Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
310 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 115 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×C7×#41 | C2 |
| hypercenter | C2×#41 | D7 |
| hypocenter | C7 | #532 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#41 | C2 | semidirect |
| 2. C2×#1157 | C2 | semidirect |
| 3. #6510 | C2 | semidirect |
| 4. #6507 | C2 | semidirect |
| 5. #6503 | C2 | semidirect |
| 6. #6502 | C2 | semidirect |
| 7. #6499 | C2 | semidirect |
| 8. C4×C22⋊D7 | C2 | semidirect |
| 9. C2×C4×Dic7 | C2 | semidirect |
| 37. C2×C4×C7 | D4 | semidirect |
| 51. C2×#41 | D7 | semidirect |
| 71. Dic7 | #41 | semidirect |
| 112. C2×C4 | C22⋊D7 | semidirect |
| 116. C7 | #532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41 | 2 |
| C2×#1157 | 2 |
| #6510 | 2 |
| #6507 | 2 |
| #6503 | 2 |
| #6502 | 2 |
| #6499 | 2 |
| C4×C22⋊D7 | 2 |
| C2×C4×Dic7 | 2 |
| #532 | 7 |