Subgroups — C₃⋊(C₃⋊#11923883) #23780919

Order 10404.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#11923883	—	3	4	no	maximal
3	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇⋊D₁₇	D₃	1	4	yes	—
5	#11923883	—	9	1	no	Hall
6	C₃×C₁₇²	Dic₃	1	4	yes	complemented
7	C₃⋊(C₃⋊#595)	—	17	18	no	maximal
8	C₁₇⋊D₁₇	C₃⋊D₃	1	1	yes	characteristic
9	C₃²×D₁₇	—	17	18	no	—
10	C₁₇²	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
11	C₃⋊#595	—	51	72	no	—
12	C₃²×C₁₇	#595	1	18	yes	complemented
13	C₃×D₁₇	—	17	72	no	—
14	#595	—	153	18	no	—
15	C₃×C₁₇	C₃⋊#595	1	72	yes	complemented
16	C₃⋊Dic₃	—	289	1	no	Hall
17	D₁₇	—	17	18	no	—
18	C₂×C₃²	—	289	1	no	—
19	C₁₇	C₃⋊(C₃⋊#595)	1	18	yes	complemented
20	Dic₃	—	867	4	no	—
21	C₃²	#11923883	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃	—	289	4	no	—
23	C₄	—	2601	1	no	Sylow
24	C₃	C₃⋊#11923883	1	4	yes	complemented
25	C₂	—	289	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₇²	C₄
prime radical, cosocle	C₃²×C₁₇⋊D₁₇	C₂
LCS	G ▷ C₃²×C₁₇²
UCS	C₁

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