Order 512.
2030 conjugacy classes of subgroups.
The subgroup lattice has 757 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | #121 |
| commutator | C22×C4 | C23×C4 |
| Frattini, cosocle | C23×C4 | C24 |
| socle | C23 | #386 |
| prime radical | C25 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. #11215 | C2 | direct (N × H) |
| 18. #2911 | C4 | semidirect |
| 21. C2×#428 | C4 | semidirect |
| 133. #428 | C2×C4 | semidirect |
| 213. C2×M16 | C4⋊C4 | semidirect |
| 214. C2×M16 | C4⋊C4 | semidirect |
| 500. M16 | C2×C4⋊C4 | semidirect |
| 753. C2 | #11215 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#2911 | 2 |
| C2×#2296 | 2 |
| C22×#344 | 2 |
| C2×#1740 | 2 |
| C2×#1733 | 2 |
| C22×#339 | 2 |
| #11215 | 2 |