← C127×#19653 #44583326
Subgroups — C127×#19653 #44583326
Order 32512.
730 conjugacy classes of subgroups.
The subgroup lattice has 204 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C127×#3229 | C2 | 1 | 4 | yes | maximal |
| 2 | C127×#3160 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#494×C127 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C127×#1716 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C127×#1707 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C127×#1450 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C22×Q16×C127 | — | 2 | 2 | no | — |
| 8 | #533×C127 | C22 | 1 | 2 | yes | — |
| 9 | C2×C4⋊Q8×C127 | C22 | 1 | 2 | yes | — |
| 10 | #500×C127 | C22 | 1 | 2 | yes | — |
| 11 | #499×C127 | — | 2 | 2 | no | — |
| 12 | #498×C127 | C22 | 1 | 2 | yes | — |
| 13 | #498×C127 | C22 | 1 | 8 | yes | — |
| 14 | #494×C127 | — | 2 | 2 | no | — |
| 15 | #494×C127 | C22 | 1 | 2 | yes | — |
| 16 | #494×C127 | C22 | 1 | 2 | yes | — |
| 17 | #487×C127 | C22 | 1 | 8 | yes | — |
| 18 | #483×C127 | — | 2 | 8 | no | — |
| 19 | #475×C127 | — | 2 | 8 | no | — |
| 20 | #431×C127 | C22 | 1 | 2 | yes | — |
| 21 | #427×C127 | — | 2 | 2 | no | — |
| 22 | C2×C4×C8×C127 | C22 | 1 | 1 | yes | characteristic |
| 23 | #322×C127 | C22 | 1 | 2 | yes | — |
| 24 | C82×C127 | C22 | 1 | 2 | yes | — |
| 25 | C22×Q8×C127 | — | 2 | 2 | no | — |
| 26 | C2×Q16×C127 | — | 2 | 4 | no | — |
| 27 | C2×Q16×C127 | — | 2 | 4 | no | — |
| 28 | C2×Q16×C127 | — | 4 | 8 | no | — |
| 29 | C22×C8×C127 | D4 | 1 | 2 | yes | — |
| 30 | C4⋊Q8×C127 | — | 2 | 4 | no | — |
| 31 | C4⋊Q8×C127 | — | 2 | 2 | no | — |
| 32 | C4⋊Q8×C127 | C23 | 1 | 4 | yes | — |
| 33 | C4⋊Q8×C127 | C23 | 1 | 4 | yes | — |
| 34 | #125×C127 | — | 2 | 2 | no | — |
| 35 | C22⋊Q8×C127 | — | 2 | 4 | no | — |
| 36 | C4×Q8×C127 | — | 2 | 4 | no | — |
| 37 | #117×C127 | — | 2 | 2 | no | — |
| 38 | C2×C4⋊C4×C127 | — | 2 | 4 | no | — |
| 39 | C2×C42×C127 | C23 | 1 | 1 | yes | characteristic |
| 40 | #107×C127 | — | 2 | 4 | no | — |
| 41 | #106×C127 | — | 2 | 4 | no | — |
| 42 | #106×C127 | — | 2 | 16 | no | — |
| 43 | C4⋊C8×C127 | D4 | 1 | 4 | yes | — |
| 44 | #103×C127 | — | 2 | 16 | no | — |
| 45 | C22⋊C8×C127 | D4 | 1 | 4 | yes | — |
| 46 | C4×C8×C127 | D4 | 1 | 2 | yes | — |
| 47 | C4×C8×C127 | C23 | 1 | 4 | yes | — |
| 48 | C4×C8×C127 | C23 | 1 | 1 | yes | characteristic |
| 49 | C4×C8×C127 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×Q8×C127 | — | 2 | 4 | no | — |
| 51 | C2×Q8×C127 | — | 2 | 4 | no | — |
| 52 | C2×Q8×C127 | — | 4 | 2 | no | — |
| 53 | C2×Q8×C127 | — | 4 | 8 | no | — |
| 54 | C22×C4×C127 | — | 4 | 2 | no | — |
| 55 | C22×C4×C127 | C2×D4 | 1 | 2 | yes | — |
| 56 | C22×C4×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 57 | Q16×C127 | — | 4 | 8 | no | — |
| 58 | Q16×C127 | — | 4 | 8 | no | — |
| 59 | C2×C8×C127 | SD16 | 1 | 8 | yes | — |
| 60 | C2×C8×C127 | C2×D4 | 1 | 8 | yes | — |
| 61 | C2×C8×C127 | C2×D4 | 1 | 2 | yes | — |
| 62 | C2×C8×C127 | C2×D4 | 1 | 2 | yes | — |
| 63 | C4⋊C4×C127 | — | 2 | 8 | no | — |
| 64 | C4⋊C4×C127 | — | 2 | 4 | no | — |
| 65 | C4⋊C4×C127 | — | 2 | 4 | no | — |
| 66 | C4⋊C4×C127 | — | 4 | 4 | no | — |
| 67 | C4⋊C4×C127 | — | 4 | 4 | no | — |
| 68 | C22⋊C4×C127 | — | 4 | 2 | no | — |
| 69 | C42×C127 | — | 4 | 2 | no | — |
| 70 | C42×C127 | C2×D4 | 1 | 1 | yes | characteristic |
| 71 | C42×C127 | C2×D4 | 1 | 2 | yes | — |
| 72 | C42×C127 | C24 | 1 | 1 | yes | characteristic |
| 73 | C23×C127 | #127 | 1 | 1 | yes | characteristic |
| 74 | Q8×C127 | — | 4 | 8 | no | — |
| 75 | Q8×C127 | — | 4 | 8 | no | — |
| 76 | Q8×C127 | — | 8 | 4 | no | — |
| 77 | C2×C4×C127 | — | 2 | 4 | no | — |
| 78 | C2×C4×C127 | — | 4 | 4 | no | — |
| 79 | C2×C4×C127 | — | 4 | 4 | no | — |
| 80 | C2×C4×C127 | — | 8 | 4 | no | — |
| 81 | C2×C4×C127 | #127 | 1 | 2 | yes | — |
| 82 | C2×C4×C127 | #127 | 1 | 1 | yes | characteristic |
| 83 | C2×C4×C127 | C2×SD16 | 1 | 4 | yes | — |
| 84 | C2×C4×C127 | C22×D4 | 1 | 1 | yes | characteristic |
| 85 | C2×C4×C127 | C22×D4 | 1 | 2 | yes | — |
| 86 | C8×C127 | — | 2 | 8 | no | — |
| 87 | C8×C127 | C2×SD16 | 1 | 4 | yes | — |
| 88 | C8×C127 | C2×SD16 | 1 | 4 | yes | — |
| 89 | C22×C127 | — | 2 | 2 | no | — |
| 90 | C22×C127 | #492 | 1 | 2 | yes | — |
| 91 | C22×C127 | C2×#127 | 1 | 1 | yes | characteristic |
| 92 | C4×C127 | — | 2 | 2 | no | — |
| 93 | C4×C127 | — | 8 | 4 | no | — |
| 94 | C4×C127 | — | 8 | 4 | no | — |
| 95 | C4×C127 | #492 | 1 | 2 | yes | — |
| 96 | C4×C127 | C22×SD16 | 1 | 2 | yes | — |
| 97 | C4×C127 | #578 | 1 | 4 | yes | — |
| 98 | #19653 | C127 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 99 | C2×C127 | — | 2 | 2 | no | — |
| 100 | C2×C127 | C2×#492 | 1 | 1 | yes | characteristic |
| 101 | C2×C127 | #3156 | 1 | 2 | yes | — |
| 102 | #3229 | C2×C127 | 1 | 4 | yes | — |
| 103 | #3160 | C2×C127 | 1 | 1 | yes | characteristic |
| 104 | C2×#494 | C2×C127 | 1 | 1 | yes | characteristic |
| 105 | #1716 | C2×C127 | 1 | 4 | yes | complemented |
| 106 | #1707 | C2×C127 | 1 | 4 | yes | complemented |
| 107 | #1450 | C2×C127 | 1 | 1 | yes | characteristic |
| 108 | C127 | #19653 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 109 | C22×Q16 | — | 2 | 2 | no | — |
| 110 | #533 | C22×C127 | 1 | 2 | yes | — |
| 111 | C2×C4⋊Q8 | C22×C127 | 1 | 2 | yes | — |
| 112 | #500 | C22×C127 | 1 | 2 | yes | — |
| 113 | #499 | — | 2 | 2 | no | — |
| 114 | #498 | C22×C127 | 1 | 2 | yes | — |
| 115 | #498 | C22×C127 | 1 | 8 | yes | — |
| 116 | #494 | — | 2 | 2 | no | — |
| 117 | #494 | C22×C127 | 1 | 2 | yes | — |
| 118 | #494 | C22×C127 | 1 | 2 | yes | — |
| 119 | #487 | C22×C127 | 1 | 8 | yes | — |
| 120 | #483 | — | 2 | 8 | no | — |
| 121 | #475 | — | 2 | 8 | no | — |
| 122 | #431 | C22×C127 | 1 | 2 | yes | — |
| 123 | #427 | — | 2 | 2 | no | — |
| 124 | C2×C4×C8 | C22×C127 | 1 | 1 | yes | characteristic |
| 125 | #322 | C22×C127 | 1 | 2 | yes | — |
| 126 | C82 | C22×C127 | 1 | 2 | yes | — |
| 127 | C22×Q8 | — | 2 | 2 | no | — |
| 128 | C2×Q16 | — | 2 | 4 | no | — |
| 129 | C2×Q16 | — | 2 | 4 | no | — |
| 130 | C2×Q16 | — | 4 | 8 | no | — |
| 131 | C22×C8 | D4×C127 | 1 | 2 | yes | — |
| 132 | C4⋊Q8 | — | 2 | 4 | no | — |
| 133 | C4⋊Q8 | — | 2 | 2 | no | — |
| 134 | C4⋊Q8 | C23×C127 | 1 | 4 | yes | — |
| 135 | C4⋊Q8 | C23×C127 | 1 | 4 | yes | — |
| 136 | #125 | — | 2 | 2 | no | — |
| 137 | C22⋊Q8 | — | 2 | 4 | no | — |
| 138 | C4×Q8 | — | 2 | 4 | no | — |
| 139 | #117 | — | 2 | 2 | no | — |
| 140 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 141 | C2×C42 | C23×C127 | 1 | 1 | yes | characteristic |
| 142 | #107 | — | 2 | 4 | no | — |
| 143 | #106 | — | 2 | 4 | no | — |
| 144 | #106 | — | 2 | 16 | no | — |
| 145 | C4⋊C8 | D4×C127 | 1 | 4 | yes | — |
| 146 | #103 | — | 2 | 16 | no | — |
| 147 | C22⋊C8 | D4×C127 | 1 | 4 | yes | — |
| 148 | C4×C8 | D4×C127 | 1 | 2 | yes | — |
| 149 | C4×C8 | C23×C127 | 1 | 1 | yes | characteristic |
| 150 | C4×C8 | C23×C127 | 1 | 4 | yes | — |
| 151 | C4×C8 | C23×C127 | 1 | 1 | yes | characteristic |
| 152 | C2×Q8 | — | 2 | 4 | no | — |
| 153 | C2×Q8 | — | 2 | 4 | no | — |
| 154 | C2×Q8 | — | 4 | 2 | no | — |
| 155 | C2×Q8 | — | 4 | 8 | no | — |
| 156 | C22×C4 | — | 4 | 2 | no | — |
| 157 | C22×C4 | C2×D4×C127 | 1 | 2 | yes | — |
| 158 | C22×C4 | C2×D4×C127 | 1 | 1 | yes | characteristic |
| 159 | Q16 | — | 4 | 8 | no | — |
| 160 | Q16 | — | 4 | 8 | no | — |
| 161 | C2×C8 | SD16×C127 | 1 | 8 | yes | — |
| 162 | C2×C8 | C2×D4×C127 | 1 | 8 | yes | — |
| 163 | C2×C8 | C2×D4×C127 | 1 | 2 | yes | — |
| 164 | C2×C8 | C2×D4×C127 | 1 | 2 | yes | — |
| 165 | C4⋊C4 | — | 2 | 8 | no | — |
| 166 | C4⋊C4 | — | 2 | 4 | no | — |
| 167 | C4⋊C4 | — | 2 | 4 | no | — |
| 168 | C4⋊C4 | — | 4 | 4 | no | — |
| 169 | C4⋊C4 | — | 4 | 4 | no | — |
| 170 | C22⋊C4 | — | 4 | 2 | no | — |
| 171 | C42 | — | 4 | 2 | no | — |
| 172 | C42 | C2×D4×C127 | 1 | 1 | yes | characteristic |
| 173 | C42 | C2×D4×C127 | 1 | 2 | yes | — |
| 174 | C42 | C24×C127 | 1 | 1 | yes | characteristic |
| 175 | C23 | #127×C127 | 1 | 1 | yes | characteristic |
| 176 | Q8 | — | 4 | 8 | no | — |
| 177 | Q8 | — | 4 | 8 | no | — |
| 178 | Q8 | — | 8 | 4 | no | — |
| 179 | C2×C4 | — | 2 | 4 | no | — |
| 180 | C2×C4 | — | 4 | 4 | no | — |
| 181 | C2×C4 | — | 4 | 4 | no | — |
| 182 | C2×C4 | — | 8 | 4 | no | — |
| 183 | C2×C4 | #127×C127 | 1 | 2 | yes | — |
| 184 | C2×C4 | #127×C127 | 1 | 1 | yes | characteristic |
| 185 | C2×C4 | C2×SD16×C127 | 1 | 4 | yes | — |
| 186 | C2×C4 | C22×D4×C127 | 1 | 1 | yes | characteristic |
| 187 | C2×C4 | C22×D4×C127 | 1 | 2 | yes | — |
| 188 | C8 | — | 2 | 8 | no | — |
| 189 | C8 | C2×SD16×C127 | 1 | 4 | yes | — |
| 190 | C8 | C2×SD16×C127 | 1 | 4 | yes | — |
| 191 | C22 | — | 2 | 2 | no | — |
| 192 | C22 | #492×C127 | 1 | 2 | yes | — |
| 193 | C22 | C2×#127×C127 | 1 | 1 | yes | characteristic |
| 194 | C4 | — | 2 | 2 | no | — |
| 195 | C4 | — | 8 | 4 | no | — |
| 196 | C4 | — | 8 | 4 | no | — |
| 197 | C4 | #492×C127 | 1 | 2 | yes | — |
| 198 | C4 | C22×SD16×C127 | 1 | 2 | yes | — |
| 199 | C4 | #578×C127 | 1 | 4 | yes | — |
| 200 | C2 | — | 2 | 2 | no | — |
| 201 | C2 | C2×#492×C127 | 1 | 1 | yes | characteristic |
| 202 | C2 | C127×#3156 | 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