Subgroups — C₃²×C₇×D₁₄₃ #31825097

Order 18018.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×D₁₄₃	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₇×C₁₁×C₁₃	C₂×C₃	1	4	yes	complemented
4	C₃²×D₁₄₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₁₄₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₇×D₁₃	—	11	1	no	maximal, Hall
7	C₃²×C₇×D₁₁	—	13	1	no	maximal, Hall
8	C₃²×C₁₁×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₁×C₁₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₄₃	C₃×C₇	1	4	yes	direct product factor
11	C₃²×C₇×C₁₃	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃²×C₇×C₁₁	D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₇×D₁₃	—	11	4	no	—
14	C₃×C₇×D₁₁	—	13	4	no	—
15	C₃×C₁₁×C₁₃	C₂×C₃×C₇	1	4	yes	complemented
16	D₁₄₃	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇×C₁₃	C₃×D₁₁	1	4	yes	complemented
18	C₃²×D₁₃	—	11	1	no	Hall
19	C₃×C₇×C₁₁	C₃×D₁₃	1	4	yes	complemented
20	C₃²×D₁₁	—	13	1	no	Hall
21	C₇×D₁₃	—	11	1	no	Hall
22	C₇×D₁₁	—	13	1	no	Hall
23	C₁₁×C₁₃	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃²×C₇	—	143	1	no	Hall
25	C₃²×C₁₃	C₇×D₁₁	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₁₁	C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₃×D₁₃	—	11	4	no	—
29	C₇×C₁₁	C₃²×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₃×D₁₁	—	13	4	no	—
31	C₃²×C₇	D₁₄₃	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₃×C₇	—	143	4	no	—
33	C₃×C₁₃	C₃×C₇×D₁₁	1	4	yes	complemented
34	C₃×C₁₁	C₃×C₇×D₁₃	1	4	yes	complemented
35	D₁₃	—	11	1	no	Hall
36	D₁₁	—	13	1	no	Hall
37	C₃×C₇	C₃×D₁₄₃	1	4	yes	direct product factor
38	C₂×C₃²	—	143	1	no	Hall
39	C₂×C₇	—	143	1	no	Hall
40	C₁₃	C₃²×C₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
41	C₁₁	C₃²×C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
42	C₃²	C₇×D₁₄₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₇	C₃²×D₁₄₃	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃	—	143	4	no	—
45	C₃	C₃×C₇×D₁₄₃	1	4	yes	direct product factor
46	C₂	—	143	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₁₄₃
commutator, cosocle, hypocenter	C₁₁×C₁₃	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁×C₁₃	C₂	semidirect
2. C₃×C₇×D₁₄₃	C₃	direct (N × H)
3. C₃×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
4. C₃²×D₁₄₃	C₇	direct (N × H)
5. C₇×D₁₄₃	C₃²	direct (N × H)
8. C₃²×C₁₁×C₁₃	C₂×C₇	semidirect
9. C₇×C₁₁×C₁₃	C₂×C₃²	semidirect
10. C₃×D₁₄₃	C₃×C₇	direct (N × H)
11. C₃²×C₇×C₁₃	D₁₁	semidirect
12. C₃²×C₇×C₁₁	D₁₃	semidirect
15. C₃×C₁₁×C₁₃	C₂×C₃×C₇	semidirect
16. D₁₄₃	C₃²×C₇	direct (N × H)
17. C₃×C₇×C₁₃	C₃×D₁₁	semidirect
19. C₃×C₇×C₁₁	C₃×D₁₃	semidirect
23. C₁₁×C₁₃	C₂×C₃²×C₇	semidirect
25. C₃²×C₁₃	C₇×D₁₁	semidirect
26. C₃²×C₁₁	C₇×D₁₃	semidirect
27. C₇×C₁₃	C₃²×D₁₁	semidirect
29. C₇×C₁₁	C₃²×D₁₃	semidirect
31. C₃²×C₇	D₁₄₃	direct (N × H)
33. C₃×C₁₃	C₃×C₇×D₁₁	semidirect
34. C₃×C₁₁	C₃×C₇×D₁₃	semidirect
37. C₃×C₇	C₃×D₁₄₃	direct (N × H)
40. C₁₃	C₃²×C₇×D₁₁	semidirect
41. C₁₁	C₃²×C₇×D₁₃	semidirect
42. C₃²	C₇×D₁₄₃	direct (N × H)
43. C₇	C₃²×D₁₄₃	direct (N × H)
45. C₃	C₃×C₇×D₁₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₁×C₁₃	2
C₃×C₇×D₁₄₃	3
C₃²×D₁₄₃	7
C₃²×C₇×D₁₃	11
C₃²×C₇×D₁₁	13

Subgroups — C32×C7×D143 #31825097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×D₁₄₃ #31825097