← #16017813
Subgroups — #16017813
Order 3328.
556 conjugacy classes of subgroups.
The subgroup lattice has 320 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11718786 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13117053 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #13117048 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #13116608 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13116585 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#11718145 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C13×#3054 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×C13×#135 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×C13×M16 | C22 | 1 | 1 | yes | characteristic |
| 10 | C13×#525 | — | 2 | 1 | no | — |
| 11 | C22×#6099 | — | 2 | 1 | no | — |
| 12 | C13×#470 | C22 | 1 | 2 | yes | — |
| 13 | C13×#469 | C22 | 1 | 2 | yes | — |
| 14 | C13×#468 | — | 2 | 2 | no | — |
| 15 | C13×#427 | C22 | 1 | 1 | yes | characteristic |
| 16 | C13×#416 | — | 2 | 1 | no | — |
| 17 | #11718786 | — | 2 | 2 | no | — |
| 18 | #11718786 | C22 | 1 | 4 | yes | — |
| 19 | C2×#88059 | — | 2 | 1 | no | — |
| 20 | C2×#88059 | C22 | 1 | 2 | yes | — |
| 21 | C2×#88052 | C22 | 1 | 2 | yes | — |
| 22 | #11718157 | C22 | 1 | 4 | yes | complemented |
| 23 | #11718155 | C22 | 1 | 4 | yes | complemented |
| 24 | #11718145 | C22 | 1 | 4 | yes | — |
| 25 | #11718079 | C22 | 1 | 8 | yes | complemented |
| 26 | C2×C13×#41 | — | 2 | 1 | no | — |
| 27 | C23×C4×C13 | D4 | 1 | 1 | yes | characteristic |
| 28 | C13×#135 | — | 2 | 2 | no | — |
| 29 | C13×#135 | — | 2 | 2 | no | — |
| 30 | C2×C13×Q16 | C23 | 1 | 1 | yes | characteristic |
| 31 | C2×C13×SD16 | — | 2 | 1 | no | — |
| 32 | C2×C13×D8 | C23 | 1 | 1 | yes | characteristic |
| 33 | C2×C13×M16 | — | 2 | 2 | no | — |
| 34 | C2×C13×M16 | — | 2 | 2 | no | — |
| 35 | C2×C13×M16 | D4 | 1 | 2 | yes | — |
| 36 | C2×C13×M16 | C23 | 1 | 2 | yes | — |
| 37 | C22×C8×C13 | D4 | 1 | 1 | yes | characteristic |
| 38 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 39 | C13×#123 | — | 4 | 1 | no | — |
| 40 | C13×C22⋊Q8 | — | 2 | 2 | no | — |
| 41 | C13×#121 | — | 2 | 2 | no | — |
| 42 | C13×#120 | — | 4 | 1 | no | — |
| 43 | C4×D4×C13 | — | 4 | 2 | no | — |
| 44 | C13×#117 | — | 2 | 1 | no | — |
| 45 | C2×#6099 | — | 2 | 2 | no | — |
| 46 | C2×#6099 | — | 2 | 4 | no | — |
| 47 | C2×#6099 | — | 4 | 2 | no | — |
| 48 | C2×#6099 | — | 4 | 1 | no | — |
| 49 | C22×#1055 | — | 4 | 1 | no | — |
| 50 | C13×#107 | — | 2 | 1 | no | — |
| 51 | C13×#106 | C23 | 1 | 2 | yes | — |
| 52 | C13×#103 | — | 2 | 2 | no | — |
| 53 | C13×#102 | — | 2 | 2 | no | — |
| 54 | #88059 | — | 2 | 4 | no | — |
| 55 | #88059 | — | 2 | 2 | no | — |
| 56 | #88059 | C23 | 1 | 4 | yes | — |
| 57 | #88052 | — | 2 | 2 | no | — |
| 58 | #88052 | C23 | 1 | 4 | yes | — |
| 59 | C2×#6090 | — | 2 | 2 | no | — |
| 60 | #33656 | — | 13 | 1 | no | maximal, Sylow |
| 61 | C24×C13 | SD16 | 1 | 1 | yes | characteristic |
| 62 | C13×#41 | — | 4 | 1 | no | — |
| 63 | C13×#41 | — | 4 | 1 | no | — |
| 64 | C13×#41 | — | 4 | 1 | no | — |
| 65 | C13×#41 | — | 4 | 1 | no | — |
| 66 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 67 | C2×D4×C13 | — | 2 | 1 | no | — |
| 68 | C2×D4×C13 | — | 4 | 2 | no | — |
| 69 | C2×D4×C13 | — | 4 | 1 | no | — |
| 70 | C22×C4×C13 | — | 2 | 1 | no | — |
| 71 | C22×C4×C13 | — | 2 | 1 | no | — |
| 72 | C22×C4×C13 | — | 2 | 1 | no | — |
| 73 | C22×C4×C13 | — | 2 | 1 | no | — |
| 74 | C22×C4×C13 | — | 4 | 1 | no | — |
| 75 | C22×C4×C13 | SD16 | 1 | 2 | yes | — |
| 76 | C22×C4×C13 | SD16 | 1 | 1 | yes | characteristic |
| 77 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 78 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 79 | C13×Q16 | — | 2 | 2 | no | — |
| 80 | C13×SD16 | — | 4 | 2 | no | — |
| 81 | C13×D8 | — | 2 | 2 | no | — |
| 82 | C13×M16 | — | 2 | 4 | no | — |
| 83 | C13×M16 | — | 2 | 4 | no | — |
| 84 | C2×C8×C13 | — | 2 | 1 | no | — |
| 85 | C2×C8×C13 | — | 2 | 1 | no | — |
| 86 | C2×C8×C13 | C2×D4 | 1 | 2 | yes | — |
| 87 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C8×C13 | #41 | 1 | 2 | yes | — |
| 89 | C2×C8×C13 | #41 | 1 | 2 | yes | — |
| 90 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 91 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 92 | C13×C4⋊C4 | — | 4 | 2 | no | — |
| 93 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 94 | C13×C22⋊C4 | — | 4 | 2 | no | — |
| 95 | C13×C22⋊C4 | — | 4 | 2 | no | — |
| 96 | C42×C13 | — | 4 | 1 | no | — |
| 97 | #6099 | — | 2 | 4 | no | — |
| 98 | #6099 | — | 4 | 4 | no | — |
| 99 | #6099 | — | 4 | 2 | no | — |
| 100 | C2×#1055 | — | 4 | 4 | no | — |
| 101 | C2×#1055 | — | 4 | 2 | no | — |
| 102 | #6090 | — | 2 | 4 | no | — |
| 103 | #3054 | D13 | 1 | 1 | yes | characteristic |
| 104 | C2×#430 | — | 13 | 1 | no | — |
| 105 | #2239 | — | 13 | 4 | no | — |
| 106 | #2238 | — | 13 | 4 | no | — |
| 107 | #2155 | — | 13 | 2 | no | — |
| 108 | #2148 | — | 13 | 2 | no | — |
| 109 | C2×#349 | — | 13 | 1 | no | — |
| 110 | C23×C13 | — | 2 | 1 | no | — |
| 111 | C23×C13 | — | 2 | 1 | no | — |
| 112 | C23×C13 | — | 4 | 1 | no | — |
| 113 | C23×C13 | — | 8 | 1 | no | — |
| 114 | C23×C13 | C2×SD16 | 1 | 2 | yes | — |
| 115 | C23×C13 | C2×SD16 | 1 | 1 | yes | characteristic |
| 116 | Q8×C13 | — | 4 | 1 | no | — |
| 117 | Q8×C13 | — | 4 | 1 | no | — |
| 118 | D4×C13 | — | 4 | 1 | no | — |
| 119 | D4×C13 | — | 4 | 1 | no | — |
| 120 | D4×C13 | — | 8 | 4 | no | — |
| 121 | D4×C13 | — | 8 | 1 | no | — |
| 122 | D4×C13 | — | 8 | 1 | no | — |
| 123 | C2×C4×C13 | — | 2 | 1 | no | — |
| 124 | C2×C4×C13 | — | 2 | 1 | no | — |
| 125 | C2×C4×C13 | — | 2 | 2 | no | — |
| 126 | C2×C4×C13 | — | 2 | 2 | no | — |
| 127 | C2×C4×C13 | — | 2 | 2 | no | — |
| 128 | C2×C4×C13 | — | 2 | 2 | no | — |
| 129 | C2×C4×C13 | — | 4 | 2 | no | — |
| 130 | C2×C4×C13 | — | 4 | 1 | no | — |
| 131 | C2×C4×C13 | — | 8 | 1 | no | — |
| 132 | C2×C4×C13 | — | 8 | 1 | no | — |
| 133 | C2×C4×C13 | #123 | 1 | 1 | yes | characteristic |
| 134 | C2×C4×C13 | #123 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C13 | C2×SD16 | 1 | 2 | yes | — |
| 136 | C2×C4×C13 | C2×SD16 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 140 | C8×C13 | — | 2 | 2 | no | — |
| 141 | C8×C13 | #123 | 1 | 2 | yes | — |
| 142 | C8×C13 | C2×#41 | 1 | 2 | yes | — |
| 143 | #1055 | — | 4 | 4 | no | — |
| 144 | C2×#135 | C2×D13 | 1 | 1 | yes | characteristic |
| 145 | C22×M16 | — | 26 | 1 | no | — |
| 146 | C22×M16 | C2×D13 | 1 | 1 | yes | characteristic |
| 147 | #525 | — | 2 | 1 | no | — |
| 148 | C2×M32 | — | 13 | 2 | no | — |
| 149 | #470 | C2×D13 | 1 | 2 | yes | — |
| 150 | #469 | C2×D13 | 1 | 2 | yes | — |
| 151 | #468 | — | 2 | 2 | no | — |
| 152 | #430 | — | 13 | 4 | no | — |
| 153 | #430 | — | 26 | 2 | no | — |
| 154 | C2×#108 | — | 13 | 2 | no | — |
| 155 | C2×#108 | — | 26 | 1 | no | — |
| 156 | #427 | C2×D13 | 1 | 1 | yes | characteristic |
| 157 | #416 | — | 2 | 1 | no | — |
| 158 | #365 | — | 13 | 8 | no | — |
| 159 | #362 | — | 13 | 4 | no | — |
| 160 | #361 | — | 13 | 4 | no | — |
| 161 | #349 | — | 13 | 4 | no | — |
| 162 | C22×C13 | — | 2 | 2 | no | — |
| 163 | C22×C13 | — | 4 | 1 | no | — |
| 164 | C22×C13 | — | 4 | 2 | no | — |
| 165 | C22×C13 | — | 4 | 2 | no | — |
| 166 | C22×C13 | — | 8 | 1 | no | — |
| 167 | C22×C13 | — | 8 | 2 | no | — |
| 168 | C22×C13 | — | 8 | 1 | no | — |
| 169 | C22×C13 | #481 | 1 | 1 | yes | characteristic |
| 170 | C22×C13 | #481 | 1 | 1 | yes | characteristic |
| 171 | C22×C13 | C22×SD16 | 1 | 1 | yes | characteristic |
| 172 | C4×C13 | — | 2 | 2 | no | — |
| 173 | C4×C13 | — | 8 | 2 | no | — |
| 174 | C4×C13 | — | 8 | 1 | no | — |
| 175 | C4×C13 | #481 | 1 | 1 | yes | characteristic |
| 176 | C4×C13 | #481 | 1 | 1 | yes | characteristic |
| 177 | C4×C13 | C2×#123 | 1 | 1 | yes | characteristic |
| 178 | C4×C13 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 179 | C2×#41 | — | 2 | 1 | no | — |
| 180 | C23×C4 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 181 | #135 | — | 2 | 2 | no | — |
| 182 | #135 | — | 2 | 2 | no | — |
| 183 | C2×Q16 | C22×D13 | 1 | 1 | yes | characteristic |
| 184 | C2×SD16 | — | 2 | 1 | no | — |
| 185 | C2×D8 | C22×D13 | 1 | 1 | yes | characteristic |
| 186 | C2×M16 | — | 2 | 2 | no | — |
| 187 | C2×M16 | — | 2 | 2 | no | — |
| 188 | C2×M16 | — | 26 | 4 | no | — |
| 189 | C2×M16 | — | 26 | 2 | no | — |
| 190 | C2×M16 | — | 52 | 2 | no | — |
| 191 | C2×M16 | — | 52 | 1 | no | — |
| 192 | C2×M16 | C22⋊D13 | 1 | 2 | yes | — |
| 193 | C2×M16 | C22×D13 | 1 | 2 | yes | — |
| 194 | C22×C8 | — | 52 | 1 | no | — |
| 195 | C22×C8 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 196 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 197 | #123 | — | 4 | 1 | no | — |
| 198 | C22⋊Q8 | — | 2 | 2 | no | — |
| 199 | #121 | — | 2 | 2 | no | — |
| 200 | #120 | — | 4 | 1 | no | — |
| 201 | C4×D4 | — | 4 | 2 | no | — |
| 202 | #117 | — | 2 | 1 | no | — |
| 203 | M32 | — | 13 | 4 | no | — |
| 204 | M32 | — | 26 | 2 | no | — |
| 205 | C2×C16 | — | 26 | 2 | no | — |
| 206 | #108 | — | 13 | 4 | no | — |
| 207 | #108 | — | 26 | 2 | no | — |
| 208 | #108 | — | 26 | 4 | no | — |
| 209 | #107 | — | 2 | 1 | no | — |
| 210 | #106 | C22×D13 | 1 | 2 | yes | — |
| 211 | #103 | — | 2 | 2 | no | — |
| 212 | #102 | — | 2 | 2 | no | — |
| 213 | C2×C13 | — | 2 | 1 | no | — |
| 214 | C2×C13 | — | 2 | 1 | no | — |
| 215 | C2×C13 | — | 2 | 1 | no | — |
| 216 | C2×C13 | — | 4 | 2 | no | — |
| 217 | C2×C13 | — | 16 | 1 | no | — |
| 218 | C2×C13 | C2×#481 | 1 | 1 | yes | characteristic |
| 219 | C24 | #6105 | 1 | 1 | yes | characteristic |
| 220 | #41 | — | 4 | 1 | no | — |
| 221 | #41 | — | 4 | 1 | no | — |
| 222 | #41 | — | 4 | 1 | no | — |
| 223 | #41 | — | 4 | 1 | no | — |
| 224 | C2×Q8 | — | 2 | 1 | no | — |
| 225 | C2×D4 | — | 2 | 1 | no | — |
| 226 | C2×D4 | — | 4 | 2 | no | — |
| 227 | C2×D4 | — | 4 | 1 | no | — |
| 228 | C22×C4 | — | 2 | 1 | no | — |
| 229 | C22×C4 | — | 2 | 1 | no | — |
| 230 | C22×C4 | — | 2 | 1 | no | — |
| 231 | C22×C4 | — | 2 | 1 | no | — |
| 232 | C22×C4 | — | 4 | 1 | no | — |
| 233 | C22×C4 | #6105 | 1 | 2 | yes | — |
| 234 | C22×C4 | #6105 | 1 | 1 | yes | characteristic |
| 235 | C22×C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 236 | C22×C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 237 | Q16 | — | 2 | 2 | no | — |
| 238 | SD16 | — | 4 | 2 | no | — |
| 239 | D8 | — | 2 | 2 | no | — |
| 240 | M16 | — | 2 | 4 | no | — |
| 241 | M16 | — | 2 | 4 | no | — |
| 242 | M16 | — | 26 | 4 | no | — |
| 243 | M16 | — | 52 | 4 | no | — |
| 244 | M16 | — | 52 | 2 | no | — |
| 245 | C2×C8 | — | 2 | 1 | no | — |
| 246 | C2×C8 | — | 2 | 1 | no | — |
| 247 | C2×C8 | — | 52 | 4 | no | — |
| 248 | C2×C8 | — | 52 | 2 | no | — |
| 249 | C2×C8 | #6129 | 1 | 2 | yes | — |
| 250 | C2×C8 | #6129 | 1 | 2 | yes | — |
| 251 | C2×C8 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 252 | C2×C8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 253 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 254 | C4⋊C4 | — | 2 | 2 | no | — |
| 255 | C4⋊C4 | — | 4 | 2 | no | — |
| 256 | C22⋊C4 | — | 4 | 1 | no | — |
| 257 | C22⋊C4 | — | 4 | 2 | no | — |
| 258 | C22⋊C4 | — | 4 | 2 | no | — |
| 259 | C42 | — | 4 | 1 | no | — |
| 260 | C16 | — | 26 | 4 | no | — |
| 261 | C13 | #33656 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 262 | C23 | — | 2 | 1 | no | — |
| 263 | C23 | — | 2 | 1 | no | — |
| 264 | C23 | — | 4 | 1 | no | — |
| 265 | C23 | — | 8 | 1 | no | — |
| 266 | C23 | C2×#6105 | 1 | 2 | yes | — |
| 267 | C23 | C2×#6105 | 1 | 1 | yes | characteristic |
| 268 | Q8 | — | 4 | 1 | no | — |
| 269 | Q8 | — | 4 | 1 | no | — |
| 270 | D4 | — | 4 | 1 | no | — |
| 271 | D4 | — | 4 | 1 | no | — |
| 272 | D4 | — | 8 | 4 | no | — |
| 273 | D4 | — | 8 | 1 | no | — |
| 274 | D4 | — | 8 | 1 | no | — |
| 275 | C2×C4 | — | 2 | 1 | no | — |
| 276 | C2×C4 | — | 2 | 1 | no | — |
| 277 | C2×C4 | — | 2 | 2 | no | — |
| 278 | C2×C4 | — | 2 | 2 | no | — |
| 279 | C2×C4 | — | 2 | 2 | no | — |
| 280 | C2×C4 | — | 2 | 2 | no | — |
| 281 | C2×C4 | — | 4 | 2 | no | — |
| 282 | C2×C4 | — | 4 | 1 | no | — |
| 283 | C2×C4 | — | 8 | 1 | no | — |
| 284 | C2×C4 | — | 8 | 1 | no | — |
| 285 | C2×C4 | C2×#6105 | 1 | 2 | yes | — |
| 286 | C2×C4 | C2×#6105 | 1 | 1 | yes | characteristic |
| 287 | C2×C4 | #88189 | 1 | 1 | yes | characteristic |
| 288 | C2×C4 | #88189 | 1 | 1 | yes | characteristic |
| 289 | C2×C4 | #88203 | 1 | 1 | yes | characteristic |
| 290 | C2×C4 | #88203 | 1 | 1 | yes | characteristic |
| 291 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 292 | C8 | — | 2 | 2 | no | — |
| 293 | C8 | — | 52 | 4 | no | — |
| 294 | C8 | #88189 | 1 | 2 | yes | — |
| 295 | C8 | C2×#6129 | 1 | 2 | yes | — |
| 296 | C22 | — | 2 | 2 | no | — |
| 297 | C22 | — | 4 | 1 | no | — |
| 298 | C22 | — | 4 | 2 | no | — |
| 299 | C22 | — | 4 | 2 | no | — |
| 300 | C22 | — | 8 | 1 | no | — |
| 301 | C22 | — | 8 | 2 | no | — |
| 302 | C22 | — | 8 | 1 | no | — |
| 303 | C22 | #11718695 | 1 | 1 | yes | characteristic |
| 304 | C22 | #11718695 | 1 | 1 | yes | characteristic |
| 305 | C22 | C22×#6105 | 1 | 1 | yes | characteristic |
| 306 | C4 | — | 2 | 2 | no | — |
| 307 | C4 | — | 8 | 2 | no | — |
| 308 | C4 | — | 8 | 1 | no | — |
| 309 | C4 | #11718695 | 1 | 1 | yes | characteristic |
| 310 | C4 | #11718695 | 1 | 1 | yes | characteristic |
| 311 | C4 | C2×#88189 | 1 | 1 | yes | characteristic |
| 312 | C4 | C2×#88203 | 1 | 1 | yes | characteristic |
| 313 | C2 | — | 2 | 1 | no | — |
| 314 | C2 | — | 2 | 1 | no | — |
| 315 | C2 | — | 2 | 1 | no | — |
| 316 | C2 | — | 4 | 2 | no | — |
| 317 | C2 | — | 16 | 1 | no | — |
| 318 | C2 | C2×#11718695 | 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