Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | C4×#41×C79 | C2 |
| prime radical | C2×#41×C79 | C22 |
| hypercenter | C4×#41 | D79 |
| hypocenter | C79 | #3504 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19099289 | C2 | semidirect |
| 2. #19099272 | C2 | semidirect |
| 3. #19099191 | C2 | semidirect |
| 4. #19099120 | C2 | semidirect |
| 5. C2×#14579153 | C2 | semidirect |
| 39. #41×C79 | Q8 | semidirect |
| 75. C79 | #3504 | semidirect |
| 103. #41 | Dic158 | semidirect |