Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
310 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C42×C7 | C22 |
| commutator | C2 | C23×C4×C7 |
| Frattini, cosocle | C22 | C24×C7 |
| socle | C22×C7 | C24 |
| prime radical | C2×C7×#41 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C7×Q8 | C2 | semidirect |
| 3. C4×C7×D4 | C2 | semidirect |
| 4. C7×#117 | C2 | semidirect |
| 5. C2×C42×C7 | C2 | semidirect |
| 6. C7×#41 | C4 | direct (N × H) |
| 16. C4×#41 | C7 | direct (N × H) |
| 18. C7×Q8 | C2×C4 | semidirect |
| 19. C7×D4 | C2×C4 | semidirect |
| 21. C2×C4×C7 | C2×C4 | semidirect |
| 27. C4×Q8 | C2×C7 | semidirect |
| 28. C4×D4 | C2×C7 | semidirect |
| 29. #117 | C2×C7 | semidirect |
| 30. C2×C42 | C2×C7 | semidirect |
| 37. C4×C7 | #41 | direct (N × H) |
| 38. #41 | C4×C7 | direct (N × H) |
| 52. Q8 | C2×C4×C7 | semidirect |
| 53. D4 | C2×C4×C7 | semidirect |
| 55. C2×C4 | C2×C4×C7 | semidirect |
| 60. C7 | C4×#41 | direct (N × H) |
| 67. C4 | C7×#41 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41 | 2 |
| C4×C7×Q8 | 2 |
| C4×C7×D4 | 2 |
| C7×#117 | 2 |
| C2×C42×C7 | 2 |
| C4×#41 | 7 |