Finite Group DatabasebetaFinite Group DatabasebetaOrder 2673.
110 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×#737 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | C11×C27⋊C3 | C3 | 1 | 8 | yes | maximal, complemented |
| 3 | C3×C11×C27 | C3 | 1 | 4 | yes | maximal, complemented |
| 4 | C11×3−1+2 | C9 | 1 | 8 | yes | — |
| 5 | C11×H(3,𝔽3) | C9 | 1 | 1 | yes | characteristic |
| 6 | C3×C9×C11 | C32 | 1 | 4 | yes | — |
| 7 | C11×C27 | C32 | 1 | 8 | yes | — |
| 8 | C11×C27 | C32 | 1 | 1 | yes | characteristic |
| 9 | #6903 | C11 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 10 | C32×C11 | C3×C9 | 1 | 4 | yes | — |
| 11 | C9×C11 | C3×C9 | 1 | 8 | yes | — |
| 12 | C9×C11 | C33 | 1 | 1 | yes | characteristic |
| 13 | #737 | C3×C11 | 1 | 1 | yes | characteristic |
| 14 | C27⋊C3 | C3×C11 | 1 | 8 | yes | complemented |
| 15 | C3×C27 | C3×C11 | 1 | 4 | yes | complemented |
| 16 | C3×C11 | — | 3 | 4 | no | — |
| 17 | C3×C11 | C32×C9 | 1 | 1 | yes | characteristic |
| 18 | 3−1+2 | C9×C11 | 1 | 8 | yes | — |
| 19 | H(3,𝔽3) | C9×C11 | 1 | 1 | yes | characteristic |
| 20 | C3×C9 | C32×C11 | 1 | 4 | yes | — |
| 21 | C27 | C32×C11 | 1 | 8 | yes | — |
| 22 | C27 | C32×C11 | 1 | 1 | yes | characteristic |
| 23 | C11 | #6903 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 24 | C32 | C3×C9×C11 | 1 | 4 | yes | — |
| 25 | C9 | C3×C9×C11 | 1 | 8 | yes | — |
| 26 | C9 | C33×C11 | 1 | 1 | yes | characteristic |
| 27 | C3 | — | 3 | 4 | no | — |
| 28 | C3 | C32×C9×C11 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C11×C27 | C32 |
| commutator | C3 | C32×C9×C11 |
| Frattini, cosocle | C9 | C33×C11 |
| socle | C3×C11 | C32×C9 |
| prime radical | C11×H(3,𝔽3) | C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C11×C27 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C11×C27⋊C3 | C3 | semidirect |
| 3. C3×C11×C27 | C3 | semidirect |
| 9. #6903 | C11 | direct (N × H) |
| 14. C27⋊C3 | C3×C11 | semidirect |
| 15. C3×C27 | C3×C11 | semidirect |
| 23. C11 | #6903 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#737 | 3 |
| C11×C27⋊C3 | 3 |
| C3×C11×C27 | 3 |
| #6903 | 11 |