Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
114 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D7 |
| commutator, socle | C22×C7 | C22×C4 |
| Fitting | C7×C4⋊C8 | C2 |
| prime radical | C22×D7 | C2×C4 |
| cosocle | C2×C4×C7 | C23 |
| hypercenter | C4⋊C8 | D7 |
| hypocenter | C7 | #424 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C7×C4⋊C8 | C2 | semidirect |
| 5. Dic7⋊C8 | C2 | semidirect |
| 6. Dic7⋊C8 | C2 | semidirect |
| 7. C4⋊(C7⋊C8) | C2 | semidirect |
| 41. C4⋊C8 | D7 | semidirect |
| 83. C7 | #424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1131 | 2 |
| C2×C8×D7 | 2 |
| #6435 | 2 |
| C7×C4⋊C8 | 2 |
| Dic7⋊C8 | 2 |
| C4⋊(C7⋊C8) | 2 |
| #424 | 7 |