Subgroups — C₃×C₇×C₁₇×D₄₇ #46776752

Order 33558.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₇×D₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₇×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×D₄₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇×C₄₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×D₄₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×D₄₇	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇×C₄₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×C₄₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇×C₁₇	—	47	1	no	maximal, Hall
11	C₇×D₄₇	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₇×C₁₇	D₄₇	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₄₇	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₄₇	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₇×C₁₇	—	47	1	no	Hall
16	C₃×C₄₇	C₂×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₇	C₃×D₄₇	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₁₇	—	47	1	no	Hall
19	D₄₇	C₃×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₇	C₇×D₄₇	1	1	yes	characteristic, direct product factor, Hall
21	C₄₇	C₂×C₃×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₇	—	47	1	no	Hall
23	C₂×C₁₇	—	47	1	no	Hall
24	C₃×C₇	C₁₇×D₄₇	1	1	yes	characteristic, direct product factor, Hall
25	C₁₇	C₃×C₇×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	—	47	1	no	Hall
27	C₇	C₃×C₁₇×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	47	1	no	Hall
29	C₃	C₇×C₁₇×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	47	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₇	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂×C₃×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₄₇	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₃×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₇×C₄₇	C₂	semidirect
2. C₇×C₁₇×D₄₇	C₃	direct (N × H)
3. C₇×C₁₇×C₄₇	C₂×C₃	semidirect
4. C₃×C₁₇×D₄₇	C₇	direct (N × H)
5. C₃×C₁₇×C₄₇	C₂×C₇	semidirect
6. C₃×C₇×D₄₇	C₁₇	direct (N × H)
7. C₁₇×D₄₇	C₃×C₇	direct (N × H)
8. C₃×C₇×C₄₇	C₂×C₁₇	semidirect
9. C₁₇×C₄₇	C₂×C₃×C₇	semidirect
11. C₇×D₄₇	C₃×C₁₇	direct (N × H)
12. C₃×C₇×C₁₇	D₄₇	direct (N × H)
13. C₇×C₄₇	C₂×C₃×C₁₇	semidirect
14. C₃×D₄₇	C₇×C₁₇	direct (N × H)
16. C₃×C₄₇	C₂×C₇×C₁₇	semidirect
17. C₇×C₁₇	C₃×D₄₇	direct (N × H)
19. D₄₇	C₃×C₇×C₁₇	direct (N × H)
20. C₃×C₁₇	C₇×D₄₇	direct (N × H)
21. C₄₇	C₂×C₃×C₇×C₁₇	semidirect
24. C₃×C₇	C₁₇×D₄₇	direct (N × H)
25. C₁₇	C₃×C₇×D₄₇	direct (N × H)
27. C₇	C₃×C₁₇×D₄₇	direct (N × H)
29. C₃	C₇×C₁₇×D₄₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₇×C₁₇×C₄₇	2
C₇×C₁₇×D₄₇	3
C₃×C₁₇×D₄₇	7
C₃×C₇×D₄₇	17
C₂×C₃×C₇×C₁₇	47

Subgroups — C3×C7×C17×D47 #46776752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₁₇×D₄₇ #46776752