Subgroups — C₃×C₃⋊#11923883 #23780911

Order 10404.

280 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	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#11923883	—	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	#11923883	—	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	18	no	maximal
13	C₁₇⋊D₁₇	C₃×D₃	1	1	yes	characteristic
14	C₃²×D₁₇	—	17	18	no	—
15	C₁₇²	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
16	C₃⋊#595	—	17	18	no	—
17	C₃×#595	—	51	18	no	—
18	C₃²×C₁₇	#595	1	18	yes	complemented
19	C₃×D₁₇	—	17	18	no	—
20	C₃×D₁₇	—	17	18	no	—
21	C₃×D₁₇	—	34	18	no	—
22	#595	—	51	18	no	—
23	C₃×C₁₇	—	2	18	no	—
24	C₃×C₁₇	C₃×#595	1	18	yes	complemented
25	C₃×C₁₇	C₃⋊#595	1	18	yes	complemented
26	C₃×Dic₃	—	289	1	no	Hall
27	D₁₇	—	17	18	no	—
28	C₂×C₃²	—	289	1	no	—
29	C₁₇	C₃×C₃⋊#595	1	18	yes	complemented
30	C₃×C₄	—	867	1	no	—
31	Dic₃	—	289	1	no	—
32	C₃²	#11923883	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃	—	289	1	no	—
34	C₂×C₃	—	289	1	no	—
35	C₂×C₃	—	578	1	no	—
36	C₄	—	867	1	no	Sylow
37	C₃	—	2	1	no	—
38	C₃	C₃×#11923883	1	1	yes	characteristic, complemented
39	C₃	C₃⋊#11923883	1	1	yes	characteristic, direct product factor
40	C₂	—	289	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₃⋊#11923883
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⋊#11923883	C₃	direct (N × H)
4. C₃²×C₁₇²	C₄	semidirect
10. C₃×C₁₇²	Dic₃	semidirect
11. C₃×C₁₇²	C₃×C₄	semidirect
15. C₁₇²	C₃×Dic₃	semidirect
18. C₃²×C₁₇	#595	semidirect
24. C₃×C₁₇	C₃×#595	semidirect
25. C₃×C₁₇	C₃⋊#595	semidirect
29. C₁₇	C₃×C₃⋊#595	semidirect
32. C₃²	#11923883	semidirect
38. C₃	C₃×#11923883	semidirect
39. C₃	C₃⋊#11923883	direct (N × H)

Subgroups — C3×C3⋊#11923883 #23780911

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₃⋊#11923883 #23780911