Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
1068 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1068 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 | C23 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | #379×C79 | C2 |
| prime radical | C25×C79 | C22 |
| hypercenter | #379 | D79 |
| hypocenter | C79 | #2848 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14579138 | C2 | semidirect |
| 3. #19098438 | C2 | semidirect |
| 4. #19098435 | C2 | semidirect |
| 5. #19098421 | C2 | semidirect |
| 8. C22×Dic158 | C22 | semidirect |
| 13. C2×C4⋊Dic79 | C22 | semidirect |
| 14. C2×Dic79⋊C4 | C22 | semidirect |
| 15. C2×Dic79⋊C4 | C22 | semidirect |
| 18. C79⋊#95 | C22 | semidirect |
| 39. C24×C79 | Q8 | semidirect |
| 71. C22×C79 | C22⋊Q8 | semidirect |
| 86. C79 | #2848 | semidirect |
| 110. C24 | Dic158 | semidirect |
| 157. C22 | #14579138 | semidirect |