Finite Group DatabasebetaFinite Group DatabasebetaOrder 25856.
632 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 632 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×C101 | B(4,𝔽2) |
| commutator | C2×Q8 | C22×C4×C101 |
| Frattini, cosocle | C22×Q8 | C23×C101 |
| prime radical | C2×2−1+4×C101 | C22 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C101 ◁ C23×C101 ◁ C22×Q8×C101 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C101×#2381 | C2 | semidirect |
| 3. C2×#356×C101 | C2 | semidirect |
| 5. C101×#1394 | C2 | semidirect |
| 10. #456×C101 | C4 | semidirect |
| 169. #13056 | C101 | direct (N × H) |
| 176. #2381 | C2×C101 | semidirect |
| 177. C2×#356 | C2×C101 | semidirect |
| 179. #1394 | C2×C101 | semidirect |
| 180. C101 | #13056 | direct (N × H) |
| 185. #456 | C4×C101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#456×C101 | 2 |
| C101×#2381 | 2 |
| C2×#356×C101 | 2 |
| C101×#1793 | 2 |
| C101×#1394 | 2 |
| #13056 | 101 |