Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D173 |
| commutator, socle, cosocle | C22×C173 | C24 |
| Frattini | C22 | C23×D173 |
| Fitting | C4×D4×C173 | C2 |
| hypercenter | C4×D4 | D173 |
| hypocenter | C173 | #525 |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14583826 | C2 | semidirect |
| 2. C22×C4×D173 | C2 | semidirect |
| 3. #19149664 | C2 | semidirect |
| 4. #19149661 | C2 | semidirect |
| 5. #19149657 | C2 | semidirect |
| 6. #19149656 | C2 | semidirect |
| 7. #19149652 | C2 | semidirect |
| 8. #19149651 | C2 | semidirect |
| 9. #19149649 | C2 | semidirect |
| 10. #19149647 | C2 | semidirect |
| 11. C4×D692 | C2 | semidirect |
| 12. C4×C22⋊D173 | C2 | semidirect |
| 13. C4×C22⋊D173 | C2 | semidirect |
| 14. #19149636 | C2 | semidirect |
| 15. C4×D4×C173 | C2 | semidirect |
| 18. C2×Dic346 | C22 | semidirect |
| 24. C2×C22⋊D173 | C22 | semidirect |
| 31. C2×C4×D173 | C22 | semidirect |
| 32. C4⋊Dic173 | C22 | semidirect |
| 33. #14583805 | C22 | semidirect |
| 34. #14583805 | C22 | semidirect |
| 35. #14583805 | C22 | semidirect |
| 36. #14583805 | C22 | semidirect |
| 38. C22⋊Dic173 | C22 | semidirect |
| 43. #14583803 | C22 | semidirect |
| 44. #14583803 | C22 | semidirect |
| 45. C4×Dic173 | C22 | semidirect |
| 48. C22×C4×C173 | C22 | semidirect |
| 49. C4⋊C4×C173 | C22 | semidirect |
| 51. C22⋊C4×C173 | C22 | semidirect |
| 52. C42×C173 | C22 | semidirect |
| 76. C4×D173 | D4 | semidirect |
| 92. C22×C173 | #41 | semidirect |
| 103. C2×D173 | #41 | semidirect |
| 122. C173 | #525 | semidirect |
| 137. C4×D4 | D173 | semidirect |
| 157. C22×C4 | C2×D173 | semidirect |
| 163. C4⋊C4 | C2×D173 | semidirect |
| 173. C22⋊C4 | C2×D173 | semidirect |
| 175. C42 | C2×D173 | semidirect |
| 225. C22 | #14583826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583826 | 2 |
| C22×C4×D173 | 2 |
| #19149664 | 2 |
| #19149661 | 2 |
| #19149657 | 2 |
| #19149656 | 2 |
| #19149652 | 2 |
| #19149651 | 2 |
| #19149649 | 2 |
| #19149647 | 2 |
| C4×D692 | 2 |
| C4×C22⋊D173 | 2 |
| #19149636 | 2 |
| C4×D4×C173 | 2 |
| #525 | 173 |