Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
144 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 144 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 | C8×C41 | C2×D4 |
| commutator | C4 | C22×C8×C41 |
| Frattini, cosocle | C2×C8 | C23×C41 |
| socle | C2×C41 | C8×D4 |
| prime radical | #135×C41 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C41 ◁ C2×C16×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#504 | C2 | semidirect |
| 3. C41×#364 | C2 | semidirect |
| 4. C41×#350 | C2 | semidirect |
| 5. C41×#346 | C2 | semidirect |
| 46. #2171 | C41 | direct (N × H) |
| 50. #504 | C2×C41 | semidirect |
| 52. #364 | C2×C41 | semidirect |
| 53. #350 | C2×C41 | semidirect |
| 54. #346 | C2×C41 | semidirect |
| 55. C41 | #2171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#504 | 2 |
| C41×#443 | 2 |
| C41×#364 | 2 |
| C41×#350 | 2 |
| C41×#346 | 2 |
| #2171 | 41 |