Subgroups — C₃⋊(C₃⋊#11923885) #23780921

Order 10404.

96 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⋊#11923885	—	3	4	no	maximal
3	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×D₁₇	D₃	1	4	yes	—
5	#11923885	—	9	1	no	Hall
6	C₃×C₁₇²	Dic₃	1	4	yes	complemented
7	C₃⋊(C₃⋊#595)	—	17	1	no	maximal
8	C₃⋊Dic₅₁	—	17	1	no	maximal
9	C₁₇×D₁₇	C₃⋊D₃	1	1	yes	characteristic
10	C₂×C₃²×C₁₇	—	17	1	no	—
11	C₃²×D₁₇	D₁₇	1	1	yes	characteristic
12	C₁₇²	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
13	C₃⋊#595	—	51	4	no	—
14	Dic₅₁	—	51	4	no	—
15	C₃²×C₁₇	—	4	4	no	—
16	C₃²×C₁₇	Dic₁₇	1	1	yes	characteristic, complemented
17	C₃²×C₁₇	#595	1	1	yes	characteristic, complemented
18	C₂×C₃×C₁₇	—	17	4	no	—
19	C₃×D₁₇	D₅₁	1	4	yes	—
20	#595	—	153	1	no	—
21	Dic₁₇	—	153	1	no	—
22	C₃×C₁₇	—	4	16	no	—
23	C₃×C₁₇	Dic₅₁	1	4	yes	complemented
24	C₃×C₁₇	C₃⋊#595	1	4	yes	complemented
25	C₃⋊Dic₃	—	289	1	no	Hall
26	C₂×C₁₇	—	17	1	no	—
27	D₁₇	C₃⋊D₅₁	1	1	yes	characteristic
28	C₂×C₃²	—	17	1	no	—
29	C₁₇	—	4	4	no	—
30	C₁₇	C₃⋊Dic₅₁	1	1	yes	characteristic, complemented
31	C₁₇	C₃⋊(C₃⋊#595)	1	1	yes	characteristic, complemented
32	Dic₃	—	867	4	no	—
33	C₃²	#11923885	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃	—	17	4	no	—
35	C₄	—	2601	1	no	Sylow
36	C₃	C₃⋊#11923885	1	4	yes	complemented
37	C₂	—	17	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.