orbit - Does the Sun turn around a big star?

Does the Sun turn around a big star?

No. Such a star, if it existed, would easily be the brightest star in the sky. You would have been taught about it early on in school if it existed. But it doesn't.

For a while it was conjectured that the Sun had a small companion star to explain a perceived periodicity in mass extinction events. This too has been ruled out by the Wide-field Infrared Survey Explorer.

What are all the intermediate subsystems up to motion around the center of the Milky Way?

Our Sun, being a single star, is a bit of an oddity. Most stars are members of multiple star systems, typically pairs.

Some stars occur in clusters. The Pleiades is a relativity nearby (440 light years) cluster of stars. Someone with extremely keen eyesight and exceptionally good viewing conditions, might be able to see 14 stars of the over 3,000 stars that form this cluster. Open clusters such as the Pleiades don't last long. The stars in an open cluster are only weakly bound to the cluster and are eventually dispersed.

A key feature of the Milky Way is its spiral arms. Our Sun is currently in a lesser arm of the Milky Way, the Orion Arm. Stars however are not gravitationally bound to spiral arms. One widely used explanation of the spiral arms is that they are gravitational traffic jams in space.

We could also ask the same beyond...

Our galaxy is a member of the Local Group, which in turn is a member of the Virgo Supercluster, which in turn is a part of the Laniakea Supercluster. Even larger scale objects include galaxy filaments. And that's where the hierarchy ends. The expansion of space overtakes gravity at such immense distances.