Subgroups — C₉⋊#16861898 #49152607

Order 37332.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16861898	—	3	1	no	maximal
3	C₉×C₁₇×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×D₆₁	D₃	1	1	yes	characteristic
5	#16861898	—	9	1	no	Hall
6	C₃×C₁₇×C₆₁	Dic₃	1	1	yes	characteristic
7	C₉⋊#6923	—	17	1	no	maximal, Hall
8	C₁₇×D₆₁	D₉	1	1	yes	characteristic
9	C₉×D₆₁	D₁₇	1	1	yes	characteristic
10	C₁₇×C₆₁	Dic₉	1	1	yes	characteristic, complemented, Hall
11	C₃⋊#6923	—	51	1	no	—
12	Dic₁₅₃	—	61	1	no	maximal, Hall
13	C₉×C₆₁	Dic₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₆₁	D₅₁	1	1	yes	characteristic
15	C₂×C₉×C₁₇	—	61	1	no	—
16	#6923	—	153	1	no	Hall
17	Dic₅₁	—	183	1	no	—
18	C₃×C₆₁	Dic₅₁	1	1	yes	characteristic
19	C₉×C₁₇	#6923	1	1	yes	characteristic, complemented, Hall
20	D₆₁	D₁₅₃	1	1	yes	characteristic
21	C₂×C₃×C₁₇	—	61	1	no	—
22	Dic₁₇	—	549	1	no	Hall
23	C₆₁	Dic₁₅₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₁₇	C₃⋊#6923	1	1	yes	characteristic
25	Dic₉	—	1037	1	no	Hall
26	C₂×C₁₇	—	61	1	no	—
27	C₂×C₉	—	61	1	no	—
28	C₁₇	C₉⋊#6923	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	3111	1	no	—
30	C₉	#16861898	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	61	1	no	—
32	C₄	—	9333	1	no	Sylow
33	C₃	C₃⋊#16861898	1	1	yes	characteristic
34	C₂	—	61	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₇×C₆₁	C₄
Frattini	C₃	C₃⋊#16861898
socle	C₃×C₁₇×C₆₁	Dic₃
prime radical	C₃×C₁₇×D₆₁	D₃
cosocle	C₉×C₁₇×D₆₁	C₂
LCS	G ▷ C₉×C₁₇×C₆₁
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.