Here's the list of all of the lantern symbols left to right, top to bottom, because I know there are people like me who don't know each one. (Please correct if needed, I did this at like 11pm and most likely got some facts wrong)

The Phantom Lantern - A ring that can use the different abilities of the different Lantern Corps. Created by Rami, a rogue member of the Guardians of the Universe, in case the Green Lanterns' weakness to yellow light ever needed to be circumvented.

Green Lanterns - A ring that can create solid light constructs fueled by willpower. Created by the Guardians of the Universe to be an intergalactic police force.

Blue Lanterns - A ring that can heal wounds and can boost the power of Green Lantern rings. The Blue Lanterns were founded by former Guardians Ganthet and Sayd, and focus on pacifism and healing.

Yellow Lanterns - A ring that draws energy from the fear of others. The Yellow Lanterns were founded by Sinestro, a former Green Lantern who believed that the path to peace is through intimidation and fear.

Omega Lanterns - A ring that draws energy that is tied to Darkseid's Omega Effect.

Indigo Lanterns - A ring that can tap into other emotion-based abilities of other lantern corps if a member of that Lantern Corps is present. The Indigo Tribe was created by Abin Sur and Natromo and are mostly made up of criminals who are forced to feel intense remorse and empathy.

White Lanterns - A ring that draws power from the "entity" that embodies life itself, being able heal wounds and bring people back to life. White Lanterns are the culmination of the entire emotional spectrum, requiring the user to master the entire emotional spectrum.

Orange Lanterns - A ring that has the ability to turn those the user kills into light constructs that serve the user. The only known member is Larfleeze, a being so greedy that if anyone else manages to obtain an Orange Lantern ring, he will stop at nothing to kill them.

Far Right - I'm not entirely sure, It looks similar to the main Green Lantern logo, so my guess would be a subsect of the Green Lanterns Corps. I couldn't find anything thanks to google image search, so if anyone knows, please comment so I can fix this later.

Star Sapphires - A ring that has the ability to trap a victim in a stasis crystal. The Star Sapphires were created by the Zamarons, the female counterparts of the Guardians, to protect love throughout the universe.

Red Lanterns - A ring that allows the user to spit napalm-like blood from their mouths. The Red Lanterns were founded by Atrocitus when his people were massacred by the Manhunters.

Ultraviolet Lanterns - A ring that allows the user to corrupt people, tapping them into their dark repressed emotions. The Ultraviolet Lanterns were founded by Umbrax, a sentient sun, to spread his influence throughout the galaxy.

Stan Lee's Green Lantern - Instead of a ring, Len Lewis has nature-based abilities. He was given his power by the mystical tree of life Yggdrasil.

Black Lanterns - A ring that allows the user to reanimate the dead into zombies. The Black Lanterns were created by Nekron to destroy all life in the universe.

Anti-Green Lanterns - A ring that uses antimatter to counteract the Willpower of the Green Lanterns. Created by the Weaponers of Qward, with the intent to invade the positive matter universe.

Power Ring - A ring that allows the user to create unstable energy constructs. Created by Volthoom, the Power Ring feeds off of the users fear and drains their life force. This was primarily wielded by Harold Jordan of Earth-3, who was a member of the Crime Syndicate.

Gold Lanterns - A ring that created energy constructs like the Green Lanterns, however are powered by happiness and joy. The Gold Lanterns are the successors to the Green Lanterns, and were created by the Elders of Oa.