← C131×#7022 #45692906
Subgroups — C131×#7022 #45692906
Order 33536.
320 conjugacy classes of subgroups.
The subgroup lattice has 234 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #1831×C131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #1767×C131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C4×C4⋊C8×C131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×C4⋊C8×C131 | — | 2 | 1 | no | — |
| 5 | C2×C4⋊C8×C131 | — | 2 | 1 | no | — |
| 6 | C2×C4⋊C8×C131 | C4 | 1 | 2 | yes | — |
| 7 | C2×#97×C131 | — | 2 | 1 | no | — |
| 8 | C2×C4×C8×C131 | C4 | 1 | 2 | yes | — |
| 9 | C43×C131 | C22 | 1 | 1 | yes | characteristic |
| 10 | #336×C131 | — | 2 | 1 | no | — |
| 11 | #336×C131 | — | 2 | 1 | no | — |
| 12 | #336×C131 | — | 2 | 1 | no | — |
| 13 | #336×C131 | C4 | 1 | 2 | yes | — |
| 14 | C22×C8×C131 | — | 2 | 2 | no | — |
| 15 | C22×C8×C131 | — | 2 | 2 | no | — |
| 16 | C22×C8×C131 | — | 2 | 2 | no | — |
| 17 | C2×C42×C131 | C2×C4 | 1 | 1 | yes | characteristic |
| 18 | C2×C42×C131 | C2×C4 | 1 | 1 | yes | characteristic |
| 19 | C2×C42×C131 | C2×C4 | 1 | 1 | yes | characteristic |
| 20 | C2×C42×C131 | D4 | 1 | 1 | yes | characteristic |
| 21 | C2×C42×C131 | D4 | 1 | 1 | yes | characteristic |
| 22 | C2×C42×C131 | D4 | 1 | 1 | yes | characteristic |
| 23 | C2×C42×C131 | Q8 | 1 | 1 | yes | characteristic |
| 24 | C4⋊C8×C131 | — | 2 | 4 | no | — |
| 25 | C4⋊C8×C131 | — | 2 | 2 | no | — |
| 26 | C4⋊C8×C131 | — | 4 | 1 | no | — |
| 27 | C4⋊C8×C131 | — | 4 | 1 | no | — |
| 28 | C4⋊C8×C131 | C8 | 1 | 4 | yes | complemented |
| 29 | #97×C131 | — | 4 | 1 | no | — |
| 30 | #97×C131 | — | 4 | 1 | no | — |
| 31 | C4×C8×C131 | — | 4 | 2 | no | — |
| 32 | C22×C4×C131 | C42 | 1 | 1 | yes | characteristic |
| 33 | C22×C4×C131 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 34 | C22×C4×C131 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 35 | C22×C4×C131 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 36 | C22×C4×C131 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 37 | C22×C4×C131 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 38 | C22×C4×C131 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 39 | C2×C8×C131 | — | 2 | 4 | no | — |
| 40 | C2×C8×C131 | — | 2 | 4 | no | — |
| 41 | C2×C8×C131 | — | 4 | 2 | no | — |
| 42 | C2×C8×C131 | — | 4 | 2 | no | — |
| 43 | C2×C8×C131 | — | 4 | 2 | no | — |
| 44 | C2×C8×C131 | — | 4 | 2 | no | — |
| 45 | C2×C8×C131 | — | 4 | 2 | no | — |
| 46 | C2×C8×C131 | — | 4 | 2 | no | — |
| 47 | C2×C8×C131 | — | 4 | 2 | no | — |
| 48 | C42×C131 | — | 2 | 1 | no | — |
| 49 | C42×C131 | — | 2 | 1 | no | — |
| 50 | C42×C131 | — | 2 | 2 | no | — |
| 51 | C42×C131 | — | 4 | 1 | no | — |
| 52 | C42×C131 | — | 4 | 1 | no | — |
| 53 | C42×C131 | — | 4 | 1 | no | — |
| 54 | C42×C131 | C2×C8 | 1 | 2 | yes | — |
| 55 | C42×C131 | M16 | 1 | 2 | yes | — |
| 56 | C42×C131 | D8 | 1 | 1 | yes | characteristic |
| 57 | C42×C131 | SD16 | 1 | 1 | yes | characteristic |
| 58 | C42×C131 | SD16 | 1 | 1 | yes | characteristic |
| 59 | C42×C131 | Q16 | 1 | 1 | yes | characteristic |
| 60 | C23×C131 | #95 | 1 | 1 | yes | characteristic |
| 61 | C2×C4×C131 | — | 2 | 1 | no | — |
| 62 | C2×C4×C131 | — | 2 | 1 | no | — |
| 63 | C2×C4×C131 | — | 2 | 1 | no | — |
| 64 | C2×C4×C131 | — | 2 | 1 | no | — |
| 65 | C2×C4×C131 | — | 2 | 1 | no | — |
| 66 | C2×C4×C131 | — | 2 | 1 | no | — |
| 67 | C2×C4×C131 | — | 2 | 1 | no | — |
| 68 | C2×C4×C131 | — | 2 | 1 | no | — |
| 69 | C2×C4×C131 | — | 2 | 1 | no | — |
| 70 | C2×C4×C131 | — | 2 | 1 | no | — |
| 71 | C2×C4×C131 | — | 2 | 1 | no | — |
| 72 | C2×C4×C131 | — | 2 | 1 | no | — |
| 73 | C2×C4×C131 | — | 2 | 1 | no | — |
| 74 | C2×C4×C131 | C4×C8 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×C131 | #97 | 1 | 1 | yes | characteristic |
| 76 | C2×C4×C131 | C22⋊C8 | 1 | 2 | yes | — |
| 77 | C2×C4×C131 | #100 | 1 | 1 | yes | characteristic |
| 78 | C2×C4×C131 | #101 | 1 | 1 | yes | characteristic |
| 79 | C2×C4×C131 | #102 | 1 | 1 | yes | characteristic |
| 80 | C2×C4×C131 | #102 | 1 | 1 | yes | characteristic |
| 81 | C2×C4×C131 | #103 | 1 | 1 | yes | characteristic |
| 82 | C2×C4×C131 | #103 | 1 | 1 | yes | characteristic |
| 83 | C2×C4×C131 | #104 | 1 | 2 | yes | — |
| 84 | C2×C4×C131 | C4⋊C8 | 1 | 2 | yes | — |
| 85 | C2×C4×C131 | #106 | 1 | 1 | yes | characteristic |
| 86 | C2×C4×C131 | #107 | 1 | 1 | yes | characteristic |
| 87 | C8×C131 | — | 4 | 4 | no | — |
| 88 | C8×C131 | — | 4 | 4 | no | — |
| 89 | C8×C131 | — | 8 | 2 | no | — |
| 90 | C22×C131 | #336 | 1 | 1 | yes | characteristic |
| 91 | C22×C131 | H(3,ℤ/4) | 1 | 1 | yes | characteristic |
| 92 | C22×C131 | #338 | 1 | 1 | yes | characteristic |
| 93 | C22×C131 | #339 | 1 | 1 | yes | characteristic |
| 94 | C22×C131 | #340 | 1 | 1 | yes | characteristic |
| 95 | C22×C131 | #343 | 1 | 1 | yes | characteristic |
| 96 | C22×C131 | #344 | 1 | 1 | yes | characteristic |
| 97 | C4×C131 | — | 2 | 1 | no | — |
| 98 | C4×C131 | — | 2 | 1 | no | — |
| 99 | C4×C131 | — | 2 | 1 | no | — |
| 100 | C4×C131 | — | 2 | 1 | no | — |
| 101 | C4×C131 | — | 2 | 1 | no | — |
| 102 | C4×C131 | — | 2 | 1 | no | — |
| 103 | C4×C131 | — | 2 | 1 | no | — |
| 104 | C4×C131 | — | 2 | 1 | no | — |
| 105 | C4×C131 | — | 2 | 2 | no | — |
| 106 | C4×C131 | — | 4 | 1 | no | — |
| 107 | C4×C131 | D4⋊C8 | 1 | 2 | yes | — |
| 108 | C4×C131 | Q8⋊C8 | 1 | 2 | yes | — |
| 109 | C2×C131 | #1275 | 1 | 1 | yes | characteristic |
| 110 | C2×C131 | #1279 | 1 | 1 | yes | characteristic |
| 111 | C2×C131 | #1283 | 1 | 1 | yes | characteristic |
| 112 | C2×C131 | #1285 | 1 | 1 | yes | characteristic |
| 113 | C2×C131 | #1286 | 1 | 1 | yes | characteristic |
| 114 | C2×C131 | #1291 | 1 | 1 | yes | characteristic |
| 115 | C2×C131 | #1292 | 1 | 1 | yes | characteristic |
| 116 | #7022 | C131 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 117 | C131 | #7022 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 118 | #1831 | C2×C131 | 1 | 1 | yes | characteristic |
| 119 | #1767 | C2×C131 | 1 | 1 | yes | characteristic |
| 120 | C4×C4⋊C8 | C2×C131 | 1 | 1 | yes | characteristic |
| 121 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 122 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 123 | C2×C4⋊C8 | C4×C131 | 1 | 2 | yes | — |
| 124 | C2×#97 | — | 2 | 1 | no | — |
| 125 | C2×C4×C8 | C4×C131 | 1 | 2 | yes | — |
| 126 | C43 | C22×C131 | 1 | 1 | yes | characteristic |
| 127 | #336 | — | 2 | 1 | no | — |
| 128 | #336 | — | 2 | 1 | no | — |
| 129 | #336 | — | 2 | 1 | no | — |
| 130 | #336 | C4×C131 | 1 | 2 | yes | — |
| 131 | C22×C8 | — | 2 | 2 | no | — |
| 132 | C22×C8 | — | 2 | 2 | no | — |
| 133 | C22×C8 | — | 2 | 2 | no | — |
| 134 | C2×C42 | C2×C4×C131 | 1 | 1 | yes | characteristic |
| 135 | C2×C42 | C2×C4×C131 | 1 | 1 | yes | characteristic |
| 136 | C2×C42 | C2×C4×C131 | 1 | 1 | yes | characteristic |
| 137 | C2×C42 | D4×C131 | 1 | 1 | yes | characteristic |
| 138 | C2×C42 | D4×C131 | 1 | 1 | yes | characteristic |
| 139 | C2×C42 | D4×C131 | 1 | 1 | yes | characteristic |
| 140 | C2×C42 | Q8×C131 | 1 | 1 | yes | characteristic |
| 141 | C4⋊C8 | — | 2 | 4 | no | — |
| 142 | C4⋊C8 | — | 2 | 2 | no | — |
| 143 | C4⋊C8 | — | 4 | 1 | no | — |
| 144 | C4⋊C8 | — | 4 | 1 | no | — |
| 145 | C4⋊C8 | C8×C131 | 1 | 4 | yes | complemented |
| 146 | #97 | — | 4 | 1 | no | — |
| 147 | #97 | — | 4 | 1 | no | — |
| 148 | C4×C8 | — | 4 | 2 | no | — |
| 149 | C22×C4 | C42×C131 | 1 | 1 | yes | characteristic |
| 150 | C22×C4 | C22⋊C4×C131 | 1 | 1 | yes | characteristic |
| 151 | C22×C4 | C22⋊C4×C131 | 1 | 1 | yes | characteristic |
| 152 | C22×C4 | C22⋊C4×C131 | 1 | 1 | yes | characteristic |
| 153 | C22×C4 | C4⋊C4×C131 | 1 | 1 | yes | characteristic |
| 154 | C22×C4 | C4⋊C4×C131 | 1 | 1 | yes | characteristic |
| 155 | C22×C4 | C4⋊C4×C131 | 1 | 1 | yes | characteristic |
| 156 | C2×C8 | — | 2 | 4 | no | — |
| 157 | C2×C8 | — | 2 | 4 | no | — |
| 158 | C2×C8 | — | 4 | 2 | no | — |
| 159 | C2×C8 | — | 4 | 2 | no | — |
| 160 | C2×C8 | — | 4 | 2 | no | — |
| 161 | C2×C8 | — | 4 | 2 | no | — |
| 162 | C2×C8 | — | 4 | 2 | no | — |
| 163 | C2×C8 | — | 4 | 2 | no | — |
| 164 | C2×C8 | — | 4 | 2 | no | — |
| 165 | C42 | — | 2 | 1 | no | — |
| 166 | C42 | — | 2 | 1 | no | — |
| 167 | C42 | — | 2 | 2 | no | — |
| 168 | C42 | — | 4 | 1 | no | — |
| 169 | C42 | — | 4 | 1 | no | — |
| 170 | C42 | — | 4 | 1 | no | — |
| 171 | C42 | C2×C8×C131 | 1 | 2 | yes | — |
| 172 | C42 | M16×C131 | 1 | 2 | yes | — |
| 173 | C42 | D8×C131 | 1 | 1 | yes | characteristic |
| 174 | C42 | SD16×C131 | 1 | 1 | yes | characteristic |
| 175 | C42 | SD16×C131 | 1 | 1 | yes | characteristic |
| 176 | C42 | Q16×C131 | 1 | 1 | yes | characteristic |
| 177 | C23 | #95×C131 | 1 | 1 | yes | characteristic |
| 178 | C2×C4 | — | 2 | 1 | no | — |
| 179 | C2×C4 | — | 2 | 1 | no | — |
| 180 | C2×C4 | — | 2 | 1 | no | — |
| 181 | C2×C4 | — | 2 | 1 | no | — |
| 182 | C2×C4 | — | 2 | 1 | no | — |
| 183 | C2×C4 | — | 2 | 1 | no | — |
| 184 | C2×C4 | — | 2 | 1 | no | — |
| 185 | C2×C4 | — | 2 | 1 | no | — |
| 186 | C2×C4 | — | 2 | 1 | no | — |
| 187 | C2×C4 | — | 2 | 1 | no | — |
| 188 | C2×C4 | — | 2 | 1 | no | — |
| 189 | C2×C4 | — | 2 | 1 | no | — |
| 190 | C2×C4 | — | 2 | 1 | no | — |
| 191 | C2×C4 | C4×C8×C131 | 1 | 1 | yes | characteristic |
| 192 | C2×C4 | #97×C131 | 1 | 1 | yes | characteristic |
| 193 | C2×C4 | C22⋊C8×C131 | 1 | 2 | yes | — |
| 194 | C2×C4 | #100×C131 | 1 | 1 | yes | characteristic |
| 195 | C2×C4 | #101×C131 | 1 | 1 | yes | characteristic |
| 196 | C2×C4 | #102×C131 | 1 | 1 | yes | characteristic |
| 197 | C2×C4 | #102×C131 | 1 | 1 | yes | characteristic |
| 198 | C2×C4 | #103×C131 | 1 | 1 | yes | characteristic |
| 199 | C2×C4 | #103×C131 | 1 | 1 | yes | characteristic |
| 200 | C2×C4 | #104×C131 | 1 | 2 | yes | — |
| 201 | C2×C4 | C4⋊C8×C131 | 1 | 2 | yes | — |
| 202 | C2×C4 | #106×C131 | 1 | 1 | yes | characteristic |
| 203 | C2×C4 | #107×C131 | 1 | 1 | yes | characteristic |
| 204 | C8 | — | 4 | 4 | no | — |
| 205 | C8 | — | 4 | 4 | no | — |
| 206 | C8 | — | 8 | 2 | no | — |
| 207 | C22 | #336×C131 | 1 | 1 | yes | characteristic |
| 208 | C22 | H(3,ℤ/4)×C131 | 1 | 1 | yes | characteristic |
| 209 | C22 | #338×C131 | 1 | 1 | yes | characteristic |
| 210 | C22 | #339×C131 | 1 | 1 | yes | characteristic |
| 211 | C22 | #340×C131 | 1 | 1 | yes | characteristic |
| 212 | C22 | #343×C131 | 1 | 1 | yes | characteristic |
| 213 | C22 | #344×C131 | 1 | 1 | yes | characteristic |
| 214 | C4 | — | 2 | 2 | no | — |
| 215 | C4 | — | 2 | 1 | no | — |
| 216 | C4 | — | 2 | 1 | no | — |
| 217 | C4 | — | 2 | 1 | no | — |
| 218 | C4 | — | 2 | 1 | no | — |
| 219 | C4 | — | 2 | 1 | no | — |
| 220 | C4 | — | 2 | 1 | no | — |
| 221 | C4 | — | 2 | 1 | no | — |
| 222 | C4 | — | 2 | 1 | no | — |
| 223 | C4 | — | 4 | 1 | no | — |
| 224 | C4 | D4⋊C8×C131 | 1 | 2 | yes | — |
| 225 | C4 | Q8⋊C8×C131 | 1 | 2 | yes | — |
| 226 | C2 | #1275×C131 | 1 | 1 | yes | characteristic |
| 227 | C2 | #1279×C131 | 1 | 1 | yes | characteristic |
| 228 | C2 | #1283×C131 | 1 | 1 | yes | characteristic |
| 229 | C2 | #1285×C131 | 1 | 1 | yes | characteristic |
| 230 | C2 | #1286×C131 | 1 | 1 | yes | characteristic |
| 231 | C2 | #1291×C131 | 1 | 1 | yes | characteristic |
| 232 | C2 | #1292×C131 | 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