Remove index.php and subdirectory in url string Joomla

I am trying to remove the subdirectory name and the index.php from a website running Joomla. I have the following setup:
../public_html/.htaccess
../public_html/subdir/htaccess.txt

I have looked through several articles such as this one that have helped me a little but I can't quite get there. I have also studied a little about the .htaccess file from articles such as this one and this one to help me with this.

The setup that works but displays the subdirectory and index.php looks like this:

cat /../public_html/.htaccess

 RewriteEngine on
    RewriteCond %{HTTP_HOST} ^(www\.)?domain\.co\.uk$ 
    RewriteCond %{REQUEST_URI} !^/subdir/ 
    RewriteCond %{REQUEST_FILENAME} !-f 
    RewriteCond %{REQUEST_FILENAME} !-d 
    RewriteRule ^(.*)$ /subdir/$1 
    RewriteCond %{HTTP_HOST} ^(www\.)?domainn\.co\.uk$ 
    RewriteRule ^(/)?$ subdir/index.php [L]

    # Use PHP5.4 as default
    AddHandler application/x-httpd-php54 .php

cat /../public_html/subdir/htaccess.txt (Joomla default)

##
# @package    Joomla
# @copyright  Copyright (C) 2005 - 2015 Open Source Matters. All rights reserved.
# @license    GNU General Public License version 2 or later; see LICENSE.txt
##

##
# READ THIS COMPLETELY IF YOU CHOOSE TO USE THIS FILE!
#
# The line just below this section: 'Options +FollowSymLinks' may cause problems
# with some server configurations.  It is required for use of mod_rewrite, but may already
# be set by your server administrator in a way that disallows changing it in
# your .htaccess file.  If using it causes your server to error out, comment it out (add # to
# beginning of line), reload your site in your browser and test your sef url's.  If they work,
# it has been set by your server administrator and you do not need it set here.
##

## No directory listings
IndexIgnore *

## Can be commented out if causes errors, see notes above.
Options +FollowSymlinks
Options -Indexes

## Mod_rewrite in use.

RewriteEngine On

## Begin - Rewrite rules to block out some common exploits.
# If you experience problems on your site block out the operations listed below
# This attempts to block the most common type of exploit `attempts` to Joomla!
#
# Block out any script trying to base64_encode data within the URL.
RewriteCond %{QUERY_STRING} base64_encode[^(]*\([^)]*\) [OR]
# Block out any script that includes a <script> tag in URL.
RewriteCond %{QUERY_STRING} (<|%3C)([^s]*s)+cript.*(>|%3E) [NC,OR]
# Block out any script trying to set a PHP GLOBALS variable via URL.
RewriteCond %{QUERY_STRING} GLOBALS(=|\[|\%[0-9A-Z]{0,2}) [OR]
# Block out any script trying to modify a _REQUEST variable via URL.
RewriteCond %{QUERY_STRING} _REQUEST(=|\[|\%[0-9A-Z]{0,2})
# Return 403 Forbidden header and show the content of the root homepage
RewriteRule .* index.php [F]
#
## End - Rewrite rules to block out some common exploits.

## Begin - Custom redirects
#
# If you need to redirect some pages, or set a canonical non-www to
# www redirect (or vice versa), place that code here. Ensure those
# redirects use the correct RewriteRule syntax and the [R=301,L] flags.
#
## End - Custom redirects

##
# Uncomment following line if your webserver's URL
# is not directly related to physical file paths.
# Update Your Joomla! Directory (just / for root).
##

# RewriteBase /

## Begin - Joomla! core SEF Section.
#
RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
#
# If the requested path and file is not /index.php and the request
# has not already been internally rewritten to the index.php script
RewriteCond %{REQUEST_URI} !^/index\.php
# and the requested path and file doesn't directly match a physical file
RewriteCond %{REQUEST_FILENAME} !-f
# and the requested path and file doesn't directly match a physical folder
RewriteCond %{REQUEST_FILENAME} !-d
# internally rewrite the request to the index.php script
RewriteRule .* index.php [L]
#
## End - Joomla! core SEF Section.

I have tried to follow the suggestions of the article mentioned above and got the files to look like this:

cat /../public_html/.htaccess.try

RewriteEngine on
RewriteCond %{HTTP_HOST} ^(www\.)?domain\.co\.uk$ [NC]
RewriteRule ^(.*)$ http://domain/$1 [R=301,L]
RewriteCond %{HTTP_HOST} ^(www\.)?domain\.co\.uk$ 
RewriteRule ^(.*)$ /subdir/$1 [PT,L,QSA]
#RewriteRule ^(/)?$ subdir/index.php [L]

# Use PHP5.4 as default
AddHandler application/x-httpd-php54 .php

cat /../public_html/subdir/htaccess.txt.try

.
.
.
# RewriteBase /
## Begin - Joomla! core SEF Section.
#
RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
#
# If the requested path and file is not /index.php and the request
# has not already been internally rewritten to the index.php script
RewriteCond %{REQUEST_URI} !^/index\.php
# and the requested path and file doesn't directly match a physical file
RewriteCond %{REQUEST_FILENAME} !-f
# and the requested path and file doesn't directly match a physical folder
RewriteCond %{REQUEST_FILENAME} !-d
# internally rewrite the request to the index.php script
RewriteRule ^(.*)$ /$1 [L]

RewriteRule ^subdir/index.php?(.*)$ /$1 [L]
#
## End - Joomla! core SEF Section.

With the two .try files saved instead of the originals, I am getting a redirection loop, as printed out by the browser:

This webpage has a redirect loop

ERR_TOO_MANY_REDIRECTS

I have also tried modifying the files myself but most of them lead to "internal server error" probably meaning the syntax written is not correct, or they overrule each other?

Any idea how the two files should look like?