The latest software for the LG G4 T-Mobile is Android 6.0 Marshmallow , software version H81120x.
To check what version of software is installed on your device:
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From the Home screen, tap Apps
> Settings
> General tab > About phone
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Tap Software info.
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View the current software under Software version.
 
Select software for more info:
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       Android 6.0 Marshmallow, software version H81120x - Release date December, 2017
- Wi-Fi Calling Fix
 - KRACK
 
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       Android 6.0 Marshmallow, software version H81120v - Release date May, 2017
- Android Security Update (2017-04-01)
 - E911 timer fix
 
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       Android 6.0 Marshmallow, software version H81120r - Release date January, 2017
- Android Security Update (2017-01-01)
 
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       Android 6.0 Marshmallow, software version H81120q - Release date December, 2016
- Android Security Update (2016-11-01)
 
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       Android 6.0 Marshmallow, software version H81120p - Release date October, 2016
- Google security patches
 - General maintenance
 
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       Android 6.0 Marshmallow, software version H81120o - Release date July, 2016
- Google security patches
 - General maintenance
 
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       Android 6.0 Marshmallow, software version H81120i - Release date February, 2016
- Android 6.0 Marshmallow Software Update
 - T-Mobile Video Calling Support added
 - General maintenance
 
 -  
       Android 5.1 Lollipop, software version H81110n - Release date August, 2015
- Security updates (including Stagefright)
 - General maintenance
 
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       Android 5.1 Lollipop, software version H81110h - Release date June, 2015
- Anti-Rollback added
 - General maintenance
 
 
Software Update
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When the software update is available, the update icon will display in the status bar at the top of the screen. Swipe down from the top and tap the notification.
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Tap RESTART & INSTALL.
 
Note: If prompted, connect to a Wi-Fi network to download the software update.
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Your device will restart to perform the update.
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When the update is complete, your phone will restart and transition through a series of alerts stating Android is upgrading.
 
Troubleshooting
If your devices has not updated, you can manually check if a new software update is available.
-  
From the Home screen, tap Apps
> Settings
> General tab > System updates
 -  
Tap Check for new system update to manually check for a new update.
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You will be prompted if a new software update is available, tap Download now. Continue from Software Update, step 1.
 
To download LG Bridge select your operating system:
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Connect your mobile device to your computer with a USB cable.
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On your mobile device, tap the USB notification in the notification panel.
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Tap Media device (MTP) if not already selected. Media device (MTP) must be selected before LG Bridge opens.
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Open LG Bridge, then from the Software update tab click Software update button to check for an available update.
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If a software update is available, select Start to update your mobile device.