Subgroups — D₃×C₇×D₁₃₁ #24927003

Order 11004.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₃₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×D₁₃₁	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₁₃₁	—	3	1	no	—
7	C₇×D₁₃₁	—	3	1	no	—
8	C₇×D₁₃₁	D₃	1	1	yes	characteristic, direct product factor
9	D₃×D₁₃₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₇×C₁₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃₉₃	C₂×C₇	1	1	yes	characteristic, complemented
12	C₃×D₁₃₁	C₂×C₇	1	1	yes	characteristic, complemented
13	D₃×C₁₃₁	C₂×C₇	1	1	yes	characteristic, complemented
14	C₂×D₁₃₁	—	3	1	no	Hall
15	C₃×C₁₃₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃₁	—	3	1	no	—
17	D₁₃₁	—	3	1	no	—
18	D₁₃₁	D₃×C₇	1	1	yes	characteristic, direct product factor
19	C₁₃₁	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₃×C₇	—	131	1	no	maximal, Hall
21	C₂×C₃×C₇	—	131	1	no	—
22	D₃×C₇	—	131	1	no	—
23	D₃×C₇	D₁₃₁	1	1	yes	characteristic, direct product factor
24	C₂²×C₇	—	393	1	no	Hall
25	C₃×C₇	C₂×D₁₃₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇	—	3	1	no	—
27	C₂×C₇	—	131	1	no	—
28	C₂×C₇	—	393	1	no	—
29	C₂×D₃	—	131	1	no	Hall
30	C₇	D₃×D₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	131	1	no	—
32	D₃	—	131	1	no	—
33	D₃	C₇×D₁₃₁	1	1	yes	characteristic, direct product factor
34	C₂²	—	393	1	no	Sylow
35	C₃	C₂×C₇×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	1	no	—
37	C₂	—	131	1	no	—
38	C₂	—	393	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₃×D₁₃₁
commutator, cosocle, hypocenter	C₃×C₁₃₁	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃₁	C₂²
LCS	G ▷ C₃×C₁₃₁
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₃₉₃	C₂	semidirect
2. D₃×C₇×C₁₃₁	C₂	semidirect
3. C₃×C₇×D₁₃₁	C₂	semidirect
5. C₃×C₇×C₁₃₁	C₂²	semidirect
8. C₇×D₁₃₁	D₃	direct (N × H)
9. D₃×D₁₃₁	C₇	direct (N × H)
10. C₇×C₁₃₁	C₂×D₃	semidirect
11. D₃₉₃	C₂×C₇	semidirect
12. C₃×D₁₃₁	C₂×C₇	semidirect
13. D₃×C₁₃₁	C₂×C₇	semidirect
15. C₃×C₁₃₁	C₂²×C₇	semidirect
18. D₁₃₁	D₃×C₇	direct (N × H)
19. C₁₃₁	C₂×D₃×C₇	semidirect
23. D₃×C₇	D₁₃₁	direct (N × H)
25. C₃×C₇	C₂×D₁₃₁	semidirect
30. C₇	D₃×D₁₃₁	direct (N × H)
33. D₃	C₇×D₁₃₁	direct (N × H)
35. C₃	C₂×C₇×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₃₉₃	2
D₃×C₇×C₁₃₁	2
C₃×C₇×D₁₃₁	2
C₂×C₇×D₁₃₁	3
D₃×D₁₃₁	7
C₂×D₃×C₇	131

Subgroups — D3×C7×D131 #24927003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×D₁₃₁ #24927003