Subgroups — #737×C₁₃₉⋊C₃ #46798676

Order 33777.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26014630	C₃	1	16	yes	maximal, complemented
2	#26014629	C₃	1	8	yes	maximal, complemented
3	#26014628	C₃	1	2	yes	maximal, complemented
4	3₋¹⁺²×C₁₃₉⋊C₃	C₃	1	8	yes	maximal, complemented
5	H(3,𝔽₃)×C₁₃₉⋊C₃	C₃	1	1	yes	maximal, characteristic
6	C₃×C₉×C₁₃₉⋊C₃	C₃	1	4	yes	maximal, complemented
7	#737×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₁₃₉⋊C₃	C₃²	1	4	yes	—
9	#16836730	C₃²	1	16	yes	complemented
10	#16836729	C₃²	1	24	yes	complemented
11	#16836728	C₃²	1	24	yes	complemented
12	C₃²⋊(C₁₃₉⋊C₃)	C₃²	1	8	yes	—
13	C₃×C₁₃₉⋊C₉	C₃²	1	8	yes	complemented
14	C₉×C₁₃₉⋊C₃	C₃²	1	1	yes	characteristic
15	C₉×C₁₃₉⋊C₃	C₃²	1	8	yes	—
16	C₉×C₁₃₉⋊C₃	C₃²	1	8	yes	complemented
17	C₉×C₁₃₉⋊C₃	C₃²	1	16	yes	complemented
18	3₋¹⁺²×C₁₃₉	C₃²	1	8	yes	complemented
19	H(3,𝔽₃)×C₁₃₉	C₃²	1	1	yes	characteristic
20	C₃×C₉×C₁₃₉	C₃²	1	4	yes	complemented
21	C₃²×C₁₃₉	C₃³	1	4	yes	—
22	C₃×C₁₃₉⋊C₃	—	3	12	no	—
23	C₃×C₁₃₉⋊C₃	C₃³	1	8	yes	—
24	C₃×C₁₃₉⋊C₃	C₃³	1	1	yes	characteristic
25	C₉×C₁₃₉	C₃³	1	8	yes	—
26	C₉×C₁₃₉	C₃³	1	1	yes	characteristic
27	C₁₃₉⋊C₉	C₃³	1	2	yes	—
28	C₁₃₉⋊C₉	C₃³	1	16	yes	—
29	C₃×C₁₃₉	—	3	4	no	—
30	C₃×C₁₃₉	C₃⁴	1	1	yes	characteristic
31	C₁₃₉⋊C₃	—	3	8	no	—
32	C₁₃₉⋊C₃	#737	1	3	yes	direct product factor
33	C₃×#737	—	139	1	no	maximal, Sylow
34	C₁₃₉	C₃×#737	1	1	yes	characteristic, complemented, Sylow
35	#737	—	139	16	no	—
36	#737	—	139	2	no	—
37	#737	—	139	8	no	—
38	#737	C₁₃₉⋊C₃	1	1	yes	characteristic, direct product factor
39	C₃×3₋¹⁺²	—	139	8	no	—
40	C₃×H(3,𝔽₃)	—	139	1	no	—
41	C₃²×C₉	—	139	4	no	—
42	C₃³	—	139	4	no	—
43	3₋¹⁺²	—	139	16	no	—
44	3₋¹⁺²	—	139	24	no	—
45	3₋¹⁺²	—	139	24	no	—
46	3₋¹⁺²	C₃×C₁₃₉⋊C₃	1	8	yes	complemented
47	H(3,𝔽₃)	—	139	8	no	—
48	H(3,𝔽₃)	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
49	C₃×C₉	—	139	8	no	—
50	C₃×C₉	—	139	8	no	—
51	C₃×C₉	—	139	16	no	—
52	C₃×C₉	—	139	1	no	—
53	C₃×C₉	—	139	8	no	—
54	C₃×C₉	C₃×C₁₃₉⋊C₃	1	4	yes	complemented
55	C₃²	—	139	1	no	—
56	C₃²	—	139	8	no	—
57	C₃²	—	417	12	no	—
58	C₃²	C₃²×C₁₃₉⋊C₃	1	4	yes	—
59	C₉	—	139	2	no	—
60	C₉	—	139	16	no	—
61	C₉	C₃²×C₁₃₉⋊C₃	1	8	yes	—
62	C₉	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
63	C₃	—	3	4	no	—
64	C₃	—	139	3	no	—
65	C₃	—	417	8	no	—
66	C₃	C₃³×C₁₃₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²×C₁₃₉⋊C₃
commutator, socle, cosocle	C₃×C₁₃₉	C₃⁴
Frattini	C₃	C₃³×C₁₃₉⋊C₃
Fitting	#737×C₁₃₉	C₃
prime radical	H(3,𝔽₃)×C₁₃₉⋊C₃	C₃
hypercenter	#737	C₁₃₉⋊C₃
hypocenter	C₁₃₉	C₃×#737
LCS	G ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₉ ◁ #737

Complements

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

N	H ≅ G/N	type
1. #26014630	C₃	semidirect
2. #26014629	C₃	semidirect
3. #26014628	C₃	semidirect
4. 3₋¹⁺²×C₁₃₉⋊C₃	C₃	semidirect
6. C₃×C₉×C₁₃₉⋊C₃	C₃	semidirect
7. #737×C₁₃₉	C₃	semidirect
9. #16836730	C₃²	semidirect
10. #16836729	C₃²	semidirect
11. #16836728	C₃²	semidirect
13. C₃×C₁₃₉⋊C₉	C₃²	semidirect
16. C₉×C₁₃₉⋊C₃	C₃²	semidirect
17. C₉×C₁₃₉⋊C₃	C₃²	semidirect
18. 3₋¹⁺²×C₁₃₉	C₃²	semidirect
20. C₃×C₉×C₁₃₉	C₃²	semidirect
32. C₁₃₉⋊C₃	#737	direct (N × H)
34. C₁₃₉	C₃×#737	semidirect
38. #737	C₁₃₉⋊C₃	direct (N × H)
46. 3₋¹⁺²	C₃×C₁₃₉⋊C₃	semidirect
54. C₃×C₉	C₃×C₁₃₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#26014630	3
#26014629	3
#26014628	3
3₋¹⁺²×C₁₃₉⋊C₃	3
H(3,𝔽₃)×C₁₃₉⋊C₃	3
C₃×C₉×C₁₃₉⋊C₃	3
#737×C₁₃₉	3
C₃×#737	139

Subgroups — #737×C139⋊C3 #46798676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #737×C₁₃₉⋊C₃ #46798676