Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
370 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C22⋊C4 | C23×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C19 ◁ C2×C22⋊C4×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 79. C22×C4×C19 | Q16 | semidirect |
| 104. #12219 | C19 | direct (N × H) |
| 240. C19 | #12219 | direct (N × H) |
| 258. C22×C4 | Q16×C19 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#2841 | 2 |
| C19×#2030 | 2 |
| C19×#1614 | 2 |
| C19×#1602 | 2 |
| C19×#1352 | 2 |
| C19×#1351 | 2 |
| C19×#1317 | 2 |
| #12219 | 19 |