Subgroups — C₄×C₇×C₁₇×C₄₇ #36375377

Order 22372.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₇×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₇×C₄₇	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₇×C₄₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₇×C₄₇	C₂×C₇	1	1	yes	characteristic
5	C₄×C₇×C₄₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₄₇	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₇×C₄₇	C₂×C₁₇	1	1	yes	characteristic
8	C₄×C₇×C₁₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₄₇	C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇×C₁₇	C₂×C₄₇	1	1	yes	characteristic
11	C₄×C₄₇	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₁₇	C₄×C₄₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₄₇	C₂×C₇×C₁₇	1	1	yes	characteristic
14	C₄×C₁₇	C₇×C₄₇	1	1	yes	characteristic, direct product factor, Hall
15	C₄₇	C₄×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₁₇	C₂×C₇×C₄₇	1	1	yes	characteristic
17	C₄×C₇	C₁₇×C₄₇	1	1	yes	characteristic, direct product factor, Hall
18	C₁₇	C₄×C₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₇	C₂×C₁₇×C₄₇	1	1	yes	characteristic
20	C₇	C₄×C₁₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₇×C₁₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₇×C₁₇×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₇×C₁₇×C₄₇
socle, prime radical	C₂×C₇×C₁₇×C₄₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₇×C₄₇	C₄	direct (N × H)
3. C₄×C₁₇×C₄₇	C₇	direct (N × H)
5. C₄×C₇×C₄₇	C₁₇	direct (N × H)
6. C₁₇×C₄₇	C₄×C₇	direct (N × H)
8. C₄×C₇×C₁₇	C₄₇	direct (N × H)
9. C₇×C₄₇	C₄×C₁₇	direct (N × H)
11. C₄×C₄₇	C₇×C₁₇	direct (N × H)
12. C₇×C₁₇	C₄×C₄₇	direct (N × H)
14. C₄×C₁₇	C₇×C₄₇	direct (N × H)
15. C₄₇	C₄×C₇×C₁₇	direct (N × H)
17. C₄×C₇	C₁₇×C₄₇	direct (N × H)
18. C₁₇	C₄×C₇×C₄₇	direct (N × H)
20. C₇	C₄×C₁₇×C₄₇	direct (N × H)
21. C₄	C₇×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
C₂×C₇×C₁₇×C₄₇	2
C₄×C₁₇×C₄₇	7
C₄×C₇×C₄₇	17
C₄×C₇×C₁₇	47

Subgroups — C4×C7×C17×C47 #36375377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₁₇×C₄₇ #36375377