Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
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×D313 |
| commutator, socle, cosocle | C22×C313 | C24 |
| Fitting | #117×C313 | C2 |
| prime radical | #23756467 | C2 |
| hypercenter | #117 | D313 |
| hypocenter | C313 | #551 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23756492 | C2 | semidirect |
| 2. #23756491 | C2 | semidirect |
| 3. #23756485 | C2 | semidirect |
| 4. #23756482 | C2 | semidirect |
| 5. #23756482 | C2 | semidirect |
| 6. #23756480 | C2 | semidirect |
| 7. #23756475 | C2 | semidirect |
| 8. #23756474 | C2 | semidirect |
| 10. C4×D1252 | C2 | semidirect |
| 11. #23756457 | C2 | semidirect |
| 12. #23756454 | C2 | semidirect |
| 13. C2×#19097538 | C2 | semidirect |
| 14. C22⋊C4×D313 | C2 | semidirect |
| 15. #117×C313 | C2 | semidirect |
| 17. C2×Dic626 | C22 | semidirect |
| 24. C2×C4×D313 | C22 | semidirect |
| 25. C4⋊Dic313 | C22 | semidirect |
| 26. #19097540 | C22 | semidirect |
| 27. #19097540 | C22 | semidirect |
| 28. #19097540 | C22 | semidirect |
| 29. #19097540 | C22 | semidirect |
| 30. #19097540 | C22 | semidirect |
| 40. #19097538 | C22 | semidirect |
| 41. #19097538 | C22 | semidirect |
| 42. #19097538 | C22 | semidirect |
| 43. C4×Dic313 | C22 | semidirect |
| 45. C4⋊C4×C313 | C22 | semidirect |
| 46. C4⋊C4×C313 | C22 | semidirect |
| 49. C42×C313 | C22 | semidirect |
| 50. C42×C313 | C22 | semidirect |
| 110. C313 | #551 | semidirect |
| 124. #117 | D313 | semidirect |
| 143. C4⋊C4 | C2×D313 | semidirect |
| 144. C4⋊C4 | C2×D313 | semidirect |
| 160. C42 | C2×D313 | semidirect |
| 161. C42 | C2×D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756492 | 2 |
| #23756491 | 2 |
| #23756485 | 2 |
| #23756482 | 2 |
| #23756480 | 2 |
| #23756475 | 2 |
| #23756474 | 2 |
| #23756467 | 2 |
| C4×D1252 | 2 |
| #23756457 | 2 |
| #23756454 | 2 |
| C2×#19097538 | 2 |
| C22⋊C4×D313 | 2 |
| #117×C313 | 2 |
| #551 | 313 |