Major ones

1. Qatar Petroleum
2. kahramma (If it can be included)
3. Qatar Foundation
4. Ashgal (Govt)
5. Qatalum
6. Waqood
7. Barwa construction
etc etc etc
There are companies like

Al-Mana who are into many business and by different brand name...
Ali Bin Ali
NBK (Mercedes Guy)
Al Jazeera ( communication and into other things too)
Tyseer (petrol pump fellow)

And then there are contractors who do projects for Govt bodies...

SNC lavalin
Syno Hydro
Siemens

Thts all I remember right now.. and neither the list is in any kind of order...
Names I recollected thts it..

Don have any list as such. and damn sleepy too..

If I remember more.. I ll post ...

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Reality is a Illusion Caused Due to Deficiency of Alcohol