Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
466 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | #120 |
| commutator, Frattini, cosocle | C24 | C23×C41 |
| prime radical | C25×C41 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C24×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#543 | C2 | semidirect |
| 3. C41×#342 | C2 | semidirect |
| 12. C24×C41 | Q8 | semidirect |
| 50. #2029 | C41 | direct (N × H) |
| 56. #543 | C2×C41 | semidirect |
| 58. #342 | C2×C41 | semidirect |
| 59. C41 | #2029 | direct (N × H) |
| 68. C24 | Q8×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#543 | 2 |
| C41×#379 | 2 |
| C41×#342 | 2 |
| #2029 | 41 |