Subgroups — C₃×C₇×D₇₃₁ #44502017

Order 30702.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₇×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₇×C₄₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₃×C₇×D₄₃	—	17	1	no	maximal, Hall
7	D₇₃₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇×C₄₃	D₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×C₄₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×D₁₇	—	43	1	no	maximal, Hall
11	C₇×D₄₃	—	17	1	no	Hall
12	C₃×C₇×C₁₇	D₄₃	1	1	yes	characteristic, complemented, Hall
13	C₇×C₄₃	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₄₃	—	17	1	no	Hall
15	C₇×D₁₇	—	43	1	no	Hall
16	C₃×C₄₃	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₇	C₃×D₄₃	1	1	yes	characteristic, complemented, Hall
18	C₃×D₁₇	—	43	1	no	Hall
19	D₄₃	—	17	1	no	Hall
20	C₃×C₁₇	C₇×D₄₃	1	1	yes	characteristic, complemented, Hall
21	C₄₃	C₃×C₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₇	—	731	1	no	Hall
23	D₁₇	—	43	1	no	Hall
24	C₃×C₇	D₇₃₁	1	1	yes	characteristic, direct product factor, Hall
25	C₁₇	C₃×C₇×D₄₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₇	—	731	1	no	Hall
27	C₇	C₃×D₇₃₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	—	731	1	no	Hall
29	C₃	C₇×D₇₃₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	731	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₇₃₁
commutator, cosocle, hypocenter	C₁₇×C₄₃	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₇×C₄₃	C₂
LCS	G ▷ C₁₇×C₄₃
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₇×C₄₃	C₂	semidirect
2. C₇×D₇₃₁	C₃	direct (N × H)
3. C₇×C₁₇×C₄₃	C₂×C₃	semidirect
4. C₃×D₇₃₁	C₇	direct (N × H)
5. C₃×C₁₇×C₄₃	C₂×C₇	semidirect
7. D₇₃₁	C₃×C₇	direct (N × H)
8. C₃×C₇×C₄₃	D₁₇	semidirect
9. C₁₇×C₄₃	C₂×C₃×C₇	semidirect
12. C₃×C₇×C₁₇	D₄₃	semidirect
13. C₇×C₄₃	C₃×D₁₇	semidirect
16. C₃×C₄₃	C₇×D₁₇	semidirect
17. C₇×C₁₇	C₃×D₄₃	semidirect
20. C₃×C₁₇	C₇×D₄₃	semidirect
21. C₄₃	C₃×C₇×D₁₇	semidirect
24. C₃×C₇	D₇₃₁	direct (N × H)
25. C₁₇	C₃×C₇×D₄₃	semidirect
27. C₇	C₃×D₇₃₁	direct (N × H)
29. C₃	C₇×D₇₃₁	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×C₄₃	2
C₇×D₇₃₁	3
C₃×D₇₃₁	7
C₃×C₇×D₄₃	17
C₃×C₇×D₁₇	43

Subgroups — C3×C7×D731 #44502017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₇₃₁ #44502017