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Your carcass will lie dead at my feet, Kal-El, and the people of this planet will kneel before me!
~ John Henry Irons while fighting Superman.
General Zod is a minor antagonist in the Arrowverse, appearing as a posthumous antagonist in Supergirl and a minor antagonist of the first season of Superman & Lois.
Zod was a notorious Kryptonian war criminal and former military general, as well as one of the few survivors from the destruction of the planet Krypton. He is also one of the archenemies (alongside Lex Luthor) of Superman, but also his most feared enemy.
On Krypton, Zod was a military general known for his extreme ruthlessness and megalomaniacal personality. Like all Kryptonians at some point, Zod had his consciousness copied into Lara Lor-Van's invention, the Eradicator, to ensure the survival of his culture and memory. Because of his crimes against Krypton, Zod was arrested and imprisoned in Fort Rozz, Krypton's maximum-security prison located within the Phantom Zone. After Krypton's destruction and Kara Zor-El's freedom from the Phantom Zone, Fort Rozz landed on Earth where everyone who was imprisoned there was free, including Zod.
Encounters with Superman
Zod repeatedly tried to take over Earth by launching massive attacks against its people, which eventually got the attention of Superman, who had engaged him in a brutal battle that deeply affected Superman and Zod. In the end, Superman had won, and Zod was either imprisoned or fled.
During the Daxamite Invasion, Superman was poisoned with silver kryptonite by the Queen of Daxamites, Rhea, who caused him to hallucinate his cousin Supergirl as the infamous Zod, hearing his threats against him and the people of Earth. Superman then began a brutal showdown thinking she was Zod.
At some point in 2018, the real Zod had encountered Superman again however, during their fight, Superman was forced to kill his mortal enemy.
After Tal-Rho forced Superman to submit to him, his father, Zeta-Rho, supplanted Zod's consciousness into Superman using the Eradicator. After a brief struggle, Superman eventually lost to Zod, allowing him control of his body. Zod went along with Tal-Rho and Zeta-Rho's plans. He later fought John Henry Irons all across the country and told him of the inevitability of Earth's fate. However, thanks to John, Lois Lane, and Superman's memories of his family, Superman was able to resist Zod's will on his mind, clearing him out and returning to normal.
Afterward, Tal-Rho then used the Eradicator one last time by performing a solar flare to destroy the Eradicator and transfer all the minds of the Kryptonians into his, including Zod's.
Revived in the future
At some point in the 31st century, Zod was revived by unknown means and battled against the Legion of Superheroes, who managed to use kryptonite against him. It was not stated what happened to Zod afterward whether he was imprisoned, killed, or just retreated.
Zod is considered to be a megalomaniacal, ruthless, egotistic, and arrogant military leader who has made a name for himself by stomping over his enemies. After losing Krypton, Zod became obsessed with conquering Earth to make a New Krypton and killing anyone who protects it to prevent anyone from opposing him, including Superman.
I will destroy your world.
~ Zod to Superman while affected by silver kryptonite.
I will kill everyone you love!
~ Zod provoking Superman while affected by silver kryptonite.
So be it. Delay the inevitable. Fight as long as you can but eventually you will fade as this new mind comes to light. Not even Superman is strong enough to resist the will of Zod.
~ Zod to Zeta-Rho after taking control of Superman's body.
You won’t stop what’s coming. None of you can stop this.
~ Zod in Superman’s body preparing to fight John Henry Irons.
This is the second live action adaptation of General Zod to not have any kind of facial hair, aside from the Smallville version. Until his last appearance in Smallville, when he then sports facial hair.
It is also the first adaptation of General Zod to have blonde hair instead of black hair.
It is possible that the version of Superman on John Henry Irons's Earth was possessed by Zod's consciousness after he was eradicated by Morgan Edge. If this was true, that means Zod is technically responsible for leading the Kryptonian army on John’s Earth and killing millions of humans and causing John’s hatred for the Earth-Prime Superman.