Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
2622 conjugacy classes of subgroups.
The subgroup lattice has 308 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C29 | C23 |
| commutator | C22 | C24×C4×C29 |
| Frattini, cosocle | C23 | C25×C29 |
| socle, prime radical | C24×C29 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C29×#125 | C2 | direct (N × H) |
| 9. C2×C29×#125 | C4 | direct (N × H) |
| 37. C29×#125 | C2×C4 | direct (N × H) |
| 98. C2×C4×#125 | C29 | direct (N × H) |
| 121. C2×C4×C29 | #125 | direct (N × H) |
| 132. C4×#125 | C2×C29 | direct (N × H) |
| 155. C4×C29 | C2×#125 | direct (N × H) |
| 156. C2×#125 | C4×C29 | direct (N × H) |
| 177. C2×C29 | C4×#125 | direct (N × H) |
| 190. #125 | C2×C4×C29 | direct (N × H) |
| 214. C29 | C2×C4×#125 | direct (N × H) |
| 274. C2×C4 | C29×#125 | direct (N × H) |
| 300. C4 | C2×C29×#125 | direct (N × H) |
| 301. C2 | C4×C29×#125 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C29×#125 | 2 |
| C4×C29×#125 | 2 |
| C2×C29×#389 | 2 |
| C2×C29×#387 | 2 |
| C2×C29×#382 | 2 |
| C2×C4×C4⋊C4×C29 | 2 |
| C2×C43×C29 | 2 |
| C2×C4×#125 | 29 |