Subgroups — C₇×C₈×C₁₇×C₃₁ #72206404

Order 29512.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₇×C₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₄×C₇×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×C₁₇×C₃₁	C₄	1	1	yes	characteristic
4	C₇×C₁₇×C₃₁	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₁₇×C₃₁	C₂×C₇	1	1	yes	characteristic
6	C₇×C₈×C₃₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₇×C₃₁	C₄×C₇	1	1	yes	characteristic
8	C₇×C₈×C₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₇×C₃₁	C₂×C₁₇	1	1	yes	characteristic
10	C₁₇×C₃₁	C₇×C₈	1	1	yes	characteristic, direct product factor, Hall
11	C₄×C₇×C₁₇	C₂×C₃₁	1	1	yes	characteristic
12	C₂×C₇×C₃₁	C₄×C₁₇	1	1	yes	characteristic
13	C₈×C₃₁	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₇×C₁₇	C₄×C₃₁	1	1	yes	characteristic
15	C₇×C₃₁	C₈×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₈×C₁₇	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₄×C₃₁	C₂×C₇×C₁₇	1	1	yes	characteristic
18	C₇×C₁₇	C₈×C₃₁	1	1	yes	characteristic, direct product factor, Hall
19	C₄×C₁₇	C₂×C₇×C₃₁	1	1	yes	characteristic
20	C₂×C₃₁	C₄×C₇×C₁₇	1	1	yes	characteristic
21	C₇×C₈	C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₇	C₄×C₇×C₃₁	1	1	yes	characteristic
23	C₃₁	C₇×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
24	C₄×C₇	C₂×C₁₇×C₃₁	1	1	yes	characteristic
25	C₁₇	C₇×C₈×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	C₄×C₁₇×C₃₁	1	1	yes	characteristic
27	C₈	C₇×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₇	C₈×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₄	C₂×C₇×C₁₇×C₃₁	1	1	yes	characteristic
30	C₂	C₄×C₇×C₁₇×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₇×C₁₇×C₃₁
socle, prime radical	C₂×C₇×C₁₇×C₃₁	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×C₃₁	C₇	direct (N × H)
4. C₇×C₁₇×C₃₁	C₈	direct (N × H)
6. C₇×C₈×C₃₁	C₁₇	direct (N × H)
8. C₇×C₈×C₁₇	C₃₁	direct (N × H)
10. C₁₇×C₃₁	C₇×C₈	direct (N × H)
13. C₈×C₃₁	C₇×C₁₇	direct (N × H)
15. C₇×C₃₁	C₈×C₁₇	direct (N × H)
16. C₈×C₁₇	C₇×C₃₁	direct (N × H)
18. C₇×C₁₇	C₈×C₃₁	direct (N × H)
21. C₇×C₈	C₁₇×C₃₁	direct (N × H)
23. C₃₁	C₇×C₈×C₁₇	direct (N × H)
25. C₁₇	C₇×C₈×C₃₁	direct (N × H)
27. C₈	C₇×C₁₇×C₃₁	direct (N × H)
28. C₇	C₈×C₁₇×C₃₁	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×C₃₁	7
C₄×C₇×C₁₇×C₃₁	2
C₇×C₈×C₃₁	17
C₇×C₈×C₁₇	31

Subgroups — C7×C8×C17×C31 #72206404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₈×C₁₇×C₃₁ #72206404