Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D83 |
| commutator, socle | C2×C83 | C23×C8 |
| Fitting | #504×C83 | C2 |
| prime radical | #41×D83 | C4 |
| cosocle | C8×C83 | C24 |
| hypercenter | #504 | D83 |
| hypocenter | C83 | #3407 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C8 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19128119 | C2 | semidirect |
| 3. #19128118 | C2 | semidirect |
| 4. #19128117 | C2 | semidirect |
| 5. C2×#14581731 | C2 | semidirect |
| 6. M32×D83 | C2 | semidirect |
| 7. #504×C83 | C2 | semidirect |
| 14. #14581732 | C22 | semidirect |
| 17. #14581731 | C22 | semidirect |
| 18. #14581731 | C22 | semidirect |
| 19. C2×C83⋊C16 | C22 | semidirect |
| 20. C16×D83 | C22 | semidirect |
| 22. M32×C83 | C22 | semidirect |
| 23. C2×C16×C83 | C22 | semidirect |
| 73. C83 | #3407 | semidirect |
| 78. #504 | D83 | semidirect |
| 93. M32 | C2×D83 | semidirect |
| 96. C2×C16 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D83 | 2 |
| #19128119 | 2 |
| #19128118 | 2 |
| #19128117 | 2 |
| C2×#14581731 | 2 |
| M32×D83 | 2 |
| #504×C83 | 2 |
| #3407 | 83 |