
| 168 | #2006 | — | 13 | 2 | no | — |
| 169 | #1963 | — | 13 | 2 | no | — |
| 170 | #1801 | — | 13 | 1 | no | — |
| 171 | #1793 | — | 13 | 2 | no | — |
| 172 | C23×C13 | — | 2 | 2 | no | — |
| 173 | C23×C13 | — | 4 | 2 | no | — |
| 174 | C23×C13 | — | 4 | 2 | no | — |
| 175 | C23×C13 | — | 4 | 1 | no | — |
| 176 | C23×C13 | — | 4 | 1 | no | — |
| 177 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 178 | C22×D13 | — | 2 | 4 | no | — |
| 179 | Q8×C13 | — | 2 | 4 | no | — |
| 180 | Q8×C13 | — | 2 | 4 | no | — |
| 181 | D4×C13 | — | 2 | 4 | no | — |
| 182 | D4×C13 | — | 4 | 2 | no | — |
| 183 | C2×C4×C13 | — | 2 | 2 | no | — |
| 184 | C2×C4×C13 | — | 2 | 2 | no | — |
| 185 | C2×C4×C13 | — | 2 | 2 | no | — |
| 186 | C2×C4×C13 | — | 2 | 2 | no | — |
| 187 | C2×C4×C13 | — | 4 | 1 | no | — |
| 188 | C2×C4×C13 | — | 4 | 1 | no | — |
| 189 | C2×C4×C13 | — | 4 | 1 | no | — |
| 190 | C2×C4×C13 | — | 4 | 1 | no | — |
| 191 | C2×C4×C13 | — | 4 | 2 | no | — |
| 192 | C2×C4×C13 | — | 4 | 1 | no | — |
| 193 | C2×C4×C13 | — | 4 | 2 | no | — |
| 194 | C2×C4×C13 | — | 4 | 1 | no | — |
| 195 | C2×C4×C13 | — | 4 | 1 | no | — |
| 196 | C2×C4×C13 | — | 4 | 1 | no | — |
| 197 | C2×C4×C13 | — | 8 | 4 | no | — |
| 198 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 199 | C2×C4×C13 | #120 | 1 | 2 | yes | — |
| 200 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×C13 | #121 | 1 | 4 | yes | — |
| 202 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 203 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 204 | C2×C4×C13 | C2×#41 | 1 | 1 | yes | characteristic |
| 205 | C2×C4×C13 | H(5,𝔽2) | 1 | 2 | yes | — |
| 206 | C22⋊D13 | — | 4 | 4 | no | — |
| 207 | C22⋊D13 | — | 4 | 4 | no | — |
| 208 | C2×Dic13 | — | 2 | 4 | no | — |
| 209 | D52 | — | 2 | 4 | no | — |
| 210 | D52 | — | 2 | 4 | no | — |
| 211 | D52 | — | 4 | 4 | no | — |
| 212 | D52 | — | 4 | 8 | no | — |
| 213 | D52 | — | 8 | 2 | no | — |
| 214 | D52 | — | 8 | 4 | no | — |
| 215 | C4×D13 | — | 4 | 16 | no | — |
| 216 | C4×D13 | — | 4 | 4 | no | — |
| 217 | C4×D13 | — | 4 | 4 | no | — |
| 218 | Dic26 | — | 2 | 4 | no | — |
| 219 | Dic26 | — | 2 | 4 | no | — |
| 220 | Dic26 | — | 4 | 8 | no | — |
| 221 | #1055 | — | 4 | 4 | no | — |
| 222 | C2×2−1+4 | — | 13 | 2 | no | — |
| 223 | C2×AGL(1,ℤ/8) | — | 13 | 4 | no | — |
| 224 | #550 | — | 26 | 2 | no | — |
| 225 | D4×Q8 | — | 26 | 2 | no | — |
| 226 | #548 | — | 26 | 4 | no | — |
| 227 | #537 | — | 13 | 2 | no | — |
| 228 | #537 | — | 26 | 2 | no | — |
| 229 | #532 | — | 13 | 2 | no | — |
| 230 | #532 | — | 26 | 2 | no | — |
| 231 | C2×#124 | C2×D13 | 1 | 1 | yes | characteristic |
| 232 | C2×C4×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 233 | C2×C4×D4 | C2×D13 | 1 | 1 | yes | characteristic |
| 234 | #463 | — | 26 | 4 | no | — |
| 235 | #461 | — | 26 | 2 | no | — |
| 236 | #459 | — | 26 | 2 | no | — |
| 237 | #454 | — | 26 | 8 | no | — |
| 238 | #423 | — | 13 | 2 | no | — |
| 239 | C2×#104 | — | 13 | 4 | no | — |
| 240 | C2×#104 | — | 13 | 4 | no | — |
| 241 | #417 | — | 13 | 4 | no | — |
| 242 | C2×#101 | — | 13 | 2 | no | — |
| 243 | #391 | C2×D13 | 1 | 1 | yes | characteristic |
| 244 | #390 | C2×D13 | 1 | 1 | yes | characteristic |
| 245 | #388 | — | 2 | 2 | no | — |
| 246 | #385 | — | 2 | 2 | no | — |
| 247 | #384 | C2×D13 | 1 | 1 | yes | characteristic |
| 248 | #376 | C2×D13 | 1 | 1 | yes | characteristic |
| 249 | #343 | — | 13 | 2 | no | — |
| 250 | C22×C13 | — | 2 | 1 | no | — |
| 251 | C22×C13 | — | 2 | 1 | no | — |
| 252 | C22×C13 | — | 4 | 4 | no | — |
| 253 | C22×C13 | — | 4 | 2 | no | — |
| 254 | C22×C13 | — | 8 | 2 | no | — |
| 255 | C22×C13 | — | 8 | 1 | no | — |
| 256 | C22×C13 | — | 8 | 1 | no | — |
| 257 | C22×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 258 | C22×C13 | C2×#121 | 1 | 1 | yes | characteristic |
| 259 | C22×C13 | #535 | 1 | 1 | yes | characteristic |
| 260 | C2×D13 | — | 4 | 4 | no | — |
| 261 | C2×D13 | — | 4 | 4 | no | — |
| 262 | C2×D13 | — | 4 | 4 | no | — |
| 263 | C4×C13 | — | 2 | 4 | no | — |
| 264 | C4×C13 | — | 2 | 1 | no | — |
| 265 | C4×C13 | — | 2 | 1 | no | — |
| 266 | C4×C13 | — | 2 | 2 | no | — |
| 267 | C4×C13 | — | 4 | 2 | no | — |
| 268 | C4×C13 | — | 4 | 2 | no | — |
| 269 | C4×C13 | — | 8 | 1 | no | — |
| 270 | C4×C13 | — | 8 | 1 | no | — |
| 271 | C4×C13 | D42 | 1 | 2 | yes | — |
| 272 | C4×C13 | #546 | 1 | 2 | yes | — |
| 273 | Dic13 | — | 4 | 4 | no | — |
| 274 | 2−1+4 | — | 26 | 4 | no | — |
| 275 | 2−1+4 | — | 26 | 4 | no | — |
| 276 | 2−1+4 | — | 52 | 4 | no | — |
| 277 | C2×#41 | — | 13 | 4 | no | — |
| 278 | C2×#41 | — | 26 | 4 | no | — |
| 279 | C2×#41 | — | 26 | 4 | no | — |
| 280 | C22×Q8 | — | 26 | 4 | no | — |
| 281 | C22×Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 282 | C22×D4 | C22×D13 | 1 | 1 | yes | characteristic |
| 283 | C23×C4 | — | 2 | 1 | no | — |
| 284 | AGL(1,ℤ/8) | — | 26 | 8 | no | — |
| 285 | AGL(1,ℤ/8) | — | 52 | 4 | no | — |
| 286 | C2×SD16 | — | 26 | 4 | no | — |
| 287 | C2×D8 | — | 26 | 4 | no | — |
| 288 | C2×M16 | — | 13 | 4 | no | — |
| 289 | C4⋊Q8 | — | 13 | 2 | no | — |
| 290 | C4⋊Q8 | — | 26 | 2 | no | — |
| 291 | #127 | — | 13 | 2 | no | — |
| 292 | #127 | — | 26 | 2 | no | — |
| 293 | #124 | — | 2 | 2 | no | — |
| 294 | #124 | — | 13 | 4 | no | — |
| 295 | #124 | — | 26 | 4 | no | — |
| 296 | #124 | D52 | 1 | 4 | yes | complemented |
| 297 | C22⋊Q8 | — | 26 | 4 | no | — |
| 298 | C22⋊Q8 | — | 26 | 8 | no | — |
| 299 | #121 | — | 26 | 4 | no | — |
| 300 | #121 | — | 26 | 8 | no | — |
| 301 | #121 | — | 26 | 2 | no | — |
| 302 | #121 | — | 26 | 2 | no | — |
| 303 | #121 | — | 26 | 4 | no | — |
| 304 | C4×Q8 | — | 2 | 2 | no | — |
| 305 | C4×Q8 | — | 2 | 2 | no | — |
| 306 | C4×D4 | — | 2 | 2 | no | — |
| 307 | C4×D4 | — | 2 | 2 | no | — |
| 308 | C4×D4 | — | 26 | 4 | no | — |
| 309 | C4×D4 | — | 26 | 4 | no | — |
| 310 | C4×D4 | — | 26 | 2 | no | — |
| 311 | C4×D4 | — | 26 | 2 | no | — |
| 312 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 313 | C2×C4⋊C4 | C22⋊D13 | 1 | 2 | yes | — |
| 314 | C2×C4⋊C4 | C22×D13 | 1 | 1 | yes | characteristic |
| 315 | C2×C4⋊C4 | C22×D13 | 1 | 1 | yes | characteristic |
| 316 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 317 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 318 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 319 | C2×C42 | C22⋊D13 | 1 | 2 | yes | — |
| 320 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 321 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 322 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 323 | C4⋊C8 | — | 26 | 2 | no | — |
| 324 | C4⋊C8 | — | 26 | 2 | no | — |
| 325 | #104 | — | 26 | 8 | no | — |
| 326 | #104 | — | 52 | 4 | no | — |
| 327 | #103 | — | 26 | 4 | no | — |
| 328 | #102 | — | 26 | 4 | no | — |
| 329 | #101 | — | 26 | 4 | no | — |
| 330 | #95 | — | 2 | 1 | no | — |
| 331 | #95 | — | 2 | 1 | no | — |
| 332 | #95 | — | 2 | 2 | no | — |
| 333 | C2×C13 | — | 2 | 1 | no | — |
| 334 | C2×C13 | — | 2 | 1 | no | — |
| 335 | C2×C13 | — | 8 | 2 | no | — |
| 336 | C2×C13 | #2408 | 1 | 1 | yes | characteristic |
| 337 | C2×C13 | #3020 | 1 | 1 | yes | characteristic |
| 338 | C2×C13 | #3021 | 1 | 1 | yes | characteristic |
| 339 | D13 | — | 8 | 4 | no | — |
| 340 | C24 | — | 2 | 1 | no | — |
| 341 | #41 | — | 26 | 4 | no | — |
| 342 | #41 | — | 26 | 4 | no | — |
| 343 | #41 | — | 26 | 4 | no | — |
| 344 | #41 | — | 26 | 4 | no | — |
| 345 | #41 | — | 52 | 8 | no | — |
| 346 | #41 | — | 52 | 8 | no | — |
| 347 | #41 | — | 52 | 8 | no | — |
| 348 | #41 | — | 52 | 8 | no | — |
| 349 | C2×Q8 | — | 2 | 2 | no | — |
| 350 | C2×Q8 | — | 2 | 2 | no | — |
| 351 | C2×Q8 | — | 13 | 4 | no | — |
| 352 | C2×Q8 | — | 26 | 4 | no | — |
| 353 | C2×Q8 | — | 52 | 8 | no | — |
| 354 | C2×Q8 | — | 52 | 8 | no | — |
| 355 | C2×Q8 | C2×D52 | 1 | 2 | yes | — |
| 356 | C2×Q8 | #6127 | 1 | 2 | yes | — |
| 357 | C2×D4 | — | 2 | 1 | no | — |
| 358 | C2×D4 | — | 2 | 2 | no | — |
| 359 | C2×D4 | — | 2 | 2 | no | — |
| 360 | C2×D4 | — | 13 | 4 | no | — |
| 361 | C2×D4 | — | 26 | 4 | no | — |
| 362 | C2×D4 | — | 26 | 4 | no | — |
| 363 | C2×D4 | — | 26 | 4 | no | — |
| 364 | C2×D4 | — | 26 | 2 | no | — |
| 365 | C2×D4 | — | 26 | 2 | no | — |
| 366 | C2×D4 | C2×D52 | 1 | 2 | yes | — |
| 367 | C22×C4 | — | 2 | 1 | no | — |
| 368 | C22×C4 | — | 2 | 1 | no | — |
| 369 | C22×C4 | — | 2 | 1 | no | — |
| 370 | C22×C4 | — | 4 | 2 | no | — |
| 371 | C22×C4 | — | 8 | 2 | no | — |
| 372 | C22×C4 | — | 26 | 8 | no | — |
| 373 | C22×C4 | — | 26 | 4 | no | — |
| 374 | C22×C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 375 | C22×C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 376 | C22×C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 377 | C22×C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 378 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 379 | SD16 | — | 52 | 8 | no | — |
| 380 | D8 | — | 52 | 8 | no | — |
| 381 | M16 | — | 26 | 4 | no | — |
| 382 | M16 | — | 26 | 4 | no | — |
| 383 | C2×C8 | — | 26 | 4 | no | — |
| 384 | C4⋊C4 | — | 2 | 4 | no | — |
| 385 | C4⋊C4 | — | 2 | 2 | no | — |
| 386 | C4⋊C4 | — | 2 | 2 | no | — |
| 387 | C4⋊C4 | — | 8 | 2 | no | — |
| 388 | C4⋊C4 | — | 26 | 4 | no | — |
| 389 | C4⋊C4 | — | 26 | 2 | no | — |
| 390 | C4⋊C4 | — | 26 | 2 | no | — |
| 391 | C22⋊C4 | — | 2 | 8 | no | — |
| 392 | C22⋊C4 | — | 4 | 1 | no | — |
| 393 | C22⋊C4 | — | 4 | 1 | no | — |
| 394 | C22⋊C4 | — | 8 | 2 | no | — |
| 395 | C22⋊C4 | — | 26 | 8 | no | — |
| 396 | C22⋊C4 | — | 26 | 4 | no | — |
| 397 | C22⋊C4 | — | 26 | 4 | no | — |
| 398 | C42 | — | 2 | 2 | no | — |
| 399 | C42 | — | 2 | 2 | no | — |
| 400 | C42 | — | 2 | 1 | no | — |
| 401 | C42 | — | 2 | 2 | no | — |
| 402 | C42 | C2×D52 | 1 | 2 | yes | — |
| 403 | C42 | D4×D13 | 1 | 2 | yes | — |
| 404 | C42 | D4×D13 | 1 | 2 | yes | — |
| 405 | C13 | #24227 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 406 | C23 | — | 2 | 2 | no | — |
| 407 | C23 | — | 4 | 2 | no | — |
| 408 | C23 | — | 4 | 2 | no | — |
| 409 | C23 | — | 4 | 1 | no | — |
| 410 | C23 | — | 4 | 1 | no | — |
| 411 | C23 | — | 26 | 4 | no | — |
| 412 | C23 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 413 | Q8 | — | 2 | 4 | no | — |
| 414 | Q8 | — | 2 | 4 | no | — |
| 415 | Q8 | — | 26 | 4 | no | — |
| 416 | Q8 | — | 26 | 4 | no | — |
| 417 | Q8 | — | 52 | 8 | no | — |
| 418 | D4 | — | 2 | 4 | no | — |
| 419 | D4 | — | 4 | 2 | no | — |
| 420 | D4 | — | 26 | 4 | no | — |
| 421 | D4 | — | 26 | 4 | no | — |
| 422 | D4 | — | 52 | 4 | no | — |
| 423 | D4 | — | 52 | 8 | no | — |
| 424 | D4 | — | 52 | 4 | no | — |
| 425 | D4 | — | 52 | 4 | no | — |
| 426 | D4 | — | 104 | 2 | no | — |
| 427 | D4 | — | 104 | 4 | no | — |
| 428 | C2×C4 | — | 2 | 2 | no | — |
| 429 | C2×C4 | — | 2 | 2 | no | — |
| 430 | C2×C4 | — | 2 | 2 | no | — |
| 431 | C2×C4 | — | 2 | 2 | no | — |
| 432 | C2×C4 | — | 4 | 1 | no | — |
| 433 | C2×C4 | — | 4 | 1 | no | — |
| 434 | C2×C4 | — | 4 | 1 | no | — |
| 435 | C2×C4 | — | 4 | 1 | no | — |
| 436 | C2×C4 | — | 4 | 2 | no | — |
| 437 | C2×C4 | — | 4 | 1 | no | — |
| 438 | C2×C4 | — | 4 | 2 | no | — |
| 439 | C2×C4 | — | 4 | 1 | no | — |
| 440 | C2×C4 | — | 4 | 1 | no | — |
| 441 | C2×C4 | — | 4 | 1 | no | — |
| 442 | C2×C4 | — | 8 | 4 | no | — |
| 443 | C2×C4 | — | 26 | 4 | no | — |
| 444 | C2×C4 | — | 52 | 16 | no | — |
| 445 | C2×C4 | — | 52 | 4 | no | — |
| 446 | C2×C4 | — | 52 | 4 | no | — |
| 447 | C2×C4 | #88184 | 1 | 4 | yes | — |
| 448 | C2×C4 | #88191 | 1 | 1 | yes | characteristic |
| 449 | C2×C4 | #88191 | 1 | 1 | yes | characteristic |
| 450 | C2×C4 | #88191 | 1 | 2 | yes | — |
| 451 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 452 | C2×C4 | C2×#6127 | 1 | 1 | yes | characteristic |
| 453 | C2×C4 | C2×D4×D13 | 1 | 2 | yes | — |
| 454 | C2×C4 | #88256 | 1 | 2 | yes | — |
| 455 | C8 | — | 52 | 4 | no | — |
| 456 | C22 | — | 2 | 1 | no | — |
| 457 | C22 | — | 2 | 1 | no | — |
| 458 | C22 | — | 4 | 4 | no | — |
| 459 | C22 | — | 4 | 2 | no | — |
| 460 | C22 | — | 8 | 2 | no | — |
| 461 | C22 | — | 8 | 1 | no | — |
| 462 | C22 | — | 8 | 1 | no | — |
| 463 | C22 | — | 52 | 4 | no | — |
| 464 | C22 | — | 52 | 4 | no | — |
| 465 | C22 | — | 52 | 4 | no | — |
| 466 | C22 | C2×#88184 | 1 | 1 | yes | characteristic |
| 467 | C22 | C2×#88191 | 1 | 1 | yes | characteristic |
| 468 | C22 | #11719535 | 1 | 1 | yes | characteristic |
| 469 | C4 | — | 2 | 1 | no | — |
| 470 | C4 | — | 2 | 1 | no | — |
| 471 | C4 | — | 2 | 2 | no | — |
| 472 | C4 | — | 2 | 4 | no | — |
| 473 | C4 | — | 4 | 2 | no | — |
| 474 | C4 | — | 4 | 2 | no | — |
| 475 | C4 | — | 8 | 1 | no | — |
| 476 | C4 | — | 8 | 1 | no | — |
| 477 | C4 | — | 52 | 4 | no | — |
| 478 | C4 | D4×D52 | 1 | 2 | yes | — |
| 479 | C4 | #11719255 | 1 | 2 | yes | — |
| 480 | C2 | — | 2 | 1 | no | — |
| 481 | C2 | — | 2 | 1 | no | — |
| 482 | C2 | — | 8 | 2 | no | — |
| 483 | C2 | — | 104 | 4 | no | — |
| 484 | C2 | #13118192 | 1 | 1 | yes | characteristic |
| 485 | C2 | #13124199 | 1 | 1 | yes | characteristic |
| 486 | C2 | #13124207 | 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