Conde Nast is not part of the ownership structure of reddit. Conde Nast is owned by the major owner of reddit, Advance Publications, but reddit has not been part of Conde Nast for years. The ownership also got more diffuse last year:

http://recode.net/2014/09/30/reddit-raises-50m-plans-to-shar...

Advance notes that they are affiliated with reddit, but that is aboot it:

http://www.advance.net/