In terms of clause analysis, does this constitute a complex sentence?

My usual grammatical spidey-sense has let me down here.

The sentence "I can’t begin to fathom how their tiny bodies would cope with what they had to carry" FEELS complex to me. I feel that

i) "how their tiny bodies would cope" is a subordinate/dependent clause.

BUT

ii) it also feels like the object of the main clause "I can’t begin to fathom".

So I’m currently labelling it like this: Main clause [I can’t begin to fathom] + subordinate clause [how their tiny bodies would cope] + prepositional phrase [with what they had to carry].

Is this correct as you understand it – I feel there’s some grammatical info I’ve missed here for this confusion to occur!