Subgroup structure of symmetric group:S8
This article gives specific information, namely, subgroup structure, about a particular group, namely: symmetric group:S8.
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FACTS TO CHECK AGAINST FOR SUBGROUP STRUCTURE: (finite group)
Lagrange's theorem (order of subgroup times index of subgroup equals order of whole group, so both divide it), |order of quotient group divides order of group (and equals index of corresponding normal subgroup)
Sylow subgroups exist, Sylow implies order-dominating, congruence condition on Sylow numbers|congruence condition on number of subgroups of given prime power order
normal Hall implies permutably complemented, Hall retract implies order-conjugate
|Number of subgroups|| 151221|
Compared with : 1,2,6,30,156,1455,11300,151221
|Number of conjugacy classes of subgroups|| 296|
Compared with : 1,2,4,11,19,56,96,296,554,1593,...
|Number of automorphism classes of subgroups|| 96|
Compared with : 1,2,4,11,19,37,96,296,554,1593,...