Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
680 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 118 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 | C2×Q8 | C22×C4×C19 |
| Frattini, cosocle | C22×Q8 | C23×C19 |
| prime radical | C2×C19×#454 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C19 ◁ C22×Q8×C19 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C19×#2379 | C2 | semidirect |
| 3. C2×C19×#355 | C2 | semidirect |
| 4. C19×#1793 | C2 | semidirect |
| 5. C19×#1394 | C2 | semidirect |
| 10. C19×#454 | C4 | semidirect |
| 25. C19×2−1+4 | C2×C4 | semidirect |
| 57. C19×#101 | C2×C4 | semidirect |
| 117. #13055 | C19 | direct (N × H) |
| 166. #2379 | C2×C19 | semidirect |
| 167. C2×#355 | C2×C19 | semidirect |
| 168. #1793 | C2×C19 | semidirect |
| 169. #1394 | C2×C19 | semidirect |
| 195. #454 | C4×C19 | semidirect |
| 217. 2−1+4 | C2×C4×C19 | semidirect |
| 249. #101 | C2×C4×C19 | semidirect |
| 253. C19 | #13055 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C19×#454 | 2 |
| C19×#2379 | 2 |
| C2×C19×#355 | 2 |
| C19×#1793 | 2 |
| C19×#1394 | 2 |
| #13055 | 19 |