← #16737835
Subgroups — #16737835
Order 3328.
1668 conjugacy classes of subgroups.
The subgroup lattice has 712 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13128758 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13128722 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13126290 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13126283 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13126078 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13126044 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13125865 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13125849 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #13125720 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #13125545 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #13125442 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #13125137 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #13125128 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #13125052 | C2 | 1 | 4 | yes | maximal, complemented |
| 15 | C13×#2923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C4×C13×#41 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11719538 | C22 | 1 | 2 | yes | — |
| 18 | #11719530 | C22 | 1 | 2 | yes | — |
| 19 | #11719286 | — | 2 | 2 | no | — |
| 20 | #11719272 | — | 2 | 2 | no | — |
| 21 | #11719263 | — | 2 | 2 | no | — |
| 22 | #11719247 | — | 2 | 2 | no | — |
| 23 | #11719246 | — | 2 | 2 | no | — |
| 24 | #11719246 | — | 2 | 2 | no | — |
| 25 | #11719245 | — | 2 | 2 | no | — |
| 26 | #11719245 | — | 2 | 2 | no | — |
| 27 | #11719240 | C22 | 1 | 1 | yes | characteristic |
| 28 | #11719240 | C22 | 1 | 1 | yes | characteristic |
| 29 | #11719228 | C22 | 1 | 2 | yes | — |
| 30 | #11719223 | C22 | 1 | 1 | yes | characteristic |
| 31 | #11719223 | C22 | 1 | 2 | yes | — |
| 32 | #11719223 | C22 | 1 | 2 | yes | — |
| 33 | #11719223 | C22 | 1 | 1 | yes | characteristic |
| 34 | #11719221 | C22 | 1 | 2 | yes | — |
| 35 | #11719184 | C22 | 1 | 2 | yes | — |
| 36 | #11719184 | C22 | 1 | 2 | yes | — |
| 37 | #11719182 | C22 | 1 | 1 | yes | characteristic |
| 38 | #11719175 | C22 | 1 | 1 | yes | characteristic |
| 39 | #11719175 | C22 | 1 | 2 | yes | — |
| 40 | #11719175 | C22 | 1 | 2 | yes | — |
| 41 | C2×#88124 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#88123 | C22 | 1 | 1 | yes | characteristic |
| 43 | C13×#433 | C22 | 1 | 2 | yes | — |
| 44 | C13×#433 | C22 | 1 | 2 | yes | — |
| 45 | C13×#432 | C22 | 1 | 2 | yes | — |
| 46 | C13×#432 | C22 | 1 | 2 | yes | — |
| 47 | C13×#424 | C22 | 1 | 2 | yes | — |
| 48 | C13×#408 | C22 | 1 | 2 | yes | — |
| 49 | C4×C13×M16 | C22 | 1 | 1 | yes | characteristic |
| 50 | C2×C13×#97 | C22 | 1 | 1 | yes | characteristic |
| 51 | #11718798 | C22 | 1 | 4 | yes | — |
| 52 | #11718795 | C22 | 1 | 4 | yes | — |
| 53 | #11718777 | C22 | 1 | 4 | yes | — |
| 54 | #11718775 | C22 | 1 | 4 | yes | — |
| 55 | #11718510 | C22 | 1 | 4 | yes | — |
| 56 | #11718510 | C22 | 1 | 4 | yes | — |
| 57 | #11718509 | C22 | 1 | 4 | yes | — |
| 58 | #11718508 | C22 | 1 | 4 | yes | — |
| 59 | #11718502 | C22 | 1 | 4 | yes | — |
| 60 | #11718490 | C22 | 1 | 4 | yes | — |
| 61 | #11718490 | C22 | 1 | 4 | yes | — |
| 62 | #11718490 | C22 | 1 | 4 | yes | — |
| 63 | #11718400 | C22 | 1 | 4 | yes | — |
| 64 | #11718399 | C22 | 1 | 4 | yes | — |
| 65 | #11718398 | C22 | 1 | 4 | yes | — |
| 66 | #11718394 | C22 | 1 | 4 | yes | — |
| 67 | #11718394 | C22 | 1 | 4 | yes | — |
| 68 | #11718384 | C22 | 1 | 4 | yes | — |
| 69 | #11718383 | C22 | 1 | 4 | yes | — |
| 70 | #11718382 | C22 | 1 | 4 | yes | — |
| 71 | #11718377 | C22 | 1 | 4 | yes | — |
| 72 | #11718376 | C22 | 1 | 2 | yes | — |
| 73 | #11718376 | C22 | 1 | 2 | yes | — |
| 74 | #11718375 | C22 | 1 | 2 | yes | — |
| 75 | #11718375 | C22 | 1 | 2 | yes | — |
| 76 | #11718371 | C22 | 1 | 4 | yes | — |
| 77 | #11718364 | C22 | 1 | 2 | yes | — |
| 78 | #11718364 | C22 | 1 | 2 | yes | — |
| 79 | #11718363 | C22 | 1 | 2 | yes | — |
| 80 | #11718363 | C22 | 1 | 2 | yes | — |
| 81 | C4×Dic52 | C22 | 1 | 4 | yes | — |
| 82 | C4×#6095 | C22 | 1 | 4 | yes | — |
| 83 | C2×C13×#41 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×#6127 | C23 | 1 | 2 | yes | — |
| 85 | C22×Dic26 | C23 | 1 | 2 | yes | — |
| 86 | C2×C13×M16 | C23 | 1 | 2 | yes | — |
| 87 | C22×C8×C13 | C23 | 1 | 2 | yes | — |
| 88 | C4×Q8×C13 | D4 | 1 | 2 | yes | — |
| 89 | C4×D4×C13 | D4 | 1 | 2 | yes | — |
| 90 | C4×D4×C13 | D4 | 1 | 2 | yes | — |
| 91 | C4×D4×C13 | D4 | 1 | 2 | yes | — |
| 92 | C13×#117 | C23 | 1 | 1 | yes | characteristic |
| 93 | C13×#117 | C23 | 1 | 1 | yes | characteristic |
| 94 | C13×#117 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 98 | #88200 | — | 2 | 2 | no | — |
| 99 | #88198 | — | 2 | 2 | no | — |
| 100 | #88193 | — | 2 | 2 | no | — |
| 101 | #88193 | — | 2 | 2 | no | — |
| 102 | #88192 | — | 2 | 2 | no | — |
| 103 | #88190 | — | 2 | 2 | no | — |
| 104 | #88189 | — | 2 | 2 | no | — |
| 105 | #88189 | — | 2 | 2 | no | — |
| 106 | #88184 | — | 2 | 2 | no | — |
| 107 | #88184 | C23 | 1 | 2 | yes | — |
| 108 | #88184 | C23 | 1 | 2 | yes | — |
| 109 | #88183 | — | 2 | 2 | no | — |
| 110 | #88183 | — | 2 | 2 | no | — |
| 111 | C4×C22⋊D13 | — | 2 | 2 | no | — |
| 112 | C4×C22⋊D13 | — | 2 | 2 | no | — |
| 113 | #88180 | — | 2 | 2 | no | — |
| 114 | #88180 | — | 2 | 2 | no | — |
| 115 | #88180 | C23 | 1 | 2 | yes | — |
| 116 | C2×C4⋊Dic13 | — | 2 | 2 | no | — |
| 117 | C2×C4⋊Dic13 | C23 | 1 | 2 | yes | — |
| 118 | #88178 | — | 2 | 2 | no | — |
| 119 | #88178 | — | 2 | 2 | no | — |
| 120 | #88178 | — | 2 | 2 | no | — |
| 121 | #88178 | C23 | 1 | 2 | yes | — |
| 122 | #88178 | C23 | 1 | 4 | yes | — |
| 123 | #88178 | C23 | 1 | 4 | yes | — |
| 124 | #88178 | C23 | 1 | 2 | yes | — |
| 125 | C2×#6101 | — | 2 | 2 | no | — |
| 126 | C2×Dic52 | C23 | 1 | 4 | yes | — |
| 127 | C2×Dic52 | C23 | 1 | 4 | yes | — |
| 128 | C2×#6095 | C23 | 1 | 4 | yes | — |
| 129 | C2×#6095 | C23 | 1 | 4 | yes | — |
| 130 | #88148 | — | 2 | 2 | no | — |
| 131 | #88148 | — | 2 | 2 | no | — |
| 132 | #88146 | — | 2 | 2 | no | — |
| 133 | C4⋊C4×D13 | — | 2 | 2 | no | — |
| 134 | #88143 | — | 2 | 2 | no | — |
| 135 | #88143 | — | 2 | 2 | no | — |
| 136 | #88143 | — | 2 | 4 | no | — |
| 137 | #88143 | — | 2 | 4 | no | — |
| 138 | #88141 | — | 2 | 4 | no | — |
| 139 | #88138 | — | 2 | 2 | no | — |
| 140 | #88138 | — | 2 | 2 | no | — |
| 141 | #88135 | — | 2 | 2 | no | — |
| 142 | #88135 | — | 2 | 2 | no | — |
| 143 | #88133 | — | 2 | 2 | no | — |
| 144 | #88133 | — | 2 | 2 | no | — |
| 145 | #88133 | — | 2 | 4 | no | — |
| 146 | #88133 | — | 2 | 4 | no | — |
| 147 | #88131 | — | 2 | 4 | no | — |
| 148 | #88130 | — | 2 | 2 | no | — |
| 149 | #88130 | — | 2 | 2 | no | — |
| 150 | #88129 | C23 | 1 | 2 | yes | — |
| 151 | #88128 | C23 | 1 | 1 | yes | characteristic |
| 152 | C4×D52 | — | 2 | 2 | no | — |
| 153 | C4×D52 | C23 | 1 | 2 | yes | — |
| 154 | C4×D52 | C23 | 1 | 2 | yes | — |
| 155 | #88126 | — | 2 | 2 | no | — |
| 156 | #88126 | — | 2 | 2 | no | — |
| 157 | #88124 | — | 2 | 2 | no | — |
| 158 | #88124 | — | 2 | 2 | no | — |
| 159 | #88124 | — | 2 | 2 | no | — |
| 160 | #88124 | C23 | 1 | 2 | yes | — |
| 161 | #88124 | C23 | 1 | 1 | yes | characteristic |
| 162 | #88124 | C23 | 1 | 1 | yes | characteristic |
| 163 | #88124 | C23 | 1 | 2 | yes | — |
| 164 | #88123 | — | 2 | 2 | no | — |
| 165 | #88123 | C23 | 1 | 2 | yes | — |
| 166 | #88123 | C23 | 1 | 2 | yes | — |
| 167 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 168 | #88123 | C23 | 1 | 2 | yes | — |
| 169 | C4×Dic26 | — | 2 | 2 | no | — |
| 170 | C4×Dic26 | — | 2 | 2 | no | — |
| 171 | C4×Dic26 | — | 2 | 2 | no | — |
| 172 | C4×Dic26 | C23 | 1 | 4 | yes | — |
| 173 | C4×Dic26 | C23 | 1 | 4 | yes | — |
| 174 | C4×Dic26 | C23 | 1 | 2 | yes | — |
| 175 | C4×Dic26 | C23 | 1 | 2 | yes | — |
| 176 | C13×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 177 | C13×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 178 | C13×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 179 | C13×C22⋊C8 | C23 | 1 | 4 | yes | — |
| 180 | C13×#97 | C23 | 1 | 2 | yes | — |
| 181 | C13×#97 | C23 | 1 | 2 | yes | — |
| 182 | C13×#97 | C23 | 1 | 2 | yes | — |
| 183 | C4×C8×C13 | C23 | 1 | 2 | yes | — |
| 184 | #88061 | C23 | 1 | 4 | yes | — |
| 185 | #88061 | C23 | 1 | 4 | yes | — |
| 186 | #88058 | C23 | 1 | 4 | yes | — |
| 187 | #88058 | C23 | 1 | 4 | yes | — |
| 188 | #88057 | C23 | 1 | 4 | yes | — |
| 189 | #88057 | C23 | 1 | 4 | yes | — |
| 190 | #88056 | C23 | 1 | 4 | yes | — |
| 191 | #88056 | C23 | 1 | 4 | yes | — |
| 192 | #88056 | C23 | 1 | 4 | yes | — |
| 193 | #88056 | C23 | 1 | 4 | yes | — |
| 194 | #88056 | C23 | 1 | 4 | yes | — |
| 195 | #88056 | C23 | 1 | 4 | yes | — |
| 196 | #61020 | — | 13 | 1 | no | maximal, Sylow |
| 197 | C13×#41 | — | 4 | 2 | no | — |
| 198 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C2×D4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C2×D4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C2×D4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 203 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 204 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 205 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 206 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 207 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 208 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 209 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 210 | C2×C22⋊D13 | — | 2 | 2 | no | — |
| 211 | C22×Dic13 | — | 2 | 2 | no | — |
| 212 | C22×Dic13 | — | 2 | 2 | no | — |
| 213 | #6127 | — | 4 | 4 | no | — |
| 214 | C2×D52 | — | 2 | 2 | no | — |
| 215 | C2×D52 | C24 | 1 | 2 | yes | — |
| 216 | C2×C4×D13 | — | 2 | 2 | no | — |
| 217 | C2×C4×D13 | — | 2 | 2 | no | — |
| 218 | C2×C4×D13 | — | 2 | 2 | no | — |
| 219 | C2×Dic26 | — | 2 | 2 | no | — |
| 220 | C2×Dic26 | — | 2 | 2 | no | — |
| 221 | C2×Dic26 | — | 4 | 4 | no | — |
| 222 | C2×Dic26 | C24 | 1 | 4 | yes | — |
| 223 | C2×Dic26 | C24 | 1 | 2 | yes | — |
| 224 | C13×M16 | — | 4 | 2 | no | — |
| 225 | C2×C8×C13 | — | 4 | 2 | no | — |
| 226 | C2×C8×C13 | C24 | 1 | 4 | yes | — |
| 227 | C2×C8×C13 | C24 | 1 | 4 | yes | — |
| 228 | C13×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 229 | C13×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 230 | C13×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 231 | C13×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 232 | C13×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 233 | C13×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 234 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 235 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 236 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 237 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 238 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 239 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 240 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 241 | C22⋊Dic13 | — | 2 | 2 | no | — |
| 242 | C22⋊Dic13 | — | 2 | 4 | no | — |
| 243 | C22⋊Dic13 | — | 2 | 4 | no | — |
| 244 | C22⋊Dic13 | — | 2 | 2 | no | — |
| 245 | C22⋊Dic13 | — | 2 | 2 | no | — |
| 246 | #6103 | — | 2 | 2 | no | — |
| 247 | #6103 | — | 2 | 2 | no | — |
| 248 | #6103 | — | 2 | 2 | no | — |
| 249 | #6103 | — | 2 | 2 | no | — |
| 250 | #6103 | — | 2 | 2 | no | — |
| 251 | #6103 | — | 2 | 2 | no | — |
| 252 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 253 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 254 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 255 | C4⋊Dic13 | — | 2 | 4 | no | — |
| 256 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 257 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 258 | C4⋊Dic13 | C24 | 1 | 4 | yes | — |
| 259 | C4⋊Dic13 | C24 | 1 | 2 | yes | — |
| 260 | C4⋊Dic13 | C24 | 1 | 2 | yes | — |
| 261 | #6101 | — | 2 | 4 | no | — |
| 262 | #6101 | — | 2 | 4 | no | — |
| 263 | #6101 | — | 2 | 4 | no | — |
| 264 | #6101 | — | 2 | 4 | no | — |
| 265 | #6101 | — | 2 | 4 | no | — |
| 266 | #6101 | — | 2 | 2 | no | — |
| 267 | #6101 | — | 2 | 2 | no | — |
| 268 | #6101 | — | 2 | 2 | no | — |
| 269 | #6101 | — | 2 | 2 | no | — |
| 270 | #6101 | — | 2 | 2 | no | — |
| 271 | #6101 | — | 2 | 2 | no | — |
| 272 | #6101 | — | 2 | 2 | no | — |
| 273 | #6101 | — | 2 | 2 | no | — |
| 274 | C4×Dic13 | — | 2 | 2 | no | — |
| 275 | C4×Dic13 | — | 2 | 4 | no | — |
| 276 | C4×Dic13 | — | 2 | 4 | no | — |
| 277 | C4×Dic13 | — | 2 | 2 | no | — |
| 278 | C4×Dic13 | — | 2 | 2 | no | — |
| 279 | Dic52 | — | 4 | 4 | no | — |
| 280 | Dic52 | — | 4 | 4 | no | — |
| 281 | #6095 | — | 4 | 4 | no | — |
| 282 | #6095 | — | 4 | 4 | no | — |
| 283 | #3512 | — | 13 | 1 | no | — |
| 284 | #3509 | — | 13 | 1 | no | — |
| 285 | #3261 | — | 13 | 2 | no | — |
| 286 | #3260 | — | 13 | 2 | no | — |
| 287 | #3240 | — | 13 | 2 | no | — |
| 288 | #3236 | — | 13 | 2 | no | — |
| 289 | #3218 | — | 13 | 2 | no | — |
| 290 | #3216 | — | 13 | 2 | no | — |
| 291 | #3201 | — | 13 | 4 | no | — |
| 292 | #3181 | — | 13 | 2 | no | — |
| 293 | #3172 | — | 13 | 2 | no | — |
| 294 | #3127 | — | 13 | 2 | no | — |
| 295 | #3126 | — | 13 | 2 | no | — |
| 296 | #3120 | — | 13 | 4 | no | — |
| 297 | #2923 | D13 | 1 | 1 | yes | characteristic, complemented |
| 298 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 300 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 301 | C22×D13 | — | 2 | 2 | no | — |
| 302 | Q8×C13 | — | 4 | 1 | no | — |
| 303 | D4×C13 | — | 4 | 1 | no | — |
| 304 | D4×C13 | — | 4 | 1 | no | — |
| 305 | D4×C13 | — | 4 | 1 | no | — |
| 306 | C2×C4×C13 | — | 2 | 2 | no | — |
| 307 | C2×C4×C13 | — | 2 | 2 | no | — |
| 308 | C2×C4×C13 | — | 2 | 2 | no | — |
| 309 | C2×C4×C13 | — | 4 | 2 | no | — |
| 310 | C2×C4×C13 | — | 4 | 2 | no | — |
| 311 | C2×C4×C13 | — | 4 | 2 | no | — |
| 312 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 313 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 314 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 315 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 316 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 317 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 318 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 319 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 320 | C22⋊D13 | — | 4 | 4 | no | — |
| 321 | C22⋊D13 | — | 8 | 2 | no | — |
| 322 | C22⋊D13 | — | 8 | 2 | no | — |
| 323 | C2×Dic13 | — | 2 | 4 | no | — |
| 324 | C2×Dic13 | — | 2 | 4 | no | — |
| 325 | C2×Dic13 | — | 2 | 2 | no | — |
| 326 | C2×Dic13 | — | 2 | 2 | no | — |
| 327 | C2×Dic13 | — | 2 | 2 | no | — |
| 328 | C2×Dic13 | — | 4 | 4 | no | — |
| 329 | C2×Dic13 | — | 8 | 2 | no | — |
| 330 | D52 | — | 2 | 4 | no | — |
| 331 | D52 | — | 8 | 2 | no | — |
| 332 | C4×D13 | — | 4 | 4 | no | — |
| 333 | C4×D13 | — | 8 | 2 | no | — |
| 334 | C4×D13 | — | 8 | 2 | no | — |
| 335 | Dic26 | — | 2 | 4 | no | — |
| 336 | Dic26 | — | 2 | 4 | no | — |
| 337 | Dic26 | — | 2 | 4 | no | — |
| 338 | Dic26 | — | 4 | 4 | no | — |
| 339 | Dic26 | — | 4 | 4 | no | — |
| 340 | C8×C13 | — | 2 | 4 | no | — |
| 341 | C8×C13 | — | 2 | 4 | no | — |
| 342 | #557 | — | 26 | 2 | no | — |
| 343 | #556 | — | 26 | 2 | no | — |
| 344 | #553 | — | 26 | 2 | no | — |
| 345 | #553 | — | 26 | 2 | no | — |
| 346 | #553 | — | 26 | 2 | no | — |
| 347 | #552 | — | 26 | 2 | no | — |
| 348 | #552 | — | 26 | 2 | no | — |
| 349 | #552 | — | 26 | 2 | no | — |
| 350 | #541 | — | 13 | 2 | no | — |
| 351 | #541 | — | 13 | 1 | no | — |
| 352 | #541 | — | 13 | 2 | no | — |
| 353 | #541 | — | 13 | 1 | no | — |
| 354 | #540 | — | 13 | 1 | no | — |
| 355 | #540 | — | 13 | 1 | no | — |
| 356 | #537 | — | 13 | 2 | no | — |
| 357 | #536 | — | 13 | 2 | no | — |
| 358 | #533 | — | 13 | 1 | no | — |
| 359 | #533 | — | 13 | 2 | no | — |
| 360 | #533 | — | 13 | 2 | no | — |
| 361 | #532 | — | 13 | 1 | no | — |
| 362 | C2×C4⋊Q8 | — | 13 | 1 | no | — |
| 363 | #529 | — | 13 | 2 | no | — |
| 364 | #529 | — | 13 | 2 | no | — |
| 365 | C2×#125 | — | 13 | 1 | no | — |
| 366 | #520 | — | 13 | 2 | no | — |
| 367 | #519 | — | 13 | 2 | no | — |
| 368 | C4×#41 | C2×D13 | 1 | 1 | yes | characteristic |
| 369 | #501 | — | 13 | 2 | no | — |
| 370 | #501 | — | 13 | 2 | no | — |
| 371 | #497 | — | 13 | 2 | no | — |
| 372 | #497 | — | 13 | 2 | no | — |
| 373 | #491 | — | 13 | 2 | no | — |
| 374 | #491 | — | 13 | 2 | no | — |
| 375 | #489 | — | 13 | 2 | no | — |
| 376 | #489 | — | 13 | 2 | no | — |
| 377 | #485 | — | 13 | 4 | no | — |
| 378 | #484 | — | 13 | 4 | no | — |
| 379 | #483 | — | 13 | 4 | no | — |
| 380 | #482 | — | 13 | 4 | no | — |
| 381 | #479 | — | 13 | 4 | no | — |
| 382 | #479 | — | 13 | 4 | no | — |
| 383 | #479 | — | 13 | 4 | no | — |
| 384 | #478 | — | 13 | 4 | no | — |
| 385 | #470 | — | 13 | 4 | no | — |
| 386 | #468 | — | 13 | 4 | no | — |
| 387 | #467 | — | 13 | 4 | no | — |
| 388 | #465 | — | 13 | 4 | no | — |
| 389 | #462 | — | 13 | 4 | no | — |
| 390 | #462 | — | 13 | 4 | no | — |
| 391 | #461 | — | 13 | 4 | no | — |
| 392 | #460 | — | 13 | 4 | no | — |
| 393 | #452 | — | 13 | 4 | no | — |
| 394 | #452 | — | 13 | 4 | no | — |
| 395 | #451 | — | 13 | 4 | no | — |
| 396 | #448 | — | 13 | 4 | no | — |
| 397 | #441 | — | 13 | 4 | no | — |
| 398 | #440 | — | 13 | 4 | no | — |
| 399 | C4×Q16 | — | 13 | 4 | no | — |
| 400 | C4×SD16 | — | 13 | 4 | no | — |
| 401 | #433 | C2×D13 | 1 | 2 | yes | — |
| 402 | #433 | C2×D13 | 1 | 2 | yes | — |
| 403 | #432 | C2×D13 | 1 | 2 | yes | — |
| 404 | #432 | C2×D13 | 1 | 2 | yes | — |
| 405 | #424 | C2×D13 | 1 | 2 | yes | — |
| 406 | #408 | C2×D13 | 1 | 2 | yes | — |
| 407 | C4×M16 | C2×D13 | 1 | 1 | yes | characteristic |
| 408 | C2×#97 | C2×D13 | 1 | 1 | yes | characteristic |
| 409 | C22×C13 | — | 2 | 2 | no | — |
| 410 | C22×C13 | — | 2 | 2 | no | — |
| 411 | C22×C13 | — | 2 | 2 | no | — |
| 412 | C22×C13 | — | 2 | 1 | no | — |
| 413 | C22×C13 | — | 2 | 1 | no | — |
| 414 | C22×C13 | — | 2 | 1 | no | — |
| 415 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 416 | C2×D13 | — | 4 | 2 | no | — |
| 417 | C2×D13 | — | 4 | 2 | no | — |
| 418 | C2×D13 | — | 4 | 2 | no | — |
| 419 | C4×C13 | — | 2 | 2 | no | — |
| 420 | C4×C13 | — | 2 | 2 | no | — |
| 421 | C4×C13 | — | 2 | 2 | no | — |
| 422 | C4×C13 | — | 2 | 2 | no | — |
| 423 | C4×C13 | — | 2 | 1 | no | — |
| 424 | C4×C13 | — | 2 | 1 | no | — |
| 425 | C4×C13 | — | 2 | 1 | no | — |
| 426 | C4×C13 | #585 | 1 | 2 | yes | — |
| 427 | Dic13 | — | 4 | 4 | no | — |
| 428 | Dic13 | — | 4 | 2 | no | — |
| 429 | Dic13 | — | 4 | 2 | no | — |
| 430 | Dic13 | — | 4 | 4 | no | — |
| 431 | Dic13 | — | 4 | 2 | no | — |
| 432 | C2×#41 | — | 13 | 2 | no | — |
| 433 | C2×#41 | C22×D13 | 1 | 1 | yes | characteristic |
| 434 | C22×Q8 | — | 13 | 2 | no | — |
| 435 | C2×Q16 | — | 13 | 4 | no | — |
| 436 | C2×Q16 | — | 13 | 4 | no | — |
| 437 | C2×SD16 | — | 13 | 4 | no | — |
| 438 | C2×SD16 | — | 13 | 4 | no | — |
| 439 | C2×M16 | C22×D13 | 1 | 2 | yes | — |
| 440 | C22×C8 | C22×D13 | 1 | 2 | yes | — |
| 441 | C4⋊Q8 | — | 13 | 2 | no | — |
| 442 | C4⋊Q8 | — | 13 | 2 | no | — |
| 443 | C4⋊Q8 | — | 13 | 2 | no | — |
| 444 | C4⋊Q8 | — | 13 | 1 | no | — |
| 445 | C4⋊Q8 | — | 26 | 2 | no | — |
| 446 | C4⋊Q8 | — | 26 | 2 | no | — |
| 447 | #127 | — | 13 | 1 | no | — |
| 448 | #126 | — | 26 | 4 | no | — |
| 449 | #126 | — | 26 | 4 | no | — |
| 450 | #126 | — | 26 | 2 | no | — |
| 451 | #126 | — | 26 | 2 | no | — |
| 452 | #126 | — | 26 | 2 | no | — |
| 453 | #126 | — | 26 | 2 | no | — |
| 454 | #125 | — | 13 | 2 | no | — |
| 455 | #125 | — | 13 | 1 | no | — |
| 456 | #125 | — | 13 | 1 | no | — |
| 457 | #125 | — | 13 | 2 | no | — |
| 458 | #125 | — | 26 | 2 | no | — |
| 459 | #125 | — | 26 | 2 | no | — |
| 460 | #125 | — | 26 | 4 | no | — |
| 461 | #125 | — | 26 | 4 | no | — |
| 462 | #125 | — | 26 | 2 | no | — |
| 463 | #125 | — | 26 | 2 | no | — |
| 464 | #125 | — | 26 | 2 | no | — |
| 465 | #124 | — | 13 | 2 | no | — |
| 466 | #124 | — | 26 | 2 | no | — |
| 467 | #123 | — | 26 | 2 | no | — |
| 468 | #123 | — | 26 | 2 | no | — |
| 469 | #123 | — | 26 | 2 | no | — |
| 470 | #123 | — | 26 | 2 | no | — |
| 471 | #123 | — | 26 | 2 | no | — |
| 472 | #123 | — | 26 | 2 | no | — |
| 473 | C22⋊Q8 | — | 13 | 2 | no | — |
| 474 | C22⋊Q8 | — | 13 | 2 | no | — |
| 475 | C22⋊Q8 | — | 13 | 4 | no | — |
| 476 | C22⋊Q8 | — | 13 | 4 | no | — |
| 477 | C22⋊Q8 | — | 26 | 2 | no | — |
| 478 | C22⋊Q8 | — | 26 | 2 | no | — |
| 479 | C22⋊Q8 | — | 26 | 2 | no | — |
| 480 | C22⋊Q8 | — | 26 | 2 | no | — |
| 481 | #121 | — | 13 | 2 | no | — |
| 482 | #121 | — | 13 | 2 | no | — |
| 483 | #121 | — | 26 | 2 | no | — |
| 484 | #121 | — | 26 | 2 | no | — |
| 485 | #121 | — | 26 | 2 | no | — |
| 486 | #121 | — | 26 | 2 | no | — |
| 487 | #121 | — | 26 | 2 | no | — |
| 488 | #121 | — | 26 | 2 | no | — |
| 489 | C4×Q8 | — | 13 | 4 | no | — |
| 490 | C4×Q8 | — | 13 | 4 | no | — |
| 491 | C4×Q8 | — | 13 | 2 | no | — |
| 492 | C4×Q8 | — | 13 | 2 | no | — |
| 493 | C4×Q8 | — | 26 | 4 | no | — |
| 494 | C4×Q8 | — | 26 | 2 | no | — |
| 495 | C4×Q8 | — | 26 | 2 | no | — |
| 496 | C4×Q8 | — | 26 | 2 | no | — |
| 497 | C4×Q8 | D52 | 1 | 2 | yes | — |
| 498 | C4×D4 | — | 13 | 2 | no | — |
| 499 | C4×D4 | — | 13 | 2 | no | — |
| 500 | C4×D4 | — | 26 | 2 | no | — |
| 501 | C4×D4 | — | 26 | 2 | no | — |
| 502 | C4×D4 | — | 26 | 2 | no | — |
| 503 | C4×D4 | — | 26 | 2 | no | — |
| 504 | C4×D4 | — | 26 | 2 | no | — |
| 505 | C4×D4 | D52 | 1 | 2 | yes | — |
| 506 | C4×D4 | D52 | 1 | 2 | yes | — |
| 507 | C4×D4 | D52 | 1 | 2 | yes | — |
| 508 | #117 | — | 13 | 2 | no | — |
| 509 | #117 | — | 26 | 2 | no | — |
| 510 | #117 | — | 26 | 2 | no | — |
| 511 | #117 | — | 26 | 2 | no | — |
| 512 | #117 | — | 26 | 4 | no | — |
| 513 | #117 | — | 26 | 2 | no | — |
| 514 | #117 | — | 26 | 2 | no | — |
| 515 | #117 | C22×D13 | 1 | 1 | yes | characteristic |
| 516 | #117 | C22×D13 | 1 | 1 | yes | characteristic |
| 517 | #117 | C22×D13 | 1 | 1 | yes | characteristic |
| 518 | C2×C4⋊C4 | — | 13 | 2 | no | — |
| 519 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 520 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 521 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 522 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 523 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 524 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 525 | #107 | — | 13 | 4 | no | — |
| 526 | #107 | — | 13 | 4 | no | — |
| 527 | #106 | — | 13 | 4 | no | — |
| 528 | #106 | — | 13 | 4 | no | — |
| 529 | C4⋊C8 | C22×D13 | 1 | 4 | yes | — |
| 530 | C4⋊C8 | C22×D13 | 1 | 4 | yes | — |
| 531 | #103 | — | 13 | 4 | no | — |
| 532 | #103 | — | 13 | 4 | no | — |
| 533 | #103 | — | 13 | 4 | no | — |
| 534 | #103 | — | 13 | 4 | no | — |
| 535 | #103 | — | 13 | 4 | no | — |
| 536 | #103 | — | 13 | 4 | no | — |
| 537 | #102 | — | 13 | 4 | no | — |
| 538 | #102 | — | 13 | 4 | no | — |
| 539 | C22⋊C8 | C22×D13 | 1 | 4 | yes | — |
| 540 | C22⋊C8 | C22×D13 | 1 | 4 | yes | — |
| 541 | #97 | C22×D13 | 1 | 2 | yes | — |
| 542 | #97 | C22×D13 | 1 | 2 | yes | — |
| 543 | #97 | C22×D13 | 1 | 2 | yes | — |
| 544 | C4×C8 | C22×D13 | 1 | 2 | yes | — |
| 545 | C2×C13 | — | 4 | 1 | no | — |
| 546 | C2×C13 | — | 4 | 1 | no | — |
| 547 | C2×C13 | — | 4 | 1 | no | — |
| 548 | C2×C13 | #3449 | 1 | 1 | yes | characteristic |
| 549 | C2×C13 | #3586 | 1 | 2 | yes | — |
| 550 | D13 | — | 8 | 2 | no | — |
| 551 | #41 | — | 4 | 2 | no | — |
| 552 | #41 | — | 52 | 4 | no | — |
| 553 | C2×Q8 | — | 13 | 2 | no | — |
| 554 | C2×Q8 | — | 13 | 4 | no | — |
| 555 | C2×Q8 | — | 26 | 2 | no | — |
| 556 | C2×Q8 | — | 26 | 2 | no | — |
| 557 | C2×Q8 | — | 52 | 4 | no | — |
| 558 | C2×Q8 | C2×D52 | 1 | 1 | yes | characteristic |
| 559 | C2×D4 | — | 13 | 2 | no | — |
| 560 | C2×D4 | — | 26 | 2 | no | — |
| 561 | C2×D4 | — | 26 | 2 | no | — |
| 562 | C2×D4 | — | 26 | 2 | no | — |
| 563 | C2×D4 | — | 26 | 2 | no | — |
| 564 | C2×D4 | C2×D52 | 1 | 1 | yes | characteristic |
| 565 | C2×D4 | C2×D52 | 1 | 1 | yes | characteristic |
| 566 | C2×D4 | C2×D52 | 1 | 1 | yes | characteristic |
| 567 | C22×C4 | — | 26 | 2 | no | — |
| 568 | C22×C4 | — | 26 | 2 | no | — |
| 569 | C22×C4 | — | 26 | 2 | no | — |
| 570 | C22×C4 | — | 26 | 2 | no | — |
| 571 | C22×C4 | — | 26 | 2 | no | — |
| 572 | C22×C4 | C2×D52 | 1 | 2 | yes | — |
| 573 | C22×C4 | C2×D52 | 1 | 2 | yes | — |
| 574 | C22×C4 | C2×D52 | 1 | 2 | yes | — |
| 575 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 576 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 577 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 578 | Q16 | — | 52 | 4 | no | — |
| 579 | Q16 | — | 52 | 4 | no | — |
| 580 | SD16 | — | 52 | 4 | no | — |
| 581 | SD16 | — | 52 | 4 | no | — |
| 582 | M16 | — | 4 | 2 | no | — |
| 583 | C2×C8 | — | 4 | 2 | no | — |
| 584 | C2×C8 | C23×D13 | 1 | 4 | yes | — |
| 585 | C2×C8 | C23×D13 | 1 | 4 | yes | — |
| 586 | C4⋊C4 | — | 13 | 4 | no | — |
| 587 | C4⋊C4 | — | 13 | 2 | no | — |
| 588 | C4⋊C4 | — | 13 | 2 | no | — |
| 589 | C4⋊C4 | — | 26 | 2 | no | — |
| 590 | C4⋊C4 | — | 26 | 2 | no | — |
| 591 | C4⋊C4 | — | 26 | 2 | no | — |
| 592 | C4⋊C4 | — | 26 | 2 | no | — |
| 593 | C4⋊C4 | — | 26 | 2 | no | — |
| 594 | C4⋊C4 | — | 26 | 2 | no | — |
| 595 | C4⋊C4 | — | 26 | 2 | no | — |
| 596 | C4⋊C4 | — | 26 | 2 | no | — |
| 597 | C4⋊C4 | — | 26 | 2 | no | — |
| 598 | C4⋊C4 | — | 26 | 4 | no | — |
| 599 | C4⋊C4 | — | 26 | 2 | no | — |
| 600 | C4⋊C4 | — | 26 | 4 | no | — |
| 601 | C4⋊C4 | — | 26 | 4 | no | — |
| 602 | C4⋊C4 | — | 26 | 2 | no | — |
| 603 | C4⋊C4 | — | 26 | 2 | no | — |
| 604 | C4⋊C4 | — | 26 | 2 | no | — |
| 605 | C4⋊C4 | — | 26 | 4 | no | — |
| 606 | C4⋊C4 | — | 26 | 4 | no | — |
| 607 | C4⋊C4 | — | 26 | 4 | no | — |
| 608 | C4⋊C4 | C2×D52 | 1 | 2 | yes | — |
| 609 | C4⋊C4 | C2×D52 | 1 | 2 | yes | — |
| 610 | C4⋊C4 | C2×D52 | 1 | 2 | yes | — |
| 611 | C22⋊C4 | — | 26 | 2 | no | — |
| 612 | C22⋊C4 | — | 26 | 4 | no | — |
| 613 | C22⋊C4 | — | 26 | 4 | no | — |
| 614 | C22⋊C4 | — | 26 | 2 | no | — |
| 615 | C22⋊C4 | — | 26 | 2 | no | — |
| 616 | C22⋊C4 | — | 26 | 2 | no | — |
| 617 | C22⋊C4 | — | 26 | 2 | no | — |
| 618 | C22⋊C4 | — | 26 | 2 | no | — |
| 619 | C22⋊C4 | — | 26 | 2 | no | — |
| 620 | C22⋊C4 | — | 26 | 2 | no | — |
| 621 | C22⋊C4 | — | 26 | 2 | no | — |
| 622 | C22⋊C4 | C2×D52 | 1 | 2 | yes | — |
| 623 | C22⋊C4 | C2×D52 | 1 | 2 | yes | — |
| 624 | C22⋊C4 | C2×D52 | 1 | 2 | yes | — |
| 625 | C42 | — | 26 | 2 | no | — |
| 626 | C42 | — | 26 | 2 | no | — |
| 627 | C42 | — | 26 | 2 | no | — |
| 628 | C42 | — | 26 | 4 | no | — |
| 629 | C42 | — | 26 | 4 | no | — |
| 630 | C42 | C2×D52 | 1 | 2 | yes | — |
| 631 | C42 | C2×D52 | 1 | 2 | yes | — |
| 632 | C42 | C2×D52 | 1 | 2 | yes | — |
| 633 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 634 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 635 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 636 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 637 | C13 | #61020 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 638 | C23 | — | 26 | 2 | no | — |
| 639 | C23 | C22×D52 | 1 | 1 | yes | characteristic |
| 640 | C23 | C22×D52 | 1 | 1 | yes | characteristic |
| 641 | C23 | C22×D52 | 1 | 1 | yes | characteristic |
| 642 | Q8 | — | 4 | 1 | no | — |
| 643 | Q8 | — | 26 | 4 | no | — |
| 644 | Q8 | — | 26 | 4 | no | — |
| 645 | Q8 | — | 26 | 4 | no | — |
| 646 | Q8 | — | 52 | 4 | no | — |
| 647 | Q8 | — | 52 | 4 | no | — |
| 648 | D4 | — | 4 | 1 | no | — |
| 649 | D4 | — | 4 | 1 | no | — |
| 650 | D4 | — | 4 | 1 | no | — |
| 651 | D4 | — | 26 | 4 | no | — |
| 652 | D4 | — | 52 | 4 | no | — |
| 653 | D4 | — | 104 | 2 | no | — |
| 654 | D4 | — | 104 | 2 | no | — |
| 655 | D4 | — | 104 | 2 | no | — |
| 656 | C2×C4 | — | 2 | 2 | no | — |
| 657 | C2×C4 | — | 2 | 2 | no | — |
| 658 | C2×C4 | — | 2 | 2 | no | — |
| 659 | C2×C4 | — | 4 | 2 | no | — |
| 660 | C2×C4 | — | 4 | 2 | no | — |
| 661 | C2×C4 | — | 4 | 2 | no | — |
| 662 | C2×C4 | — | 26 | 4 | no | — |
| 663 | C2×C4 | — | 26 | 2 | no | — |
| 664 | C2×C4 | — | 26 | 4 | no | — |
| 665 | C2×C4 | — | 26 | 2 | no | — |
| 666 | C2×C4 | — | 26 | 2 | no | — |
| 667 | C2×C4 | — | 52 | 4 | no | — |
| 668 | C2×C4 | — | 52 | 4 | no | — |
| 669 | C2×C4 | — | 104 | 2 | no | — |
| 670 | C2×C4 | — | 104 | 2 | no | — |
| 671 | C2×C4 | — | 104 | 2 | no | — |
| 672 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 673 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 674 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 675 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 676 | C2×C4 | C22×D52 | 1 | 2 | yes | — |
| 677 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 678 | C2×C4 | C22×D52 | 1 | 1 | yes | characteristic |
| 679 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 680 | C8 | — | 2 | 4 | no | — |
| 681 | C8 | — | 2 | 4 | no | — |
| 682 | C22 | — | 2 | 2 | no | — |
| 683 | C22 | — | 2 | 2 | no | — |
| 684 | C22 | — | 2 | 2 | no | — |
| 685 | C22 | — | 2 | 1 | no | — |
| 686 | C22 | — | 2 | 1 | no | — |
| 687 | C22 | — | 2 | 1 | no | — |
| 688 | C22 | — | 52 | 2 | no | — |
| 689 | C22 | — | 52 | 2 | no | — |
| 690 | C22 | — | 52 | 2 | no | — |
| 691 | C22 | C23×D52 | 1 | 1 | yes | characteristic |
| 692 | C4 | — | 2 | 2 | no | — |
| 693 | C4 | — | 2 | 2 | no | — |
| 694 | C4 | — | 2 | 2 | no | — |
| 695 | C4 | — | 2 | 2 | no | — |
| 696 | C4 | — | 2 | 1 | no | — |
| 697 | C4 | — | 2 | 1 | no | — |
| 698 | C4 | — | 2 | 1 | no | — |
| 699 | C4 | — | 52 | 2 | no | — |
| 700 | C4 | — | 52 | 2 | no | — |
| 701 | C4 | — | 52 | 4 | no | — |
| 702 | C4 | — | 52 | 2 | no | — |
| 703 | C4 | — | 52 | 4 | no | — |
| 704 | C4 | #11719648 | 1 | 2 | yes | — |
| 705 | C2 | — | 4 | 1 | no | — |
| 706 | C2 | — | 4 | 1 | no | — |
| 707 | C2 | — | 4 | 1 | no | — |
| 708 | C2 | — | 104 | 2 | no | — |
| 709 | C2 | #13128169 | 1 | 1 | yes | characteristic |
| 710 | C2 | #13129624 | 1 | 2 | yes | — |
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