Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
160 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 100 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 | C4 | C22×C8×C41 |
| Frattini, cosocle | C42 | C23×C41 |
| socle, prime radical | C22×C41 | C4×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ C4×C8×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 17. Q16×C41 | C8 | semidirect |
| 46. #1579 | C41 | direct (N × H) |
| 55. C41 | #1579 | direct (N × H) |
| 67. Q16 | C8×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×C41 | 2 |
| C4×Q16×C41 | 2 |
| C41×#334 | 2 |
| C41×Q8⋊C8 | 2 |
| C41×#322 | 2 |
| #1579 | 41 |