can we download the operating system of mac online ( without using app store ) ?

"Can" means "are able to". We are able to download anything we find. We may not legally violate copyright laws. Mac OS X belongs to Apple. They never give it to you.

If you are asking if Apple provides any Web download of any version of OS X, the answer is "NO".

If you find it on any website, that is an illegal act. Apple does not allow anyone to offer their software for web download.

PLEASE EXPLAIN WHY YOU CANNOT USE THE APP STORE.
If you are wanting to install OS 10.11 on a Mac that is running OS 10.5, download in App Store from a newer Mac.
If you are trying to hack a PC to run OS X, start a new question, and put "hackintosh" in the main title of it, so we Mac users don't waste a lot of time trying to help you with a non-existent Mac.

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