Subgroups — C₃⋊#24922678 #44545111

Order 32028.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₁₅₇	C₂	1	1	yes	maximal, characteristic
2	#24922678	—	3	1	no	maximal, Hall
3	C₃×C₁₇×C₁₅₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₇×D₁₅₇	D₃	1	1	yes	characteristic
5	C₁₇×C₁₅₇	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₃⋊#10597845	—	17	1	no	maximal, Hall
7	C₃×D₁₅₇	D₁₇	1	1	yes	characteristic
8	#10597845	—	51	1	no	Hall
9	C₃×C₁₅₇	Dic₁₇	1	1	yes	characteristic, complemented, Hall
10	D₁₅₇	D₅₁	1	1	yes	characteristic
11	Dic₅₁	—	157	1	no	maximal, Hall
12	C₁₅₇	Dic₅₁	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₇	—	157	1	no	—
14	Dic₁₇	—	471	1	no	Hall
15	C₃×C₁₇	#10597845	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇	—	157	1	no	—
17	C₁₇	C₃⋊#10597845	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	2669	1	no	Hall
19	C₂×C₃	—	157	1	no	—
20	C₄	—	8007	1	no	Sylow
21	C₃	#24922678	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	157	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₇×C₁₅₇	C₄
prime radical, cosocle	C₃×C₁₇×D₁₅₇	C₂
LCS	G ▷ C₃×C₁₇×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.