Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
952 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C4×C22⋊C4×C79 | C2 |
| hypercenter | C4×C22⋊C4 | D79 |
| hypocenter | C79 | #2431 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11929624 | C2 | semidirect |
| 2. C2×#14579158 | C2 | semidirect |
| 3. C2×#14579149 | C2 | semidirect |
| 4. C2×#14579135 | C2 | semidirect |
| 5. #19098472 | C2 | semidirect |
| 6. #19098469 | C2 | semidirect |
| 7. #19098465 | C2 | semidirect |
| 8. #19098441 | C2 | semidirect |
| 9. C4×C22⋊C4×C79 | C2 | semidirect |
| 38. C2×Dic158 | D4 | semidirect |
| 47. C2×D316 | D4 | semidirect |
| 65. C22×C4×C79 | D4 | semidirect |
| 101. C2×C4×C79 | #41 | semidirect |
| 149. C79 | #2431 | semidirect |
| 158. C4×C22⋊C4 | D79 | semidirect |
| 210. C22×C4 | D316 | semidirect |
| 262. C2×C4 | #11929624 | semidirect |