Subgroups — C₃⋊(C₃⋊#11923884) #23780920

Order 10404.

168 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⋊#11923884	—	3	4	no	maximal
3	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇⋊D₁₇	D₃	1	4	yes	—
5	#11923884	—	9	1	no	Hall
6	C₃×C₁₇²	Dic₃	1	4	yes	complemented
7	C₃⋊(C₃⋊#595)	—	17	2	no	maximal
8	C₁₇⋊D₁₇	C₃⋊D₃	1	1	yes	characteristic
9	C₃²×D₁₇	—	17	2	no	—
10	C₃²×D₁₇	—	34	8	no	—
11	C₁₇²	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
12	C₃⋊#595	—	51	8	no	—
13	C₃²×C₁₇	—	2	8	no	—
14	C₃²×C₁₇	#595	1	2	yes	complemented
15	C₃×D₁₇	—	17	8	no	—
16	C₃×D₁₇	—	34	32	no	—
17	#595	—	153	2	no	—
18	C₃×C₁₇	—	2	32	no	—
19	C₃×C₁₇	C₃⋊#595	1	8	yes	complemented
20	C₃⋊Dic₃	—	289	1	no	Hall
21	D₁₇	—	17	2	no	—
22	D₁₇	—	34	8	no	—
23	C₂×C₃²	—	289	1	no	—
24	C₁₇	—	2	8	no	—
25	C₁₇	C₃⋊(C₃⋊#595)	1	2	yes	complemented
26	Dic₃	—	867	4	no	—
27	C₃²	#11923884	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	289	4	no	—
29	C₄	—	2601	1	no	Sylow
30	C₃	C₃⋊#11923884	1	4	yes	complemented
31	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.