Finite Group DatabasebetaFinite Group DatabasebetaOrder 2673.
100 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C11×C9⋊C9 | C3 | 1 | 8 | yes | maximal, complemented |
| 2 | C11×C32⋊C9 | C3 | 1 | 4 | yes | maximal |
| 3 | C92×C11 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C33×C11 | C32 | 1 | 1 | yes | characteristic |
| 5 | C3×C9×C11 | C32 | 1 | 4 | yes | — |
| 6 | C3×C9×C11 | C32 | 1 | 8 | yes | — |
| 7 | #6898 | C11 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 8 | C32×C11 | — | 3 | 4 | no | — |
| 9 | C32×C11 | C33 | 1 | 1 | yes | characteristic |
| 10 | C9×C11 | — | 3 | 4 | no | — |
| 11 | C9×C11 | — | 3 | 8 | no | — |
| 12 | C9⋊C9 | C3×C11 | 1 | 8 | yes | complemented |
| 13 | C32⋊C9 | C3×C11 | 1 | 4 | yes | — |
| 14 | C92 | C3×C11 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×C11 | — | 9 | 1 | no | — |
| 16 | C3×C11 | #737 | 1 | 4 | yes | — |
| 17 | C33 | C32×C11 | 1 | 1 | yes | characteristic |
| 18 | C3×C9 | C32×C11 | 1 | 4 | yes | — |
| 19 | C3×C9 | C32×C11 | 1 | 8 | yes | — |
| 20 | C11 | #6898 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 21 | C32 | — | 3 | 4 | no | — |
| 22 | C32 | C33×C11 | 1 | 1 | yes | characteristic |
| 23 | C9 | — | 3 | 4 | no | — |
| 24 | C9 | — | 3 | 8 | no | — |
| 25 | C3 | — | 9 | 1 | no | — |
| 26 | C3 | C11×#737 | 1 | 4 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C11 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C11 |
| prime radical | C33×C11 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×C9⋊C9 | C3 | semidirect |
| 3. C92×C11 | C3 | semidirect |
| 7. #6898 | C11 | direct (N × H) |
| 12. C9⋊C9 | C3×C11 | semidirect |
| 14. C92 | C3×C11 | semidirect |
| 20. C11 | #6898 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×C9⋊C9 | 3 |
| C11×C32⋊C9 | 3 |
| C92×C11 | 3 |
| #6898 | 11 |