It is all the Shiites who have helped Hamas/Gaza militarily. Shia Iran, Hezbollah and Syria are all Shia or Shia-linked countries/entities. Syria is Arab nationalist, but Assad is a practicing Alawite, which is a Shia offshoot as I understand it.
Sunni and Shia fundamentalists do not get along as I understand it. There have been efforts in history, I think, to bridge the divide but Sunni/Shia relations are strained in many parts of the Middle East, currently, as per my understanding.
Qatar is presently trying to work to bring Hamas under its thumb in Gaza. I think Hezbollah and Hamas, however being the tips of the spear against Israel — there’s a bond there — (and with Hezbollah’s strong ties to Syria and Iran), I don’t think Qatar has fully succeeded yet with the designs that it has on Gaza. Egypt/Mohamed Morsi is immensely influenced by Qatar, but I’ve not seen where he’s helping in their plans vis a vis Gaza. Morsi could be a valuable tool for them, but then again he’s got so many of his own internal problems.
The Axis of Resistance was Hezbollah, Hamas, Syria, and Iran. I don’t know if Hamas is presently a “good standing member”, or not at all. As I’d said earlier I think Hezbollah and Hamas have an affinity for one another (and will continue to do so), they see the beast front-and-center, and so thusly they share and compare notes — and so I can’t see them totally breaking from one another. Remember it was Iranian Fajr-5 rockets that went through the US-taxpayer funded Iron Dome in Operation Pillar.
A final consideration to everyone. There is a group called the Alevis in the Middle East. I don’t know that much about them. They are mainly — if not entirely — Kurdish, and the same can be said for that exist/live in Turkey. I read an article from a very “learned” commentator recently, who was writing about all of the Alevis in Syria! Not rubbing it in, of course, I have the courtesy not to mention the writer’s name, and I’ve even read that some Middle Easterners are capable of confusing these two groups/identities!
Correction: I was inaccurate in saying Alevis are generally Kurds. Though it is accurate to say, it is a religion mainly of Turkey. According to Wiki 20% of Alevis are Kurds.