← #15774719
Subgroups — #15774719
Order 3328.
206 conjugacy classes of subgroups.
The subgroup lattice has 196 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13116745 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×#6090 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13112906 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Q8⋊#6090 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | Q8⋊#6090 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #13112753 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C8×C13×Q16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C8×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 9 | C8×Q8×C13 | C22 | 1 | 1 | yes | characteristic |
| 10 | C4×C13×Q16 | C4 | 1 | 1 | yes | characteristic |
| 11 | C13×#335 | C4 | 1 | 1 | yes | characteristic |
| 12 | C13×Q8⋊C8 | C4 | 1 | 1 | yes | characteristic |
| 13 | C13×Q8⋊C8 | C4 | 1 | 1 | yes | characteristic |
| 14 | C82×C13 | C22 | 1 | 1 | yes | characteristic |
| 15 | C4⋊#6090 | — | 2 | 1 | no | — |
| 16 | C4⋊#6090 | — | 2 | 1 | no | — |
| 17 | C4⋊#6090 | C22 | 1 | 1 | yes | characteristic |
| 18 | C4⋊#6090 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11718053 | — | 2 | 1 | no | — |
| 20 | C4×#6090 | — | 2 | 1 | no | — |
| 21 | C4×#6090 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×#6090 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C13×Q16 | C8 | 1 | 1 | yes | characteristic |
| 24 | C4×Q8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 25 | C4×Q8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 26 | C13×#107 | C8 | 1 | 1 | yes | characteristic |
| 27 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 28 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 29 | C13×C4⋊C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C13×C4⋊C8 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C13×#103 | C8 | 1 | 1 | yes | characteristic |
| 32 | C13×#103 | C8 | 1 | 1 | yes | characteristic |
| 33 | C4×C8×C13 | — | 2 | 1 | no | — |
| 34 | C4×C8×C13 | — | 2 | 1 | no | — |
| 35 | C4×C8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C4×C8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C4×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×#6090 | — | 2 | 1 | no | — |
| 39 | C2×#6090 | — | 2 | 1 | no | — |
| 40 | C2×#6090 | — | 2 | 1 | no | — |
| 41 | C2×#6090 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×#6090 | D4 | 1 | 1 | yes | characteristic |
| 43 | #12053 | — | 13 | 1 | no | maximal, Sylow |
| 44 | C2×Q8×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 45 | C2×Q8×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 46 | C13×Q16 | — | 2 | 2 | no | — |
| 47 | C2×C8×C13 | — | 2 | 1 | no | — |
| 48 | C2×C8×C13 | — | 2 | 1 | no | — |
| 49 | C2×C8×C13 | — | 2 | 1 | no | — |
| 50 | C2×C8×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 51 | C2×C8×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 52 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 53 | C2×C8×C13 | #41 | 1 | 1 | yes | characteristic |
| 54 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 55 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 56 | C13×C4⋊C4 | C2×C8 | 1 | 1 | yes | characteristic |
| 57 | C13×C4⋊C4 | C2×C8 | 1 | 1 | yes | characteristic |
| 58 | C42×C13 | — | 2 | 1 | no | — |
| 59 | C42×C13 | — | 2 | 1 | no | — |
| 60 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 61 | #6090 | — | 2 | 2 | no | — |
| 62 | #6090 | — | 2 | 1 | no | — |
| 63 | #6090 | — | 4 | 1 | no | — |
| 64 | #6090 | — | 4 | 1 | no | — |
| 65 | #6090 | Q16 | 1 | 2 | yes | complemented |
| 66 | #2183 | — | 13 | 1 | no | — |
| 67 | Q8×C16 | — | 13 | 1 | no | — |
| 68 | C8×Q16 | D13 | 1 | 1 | yes | characteristic |
| 69 | #1370 | — | 13 | 1 | no | — |
| 70 | Q8⋊C16 | — | 13 | 1 | no | — |
| 71 | Q8⋊C16 | — | 13 | 1 | no | — |
| 72 | #1311 | — | 13 | 1 | no | — |
| 73 | Q8×C13 | — | 2 | 1 | no | — |
| 74 | Q8×C13 | — | 2 | 1 | no | — |
| 75 | Q8×C13 | — | 2 | 1 | no | — |
| 76 | Q8×C13 | M32 | 1 | 2 | yes | — |
| 77 | C2×C4×C13 | — | 2 | 1 | no | — |
| 78 | C2×C4×C13 | — | 2 | 1 | no | — |
| 79 | C2×C4×C13 | — | 2 | 1 | no | — |
| 80 | C2×C4×C13 | — | 2 | 1 | no | — |
| 81 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C4×C13 | C22×C8 | 1 | 1 | yes | characteristic |
| 83 | C2×C4×C13 | #131 | 1 | 1 | yes | characteristic |
| 84 | C8×C13 | — | 2 | 1 | no | — |
| 85 | C8×C13 | — | 2 | 1 | no | — |
| 86 | C8×C13 | — | 2 | 1 | no | — |
| 87 | C8×C13 | — | 4 | 1 | no | — |
| 88 | C8×C13 | — | 4 | 1 | no | — |
| 89 | C8×C13 | — | 4 | 1 | no | — |
| 90 | C8×C13 | C2×Q16 | 1 | 1 | yes | characteristic |
| 91 | C8×C13 | #135 | 1 | 1 | yes | characteristic |
| 92 | C8×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 93 | C8×Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 94 | C4×Q16 | Dic13 | 1 | 1 | yes | characteristic |
| 95 | C4⋊C16 | — | 13 | 1 | no | — |
| 96 | C4⋊C16 | — | 13 | 1 | no | — |
| 97 | C4⋊C16 | — | 26 | 1 | no | — |
| 98 | C4⋊C16 | — | 26 | 1 | no | — |
| 99 | #346 | — | 26 | 1 | no | — |
| 100 | C4×C16 | — | 13 | 1 | no | — |
| 101 | C4×C16 | — | 13 | 1 | no | — |
| 102 | C4×C16 | — | 26 | 1 | no | — |
| 103 | #335 | Dic13 | 1 | 1 | yes | characteristic |
| 104 | Q8⋊C8 | Dic13 | 1 | 1 | yes | characteristic |
| 105 | Q8⋊C8 | Dic13 | 1 | 1 | yes | characteristic |
| 106 | C82 | C2×D13 | 1 | 1 | yes | characteristic |
| 107 | C22×C13 | C8×D4 | 1 | 1 | yes | characteristic |
| 108 | C4×C13 | — | 2 | 2 | no | — |
| 109 | C4×C13 | — | 2 | 1 | no | — |
| 110 | C4×C13 | — | 4 | 1 | no | — |
| 111 | C4×C13 | — | 4 | 1 | no | — |
| 112 | C4×C13 | — | 4 | 1 | no | — |
| 113 | C4×C13 | C4×Q16 | 1 | 1 | yes | characteristic |
| 114 | C4×C13 | #443 | 1 | 1 | yes | characteristic |
| 115 | C4×C13 | C2×M32 | 1 | 1 | yes | characteristic |
| 116 | C4×C13 | #504 | 1 | 1 | yes | characteristic |
| 117 | C2×Q16 | #1055 | 1 | 1 | yes | characteristic |
| 118 | C4×Q8 | C2×Dic13 | 1 | 1 | yes | characteristic |
| 119 | C4×Q8 | C2×Dic13 | 1 | 1 | yes | characteristic |
| 120 | C2×C16 | — | 13 | 1 | no | — |
| 121 | C2×C16 | — | 13 | 1 | no | — |
| 122 | C2×C16 | — | 26 | 1 | no | — |
| 123 | C2×C16 | — | 26 | 1 | no | — |
| 124 | C2×C16 | — | 26 | 1 | no | — |
| 125 | #107 | #1055 | 1 | 1 | yes | characteristic |
| 126 | C4⋊C8 | — | 2 | 1 | no | — |
| 127 | C4⋊C8 | — | 2 | 1 | no | — |
| 128 | C4⋊C8 | C2×Dic13 | 1 | 1 | yes | characteristic |
| 129 | C4⋊C8 | C2×Dic13 | 1 | 1 | yes | characteristic |
| 130 | #103 | #1055 | 1 | 1 | yes | characteristic |
| 131 | #103 | #1055 | 1 | 1 | yes | characteristic |
| 132 | C4×C8 | — | 2 | 1 | no | — |
| 133 | C4×C8 | — | 2 | 1 | no | — |
| 134 | C4×C8 | C2×Dic13 | 1 | 1 | yes | characteristic |
| 135 | C4×C8 | C2×Dic13 | 1 | 1 | yes | characteristic |
| 136 | C4×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 137 | C2×C13 | C8×Q16 | 1 | 1 | yes | characteristic |
| 138 | C2×C13 | #2168 | 1 | 1 | yes | characteristic |
| 139 | C2×C13 | #2171 | 1 | 1 | yes | characteristic |
| 140 | C2×Q8 | C2×#1055 | 1 | 1 | yes | characteristic |
| 141 | C2×Q8 | C2×#1055 | 1 | 1 | yes | characteristic |
| 142 | Q16 | — | 2 | 2 | no | — |
| 143 | C2×C8 | — | 2 | 1 | no | — |
| 144 | C2×C8 | — | 2 | 1 | no | — |
| 145 | C2×C8 | — | 2 | 1 | no | — |
| 146 | C2×C8 | C2×#1055 | 1 | 1 | yes | characteristic |
| 147 | C2×C8 | C2×#1055 | 1 | 1 | yes | characteristic |
| 148 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 149 | C2×C8 | #6129 | 1 | 1 | yes | characteristic |
| 150 | C4⋊C4 | — | 2 | 1 | no | — |
| 151 | C4⋊C4 | — | 2 | 1 | no | — |
| 152 | C4⋊C4 | C2×#1055 | 1 | 1 | yes | characteristic |
| 153 | C4⋊C4 | C2×#1055 | 1 | 1 | yes | characteristic |
| 154 | C42 | — | 2 | 1 | no | — |
| 155 | C42 | — | 2 | 1 | no | — |
| 156 | C42 | C22×Dic13 | 1 | 1 | yes | characteristic |
| 157 | C16 | — | 13 | 2 | no | — |
| 158 | C16 | — | 26 | 2 | no | — |
| 159 | C16 | — | 26 | 1 | no | — |
| 160 | C16 | — | 52 | 1 | no | — |
| 161 | C16 | — | 52 | 1 | no | — |
| 162 | C13 | #12053 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 163 | Q8 | — | 2 | 1 | no | — |
| 164 | Q8 | — | 2 | 1 | no | — |
| 165 | Q8 | — | 2 | 1 | no | — |
| 166 | Q8 | #88052 | 1 | 2 | yes | — |
| 167 | C2×C4 | — | 2 | 1 | no | — |
| 168 | C2×C4 | — | 2 | 1 | no | — |
| 169 | C2×C4 | — | 2 | 1 | no | — |
| 170 | C2×C4 | — | 2 | 1 | no | — |
| 171 | C2×C4 | C22×#1055 | 1 | 1 | yes | characteristic |
| 172 | C2×C4 | D4×Dic13 | 1 | 1 | yes | characteristic |
| 173 | C2×C4 | #88202 | 1 | 1 | yes | characteristic |
| 174 | C8 | — | 2 | 1 | no | — |
| 175 | C8 | — | 2 | 1 | no | — |
| 176 | C8 | — | 2 | 1 | no | — |
| 177 | C8 | — | 4 | 1 | no | — |
| 178 | C8 | — | 4 | 1 | no | — |
| 179 | C8 | — | 4 | 1 | no | — |
| 180 | C8 | Q16×D13 | 1 | 1 | yes | characteristic |
| 181 | C8 | #88173 | 1 | 1 | yes | characteristic |
| 182 | C22 | D4×#1055 | 1 | 1 | yes | characteristic |
| 183 | C4 | — | 2 | 1 | no | — |
| 184 | C4 | — | 2 | 2 | no | — |
| 185 | C4 | — | 4 | 1 | no | — |
| 186 | C4 | — | 4 | 1 | no | — |
| 187 | C4 | — | 4 | 1 | no | — |
| 188 | C4 | C2×#88052 | 1 | 1 | yes | characteristic |
| 189 | C4 | #11718801 | 1 | 1 | yes | characteristic |
| 190 | C4 | Q16×Dic13 | 1 | 1 | yes | characteristic |
| 191 | C4 | #11718857 | 1 | 1 | yes | characteristic |
| 192 | C2 | Q16×#1055 | 1 | 1 | yes | characteristic |
| 193 | C2 | #13116662 | 1 | 1 | yes | characteristic |
| 194 | C2 | #13116678 | 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