Logo center, Menu above with menu left and social icons right

I would like to set up the header like this – see image below. I set “Menu and Logo Position” to “Logo center, Menu above.” I was able to float the menu left with:

.html_header_top.html_logo_center .main_menu ul:first-child {
  float: left;
}

But I can’t get the icons up where they are in the image:

If you show me the PHP modifications I can work out the CSS

Thanks so much for any assistance
David