Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
1258 conjugacy classes of subgroups; only the 455 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 455 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 | #3549 |
| 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. #19099305 | C2 | semidirect |
| 2. #19099275 | C2 | semidirect |
| 3. #19099195 | C2 | semidirect |
| 4. #19099131 | C2 | semidirect |
| 5. #19099128 | C2 | semidirect |
| 6. #19099112 | C2 | semidirect |
| 7. H(3,𝔽4)×C79 | C2 | semidirect |
| 8. C2×#11929625 | C22 | semidirect |
| 9. C2×#11929623 | C22 | semidirect |
| 10. C22×C22⋊D79 | C22 | semidirect |
| 11. C2×D4×D79 | C22 | semidirect |
| 12. #14579159 | C22 | semidirect |
| 13. #14579158 | C22 | semidirect |
| 15. #14579157 | C22 | semidirect |
| 16. #14579150 | C22 | semidirect |
| 17. #14579149 | C22 | semidirect |
| 18. #14579147 | C22 | semidirect |
| 19. #14579134 | C22 | semidirect |
| 20. #14579134 | C22 | semidirect |
| 21. #14579133 | C22 | semidirect |
| 22. #14579131 | C22 | semidirect |
| 23. #14579131 | C22 | semidirect |
| 24. #14579130 | C22 | semidirect |
| 25. #14579129 | C22 | semidirect |
| 26. (C22⋊D79)⋊C4 | C22 | semidirect |
| 27. #14579118 | C22 | semidirect |
| 28. #14579117 | C22 | semidirect |
| 29. C42×D79 | C22 | semidirect |
| 30. #124×C79 | C22 | semidirect |
| 31. #124×C79 | C22 | semidirect |
| 32. #120×C79 | C22 | semidirect |
| 102. C79 | #3549 | semidirect |
| 104. H(3,𝔽4) | D79 | semidirect |
| 121. #124 | C2×D79 | semidirect |
| 122. #124 | C2×D79 | semidirect |
| 130. #120 | C2×D79 | semidirect |