Subgroups — C₃⋊(C₃⋊#16813360) #44570021

Order 32436.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16813360	—	3	4	no	maximal
3	C₃²×C₁₇×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×D₅₃	D₃	1	4	yes	—
5	#16813360	—	9	1	no	Hall
6	C₃×C₁₇×C₅₃	Dic₃	1	4	yes	complemented
7	C₃⋊(C₃⋊#6157)	—	17	1	no	maximal, Hall
8	C₁₇×D₅₃	C₃⋊D₃	1	1	yes	characteristic
9	C₃²×D₅₃	D₁₇	1	1	yes	characteristic
10	C₁₇×C₅₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
11	C₃⋊#6157	—	51	4	no	—
12	C₃⋊Dic₅₁	—	53	1	no	maximal, Hall
13	C₃²×C₅₃	Dic₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₅₃	D₅₁	1	4	yes	—
15	C₂×C₃²×C₁₇	—	53	1	no	—
16	#6157	—	153	1	no	Hall
17	Dic₅₁	—	159	4	no	—
18	C₃×C₅₃	Dic₅₁	1	4	yes	complemented
19	C₃²×C₁₇	#6157	1	1	yes	characteristic, complemented, Hall
20	D₅₃	C₃⋊D₅₁	1	1	yes	characteristic
21	C₂×C₃×C₁₇	—	53	4	no	—
22	Dic₁₇	—	477	1	no	Hall
23	C₅₃	C₃⋊Dic₅₁	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₁₇	C₃⋊#6157	1	4	yes	complemented
25	C₃⋊Dic₃	—	901	1	no	Hall
26	C₂×C₁₇	—	53	1	no	—
27	C₂×C₃²	—	53	1	no	—
28	C₁₇	C₃⋊(C₃⋊#6157)	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	2703	4	no	—
30	C₃²	#16813360	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	53	4	no	—
32	C₄	—	8109	1	no	Sylow
33	C₃	C₃⋊#16813360	1	4	yes	complemented
34	C₂	—	53	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₇×C₅₃	C₄
prime radical, cosocle	C₃²×C₁₇×D₅₃	C₂
LCS	G ▷ C₃²×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.