Finite Group DatabasebetaFinite Group DatabasebetaOrder 36771.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×C103⋊C17 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | (C103⋊C3)⋊C17 | — | 7 | 1 | no | maximal, Hall |
| 3 | #14524189 | C17 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 4 | C103⋊C17 | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented, Hall |
| 5 | C7×C103 | C3×C17 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | C17×ΓL(1,𝔽8) | — | 103 | 1 | no | maximal, Hall |
| 7 | C103⋊C3 | — | 7 | 1 | no | Hall |
| 8 | C7×C17 | — | 103 | 1 | no | Hall |
| 9 | C103 | C17×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C3×C17 | — | 721 | 1 | no | Hall |
| 11 | ΓL(1,𝔽8) | — | 103 | 1 | no | Hall |
| 12 | C17 | — | 103 | 1 | no | Sylow |
| 13 | C7 | (C103⋊C3)⋊C17 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C3 | — | 721 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C103 | C3×C17 |
| LCS | G ▷ C7×C103 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×C103⋊C17 | C3 | semidirect |
| 3. #14524189 | C17 | semidirect |
| 4. C103⋊C17 | ΓL(1,𝔽8) | semidirect |
| 5. C7×C103 | C3×C17 | semidirect |
| 9. C103 | C17×ΓL(1,𝔽8) | semidirect |
| 13. C7 | (C103⋊C3)⋊C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C103⋊C17 | 3 |
| (C103⋊C3)⋊C17 | 7 |
| #14524189 | 17 |
| C17×ΓL(1,𝔽8) | 103 |