Business Combinations and Acquisitions (Details) - USD ($) $ / shares in Units, $ in Thousands					3 Months Ended
	Nov. 23, 2020	Nov. 20, 2020	Feb. 11, 2020	Feb. 10, 2020	Jun. 27, 2021	Sep. 27, 2020	Dec. 31, 2020
Business Acquisition [Line Items]
Common stock par value (in dollars per share)					$ 0.0001		$ 0.0001
Goodwill					$ 593,171		$ 590,668
PE Shay Holdings, LLC
Business Acquisition [Line Items]
Post-closing adjustment payments						$ 20,200
PAE Management
Business Acquisition [Line Items]
Post-closing adjustment payments						$ 1,000
Class A Common Stock
Business Acquisition [Line Items]
Common stock par value (in dollars per share)					$ 0.0001
Shay Holding Corporation Merger
Business Acquisition [Line Items]
Aggregate cash consideration paid			$ 424,200
Transaction costs			$ 3,400
Shay Holding Corporation Merger | Earn-Out Shares
Business Acquisition [Line Items]
Period following completion of business combination (in years)			5 years	5 years
Shay Holding Corporation Merger | Additional Paid-in Capital
Business Acquisition [Line Items]
Acquisition fees and expenses			$ 18,200
Shay Holding Corporation Merger | Class A Common Stock
Business Acquisition [Line Items]
Consideration paid (in shares)			21,127,823
Shay Holding Corporation Merger | Class A Common Stock | Earn-Out Shares
Business Acquisition [Line Items]
Maximum additional earn-out (in shares)			4,000,000	4,000,000
CENTRA
Business Acquisition [Line Items]
Post-closing adjustment payments					$ 1,400
Outstanding capital stock acquired (as a percent)		100.00%
Business combination, consideration transferred		$ 225,300
Assets acquired		177,400
Liabilities assumed		77,200
Goodwill		126,400
Intangible assets acquired		$ 74,100
Metis Solution
Business Acquisition [Line Items]
Post-closing adjustment payments					$ 500
Outstanding capital stock acquired (as a percent)	100.00%
Business combination, consideration transferred	$ 95,700
Assets acquired	60,400
Liabilities assumed	20,700
Goodwill	56,500
Intangible assets acquired	$ 37,800