Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
338 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 116 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 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C41 |
| Frattini, cosocle | C22×C4 | C23×C41 |
| prime radical | C24×C41 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#101×C41 | C2 | semidirect |
| 5. C41×#343 | C2 | semidirect |
| 88. C22×C41 | #101 | semidirect |
| 98. #1901 | C41 | direct (N × H) |
| 107. C2×#101 | C2×C41 | semidirect |
| 109. #343 | C2×C41 | semidirect |
| 110. C41 | #1901 | direct (N × H) |
| 193. C22 | #101×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×M16×C41 | 2 |
| C2×C22⋊Q8×C41 | 2 |
| C2×#101×C41 | 2 |
| C41×#407 | 2 |
| C41×#343 | 2 |
| #1901 | 41 |