Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
216 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C79 | #121 |
| commutator | C2×C4 | C22×C4×C79 |
| Frattini, cosocle | C22×C4 | C23×C79 |
| socle | C2×C79 | #388 |
| prime radical | C2×#41×C79 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C79 ◁ C22×C4×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #430×C79 | C2 | semidirect |
| 5. C4×M16×C79 | C2 | semidirect |
| 6. #344×C79 | C2 | semidirect |
| 7. #339×C79 | C2 | semidirect |
| 19. #101×C79 | C4 | semidirect |
| 20. #100×C79 | C4 | semidirect |
| 95. #1932 | C79 | direct (N × H) |
| 96. C79 | #1932 | direct (N × H) |
| 97. #430 | C2×C79 | semidirect |
| 101. C4×M16 | C2×C79 | semidirect |
| 102. #344 | C2×C79 | semidirect |
| 103. #339 | C2×C79 | semidirect |
| 115. #101 | C4×C79 | semidirect |
| 116. #100 | C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #430×C79 | 2 |
| #421×C79 | 2 |
| C2×#104×C79 | 2 |
| #413×C79 | 2 |
| C4×M16×C79 | 2 |
| #344×C79 | 2 |
| #339×C79 | 2 |
| #1932 | 79 |