← #16727264
Subgroups — #16727264
Order 3328.
2604 conjugacy classes of subgroups.
The subgroup lattice has 340 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13129610 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13129549 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13123752 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #13123745 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #13123738 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×#11718555 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #13123381 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13123262 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C13×#2916 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11719648 | C22 | 1 | 2 | yes | — |
| 11 | C13×#568 | C22 | 1 | 2 | yes | — |
| 12 | C2×C13×#131 | C22 | 1 | 1 | yes | characteristic |
| 13 | #41×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#88202 | C22 | 1 | 1 | yes | characteristic |
| 15 | #11719458 | C4 | 1 | 4 | yes | complemented |
| 16 | #11719457 | C4 | 1 | 4 | yes | complemented |
| 17 | #11719456 | C4 | 1 | 8 | yes | complemented |
| 18 | #11719455 | — | 2 | 8 | no | — |
| 19 | D13×#131 | — | 2 | 8 | no | — |
| 20 | #11719453 | C22 | 1 | 6 | yes | — |
| 21 | #11719450 | C22 | 1 | 12 | yes | complemented |
| 22 | C2×#88161 | C22 | 1 | 12 | yes | complemented |
| 23 | C2×#88158 | C22 | 1 | 6 | yes | — |
| 24 | C13×#430 | C22 | 1 | 6 | yes | complemented |
| 25 | C2×C13×#108 | C22 | 1 | 6 | yes | complemented |
| 26 | #11718800 | C22 | 1 | 12 | yes | complemented |
| 27 | C2×#88065 | C22 | 1 | 12 | yes | complemented |
| 28 | #11718783 | C22 | 1 | 3 | yes | complemented |
| 29 | M16×Dic13 | C22 | 1 | 3 | yes | complemented |
| 30 | #11718762 | C22 | 1 | 3 | yes | complemented |
| 31 | C2×#88055 | C22 | 1 | 3 | yes | complemented |
| 32 | #11718556 | C22 | 1 | 24 | yes | complemented |
| 33 | #11718555 | C22 | 1 | 4 | yes | complemented |
| 34 | #11718555 | C22 | 1 | 12 | yes | complemented |
| 35 | #11718555 | C22 | 1 | 12 | yes | complemented |
| 36 | #11718555 | C22 | 1 | 12 | yes | complemented |
| 37 | C2×C13×#41 | C23 | 1 | 1 | yes | characteristic |
| 38 | #88257 | C2×C4 | 1 | 8 | yes | — |
| 39 | #88256 | C2×C4 | 1 | 8 | yes | — |
| 40 | #41×D13 | — | 2 | 8 | no | — |
| 41 | #88254 | — | 2 | 2 | no | — |
| 42 | #88251 | — | 2 | 6 | no | — |
| 43 | C2×#6127 | C23 | 1 | 12 | yes | — |
| 44 | C13×#131 | — | 2 | 8 | no | — |
| 45 | C13×#131 | C2×C4 | 1 | 4 | yes | — |
| 46 | C13×#131 | C2×C4 | 1 | 4 | yes | — |
| 47 | C2×C13×M16 | C23 | 1 | 12 | yes | — |
| 48 | C2×C13×M16 | C23 | 1 | 3 | yes | — |
| 49 | C22×C8×C13 | C23 | 1 | 3 | yes | — |
| 50 | #88202 | D4 | 1 | 8 | yes | — |
| 51 | Q8×Dic13 | — | 2 | 1 | no | — |
| 52 | D4×Dic13 | — | 2 | 3 | no | — |
| 53 | #88180 | C23 | 1 | 3 | yes | — |
| 54 | C2×C4×Dic13 | C23 | 1 | 3 | yes | — |
| 55 | C2×#6099 | C23 | 1 | 3 | yes | — |
| 56 | C22×#1055 | C23 | 1 | 3 | yes | — |
| 57 | #88163 | C2×C4 | 1 | 24 | yes | complemented |
| 58 | #88162 | C2×C4 | 1 | 24 | yes | complemented |
| 59 | #88161 | — | 2 | 12 | no | — |
| 60 | #88161 | — | 2 | 12 | no | — |
| 61 | #88161 | C23 | 1 | 8 | yes | — |
| 62 | #88161 | C23 | 1 | 24 | yes | — |
| 63 | M16×D13 | — | 2 | 24 | no | — |
| 64 | C2×Dic52 | C2×C4 | 1 | 6 | yes | complemented |
| 65 | #88158 | C2×C4 | 1 | 12 | yes | complemented |
| 66 | #88158 | C2×C4 | 1 | 12 | yes | complemented |
| 67 | #88158 | C23 | 1 | 4 | yes | — |
| 68 | #88158 | C23 | 1 | 12 | yes | — |
| 69 | C2×D104 | C2×C4 | 1 | 6 | yes | complemented |
| 70 | C2×#6095 | C2×C4 | 1 | 12 | yes | complemented |
| 71 | #88155 | — | 2 | 24 | no | — |
| 72 | C2×#6094 | — | 2 | 12 | no | — |
| 73 | C2×C8×D13 | — | 2 | 12 | no | — |
| 74 | C13×#108 | C23 | 1 | 4 | yes | — |
| 75 | C13×#108 | C23 | 1 | 12 | yes | — |
| 76 | #88065 | C23 | 1 | 8 | yes | — |
| 77 | #88065 | C23 | 1 | 24 | yes | — |
| 78 | #88055 | C23 | 1 | 1 | yes | characteristic |
| 79 | #88055 | C23 | 1 | 3 | yes | — |
| 80 | #88055 | C23 | 1 | 3 | yes | — |
| 81 | #88055 | C23 | 1 | 3 | yes | — |
| 82 | C8×Dic13 | C23 | 1 | 6 | yes | — |
| 83 | #60184 | — | 13 | 1 | no | maximal, Sylow |
| 84 | C13×#41 | C22×C4 | 1 | 4 | yes | — |
| 85 | C13×#41 | C2×D4 | 1 | 4 | yes | — |
| 86 | C2×Q8×C13 | #41 | 1 | 1 | yes | characteristic |
| 87 | C2×D4×C13 | #41 | 1 | 3 | yes | — |
| 88 | C22×C4×C13 | C24 | 1 | 3 | yes | — |
| 89 | C2×C22⋊D13 | — | 2 | 12 | no | — |
| 90 | C22×Dic13 | — | 2 | 3 | no | — |
| 91 | #6131 | — | 2 | 8 | no | — |
| 92 | Q8×D13 | — | 2 | 8 | no | — |
| 93 | #6129 | — | 2 | 24 | no | — |
| 94 | D4×D13 | — | 2 | 24 | no | — |
| 95 | #6127 | — | 2 | 12 | no | — |
| 96 | #6127 | — | 2 | 12 | no | — |
| 97 | #6127 | C22×C4 | 1 | 24 | yes | — |
| 98 | #6127 | C24 | 1 | 8 | yes | — |
| 99 | C2×D52 | C22×C4 | 1 | 12 | yes | — |
| 100 | C2×C4×D13 | — | 2 | 12 | no | — |
| 101 | C2×Dic26 | C22×C4 | 1 | 12 | yes | — |
| 102 | C13×M16 | — | 2 | 12 | no | — |
| 103 | C13×M16 | C22×C4 | 1 | 12 | yes | — |
| 104 | C13×M16 | C24 | 1 | 8 | yes | — |
| 105 | C2×C8×C13 | — | 2 | 12 | no | — |
| 106 | C2×C8×C13 | C22×C4 | 1 | 6 | yes | — |
| 107 | C2×C8×C13 | C22×C4 | 1 | 6 | yes | — |
| 108 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 109 | C2×C8×C13 | C24 | 1 | 3 | yes | — |
| 110 | C22⋊Dic13 | — | 2 | 3 | no | — |
| 111 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 112 | C4×Dic13 | — | 2 | 3 | no | — |
| 113 | C4×Dic13 | C24 | 1 | 1 | yes | characteristic |
| 114 | C4×Dic13 | C24 | 1 | 3 | yes | — |
| 115 | #6099 | C2×D4 | 1 | 12 | yes | — |
| 116 | C2×#1055 | C2×D4 | 1 | 12 | yes | — |
| 117 | C2×#1055 | C24 | 1 | 1 | yes | characteristic |
| 118 | C2×#1055 | C24 | 1 | 3 | yes | — |
| 119 | Dic52 | C22×C4 | 1 | 4 | yes | — |
| 120 | Dic52 | C22×C4 | 1 | 12 | yes | — |
| 121 | D104 | C22×C4 | 1 | 4 | yes | — |
| 122 | D104 | C22×C4 | 1 | 12 | yes | — |
| 123 | #6095 | C22×C4 | 1 | 8 | yes | — |
| 124 | #6095 | C22×C4 | 1 | 24 | yes | — |
| 125 | #6094 | — | 2 | 8 | no | — |
| 126 | #6094 | — | 2 | 24 | no | — |
| 127 | C8×D13 | — | 2 | 8 | no | — |
| 128 | C8×D13 | — | 2 | 24 | no | — |
| 129 | #3584 | — | 13 | 1 | no | — |
| 130 | #3573 | — | 13 | 2 | no | — |
| 131 | #2957 | — | 13 | 6 | no | — |
| 132 | #2956 | — | 13 | 6 | no | — |
| 133 | #2955 | — | 13 | 6 | no | — |
| 134 | C2×#444 | — | 13 | 6 | no | — |
| 135 | #2916 | D13 | 1 | 1 | yes | characteristic, complemented |
| 136 | #2901 | — | 13 | 2 | no | — |
| 137 | #2875 | — | 13 | 1 | no | — |
| 138 | C23×C13 | C2×#41 | 1 | 3 | yes | — |
| 139 | C22×D13 | — | 2 | 12 | no | — |
| 140 | Q8×C13 | C4×D4 | 1 | 4 | yes | — |
| 141 | D4×C13 | C4×D4 | 1 | 12 | yes | — |
| 142 | C2×C4×C13 | C23×C4 | 1 | 6 | yes | — |
| 143 | C2×C4×C13 | C22×D4 | 1 | 6 | yes | — |
| 144 | C2×C4×C13 | C2×#41 | 1 | 3 | yes | — |
| 145 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 146 | C22⋊D13 | — | 2 | 24 | no | — |
| 147 | C22⋊D13 | — | 2 | 8 | no | — |
| 148 | C2×Dic13 | — | 2 | 12 | no | — |
| 149 | C2×Dic13 | — | 2 | 1 | no | — |
| 150 | C2×Dic13 | — | 2 | 3 | no | — |
| 151 | C2×Dic13 | — | 8 | 3 | no | — |
| 152 | D52 | — | 2 | 12 | no | — |
| 153 | D52 | C23×C4 | 1 | 8 | yes | — |
| 154 | C4×D13 | — | 2 | 24 | no | — |
| 155 | C4×D13 | — | 2 | 8 | no | — |
| 156 | Dic26 | — | 2 | 12 | no | — |
| 157 | Dic26 | C23×C4 | 1 | 8 | yes | — |
| 158 | C8×C13 | — | 2 | 8 | no | — |
| 159 | C8×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 160 | C8×C13 | C23×C4 | 1 | 6 | yes | — |
| 161 | C8×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 162 | #1055 | C22×D4 | 1 | 2 | yes | — |
| 163 | #1055 | C22×D4 | 1 | 6 | yes | — |
| 164 | #585 | — | 13 | 2 | no | — |
| 165 | #578 | — | 13 | 4 | no | — |
| 166 | #577 | — | 13 | 8 | no | — |
| 167 | #576 | — | 13 | 4 | no | — |
| 168 | #575 | — | 13 | 6 | no | — |
| 169 | C2×#135 | — | 13 | 6 | no | — |
| 170 | #568 | — | 13 | 12 | no | — |
| 171 | #568 | — | 26 | 8 | no | — |
| 172 | #568 | C2×D13 | 1 | 2 | yes | — |
| 173 | C2×#131 | — | 13 | 1 | no | — |
| 174 | C2×#131 | — | 13 | 12 | no | — |
| 175 | C2×#131 | — | 26 | 8 | no | — |
| 176 | C2×#131 | C2×D13 | 1 | 1 | yes | characteristic |
| 177 | C4×#41 | — | 13 | 1 | no | — |
| 178 | #444 | — | 13 | 4 | no | — |
| 179 | #444 | — | 13 | 12 | no | — |
| 180 | #444 | — | 13 | 12 | no | — |
| 181 | #444 | — | 13 | 12 | no | — |
| 182 | #443 | — | 13 | 24 | no | — |
| 183 | #430 | C2×D13 | 1 | 6 | yes | complemented |
| 184 | C2×#108 | C2×D13 | 1 | 6 | yes | complemented |
| 185 | #421 | — | 13 | 12 | no | — |
| 186 | C2×#104 | — | 13 | 12 | no | — |
| 187 | #405 | — | 13 | 3 | no | — |
| 188 | #405 | — | 13 | 3 | no | — |
| 189 | C4×M16 | — | 13 | 3 | no | — |
| 190 | C2×#97 | — | 13 | 3 | no | — |
| 191 | C22×C13 | — | 4 | 3 | no | — |
| 192 | C22×C13 | C2×C4×D4 | 1 | 6 | yes | — |
| 193 | C22×C13 | C22×#41 | 1 | 1 | yes | characteristic |
| 194 | C2×D13 | — | 2 | 8 | no | — |
| 195 | C2×D13 | — | 8 | 12 | no | — |
| 196 | C4×C13 | C2×C4×D4 | 1 | 6 | yes | — |
| 197 | C4×C13 | C24×C4 | 1 | 1 | yes | characteristic |
| 198 | C4×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 199 | Dic13 | — | 2 | 8 | no | — |
| 200 | Dic13 | — | 4 | 3 | no | — |
| 201 | Dic13 | — | 4 | 1 | no | — |
| 202 | 2−1+4 | — | 13 | 8 | no | — |
| 203 | 2−1+4 | — | 26 | 2 | no | — |
| 204 | H(5,𝔽2) | — | 13 | 8 | no | — |
| 205 | H(5,𝔽2) | — | 26 | 6 | no | — |
| 206 | C2×#41 | — | 13 | 12 | no | — |
| 207 | C2×#41 | — | 26 | 8 | no | — |
| 208 | C2×#41 | C22×D13 | 1 | 1 | yes | characteristic |
| 209 | #137 | — | 13 | 24 | no | — |
| 210 | AGL(1,ℤ/8) | — | 13 | 24 | no | — |
| 211 | #135 | — | 13 | 12 | no | — |
| 212 | #135 | — | 13 | 12 | no | — |
| 213 | #135 | — | 13 | 4 | no | — |
| 214 | #135 | — | 13 | 12 | no | — |
| 215 | C2×Q16 | — | 13 | 6 | no | — |
| 216 | C2×SD16 | — | 13 | 12 | no | — |
| 217 | C2×D8 | — | 13 | 6 | no | — |
| 218 | #131 | — | 2 | 8 | no | — |
| 219 | #131 | — | 13 | 8 | no | — |
| 220 | #131 | — | 13 | 8 | no | — |
| 221 | #131 | — | 13 | 24 | no | — |
| 222 | #131 | — | 26 | 24 | no | — |
| 223 | #131 | — | 26 | 12 | no | — |
| 224 | #131 | — | 26 | 12 | no | — |
| 225 | #131 | C4×D13 | 1 | 4 | yes | — |
| 226 | #131 | C4×D13 | 1 | 4 | yes | — |
| 227 | C2×M16 | — | 13 | 3 | no | — |
| 228 | C2×M16 | — | 26 | 12 | no | — |
| 229 | C2×M16 | — | 26 | 24 | no | — |
| 230 | C2×M16 | C22×D13 | 1 | 12 | yes | — |
| 231 | C2×M16 | C22×D13 | 1 | 3 | yes | — |
| 232 | C22×C8 | — | 13 | 3 | no | — |
| 233 | C22×C8 | — | 26 | 12 | no | — |
| 234 | C22×C8 | C22×D13 | 1 | 3 | yes | — |
| 235 | C4×Q8 | — | 26 | 1 | no | — |
| 236 | C4×D4 | — | 26 | 3 | no | — |
| 237 | #117 | — | 13 | 3 | no | — |
| 238 | C2×C42 | — | 13 | 3 | no | — |
| 239 | #108 | C22×D13 | 1 | 4 | yes | — |
| 240 | #108 | C22×D13 | 1 | 12 | yes | — |
| 241 | #104 | — | 13 | 8 | no | — |
| 242 | #104 | — | 13 | 24 | no | — |
| 243 | #97 | — | 13 | 1 | no | — |
| 244 | #97 | — | 13 | 3 | no | — |
| 245 | #97 | — | 13 | 3 | no | — |
| 246 | #97 | — | 13 | 3 | no | — |
| 247 | C4×C8 | — | 13 | 6 | no | — |
| 248 | C2×C13 | — | 2 | 1 | no | — |
| 249 | C2×C13 | — | 2 | 6 | no | — |
| 250 | C2×C13 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 251 | D13 | — | 4 | 8 | no | — |
| 252 | #41 | — | 13 | 24 | no | — |
| 253 | #41 | — | 13 | 8 | no | — |
| 254 | #41 | — | 26 | 8 | no | — |
| 255 | #41 | — | 26 | 24 | no | — |
| 256 | #41 | — | 26 | 12 | no | — |
| 257 | #41 | — | 26 | 12 | no | — |
| 258 | #41 | C2×C4×D13 | 1 | 4 | yes | — |
| 259 | #41 | D4×D13 | 1 | 4 | yes | — |
| 260 | C2×Q8 | — | 13 | 12 | no | — |
| 261 | C2×Q8 | — | 26 | 8 | no | — |
| 262 | C2×Q8 | #6131 | 1 | 1 | yes | characteristic |
| 263 | C2×D4 | — | 13 | 12 | no | — |
| 264 | C2×D4 | — | 26 | 12 | no | — |
| 265 | C2×D4 | — | 26 | 24 | no | — |
| 266 | C2×D4 | #6131 | 1 | 3 | yes | — |
| 267 | C22×C4 | — | 26 | 12 | no | — |
| 268 | C22×C4 | — | 26 | 3 | no | — |
| 269 | C22×C4 | C23×D13 | 1 | 3 | yes | — |
| 270 | Q16 | — | 13 | 4 | no | — |
| 271 | Q16 | — | 13 | 12 | no | — |
| 272 | SD16 | — | 13 | 8 | no | — |
| 273 | SD16 | — | 13 | 24 | no | — |
| 274 | D8 | — | 13 | 4 | no | — |
| 275 | D8 | — | 13 | 12 | no | — |
| 276 | M16 | — | 2 | 12 | no | — |
| 277 | M16 | — | 13 | 12 | no | — |
| 278 | M16 | — | 26 | 8 | no | — |
| 279 | M16 | — | 26 | 24 | no | — |
| 280 | M16 | C2×C4×D13 | 1 | 12 | yes | — |
| 281 | M16 | C23×D13 | 1 | 8 | yes | — |
| 282 | C2×C8 | — | 2 | 12 | no | — |
| 283 | C2×C8 | — | 13 | 12 | no | — |
| 284 | C2×C8 | — | 13 | 3 | no | — |
| 285 | C2×C8 | — | 13 | 1 | no | — |
| 286 | C2×C8 | — | 26 | 8 | no | — |
| 287 | C2×C8 | — | 26 | 24 | no | — |
| 288 | C2×C8 | C2×C4×D13 | 1 | 6 | yes | — |
| 289 | C2×C8 | C2×C4×D13 | 1 | 6 | yes | — |
| 290 | C2×C8 | C23×D13 | 1 | 3 | yes | — |
| 291 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 292 | C4⋊C4 | — | 26 | 3 | no | — |
| 293 | C22⋊C4 | — | 26 | 3 | no | — |
| 294 | C42 | — | 13 | 3 | no | — |
| 295 | C42 | — | 13 | 1 | no | — |
| 296 | C42 | — | 26 | 3 | no | — |
| 297 | C13 | #60184 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 298 | C23 | — | 26 | 12 | no | — |
| 299 | C23 | C2×#6131 | 1 | 3 | yes | — |
| 300 | Q8 | — | 13 | 8 | no | — |
| 301 | Q8 | — | 26 | 12 | no | — |
| 302 | Q8 | #88147 | 1 | 4 | yes | — |
| 303 | D4 | — | 13 | 8 | no | — |
| 304 | D4 | — | 26 | 24 | no | — |
| 305 | D4 | — | 26 | 8 | no | — |
| 306 | D4 | — | 26 | 12 | no | — |
| 307 | D4 | #88147 | 1 | 12 | yes | — |
| 308 | C2×C4 | — | 26 | 12 | no | — |
| 309 | C2×C4 | — | 26 | 24 | no | — |
| 310 | C2×C4 | — | 26 | 8 | no | — |
| 311 | C2×C4 | — | 26 | 1 | no | — |
| 312 | C2×C4 | — | 26 | 3 | no | — |
| 313 | C2×C4 | — | 104 | 3 | no | — |
| 314 | C2×C4 | C22×C4×D13 | 1 | 6 | yes | — |
| 315 | C2×C4 | C2×D4×D13 | 1 | 6 | yes | — |
| 316 | C2×C4 | C2×#6131 | 1 | 3 | yes | — |
| 317 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 318 | C8 | — | 2 | 8 | no | — |
| 319 | C8 | — | 13 | 2 | no | — |
| 320 | C8 | — | 13 | 6 | no | — |
| 321 | C8 | C22×C4×D13 | 1 | 1 | yes | characteristic |
| 322 | C8 | C22×C4×D13 | 1 | 1 | yes | characteristic |
| 323 | C8 | C22×C4×D13 | 1 | 6 | yes | — |
| 324 | C22 | — | 4 | 3 | no | — |
| 325 | C22 | — | 26 | 8 | no | — |
| 326 | C22 | — | 104 | 12 | no | — |
| 327 | C22 | C2×#88147 | 1 | 6 | yes | — |
| 328 | C22 | C22×#6131 | 1 | 1 | yes | characteristic |
| 329 | C4 | — | 26 | 8 | no | — |
| 330 | C4 | — | 52 | 3 | no | — |
| 331 | C4 | — | 52 | 1 | no | — |
| 332 | C4 | C2×#88147 | 1 | 6 | yes | — |
| 333 | C4 | C23×C4×D13 | 1 | 1 | yes | characteristic |
| 334 | C4 | C22×D4×D13 | 1 | 1 | yes | characteristic |
| 335 | C2 | — | 2 | 1 | no | — |
| 336 | C2 | — | 2 | 6 | no | — |
| 337 | C2 | — | 52 | 8 | no | — |
| 338 | C2 | C22×#88147 | 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