Subgroups — C₃×#26043014 #46856042

Order 35028.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#15668589	C₂	1	1	yes	maximal, characteristic
2	#26043014	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×Dic₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#15668589	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×#15668589	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₇×C₁₃₉	C₂×C₃	1	1	yes	characteristic
7	C₃×(C₁₃₉⋊C₃)⋊C₄	—	7	1	no	maximal, Hall
8	C₇×Dic₁₃₉	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₁₃₉	C₃×C₄	1	1	yes	characteristic, complemented
10	#15668589	C₃×C₄	1	3	yes	complemented
11	C₂×C₃×C₁₃₉⋊C₃	—	7	1	no	—
12	C₂×C₇×C₁₃₉	C₂×C₃²	1	1	yes	characteristic
13	C₃×Dic₁₃₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	(C₁₃₉⋊C₃)⋊C₄	—	7	3	no	—
15	C₃×C₁₃₉⋊C₃	—	7	1	no	Hall
16	C₇×C₁₃₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₃₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₂×C₁₃₉⋊C₃	—	7	3	no	—
19	Dic₁₃₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₃₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
21	C₁₃₉⋊C₃	—	7	3	no	—
22	C₂×C₁₃₉	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
23	C₃×C₄×ΓL(1,𝔽₈)	—	139	1	no	maximal, Hall
24	C₁₃₉	C₃×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×ΓL(1,𝔽₈)	—	139	1	no	—
26	C₃×C₄×C₇	—	139	1	no	—
27	C₄×ΓL(1,𝔽₈)	—	139	3	no	—
28	C₃×ΓL(1,𝔽₈)	—	139	1	no	Hall
29	C₂×C₃×C₇	D₁₃₉⋊C₃	1	1	yes	characteristic
30	C₂×ΓL(1,𝔽₈)	—	139	3	no	—
31	C₃²×C₄	—	973	1	no	Hall
32	C₄×C₇	—	139	1	no	Hall
33	C₃×C₇	(C₁₃₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
34	ΓL(1,𝔽₈)	—	139	3	no	—
35	C₂×C₃²	—	973	1	no	—
36	C₂×C₇	C₃×D₁₃₉⋊C₃	1	1	yes	characteristic
37	C₃×C₄	—	139	1	no	—
38	C₃×C₄	—	973	3	no	—
39	C₃²	—	973	1	no	Sylow
40	C₇	C₃×(C₁₃₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	973	3	no	—
42	C₂×C₃	#19154245	1	1	yes	characteristic
43	C₄	—	139	1	no	Sylow
44	C₃	—	973	3	no	—
45	C₃	#26043014	1	1	yes	characteristic, direct product factor
46	C₂	C₃×#19154245	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#19154245
commutator, hypocenter	C₇×C₁₃₉	C₃²×C₄
Frattini	C₂	C₃×#19154245
Fitting, socle	C₂×C₃×C₇×C₁₃₉	C₂×C₃
prime radical	C₂×C₃×#15668589	C₂
cosocle	C₂×C₇×C₁₃₉	C₂×C₃²
LCS	G ▷ C₇×C₁₃₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. #26043014	C₃	direct (N × H)
3. C₃×C₇×Dic₁₃₉	C₃	semidirect
4. C₃×#15668589	C₄	semidirect
8. C₇×Dic₁₃₉	C₃²	semidirect
9. C₃×C₇×C₁₃₉	C₃×C₄	semidirect
10. #15668589	C₃×C₄	semidirect
13. C₃×Dic₁₃₉	ΓL(1,𝔽₈)	semidirect
16. C₇×C₁₃₉	C₃²×C₄	semidirect
19. Dic₁₃₉	C₃×ΓL(1,𝔽₈)	semidirect
20. C₃×C₁₃₉	C₄×ΓL(1,𝔽₈)	semidirect
24. C₁₃₉	C₃×C₄×ΓL(1,𝔽₈)	semidirect
33. C₃×C₇	(C₁₃₉⋊C₃)⋊C₄	semidirect
40. C₇	C₃×(C₁₃₉⋊C₃)⋊C₄	semidirect
45. C₃	#26043014	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#15668589	2
#26043014	3
C₃×C₇×Dic₁₃₉	3
C₃×(C₁₃₉⋊C₃)⋊C₄	7
C₃×C₄×ΓL(1,𝔽₈)	139

Subgroups — C3×#26043014 #46856042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#26043014 #46856042