← #16015625
Subgroups — #16015625
Order 3328.
1114 conjugacy classes of subgroups.
The subgroup lattice has 230 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13127939 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#11718801 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13116464 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C2×#11718153 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C13×#3573 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C13×#585 | C4 | 1 | 1 | yes | characteristic |
| 7 | C13×#568 | — | 2 | 4 | no | — |
| 8 | C13×#568 | C4 | 1 | 6 | yes | — |
| 9 | C13×#568 | C4 | 1 | 1 | yes | characteristic |
| 10 | C2×C13×#131 | — | 2 | 4 | no | — |
| 11 | C2×C13×#131 | C22 | 1 | 6 | yes | — |
| 12 | C2×C13×#131 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11718801 | — | 2 | 4 | no | — |
| 14 | #11718801 | — | 2 | 4 | no | — |
| 15 | C2×#88052 | C22 | 1 | 6 | yes | complemented |
| 16 | C2×#88052 | C22 | 1 | 3 | yes | complemented |
| 17 | C22×#6090 | C22 | 1 | 3 | yes | complemented |
| 18 | #11718153 | C22 | 1 | 4 | yes | complemented |
| 19 | #11718153 | C22 | 1 | 12 | yes | complemented |
| 20 | C13×2−1+4 | — | 2 | 1 | no | — |
| 21 | C13×2−1+4 | C8 | 1 | 4 | yes | — |
| 22 | C13×H(5,𝔽2) | — | 2 | 3 | no | — |
| 23 | C13×H(5,𝔽2) | C8 | 1 | 4 | yes | — |
| 24 | C2×C13×#41 | — | 2 | 4 | no | — |
| 25 | C2×C13×#41 | C2×C4 | 1 | 6 | yes | — |
| 26 | C2×C13×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C13×#131 | — | 2 | 4 | no | — |
| 28 | C13×#131 | — | 2 | 12 | no | — |
| 29 | C13×#131 | — | 2 | 6 | no | — |
| 30 | C13×#131 | — | 2 | 6 | no | — |
| 31 | C13×#131 | C2×C4 | 1 | 12 | yes | — |
| 32 | C13×#131 | D4 | 1 | 4 | yes | — |
| 33 | C13×#131 | D4 | 1 | 4 | yes | — |
| 34 | C13×#131 | C23 | 1 | 4 | yes | — |
| 35 | C2×C13×M16 | — | 2 | 12 | no | — |
| 36 | C2×C13×M16 | — | 2 | 6 | no | — |
| 37 | C2×C13×M16 | C2×C4 | 1 | 6 | yes | — |
| 38 | C2×C13×M16 | C2×C4 | 1 | 3 | yes | — |
| 39 | C22×C8×C13 | — | 2 | 6 | no | — |
| 40 | C22×C8×C13 | C23 | 1 | 3 | yes | — |
| 41 | #88052 | — | 2 | 6 | no | — |
| 42 | #88052 | — | 2 | 6 | no | — |
| 43 | #88052 | C23 | 1 | 4 | yes | — |
| 44 | C2×#6090 | — | 2 | 6 | no | — |
| 45 | C2×#6090 | — | 2 | 6 | no | — |
| 46 | C2×#6090 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×#6090 | C23 | 1 | 3 | yes | — |
| 48 | #33340 | — | 13 | 1 | no | maximal, Sylow |
| 49 | C13×#41 | — | 2 | 4 | no | — |
| 50 | C13×#41 | — | 2 | 12 | no | — |
| 51 | C13×#41 | — | 2 | 6 | no | — |
| 52 | C13×#41 | — | 2 | 6 | no | — |
| 53 | C13×#41 | C22⋊C4 | 1 | 4 | yes | — |
| 54 | C13×#41 | C2×C8 | 1 | 12 | yes | — |
| 55 | C13×#41 | C2×C8 | 1 | 4 | yes | — |
| 56 | C13×#41 | C22×C4 | 1 | 4 | yes | — |
| 57 | C2×Q8×C13 | — | 2 | 4 | no | — |
| 58 | C2×Q8×C13 | C2×C8 | 1 | 6 | yes | — |
| 59 | C2×Q8×C13 | M16 | 1 | 1 | yes | characteristic |
| 60 | C2×D4×C13 | — | 2 | 6 | no | — |
| 61 | C2×D4×C13 | — | 2 | 12 | no | — |
| 62 | C2×D4×C13 | C2×C8 | 1 | 6 | yes | — |
| 63 | C2×D4×C13 | M16 | 1 | 3 | yes | — |
| 64 | C22×C4×C13 | — | 2 | 6 | no | — |
| 65 | C22×C4×C13 | C22×C4 | 1 | 3 | yes | — |
| 66 | C13×M16 | — | 2 | 6 | no | — |
| 67 | C13×M16 | — | 2 | 12 | no | — |
| 68 | C13×M16 | — | 2 | 4 | no | — |
| 69 | C13×M16 | C22⋊C4 | 1 | 12 | yes | — |
| 70 | C13×M16 | C22×C4 | 1 | 4 | yes | — |
| 71 | C2×C8×C13 | — | 2 | 6 | no | — |
| 72 | C2×C8×C13 | — | 2 | 12 | no | — |
| 73 | C2×C8×C13 | — | 2 | 4 | no | — |
| 74 | C2×C8×C13 | C22×C4 | 1 | 3 | yes | — |
| 75 | C2×C8×C13 | C2×D4 | 1 | 6 | yes | — |
| 76 | C2×C8×C13 | C2×D4 | 1 | 6 | yes | — |
| 77 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 78 | #6090 | — | 2 | 1 | no | — |
| 79 | #6090 | — | 2 | 4 | no | — |
| 80 | #6090 | — | 2 | 3 | no | — |
| 81 | #3573 | D13 | 1 | 1 | yes | characteristic |
| 82 | #3407 | — | 13 | 1 | no | — |
| 83 | C2×#504 | — | 13 | 1 | no | — |
| 84 | #2117 | — | 13 | 6 | no | — |
| 85 | C2×#350 | — | 13 | 6 | no | — |
| 86 | C23×C13 | — | 2 | 6 | no | — |
| 87 | C23×C13 | C2×M16 | 1 | 3 | yes | — |
| 88 | Q8×C13 | — | 2 | 6 | no | — |
| 89 | Q8×C13 | C22⋊C8 | 1 | 4 | yes | — |
| 90 | Q8×C13 | C22×C8 | 1 | 4 | yes | — |
| 91 | D4×C13 | — | 2 | 4 | no | — |
| 92 | D4×C13 | — | 2 | 12 | no | — |
| 93 | D4×C13 | — | 2 | 6 | no | — |
| 94 | D4×C13 | C22⋊C8 | 1 | 12 | yes | — |
| 95 | D4×C13 | C22×C8 | 1 | 4 | yes | — |
| 96 | C2×C4×C13 | — | 2 | 6 | no | — |
| 97 | C2×C4×C13 | — | 2 | 4 | no | — |
| 98 | C2×C4×C13 | — | 2 | 12 | no | — |
| 99 | C2×C4×C13 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 100 | C2×C4×C13 | C22×C8 | 1 | 6 | yes | — |
| 101 | C2×C4×C13 | C2×M16 | 1 | 3 | yes | — |
| 102 | C2×C4×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 103 | C8×C13 | — | 2 | 4 | no | — |
| 104 | C8×C13 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 105 | C8×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 106 | C8×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 107 | #585 | Dic13 | 1 | 1 | yes | characteristic |
| 108 | #568 | — | 2 | 4 | no | — |
| 109 | #568 | Dic13 | 1 | 6 | yes | — |
| 110 | #568 | Dic13 | 1 | 1 | yes | characteristic |
| 111 | C2×#131 | — | 2 | 4 | no | — |
| 112 | C2×#131 | C2×D13 | 1 | 6 | yes | — |
| 113 | C2×#131 | C2×D13 | 1 | 1 | yes | characteristic |
| 114 | #504 | — | 26 | 4 | no | — |
| 115 | #504 | — | 26 | 4 | no | — |
| 116 | C2×M32 | — | 13 | 3 | no | — |
| 117 | C2×M32 | — | 13 | 6 | no | — |
| 118 | C22×C16 | — | 13 | 3 | no | — |
| 119 | #350 | — | 13 | 4 | no | — |
| 120 | #350 | — | 13 | 12 | no | — |
| 121 | C22×C13 | — | 2 | 4 | no | — |
| 122 | C22×C13 | — | 4 | 3 | no | — |
| 123 | C22×C13 | — | 8 | 6 | no | — |
| 124 | C22×C13 | C2×C22⋊C8 | 1 | 6 | yes | — |
| 125 | C22×C13 | C22×M16 | 1 | 1 | yes | characteristic |
| 126 | C4×C13 | — | 2 | 4 | no | — |
| 127 | C4×C13 | C2×C22⋊C8 | 1 | 6 | yes | — |
| 128 | C4×C13 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 129 | C4×C13 | C23×C8 | 1 | 1 | yes | characteristic |
| 130 | 2−1+4 | — | 2 | 1 | no | — |
| 131 | 2−1+4 | #1055 | 1 | 4 | yes | — |
| 132 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 133 | H(5,𝔽2) | #1055 | 1 | 4 | yes | — |
| 134 | C2×#41 | — | 2 | 4 | no | — |
| 135 | C2×#41 | C2×Dic13 | 1 | 6 | yes | — |
| 136 | C2×#41 | C2×Dic13 | 1 | 1 | yes | characteristic |
| 137 | #131 | — | 2 | 4 | no | — |
| 138 | #131 | — | 2 | 12 | no | — |
| 139 | #131 | — | 2 | 6 | no | — |
| 140 | #131 | — | 2 | 6 | no | — |
| 141 | #131 | C2×Dic13 | 1 | 12 | yes | — |
| 142 | #131 | C22⋊D13 | 1 | 4 | yes | — |
| 143 | #131 | C22⋊D13 | 1 | 4 | yes | — |
| 144 | #131 | C22×D13 | 1 | 4 | yes | — |
| 145 | C2×M16 | — | 2 | 12 | no | — |
| 146 | C2×M16 | — | 2 | 6 | no | — |
| 147 | C2×M16 | C2×Dic13 | 1 | 6 | yes | — |
| 148 | C2×M16 | C2×Dic13 | 1 | 3 | yes | — |
| 149 | C22×C8 | — | 2 | 6 | no | — |
| 150 | C22×C8 | C22×D13 | 1 | 3 | yes | — |
| 151 | M32 | — | 13 | 4 | no | — |
| 152 | M32 | — | 26 | 6 | no | — |
| 153 | M32 | — | 26 | 6 | no | — |
| 154 | C2×C16 | — | 13 | 1 | no | — |
| 155 | C2×C16 | — | 13 | 3 | no | — |
| 156 | C2×C16 | — | 26 | 6 | no | — |
| 157 | C2×C16 | — | 26 | 6 | no | — |
| 158 | C2×C13 | — | 2 | 1 | no | — |
| 159 | C2×C13 | — | 2 | 6 | no | — |
| 160 | C2×C13 | — | 4 | 4 | no | — |
| 161 | C2×C13 | C22×C22⋊C8 | 1 | 1 | yes | characteristic |
| 162 | #41 | — | 2 | 4 | no | — |
| 163 | #41 | — | 2 | 12 | no | — |
| 164 | #41 | — | 2 | 6 | no | — |
| 165 | #41 | — | 2 | 6 | no | — |
| 166 | #41 | C2×#1055 | 1 | 12 | yes | — |
| 167 | #41 | C2×#1055 | 1 | 4 | yes | — |
| 168 | #41 | C22⋊Dic13 | 1 | 4 | yes | — |
| 169 | #41 | C22×Dic13 | 1 | 4 | yes | — |
| 170 | C2×Q8 | — | 2 | 4 | no | — |
| 171 | C2×Q8 | C2×#1055 | 1 | 6 | yes | — |
| 172 | C2×Q8 | #6099 | 1 | 1 | yes | characteristic |
| 173 | C2×D4 | — | 2 | 6 | no | — |
| 174 | C2×D4 | — | 2 | 12 | no | — |
| 175 | C2×D4 | C2×#1055 | 1 | 6 | yes | — |
| 176 | C2×D4 | #6099 | 1 | 3 | yes | — |
| 177 | C22×C4 | — | 2 | 6 | no | — |
| 178 | C22×C4 | C22×Dic13 | 1 | 3 | yes | — |
| 179 | M16 | — | 2 | 6 | no | — |
| 180 | M16 | — | 2 | 12 | no | — |
| 181 | M16 | — | 2 | 4 | no | — |
| 182 | M16 | C22⋊Dic13 | 1 | 12 | yes | — |
| 183 | M16 | C22×Dic13 | 1 | 4 | yes | — |
| 184 | C2×C8 | — | 2 | 6 | no | — |
| 185 | C2×C8 | — | 2 | 12 | no | — |
| 186 | C2×C8 | — | 2 | 4 | no | — |
| 187 | C2×C8 | C22×Dic13 | 1 | 3 | yes | — |
| 188 | C2×C8 | C2×C22⋊D13 | 1 | 6 | yes | — |
| 189 | C2×C8 | C2×C22⋊D13 | 1 | 6 | yes | — |
| 190 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 191 | C16 | — | 26 | 1 | no | — |
| 192 | C16 | — | 26 | 3 | no | — |
| 193 | C16 | — | 26 | 4 | no | — |
| 194 | C13 | #33340 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 195 | C23 | — | 2 | 6 | no | — |
| 196 | C23 | C2×#6099 | 1 | 3 | yes | — |
| 197 | Q8 | — | 2 | 6 | no | — |
| 198 | Q8 | C22⋊#1055 | 1 | 4 | yes | — |
| 199 | Q8 | C22×#1055 | 1 | 4 | yes | — |
| 200 | D4 | — | 2 | 4 | no | — |
| 201 | D4 | — | 2 | 12 | no | — |
| 202 | D4 | — | 2 | 6 | no | — |
| 203 | D4 | C22⋊#1055 | 1 | 12 | yes | — |
| 204 | D4 | C22×#1055 | 1 | 4 | yes | — |
| 205 | C2×C4 | — | 2 | 6 | no | — |
| 206 | C2×C4 | — | 2 | 4 | no | — |
| 207 | C2×C4 | — | 2 | 12 | no | — |
| 208 | C2×C4 | C22×#1055 | 1 | 6 | yes | — |
| 209 | C2×C4 | C2×#6099 | 1 | 3 | yes | — |
| 210 | C2×C4 | C2×C22⋊Dic13 | 1 | 6 | yes | — |
| 211 | C2×C4 | C23×Dic13 | 1 | 1 | yes | characteristic |
| 212 | C8 | — | 2 | 4 | no | — |
| 213 | C8 | C2×C22⋊Dic13 | 1 | 6 | yes | — |
| 214 | C8 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 215 | C8 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 216 | C22 | — | 2 | 4 | no | — |
| 217 | C22 | — | 4 | 3 | no | — |
| 218 | C22 | — | 8 | 6 | no | — |
| 219 | C22 | C2×C22⋊#1055 | 1 | 6 | yes | — |
| 220 | C22 | C22×#6099 | 1 | 1 | yes | characteristic |
| 221 | C4 | — | 2 | 4 | no | — |
| 222 | C4 | C2×C22⋊#1055 | 1 | 6 | yes | — |
| 223 | C4 | C23×#1055 | 1 | 1 | yes | characteristic |
| 224 | C4 | C22×C22⋊Dic13 | 1 | 1 | yes | characteristic |
| 225 | C2 | — | 2 | 1 | no | — |
| 226 | C2 | — | 2 | 6 | no | — |
| 227 | C2 | — | 4 | 4 | no | — |
| 228 | C2 | C22×C22⋊#1055 | 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