Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
736 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C127 | C22⋊C4 |
| commutator | C22 | C23×C4×C127 |
| Frattini, cosocle | C2×C4 | C24×C127 |
| prime radical | C24×C127 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#101×C127 | C2 | direct (N × H) |
| 13. #101×C127 | C22 | direct (N × H) |
| 49. C22×C127 | #101 | direct (N × H) |
| 58. C2×C127 | C2×#101 | direct (N × H) |
| 60. C22×#101 | C127 | direct (N × H) |
| 61. C127 | C22×#101 | direct (N × H) |
| 64. C2×#101 | C2×C127 | direct (N × H) |
| 74. #101 | C22×C127 | direct (N × H) |
| 110. C22 | #101×C127 | direct (N × H) |
| 119. C2 | C2×#101×C127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×C127 | 2 |
| C22×M16×C127 | 2 |
| C2×#101×C127 | 2 |
| C22×#101 | 127 |