Subgroups — C₃×C₃⋊#11923884 #23780912

Order 10404.

152 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	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#11923884	—	3	1	no	maximal
4	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇⋊D₁₇	—	2	1	no	—
6	C₃×C₁₇⋊D₁₇	D₃	1	1	yes	characteristic
7	C₃×C₁₇⋊D₁₇	C₂×C₃	1	1	yes	characteristic
8	#11923884	—	3	1	no	Hall
9	C₃×C₁₇²	—	2	1	no	—
10	C₃×C₁₇²	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₁₇²	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×C₃⋊#595	—	17	2	no	maximal
13	C₁₇⋊D₁₇	C₃×D₃	1	1	yes	characteristic
14	C₃²×D₁₇	—	17	2	no	—
15	C₃²×D₁₇	—	34	8	no	—
16	C₁₇²	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
17	C₃⋊#595	—	17	2	no	—
18	C₃×#595	—	51	2	no	—
19	C₃²×C₁₇	—	2	8	no	—
20	C₃²×C₁₇	#595	1	2	yes	complemented
21	C₃×D₁₇	—	17	2	no	—
22	C₃×D₁₇	—	17	2	no	—
23	C₃×D₁₇	—	34	8	no	—
24	C₃×D₁₇	—	34	8	no	—
25	C₃×D₁₇	—	34	2	no	—
26	C₃×D₁₇	—	34	16	no	—
27	#595	—	51	2	no	—
28	C₃×C₁₇	—	2	16	no	—
29	C₃×C₁₇	—	2	2	no	—
30	C₃×C₁₇	—	2	8	no	—
31	C₃×C₁₇	—	2	8	no	—
32	C₃×C₁₇	C₃×#595	1	2	yes	complemented
33	C₃×C₁₇	C₃⋊#595	1	2	yes	complemented
34	C₃×Dic₃	—	289	1	no	Hall
35	D₁₇	—	17	2	no	—
36	D₁₇	—	34	8	no	—
37	C₂×C₃²	—	289	1	no	—
38	C₁₇	—	2	8	no	—
39	C₁₇	C₃×C₃⋊#595	1	2	yes	complemented
40	C₃×C₄	—	867	1	no	—
41	Dic₃	—	289	1	no	—
42	C₃²	#11923884	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	289	1	no	—
44	C₂×C₃	—	289	1	no	—
45	C₂×C₃	—	578	1	no	—
46	C₄	—	867	1	no	Sylow
47	C₃	—	2	1	no	—
48	C₃	C₃×#11923884	1	1	yes	characteristic, complemented
49	C₃	C₃⋊#11923884	1	1	yes	characteristic, direct product factor
50	C₂	—	289	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊#11923884
commutator, hypocenter	C₃×C₁₇²	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇²	C₄
prime radical	C₃²×C₁₇⋊D₁₇	C₂
cosocle	C₃×C₁₇⋊D₁₇	C₂×C₃
LCS	G ▷ C₃×C₁₇²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃⋊#11923884	C₃	direct (N × H)
4. C₃²×C₁₇²	C₄	semidirect
10. C₃×C₁₇²	Dic₃	semidirect
11. C₃×C₁₇²	C₃×C₄	semidirect
16. C₁₇²	C₃×Dic₃	semidirect
20. C₃²×C₁₇	#595	semidirect
32. C₃×C₁₇	C₃×#595	semidirect
33. C₃×C₁₇	C₃⋊#595	semidirect
39. C₁₇	C₃×C₃⋊#595	semidirect
42. C₃²	#11923884	semidirect
48. C₃	C₃×#11923884	semidirect
49. C₃	C₃⋊#11923884	direct (N × H)

Subgroups — C3×C3⋊#11923884 #23780912

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₃⋊#11923884 #23780912