Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
356 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C41 |
| socle | C22×C41 | C22×D4 |
| prime radical | C23×C41 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#500 | C2 | semidirect |
| 3. C41×#499 | C2 | semidirect |
| 4. C41×#498 | C2 | semidirect |
| 22. C2×C8×C41 | Q8 | semidirect |
| 52. #3160 | C41 | direct (N × H) |
| 57. #500 | C2×C41 | semidirect |
| 58. #499 | C2×C41 | semidirect |
| 59. #498 | C2×C41 | semidirect |
| 62. C41 | #3160 | direct (N × H) |
| 78. C2×C8 | Q8×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#533 | 2 |
| C41×#500 | 2 |
| C41×#499 | 2 |
| C41×#498 | 2 |
| C41×#427 | 2 |
| C2×C4×C8×C41 | 2 |
| #3160 | 41 |