← #14723082
Subgroups — #14723082
Order 2816.
612 conjugacy classes of subgroups.
The subgroup lattice has 240 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13077748 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #41×C11⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #13067407 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #13067404 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #13067374 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #13067362 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C11×#2991 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C4×C11×#41 | C22 | 1 | 1 | yes | characteristic |
| 9 | C8×Q8×C11 | — | 2 | 1 | no | — |
| 10 | C11×#436 | — | 2 | 3 | no | — |
| 11 | C11×#431 | C22 | 1 | 3 | yes | — |
| 12 | C11×#423 | C22 | 1 | 3 | yes | — |
| 13 | Q8×C11⋊C8 | — | 2 | 1 | no | — |
| 14 | Q8×C11⋊C8 | C4 | 1 | 1 | yes | characteristic |
| 15 | Q8×C11⋊C8 | C4 | 1 | 1 | yes | characteristic |
| 16 | #10622625 | — | 2 | 3 | no | — |
| 17 | D4×C11⋊C8 | C4 | 1 | 3 | yes | — |
| 18 | D4×C11⋊C8 | C4 | 1 | 3 | yes | — |
| 19 | #10622538 | C22 | 1 | 3 | yes | — |
| 20 | #10622538 | C22 | 1 | 3 | yes | — |
| 21 | #10622537 | C22 | 1 | 3 | yes | — |
| 22 | C2×C4×C11⋊C8 | C22 | 1 | 3 | yes | — |
| 23 | #10622118 | C22 | 1 | 3 | yes | — |
| 24 | #10622118 | C22 | 1 | 3 | yes | — |
| 25 | #10622117 | C22 | 1 | 1 | yes | characteristic |
| 26 | #10622117 | C22 | 1 | 3 | yes | — |
| 27 | #10622117 | C22 | 1 | 6 | yes | — |
| 28 | C2×C11×#41 | Q8 | 1 | 1 | yes | characteristic |
| 29 | C2×C11×M16 | — | 2 | 3 | no | — |
| 30 | C4×Q8×C11 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C4×Q8×C11 | D4 | 1 | 1 | yes | characteristic |
| 32 | C4×D4×C11 | C2×C4 | 1 | 3 | yes | — |
| 33 | C4×D4×C11 | D4 | 1 | 3 | yes | — |
| 34 | C11×#117 | Q8 | 1 | 3 | yes | — |
| 35 | C2×C42×C11 | C23 | 1 | 3 | yes | — |
| 36 | C2×#4318 | — | 2 | 3 | no | — |
| 37 | C22×C11⋊C8 | C2×C4 | 1 | 3 | yes | — |
| 38 | C22×C11⋊C8 | C2×C4 | 1 | 3 | yes | — |
| 39 | C11×C4⋊C8 | — | 2 | 3 | no | — |
| 40 | C11×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 41 | C11×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 42 | C11×C22⋊C8 | — | 2 | 3 | no | — |
| 43 | C4×C8×C11 | — | 2 | 3 | no | — |
| 44 | C22⋊(C11⋊C8) | — | 2 | 3 | no | — |
| 45 | C22⋊(C11⋊C8) | C2×C4 | 1 | 6 | yes | — |
| 46 | C4⋊(C11⋊C8) | — | 2 | 3 | no | — |
| 47 | C4⋊(C11⋊C8) | C2×C4 | 1 | 3 | yes | — |
| 48 | C4⋊(C11⋊C8) | C2×C4 | 1 | 3 | yes | — |
| 49 | C4⋊(C11⋊C8) | C23 | 1 | 3 | yes | — |
| 50 | C4⋊(C11⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 51 | C4×C11⋊C8 | — | 2 | 3 | no | — |
| 52 | C4×C11⋊C8 | C2×C4 | 1 | 3 | yes | — |
| 53 | C4×C11⋊C8 | C2×C4 | 1 | 3 | yes | — |
| 54 | C4×C11⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 55 | C4×C11⋊C8 | C23 | 1 | 3 | yes | — |
| 56 | #17837 | — | 11 | 1 | no | maximal, Sylow |
| 57 | C11×#41 | — | 2 | 4 | no | — |
| 58 | C2×Q8×C11 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 59 | C2×D4×C11 | C4⋊C4 | 1 | 3 | yes | — |
| 60 | C22×C4×C11 | C22×C4 | 1 | 3 | yes | — |
| 61 | C22×C4×C11 | C2×D4 | 1 | 3 | yes | — |
| 62 | C22×C4×C11 | C2×Q8 | 1 | 3 | yes | — |
| 63 | C11×M16 | — | 8 | 3 | no | — |
| 64 | C2×C8×C11 | — | 2 | 1 | no | — |
| 65 | C2×C8×C11 | — | 2 | 3 | no | — |
| 66 | C11×C4⋊C4 | C4⋊C4 | 1 | 3 | yes | — |
| 67 | C11×C4⋊C4 | C4⋊C4 | 1 | 3 | yes | — |
| 68 | C11×C22⋊C4 | C4⋊C4 | 1 | 6 | yes | — |
| 69 | C42×C11 | C22×C4 | 1 | 3 | yes | — |
| 70 | C42×C11 | C2×D4 | 1 | 3 | yes | — |
| 71 | C42×C11 | C2×Q8 | 1 | 3 | yes | — |
| 72 | C42×C11 | C24 | 1 | 1 | yes | characteristic |
| 73 | #4318 | — | 8 | 3 | no | — |
| 74 | C2×C11⋊C8 | — | 2 | 6 | no | — |
| 75 | C2×C11⋊C8 | — | 2 | 1 | no | — |
| 76 | C2×C11⋊C8 | — | 2 | 3 | no | — |
| 77 | C2×C11⋊C8 | — | 4 | 3 | no | — |
| 78 | C2×C11⋊C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 79 | C2×C11⋊C8 | C22×C4 | 1 | 3 | yes | — |
| 80 | C2×C11⋊C8 | C22×C4 | 1 | 3 | yes | — |
| 81 | C2×C11⋊C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 82 | #2991 | — | 11 | 1 | no | — |
| 83 | #2991 | D11 | 1 | 1 | yes | characteristic |
| 84 | C8×#41 | — | 11 | 1 | no | — |
| 85 | #1574 | — | 11 | 3 | no | — |
| 86 | #1574 | — | 11 | 3 | no | — |
| 87 | #1567 | — | 11 | 3 | no | — |
| 88 | #1564 | — | 11 | 3 | no | — |
| 89 | C23×C11 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 90 | Q8×C11 | #108 | 1 | 4 | yes | — |
| 91 | D4×C11 | — | 2 | 6 | no | — |
| 92 | C2×C4×C11 | — | 2 | 3 | no | — |
| 93 | C2×C4×C11 | — | 2 | 3 | no | — |
| 94 | C2×C4×C11 | — | 2 | 3 | no | — |
| 95 | C2×C4×C11 | — | 2 | 3 | no | — |
| 96 | C2×C4×C11 | — | 2 | 6 | no | — |
| 97 | C2×C4×C11 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 98 | C2×C4×C11 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 99 | C2×C4×C11 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 100 | C2×C4×C11 | C23×C4 | 1 | 1 | yes | characteristic |
| 101 | C2×C4×C11 | C22×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C4×C11 | C22×Q8 | 1 | 1 | yes | characteristic |
| 103 | C8×C11 | — | 4 | 3 | no | — |
| 104 | C8×C11 | — | 4 | 1 | no | — |
| 105 | C11⋊C8 | — | 2 | 3 | no | — |
| 106 | C11⋊C8 | — | 2 | 1 | no | — |
| 107 | C11⋊C8 | — | 2 | 3 | no | — |
| 108 | C11⋊C8 | — | 4 | 3 | no | — |
| 109 | C11⋊C8 | — | 4 | 1 | no | — |
| 110 | C11⋊C8 | #131 | 1 | 2 | yes | — |
| 111 | C4×#41 | C2×D11 | 1 | 1 | yes | characteristic |
| 112 | C8×Q8 | — | 2 | 1 | no | — |
| 113 | C8×Q8 | — | 11 | 1 | no | — |
| 114 | C8×Q8 | — | 11 | 1 | no | — |
| 115 | C8×Q8 | — | 22 | 1 | no | — |
| 116 | #436 | — | 2 | 3 | no | — |
| 117 | #436 | — | 22 | 3 | no | — |
| 118 | C8×D4 | — | 11 | 3 | no | — |
| 119 | C8×D4 | — | 11 | 3 | no | — |
| 120 | #431 | — | 11 | 3 | no | — |
| 121 | #431 | — | 11 | 3 | no | — |
| 122 | #431 | C2×D11 | 1 | 3 | yes | — |
| 123 | #423 | — | 11 | 3 | no | — |
| 124 | #423 | C2×D11 | 1 | 3 | yes | — |
| 125 | C2×C4×C8 | — | 11 | 3 | no | — |
| 126 | #335 | — | 11 | 1 | no | — |
| 127 | #335 | — | 11 | 3 | no | — |
| 128 | #335 | — | 11 | 6 | no | — |
| 129 | #334 | — | 11 | 3 | no | — |
| 130 | #334 | — | 11 | 3 | no | — |
| 131 | C22×C11 | — | 2 | 3 | no | — |
| 132 | C22×C11 | — | 2 | 3 | no | — |
| 133 | C22×C11 | — | 2 | 3 | no | — |
| 134 | C22×C11 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 135 | C4×C11 | — | 2 | 3 | no | — |
| 136 | C4×C11 | — | 2 | 3 | no | — |
| 137 | C4×C11 | — | 2 | 1 | no | — |
| 138 | C4×C11 | C2×#108 | 1 | 6 | yes | — |
| 139 | C4×C11 | C2×#131 | 1 | 1 | yes | characteristic |
| 140 | C4×C11 | #568 | 1 | 1 | yes | characteristic |
| 141 | C4×C11 | #576 | 1 | 1 | yes | characteristic |
| 142 | C4×C11 | #578 | 1 | 1 | yes | characteristic |
| 143 | C2×#41 | Dic22 | 1 | 1 | yes | characteristic |
| 144 | C2×M16 | — | 2 | 3 | no | — |
| 145 | C2×M16 | — | 22 | 3 | no | — |
| 146 | C22×C8 | — | 11 | 3 | no | — |
| 147 | C22×C8 | — | 11 | 3 | no | — |
| 148 | C4×Q8 | C4×D11 | 1 | 1 | yes | characteristic |
| 149 | C4×Q8 | C22⋊D11 | 1 | 1 | yes | characteristic |
| 150 | C4×D4 | C4×D11 | 1 | 3 | yes | — |
| 151 | C4×D4 | C22⋊D11 | 1 | 3 | yes | — |
| 152 | #117 | Dic22 | 1 | 3 | yes | — |
| 153 | C2×C42 | C22×D11 | 1 | 3 | yes | — |
| 154 | C4⋊C8 | — | 2 | 3 | no | — |
| 155 | C4⋊C8 | — | 11 | 3 | no | — |
| 156 | C4⋊C8 | — | 11 | 3 | no | — |
| 157 | C4⋊C8 | — | 11 | 1 | no | — |
| 158 | C4⋊C8 | — | 11 | 3 | no | — |
| 159 | C4⋊C8 | — | 22 | 3 | no | — |
| 160 | C4⋊C8 | C22×D11 | 1 | 1 | yes | characteristic |
| 161 | C4⋊C8 | C22×D11 | 1 | 3 | yes | — |
| 162 | C22⋊C8 | — | 2 | 3 | no | — |
| 163 | C22⋊C8 | — | 11 | 6 | no | — |
| 164 | C22⋊C8 | — | 22 | 3 | no | — |
| 165 | C4×C8 | — | 2 | 3 | no | — |
| 166 | C4×C8 | — | 11 | 3 | no | — |
| 167 | C4×C8 | — | 11 | 3 | no | — |
| 168 | C4×C8 | — | 11 | 3 | no | — |
| 169 | C4×C8 | — | 11 | 1 | no | — |
| 170 | C4×C8 | — | 22 | 3 | no | — |
| 171 | C2×C11 | — | 4 | 3 | no | — |
| 172 | C2×C11 | #2906 | 1 | 1 | yes | characteristic |
| 173 | C2×C11 | #2913 | 1 | 1 | yes | characteristic |
| 174 | C2×C11 | C22×#108 | 1 | 1 | yes | characteristic |
| 175 | #41 | — | 2 | 4 | no | — |
| 176 | C2×Q8 | Dic11⋊C4 | 1 | 1 | yes | characteristic |
| 177 | C2×D4 | Dic11⋊C4 | 1 | 3 | yes | — |
| 178 | C22×C4 | C2×Dic22 | 1 | 3 | yes | — |
| 179 | C22×C4 | C2×C4×D11 | 1 | 3 | yes | — |
| 180 | C22×C4 | C2×C22⋊D11 | 1 | 3 | yes | — |
| 181 | M16 | — | 8 | 3 | no | — |
| 182 | M16 | — | 88 | 3 | no | — |
| 183 | C2×C8 | — | 2 | 1 | no | — |
| 184 | C2×C8 | — | 2 | 3 | no | — |
| 185 | C2×C8 | — | 11 | 1 | no | — |
| 186 | C2×C8 | — | 11 | 1 | no | — |
| 187 | C2×C8 | — | 11 | 3 | no | — |
| 188 | C2×C8 | — | 11 | 3 | no | — |
| 189 | C2×C8 | — | 22 | 6 | no | — |
| 190 | C2×C8 | — | 22 | 1 | no | — |
| 191 | C2×C8 | — | 22 | 3 | no | — |
| 192 | C2×C8 | — | 44 | 3 | no | — |
| 193 | C4⋊C4 | Dic11⋊C4 | 1 | 3 | yes | — |
| 194 | C4⋊C4 | Dic11⋊C4 | 1 | 3 | yes | — |
| 195 | C22⋊C4 | Dic11⋊C4 | 1 | 6 | yes | — |
| 196 | C42 | C2×Dic22 | 1 | 3 | yes | — |
| 197 | C42 | C2×C4×D11 | 1 | 3 | yes | — |
| 198 | C42 | C2×C22⋊D11 | 1 | 3 | yes | — |
| 199 | C42 | C23×D11 | 1 | 1 | yes | characteristic |
| 200 | C11 | #17837 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 201 | C23 | C2×Dic11⋊C4 | 1 | 3 | yes | — |
| 202 | Q8 | #66886 | 1 | 4 | yes | — |
| 203 | D4 | — | 2 | 6 | no | — |
| 204 | C2×C4 | — | 2 | 6 | no | — |
| 205 | C2×C4 | — | 2 | 3 | no | — |
| 206 | C2×C4 | — | 2 | 3 | no | — |
| 207 | C2×C4 | — | 2 | 3 | no | — |
| 208 | C2×C4 | — | 2 | 3 | no | — |
| 209 | C2×C4 | C2×Dic11⋊C4 | 1 | 3 | yes | — |
| 210 | C2×C4 | C2×Dic11⋊C4 | 1 | 3 | yes | — |
| 211 | C2×C4 | C2×Dic11⋊C4 | 1 | 3 | yes | — |
| 212 | C2×C4 | C22×Dic22 | 1 | 1 | yes | characteristic |
| 213 | C2×C4 | C22×C4×D11 | 1 | 1 | yes | characteristic |
| 214 | C2×C4 | C22×C22⋊D11 | 1 | 1 | yes | characteristic |
| 215 | C8 | — | 4 | 3 | no | — |
| 216 | C8 | — | 4 | 1 | no | — |
| 217 | C8 | — | 11 | 2 | no | — |
| 218 | C8 | — | 22 | 3 | no | — |
| 219 | C8 | — | 22 | 1 | no | — |
| 220 | C8 | — | 22 | 3 | no | — |
| 221 | C8 | — | 44 | 3 | no | — |
| 222 | C8 | — | 44 | 1 | no | — |
| 223 | C22 | — | 2 | 3 | no | — |
| 224 | C22 | — | 2 | 3 | no | — |
| 225 | C22 | — | 2 | 3 | no | — |
| 226 | C22 | C22×Dic11⋊C4 | 1 | 1 | yes | characteristic |
| 227 | C4 | — | 2 | 3 | no | — |
| 228 | C4 | — | 2 | 3 | no | — |
| 229 | C4 | — | 2 | 1 | no | — |
| 230 | C4 | C2×#66886 | 1 | 6 | yes | — |
| 231 | C4 | D11×#131 | 1 | 1 | yes | characteristic |
| 232 | C4 | #10623281 | 1 | 1 | yes | characteristic |
| 233 | C4 | #10623366 | 1 | 1 | yes | characteristic |
| 234 | C4 | #10623369 | 1 | 1 | yes | characteristic |
| 235 | C2 | — | 4 | 3 | no | — |
| 236 | C2 | #13077182 | 1 | 1 | yes | characteristic |
| 237 | C2 | #13077214 | 1 | 1 | yes | characteristic |
| 238 | C2 | C22×#66886 | 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