Finite Group DatabasebetaFinite Group DatabasebetaOrder 486.
105 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6866 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C32×C3⋊D3 | — | 3 | 1 | no | maximal |
| 3 | #4181 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C34 | D3 | 1 | 1 | yes | characteristic |
| 5 | C32⋊C9 | — | 2 | 1 | no | — |
| 6 | C32⋊C9 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 7 | C3×C3⋊D3 | — | 3 | 3 | no | — |
| 8 | C3×C3⋊D3 | — | 3 | 1 | no | — |
| 9 | C32×D3 | — | 9 | 1 | no | — |
| 10 | C32×D3 | — | 9 | 2 | no | — |
| 11 | C32×D3 | — | 9 | 1 | no | — |
| 12 | C3×D9 | — | 9 | 1 | no | — |
| 13 | C33 | — | 2 | 1 | no | — |
| 14 | C33 | — | 3 | 3 | no | — |
| 15 | C33 | — | 3 | 1 | no | — |
| 16 | C33 | — | 3 | 2 | no | — |
| 17 | C33 | — | 6 | 3 | no | — |
| 18 | C33 | D9 | 1 | 1 | yes | characteristic, complemented |
| 19 | C33 | C3×D3 | 1 | 1 | yes | characteristic |
| 20 | C3×C9 | — | 3 | 1 | no | — |
| 21 | C3×C9 | — | 6 | 1 | no | — |
| 22 | C2×C32 | — | 27 | 1 | no | — |
| 23 | C3⋊D3 | — | 3 | 1 | no | — |
| 24 | C3×D3 | — | 9 | 3 | no | — |
| 25 | C3×D3 | — | 9 | 6 | no | — |
| 26 | C3×D3 | — | 9 | 3 | no | — |
| 27 | C3×D3 | — | 9 | 1 | no | — |
| 28 | C3×D3 | — | 9 | 1 | no | — |
| 29 | C3×D3 | — | 9 | 2 | no | — |
| 30 | D9 | — | 9 | 1 | no | — |
| 31 | C32 | — | 3 | 3 | no | — |
| 32 | C32 | — | 3 | 1 | no | — |
| 33 | C32 | — | 3 | 1 | no | — |
| 34 | C32 | — | 3 | 6 | no | — |
| 35 | C32 | — | 3 | 3 | no | — |
| 36 | C32 | — | 6 | 1 | no | — |
| 37 | C32 | — | 6 | 3 | no | — |
| 38 | C32 | — | 6 | 6 | no | — |
| 39 | C32 | — | 6 | 3 | no | — |
| 40 | C32 | — | 6 | 1 | no | — |
| 41 | C32 | C3×D9 | 1 | 1 | yes | characteristic |
| 42 | C32 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 43 | C32 | AGL(1,ℤ/9) | 1 | 2 | yes | — |
| 44 | C9 | — | 9 | 1 | no | — |
| 45 | C9 | — | 18 | 1 | no | — |
| 46 | C2×C3 | — | 27 | 3 | no | — |
| 47 | C2×C3 | — | 27 | 1 | no | — |
| 48 | D3 | — | 9 | 1 | no | — |
| 49 | D3 | — | 9 | 2 | no | — |
| 50 | D3 | — | 9 | 1 | no | — |
| 51 | C3 | — | 2 | 1 | no | — |
| 52 | C3 | — | 3 | 1 | no | — |
| 53 | C3 | — | 3 | 2 | no | — |
| 54 | C3 | — | 3 | 3 | no | — |
| 55 | C3 | — | 6 | 3 | no | — |
| 56 | C3 | #4169 | 1 | 1 | yes | characteristic |
| 57 | C3 | #4174 | 1 | 1 | yes | characteristic |
| 58 | C2 | — | 27 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #4169 |
| commutator, cosocle, hypocenter | C32⋊C9 | C2×C3 |
| Frattini | C33 | C3×D3 |
| Fitting | #6866 | C2 |
| socle | C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #6866 | C2 | semidirect |
| 3. #4181 | C3 | semidirect |
| 6. C32⋊C9 | C2×C3 | semidirect |
| 18. C33 | D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6866 | 2 |
| C32×C3⋊D3 | 3 |
| #4181 | 3 |