Subgroups — C₃⋊#22551026 #37587643

Order 24492.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₀₄₁	C₂	1	1	yes	maximal, characteristic
2	#22551026	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₁₅₇	C₄	1	1	yes	characteristic, complemented, Hall
4	D₂₀₄₁	D₃	1	1	yes	characteristic
5	C₁₃×C₁₅₇	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊#10597845	—	13	1	no	maximal, Hall
7	C₃×D₁₅₇	—	13	1	no	—
8	#10597845	—	39	1	no	Hall
9	C₃×C₁₅₇	#261	1	1	yes	characteristic, complemented, Hall
10	D₁₅₇	—	13	1	no	—
11	C₁₅₇	C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
12	C₃⋊#261	—	157	1	no	maximal, Hall
13	C₃×D₁₃	—	157	1	no	—
14	#261	—	471	1	no	Hall
15	C₃×C₁₃	#10597845	1	1	yes	characteristic, complemented, Hall
16	D₁₃	—	157	1	no	—
17	C₁₃	C₃⋊#10597845	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	2041	1	no	Hall
19	C₂×C₃	—	2041	1	no	—
20	C₄	—	6123	1	no	Sylow
21	C₃	#22551026	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	2041	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃×C₁₅₇	C₄
prime radical, cosocle	C₃×D₂₀₄₁	C₂
LCS	G ▷ C₃×C₁₃×C₁₅₇
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.