Finite Group DatabasebetaFinite Group DatabasebetaOrder 30848.
442 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C241 | C2×D4 |
| commutator | C2×C4 | C22×C4×C241 |
| Frattini, cosocle | C22×C4 | C23×C241 |
| socle | C22×C241 | C2×C22⋊C4 |
| prime radical | #525×C241 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C241 ◁ C23×C4×C241 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C42×C241 | C2 | semidirect |
| 3. C2×#104×C241 | C2 | semidirect |
| 4. #407×C241 | C2 | semidirect |
| 5. #339×C241 | C2 | semidirect |
| 11. C22⋊Q8×C241 | C4 | semidirect |
| 12. #121×C241 | C4 | semidirect |
| 24. C2×Q8×C241 | C2×C4 | semidirect |
| 27. C2×D4×C241 | C2×C4 | semidirect |
| 42. C4⋊C4×C241 | C2×C4 | semidirect |
| 49. C42×C241 | D4 | semidirect |
| 84. C22×C241 | #104 | semidirect |
| 100. C241 | #1896 | direct (N × H) |
| 101. #1896 | C241 | direct (N × H) |
| 103. C22×C42 | C2×C241 | semidirect |
| 104. C2×#104 | C2×C241 | semidirect |
| 105. #407 | C2×C241 | semidirect |
| 106. #339 | C2×C241 | semidirect |
| 112. C22⋊Q8 | C4×C241 | semidirect |
| 113. #121 | C4×C241 | semidirect |
| 125. C2×Q8 | C2×C4×C241 | semidirect |
| 128. C2×D4 | C2×C4×C241 | semidirect |
| 143. C4⋊C4 | C2×C4×C241 | semidirect |
| 150. C42 | D4×C241 | semidirect |
| 185. C22 | #104×C241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #525×C241 | 2 |
| C22×C42×C241 | 2 |
| C2×#104×C241 | 2 |
| #407×C241 | 2 |
| #339×C241 | 2 |
| #1896 | 241 |