Finite Group DatabasebetaFinite Group DatabasebetaOrder 8400.
496 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72218916 |
| commutator, hypocenter | C52×C7 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C7 | C2×C3×C4 |
| prime radical | C2×(C5⋊AGL(1,𝔽7))⋊D5 | C2 |
| cosocle | C7×C5⋊D5 | C23×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C5⋊AGL(1,𝔽7))⋊D5 | 2 |
| C2×ΓL(1,𝔽8)×#1044 | 2 |
| C2×#13063833 | 3 |
| C2×ΓL(1,𝔽8)⋊#1043 | 2 |
| #72218916 | 2 |
| C2×AGL(1,𝔽5)×AGL(1,𝔽7) | 5 |
| C2×C3×D5⋊AGL(1,𝔽5) | 7 |