Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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 | C2×C42×C7 | C2 |
| prime radical | #6493 | C2 |
| hypercenter | C2×C42 | D7 |
| hypocenter | C7 | #529 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C42×C7 | C2 | semidirect |
| 3. #6492 | C2 | semidirect |
| 4. C4×C22⋊D7 | C2 | semidirect |
| 5. #6487 | C2 | semidirect |
| 6. #6439 | C2 | semidirect |
| 7. #6438 | C2 | semidirect |
| 8. C4×D28 | C2 | semidirect |
| 9. #6435 | C2 | semidirect |
| 10. #6433 | C2 | semidirect |
| 11. C4×Dic14 | C2 | semidirect |
| 64. C2×C42 | D7 | semidirect |
| 127. C7 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×C7 | 2 |
| #6493 | 2 |
| #6492 | 2 |
| C4×C22⋊D7 | 2 |
| #6487 | 2 |
| #6439 | 2 |
| #6438 | 2 |
| C4×D28 | 2 |
| #6435 | 2 |
| #6433 | 2 |
| C4×Dic14 | 2 |
| #529 | 7 |