Subgroups — C₃×C₈×C₁₇×C₄₇ #72196863

Order 19176.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₇×C₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₄×C₁₇×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₁₇×C₄₇	C₄	1	1	yes	characteristic
4	C₄×C₁₇×C₄₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₇×C₄₇	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₁₇×C₄₇	C₃×C₄	1	1	yes	characteristic
7	C₃×C₈×C₄₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₄₇	C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₄×C₄₇	C₂×C₁₇	1	1	yes	characteristic
10	C₃×C₈×C₁₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₈×C₄₇	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₄₇	C₄×C₁₇	1	1	yes	characteristic
13	C₃×C₄×C₁₇	C₂×C₄₇	1	1	yes	characteristic
14	C₄×C₄₇	C₂×C₃×C₁₇	1	1	yes	characteristic
15	C₃×C₄₇	C₈×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₈×C₁₇	C₃×C₄₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₁₇	C₄×C₄₇	1	1	yes	characteristic
18	C₂×C₄₇	C₃×C₄×C₁₇	1	1	yes	characteristic
19	C₄×C₁₇	C₂×C₃×C₄₇	1	1	yes	characteristic
20	C₃×C₁₇	C₈×C₄₇	1	1	yes	characteristic, direct product factor, Hall
21	C₄₇	C₃×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₁₇	C₃×C₄×C₄₇	1	1	yes	characteristic
23	C₃×C₈	C₁₇×C₄₇	1	1	yes	characteristic, direct product factor, Hall
24	C₁₇	C₃×C₈×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₄	C₂×C₁₇×C₄₇	1	1	yes	characteristic
26	C₈	C₃×C₁₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₄×C₁₇×C₄₇	1	1	yes	characteristic
28	C₄	C₂×C₃×C₁₇×C₄₇	1	1	yes	characteristic
29	C₃	C₈×C₁₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₃×C₄×C₁₇×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₇×C₄₇
socle, prime radical	C₂×C₃×C₁₇×C₄₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈×C₁₇×C₄₇	C₃	direct (N × H)
5. C₃×C₁₇×C₄₇	C₈	direct (N × H)
7. C₃×C₈×C₄₇	C₁₇	direct (N × H)
8. C₁₇×C₄₇	C₃×C₈	direct (N × H)
10. C₃×C₈×C₁₇	C₄₇	direct (N × H)
11. C₈×C₄₇	C₃×C₁₇	direct (N × H)
15. C₃×C₄₇	C₈×C₁₇	direct (N × H)
16. C₈×C₁₇	C₃×C₄₇	direct (N × H)
20. C₃×C₁₇	C₈×C₄₇	direct (N × H)
21. C₄₇	C₃×C₈×C₁₇	direct (N × H)
23. C₃×C₈	C₁₇×C₄₇	direct (N × H)
24. C₁₇	C₃×C₈×C₄₇	direct (N × H)
26. C₈	C₃×C₁₇×C₄₇	direct (N × H)
29. C₃	C₈×C₁₇×C₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×C₁₇×C₄₇	3
C₃×C₄×C₁₇×C₄₇	2
C₃×C₈×C₄₇	17
C₃×C₈×C₁₇	47

Subgroups — C3×C8×C17×C47 #72196863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×C₁₇×C₄₇ #72196863