Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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×D7 |
| commutator, socle, cosocle | C22×C7 | C24 |
| Frattini | C22 | C23×D7 |
| Fitting | C4×C7×D4 | C2 |
| prime radical | #6502 | C2 |
| hypercenter | C4×D4 | D7 |
| hypocenter | C7 | #529 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C7×D4 | C2 | semidirect |
| 3. #6498 | C2 | semidirect |
| 4. C4×C22⋊D7 | C2 | semidirect |
| 5. C4×C22⋊D7 | C2 | semidirect |
| 6. #6489 | C2 | semidirect |
| 7. C2×C4×Dic7 | C2 | semidirect |
| 8. #6461 | C2 | semidirect |
| 9. #6452 | C2 | semidirect |
| 10. #6449 | C2 | semidirect |
| 11. #6448 | C2 | semidirect |
| 12. #6442 | C2 | semidirect |
| 13. #6441 | C2 | semidirect |
| 14. #6435 | C2 | semidirect |
| 15. C4×Dic14 | C2 | semidirect |
| 87. C4×D4 | D7 | semidirect |
| 178. C7 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×D4 | 2 |
| #6502 | 2 |
| #6498 | 2 |
| C4×C22⋊D7 | 2 |
| #6489 | 2 |
| C2×C4×Dic7 | 2 |
| #6461 | 2 |
| #6452 | 2 |
| #6449 | 2 |
| #6448 | 2 |
| #6442 | 2 |
| #6441 | 2 |
| #6435 | 2 |
| C4×Dic14 | 2 |
| #529 | 7 |