In short, yes, you can have sentences without subjects.
First, though, with reference to your two candidate sentences, what do you mean by "without a subject"? Taking the imperative example ("Check on those girls"), there is clearly no subject visibly or audibly present, but most (not all) grammarians have contended that the subject is there by implication: "Subjectless imperatives are typically assumed to contain phonologically-null subjects that are specified for 2nd
person" (Anatol Stefanowitch, University of Bremen: http://www.stefanowitsch.de/anatol/fu-berlin/p/ms-stefanowitsch2003_eicba.pdf ).
And as others said, "To check on those girls" isn't a complete sentence on its own. In context, there is something else elided. ("Where are you going?" - "[I am going] to check on those girls.")
That said, I believe sentences can lack subjects (and verbs). Most people will consider "Darn!" or "Hello" to be a sentence.
Fowler's Modern English Usage (2nd ed., 1965) gives examples such as "And what of the will to power?"; "So far so good"; "So then"; "Now for his other arguments".
Traditionally many of these are explained by saying that there must be missing, understood material that has been elided, but this is really rather a stretch and requires forcing the material to fit a model rather than analysing it neutrally. As Fowler says: "it would be straining language to say that they are elliptical in the sense that 'a subject of predicate of verb (or more)' must be 'understood'" and yet they "cannot be denied the right to be called sentences."
One final point: the answer to your question also depends on how you define a "complete sentence". If you choose to define it such that a sentence without a subject is incomplete, then it becomes axiomatic that a complete sentence must have a subject. In that case, though, your whole enquiry would have been pointless.