Finite Group DatabasebetaFinite Group DatabasebetaOrder 3904.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×D61 |
| commutator, socle, cosocle | C22×C61 | C24 |
| Fitting | C22⋊Q8×C61 | C2 |
| prime radical | C2×#11758222 | C2 |
| hypercenter | C22⋊Q8 | D61 |
| hypocenter | C61 | #536 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×D61 | C2 | semidirect |
| 3. #14519776 | C2 | semidirect |
| 4. #14519763 | C2 | semidirect |
| 5. #14519762 | C2 | semidirect |
| 6. #14519759 | C2 | semidirect |
| 7. #14519757 | C2 | semidirect |
| 8. #14519756 | C2 | semidirect |
| 9. #14519753 | C2 | semidirect |
| 10. #14519735 | C2 | semidirect |
| 11. C22⋊Q8×C61 | C2 | semidirect |
| 84. C61 | #536 | semidirect |
| 94. C22⋊Q8 | D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758222 | 2 |
| C2×Q8×D61 | 2 |
| #14519776 | 2 |
| #14519763 | 2 |
| #14519762 | 2 |
| #14519759 | 2 |
| #14519757 | 2 |
| #14519756 | 2 |
| #14519753 | 2 |
| #14519735 | 2 |
| C22⋊Q8×C61 | 2 |
| #536 | 61 |