Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
142 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #1402 |
| commutator | C4⋊Q8 | C2×C4×C29 |
| Frattini, cosocle | #494 | C22×C29 |
| prime radical | C22×C29 | AΣL(1,𝔽16) |
| LCS | G ▷ C4⋊Q8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C29 ◁ C2×C4×C29 ◁ C42×C29 ◁ C29×#494 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 42. #7522 | C29 | direct (N × H) |
| 91. C29 | #7522 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1633 | 2 |
| C29×#1411 | 2 |
| C29×#1358 | 2 |
| #7522 | 29 |