Burning Cover

Burning Cover is a quest in Fallout 4. It is the aftermath of failing Underground Undercover and becoming branded an enemy of The Institute.

Quick walkthrough

 * 1) Report to Desdemona
 * 2) Find the Minutemen or talk to Preston

Detailed walkthrough
This quest is fairly straightforward and only requires talking to two people.

The Sole Survivor has blown the cover, and must speak to Desdemona for the next step. When talking to her, she explains that there is little hope for rescuing any synths now that communication with Z1-14 is lost, and that the Railroad numbers are too few to challenge the Institute directly. She instructs seeking out (or requests help from) the Minuteman, as they are the only army capable of forcibly freeing the synths. Desdemona also thinks the Minuteman might be able to find another way into the Institute with the data found in the holotape.

If one didn't complete When Freedom Calls, Desdemona hears there's a remnant operating around Concord. That's all the info given to seek them out. When Freedom Calls needs to be completed before turning in Burning Cover. See respected article for more details on that particular quest.

If When Freedom Calls is completed, the next step is to talk to Preston Garvey. Depending on how far the Sole Survivor had advanced in the Minuteman storyline determines his reaction, but ultimately will agree to support. This marks the completion of Burning Cover.