Infinity Badges went private when it got near full capacity. Several members formed Infinity Badges 2.0, and encouraged those who were active in the old channel to migrate to it. Aside from that channel, there is Inf Badge Seeker, Infinity Hamidon, which isn't really focused on Hamidon raiding anymore, and several other well-populated global channels.
I don't really have what you'd call an active supergroup, or I'd invite you to mine, but getting into the more-active channels will certainly get you teams, and might even get you involved in some active supergroups.
Enjoy your time on Infinity. I've made characters on every server, but I always come home to Infinity for the community that I know and care about.
"I wish my life was a non-stop Hollywood movie show,
A fantasy world of celluloid villains and heroes."
Sort of hello! 
You should be aware that most of the big channels are set so that new people joining are automatically silenced. This was done due to problems with gold farmers joining and spamming the channels. When you join a channel, you will need to be unsilenced. Look at who is online on the channel (on the friends window, set the dropdown box to the channel name to see who is on). Anyone with a big star next to their name is an operator and can unsilence you. Send them a tell to ask.
I would also recommend those channels: Inf Badge Seeker and Infinity Hamidon. I'm an operator on Infinity Hamidon so I can unsilence you if I'm online. These are public channels so you can join from the chat interface or by typing /chanjoin "Infinity Hamidon" (You need the quotes because the name has a space in it.)
Keep in mind that, when you join a channel, it automatically adds it to the chat window for that character ONLY. I would suggest you join a few channels, arrange your chat tabs how you want, then type /chatsave
That will save the chat channels and settings as your default so it is set for all new characters. Also, you can load it to any other character by typing /chatload
It sounds like you're a bit more into villains. I don't play red side as much as blue. While I run a coalition of several supergroups on blue side, when on red, I steer my SG members and friends to a VG called the Onyx Debtinators. (They also have a blue side SG, Titanium Debtinators.) I'm an officer in there and an operator on the SG/VG private channel. My global names are @Ironblade One and @Ironblade Too so send me a tell if you see me online. (You can find me by looking at who is online on either of the global channels mentioned.)
Paragon City Search And Rescue
The Mentor Project
Welcome to Infinity Bexx! I hope you've been enjoying your stay thus far. Ms. Mesmer and Ironblade beat me to the punch, but I'll echo their choice of global channels and add a few others. I'm part of Inf Badge Seeker, Infinity Hamidon, Infinity Badges 2.0, Infinity TFs, and AE Anonymous. AE Anon is a general purpose LFT channel that covers pretty much everything except AE missions. I've had good luck with all of them, especially IBS and Badges 2.0.
I'm still new to the server myself (about 2 months now) so I can't make any recommendations there. Hooking up with people in one of the global channels or joining one of the weekly TFs posted on the forums is a great way to meet people and make new friends though. I run my own little solo SG but have formed a network of friends thanks to these awesome resources. You could also try looking at the Top 100 SGs listing at the Registrar in Port Oaks/Atlas Park, too. Lots of SG include ways to contact SG leaders in their registrar info.
If there's anything else you need or if you have any questions, please don't hesitate to ask. Hope to run into you on the globals sometime!
Well Hello and welcome to the server! sorry im late on this train!
This server is full of some awesome people and theres always something going on. Im sure you will find a group of folks that fits what your looking for!
The Official Resident Fanboi of dUmb
Always Allow/Disallow Mystic Fortune Prompt!
PCSAR
Yo.
Welcome back to infinity.
Founder of Life and Death Brigade
Infinity and Exalted
"Doc has a sexy voice" - L'amara
I'm late too, but hello! Give me a poke if you see me buzzing around and we can team some! 
♥Gabz
Official Realtor of Infinity
The Highly Unlikelies - Victory PvP
Globally @Gabriella of Mercy
Paragon City Search & Rescue
Hi, I've been playing on infinity for some time, I'm level 31 and I've been playing solo so far. However, I'd like to join a SG or find others that enjoy playing. I play every day and I am just interested in finding others on the server. I tried joining the channel 'Infinity Badges' but since it's a private channel, I haven't been able to get any info on joining the channel from global chat broadcast. Anyone out there that plays pretty regularly and enjoys meeting new people and playing the game?
Thanks
Edit:
Oops, I should have been more specific. I have a level 31 villain. I also have a level 20 hero and just barely started a going rogue character that I haven't really touched yet.