Subgroups — D₃×D₇×C₁₃₁ #24927005

Order 11004.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₁×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₇×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₇×C₁₃₁	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₁₃₁	—	3	1	no	—
7	D₇×C₁₃₁	—	3	1	no	—
8	D₇×C₁₃₁	D₃	1	1	yes	characteristic, direct product factor
9	C₂×D₃×C₁₃₁	—	7	1	no	maximal, Hall
10	C₇×C₁₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₃₁	—	7	1	no	—
12	D₃×C₁₃₁	—	7	1	no	—
13	D₃×C₁₃₁	D₇	1	1	yes	characteristic, direct product factor
14	C₂²×C₁₃₁	—	21	1	no	Hall
15	C₃×C₁₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃₁	—	3	1	no	—
17	C₂×C₁₃₁	—	7	1	no	—
18	C₂×C₁₃₁	—	21	1	no	—
19	C₁₃₁	D₃×D₇	1	1	yes	characteristic, direct product factor, Sylow
20	D₃×D₇	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	D₂₁	C₂×C₁₃₁	1	1	yes	characteristic, complemented
22	C₃×D₇	C₂×C₁₃₁	1	1	yes	characteristic, complemented
23	D₃×C₇	C₂×C₁₃₁	1	1	yes	characteristic, complemented
24	C₂×D₇	—	3	1	no	Hall
25	C₃×C₇	C₂²×C₁₃₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇	—	3	1	no	—
27	D₇	—	3	1	no	—
28	D₇	D₃×C₁₃₁	1	1	yes	characteristic, direct product factor
29	C₂×D₃	—	7	1	no	Hall
30	C₇	C₂×D₃×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	7	1	no	—
32	D₃	—	7	1	no	—
33	D₃	D₇×C₁₃₁	1	1	yes	characteristic, direct product factor
34	C₂²	—	21	1	no	Sylow
35	C₃	C₂×D₇×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	7	1	no	—
38	C₂	—	21	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃₁	D₃×D₇
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₁₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃₁	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₁₃₁

Complements

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

N	H ≅ G/N	type
1. D₂₁×C₁₃₁	C₂	semidirect
2. D₃×C₇×C₁₃₁	C₂	semidirect
3. C₃×D₇×C₁₃₁	C₂	semidirect
5. C₃×C₇×C₁₃₁	C₂²	semidirect
8. D₇×C₁₃₁	D₃	direct (N × H)
10. C₇×C₁₃₁	C₂×D₃	semidirect
13. D₃×C₁₃₁	D₇	direct (N × H)
15. C₃×C₁₃₁	C₂×D₇	semidirect
19. C₁₃₁	D₃×D₇	direct (N × H)
20. D₃×D₇	C₁₃₁	direct (N × H)
21. D₂₁	C₂×C₁₃₁	semidirect
22. C₃×D₇	C₂×C₁₃₁	semidirect
23. D₃×C₇	C₂×C₁₃₁	semidirect
25. C₃×C₇	C₂²×C₁₃₁	semidirect
28. D₇	D₃×C₁₃₁	direct (N × H)
30. C₇	C₂×D₃×C₁₃₁	semidirect
33. D₃	D₇×C₁₃₁	direct (N × H)
35. C₃	C₂×D₇×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
D₂₁×C₁₃₁	2
D₃×C₇×C₁₃₁	2
C₃×D₇×C₁₃₁	2
C₂×D₇×C₁₃₁	3
C₂×D₃×C₁₃₁	7
D₃×D₇	131

Subgroups — D3×D7×C131 #24927005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₇×C₁₃₁ #24927005