I think the only "subsidy" they get are indirect benefits, e.g.:
- a low/no tax state, which allows them to offer attractive salary and benefit packages (as regulars on this board know, it's basically, free accommodation and living costs) which reduces their cost of labour compared to other carriers
- as EK lease the vast majority of their aircraft, the interest rate they pay is the best in the market considering EK's financial position (healthily profitable) and implicit debt guarantees from the emirate of Dubai

The subsidy that people imply is generally fuel - which actually isn't subsidised at all. In fact, if you look at the recent financial history of Dubai, EK actually contributed to the Dubai treasury during their recent problems I think...

The other benefit is the 30 odd percent discount they get on their widebodies, which I would assume is at the top end that Airbus and Boeing offer considering EK's purchase power.