In plain English
FAR 52.216-18, Ordering, is a contract clause prescribed at FAR 16.506(a), most recently dated Aug 2020. 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
We scanned the full clause text and found no sentence directing the contractor to insert this clause into subcontracts. That is a statement about the text, not legal advice: a prime contractor may still flow terms down contractually, an agency supplement (DFARS, VAAR, …) may add requirements, and clauses listed below (if any) may order this clause into subcontracts from the outside.
Where it's prescribed
As prescribed in 16.506(a), insert the following clause:
Prescribing reference: FAR 16.506(a).
The official text, verbatim
As prescribed in 16.506(a), insert the following clause:
Ordering (Aug 2020)
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(a) Any supplies and services to be furnished under this contract shall be ordered by issuance of delivery orders or task orders by the individuals or activities designated in the Schedule. Such orders may be issued from __________ through ____________ [insert dates].
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(b) All delivery orders or task orders are subject to the terms and conditions of this contract. In the event of conflict between a delivery order or task order and this contract, the contract shall control.
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(c) A delivery order or task order is considered "issued" when—
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(1) If sent by mail (includes transmittal by U.S. mail or private delivery service), the Government deposits the order in the mail;
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(2) If sent by fax, the Government transmits the order to the Contractor's fax number; or
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(3) If sent electronically, the Government either—
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(i) Posts a copy of the delivery order or task order to a Government document access system, and notice is sent to the Contractor; or
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(ii) Distributes the delivery order or task order via email to the Contractor's email address.
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(d) Orders may be issued by methods other than those enumerated in this clause only if authorized in the contract.
(End of clause)