How to install .net framework 4.6.1 runtime on Windows Server 2012 R2

I spun up a aws EC2 instance Windows Server 2012 R2.

It comes pre-loaded with .Net 4.5.

But I'm running code that requires 4.6.1.

I tried both the online and offline installers. I'm an admin. I'm selecting "run as administrator" on the installer(s). It extracts the package. The install progress bar reaches complete. Either way, I get the same error message:

The error message is not helpful and I do not know how to proceed.

The log file shows the following:

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OS Version = 6.3.9600, SP = 0.0, Platform 2
 OS Description = Win2k12R2 - x64 Standard Edition 


MSI = 5.0.9600.19082
 Windows servicing = 6.3.9600.18384


CommandLine = D:\0ce7916d947e0ebb7a5825cc0c\\Setup.exe /x86 /x64 /redist
 TimeZone = Pacific Standard Time
 Initial LCID = 1033

 Using Simultaneous Download and Install mechanism

Operation: Installing

Package Name = Microsoft .NET Framework 4.6.1 Setup
 Package Version = 4.6.01055

User Experience Data Collection Policy: Disabled

Number of applicable items: 6

 Exe (D:\0ce7916d947e0ebb7a5825cc0c\SetupUtility.exe) succeeded.

 Exe (D:\0ce7916d947e0ebb7a5825cc0c\SetupUtility.exe) succeeded.

 Exe (D:\0ce7916d947e0ebb7a5825cc0c\x64-Windows8.1-KB3102467-x64.cab) failed with 0x57 - The parameter is incorrect. .
 Final Result: Installation failed with error code: (0x00000057), "The parameter is incorrect. " (Elapsed time: 0 00:00:49).

This can be caused if the Windows Modules Installer service is disabled.