← #16806756
Subgroups — #16806756
Order 3328.
716 conjugacy classes of subgroups.
The subgroup lattice has 270 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13131804 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13131406 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13131056 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13131055 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13131051 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C2×#11718218 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #13127937 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #41×#261 | C4 | 1 | 1 | yes | characteristic |
| 9 | D13⋊#131 | C4 | 1 | 1 | yes | characteristic |
| 10 | D13×#131 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11719162 | C4 | 1 | 2 | yes | complemented |
| 12 | #11719099 | C4 | 1 | 3 | yes | — |
| 13 | M16×#261 | C4 | 1 | 3 | yes | — |
| 14 | #11719096 | C4 | 1 | 6 | yes | complemented |
| 15 | #11719089 | C22 | 1 | 3 | yes | — |
| 16 | C2×#88100 | C22 | 1 | 3 | yes | — |
| 17 | D13⋊M32 | C22 | 1 | 3 | yes | — |
| 18 | C2×#88098 | C22 | 1 | 3 | yes | — |
| 19 | C13×#504 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #11718801 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | #11718568 | C4 | 1 | 3 | yes | complemented |
| 22 | D13×M32 | C22 | 1 | 3 | yes | — |
| 23 | #11718562 | C4 | 1 | 3 | yes | complemented |
| 24 | C2×#88038 | C22 | 1 | 3 | yes | — |
| 25 | #11718218 | C22 | 1 | 1 | yes | characteristic |
| 26 | #11718218 | C22 | 1 | 3 | yes | — |
| 27 | #11718218 | C22 | 1 | 3 | yes | — |
| 28 | #11718218 | C22 | 1 | 3 | yes | — |
| 29 | #11718217 | C22 | 1 | 6 | yes | — |
| 30 | #41×D13 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | Q8×#261 | — | 2 | 1 | no | — |
| 32 | #88240 | — | 2 | 1 | no | — |
| 33 | D4×#261 | — | 2 | 3 | no | — |
| 34 | #88238 | — | 2 | 3 | no | — |
| 35 | #88237 | C2×C4 | 1 | 3 | yes | — |
| 36 | C2×C4×#261 | C2×C4 | 1 | 3 | yes | — |
| 37 | D13⋊M16 | C2×C4 | 1 | 3 | yes | — |
| 38 | C2×D13⋊C8 | C2×C4 | 1 | 3 | yes | — |
| 39 | C13×#131 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | #88202 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | #88161 | C2×C4 | 1 | 3 | yes | — |
| 42 | M16×D13 | C2×C4 | 1 | 3 | yes | — |
| 43 | #88155 | C2×C4 | 1 | 3 | yes | — |
| 44 | C2×C8×D13 | C23 | 1 | 3 | yes | — |
| 45 | #88106 | C2×C4 | 1 | 6 | yes | complemented |
| 46 | C2×#6092 | C2×C4 | 1 | 6 | yes | complemented |
| 47 | #88100 | C2×C4 | 1 | 3 | yes | — |
| 48 | #88100 | C2×C4 | 1 | 3 | yes | — |
| 49 | #88100 | C23 | 1 | 3 | yes | — |
| 50 | #88100 | C23 | 1 | 1 | yes | characteristic |
| 51 | C8×#261 | C2×C4 | 1 | 6 | yes | — |
| 52 | #88098 | C2×C4 | 1 | 6 | yes | complemented |
| 53 | #88098 | C23 | 1 | 3 | yes | — |
| 54 | #88098 | C23 | 1 | 1 | yes | characteristic |
| 55 | D13⋊C16 | C2×C4 | 1 | 6 | yes | complemented |
| 56 | C13×M32 | C2×C4 | 1 | 3 | yes | complemented |
| 57 | C2×C13×C16 | C2×C4 | 1 | 3 | yes | complemented |
| 58 | #88052 | C2×C4 | 1 | 3 | yes | complemented |
| 59 | C2×#6090 | C2×C4 | 1 | 3 | yes | complemented |
| 60 | #88038 | C2×C4 | 1 | 3 | yes | complemented |
| 61 | #88038 | C2×C4 | 1 | 3 | yes | complemented |
| 62 | #88038 | C23 | 1 | 3 | yes | — |
| 63 | #88038 | C23 | 1 | 1 | yes | characteristic |
| 64 | C16×D13 | C2×C4 | 1 | 6 | yes | complemented |
| 65 | #33329 | — | 13 | 1 | no | maximal, Sylow |
| 66 | C22×#261 | — | 2 | 3 | no | — |
| 67 | C13×#41 | C42 | 1 | 1 | yes | characteristic |
| 68 | #6131 | M16 | 1 | 1 | yes | characteristic |
| 69 | Q8×D13 | M16 | 1 | 1 | yes | characteristic |
| 70 | #6129 | M16 | 1 | 3 | yes | — |
| 71 | D4×D13 | M16 | 1 | 3 | yes | — |
| 72 | #6127 | C42 | 1 | 3 | yes | — |
| 73 | C2×C4×D13 | C22×C4 | 1 | 3 | yes | — |
| 74 | C22⋊#261 | — | 2 | 3 | no | — |
| 75 | #6122 | — | 2 | 3 | no | — |
| 76 | C2×#1057 | — | 2 | 3 | no | — |
| 77 | C4⋊#261 | — | 2 | 3 | no | — |
| 78 | C4×#261 | — | 2 | 3 | no | — |
| 79 | C4×#261 | C22×C4 | 1 | 3 | yes | — |
| 80 | C4×#261 | C22×C4 | 1 | 1 | yes | characteristic |
| 81 | #6118 | — | 2 | 3 | no | — |
| 82 | D13⋊C8 | — | 2 | 3 | no | — |
| 83 | D13⋊C8 | C22×C4 | 1 | 3 | yes | — |
| 84 | D13⋊C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 85 | C13×M16 | C42 | 1 | 3 | yes | — |
| 86 | C2×C8×C13 | C22×C4 | 1 | 3 | yes | — |
| 87 | #6099 | C42 | 1 | 3 | yes | — |
| 88 | C2×#1055 | C22×C4 | 1 | 3 | yes | — |
| 89 | #6094 | C42 | 1 | 6 | yes | — |
| 90 | C8×D13 | C22×C4 | 1 | 3 | yes | — |
| 91 | C8×D13 | C22×C4 | 1 | 3 | yes | — |
| 92 | C8×D13 | C22×C4 | 1 | 3 | yes | — |
| 93 | C8×D13 | C24 | 1 | 1 | yes | characteristic |
| 94 | #6092 | C22×C4 | 1 | 6 | yes | — |
| 95 | #6092 | C22×C4 | 1 | 2 | yes | — |
| 96 | C13×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 97 | C13×C16 | C22×C4 | 1 | 3 | yes | — |
| 98 | #6090 | C22×C4 | 1 | 3 | yes | — |
| 99 | #6090 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | #3407 | — | 13 | 1 | no | — |
| 101 | #3407 | — | 13 | 1 | no | — |
| 102 | #2875 | — | 13 | 1 | no | — |
| 103 | #2110 | — | 13 | 3 | no | — |
| 104 | #2110 | — | 13 | 3 | no | — |
| 105 | C2×#347 | — | 13 | 3 | no | — |
| 106 | C2×#347 | — | 13 | 3 | no | — |
| 107 | C22×D13 | C2×M16 | 1 | 3 | yes | — |
| 108 | C2×#261 | — | 2 | 1 | no | — |
| 109 | C2×#261 | — | 2 | 3 | no | — |
| 110 | C2×#261 | — | 8 | 3 | no | — |
| 111 | Q8×C13 | #97 | 1 | 1 | yes | characteristic |
| 112 | D4×C13 | #97 | 1 | 3 | yes | — |
| 113 | C2×C4×C13 | C2×C42 | 1 | 3 | yes | — |
| 114 | C22⋊D13 | #97 | 1 | 6 | yes | — |
| 115 | C2×Dic13 | C2×M16 | 1 | 3 | yes | — |
| 116 | D52 | #97 | 1 | 3 | yes | — |
| 117 | C4×D13 | C2×C42 | 1 | 3 | yes | — |
| 118 | C4×D13 | C2×M16 | 1 | 3 | yes | — |
| 119 | C4×D13 | C2×M16 | 1 | 3 | yes | — |
| 120 | C4×D13 | C23×C4 | 1 | 1 | yes | characteristic |
| 121 | Dic26 | #97 | 1 | 3 | yes | — |
| 122 | #1057 | — | 2 | 1 | no | — |
| 123 | #1057 | — | 2 | 3 | no | — |
| 124 | C8×C13 | C2×C42 | 1 | 3 | yes | — |
| 125 | C8×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 126 | #1055 | C2×C42 | 1 | 3 | yes | — |
| 127 | #1055 | C23×C4 | 1 | 1 | yes | characteristic |
| 128 | C2×#131 | — | 13 | 1 | no | — |
| 129 | C2×#131 | — | 13 | 1 | no | — |
| 130 | C4×#41 | — | 13 | 1 | no | — |
| 131 | #504 | — | 13 | 6 | no | — |
| 132 | #504 | — | 13 | 2 | no | — |
| 133 | #504 | — | 13 | 1 | no | — |
| 134 | #504 | — | 13 | 3 | no | — |
| 135 | #504 | — | 13 | 3 | no | — |
| 136 | #504 | #261 | 1 | 1 | yes | characteristic, complemented |
| 137 | C2×M32 | — | 13 | 3 | no | — |
| 138 | C2×M32 | — | 13 | 3 | no | — |
| 139 | C2×M32 | — | 13 | 3 | no | — |
| 140 | C2×M32 | — | 13 | 3 | no | — |
| 141 | #405 | — | 13 | 3 | no | — |
| 142 | #405 | — | 13 | 3 | no | — |
| 143 | C4×M16 | — | 13 | 3 | no | — |
| 144 | C2×#97 | — | 13 | 3 | no | — |
| 145 | #347 | — | 13 | 1 | no | — |
| 146 | #347 | — | 13 | 3 | no | — |
| 147 | #347 | — | 13 | 6 | no | — |
| 148 | #347 | — | 13 | 3 | no | — |
| 149 | #347 | — | 13 | 3 | no | — |
| 150 | C22×C13 | C2×#97 | 1 | 3 | yes | — |
| 151 | C2×D13 | — | 4 | 3 | no | — |
| 152 | C2×D13 | C2×#97 | 1 | 3 | yes | — |
| 153 | C2×D13 | C22×M16 | 1 | 1 | yes | characteristic |
| 154 | #261 | — | 4 | 3 | no | — |
| 155 | #261 | — | 4 | 1 | no | — |
| 156 | C4×C13 | C2×#97 | 1 | 3 | yes | — |
| 157 | C4×C13 | C22×C42 | 1 | 1 | yes | characteristic |
| 158 | Dic13 | C2×#97 | 1 | 3 | yes | — |
| 159 | Dic13 | C22×M16 | 1 | 1 | yes | characteristic |
| 160 | C2×#41 | — | 13 | 1 | no | — |
| 161 | #131 | — | 13 | 1 | no | — |
| 162 | #131 | — | 13 | 3 | no | — |
| 163 | #131 | — | 13 | 3 | no | — |
| 164 | #131 | — | 26 | 3 | no | — |
| 165 | #131 | — | 26 | 1 | no | — |
| 166 | #131 | C2×#261 | 1 | 1 | yes | characteristic |
| 167 | C2×M16 | — | 13 | 3 | no | — |
| 168 | C2×M16 | — | 13 | 3 | no | — |
| 169 | C22×C8 | — | 13 | 3 | no | — |
| 170 | C22×C8 | — | 13 | 3 | no | — |
| 171 | C4×Q8 | — | 26 | 1 | no | — |
| 172 | C4×D4 | — | 26 | 3 | no | — |
| 173 | #117 | — | 13 | 3 | no | — |
| 174 | C2×C42 | — | 13 | 3 | no | — |
| 175 | M32 | — | 13 | 6 | no | — |
| 176 | M32 | — | 13 | 3 | no | — |
| 177 | M32 | — | 13 | 1 | no | — |
| 178 | M32 | — | 13 | 6 | no | — |
| 179 | M32 | — | 13 | 3 | no | — |
| 180 | M32 | — | 13 | 3 | no | — |
| 181 | M32 | — | 13 | 1 | no | — |
| 182 | M32 | — | 13 | 3 | no | — |
| 183 | M32 | — | 13 | 3 | no | — |
| 184 | M32 | C2×#261 | 1 | 3 | yes | complemented |
| 185 | C2×C16 | — | 13 | 6 | no | — |
| 186 | C2×C16 | — | 13 | 6 | no | — |
| 187 | C2×C16 | — | 13 | 3 | no | — |
| 188 | C2×C16 | — | 13 | 6 | no | — |
| 189 | C2×C16 | C2×#261 | 1 | 3 | yes | complemented |
| 190 | #97 | — | 13 | 3 | no | — |
| 191 | #97 | — | 13 | 3 | no | — |
| 192 | #97 | — | 13 | 1 | no | — |
| 193 | #97 | — | 13 | 3 | no | — |
| 194 | C4×C8 | — | 13 | 6 | no | — |
| 195 | C2×C13 | — | 2 | 3 | no | — |
| 196 | C2×C13 | C22×#97 | 1 | 1 | yes | characteristic |
| 197 | D13 | — | 2 | 1 | no | — |
| 198 | D13 | — | 2 | 3 | no | — |
| 199 | #41 | — | 13 | 1 | no | — |
| 200 | #41 | — | 13 | 3 | no | — |
| 201 | #41 | — | 13 | 3 | no | — |
| 202 | #41 | C4×#261 | 1 | 1 | yes | characteristic |
| 203 | C2×Q8 | — | 13 | 1 | no | — |
| 204 | C2×D4 | — | 13 | 3 | no | — |
| 205 | C22×C4 | — | 13 | 3 | no | — |
| 206 | C22×C4 | — | 26 | 3 | no | — |
| 207 | M16 | — | 13 | 3 | no | — |
| 208 | M16 | — | 13 | 6 | no | — |
| 209 | M16 | — | 26 | 3 | no | — |
| 210 | M16 | — | 26 | 3 | no | — |
| 211 | M16 | C4×#261 | 1 | 3 | yes | — |
| 212 | C2×C8 | — | 13 | 3 | no | — |
| 213 | C2×C8 | — | 13 | 3 | no | — |
| 214 | C2×C8 | — | 13 | 3 | no | — |
| 215 | C2×C8 | — | 13 | 1 | no | — |
| 216 | C2×C8 | — | 13 | 3 | no | — |
| 217 | C2×C8 | — | 13 | 3 | no | — |
| 218 | C2×C8 | — | 13 | 1 | no | — |
| 219 | C2×C8 | — | 26 | 3 | no | — |
| 220 | C2×C8 | — | 26 | 3 | no | — |
| 221 | C2×C8 | C22×#261 | 1 | 3 | yes | — |
| 222 | C4⋊C4 | — | 26 | 3 | no | — |
| 223 | C22⋊C4 | — | 26 | 3 | no | — |
| 224 | C42 | — | 13 | 3 | no | — |
| 225 | C42 | — | 13 | 1 | no | — |
| 226 | C42 | — | 26 | 3 | no | — |
| 227 | C16 | — | 13 | 6 | no | — |
| 228 | C16 | — | 13 | 2 | no | — |
| 229 | C16 | — | 13 | 1 | no | — |
| 230 | C16 | — | 13 | 3 | no | — |
| 231 | C16 | C22×#261 | 1 | 3 | yes | — |
| 232 | C16 | C22×#261 | 1 | 1 | yes | characteristic |
| 233 | C13 | #33329 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 234 | C23 | — | 13 | 3 | no | — |
| 235 | Q8 | — | 13 | 3 | no | — |
| 236 | Q8 | #88100 | 1 | 1 | yes | characteristic |
| 237 | D4 | — | 13 | 6 | no | — |
| 238 | D4 | — | 13 | 3 | no | — |
| 239 | D4 | #88100 | 1 | 3 | yes | — |
| 240 | C2×C4 | — | 13 | 3 | no | — |
| 241 | C2×C4 | — | 13 | 3 | no | — |
| 242 | C2×C4 | — | 13 | 3 | no | — |
| 243 | C2×C4 | — | 13 | 1 | no | — |
| 244 | C2×C4 | — | 13 | 3 | no | — |
| 245 | C2×C4 | — | 26 | 1 | no | — |
| 246 | C2×C4 | — | 26 | 3 | no | — |
| 247 | C2×C4 | — | 104 | 3 | no | — |
| 248 | C2×C4 | C2×C4×#261 | 1 | 3 | yes | — |
| 249 | C8 | — | 13 | 1 | no | — |
| 250 | C8 | — | 13 | 3 | no | — |
| 251 | C8 | — | 26 | 1 | no | — |
| 252 | C8 | — | 26 | 3 | no | — |
| 253 | C8 | C2×C4×#261 | 1 | 3 | yes | — |
| 254 | C8 | C23×#261 | 1 | 1 | yes | characteristic |
| 255 | C22 | — | 13 | 1 | no | — |
| 256 | C22 | — | 13 | 3 | no | — |
| 257 | C22 | — | 52 | 3 | no | — |
| 258 | C22 | C2×#88100 | 1 | 3 | yes | — |
| 259 | C4 | — | 13 | 1 | no | — |
| 260 | C4 | — | 13 | 3 | no | — |
| 261 | C4 | — | 52 | 3 | no | — |
| 262 | C4 | — | 52 | 1 | no | — |
| 263 | C4 | C2×#88100 | 1 | 3 | yes | — |
| 264 | C4 | C22×C4×#261 | 1 | 1 | yes | characteristic |
| 265 | C2 | — | 2 | 3 | no | — |
| 266 | C2 | — | 26 | 1 | no | — |
| 267 | C2 | — | 26 | 3 | no | — |
| 268 | C2 | C22×#88100 | 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