Subgroups — PSL(2,𝔽₁₇) #72209593

Order 2448.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3633	—	18	1	no	maximal
2	#595	—	18	1	no	—
3	D₁₇	—	18	1	no	—
4	S₄	—	102	2	no	maximal
5	D₉	—	136	1	no	maximal
6	C₁₇	—	18	1	no	Sylow
7	D₈	—	153	1	no	maximal, Sylow
8	A₄	—	102	2	no	—
9	C₉	—	136	1	no	Sylow
10	D₄	—	153	2	no	—
11	C₈	—	153	1	no	—
12	D₃	—	408	1	no	—
13	C₂²	—	102	2	no	—
14	C₄	—	153	1	no	—
15	C₃	—	136	1	no	—
16	C₂	—	153	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.