The founding principle to SEO is brand identification. The more you do to model your web presence after successful major brands, the more you will naturally earn trust and authority big brands earn. That in turn boosts all other aspects of SEO.
To achieve this specific to subsidiaries, you establish a parent company corporate site, and a stand-alone domain for each subsidiary. Every site however, needs to utilize the most sustainable SEO methods possible. You can't just slap up sites with a few pages and expect them to rank or pull in highly qualified visitors without serious focus.
Only link back to the parent company site and other subsidiary sites from your "About", and "Contact" sections unless you believe it's valuable from a visibility perspective to link from every page. HOWEVER if you link from every page, they should be nofollow links. if you do mass volume links from site to site and they're not nofollowed, that leaves you highly exposed to potential algorithm penalties.
If you want each subsidiary to succeed as its own brand you will need separate social channels for each as well. Again though, they'll only be helpful long-term if you have the resources to maintain them in quality engagement ways.
There are many other rules and guidelines (like "keep duplication of content to as near zero as possible") however that's the core concept that addresses your question here.