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If you are a lawyer or an experienced businessperson, please help with this. It's urgent!

Can a registered business own (not like a subsidiary, but like a mother) a social group without a need to register that group separately?

Let me expantiate.....

Let's say I have a registered business named Goldman Sachs, and we're into T-shirts and other item s branding, can I float a social group (like an online thing) that, say, gives out free T-shirts, and then, as a publicity stunt, maybe get some skaters wearing these shirts and sharing to random people on the street in the name of that social group (which is based mostly online, and which is directly owned by Goldman Sachs, my Branding company) without offending the law? This social group does not directly engage in business transactions, neither does it have a physical address; it is 100% dependent on Goldman Sachs to operate at all. It is just a front, a hype, a loud-mouthed escort that gets attention.
Is this a no-problem situation or are there legal concerns? If there are, what are they? That's my question.

Hope my explanation is clear to you, but ask me if it isn't. Thanks in advance, for your response, lawyers and business experts!