Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
2304360 conjugacy classes of subgroups; only the 1581160 normal subgroups are shown.
This group has 2304360 conjugacy classes of subgroups — too many to draw. Only its 1581160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C28 | D4 |
| commutator | C4 | C27×C4 |
| Frattini, cosocle | C2×C4 | C28 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C28 ◁ C27×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×#106 | C2 | direct (N × H) |
| 6. C26×C8 | C4 | semidirect |
| 10. C24×#106 | C22 | direct (N × H) |
| 18. C25×C8 | C2×C4 | semidirect |
| 22. C23×#106 | C23 | direct (N × H) |
| 33. C24×C8 | C22×C4 | semidirect |
| 37. C22×#106 | C24 | direct (N × H) |
| 38. C26 | #106 | direct (N × H) |
| 49. C23×C8 | C23×C4 | semidirect |
| 53. C2×#106 | C25 | direct (N × H) |
| 54. C25 | C2×#106 | direct (N × H) |
| 65. C22×C8 | C24×C4 | semidirect |
| 69. #106 | C26 | direct (N × H) |
| 70. C24 | C22×#106 | direct (N × H) |
| 81. C2×C8 | C25×C4 | semidirect |
| 85. C23 | C23×#106 | direct (N × H) |
| 96. C8 | C26×C4 | semidirect |
| 97. C22 | C24×#106 | direct (N × H) |
| 106. C2 | C25×#106 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#106 | 2 |
| C26×C4⋊C4 | 2 |
| C27×C8 | 2 |