Primary Group- a small social group whose members share personal and lasting relationships.
a. This term can be seen perfectly by the Griffin family. The are an odd family, but they all love each other in the end despite the conflicts differences that can be vividly seen. The Griffin's have many personal relationships with each other, just like a family.

Groupthink- the tendency of group members to conform, resulting in a narrow view of some issue.
a. This can be seen in the episode "One if by Clam, Two if by Sea" when the group of Peter, Joe, Quagmire, and Cleveland are upended from their favorite bar by a bunch of British tea-drinkers. They are then poised to take back their bar. The group of pals all agree that it's not alright to be upended from their favorite hangout spot. They eventually regain the bar.

Out-group- a social group toward which a person feels a sense of competition or opposition.
a. An example of this term can be seen in multiple episodes with Meg Griffin at James Woods High School. She often tries to talk to and become friends with the popular group of girls. She just wants to be one of them and have some friends, but is usually shut down and looked at as funny.

Rationality- a way of thinking that emphasizes deliberate, matter-of-fact calculation of the most efficient way to accomplish a particular task.
a. Stewie possesses much rationality in his thinking. Throughout the show he is trying to kill Lois because he is an evil, genius baby. In many episodes he tries to kill her with a new invention, but often fails. He then speaks several sentences about how he could fix his contraption to make it more efficient. ("Death has a Shadow")

Dyad- a social group with two members.
a. Throughout many episodes in the show, Stewie interacts with his teddy bear named Rupert. They would be an example of a dyad since they spend almost all day together and Stewie basically thinks of him as a real person. This is heavily shown in an episode where Stewie loses Rupert and he is crushed.

Triad- a social group with three members.
a. Many times throughout the show, the main characters that are portrayed as being the closest are Stewie, Brian, and Peter. They spend the majority of their time together while they're at home and they are a triad for this reason.

In-group- a social group toward which a member feels respect and loyalty.
a. Many episodes show a group of friends together (usually at the Drunken Clam) that includes Peter. His main friends in this in-group would be Cleveland, Quagmire, Peter, and Joe. They are best friends and spend countless hours together talking about random things or doing random activities.

Network- a web of weak social ties.
a. The main network that is described in Family Guy would have to be the news station there. The two co-anchors are famous together and are always on the show. They're reporter that is usually at the scene, whom they call "Our Asian Reporter," is also a common sight on the news.

Stewie oftens strikes this pose, thinking rationaly about his evil plans to take over the world.

This picture shows the group of friends at the Drunken Clam