Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D39 |
| commutator, socle, cosocle | C2×C3×C13 | C24 |
| Frattini | C2 | C23×D39 |
| Fitting | C3×C13×#41 | C2 |
| hypercenter | #41 | D39 |
| hypocenter | C3×C13 | C2×#41 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C13×#41 | C2 | semidirect |
| 2. #10597794 | C2 | semidirect |
| 3. Q8×D39 | C2 | semidirect |
| 4. #10597792 | C2 | semidirect |
| 5. D4×D39 | C2 | semidirect |
| 6. #10597790 | C2 | semidirect |
| 7. C2×C4×D39 | C2 | semidirect |
| 10. C3×Q8×C13 | C22 | semidirect |
| 11. C3×D4×C13 | C22 | semidirect |
| 12. C2×C3×C4×C13 | C22 | semidirect |
| 13. #64625 | C22 | semidirect |
| 14. C2×Dic39 | C22 | semidirect |
| 15. D156 | C22 | semidirect |
| 18. C4×D39 | C22 | semidirect |
| 19. C4×D39 | C22 | semidirect |
| 20. Dic78 | C22 | semidirect |
| 21. C13×#41 | D3 | semidirect |
| 37. Q8×C13 | C2×D3 | semidirect |
| 38. D4×C13 | C2×D3 | semidirect |
| 39. C2×C4×C13 | C2×D3 | semidirect |
| 52. D39 | #41 | direct (N × H) |
| 61. C3×#41 | D13 | semidirect |
| 68. C3×C13 | C2×#41 | semidirect |
| 75. C3×Q8 | C2×D13 | semidirect |
| 76. C3×D4 | C2×D13 | semidirect |
| 77. C2×C3×C4 | C2×D13 | semidirect |
| 89. #41 | D39 | direct (N × H) |
| 93. C13 | D3×#41 | semidirect |
| 104. Q8 | C2×D39 | semidirect |
| 107. D4 | C2×D39 | semidirect |
| 113. C2×C4 | C2×D39 | semidirect |
| 126. C3 | #41×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C13×#41 | 2 |
| #10597794 | 2 |
| Q8×D39 | 2 |
| #10597792 | 2 |
| D4×D39 | 2 |
| #10597790 | 2 |
| C2×C4×D39 | 2 |
| #41×D13 | 3 |
| D3×#41 | 13 |