Fewest GLOs with all of the Greek Letters among them.
 

Theoretically, all 24 Greek Letters could be covered among Eight three letter Greek Organizations, but I'm pretty sure you can't do that among the Social Greeks. (I think out of the NPC, NIC and NPHC, the only organization with Upsilon is Delta Upsilon, which is only two letters), so anyone got any idea how to cover the 24 greek letters with nine or ten GLOs?

Do any names contain eta?

Checks wikipedia...Nope. How many does it take to get the 23 letters then?

Well, at Illinois, 4-H house is considered a social Greek organization, and they sometimes go by "Etas", for obvious reasons. It's a stretch, but we're obviously just playing around with this anyway.

*coughs*You sure about that?

You are right, Delta Upsilon isn't the only Upsilon, but are there any with three letters including Upsilon?

Interestingly, there was a national sorority, Eta Upsilon Gamma. founded in 1901 and confined its chapters to junior (2 year) colleges. Not sure when it & the other junior college sororities folded. When the parent institutions went to a full four year curric. three of their chapters ultimately joined Alpha Chi Omega, Alpha Xi Delta & Zeta Tau Alpha.

Greek Alphabet:
Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω

Okay... so we obviously have to start with the odd letters, so

Alpha Xi Delta
Psi Upsilon
Sigma Gamma Rho

We have left:
Β Ε Ζ Η Θ Ι Κ Λ Μ Ν Ο Π Τ Φ Χ Ω

Not sure how best to combine those . Add Chi O and Phi Mu, maybe? I'm only super familiar with NPC and a few NIC.

Alpha Xi Delta
Psi Upsilon
Sigma Gamma Rho
Zeta Phi Beta
Chi Omega

We have left:
Ε Η Θ Ι Κ Λ Μ Ν Ο Π Τ

May have worked myself into a corner with this one and will have to repeat some letters to get out.

Alpha Xi Delta
Psi Upsilon
Sigma Gamma Rho
Zeta Phi Beta
Chi Omega
Lambda Chi Alpha

We have left
EHΘIKMNΟ Π Τ

Wouldn't Alpha Kappa Lambda have been a better addition?

Here's my try, going a little out of the NPC, NPHC and NIC, but staying social/single-sex:

Sigma Beta Rho (NAPA/NIC)
Theta Nu Xi (NMGC)
Zeta Tau Alpha (NPC)
Omega Psi Phi (NPHC)
Delta Kappa Epsilon (NIC)
Alpha Omicron Pi (NPC)
Lambda Sigma Upsilon (NALFO/NIC)
Gamma Eta (NMGC)
Iota Phi Theta (NPHC/NIC)*
Phi Mu (NPC)
Chi Phi


That's 11 GLOs with all letters used and (I think) only Alpha, Delta, Theta*, Sigma and Phi used by more than one group, and only Phi (and maybe Sigma*) used by more than two groups.


* If Sigma Alpha Iota (NIMC/PFA) is used instead of Iota Phi Theta, then Theta would only be used once, leaving just three "repeating" letters and would reduce the use of Phi, but Sigma would be used by three groups instead of two. But naraht specified "social" GLOs, and I'm not sure whether SAI considers itself social, professional or something in between.

I was about to say, you have to use AOII...I'm not aware of any other group using Omicron. Good job, MC!