Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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 | #124×C313 | C2 |
| hypercenter | #124 | D313 |
| hypocenter | C313 | #538 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23756491 | C2 | semidirect |
| 2. #23756490 | C2 | semidirect |
| 3. #23756486 | C2 | semidirect |
| 4. #23756481 | C2 | semidirect |
| 5. #23756479 | C2 | semidirect |
| 6. #23756473 | C2 | semidirect |
| 7. #23756470 | C2 | semidirect |
| 8. #23756470 | C2 | semidirect |
| 9. #23756469 | C2 | semidirect |
| 10. #23756467 | C2 | semidirect |
| 11. #23756465 | C2 | semidirect |
| 12. C4×D1252 | C2 | semidirect |
| 13. #23756457 | C2 | semidirect |
| 14. C22⋊C4×D313 | C2 | semidirect |
| 15. #124×C313 | C2 | semidirect |
| 22. C2×C22⋊D313 | C22 | semidirect |
| 23. C22×Dic313 | C22 | semidirect |
| 26. C2×C4×D313 | C22 | semidirect |
| 27. C4⋊Dic313 | C22 | semidirect |
| 28. C4⋊Dic313 | C22 | semidirect |
| 29. #19097540 | C22 | semidirect |
| 30. #19097540 | C22 | semidirect |
| 31. #19097540 | C22 | semidirect |
| 32. #19097540 | C22 | semidirect |
| 41. #19097538 | C22 | semidirect |
| 42. #19097538 | C22 | semidirect |
| 43. C4×Dic313 | C22 | semidirect |
| 44. C2×Q8×C313 | C22 | semidirect |
| 48. C22⋊C4×C313 | C22 | semidirect |
| 49. C22⋊C4×C313 | C22 | semidirect |
| 50. C42×C313 | C22 | semidirect |
| 116. C313 | #538 | semidirect |
| 121. #124 | D313 | semidirect |
| 134. C2×Q8 | C2×D313 | semidirect |
| 164. C22⋊C4 | C2×D313 | semidirect |
| 165. C22⋊C4 | C2×D313 | semidirect |
| 167. C42 | C2×D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756491 | 2 |
| #23756490 | 2 |
| #23756486 | 2 |
| #23756481 | 2 |
| #23756479 | 2 |
| #23756473 | 2 |
| #23756470 | 2 |
| #23756469 | 2 |
| #23756467 | 2 |
| #23756465 | 2 |
| C4×D1252 | 2 |
| #23756457 | 2 |
| C22⋊C4×D313 | 2 |
| #124×C313 | 2 |
| #538 | 313 |