If it’s every weekend, it’s called Wochenaufenhalt, you’d need to research the rules in Zug and Italy.
https://en.comparis.ch/immobilien/umzug/vor-dem-umzug/wochenaufenthalt
(see last section)
So now we have three variables 
Zurich -: rental apartment but sublet to someone else
Zug -: another rental apartment but empty on weekends
Italy -: where you spend weekends
Working in Zurich, living in Zug & weekends in Italy. This might cause a problem with your “Center of life” topic. You might not be able to claim Zug as your residence when you don’t really live there & treat it as a hotel.
Center of life is where you spend your weekends and where your family is.
If I were you , I would ensure
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Zug apartment is big enough, not shared with another tenant (unless it’s your family) and seems like for someone who actually lives there. You have a rental contract under your name.
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Zurich apartment-: you have no connection with it other than collecting rent. This means you don’t live there for any single day.
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Travel to Italy very often -; check with Cross border lawyer
As I explained earlier. If your real intention is to evade tax, you will get caught at some point and then tax office will find a way to prove it. They are dealing with such cases everyday.
If your real intention is not to evade taxes but to live in Zug then no tax office in world can go after you.
In the end truth always wins because it is consistent
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This 180 days thing is for tax domicile.
For social security , there is another limit as far as I know.
I understand that is quite complex, in that case I will just give up the apartment in Zurich.
Yeah. But even if you sublet it, it’s not such a big deal. Just don’t make it like AirBNB and make it longer term which makes sense.