Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
42 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Dic1504 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C47⋊C128 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C47×Q128 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Dic752 | — | 2 | 1 | no | — |
| 5 | C47×Q64 | — | 2 | 1 | no | — |
| 6 | C47×C64 | C22 | 1 | 1 | yes | characteristic |
| 7 | Dic376 | — | 4 | 1 | no | — |
| 8 | Q32×C47 | — | 4 | 1 | no | — |
| 9 | C32×C47 | D4 | 1 | 1 | yes | characteristic |
| 10 | Q16×C47 | — | 8 | 1 | no | — |
| 11 | Dic188 | — | 8 | 1 | no | — |
| 12 | C16×C47 | D8 | 1 | 1 | yes | characteristic |
| 13 | Q8×C47 | — | 16 | 1 | no | — |
| 14 | Dic94 | — | 16 | 1 | no | — |
| 15 | C8×C47 | D16 | 1 | 1 | yes | characteristic |
| 16 | Q256 | — | 47 | 1 | no | maximal, Sylow |
| 17 | C4×C47 | — | 32 | 1 | no | — |
| 18 | C4×C47 | D32 | 1 | 1 | yes | characteristic |
| 19 | Dic47 | — | 32 | 1 | no | — |
| 20 | Q128 | — | 47 | 1 | no | — |
| 21 | Q128 | D47 | 1 | 1 | yes | characteristic |
| 22 | C128 | — | 47 | 1 | no | — |
| 23 | C2×C47 | D64 | 1 | 1 | yes | characteristic |
| 24 | Q64 | — | 2 | 1 | no | — |
| 25 | Q64 | — | 94 | 1 | no | — |
| 26 | C64 | C2×D47 | 1 | 1 | yes | characteristic |
| 27 | C47 | Q256 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 28 | Q32 | — | 4 | 1 | no | — |
| 29 | Q32 | — | 188 | 1 | no | — |
| 30 | C32 | C22⋊D47 | 1 | 1 | yes | characteristic |
| 31 | Q16 | — | 8 | 1 | no | — |
| 32 | Q16 | — | 376 | 1 | no | — |
| 33 | C16 | #10625334 | 1 | 1 | yes | characteristic |
| 34 | Q8 | — | 16 | 1 | no | — |
| 35 | Q8 | — | 752 | 1 | no | — |
| 36 | C8 | #13093965 | 1 | 1 | yes | characteristic |
| 37 | C4 | — | 32 | 1 | no | — |
| 38 | C4 | — | 1504 | 1 | no | — |
| 39 | C4 | #15688958 | 1 | 1 | yes | characteristic |
| 40 | C2 | #20241600 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #20241600 |
| commutator, cosocle | C47×C64 | C22 |
| Frattini | C64 | C2×D47 |
| Fitting | C47×Q128 | C2 |
| socle, prime radical | C2×C47 | D64 |
| hypercenter | Q128 | D47 |
| hypocenter | C47 | Q256 |
| LCS | G ▷ C47×C64 ▷ C32×C47 ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ C64 ◁ Q128 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 27. C47 | Q256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic1504 | 2 |
| C47⋊C128 | 2 |
| C47×Q128 | 2 |
| Q256 | 47 |