Subgroup structure of special linear group:SL(2,9)

This article gives specific information, namely, subgroup structure, about a particular group, namely: special linear group:SL(2,9).
View subgroup structure of particular groups | View other specific information about special linear group:SL(2,9)

This article describes the subgroup structure of special linear group:SL(2,9), which is the special linear group of degree two over field:F9. The group has order 720.

Family contexts

Family name	Parameter values	General discussion of subgroup structure of family
special linear group of degree two	field:F9, i.e., the group $SL(2,9)$	subgroup structure of special linear group of degree two over a finite field
double cover of alternating group $2\cdot A_n$	degree $n=6$, i.e., the group $2\cdot A_6$	subgroup structure of double cover of alternating group

Tables for quick information

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

Quick summary

Item	Value
number of subgroups	588
number of conjugacy classes of subgroups	27
number of automorphism classes of subgroups	PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] One of the people editing this page intended to fill in this information at a later stage, but hasn't gotten around to doing it yet. If you see this placeholder for a long time, file an error report at the error reporting page.