Subgroups — #24922677⋊C₃ #44545091

Order 32028.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇×C₁₅₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#24922677	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇×C₁₅₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic
5	C₁₇×C₁₅₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	Dic₁₅₇⋊C₃	—	17	1	no	maximal, Hall
7	C₂×C₁₅₇⋊C₃	—	17	1	no	—
8	Dic₁₅₇	—	17	1	no	Hall
9	C₁₅₇⋊C₃	#595	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₅₇	—	17	1	no	—
11	C₃×#595	—	157	1	no	maximal, Hall
12	C₁₅₇	C₃×#595	1	1	yes	characteristic, complemented, Sylow
13	C₃×D₁₇	—	157	1	no	—
14	#595	—	157	1	no	Hall
15	C₃×C₁₇	—	157	1	no	Hall
16	D₁₇	D₁₅₇⋊C₃	1	1	yes	characteristic
17	C₁₇	Dic₁₅₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2669	1	no	Hall
19	C₂×C₃	—	2669	1	no	—
20	C₄	—	2669	1	no	Sylow
21	C₃	—	157	1	no	Sylow
22	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₇×C₁₅₇	C₃×C₄
prime radical	D₁₇×C₁₅₇⋊C₃	C₂
cosocle	D₁₇×C₁₅₇	C₂×C₃
LCS	G ▷ 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.