Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D83 |
| commutator, cosocle | C16×C83 | C23 |
| Frattini | C16 | C22×D83 |
| Fitting | D32×C83 | C2 |
| socle | C2×C83 | C2×D16 |
| hypercenter | D32 | D83 |
| hypocenter | C83 | #2263 |
| LCS | G ▷ C16×C83 ▷ C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19128130 | C2 | semidirect |
| 2. D16×D83 | C2 | semidirect |
| 3. #19127540 | C2 | semidirect |
| 4. #19127539 | C2 | semidirect |
| 5. #19127536 | C2 | semidirect |
| 6. #19127534 | C2 | semidirect |
| 7. D32×C83 | C2 | semidirect |
| 10. Dic664 | C22 | semidirect |
| 15. C83⋊C32 | C22 | semidirect |
| 17. D16×C83 | C22 | semidirect |
| 18. C32×C83 | C22 | semidirect |
| 55. C83 | #2263 | semidirect |
| 61. D32 | D83 | semidirect |
| 70. D16 | C2×D83 | semidirect |
| 73. C32 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128130 | 2 |
| D16×D83 | 2 |
| #19127540 | 2 |
| #19127539 | 2 |
| #19127536 | 2 |
| #19127534 | 2 |
| D32×C83 | 2 |
| #2263 | 83 |