Finite Group DatabasebetaFinite Group DatabasebetaOrder 10048.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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 | C23×D157 |
| commutator, socle, cosocle | C22×C157 | C24 |
| Fitting | C22⋊Q8×C157 | C2 |
| hypercenter | C22⋊Q8 | D157 |
| hypocenter | C157 | #525 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14578955 | C2 | semidirect |
| 2. C22×C4×D157 | C2 | semidirect |
| 3. #19097756 | C2 | semidirect |
| 4. #19097747 | C2 | semidirect |
| 5. #19097746 | C2 | semidirect |
| 6. #19097745 | C2 | semidirect |
| 7. #19097741 | C2 | semidirect |
| 8. #19097733 | C2 | semidirect |
| 9. #19097731 | C2 | semidirect |
| 10. #19097729 | C2 | semidirect |
| 11. C22⋊Q8×C157 | C2 | semidirect |
| 16. C2×D628 | C22 | semidirect |
| 24. C2×C4×D157 | C22 | semidirect |
| 25. C4⋊Dic157 | C22 | semidirect |
| 26. #14578933 | C22 | semidirect |
| 29. #14578931 | C22 | semidirect |
| 30. #14578931 | C22 | semidirect |
| 31. C4×Dic157 | C22 | semidirect |
| 32. C2×Q8×C157 | C22 | semidirect |
| 34. C4⋊C4×C157 | C22 | semidirect |
| 35. C4⋊C4×C157 | C22 | semidirect |
| 55. C4×D157 | D4 | semidirect |
| 65. C22×C157 | #41 | semidirect |
| 76. C2×D157 | #41 | semidirect |
| 91. C157 | #525 | semidirect |
| 97. C22⋊Q8 | D157 | semidirect |
| 106. C2×Q8 | C2×D157 | semidirect |
| 121. C4⋊C4 | C2×D157 | semidirect |
| 122. C4⋊C4 | C2×D157 | semidirect |
| 167. C22 | #14578955 | semidirect |