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As we know, the normal subgroups can be found by inspection from the character table of a group G,my question is if all subgroups can be found by the character table of a group G, if not, then what "good" results can we get?

I am sorry,my question is not clear.

what I want to know is if we can caculate the number of Sylow subgroups by character table.

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    $\begingroup$ Note that the group of the square and the quaternion group have identical character tables but very different subgroup structures. $\endgroup$ Oct 11, 2013 at 4:37
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    $\begingroup$ @BruceThou, please ask all your question in the question body (you can edit your question by following the `edit' link that you (hopefully) can find right after the question) $\endgroup$ Oct 11, 2013 at 5:30
  • $\begingroup$ What do you mean by "find"? The way we can find the normal subgroups is as unions of conjugacy classes. For arbitrary subgroups, this will of course not be the sort of thing to look for, so do you mean "determine orders and isomorphism classes" or something stronger? $\endgroup$ Oct 11, 2013 at 7:01

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