← C2×#13082764 #15660675
Subgroups — C2×#13082764 #15660675
Order 2816.
6554 conjugacy classes of subgroups.
The subgroup lattice has 216 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13082764 | C2 | 1 | 32 | yes | maximal, direct product factor |
| 2 | C2×#10623230 | C2 | 1 | 10 | yes | maximal, complemented |
| 3 | C2×#10623231 | C2 | 1 | 5 | yes | maximal, complemented |
| 4 | C2×#10623219 | C2 | 1 | 5 | yes | maximal, complemented |
| 5 | C2×#10623222 | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | C2×C11×#564 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C11×#564 | C22 | 1 | 16 | yes | complemented |
| 8 | C2×C11×#125 | C22 | 1 | 10 | yes | — |
| 9 | C2×C11×#125 | C22 | 1 | 5 | yes | — |
| 10 | #10623231 | C22 | 1 | 80 | yes | complemented |
| 11 | #10623230 | C22 | 1 | 160 | yes | complemented |
| 12 | #10623222 | C22 | 1 | 160 | yes | complemented |
| 13 | #10623219 | C22 | 1 | 80 | yes | complemented |
| 14 | C2×#66951 | C22 | 1 | 20 | yes | — |
| 15 | C2×#66950 | C22 | 1 | 10 | yes | — |
| 16 | C2×#66949 | C22 | 1 | 20 | yes | — |
| 17 | C2×#66948 | C22 | 1 | 10 | yes | — |
| 18 | C2×#66947 | C22 | 1 | 20 | yes | — |
| 19 | C2×#66946 | C22 | 1 | 10 | yes | — |
| 20 | C2×#66945 | C22 | 1 | 10 | yes | — |
| 21 | C2×#66941 | C22 | 1 | 10 | yes | — |
| 22 | C2×#66940 | C22 | 1 | 10 | yes | — |
| 23 | C2×#66928 | C22 | 1 | 10 | yes | — |
| 24 | C2×C42×D11 | C22 | 1 | 5 | yes | — |
| 25 | C2×#66923 | C22 | 1 | 5 | yes | — |
| 26 | C22×D44 | C23 | 1 | 10 | yes | — |
| 27 | C22×C4×D11 | C23 | 1 | 5 | yes | — |
| 28 | C22×C4×D11 | C23 | 1 | 10 | yes | — |
| 29 | C22×Dic22 | C23 | 1 | 10 | yes | — |
| 30 | C11×#125 | C23 | 1 | 40 | yes | — |
| 31 | C11×#125 | C23 | 1 | 80 | yes | — |
| 32 | C2×C11×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 33 | C2×C11×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 34 | C2×C11×C4⋊C4 | C23 | 1 | 10 | yes | — |
| 35 | C2×C42×C11 | C23 | 1 | 5 | yes | — |
| 36 | C2×(C2×D11)⋊C4 | C23 | 1 | 20 | yes | — |
| 37 | C2×(C2×D11)⋊C4 | C23 | 1 | 20 | yes | — |
| 38 | C2×C4⋊Dic11 | C23 | 1 | 10 | yes | — |
| 39 | C2×Dic11⋊C4 | C23 | 1 | 20 | yes | — |
| 40 | C2×C4×Dic11 | C23 | 1 | 10 | yes | — |
| 41 | C2×C4×Dic11 | C23 | 1 | 5 | yes | — |
| 42 | #66951 | C23 | 1 | 160 | yes | — |
| 43 | #66950 | C23 | 1 | 80 | yes | — |
| 44 | #66949 | C23 | 1 | 160 | yes | — |
| 45 | #66948 | C23 | 1 | 80 | yes | — |
| 46 | #66947 | C23 | 1 | 160 | yes | — |
| 47 | #66946 | C23 | 1 | 80 | yes | — |
| 48 | #66945 | C23 | 1 | 80 | yes | — |
| 49 | #66941 | C23 | 1 | 80 | yes | — |
| 50 | #66940 | C23 | 1 | 80 | yes | — |
| 51 | #66928 | C23 | 1 | 80 | yes | — |
| 52 | C42×D11 | C23 | 1 | 40 | yes | — |
| 53 | #66923 | C23 | 1 | 40 | yes | — |
| 54 | C2×#3531 | — | 11 | 1 | no | maximal, Sylow |
| 55 | C23×D11 | C24 | 1 | 5 | yes | — |
| 56 | C22×C4×C11 | C24 | 1 | 10 | yes | — |
| 57 | C22×C4×C11 | C24 | 1 | 5 | yes | — |
| 58 | C22×Dic11 | C24 | 1 | 10 | yes | — |
| 59 | C22×Dic11 | C24 | 1 | 1 | yes | characteristic |
| 60 | C2×D44 | — | 4 | 20 | no | — |
| 61 | C2×D44 | C24 | 1 | 40 | yes | — |
| 62 | C2×C4×D11 | — | 2 | 20 | no | — |
| 63 | C2×C4×D11 | — | 4 | 20 | no | — |
| 64 | C2×C4×D11 | C24 | 1 | 20 | yes | — |
| 65 | C2×C4×D11 | C24 | 1 | 40 | yes | — |
| 66 | C2×Dic22 | — | 4 | 20 | no | — |
| 67 | C2×Dic22 | C24 | 1 | 40 | yes | — |
| 68 | C11×C4⋊C4 | C24 | 1 | 40 | yes | — |
| 69 | C11×C4⋊C4 | C24 | 1 | 40 | yes | — |
| 70 | C11×C4⋊C4 | C24 | 1 | 40 | yes | — |
| 71 | C42×C11 | C24 | 1 | 20 | yes | — |
| 72 | (C2×D11)⋊C4 | C24 | 1 | 80 | yes | — |
| 73 | (C2×D11)⋊C4 | C24 | 1 | 80 | yes | — |
| 74 | C4⋊Dic11 | C24 | 1 | 40 | yes | — |
| 75 | Dic11⋊C4 | C24 | 1 | 80 | yes | — |
| 76 | C4×Dic11 | C24 | 1 | 40 | yes | — |
| 77 | C4×Dic11 | C24 | 1 | 20 | yes | — |
| 78 | #3531 | — | 11 | 32 | no | — |
| 79 | C2×#564 | D11 | 1 | 1 | yes | characteristic, complemented |
| 80 | C2×#563 | — | 11 | 10 | no | — |
| 81 | C2×#562 | — | 11 | 5 | no | — |
| 82 | C2×#533 | — | 11 | 5 | no | — |
| 83 | C2×#529 | — | 11 | 10 | no | — |
| 84 | C23×C11 | C25 | 1 | 1 | yes | characteristic |
| 85 | C22×D11 | — | 2 | 10 | no | — |
| 86 | C22×D11 | — | 2 | 20 | no | — |
| 87 | C22×D11 | C25 | 1 | 10 | yes | — |
| 88 | C2×C4×C11 | — | 2 | 10 | no | — |
| 89 | C2×C4×C11 | — | 2 | 20 | no | — |
| 90 | C2×C4×C11 | C25 | 1 | 20 | yes | — |
| 91 | C2×C4×C11 | C25 | 1 | 10 | yes | — |
| 92 | C2×Dic11 | — | 2 | 20 | no | — |
| 93 | C2×Dic11 | 2−1+4 | 1 | 4 | yes | — |
| 94 | C2×Dic11 | C25 | 1 | 20 | yes | — |
| 95 | C2×Dic11 | C25 | 1 | 2 | yes | — |
| 96 | D44 | — | 4 | 40 | no | — |
| 97 | C4×D11 | — | 2 | 40 | no | — |
| 98 | C4×D11 | — | 4 | 40 | no | — |
| 99 | Dic22 | — | 4 | 40 | no | — |
| 100 | #564 | C2×D11 | 1 | 16 | yes | complemented |
| 101 | #563 | — | 11 | 160 | no | — |
| 102 | #562 | — | 11 | 80 | no | — |
| 103 | #533 | — | 11 | 80 | no | — |
| 104 | C2×C4⋊Q8 | — | 11 | 10 | no | — |
| 105 | #529 | — | 11 | 160 | no | — |
| 106 | C2×#126 | — | 11 | 20 | no | — |
| 107 | C2×#125 | — | 11 | 5 | no | — |
| 108 | C2×#125 | C2×D11 | 1 | 10 | yes | — |
| 109 | C2×#125 | C2×D11 | 1 | 5 | yes | — |
| 110 | C2×#124 | — | 11 | 10 | no | — |
| 111 | C2×#123 | — | 11 | 20 | no | — |
| 112 | C2×C22⋊Q8 | — | 11 | 20 | no | — |
| 113 | C2×C22⋊Q8 | — | 11 | 10 | no | — |
| 114 | C2×#121 | — | 11 | 10 | no | — |
| 115 | C2×C4×Q8 | — | 11 | 10 | no | — |
| 116 | C2×C4×D4 | — | 11 | 10 | no | — |
| 117 | C2×#117 | — | 11 | 10 | no | — |
| 118 | C22×C42 | — | 11 | 5 | no | — |
| 119 | C22×C11 | C2×2−1+4 | 1 | 2 | yes | — |
| 120 | C22×C11 | #585 | 1 | 4 | yes | — |
| 121 | C22×C11 | C26 | 1 | 1 | yes | characteristic |
| 122 | C2×D11 | — | 2 | 10 | no | — |
| 123 | C2×D11 | — | 2 | 20 | no | — |
| 124 | C2×D11 | — | 4 | 20 | no | — |
| 125 | C4×C11 | — | 2 | 10 | no | — |
| 126 | C4×C11 | — | 2 | 20 | no | — |
| 127 | Dic11 | — | 2 | 20 | no | — |
| 128 | Dic11 | C2×2−1+4 | 1 | 4 | yes | — |
| 129 | C22×Q8 | — | 11 | 10 | no | — |
| 130 | C22×D4 | — | 11 | 10 | no | — |
| 131 | C23×C4 | — | 11 | 5 | no | — |
| 132 | C23×C4 | — | 11 | 10 | no | — |
| 133 | C4⋊Q8 | — | 11 | 80 | no | — |
| 134 | #126 | — | 11 | 160 | no | — |
| 135 | #125 | — | 11 | 40 | no | — |
| 136 | #125 | C22×D11 | 1 | 80 | yes | — |
| 137 | #125 | C22×D11 | 1 | 40 | yes | — |
| 138 | #124 | — | 11 | 80 | no | — |
| 139 | #123 | — | 11 | 160 | no | — |
| 140 | C22⋊Q8 | — | 11 | 80 | no | — |
| 141 | C22⋊Q8 | — | 11 | 160 | no | — |
| 142 | #121 | — | 11 | 80 | no | — |
| 143 | C4×Q8 | — | 11 | 80 | no | — |
| 144 | C4×D4 | — | 11 | 80 | no | — |
| 145 | #117 | — | 11 | 80 | no | — |
| 146 | C2×C4⋊C4 | — | 11 | 10 | no | — |
| 147 | C2×C4⋊C4 | — | 11 | 20 | no | — |
| 148 | C2×C4⋊C4 | C22×D11 | 1 | 10 | yes | — |
| 149 | C2×C4⋊C4 | C22×D11 | 1 | 10 | yes | — |
| 150 | C2×C4⋊C4 | C22×D11 | 1 | 10 | yes | — |
| 151 | C2×C22⋊C4 | — | 11 | 20 | no | — |
| 152 | C2×C22⋊C4 | — | 11 | 20 | no | — |
| 153 | C2×C42 | — | 11 | 10 | no | — |
| 154 | C2×C42 | — | 11 | 5 | no | — |
| 155 | C2×C42 | — | 11 | 40 | no | — |
| 156 | C2×C42 | C22×D11 | 1 | 5 | yes | — |
| 157 | C2×C11 | #3531 | 1 | 4 | yes | complemented |
| 158 | C2×C11 | C22×2−1+4 | 1 | 1 | yes | characteristic |
| 159 | C2×C11 | C2×#585 | 1 | 2 | yes | — |
| 160 | D11 | — | 4 | 10 | no | — |
| 161 | C24 | — | 11 | 5 | no | — |
| 162 | C2×Q8 | — | 11 | 40 | no | — |
| 163 | C2×Q8 | — | 44 | 20 | no | — |
| 164 | C2×D4 | — | 11 | 40 | no | — |
| 165 | C2×D4 | — | 44 | 20 | no | — |
| 166 | C22×C4 | — | 11 | 1 | no | — |
| 167 | C22×C4 | — | 11 | 10 | no | — |
| 168 | C22×C4 | — | 11 | 20 | no | — |
| 169 | C22×C4 | — | 11 | 40 | no | — |
| 170 | C22×C4 | — | 22 | 20 | no | — |
| 171 | C22×C4 | — | 44 | 20 | no | — |
| 172 | C22×C4 | C23×D11 | 1 | 5 | yes | — |
| 173 | C22×C4 | C23×D11 | 1 | 10 | yes | — |
| 174 | C4⋊C4 | — | 11 | 40 | no | — |
| 175 | C4⋊C4 | — | 11 | 80 | no | — |
| 176 | C4⋊C4 | C23×D11 | 1 | 40 | yes | — |
| 177 | C4⋊C4 | C23×D11 | 1 | 40 | yes | — |
| 178 | C4⋊C4 | C23×D11 | 1 | 40 | yes | — |
| 179 | C22⋊C4 | — | 11 | 80 | no | — |
| 180 | C22⋊C4 | — | 11 | 80 | no | — |
| 181 | C42 | — | 11 | 40 | no | — |
| 182 | C42 | — | 11 | 20 | no | — |
| 183 | C42 | C23×D11 | 1 | 20 | yes | — |
| 184 | C11 | C2×#3531 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 185 | C23 | — | 11 | 10 | no | — |
| 186 | C23 | — | 22 | 10 | no | — |
| 187 | C23 | — | 22 | 20 | no | — |
| 188 | C23 | C24×D11 | 1 | 1 | yes | characteristic |
| 189 | Q8 | — | 44 | 40 | no | — |
| 190 | D4 | — | 44 | 40 | no | — |
| 191 | C2×C4 | — | 2 | 10 | no | — |
| 192 | C2×C4 | — | 2 | 20 | no | — |
| 193 | C2×C4 | — | 11 | 4 | no | — |
| 194 | C2×C4 | — | 11 | 2 | no | — |
| 195 | C2×C4 | — | 11 | 20 | no | — |
| 196 | C2×C4 | — | 22 | 40 | no | — |
| 197 | C2×C4 | — | 22 | 20 | no | — |
| 198 | C2×C4 | — | 44 | 40 | no | — |
| 199 | C2×C4 | C24×D11 | 1 | 10 | yes | — |
| 200 | C2×C4 | C24×D11 | 1 | 20 | yes | — |
| 201 | C22 | — | 22 | 10 | no | — |
| 202 | C22 | — | 22 | 20 | no | — |
| 203 | C22 | — | 44 | 20 | no | — |
| 204 | C22 | D11×2−1+4 | 1 | 2 | yes | — |
| 205 | C22 | #10623457 | 1 | 4 | yes | — |
| 206 | C22 | C25×D11 | 1 | 1 | yes | characteristic |
| 207 | C4 | — | 2 | 10 | no | — |
| 208 | C4 | — | 2 | 20 | no | — |
| 209 | C4 | — | 11 | 4 | no | — |
| 210 | C4 | — | 22 | 20 | no | — |
| 211 | C2 | — | 44 | 10 | no | — |
| 212 | C2 | #13082764 | 1 | 4 | yes | direct product factor |
| 213 | C2 | C2×D11×2−1+4 | 1 | 1 | yes | characteristic |
| 214 | C2 | C2×#10623457 | 1 | 2 | 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