Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Frattini | C22 | C23×D47 |
| Fitting | C4×D4×C47 | C2 |
| hypercenter | C4×D4 | D47 |
| hypocenter | C47 | #525 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625350 | C2 | semidirect |
| 2. C22×C4×D47 | C2 | semidirect |
| 3. #13094009 | C2 | semidirect |
| 4. #13094006 | C2 | semidirect |
| 5. #13094002 | C2 | semidirect |
| 6. #13094001 | C2 | semidirect |
| 7. #13093997 | C2 | semidirect |
| 8. #13093996 | C2 | semidirect |
| 9. #13093994 | C2 | semidirect |
| 10. #13093992 | C2 | semidirect |
| 11. C4×D188 | C2 | semidirect |
| 12. C4×C22⋊D47 | C2 | semidirect |
| 13. C4×C22⋊D47 | C2 | semidirect |
| 14. #13093981 | C2 | semidirect |
| 15. C4×D4×C47 | C2 | semidirect |
| 19. C22×C4×C47 | C22 | semidirect |
| 23. C2×C22⋊D47 | C22 | semidirect |
| 33. C2×C4×D47 | C22 | semidirect |
| 34. C2×Dic94 | C22 | semidirect |
| 35. C4⋊C4×C47 | C22 | semidirect |
| 37. C22⋊C4×C47 | C22 | semidirect |
| 38. C42×C47 | C22 | semidirect |
| 40. C22⋊Dic47 | C22 | semidirect |
| 45. (C2×D47)⋊C4 | C22 | semidirect |
| 46. (C2×D47)⋊C4 | C22 | semidirect |
| 47. C4⋊Dic47 | C22 | semidirect |
| 48. Dic47⋊C4 | C22 | semidirect |
| 49. Dic47⋊C4 | C22 | semidirect |
| 50. Dic47⋊C4 | C22 | semidirect |
| 51. Dic47⋊C4 | C22 | semidirect |
| 52. C4×Dic47 | C22 | semidirect |
| 85. C4×D47 | D4 | semidirect |
| 92. C22×C47 | #41 | semidirect |
| 103. C2×D47 | #41 | semidirect |
| 123. C47 | #525 | semidirect |
| 137. C4×D4 | D47 | semidirect |
| 157. C22×C4 | C2×D47 | semidirect |
| 163. C4⋊C4 | C2×D47 | semidirect |
| 173. C22⋊C4 | C2×D47 | semidirect |
| 175. C42 | C2×D47 | semidirect |
| 225. C22 | #10625350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625350 | 2 |
| C22×C4×D47 | 2 |
| #13094009 | 2 |
| #13094006 | 2 |
| #13094002 | 2 |
| #13094001 | 2 |
| #13093997 | 2 |
| #13093996 | 2 |
| #13093994 | 2 |
| #13093992 | 2 |
| C4×D188 | 2 |
| C4×C22⋊D47 | 2 |
| #13093981 | 2 |
| C4×D4×C47 | 2 |
| #525 | 47 |