Usar "of that" ou "that"?

Hello.

Yesterday I was reading when I found the following sentence:

" The wildest imaginings that dark rumour had ever suggested to him fell altogether short of the real dread of that place."

My doubt is if it would be wrong or not to use "of" after "imaginings" and, if it is wrong, why?

Thanks in advance.

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Quite simply put, yes, it would be wrong. You can see the problem when you look at the actual translation:
"The wildest imaginings that dark rumour had ever suggested to him fell altogether short of the real dread of that place."

"Os mais estranhos pensamentos que os rumores haviam-lhe sugerido ficaram completamente aquém do real terror daquele local".
The word "that" functions as a relative pronoun, and stands by itself as a sort of connector between "wildest imaginings" and "dark rumor". There is no room for "of" in between. A simpler but similarly structured and therefore equally incorrect sentence would be:

"The shirt of that he gave me was very expensive." (Wrong)

The very same logic applies to your example.