← #16015961
Subgroups — #16015961
Order 3328.
658 conjugacy classes of subgroups.
The subgroup lattice has 212 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11718801 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13123436 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13116625 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13116622 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13116618 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C2×#11718081 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C13×#2913 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×C13×#131 | C22 | 1 | 1 | yes | characteristic |
| 9 | C13×#520 | — | 2 | 1 | no | — |
| 10 | #11719532 | — | 2 | 1 | no | — |
| 11 | C13×#428 | — | 2 | 3 | no | — |
| 12 | C13×#427 | C22 | 1 | 3 | yes | — |
| 13 | C2×C13×#107 | C22 | 1 | 3 | yes | — |
| 14 | #11718801 | C4 | 1 | 8 | yes | complemented |
| 15 | #11718782 | — | 2 | 3 | no | — |
| 16 | #11718767 | C22 | 1 | 3 | yes | — |
| 17 | C2×#88058 | C22 | 1 | 3 | yes | — |
| 18 | C2×#88052 | C22 | 1 | 3 | yes | — |
| 19 | C22×#6090 | C22 | 1 | 3 | yes | — |
| 20 | #11718082 | C22 | 1 | 3 | yes | — |
| 21 | #11718082 | C22 | 1 | 3 | yes | — |
| 22 | #11718081 | C22 | 1 | 3 | yes | — |
| 23 | #11718081 | C22 | 1 | 6 | yes | — |
| 24 | #11718081 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C13×#41 | D4 | 1 | 1 | yes | characteristic |
| 26 | C13×#131 | C2×C4 | 1 | 4 | yes | — |
| 27 | C13×#131 | Q8 | 1 | 4 | yes | — |
| 28 | C2×C13×M16 | D4 | 1 | 3 | yes | — |
| 29 | C22×C8×C13 | C23 | 1 | 3 | yes | — |
| 30 | C4×Q8×C13 | — | 4 | 1 | no | — |
| 31 | C4×D4×C13 | — | 4 | 3 | no | — |
| 32 | C13×#117 | — | 2 | 3 | no | — |
| 33 | C2×C13×C4⋊C4 | — | 2 | 3 | no | — |
| 34 | Q8×Dic13 | — | 4 | 1 | no | — |
| 35 | D4×Dic13 | — | 4 | 3 | no | — |
| 36 | #88180 | — | 2 | 3 | no | — |
| 37 | C2×C4⋊Dic13 | — | 2 | 3 | no | — |
| 38 | C13×#107 | — | 2 | 3 | no | — |
| 39 | C13×#107 | C23 | 1 | 3 | yes | — |
| 40 | C13×#107 | C23 | 1 | 1 | yes | characteristic |
| 41 | C13×#106 | — | 2 | 3 | no | — |
| 42 | #88058 | — | 2 | 3 | no | — |
| 43 | #88058 | C23 | 1 | 3 | yes | — |
| 44 | #88058 | C23 | 1 | 1 | yes | characteristic |
| 45 | #88057 | — | 2 | 3 | no | — |
| 46 | #88052 | C2×C4 | 1 | 12 | yes | complemented |
| 47 | C2×#6090 | C2×C4 | 1 | 12 | yes | complemented |
| 48 | C2×#6090 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×#6090 | C23 | 1 | 3 | yes | — |
| 50 | #33410 | — | 13 | 1 | no | maximal, Sylow |
| 51 | C13×#41 | C4⋊C4 | 1 | 4 | yes | — |
| 52 | C13×#41 | Q16 | 1 | 4 | yes | — |
| 53 | C2×Q8×C13 | D8 | 1 | 1 | yes | characteristic |
| 54 | C2×D4×C13 | D8 | 1 | 3 | yes | — |
| 55 | C22×C4×C13 | — | 4 | 3 | no | — |
| 56 | C22×C4×C13 | C2×D4 | 1 | 3 | yes | — |
| 57 | C22×Dic13 | — | 4 | 3 | no | — |
| 58 | C13×M16 | C4⋊C4 | 1 | 12 | yes | — |
| 59 | C2×C8×C13 | C22×C4 | 1 | 6 | yes | — |
| 60 | C2×C8×C13 | C2×D4 | 1 | 3 | yes | — |
| 61 | C2×C8×C13 | C2×Q8 | 1 | 6 | yes | — |
| 62 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 63 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 64 | C13×C4⋊C4 | — | 2 | 3 | no | — |
| 65 | C13×C4⋊C4 | — | 4 | 3 | no | — |
| 66 | C13×C22⋊C4 | — | 4 | 3 | no | — |
| 67 | C42×C13 | — | 4 | 3 | no | — |
| 68 | C22⋊Dic13 | — | 4 | 3 | no | — |
| 69 | C4⋊Dic13 | — | 2 | 3 | no | — |
| 70 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 71 | C4⋊Dic13 | — | 4 | 3 | no | — |
| 72 | C4×Dic13 | — | 4 | 3 | no | — |
| 73 | #6090 | C22×C4 | 1 | 2 | yes | — |
| 74 | #6090 | C22×C4 | 1 | 6 | yes | — |
| 75 | C2×#504 | — | 13 | 1 | no | — |
| 76 | #2913 | — | 13 | 1 | no | — |
| 77 | #2913 | D13 | 1 | 1 | yes | characteristic |
| 78 | #2159 | — | 13 | 3 | no | — |
| 79 | #2159 | — | 13 | 3 | no | — |
| 80 | #2158 | — | 13 | 3 | no | — |
| 81 | C2×#366 | — | 13 | 3 | no | — |
| 82 | C23×C13 | C2×D8 | 1 | 3 | yes | — |
| 83 | Q8×C13 | #107 | 1 | 4 | yes | — |
| 84 | D4×C13 | #107 | 1 | 12 | yes | — |
| 85 | C2×C4×C13 | — | 4 | 1 | no | — |
| 86 | C2×C4×C13 | — | 4 | 3 | no | — |
| 87 | C2×C4×C13 | — | 16 | 3 | no | — |
| 88 | C2×C4×C13 | C2×C4⋊C4 | 1 | 6 | yes | — |
| 89 | C2×C4×C13 | C2×D8 | 1 | 3 | yes | — |
| 90 | C2×C4×C13 | C2×Q16 | 1 | 6 | yes | — |
| 91 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 92 | C2×Dic13 | — | 4 | 1 | no | — |
| 93 | C2×Dic13 | — | 4 | 3 | no | — |
| 94 | C2×Dic13 | — | 16 | 3 | no | — |
| 95 | C8×C13 | C2×C4⋊C4 | 1 | 6 | yes | — |
| 96 | C8×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 97 | C8×C13 | C22×Q8 | 1 | 1 | yes | characteristic |
| 98 | C2×#131 | C2×D13 | 1 | 1 | yes | characteristic |
| 99 | #520 | — | 2 | 1 | no | — |
| 100 | #520 | — | 26 | 1 | no | — |
| 101 | #504 | — | 13 | 8 | no | — |
| 102 | C2×M32 | — | 13 | 3 | no | — |
| 103 | C22×C16 | — | 13 | 3 | no | — |
| 104 | #428 | — | 2 | 3 | no | — |
| 105 | #428 | — | 26 | 3 | no | — |
| 106 | #427 | — | 13 | 3 | no | — |
| 107 | #427 | C2×D13 | 1 | 3 | yes | — |
| 108 | C2×#107 | — | 13 | 3 | no | — |
| 109 | C2×#107 | C2×D13 | 1 | 3 | yes | — |
| 110 | #367 | — | 13 | 3 | no | — |
| 111 | #367 | — | 13 | 3 | no | — |
| 112 | #366 | — | 13 | 3 | no | — |
| 113 | #366 | — | 13 | 6 | no | — |
| 114 | #366 | — | 13 | 1 | no | — |
| 115 | C22×C13 | — | 2 | 3 | no | — |
| 116 | C22×C13 | — | 2 | 3 | no | — |
| 117 | C22×C13 | C2×#107 | 1 | 6 | yes | — |
| 118 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 119 | C4×C13 | — | 8 | 3 | no | — |
| 120 | C4×C13 | — | 8 | 1 | no | — |
| 121 | C4×C13 | C2×#107 | 1 | 6 | yes | — |
| 122 | C4×C13 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 123 | C4×C13 | C22×Q16 | 1 | 1 | yes | characteristic |
| 124 | Dic13 | — | 8 | 3 | no | — |
| 125 | Dic13 | — | 8 | 1 | no | — |
| 126 | C2×#41 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 127 | #131 | Dic26 | 1 | 4 | yes | — |
| 128 | #131 | C4×D13 | 1 | 4 | yes | — |
| 129 | C2×M16 | C22⋊D13 | 1 | 3 | yes | — |
| 130 | C22×C8 | C22×D13 | 1 | 3 | yes | — |
| 131 | C4×Q8 | — | 4 | 1 | no | — |
| 132 | C4×Q8 | — | 52 | 1 | no | — |
| 133 | C4×D4 | — | 4 | 3 | no | — |
| 134 | C4×D4 | — | 52 | 3 | no | — |
| 135 | #117 | — | 2 | 3 | no | — |
| 136 | #117 | — | 26 | 3 | no | — |
| 137 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 138 | C2×C4⋊C4 | — | 26 | 3 | no | — |
| 139 | M32 | — | 13 | 12 | no | — |
| 140 | C2×C16 | — | 13 | 12 | no | — |
| 141 | C2×C16 | — | 13 | 1 | no | — |
| 142 | C2×C16 | — | 13 | 3 | no | — |
| 143 | #107 | — | 2 | 3 | no | — |
| 144 | #107 | — | 13 | 3 | no | — |
| 145 | #107 | — | 13 | 1 | no | — |
| 146 | #107 | — | 26 | 3 | no | — |
| 147 | #107 | C22×D13 | 1 | 3 | yes | — |
| 148 | #107 | C22×D13 | 1 | 1 | yes | characteristic |
| 149 | #106 | — | 2 | 3 | no | — |
| 150 | #106 | — | 26 | 3 | no | — |
| 151 | C2×C13 | — | 2 | 6 | no | — |
| 152 | C2×C13 | C22×#107 | 1 | 1 | yes | characteristic |
| 153 | C2×C13 | #3415 | 1 | 1 | yes | characteristic |
| 154 | C2×C13 | #3417 | 1 | 1 | yes | characteristic |
| 155 | #41 | #6101 | 1 | 4 | yes | — |
| 156 | #41 | #6107 | 1 | 4 | yes | — |
| 157 | C2×Q8 | #6104 | 1 | 1 | yes | characteristic |
| 158 | C2×D4 | #6104 | 1 | 3 | yes | — |
| 159 | C22×C4 | — | 4 | 3 | no | — |
| 160 | C22×C4 | — | 52 | 3 | no | — |
| 161 | C22×C4 | C2×C22⋊D13 | 1 | 3 | yes | — |
| 162 | M16 | #6101 | 1 | 12 | yes | — |
| 163 | C2×C8 | C2×Dic26 | 1 | 6 | yes | — |
| 164 | C2×C8 | C2×C4×D13 | 1 | 6 | yes | — |
| 165 | C2×C8 | C2×C22⋊D13 | 1 | 3 | yes | — |
| 166 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 167 | C4⋊C4 | — | 2 | 1 | no | — |
| 168 | C4⋊C4 | — | 2 | 3 | no | — |
| 169 | C4⋊C4 | — | 4 | 3 | no | — |
| 170 | C4⋊C4 | — | 26 | 1 | no | — |
| 171 | C4⋊C4 | — | 26 | 3 | no | — |
| 172 | C4⋊C4 | — | 52 | 3 | no | — |
| 173 | C22⋊C4 | — | 4 | 3 | no | — |
| 174 | C22⋊C4 | — | 52 | 3 | no | — |
| 175 | C42 | — | 4 | 3 | no | — |
| 176 | C42 | — | 52 | 3 | no | — |
| 177 | C16 | — | 13 | 2 | no | — |
| 178 | C16 | — | 13 | 6 | no | — |
| 179 | C13 | #33410 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 180 | C23 | C2×#6104 | 1 | 3 | yes | — |
| 181 | Q8 | #88047 | 1 | 4 | yes | — |
| 182 | D4 | #88047 | 1 | 12 | yes | — |
| 183 | C2×C4 | — | 4 | 1 | no | — |
| 184 | C2×C4 | — | 4 | 3 | no | — |
| 185 | C2×C4 | — | 16 | 3 | no | — |
| 186 | C2×C4 | — | 52 | 1 | no | — |
| 187 | C2×C4 | — | 52 | 3 | no | — |
| 188 | C2×C4 | — | 208 | 3 | no | — |
| 189 | C2×C4 | C2×#6101 | 1 | 6 | yes | — |
| 190 | C2×C4 | C2×#6104 | 1 | 3 | yes | — |
| 191 | C2×C4 | C2×#6107 | 1 | 6 | yes | — |
| 192 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 193 | C8 | C2×#6101 | 1 | 6 | yes | — |
| 194 | C8 | C22×Dic26 | 1 | 1 | yes | characteristic |
| 195 | C8 | C22×C4×D13 | 1 | 1 | yes | characteristic |
| 196 | C22 | — | 2 | 3 | no | — |
| 197 | C22 | — | 2 | 3 | no | — |
| 198 | C22 | C2×#88047 | 1 | 6 | yes | — |
| 199 | C22 | C22×#6104 | 1 | 1 | yes | characteristic |
| 200 | C4 | — | 8 | 3 | no | — |
| 201 | C4 | — | 8 | 1 | no | — |
| 202 | C4 | — | 104 | 3 | no | — |
| 203 | C4 | — | 104 | 1 | no | — |
| 204 | C4 | C2×#88047 | 1 | 6 | yes | — |
| 205 | C4 | C22×#6101 | 1 | 1 | yes | characteristic |
| 206 | C4 | C22×#6107 | 1 | 1 | yes | characteristic |
| 207 | C2 | — | 2 | 6 | no | — |
| 208 | C2 | C22×#88047 | 1 | 1 | yes | characteristic |
| 209 | C2 | #13127975 | 1 | 1 | yes | characteristic |
| 210 | C2 | #13127987 | 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