Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D19 |
| commutator, cosocle | C4×C19 | C25 |
| Frattini | C4 | C24×D19 |
| Fitting | C19×#585 | C2 |
| socle | C2×C19 | C23×D4 |
| hypercenter | #585 | D19 |
| hypocenter | C19 | #3585 |
| LCS | G ▷ C4×C19 ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597435 | C2 | semidirect |
| 2. #11927352 | C2 | semidirect |
| 3. #11927347 | C2 | semidirect |
| 4. #11927342 | C2 | semidirect |
| 5. C2×#10597395 | C2 | semidirect |
| 6. #11927311 | C2 | semidirect |
| 7. C19×#585 | C2 | semidirect |
| 9. C19×2−1+4 | C22 | semidirect |
| 11. C19×H(5,𝔽2) | C22 | semidirect |
| 14. C2×#41×C19 | C22 | semidirect |
| 16. #10597435 | C22 | semidirect |
| 19. C2×#64541 | C22 | semidirect |
| 20. C22×D76 | C22 | semidirect |
| 21. #10597397 | C22 | semidirect |
| 22. #10597396 | C22 | semidirect |
| 23. #10597395 | C22 | semidirect |
| 24. #10597395 | C22 | semidirect |
| 25. #10597394 | C22 | semidirect |
| 26. #10597388 | C22 | semidirect |
| 27. C2×#64527 | C22 | semidirect |
| 28. #10597378 | C22 | semidirect |
| 29. C2×#64525 | C22 | semidirect |
| 30. C2×#64520 | C22 | semidirect |
| 39. #41×C19 | C23 | semidirect |
| 42. C2×Q8×C19 | C23 | semidirect |
| 46. C2×D4×C19 | C23 | semidirect |
| 60. #64528 | C23 | semidirect |
| 61. #64527 | C23 | semidirect |
| 62. #64526 | C23 | semidirect |
| 63. #64525 | C23 | semidirect |
| 65. #64520 | C23 | semidirect |
| 66. C2×C19⋊C8 | C23 | semidirect |
| 110. #585 | D19 | semidirect |
| 123. 2−1+4 | C2×D19 | semidirect |
| 127. H(5,𝔽2) | C2×D19 | semidirect |
| 132. C2×#41 | C2×D19 | semidirect |
| 145. C19 | #3585 | semidirect |
| 157. #41 | C22×D19 | semidirect |
| 161. C2×Q8 | C22×D19 | semidirect |
| 171. C2×D4 | C22×D19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597435 | 2 |
| #11927352 | 2 |
| #11927347 | 2 |
| #11927342 | 2 |
| C2×#10597395 | 2 |
| #11927311 | 2 |
| C19×#585 | 2 |
| #3585 | 19 |