Ignoring for a minute whether a C corporation is the right choice of entity for a subsidiary of an S corporation–which it may or may not be, depending on the circumstances–the technical answer to the question is:
Yes! An S corporation can own a C corporation.
That wasn’t always the case. In the past, Internal Revenue Code Section 1361(b)(2) used to prevent S corporations from being part of an affiliated group of corporations. The rule stated generally that an S corporation couldn’t own 80% or more of the stock of another corporation.
This changed when the Small Business Job Protection Act of 1996 amended Section 1362(b)(2) to remove this prohibition. So, starting in 1997, S corporations can own subsidiary C corporations.