Subgroups — C₃²×C₁₇×#595 #23780904

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×C₁₇×#595	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×D₁₇	C₂×C₃	1	4	yes	—
5	C₁₇×#595	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₇²	C₃×C₄	1	4	yes	complemented
7	C₃²×#595	C₁₇	1	1	yes	maximal, characteristic, direct product factor
8	C₃²×C₄×C₁₇	—	17	1	no	maximal
9	C₁₇×D₁₇	C₂×C₃²	1	1	yes	characteristic
10	C₂×C₃²×C₁₇	—	17	1	no	—
11	C₃²×D₁₇	C₂×C₁₇	1	1	yes	characteristic
12	C₁₇²	C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
13	C₃×#595	C₃×C₁₇	1	4	yes	direct product factor
14	C₃×C₄×C₁₇	—	17	4	no	—
15	C₃²×C₁₇	—	4	4	no	—
16	C₃²×C₁₇	C₄×C₁₇	1	1	yes	characteristic, complemented
17	C₃²×C₁₇	#595	1	1	yes	characteristic, direct product factor
18	C₂×C₃×C₁₇	—	17	4	no	—
19	C₃×D₁₇	C₂×C₃×C₁₇	1	4	yes	—
20	#595	C₃²×C₁₇	1	1	yes	characteristic, direct product factor
21	C₄×C₁₇	—	17	1	no	—
22	C₃×C₁₇	—	4	16	no	—
23	C₃×C₁₇	C₃×C₄×C₁₇	1	4	yes	complemented
24	C₃×C₁₇	C₃×#595	1	4	yes	direct product factor
25	C₃²×C₄	—	17	1	no	Hall
26	C₂×C₁₇	—	17	1	no	—
27	D₁₇	C₂×C₃²×C₁₇	1	1	yes	characteristic
28	C₂×C₃²	—	17	1	no	—
29	C₁₇	—	4	4	no	—
30	C₁₇	C₃²×C₄×C₁₇	1	1	yes	characteristic, complemented
31	C₁₇	C₃²×#595	1	1	yes	characteristic, direct product factor
32	C₃×C₄	—	17	4	no	—
33	C₃²	C₁₇×#595	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₃	—	17	4	no	—
35	C₄	—	17	1	no	Sylow
36	C₃	C₃×C₁₇×#595	1	4	yes	direct product factor
37	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₁₇	#595
commutator, hypocenter	C₁₇	C₃²×C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇²	C₄
prime radical	C₃²×C₁₇×D₁₇	C₂
cosocle	D₁₇	C₂×C₃²×C₁₇
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃²×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₇×#595	C₃	direct (N × H)
3. C₃²×C₁₇²	C₄	semidirect
5. C₁₇×#595	C₃²	direct (N × H)
6. C₃×C₁₇²	C₃×C₄	semidirect
7. C₃²×#595	C₁₇	direct (N × H)
12. C₁₇²	C₃²×C₄	semidirect
13. C₃×#595	C₃×C₁₇	direct (N × H)
16. C₃²×C₁₇	C₄×C₁₇	semidirect
17. C₃²×C₁₇	#595	direct (N × H)
20. #595	C₃²×C₁₇	direct (N × H)
23. C₃×C₁₇	C₃×C₄×C₁₇	semidirect
24. C₃×C₁₇	C₃×#595	direct (N × H)
30. C₁₇	C₃²×C₄×C₁₇	semidirect
31. C₁₇	C₃²×#595	direct (N × H)
33. C₃²	C₁₇×#595	direct (N × H)
36. C₃	C₃×C₁₇×#595	direct (N × H)

Subgroups — C32×C17×#595 #23780904

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₁₇×#595 #23780904