Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
512 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 192 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C41 |
| prime radical | C22×D4×C41 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#125×C41 | C2 | semidirect |
| 3. C41×#399 | C2 | semidirect |
| 4. C41×#398 | C2 | semidirect |
| 5. C41×#397 | C2 | semidirect |
| 7. C41×#385 | C2 | semidirect |
| 8. C41×#383 | C2 | semidirect |
| 89. #2633 | C41 | direct (N × H) |
| 95. C2×#125 | C2×C41 | semidirect |
| 97. #399 | C2×C41 | semidirect |
| 98. #398 | C2×C41 | semidirect |
| 99. #397 | C2×C41 | semidirect |
| 101. #385 | C2×C41 | semidirect |
| 102. #383 | C2×C41 | semidirect |
| 103. C41 | #2633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#125×C41 | 2 |
| C2×C4×D4×C41 | 2 |
| C41×#399 | 2 |
| C41×#398 | 2 |
| C41×#397 | 2 |
| C41×#394 | 2 |
| C41×#385 | 2 |
| C41×#383 | 2 |
| #2633 | 41 |