Apache mod-rewrite .htaccess subdomain redirect issue - php

Question

I'm struggling to get my .htaccess configured properly to setup a subdomain redirect for specific subdomains. I want to redirect (not mask) a subdomain to a specific page and repeat this configuration multiple times.
I'm hosted on a Google Compute Engine currently using Cloud DNS (used to host on Godaddy in which subdomain management was very simple)
before:
# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
after:
# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteCond %{HTTP_HOST} ^sat.theteachertutors.com$ [NC]
RewriteRule ^(.*)$ /private-sat-act-tutoring/$1 [L]
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>
I tried the config above but the redirect does not work. The target url is: https://www.theteachertutors.com/private-sat-act-tutoring/
Any guidance/tips would be most appreciated. I've search for other examples but can't get this configuration to work at all, ie: http://sat.theteachertutors.com
Thanks

Answer 1

You were close to the solution, change the rewrite rule to this:
RewriteRule ^(.*)$ https://www.theteachertutors.com/private-sat-act-tutoring/$1 [R=301,L]
When you are redirecting to another domain/subdomain you have to use the full URL. Also I use R=301 to mark the redirect as a permanent redirect (by default rules that point to another domain use a 302 redirect).