← C2×#13066757 #14673979
Subgroups — C2×#13066757 #14673979
Order 2816.
294 conjugacy classes of subgroups.
The subgroup lattice has 220 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#10622514 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#10622137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13066757 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 4 | C22×C11×C32 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#66954 | C4 | 1 | 1 | yes | characteristic |
| 6 | C22×C11×C16 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×#66876 | C4 | 1 | 1 | yes | characteristic |
| 8 | #10622514 | — | 2 | 1 | no | — |
| 9 | #10622514 | — | 2 | 1 | no | — |
| 10 | #10622514 | C4 | 1 | 2 | yes | — |
| 11 | #10622514 | C22 | 1 | 2 | yes | — |
| 12 | C2×#66862 | — | 2 | 1 | no | — |
| 13 | C2×C16×D11 | — | 2 | 1 | no | — |
| 14 | C2×C11×C32 | — | 2 | 1 | no | — |
| 15 | C2×C11×C32 | — | 2 | 1 | no | — |
| 16 | C2×C11×C32 | C22 | 1 | 2 | yes | complemented |
| 17 | #10622137 | — | 2 | 1 | no | — |
| 18 | #10622137 | C22 | 1 | 2 | yes | complemented |
| 19 | C2×C11⋊C32 | — | 2 | 1 | no | — |
| 20 | C2×#4339 | C8 | 1 | 1 | yes | characteristic |
| 21 | C22×C8×C11 | C2×C4 | 1 | 1 | yes | characteristic |
| 22 | C2×#4318 | C8 | 1 | 1 | yes | characteristic |
| 23 | #66954 | — | 2 | 1 | no | — |
| 24 | #66954 | — | 2 | 1 | no | — |
| 25 | #66954 | C8 | 1 | 2 | yes | — |
| 26 | #66954 | C2×C4 | 1 | 2 | yes | — |
| 27 | C2×#4313 | — | 2 | 1 | no | — |
| 28 | C2×C8×D11 | — | 2 | 1 | no | — |
| 29 | C2×C11×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C2×C11×C16 | D4 | 1 | 1 | yes | characteristic |
| 31 | C2×C11×C16 | D4 | 1 | 1 | yes | characteristic |
| 32 | C2×C11×C16 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×C11×C16 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×C11×C16 | C23 | 1 | 1 | yes | characteristic |
| 35 | #66876 | — | 2 | 1 | no | — |
| 36 | #66876 | C2×C4 | 1 | 2 | yes | — |
| 37 | C2×C11⋊C16 | — | 2 | 1 | no | — |
| 38 | #66862 | — | 2 | 2 | no | — |
| 39 | #66862 | — | 2 | 2 | no | — |
| 40 | C16×D11 | — | 2 | 2 | no | — |
| 41 | C16×D11 | — | 2 | 2 | no | — |
| 42 | C11×C32 | — | 2 | 2 | no | — |
| 43 | C11⋊C32 | — | 2 | 2 | no | — |
| 44 | C2×#1401 | — | 11 | 1 | no | maximal, Sylow |
| 45 | C22×C4×C11 | C2×C8 | 1 | 1 | yes | characteristic |
| 46 | C2×C22⋊D11 | — | 2 | 1 | no | — |
| 47 | #4339 | — | 2 | 1 | no | — |
| 48 | #4339 | — | 2 | 1 | no | — |
| 49 | #4339 | C16 | 1 | 2 | yes | — |
| 50 | #4339 | C2×C8 | 1 | 2 | yes | — |
| 51 | C2×D44 | C16 | 1 | 1 | yes | characteristic |
| 52 | C2×C4×D11 | — | 2 | 1 | no | — |
| 53 | C2×Dic22 | C16 | 1 | 1 | yes | characteristic |
| 54 | C2×C8×C11 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 55 | C2×C8×C11 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 56 | C2×C8×C11 | C2×C8 | 1 | 1 | yes | characteristic |
| 57 | C2×C8×C11 | M16 | 1 | 1 | yes | characteristic |
| 58 | C2×C8×C11 | M16 | 1 | 1 | yes | characteristic |
| 59 | C2×C8×C11 | C22×C4 | 1 | 1 | yes | characteristic |
| 60 | #4318 | — | 2 | 1 | no | — |
| 61 | #4318 | C2×C8 | 1 | 2 | yes | — |
| 62 | C2×C11⋊C8 | — | 2 | 1 | no | — |
| 63 | #4313 | — | 2 | 2 | no | — |
| 64 | #4313 | — | 2 | 2 | no | — |
| 65 | C8×D11 | — | 2 | 2 | no | — |
| 66 | C8×D11 | — | 2 | 2 | no | — |
| 67 | C11×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 68 | C11×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 69 | C11×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | C11×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C11⋊C16 | — | 2 | 2 | no | — |
| 72 | C2×#504 | — | 11 | 1 | no | — |
| 73 | C2×M64 | — | 11 | 1 | no | — |
| 74 | C22×C32 | D11 | 1 | 1 | yes | characteristic, complemented |
| 75 | #1401 | — | 11 | 4 | no | — |
| 76 | C23×C11 | M32 | 1 | 1 | yes | characteristic |
| 77 | C22×D11 | — | 2 | 1 | no | — |
| 78 | C2×C4×C11 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 79 | C2×C4×C11 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 80 | C2×C4×C11 | C2×C16 | 1 | 1 | yes | characteristic |
| 81 | C2×C4×C11 | C2×C16 | 1 | 1 | yes | characteristic |
| 82 | C2×C4×C11 | M32 | 1 | 1 | yes | characteristic |
| 83 | C2×C4×C11 | C22×C8 | 1 | 1 | yes | characteristic |
| 84 | C22⋊D11 | — | 2 | 2 | no | — |
| 85 | C22⋊D11 | — | 2 | 2 | no | — |
| 86 | C2×Dic11 | — | 2 | 1 | no | — |
| 87 | D44 | — | 2 | 1 | no | — |
| 88 | D44 | C2×C16 | 1 | 2 | yes | — |
| 89 | C4×D11 | — | 2 | 2 | no | — |
| 90 | C4×D11 | — | 2 | 2 | no | — |
| 91 | Dic22 | — | 2 | 1 | no | — |
| 92 | Dic22 | C2×C16 | 1 | 2 | yes | — |
| 93 | C8×C11 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 94 | C8×C11 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 95 | C8×C11 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C8×C11 | C2×M16 | 1 | 1 | yes | characteristic |
| 97 | C11⋊C8 | — | 2 | 2 | no | — |
| 98 | C2×#131 | — | 11 | 1 | no | — |
| 99 | #504 | — | 11 | 2 | no | — |
| 100 | #504 | — | 11 | 2 | no | — |
| 101 | #504 | — | 22 | 1 | no | — |
| 102 | #504 | — | 22 | 1 | no | — |
| 103 | C2×M32 | — | 11 | 1 | no | — |
| 104 | C2×M32 | — | 22 | 1 | no | — |
| 105 | C22×C16 | — | 22 | 1 | no | — |
| 106 | C22×C16 | C2×D11 | 1 | 1 | yes | characteristic |
| 107 | M64 | — | 11 | 2 | no | — |
| 108 | M64 | — | 22 | 1 | no | — |
| 109 | C2×C32 | — | 2 | 1 | no | — |
| 110 | C2×C32 | — | 2 | 1 | no | — |
| 111 | C2×C32 | — | 22 | 1 | no | — |
| 112 | C2×C32 | C2×D11 | 1 | 2 | yes | complemented |
| 113 | C22×C11 | — | 2 | 2 | no | — |
| 114 | C22×C11 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 115 | C22×C11 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 116 | C22×C11 | C2×M32 | 1 | 1 | yes | characteristic |
| 117 | C2×D11 | — | 2 | 2 | no | — |
| 118 | C2×D11 | — | 4 | 2 | no | — |
| 119 | C4×C11 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 120 | C4×C11 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 121 | C4×C11 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 122 | C4×C11 | C22×C16 | 1 | 1 | yes | characteristic |
| 123 | Dic11 | — | 2 | 2 | no | — |
| 124 | C2×#41 | — | 11 | 1 | no | — |
| 125 | #131 | — | 11 | 2 | no | — |
| 126 | #131 | — | 11 | 2 | no | — |
| 127 | #131 | — | 22 | 1 | no | — |
| 128 | #131 | — | 22 | 1 | no | — |
| 129 | C2×M16 | — | 11 | 1 | no | — |
| 130 | C2×M16 | — | 22 | 1 | no | — |
| 131 | C22×C8 | — | 22 | 1 | no | — |
| 132 | C22×C8 | C4×D11 | 1 | 1 | yes | characteristic |
| 133 | M32 | — | 11 | 2 | no | — |
| 134 | M32 | — | 22 | 1 | no | — |
| 135 | M32 | — | 22 | 2 | no | — |
| 136 | M32 | — | 22 | 2 | no | — |
| 137 | C2×C16 | — | 22 | 1 | no | — |
| 138 | C2×C16 | — | 22 | 2 | no | — |
| 139 | C2×C16 | — | 22 | 2 | no | — |
| 140 | C2×C16 | C4×D11 | 1 | 1 | yes | characteristic |
| 141 | C2×C16 | D44 | 1 | 1 | yes | characteristic |
| 142 | C2×C16 | D44 | 1 | 1 | yes | characteristic |
| 143 | C2×C16 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 144 | C2×C16 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 145 | C2×C16 | C22×D11 | 1 | 1 | yes | characteristic |
| 146 | C32 | — | 2 | 2 | no | — |
| 147 | C32 | — | 22 | 2 | no | — |
| 148 | C2×C11 | — | 2 | 1 | no | — |
| 149 | C2×C11 | — | 2 | 1 | no | — |
| 150 | C2×C11 | #1401 | 1 | 2 | yes | complemented |
| 151 | C2×C11 | C2×C22⋊C16 | 1 | 1 | yes | characteristic |
| 152 | D11 | — | 4 | 2 | no | — |
| 153 | #41 | — | 11 | 2 | no | — |
| 154 | #41 | — | 11 | 2 | no | — |
| 155 | #41 | — | 22 | 1 | no | — |
| 156 | #41 | — | 22 | 1 | no | — |
| 157 | C2×Q8 | — | 11 | 1 | no | — |
| 158 | C2×D4 | — | 11 | 1 | no | — |
| 159 | C2×D4 | — | 22 | 1 | no | — |
| 160 | C22×C4 | — | 22 | 1 | no | — |
| 161 | C22×C4 | C8×D11 | 1 | 1 | yes | characteristic |
| 162 | M16 | — | 11 | 2 | no | — |
| 163 | M16 | — | 22 | 1 | no | — |
| 164 | M16 | — | 22 | 2 | no | — |
| 165 | M16 | — | 22 | 2 | no | — |
| 166 | C2×C8 | — | 22 | 1 | no | — |
| 167 | C2×C8 | — | 22 | 2 | no | — |
| 168 | C2×C8 | — | 22 | 2 | no | — |
| 169 | C2×C8 | C8×D11 | 1 | 1 | yes | characteristic |
| 170 | C2×C8 | #4313 | 1 | 1 | yes | characteristic |
| 171 | C2×C8 | #4313 | 1 | 1 | yes | characteristic |
| 172 | C2×C8 | (C2×D11)⋊C4 | 1 | 1 | yes | characteristic |
| 173 | C2×C8 | (C2×D11)⋊C4 | 1 | 1 | yes | characteristic |
| 174 | C2×C8 | C2×C4×D11 | 1 | 1 | yes | characteristic |
| 175 | C16 | — | 22 | 2 | no | — |
| 176 | C16 | (C2×D11)⋊C4 | 1 | 1 | yes | characteristic |
| 177 | C16 | (C2×D11)⋊C4 | 1 | 1 | yes | characteristic |
| 178 | C16 | C2×D44 | 1 | 1 | yes | characteristic |
| 179 | C16 | C2×C22⋊D11 | 1 | 1 | yes | characteristic |
| 180 | C11 | C2×#1401 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 181 | C23 | — | 22 | 1 | no | — |
| 182 | C23 | #66862 | 1 | 1 | yes | characteristic |
| 183 | Q8 | — | 11 | 2 | no | — |
| 184 | Q8 | — | 22 | 1 | no | — |
| 185 | D4 | — | 11 | 2 | no | — |
| 186 | D4 | — | 22 | 2 | no | — |
| 187 | D4 | — | 22 | 2 | no | — |
| 188 | D4 | — | 22 | 1 | no | — |
| 189 | C2×C4 | — | 22 | 1 | no | — |
| 190 | C2×C4 | — | 22 | 2 | no | — |
| 191 | C2×C4 | — | 22 | 2 | no | — |
| 192 | C2×C4 | C16×D11 | 1 | 1 | yes | characteristic |
| 193 | C2×C4 | C16×D11 | 1 | 1 | yes | characteristic |
| 194 | C2×C4 | #66862 | 1 | 1 | yes | characteristic |
| 195 | C2×C4 | (C2×D11)⋊C8 | 1 | 1 | yes | characteristic |
| 196 | C2×C4 | (C2×D11)⋊C8 | 1 | 1 | yes | characteristic |
| 197 | C2×C4 | C2×C8×D11 | 1 | 1 | yes | characteristic |
| 198 | C8 | — | 22 | 2 | no | — |
| 199 | C8 | (C2×D11)⋊C8 | 1 | 1 | yes | characteristic |
| 200 | C8 | (C2×D11)⋊C8 | 1 | 1 | yes | characteristic |
| 201 | C8 | C2×#4313 | 1 | 1 | yes | characteristic |
| 202 | C8 | C2×(C2×D11)⋊C4 | 1 | 1 | yes | characteristic |
| 203 | C22 | — | 2 | 2 | no | — |
| 204 | C22 | — | 22 | 2 | no | — |
| 205 | C22 | — | 44 | 2 | no | — |
| 206 | C22 | (C2×D11)⋊C16 | 1 | 1 | yes | characteristic |
| 207 | C22 | (C2×D11)⋊C16 | 1 | 1 | yes | characteristic |
| 208 | C22 | C2×#66862 | 1 | 1 | yes | characteristic |
| 209 | C4 | — | 22 | 2 | no | — |
| 210 | C4 | (C2×D11)⋊C16 | 1 | 1 | yes | characteristic |
| 211 | C4 | (C2×D11)⋊C16 | 1 | 1 | yes | characteristic |
| 212 | C4 | C2×C16×D11 | 1 | 1 | yes | characteristic |
| 213 | C4 | C2×(C2×D11)⋊C8 | 1 | 1 | yes | characteristic |
| 214 | C2 | — | 2 | 1 | no | — |
| 215 | C2 | — | 2 | 1 | no | — |
| 216 | C2 | — | 44 | 2 | no | — |
| 217 | C2 | #13066757 | 1 | 2 | yes | direct product factor |
| 218 | C2 | C2×(C2×D11)⋊C16 | 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