Subgroups — #46828255

Order 34476.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇⋊#11759815	C₂	1	1	yes	maximal, characteristic
2	#26040106	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×#92788	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃⋊D₂₂₁	C₂×C₃	1	1	yes	characteristic
5	C₁₃²×C₁₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#11725131⋊C₃	—	13	14	no	maximal
7	#14523144	—	17	1	no	maximal, Hall
8	C₁₇⋊(D₁₃⋊C₃)	—	13	14	no	—
9	#11759815	—	17	1	no	—
10	#11725131	—	13	14	no	—
11	#10621728	—	17	1	no	Hall
12	C₁₇×C₁₃⋊C₃	—	13	14	no	—
13	#92788	#595	1	1	yes	characteristic, complemented, Hall
14	D₂₂₁	—	13	14	no	—
15	C₁₃⋊D₁₃	—	17	1	no	—
16	C₁₃×C₁₇	AGL(1,𝔽₁₃)	1	14	yes	complemented
17	C₃×#595	—	169	1	no	Hall
18	C₁₃²	C₃×#595	1	1	yes	characteristic, complemented, Sylow
19	AGL(1,𝔽₁₃)	—	221	14	no	—
20	C₃×D₁₇	—	169	1	no	—
21	D₁₃⋊C₃	—	221	14	no	—
22	#595	—	169	1	no	Hall
23	#261	—	221	14	no	—
24	C₃×C₁₇	—	169	1	no	Hall
25	C₁₃⋊C₃	—	13	14	no	—
26	D₁₇	—	169	1	no	—
27	D₁₃	—	221	14	no	—
28	C₁₇	#14523144	1	1	yes	characteristic, complemented, Sylow
29	C₁₃	#11725131⋊C₃	1	14	yes	complemented
30	C₃×C₄	—	2873	1	no	Hall
31	C₂×C₃	—	2873	1	no	—
32	C₄	—	2873	1	no	Sylow
33	C₃	—	169	1	no	Sylow
34	C₂	—	2873	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃²×C₁₇	C₃×C₄
prime radical	C₁₇⋊#11759815	C₂
cosocle	C₁₃⋊D₂₂₁	C₂×C₃
LCS	G ▷ C₁₃²×C₁₇
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

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