Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#1999 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C19×C22⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×#3189 | C2 | semidirect |
| 2. C19×#2187 | C2 | semidirect |
| 4. C19×#1348 | C2 | semidirect |
| 5. C19×#1314 | C2 | semidirect |
| 24. C2×Q16×C19 | D4 | semidirect |
| 43. C19×#107 | D4 | semidirect |
| 90. #12103 | C19 | direct (N × H) |
| 102. C23×C19 | SD32 | semidirect |
| 130. #3189 | C2×C19 | semidirect |
| 131. #2187 | C2×C19 | semidirect |
| 133. #1348 | C2×C19 | semidirect |
| 134. #1314 | C2×C19 | semidirect |
| 184. C2×Q16 | D4×C19 | semidirect |
| 203. #107 | D4×C19 | semidirect |
| 208. C19 | #12103 | direct (N × H) |
| 262. C23 | C19×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×#3189 | 2 |
| C19×#2187 | 2 |
| C19×#1999 | 2 |
| C19×#1348 | 2 |
| C19×#1314 | 2 |
| #12103 | 19 |