A peculiarity of English is, that it has so many borrowed words. The clause introduced by that is equivalent to a noun, and is an +Attribute Complement+ relating to peculiarity.
Your future depends very much on who your companions are. The clause who your companions are is equivalent to a noun, and is the +Principal Term+ of a +Phrase+ introduced by the preposition on.
A clause that does the work of a noun is a +Noun Clause+.
Analysis.
The +noun clause+ may be used as +subject+.
1. That the earth is round has been proved.
That
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'
earth | is ' \ round
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\the | |
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/ \ | has been proved
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+Explanation+.—The clause that the earth is round is used like a noun as the subject of has been proved. The conjunction that [Footnote: "That was originally the neuter demonstrative pronoun, used to point to the fact stated in an independent sentence; as, It was good; he saw that. By an inversion of the order this became, He saw that (namely) it was good, and so passed into the form He saw that it was good, where that has been transferred to the accessory clause, and has become a mere sign of grammatical subordination."—C. P. Mason.] introduces the noun clause.
This is a peculiar kind of complex sentence. Strictly speaking, there is here no principal clause, for the whole sentence cannot be called a clause, i.e., a part of a sentence. We may say that it is a complex sentence in which the whole sentence takes the place of a principal clause.
2. That the same word is used for the soul of man and for a glass of gin is singular. 3. "What have I done?" is asked by the knave and the thief. 4. Who was the discoverer of America is not yet fully determined by historians.