Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D101 |
| commutator, socle, cosocle | C23×C101 | C24 |
| Fitting | #379×C101 | C2 |
| prime radical | C2×#15692224 | C2 |
| hypercenter | #379 | D101 |
| hypocenter | C101 | #2849 |
| LCS | G ▷ C23×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic101 | C2 | semidirect |
| 2. C2×#15692239 | C2 | semidirect |
| 4. #20265054 | C2 | semidirect |
| 5. #20265052 | C2 | semidirect |
| 6. #20265038 | C2 | semidirect |
| 7. #379×C101 | C2 | semidirect |
| 16. C2×C4⋊Dic101 | C22 | semidirect |
| 19. C2×#13108051 | C22 | semidirect |
| 20. #15692162 | C22 | semidirect |
| 34. C22×Dic101 | D4 | semidirect |
| 84. C22×C101 | #123 | semidirect |
| 102. C101 | #2849 | semidirect |
| 109. #379 | D101 | semidirect |
| 189. C22 | #15692239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic101 | 2 |
| C2×#15692239 | 2 |
| C2×#15692224 | 2 |
| #20265054 | 2 |
| #20265052 | 2 |
| #20265038 | 2 |
| #379×C101 | 2 |
| #2849 | 101 |