Finite Group DatabasebetaFinite Group Databasebeta← C11⋊((C17⋊D17)⋊C3) #34061702
Order 19074.
40 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×C172⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C11⋊(C17⋊D17) | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C11×C172 | C2×C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | (C17⋊D17)⋊C3 | — | 11 | 1 | no | maximal, Hall |
| 5 | C172⋊C3 | D11 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C17⋊D17 | — | 11 | 1 | no | Hall |
| 7 | D187 | — | 51 | 6 | no | — |
| 8 | C172 | C3×D11 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C11×C17 | — | 3 | 6 | no | — |
| 10 | C3×D11 | — | 289 | 1 | no | maximal, Hall |
| 11 | D17 | — | 561 | 6 | no | — |
| 12 | C3×C11 | — | 289 | 1 | no | Hall |
| 13 | D11 | — | 289 | 1 | no | Hall |
| 14 | C17 | — | 3 | 6 | no | — |
| 15 | C11 | (C17⋊D17)⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C2×C3 | — | 3179 | 1 | no | Hall |
| 17 | C3 | — | 289 | 1 | no | Sylow |
| 18 | C2 | — | 3179 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C172 | C2×C3 |
| LCS | G ▷ C11×C172 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×C172⋊C3 | C2 | semidirect |
| 2. C11⋊(C17⋊D17) | C3 | semidirect |
| 3. C11×C172 | C2×C3 | semidirect |
| 5. C172⋊C3 | D11 | semidirect |
| 8. C172 | C3×D11 | semidirect |
| 15. C11 | (C17⋊D17)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×C172⋊C3 | 2 |
| C11⋊(C17⋊D17) | 3 |
| (C17⋊D17)⋊C3 | 11 |
| C3×D11 | 289 |