Finite Group DatabasebetaFinite Group DatabasebetaOrder 25856.
380 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 70 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×C101 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C4⋊C4 | C23×C101 |
| prime radical | #537×C101 | C22 |
| LCS | G ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C23×C101 ◁ C2×C4⋊C4×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C101×#2833 | C2 | semidirect |
| 5. C101×#1353 | C2 | semidirect |
| 6. C101×#1346 | C2 | semidirect |
| 7. C101×#1319 | C2 | semidirect |
| 170. #12201 | C101 | direct (N × H) |
| 177. #2833 | C2×C101 | semidirect |
| 181. #1353 | C2×C101 | semidirect |
| 182. #1346 | C2×C101 | semidirect |
| 183. #1319 | C2×C101 | semidirect |
| 184. C101 | #12201 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C101×#2833 | 2 |
| C101×#2007 | 2 |
| C101×#1616 | 2 |
| C101×#1610 | 2 |
| C101×#1353 | 2 |
| C101×#1346 | 2 |
| C101×#1319 | 2 |
| #12201 | 101 |