← #13559900
Subgroups — #13559900
Order 1792.
4086 conjugacy classes of subgroups.
The subgroup lattice has 210 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#90168 | C2 | 1 | 6 | yes | maximal, complemented |
| 2 | C2×C43×C7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11739526 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #11730763 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11730758 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #11730756 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C4×#6437 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | C22×#1157 | C22 | 1 | 4 | yes | — |
| 9 | C22×C42×C7 | C22 | 1 | 4 | yes | — |
| 10 | C22×C42×C7 | C22 | 1 | 3 | yes | — |
| 11 | C2×#6493 | C22 | 1 | 24 | yes | — |
| 12 | #90168 | — | 2 | 48 | no | — |
| 13 | C2×#6438 | C22 | 1 | 12 | yes | — |
| 14 | C2×#6437 | C22 | 1 | 6 | yes | — |
| 15 | C2×#6437 | C22 | 1 | 8 | yes | — |
| 16 | C2×C4×D28 | C22 | 1 | 24 | yes | — |
| 17 | C2×#6432 | C22 | 1 | 6 | yes | — |
| 18 | C43×C7 | C22 | 1 | 4 | yes | — |
| 19 | C43×C7 | C22 | 1 | 1 | yes | characteristic |
| 20 | C43×C7 | C22 | 1 | 3 | yes | — |
| 21 | #89711 | C22 | 1 | 48 | yes | — |
| 22 | #89707 | C22 | 1 | 8 | yes | — |
| 23 | #36644 | — | 7 | 1 | no | maximal, Sylow |
| 24 | C23×C4×C7 | C23 | 1 | 6 | yes | — |
| 25 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 26 | C22×C22⋊D7 | C23 | 1 | 8 | yes | — |
| 27 | C2×#1157 | — | 2 | 48 | no | — |
| 28 | C22×D28 | C23 | 1 | 24 | yes | — |
| 29 | C22×D28 | C23 | 1 | 4 | yes | — |
| 30 | C22×C4×D7 | C23 | 1 | 8 | yes | — |
| 31 | C22×Dic14 | C23 | 1 | 4 | yes | — |
| 32 | C2×C42×C7 | — | 2 | 16 | no | — |
| 33 | C2×C42×C7 | D4 | 1 | 24 | yes | complemented |
| 34 | C2×C42×C7 | C23 | 1 | 12 | yes | — |
| 35 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 36 | C2×C42×C7 | C23 | 1 | 6 | yes | — |
| 37 | C2×C42×C7 | C23 | 1 | 3 | yes | — |
| 38 | C2×C42×C7 | C23 | 1 | 4 | yes | — |
| 39 | #6493 | — | 2 | 96 | no | — |
| 40 | C2×(C2×D7)⋊C4 | C23 | 1 | 48 | yes | — |
| 41 | C2×C4⋊Dic7 | C23 | 1 | 24 | yes | — |
| 42 | #6438 | — | 2 | 48 | no | — |
| 43 | #6437 | — | 2 | 24 | no | — |
| 44 | #6437 | — | 2 | 32 | no | — |
| 45 | C4×D28 | — | 2 | 96 | no | — |
| 46 | #6432 | — | 2 | 24 | no | — |
| 47 | C2×#532 | — | 7 | 6 | no | — |
| 48 | #2868 | — | 7 | 1 | no | — |
| 49 | #2867 | — | 7 | 1 | no | — |
| 50 | #2858 | — | 7 | 6 | no | — |
| 51 | #2856 | — | 7 | 8 | no | — |
| 52 | C4×#127 | — | 7 | 8 | no | — |
| 53 | C2×C43 | D7 | 1 | 1 | yes | characteristic, complemented |
| 54 | C24×C7 | C24 | 1 | 1 | yes | characteristic |
| 55 | C23×D7 | C24 | 1 | 8 | yes | — |
| 56 | C22×C4×C7 | — | 2 | 24 | no | — |
| 57 | C22×C4×C7 | C2×D4 | 1 | 24 | yes | — |
| 58 | C22×C4×C7 | C2×D4 | 1 | 12 | yes | — |
| 59 | C22×C4×C7 | C24 | 1 | 6 | yes | — |
| 60 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 61 | C22×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 62 | C22×C4×C7 | C24 | 1 | 6 | yes | — |
| 63 | C2×C22⋊D7 | — | 2 | 48 | no | — |
| 64 | C22×Dic7 | C24 | 1 | 8 | yes | — |
| 65 | #1157 | — | 4 | 64 | no | — |
| 66 | C2×D28 | — | 2 | 48 | no | — |
| 67 | C2×D28 | — | 2 | 24 | no | — |
| 68 | C2×D28 | — | 2 | 96 | no | — |
| 69 | C2×C4×D7 | — | 2 | 48 | no | — |
| 70 | C2×Dic14 | — | 2 | 24 | no | — |
| 71 | C42×C7 | — | 2 | 24 | no | — |
| 72 | C42×C7 | C2×D4 | 1 | 12 | yes | — |
| 73 | C42×C7 | C2×D4 | 1 | 24 | yes | — |
| 74 | C42×C7 | C2×D4 | 1 | 12 | yes | — |
| 75 | C42×C7 | #41 | 1 | 16 | yes | complemented |
| 76 | (C2×D7)⋊C4 | — | 2 | 96 | no | — |
| 77 | C4⋊Dic7 | — | 2 | 48 | no | — |
| 78 | C22×#41 | — | 7 | 4 | no | — |
| 79 | #532 | — | 14 | 48 | no | — |
| 80 | C2×C4⋊Q8 | — | 7 | 6 | no | — |
| 81 | C2×#127 | — | 7 | 8 | no | — |
| 82 | C2×#127 | — | 7 | 6 | no | — |
| 83 | C2×#124 | — | 7 | 12 | no | — |
| 84 | C2×#121 | — | 7 | 24 | no | — |
| 85 | C2×C4×D4 | — | 7 | 24 | no | — |
| 86 | C22×C42 | C2×D7 | 1 | 4 | yes | — |
| 87 | C22×C42 | C2×D7 | 1 | 3 | yes | — |
| 88 | #390 | — | 7 | 48 | no | — |
| 89 | #384 | — | 7 | 8 | no | — |
| 90 | C43 | C2×D7 | 1 | 4 | yes | — |
| 91 | C43 | C2×D7 | 1 | 3 | yes | — |
| 92 | C43 | C2×D7 | 1 | 1 | yes | characteristic |
| 93 | C23×C7 | — | 2 | 4 | no | — |
| 94 | C23×C7 | C22×D4 | 1 | 6 | yes | — |
| 95 | C23×C7 | C25 | 1 | 1 | yes | characteristic |
| 96 | C22×D7 | — | 2 | 24 | no | — |
| 97 | C22×D7 | — | 2 | 32 | no | — |
| 98 | C2×C4×C7 | — | 2 | 12 | no | — |
| 99 | C2×C4×C7 | — | 2 | 48 | no | — |
| 100 | C2×C4×C7 | #127 | 1 | 16 | yes | complemented |
| 101 | C2×C4×C7 | C22×D4 | 1 | 12 | yes | — |
| 102 | C2×C4×C7 | C22×D4 | 1 | 6 | yes | — |
| 103 | C2×C4×C7 | C22×D4 | 1 | 6 | yes | — |
| 104 | C2×C4×C7 | C22×D4 | 1 | 12 | yes | — |
| 105 | C2×C4×C7 | C2×#41 | 1 | 24 | yes | — |
| 106 | C22⋊D7 | — | 4 | 32 | no | — |
| 107 | C2×Dic7 | — | 2 | 24 | no | — |
| 108 | D28 | — | 4 | 16 | no | — |
| 109 | D28 | — | 4 | 96 | no | — |
| 110 | C4×D7 | — | 4 | 32 | no | — |
| 111 | Dic14 | — | 4 | 16 | no | — |
| 112 | C2×#41 | — | 14 | 48 | no | — |
| 113 | C22×Q8 | — | 7 | 4 | no | — |
| 114 | C22×D4 | — | 7 | 8 | no | — |
| 115 | C22×D4 | — | 7 | 24 | no | — |
| 116 | C22×D4 | — | 7 | 4 | no | — |
| 117 | C23×C4 | — | 7 | 8 | no | — |
| 118 | C23×C4 | C22×D7 | 1 | 6 | yes | — |
| 119 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 120 | C4⋊Q8 | — | 14 | 24 | no | — |
| 121 | #127 | — | 14 | 24 | no | — |
| 122 | #127 | — | 14 | 32 | no | — |
| 123 | #124 | — | 14 | 48 | no | — |
| 124 | #121 | — | 14 | 96 | no | — |
| 125 | C4×D4 | — | 14 | 96 | no | — |
| 126 | C2×C4⋊C4 | — | 7 | 24 | no | — |
| 127 | C2×C22⋊C4 | — | 7 | 48 | no | — |
| 128 | C2×C42 | — | 2 | 16 | no | — |
| 129 | C2×C42 | D28 | 1 | 24 | yes | complemented |
| 130 | C2×C42 | C22×D7 | 1 | 12 | yes | — |
| 131 | C2×C42 | C22×D7 | 1 | 3 | yes | — |
| 132 | C2×C42 | C22×D7 | 1 | 3 | yes | — |
| 133 | C2×C42 | C22×D7 | 1 | 6 | yes | — |
| 134 | C2×C42 | C22×D7 | 1 | 4 | yes | — |
| 135 | C22×C7 | — | 2 | 12 | no | — |
| 136 | C22×C7 | C2×#127 | 1 | 4 | yes | — |
| 137 | C22×C7 | C23×D4 | 1 | 3 | yes | — |
| 138 | C22×C7 | C22×#41 | 1 | 4 | yes | — |
| 139 | C2×D7 | — | 4 | 8 | no | — |
| 140 | C2×D7 | — | 4 | 48 | no | — |
| 141 | C4×C7 | — | 2 | 12 | no | — |
| 142 | C4×C7 | C2×#127 | 1 | 4 | yes | — |
| 143 | C4×C7 | C2×#127 | 1 | 4 | yes | — |
| 144 | C4×C7 | #532 | 1 | 24 | yes | complemented |
| 145 | Dic7 | — | 4 | 8 | no | — |
| 146 | C24 | — | 7 | 8 | no | — |
| 147 | C24 | C23×D7 | 1 | 1 | yes | characteristic |
| 148 | #41 | — | 28 | 64 | no | — |
| 149 | C2×Q8 | — | 14 | 24 | no | — |
| 150 | C2×D4 | — | 14 | 48 | no | — |
| 151 | C2×D4 | — | 14 | 48 | no | — |
| 152 | C2×D4 | — | 14 | 24 | no | — |
| 153 | C2×D4 | — | 14 | 96 | no | — |
| 154 | C22×C4 | — | 2 | 24 | no | — |
| 155 | C22×C4 | — | 7 | 8 | no | — |
| 156 | C22×C4 | — | 14 | 48 | no | — |
| 157 | C22×C4 | C2×D28 | 1 | 24 | yes | — |
| 158 | C22×C4 | C2×D28 | 1 | 12 | yes | — |
| 159 | C22×C4 | C23×D7 | 1 | 6 | yes | — |
| 160 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 161 | C22×C4 | C23×D7 | 1 | 6 | yes | — |
| 162 | C22×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 163 | C4⋊C4 | — | 14 | 48 | no | — |
| 164 | C22⋊C4 | — | 14 | 96 | no | — |
| 165 | C42 | — | 2 | 24 | no | — |
| 166 | C42 | C2×D28 | 1 | 24 | yes | — |
| 167 | C42 | C2×D28 | 1 | 12 | yes | — |
| 168 | C42 | C2×D28 | 1 | 12 | yes | — |
| 169 | C42 | #1157 | 1 | 16 | yes | complemented |
| 170 | C2×C7 | — | 2 | 4 | no | — |
| 171 | C2×C7 | C22×#127 | 1 | 1 | yes | characteristic |
| 172 | C2×C7 | C2×#532 | 1 | 6 | yes | — |
| 173 | D7 | — | 8 | 8 | no | — |
| 174 | C23 | — | 2 | 4 | no | — |
| 175 | C23 | — | 14 | 24 | no | — |
| 176 | C23 | — | 14 | 32 | no | — |
| 177 | C23 | C22×D28 | 1 | 6 | yes | — |
| 178 | C23 | C24×D7 | 1 | 1 | yes | characteristic |
| 179 | Q8 | — | 28 | 16 | no | — |
| 180 | D4 | — | 28 | 32 | no | — |
| 181 | D4 | — | 28 | 16 | no | — |
| 182 | D4 | — | 28 | 96 | no | — |
| 183 | C2×C4 | — | 2 | 12 | no | — |
| 184 | C2×C4 | — | 2 | 48 | no | — |
| 185 | C2×C4 | — | 14 | 24 | no | — |
| 186 | C2×C4 | — | 28 | 32 | no | — |
| 187 | C2×C4 | #6437 | 1 | 16 | yes | complemented |
| 188 | C2×C4 | C22×D28 | 1 | 12 | yes | — |
| 189 | C2×C4 | C22×D28 | 1 | 6 | yes | — |
| 190 | C2×C4 | C22×D28 | 1 | 6 | yes | — |
| 191 | C2×C4 | C22×D28 | 1 | 12 | yes | — |
| 192 | C2×C4 | C2×#1157 | 1 | 24 | yes | — |
| 193 | C7 | #36644 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 194 | C22 | — | 2 | 12 | no | — |
| 195 | C22 | — | 28 | 8 | no | — |
| 196 | C22 | — | 28 | 48 | no | — |
| 197 | C22 | C2×#6437 | 1 | 4 | yes | — |
| 198 | C22 | C23×D28 | 1 | 3 | yes | — |
| 199 | C22 | C22×#1157 | 1 | 4 | yes | — |
| 200 | C4 | — | 2 | 12 | no | — |
| 201 | C4 | — | 28 | 8 | no | — |
| 202 | C4 | C2×#6437 | 1 | 4 | yes | — |
| 203 | C4 | C2×#6437 | 1 | 4 | yes | — |
| 204 | C4 | #90168 | 1 | 24 | yes | complemented |
| 205 | C2 | — | 2 | 4 | no | — |
| 206 | C2 | — | 56 | 8 | no | — |
| 207 | C2 | C22×#6437 | 1 | 1 | yes | characteristic |
| 208 | C2 | C2×#90168 | 1 | 6 | yes | — |
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