Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
662 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#493 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C19×SD32 | C2 | semidirect |
| 3. C2×C19×#357 | C2 | semidirect |
| 4. C19×#1969 | C2 | semidirect |
| 5. C19×#1374 | C2 | semidirect |
| 26. C2×Q16×C19 | D4 | semidirect |
| 45. C2×C16×C19 | D4 | semidirect |
| 89. #13328 | C19 | direct (N × H) |
| 112. C2×C4×C19 | SD32 | semidirect |
| 122. C22×SD32 | C2×C19 | semidirect |
| 124. C2×#357 | C2×C19 | semidirect |
| 125. #1969 | C2×C19 | semidirect |
| 126. #1374 | C2×C19 | semidirect |
| 170. C2×Q16 | D4×C19 | semidirect |
| 189. C2×C16 | D4×C19 | semidirect |
| 194. C19 | #13328 | direct (N × H) |
| 256. C2×C4 | C19×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C19×SD32 | 2 |
| C2×C19×#493 | 2 |
| C2×C19×#357 | 2 |
| C19×#1969 | 2 |
| C19×#1374 | 2 |
| #13328 | 19 |