What is this sentence?
"Lead it to the water's edge and shove it in?"
It's got a question mark, and it is performing the function of a question. But it has no subject, and doesn't have the grammatical features of a question (question words, flipped subject/verb helpers, or tags). So it's a fragment.
Which reveals something important about fragments: they can be from different sentence types.
A lot of fragments come from statements, like this:
Once they locked me up all day long. And (they locked me up) all night.
Now we have an example of a fragment that has come from a question:
(should she) Lead it to the water's edge and shove it in?
What about commands? What would a fragment of a command look like? We've actually already seen one:
"Dr. Livesey take the north side, if you please; Jim, (take) the east, Gray, (take the) west."
Exclamations? Exclamations are the only sentence type you won't find fragments of. Can you think why that would be the case?