Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
456 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C22⋊C4 |
| commutator | C22 | C22×C8×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C25×C41 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C8×C41 | C2 | semidirect |
| 3. C41×#323 | C2 | direct (N × H) |
| 13. C22⋊C8×C41 | C22 | semidirect |
| 19. C24×C41 | C8 | semidirect |
| 52. C23×C41 | C2×C8 | semidirect |
| 89. C2×#323 | C41 | direct (N × H) |
| 94. C2×C41 | #323 | direct (N × H) |
| 99. C2×C22⋊C8 | C2×C41 | semidirect |
| 100. #323 | C2×C41 | direct (N × H) |
| 101. C41 | C2×#323 | direct (N × H) |
| 111. C22⋊C8 | C22×C41 | semidirect |
| 117. C24 | C8×C41 | semidirect |
| 150. C23 | C2×C8×C41 | semidirect |
| 191. C2 | C41×#323 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C4×C41 | 2 |
| C2×C22⋊C8×C41 | 2 |
| C41×#323 | 2 |
| C2×#323 | 41 |