Finite Group DatabasebetaFinite Group DatabasebetaOrder 9513.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C7×C151 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | C151⋊C9 | — | 7 | 1 | no | maximal, Hall |
| 3 | C7×C151 | C9 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | C3×C151 | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 5 | C151 | C7⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | C7⋊C9 | — | 151 | 1 | no | maximal, Hall |
| 7 | C3×C7 | C151⋊C3 | 1 | 1 | yes | characteristic |
| 8 | C9 | — | 1057 | 1 | no | Sylow |
| 9 | C7 | C151⋊C9 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | C3 | #15691749 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15691749 |
| commutator, hypocenter | C7×C151 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C151 | C3 |
| LCS | G ▷ C7×C151 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C7×C151 | C9 | semidirect |
| 5. C151 | C7⋊C9 | semidirect |
| 9. C7 | C151⋊C9 | semidirect |