Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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 | C2×C23 | C23×C4 |
| Fitting | C4×D4×C23 | C2 |
| socle, cosocle | C22×C23 | C24 |
| prime radical | C2×D4×D23 | C2 |
| hypercenter | C4×D4 | D23 |
| hypocenter | C23 | #518 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×D4×C23 | C2 | semidirect |
| 3. D4×Dic23 | C2 | semidirect |
| 4. C4×C22⋊D23 | C2 | semidirect |
| 5. C2×(C2×D23)⋊C4 | C2 | semidirect |
| 6. #10625064 | C2 | semidirect |
| 7. #10625063 | C2 | semidirect |
| 8. (C22⋊D23)⋊C4 | C2 | semidirect |
| 9. C22⋊C4×D23 | C2 | semidirect |
| 10. C4×D92 | C2 | semidirect |
| 11. #10625043 | C2 | semidirect |
| 14. C22×C4×C23 | C22 | semidirect |
| 16. C22×Dic23 | C22 | semidirect |
| 17. D4×D23 | C4 | semidirect |
| 20. C2×C4×D23 | C22 | semidirect |
| 21. C2×C4×D23 | C22 | semidirect |
| 22. C4⋊C4×C23 | C22 | semidirect |
| 23. C22⋊C4×C23 | C22 | semidirect |
| 24. C42×C23 | C22 | semidirect |
| 25. C22⋊Dic23 | C22 | semidirect |
| 29. (C2×D23)⋊C4 | C22 | semidirect |
| 30. (C2×D23)⋊C4 | C22 | semidirect |
| 31. C4⋊Dic23 | C22 | semidirect |
| 32. Dic23⋊C4 | C22 | semidirect |
| 33. Dic23⋊C4 | C22 | semidirect |
| 34. C4×Dic23 | C22 | semidirect |
| 35. C4×Dic23 | C22 | semidirect |
| 39. C22×D23 | C2×C4 | semidirect |
| 42. D4×C23 | C2×C4 | semidirect |
| 48. C22⋊D23 | C2×C4 | semidirect |
| 54. D92 | C2×C4 | semidirect |
| 57. C4×D23 | C2×C4 | semidirect |
| 90. C4×D4 | D23 | semidirect |
| 95. C23 | #518 | semidirect |
| 105. C22×C4 | C2×D23 | semidirect |
| 109. C4⋊C4 | C2×D23 | semidirect |
| 116. C22⋊C4 | C2×D23 | semidirect |
| 119. C42 | C2×D23 | semidirect |
| 128. D4 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D23 | 2 |
| C4×D4×C23 | 2 |
| D4×Dic23 | 2 |
| C4×C22⋊D23 | 2 |
| C2×(C2×D23)⋊C4 | 2 |
| #10625064 | 2 |
| #10625063 | 2 |
| (C22⋊D23)⋊C4 | 2 |
| C22⋊C4×D23 | 2 |
| C4×D92 | 2 |
| #10625043 | 2 |
| #518 | 23 |