Finite Group DatabasebetaFinite Group DatabasebetaOrder 23100.
120 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D11×#3874 |
| commutator, cosocle, hypocenter | C11×C52⋊C3 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C11 | C2×D3 |
| LCS | G ▷ C11×C52⋊C3 | |
| UCS | C1 ◁ C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×D11×C52⋊C3 | C2 | semidirect |
| 2. C7×C11⋊#3874 | C2 | semidirect |
| 3. C7×C11×#3874 | C2 | semidirect |
| 5. C7×C11×C52⋊C3 | C22 | semidirect |
| 8. C52×C7×D11 | D3 | semidirect |
| 9. D11×#3874 | C7 | direct (N × H) |
| 11. C52×C7×C11 | C2×D3 | semidirect |
| 12. D11×C52⋊C3 | C2×C7 | semidirect |
| 13. C11⋊#3874 | C2×C7 | semidirect |
| 14. C11×#3874 | C2×C7 | semidirect |
| 20. C7×#3874 | D11 | direct (N × H) |
| 22. C11×C52⋊C3 | C22×C7 | semidirect |
| 32. C52×D11 | D3×C7 | semidirect |
| 33. C7×C52⋊C3 | C2×D11 | semidirect |
| 44. C52×C11 | C2×D3×C7 | semidirect |
| 48. C52×C7 | D3×D11 | semidirect |
| 51. C7×D11 | #3874 | direct (N × H) |
| 54. #3874 | C7×D11 | direct (N × H) |
| 66. C7×C11 | C2×#3874 | semidirect |
| 67. C52⋊C3 | C2×C7×D11 | semidirect |
| 90. C52 | D3×C7×D11 | semidirect |
| 93. D11 | C7×#3874 | direct (N × H) |
| 101. C11 | C2×C7×#3874 | semidirect |
| 108. C7 | D11×#3874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D11×C52⋊C3 | 2 |
| C7×C11⋊#3874 | 2 |
| C7×C11×#3874 | 2 |
| C5×C7×D5×D11 | 3 |
| D11×#3874 | 7 |
| C2×C7×#3874 | 11 |
| D3×C7×D11 | 25 |