Institutionalized

Institutionalized is a main story quest and an achievement/trophy in Fallout 4.

Detailed walkthrough
After successfully teleporting into the Institute, the Sole Survivor will be greeted by a voice coming from hidden speakers. It's possible to acquire the holotape needed for Inside Job at this time, as the console is right at the entry/exit point of the Institute. After following the voice through the empty Institute corridors and into an elevator, the Sole Survivor eventually enters a room to find a scared and confused acting child. When discovered to be a 10 year aged synthetic Shaun, a man named Father enters the room and shuts him down with a code phrase. He will then initiate conversation with the Sole Survivor which reveals that he is the real Shaun and the director of the Institute, as well as several other details regarding the Sole Survivor's situation and the details surrounding his initial kidnapping by the Institute. After speaking with him and agreeing to join the Institute (alternatively stalling by telling him they want to think about it), the player character is free to explore the facility.

Speak to Clayton Holdren, Allie Filmore, Justin Ayo, and Madison Li, who installs a relay into the player character's Pip-Boy, allowing fast travel to and from the Institute.

Bugs

 * If an unnamed NPC is killed after the Sole Survivor talks to Father, but hasn't officially agreed to join yet by choosing the "Don't Know" option, the quest updates to "Exit the Institute" however it becomes impossible to leave. Furthermore, the quest will not update should the Sole Survivor change their mind and tell Shaun they will join.
 * This can be fixed by killing a named NPC and becoming officially banished from the Institute. Otherwise, an earlier save must be reloaded.
 * When you finish the goal of "speak with the department heads", and the notification comes up on screen that you may now fast travel to and from the Institute, the game freezes and crashes.
 * You will not be able to speak to the child if you are wearing a power armor helmet with the mod that highlights life forms red. Go back to an earlier save, remove that mod or item, and the scenario should run normally.
 * Dr. Madison Li may not start a conversation with the Sole Survivor. This can be fixed by forcing the quest to the next stage (setstage mq207 200), which will then grant you fast travel access and start the next quest. The same can happen to other staff members. For PS4 and Xbox One, reloading a previous save and trying to initiate dialogue again with the Doctor may help fix this.
 * Father sometimes never shows up. On PC you can use the console command to move Father to your position. The script is waiting for you to talk to the child - so you don't really need to use the console code.
 * Also Clayton Holdren will not be able to speak to you for some reason. Maybe because you went somewhere else while you were supposed to meet him. He shows up on the pip-boy HUD as being in the Synth Retention Bureau, but his location is not reachable.
 * If you were to kill Father before he talks to you, Institute personal can call you a traitor or say "He Trusted you!". This happens even though you didn't start the quest Banished from the Institute.
 * If you were to kill Father after he talks to you, you may not be able to use the elevator to leave.
 * This can be fixed if you kill Father as soon as you are done talking to him.

Учреждение закрытого типа Установа закритого типу