Several... Assuming the title doesn't match your query for some other reason though... No https here...
Why are you specifying HTTP/1.1? Won't 1.0 suffice? Are you using software virtual servers? If not, use 10 and no host: header. if you re using virtual servers, then IS the virtual called 192.3.22.3? Or something else? If it's something else, then the host won't match and the request will fail.
For later versions of LTM you're missing the extra \r\n off the end of the query too (HTTP/1.0 and HTTP/1.1 need a blank link to tell the server you've finished the multi-line query)
Failing those quick ones, what is the response when you telnet to the port and perform the request by hand? Any clues in there? If this really IS an HTTPS serve you're querying, you can use openssl to open a connection and talk HTTP to it. eg..
openssl s_client -connect :
and then copy & paste (Or type) the multi-line request and check the return.
H