Subgroups — C₃⋊#16813359 #24925213

Order 10812.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₇×C₅₃	C₂	1	1	yes	maximal, characteristic
2	#16813359	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₇×C₅₃	D₃	1	1	yes	characteristic
5	C₁₇×C₅₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₁₅₉	—	17	1	no	maximal, Hall
7	C₂×C₃×C₅₃	—	17	1	no	—
8	Dic₅₃	—	51	1	no	Hall
9	C₃⋊#595	—	53	1	no	maximal, Hall
10	C₃×C₅₃	#595	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅₃	—	17	1	no	—
12	C₃×D₁₇	D₅₃	1	1	yes	characteristic
13	#595	—	159	1	no	Hall
14	C₅₃	C₃⋊#595	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₇	Dic₅₃	1	1	yes	characteristic, complemented, Hall
16	D₁₇	D₁₅₉	1	1	yes	characteristic
17	C₁₇	Dic₁₅₉	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	901	1	no	Hall
19	C₂×C₃	—	17	1	no	—
20	C₄	—	2703	1	no	Sylow
21	C₃	#16813359	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₇×C₅₃	C₄
prime radical, cosocle	C₃×D₁₇×C₅₃	C₂
LCS	G ▷ C₃×C₁₇×C₅₃
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.