Subgroups — C₉⋊#11923883 #23780849

Order 10404.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#11923883	—	3	1	no	maximal
3	C₉×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇⋊D₁₇	D₃	1	1	yes	characteristic
5	#11923883	—	9	1	no	Hall
6	C₃×C₁₇²	Dic₃	1	1	yes	characteristic
7	C₉⋊#595	—	17	18	no	maximal
8	C₁₇⋊D₁₇	D₉	1	1	yes	characteristic
9	C₉×D₁₇	—	17	18	no	—
10	C₁₇²	Dic₉	1	1	yes	characteristic, complemented, Sylow
11	C₃⋊#595	—	51	18	no	—
12	C₉×C₁₇	#595	1	18	yes	complemented
13	C₃×D₁₇	—	17	18	no	—
14	#595	—	153	18	no	—
15	C₃×C₁₇	C₃⋊#595	1	18	yes	—
16	Dic₉	—	289	1	no	Hall
17	D₁₇	—	17	18	no	—
18	C₂×C₉	—	289	1	no	—
19	C₁₇	C₉⋊#595	1	18	yes	complemented
20	Dic₃	—	867	1	no	—
21	C₉	#11923883	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃	—	289	1	no	—
23	C₄	—	2601	1	no	Sylow
24	C₃	C₃⋊#11923883	1	1	yes	characteristic
25	C₂	—	289	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₇²	C₄
Frattini	C₃	C₃⋊#11923883
socle	C₃×C₁₇²	Dic₃
prime radical	C₃×C₁₇⋊D₁₇	D₃
cosocle	C₉×C₁₇⋊D₁₇	C₂
LCS	G ▷ C₉×C₁₇²
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.