Most people have multiple friend groups. And for better or for worse, they don't always mix. My best friends are happy to have me hang out with their other friends. But, medium friends tend not to invite me to hang out with their other friend groups as often. While this may seem obvious, it can be hard to figure out with new platonic / romantic relationships.
With new relationships, it's easy to rationalize that you're not being invited because you haven't known each other very long. When in reality, people are typically happy to introduce friends that they think will get along. So, if a friend doesn't invite you to hang out with his/her friends, it's fair to assume that he/she probably has some reservations about his/her relationship with you. If you're trying to deepen a relationship, watch out for this.