Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D503 |
| commutator, socle, cosocle | C22×C503 | C24 |
| Fitting | #123×C503 | C2 |
| prime radical | #30632832 | C2 |
| hypercenter | #123 | D503 |
| hypocenter | C503 | #551 |
| LCS | G ▷ C22×C503 ▷ C503 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30632859 | C2 | semidirect |
| 2. #30632859 | C2 | semidirect |
| 3. #30632850 | C2 | semidirect |
| 4. #30632848 | C2 | semidirect |
| 5. #30632846 | C2 | semidirect |
| 6. #30632844 | C2 | semidirect |
| 7. #30632841 | C2 | semidirect |
| 9. D4×Dic503 | C2 | semidirect |
| 10. (C22⋊D503)⋊C4 | C2 | semidirect |
| 11. #30632823 | C2 | semidirect |
| 12. #30632822 | C2 | semidirect |
| 13. C2×(C2×D503)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D503 | C2 | semidirect |
| 15. #123×C503 | C2 | semidirect |
| 17. C2×Dic1006 | C22 | semidirect |
| 21. C22×Dic503 | C22 | semidirect |
| 24. C4⋊Dic503 | C22 | semidirect |
| 25. C4⋊Dic503 | C22 | semidirect |
| 26. C4⋊Dic503 | C22 | semidirect |
| 27. C4⋊Dic503 | C22 | semidirect |
| 28. Dic503⋊C4 | C22 | semidirect |
| 29. Dic503⋊C4 | C22 | semidirect |
| 32. C22⋊Dic503 | C22 | semidirect |
| 41. C4×Dic503 | C22 | semidirect |
| 42. C4×Dic503 | C22 | semidirect |
| 43. C4×Dic503 | C22 | semidirect |
| 46. C4⋊C4×C503 | C22 | semidirect |
| 47. C4⋊C4×C503 | C22 | semidirect |
| 49. C22⋊C4×C503 | C22 | semidirect |
| 50. C22⋊C4×C503 | C22 | semidirect |
| 110. C503 | #551 | semidirect |
| 117. #123 | D503 | semidirect |
| 143. C4⋊C4 | C2×D503 | semidirect |
| 144. C4⋊C4 | C2×D503 | semidirect |
| 157. C22⋊C4 | C2×D503 | semidirect |
| 158. C22⋊C4 | C2×D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632859 | 2 |
| #30632850 | 2 |
| #30632848 | 2 |
| #30632846 | 2 |
| #30632844 | 2 |
| #30632841 | 2 |
| #30632832 | 2 |
| D4×Dic503 | 2 |
| (C22⋊D503)⋊C4 | 2 |
| #30632823 | 2 |
| #30632822 | 2 |
| C2×(C2×D503)⋊C4 | 2 |
| C22⋊C4×D503 | 2 |
| #123×C503 | 2 |
| #551 | 503 |