In plain English
FAR 52.214-4, False Statements in Bids, is a solicitation provision prescribed at FAR 14.201-6(b)(2), most recently dated Apr 1984. The complete official text is reproduced below, verbatim, from GSA's published FAR source files.
Its text contains no sentence requiring insertion into subcontracts; see the flowdown section below for what that does and does not mean.
Does it flow down to subcontracts?
No flowdown mandate found in the clause text
This is a solicitation provision — it applies to offerors when submitting an offer, not to contract performance, so subcontract flowdown is generally not the operative question for it.
Where it's prescribed
As prescribed in 14.201-6(b)(2), insert the following provision in all invitations for bids:
Prescribing reference: FAR 14.201-6(b)(2).
The official text, verbatim
As prescribed in 14.201-6(b)(2), insert the following provision in all invitations for bids:
False Statements in Bids (Apr 1984)
Bidders must provide full, accurate, and complete information as required by this solicitation and its attachments. The penalty for making false statements in bids is prescribed in 18 U.S.C. 1001.
(End of provision)