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. The voice invites the player to enter an elevator. When the elevator opens, the door to the relay room locks closed, and the quest begins.

It is possible to acquire the required data using the holotape provided for Inside Job or Outside the Wire at this time, as the console is right at the entry/exit point of the Institute. If using the relay room to depart (rather than using the Pip-Boy directly to fast travel) then the network scan must be carried out, or the doors to the relay room will not open.

After following the voice through the empty Institute corridors and up another elevator, the Sole Survivor eventually enters a room to find a scared and confused child. When discovered to be a 10-year-old synthetic Shaun, a man named Father enters the room and shuts him down with a code phrase. He will then initiate a 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 is free to explore the facility. If they disagree to join or to consider joining, the doors remain locked and it is not possible to proceed beyond Father's quarters.

Speak to Clayton Holdren, Allie Filmore, Justin Ayo, and Madison Li, the latter of which installs a relay into the player's Pip-Boy, allowing fast travel to and from the Institute and resolving this quest, starting the following quest Synth Retention automatically. Alternatively, one can refuse to work with the Institute, in which case Father will tell the player to leave, or attack Father, to end the quest on hostile terms and be banished from the Institute.

If combat is detected in the Institute a number of synths will spawn along the exit route to the relay room. The number of spawned synths increases as time passes. If some form of agreement has been reached with Father before initiating combat, synths and Institute personnel will also enter through the now-unlocked doors to attack the player character. The door to the relay room is locked unless the network scanner holotape was previously used (in any Institute terminal); if necessary, complete the network scan now to open the relay room door. Regardless of whether combat was initiated, or whether one leaves peacefully, on entering the relay room the player character will be automatically teleported to the C.I.T. ruins, completing Institutionalized, and will never be able to return to the Institute. It is possible to speak to Father again and change one's mind only if combat has not been detected and if one has not yet exited the Institute.

Bugs

 * If an unnamed NPC is killed after the Sole Survivor talks to Father, but has not 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 the player finishes the goal of "speak with the department heads", and the notification comes up on screen that they may now fast travel to and from the Institute, the game freezes and crashes.
 * The player character will not be able to speak to the child if they are wearing a power armor helmet with the targeting mod. Go back to an earlier save, remove the 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, which will then grant 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 the player's position.
 * The script is waiting for the player to talk to the child - so they do not really need to use the console code.
 * Also Clayton Holdren will not be able to speak to the player for some reason. He shows up on the Pip-Boy HUD as being in the Synth Retention Bureau, but his location is not reachable.
 * If the player character kills Father after he talks to them, one may not be able to use the elevator to leave.
 * This can be fixed if the player character kills Father as soon as they are done talking to him.
 * If one finds that Shaun does not deactivate after hearing Father's shutdown code, load a saved game from before talking to Shaun, and this time instead of talking to Shaun, one can open console and type . Father will walk in and Shaun will shut down.