Yes… a corporation (entity type) that has taken a c-election (tax election) can be the sole member of an LLC which owns all the shares of another corporation (entity type) that has taken an s-election (tax election) - but the LLC must not elect to be treated as a disregarded entity.
Note that entity type (LLC, corporation, sole proprietorship, general or limited partnership) has nothing to do with the tax election. An LLC (the entity) can just as easily file to be treated as an s-corporation (tax election) without having to be a corporation. I hope I’ve made this concept clear to you, as it allows you to just as easily own the LLC that is treated as an s-corp, without the need for the LLC and the s-corp.
The big answer is YES. But the bigger question is WHY? If you are an emerging company and looking to invest in a venture, why not set it up as just an LLC or a limited partnership? There are too many tax and other issues that can be less complicated with a direct route.