Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
286 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C113 | AΣL(1,𝔽16) |
| commutator | C2×D4 | C42×C113 |
| Frattini, cosocle | #532 | C22×C113 |
| socle | C2×C113 | #1390 |
| prime radical | #532×C113 | C22 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C113 ◁ C2×C4×C113 ◁ C22×C4×C113 ◁ #532×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #568×C113 | C4 | semidirect |
| 8. #410×C113 | C4 | semidirect |
| 11. #353×C113 | C4 | semidirect |
| 14. #329×C113 | C4 | semidirect |
| 113. #7486 | C113 | direct (N × H) |
| 122. C113 | #7486 | direct (N × H) |
| 123. #568 | C4×C113 | semidirect |
| 127. #410 | C4×C113 | semidirect |
| 130. #353 | C4×C113 | semidirect |
| 133. #329 | C4×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C113×#2126 | 2 |
| C113×#1884 | 2 |
| C113×#1525 | 2 |
| #7486 | 113 |