Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 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 | H(3,𝔽4)×C79 | C2 |
| hypercenter | H(3,𝔽4) | D79 |
| hypocenter | C79 | #3568 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19099313 | C2 | semidirect |
| 2. #19099282 | C2 | semidirect |
| 3. #19099244 | C2 | semidirect |
| 4. #19099177 | C2 | semidirect |
| 5. #19099148 | C2 | semidirect |
| 6. #19099092 | C2 | semidirect |
| 7. H(3,𝔽4)×C79 | C2 | semidirect |
| 8. #14579159 | C22 | semidirect |
| 9. #14579155 | C22 | semidirect |
| 10. #14579154 | C22 | semidirect |
| 11. #14579154 | C22 | semidirect |
| 12. #14579154 | C22 | semidirect |
| 13. #14579154 | C22 | semidirect |
| 14. #14579153 | C22 | semidirect |
| 16. #14579147 | C22 | semidirect |
| 17. #14579143 | C22 | semidirect |
| 20. #14579138 | C22 | semidirect |
| 21. #14579138 | C22 | semidirect |
| 22. #14579138 | C22 | semidirect |
| 23. #14579137 | C22 | semidirect |
| 26. #14579130 | C22 | semidirect |
| 27. Q8×Dic79 | C22 | semidirect |
| 28. C4×Dic158 | C22 | semidirect |
| 31. (C22⋊D79)⋊C4 | C22 | semidirect |
| 32. #14579117 | C22 | semidirect |
| 33. #14579117 | C22 | semidirect |
| 34. C2×C22⋊Dic79 | C22 | semidirect |
| 35. C42×D79 | C22 | semidirect |
| 101. C79 | #3568 | semidirect |
| 103. H(3,𝔽4) | D79 | semidirect |