Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
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×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Fitting | C22⋊Q8×C47 | C2 |
| prime radical | #13093994 | C2 |
| hypercenter | C22⋊Q8 | D47 |
| hypocenter | C47 | #551 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13094019 | C2 | semidirect |
| 2. #13094019 | C2 | semidirect |
| 3. #13094013 | C2 | semidirect |
| 4. #13094009 | C2 | semidirect |
| 5. #13094009 | C2 | semidirect |
| 6. #13094008 | C2 | semidirect |
| 7. #13094000 | C2 | semidirect |
| 9. #13093986 | C2 | semidirect |
| 10. C4×C22⋊D47 | C2 | semidirect |
| 11. #13093982 | C2 | semidirect |
| 12. #13093980 | C2 | semidirect |
| 13. C2×(C2×D47)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D47 | C2 | semidirect |
| 15. C22⋊Q8×C47 | C2 | semidirect |
| 17. C2×Q8×C47 | C22 | semidirect |
| 25. C2×C4×D47 | C22 | semidirect |
| 26. C4⋊C4×C47 | C22 | semidirect |
| 27. C4⋊C4×C47 | C22 | semidirect |
| 28. C4⋊C4×C47 | C22 | semidirect |
| 40. (C2×D47)⋊C4 | C22 | semidirect |
| 41. (C2×D47)⋊C4 | C22 | semidirect |
| 42. (C2×D47)⋊C4 | C22 | semidirect |
| 43. C4⋊Dic47 | C22 | semidirect |
| 44. C4⋊Dic47 | C22 | semidirect |
| 45. Dic47⋊C4 | C22 | semidirect |
| 46. Dic47⋊C4 | C22 | semidirect |
| 47. Dic47⋊C4 | C22 | semidirect |
| 48. C4×Dic47 | C22 | semidirect |
| 49. C4×Dic47 | C22 | semidirect |
| 50. C4×Dic47 | C22 | semidirect |
| 111. C47 | #551 | semidirect |
| 119. C22⋊Q8 | D47 | semidirect |
| 128. C2×Q8 | C2×D47 | semidirect |
| 142. C4⋊C4 | C2×D47 | semidirect |
| 143. C4⋊C4 | C2×D47 | semidirect |
| 144. C4⋊C4 | C2×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094019 | 2 |
| #13094013 | 2 |
| #13094009 | 2 |
| #13094008 | 2 |
| #13094000 | 2 |
| #13093994 | 2 |
| #13093986 | 2 |
| C4×C22⋊D47 | 2 |
| #13093982 | 2 |
| #13093980 | 2 |
| C2×(C2×D47)⋊C4 | 2 |
| C22⋊C4×D47 | 2 |
| C22⋊Q8×C47 | 2 |
| #551 | 47 |