Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
548 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | #120 |
| commutator | C23 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| socle | C2×C41 | #379 |
| prime radical | C41×#585 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C22×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#413 | C2 | semidirect |
| 3. C41×#408 | C2 | semidirect |
| 9. C2×M16×C41 | C22 | semidirect |
| 10. C22×C8×C41 | C22 | semidirect |
| 55. #1791 | C41 | direct (N × H) |
| 60. #413 | C2×C41 | semidirect |
| 61. #408 | C2×C41 | semidirect |
| 62. C41 | #1791 | direct (N × H) |
| 68. C2×M16 | C22×C41 | semidirect |
| 69. C22×C8 | C22×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#585 | 2 |
| C41×#413 | 2 |
| C41×#408 | 2 |
| #1791 | 41 |