Hey jaewook ,
First of all, welcome to the Buttonizer Community 🥳
Good question! Yes that is possible, however, you will need to reconnect and follow the steps create a new site for your subdomain (then you can manage them both seperately).
When you duplicate a site, it will duplicate the sites authorization code as well, which is also connected to your main site. This is why the buttons on the main site change as well.
Per account you can create an unlimited amount of (sub)domains. So you can keep using the same account 🙂
If you want to use the same domain (in Buttonizer) and not make seperate sites, you could also make use page rules to show and hide groups/buttons on different pages (using URL starts).
Let me know if this helps or you need any assitance 😁