Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#4223 |
| commutator, socle | C2×C41 | C23×C4 |
| Fitting | #41×C41 | C4 |
| prime radical | #41×D41 | C2 |
| cosocle | C2×D41 | C24 |
| hypercenter | #41 | #4223 |
| hypocenter | C41 | #520 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×#4223 | C2 | semidirect |
| 2. D4×#4223 | C2 | semidirect |
| 3. #13050243 | C2 | semidirect |
| 4. C2×C4⋊#4223 | C2 | semidirect |
| 7. #41×C41 | C4 | semidirect |
| 8. #10620310 | C4 | semidirect |
| 10. #10620308 | C4 | semidirect |
| 12. #10620306 | C4 | semidirect |
| 23. Q8×C41 | C2×C4 | semidirect |
| 24. D4×C41 | C2×C4 | semidirect |
| 25. C2×C4×C41 | C2×C4 | semidirect |
| 26. C22⋊D41 | C2×C4 | semidirect |
| 27. C2×Dic41 | C2×C4 | semidirect |
| 28. D164 | C2×C4 | semidirect |
| 29. C4×D41 | C2×C4 | semidirect |
| 30. C4×D41 | C2×C4 | semidirect |
| 33. Dic82 | C2×C4 | semidirect |
| 51. C41 | #520 | semidirect |
| 60. #41 | #4223 | semidirect |
| 72. Q8 | C2×#4223 | semidirect |
| 75. D4 | C2×#4223 | semidirect |
| 84. C2×C4 | C2×#4223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#4223 | 2 |
| D4×#4223 | 2 |
| #13050243 | 2 |
| C2×C4⋊#4223 | 2 |
| #41×D41 | 2 |
| #520 | 41 |