Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
390 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #354 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | #127 | C23×C19 |
| prime radical | C2×C19×#127 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C19 ◁ C22×C4×C19 ◁ C2×C19×#127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C19×#1412 | C2 | direct (N × H) |
| 5. C2×C19×#125 | C4 | semidirect |
| 7. C19×#490 | C4 | semidirect |
| 11. C2×C19×#97 | C4 | semidirect |
| 23. C19×#125 | C2×C4 | semidirect |
| 33. C19×#97 | C2×C4 | semidirect |
| 60. C2×#1412 | C19 | direct (N × H) |
| 87. #1412 | C2×C19 | direct (N × H) |
| 105. C2×#125 | C4×C19 | semidirect |
| 107. #490 | C4×C19 | semidirect |
| 111. C2×#97 | C4×C19 | semidirect |
| 118. C2×C19 | #1412 | direct (N × H) |
| 129. #125 | C2×C4×C19 | semidirect |
| 139. #97 | C2×C4×C19 | semidirect |
| 140. C19 | C2×#1412 | direct (N × H) |
| 211. C2 | C19×#1412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C19×#490 | 2 |
| C2×C19×#353 | 2 |
| C19×#1412 | 2 |
| C2×#1412 | 19 |