There have been a few online Mindmappers that I have liked over the years. https://bubbl.us/ is nice because you can easily make a mindmap without logging in, and it lets you export it as an image. http://www.mindomo.com is one of the most fully featured services that has almost the same control as a desktop program, and has done since before 2008 when I first used it.
My current favourite is https://coggle.it because it is so simple for students to use (although you do now have to log in to use it). There are few bells or whistles, just clean lines and text that is really simple to edit, even on an ipad. I just have this little example here
This shows it being used on an iPad