Definitely. You only file a single C corporation tax return.
Since the C corporation is the sole owner of the LLC, the LLC is considered a disregarded entity. In this context, the LLC is now treated as if it were a division of the C corporation.
Treating this as a division is different than if it were a subsidiary. If this were a subsidiary, the C corporation would be eligible to file a consolidated tax return. A division is just included in the C corporation activity and no consolidated return is filed.
Hopefully the above is clear and you understand the difference between the division filing and a consolidated return filing. Division filing is one single tax return. A consolidated return filing is multiple company returns that get pulled into one single consolidated tax return. The consolidated tax return filing is much more complicated.