Hi,
Sorry but I do not understand . can you explain me better?

Hi,
Yes with conditions.

Example: you can create a radio field with these parameters:
- Show on registration
- Hidden on Edit profile
- Required
- Options:
1|Group 1
2|Group 2
.....
- Set conditions
if equal to custom value "1" add to Group 1
if equal to custom value "2" add to Group 2
.....

Still does not mean that you can choose from the frontend user group site where registered

Why? you can insert dropdown(select) or radio with option and condition to choose which group.

Another example:
You can add this in option list
1|Author
2|Editor
3|Publisher
4|All

and set condition:
if equal to custom value "1" add to Author
if equal to custom value "2" add to Editor
if equal to custom value "3" add to Publisher
if equal to custom value "4" add to Author,Editor,Publisher

In registration the user see a list of groups (choose group on registration)

You can mix group based on fields value.
Another advantage is that you can translate the group name (Joomla does not allow it)
1|T_AUTHOR
2|T_EDITOR
3|T_PUBLISHER
You can configure translations from Administration->language manager->Overrides