Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
304 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #386 |
| commutator | C2×C4 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C2×#41×C41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C22×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C41×#419 | C2 | semidirect |
| 5. C2×#101×C41 | C2 | semidirect |
| 6. C41×#344 | C2 | semidirect |
| 7. C41×#338 | C2 | semidirect |
| 12. C2×Q16×C41 | C4 | semidirect |
| 13. C2×SD16×C41 | C4 | semidirect |
| 102. #1902 | C41 | direct (N × H) |
| 111. #419 | C2×C41 | semidirect |
| 112. C2×#101 | C2×C41 | semidirect |
| 113. #344 | C2×C41 | semidirect |
| 114. #338 | C2×C41 | semidirect |
| 115. C41 | #1902 | direct (N × H) |
| 120. C2×Q16 | C4×C41 | semidirect |
| 121. C2×SD16 | C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#137×C41 | 2 |
| C41×#568 | 2 |
| C41×#421 | 2 |
| C41×#419 | 2 |
| C2×#101×C41 | 2 |
| C41×#344 | 2 |
| C41×#338 | 2 |
| #1902 | 41 |