Submenu doesn't get displayed - html

Question

I'm trying to make sub-menus for my menu, but something just isn't right and doesn't pop out like I want.
<div class="navbox">
<ul class="nav">
<li>Program</li>
<li><ul>
<li>Teknik</li>
<li>Naturvetenskap</li>
<li>El</li>
</ul></li>
</ul></div>
* { margin:0;
padding:0;
}
html {height: 100%;}
body{
position: relative;
height: 100%;
background: -webkit-gradient(linear, left top, left bottom, from(#ccc), to(#fff));
}
.navbox {
position: relative;
float: left;
}
ul.nav {
list-style: none;
display: block;
width: 200px;
position: relative;
top: 100px;
left: 100px;
padding: 60px 0 60px 0;
background: url(shad2.png) no-repeat;
-webkit-background-size: 50% 100%;
display: inline-table;
}
li {
margin: 5px 0 0 0;
}
ul.nav li a {
-webkit-transition: all 0.3s ease-out;
background: #cbcbcb url(border.png) no-repeat;
color: #174867;
padding: 7px 15px 7px 15px;
-webkit-border-top-right-radius: 10px;
-webkit-border-bottom-right-radius: 10px;
width: 100px;
display: block;
text-decoration: none;
-webkit-box-shadow: 2px 2px 4px #888;
}
ul.nav li :hover {
background: #ebebeb url(border.png) no-repeat;
color: #67a5cd;
padding: 7px 15px 7px 30px;
}
The problem with the code is that I want to get the link "Program" to display the submenus under, "Teknik" "Naturvetenskap" "El" but I just can't get them to pop out under. I can't get them to pop out at all, and that's all I need, I'll have to deal with design later.

Answer 1

Made it into a codepen for you - http://codepen.io/anon/pen/pxfKE - and tried to answer what I think you were looking for. It should be pretty self explanatory, but let me know if you need help understanding it :)