Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
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×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Fitting | C4×D4×C23 | C2 |
| prime radical | #10625108 | C2 |
| hypercenter | C4×D4 | D23 |
| hypocenter | C23 | #551 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×D4×C23 | C2 | semidirect |
| 3. #10625106 | C2 | semidirect |
| 4. #10625100 | C2 | semidirect |
| 5. C4×C22⋊D23 | C2 | semidirect |
| 6. C2×(C2×D23)⋊C4 | C2 | semidirect |
| 7. #10625095 | C2 | semidirect |
| 8. #10625069 | C2 | semidirect |
| 9. #10625067 | C2 | semidirect |
| 10. #10625056 | C2 | semidirect |
| 11. #10625054 | C2 | semidirect |
| 12. C22⋊C4×D23 | C2 | semidirect |
| 13. #10625048 | C2 | semidirect |
| 14. #10625047 | C2 | semidirect |
| 15. #10625043 | C2 | semidirect |
| 19. C22×C4×C23 | C22 | semidirect |
| 25. C2×Dic46 | C22 | semidirect |
| 26. C4⋊C4×C23 | C22 | semidirect |
| 28. C22⋊C4×C23 | C22 | semidirect |
| 29. C42×C23 | C22 | semidirect |
| 32. C22⋊Dic23 | C22 | semidirect |
| 33. C22⋊Dic23 | C22 | semidirect |
| 42. C4⋊Dic23 | C22 | semidirect |
| 43. Dic23⋊C4 | C22 | semidirect |
| 44. Dic23⋊C4 | C22 | semidirect |
| 45. Dic23⋊C4 | C22 | semidirect |
| 46. Dic23⋊C4 | C22 | semidirect |
| 47. Dic23⋊C4 | C22 | semidirect |
| 48. Dic23⋊C4 | C22 | semidirect |
| 49. C4×Dic23 | C22 | semidirect |
| 50. C4×Dic23 | C22 | semidirect |
| 121. C4×D4 | D23 | semidirect |
| 126. C23 | #551 | semidirect |
| 136. C22×C4 | C2×D23 | semidirect |
| 144. C4⋊C4 | C2×D23 | semidirect |
| 158. C22⋊C4 | C2×D23 | semidirect |
| 161. C42 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C23 | 2 |
| #10625108 | 2 |
| #10625106 | 2 |
| #10625100 | 2 |
| C4×C22⋊D23 | 2 |
| C2×(C2×D23)⋊C4 | 2 |
| #10625095 | 2 |
| #10625069 | 2 |
| #10625067 | 2 |
| #10625056 | 2 |
| #10625054 | 2 |
| C22⋊C4×D23 | 2 |
| #10625048 | 2 |
| #10625047 | 2 |
| #10625043 | 2 |
| #551 | 23 |