Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
992 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 142 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×C41 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C41 |
| Frattini, cosocle | C22×D4 | C23×C41 |
| prime radical | C2×C41×H(3,𝔽4) | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C41 ◁ C22×D4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C41×#354 | C2 | semidirect |
| 3. C2×C41×AΣL(1,𝔽16) | C2 | semidirect |
| 4. C41×#1889 | C2 | semidirect |
| 5. C41×#1885 | C2 | semidirect |
| 8. C41×H(3,𝔽4) | C4 | semidirect |
| 68. C24×C41 | C22⋊C4 | semidirect |
| 75. C2×Q8×C41 | C22⋊C4 | semidirect |
| 111. C22⋊C4×C41 | C22⋊C4 | semidirect |
| 115. C42×C41 | C22⋊C4 | semidirect |
| 160. #12763 | C41 | direct (N × H) |
| 187. C2×#354 | C2×C41 | semidirect |
| 188. C2×AΣL(1,𝔽16) | C2×C41 | semidirect |
| 189. #1889 | C2×C41 | semidirect |
| 190. #1885 | C2×C41 | semidirect |
| 200. H(3,𝔽4) | C4×C41 | semidirect |
| 216. C41 | #12763 | direct (N × H) |
| 261. C24 | C22⋊C4×C41 | semidirect |
| 268. C2×Q8 | C22⋊C4×C41 | semidirect |
| 304. C22⋊C4 | C22⋊C4×C41 | semidirect |
| 308. C42 | C22⋊C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×H(3,𝔽4) | 2 |
| C2×C41×#354 | 2 |
| C2×C41×AΣL(1,𝔽16) | 2 |
| C41×#1889 | 2 |
| C41×#1885 | 2 |
| #12763 | 41 |