Subgroups — #46798648

Order 33777.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16836730	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#16836730	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃²⋊(C₁₃₉⋊C₃)	C₃	1	1	yes	maximal, characteristic
4	#26014615	C₃	1	9	yes	maximal, complemented
5	C₃×3₋¹⁺²×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₁₃₉⋊C₃	—	3	1	no	—
7	#16836730	—	3	1	no	—
8	#16836730	—	3	1	no	—
9	#16836730	—	3	1	no	—
10	#16836730	—	3	1	no	—
11	#16836730	—	3	1	no	—
12	#16836730	C₃²	1	3	yes	complemented
13	C₃²⋊(C₁₃₉⋊C₃)	—	3	1	no	—
14	C₃²⋊(C₁₃₉⋊C₃)	—	3	1	no	—
15	C₃²⋊(C₁₃₉⋊C₃)	C₃²	1	3	yes	—
16	C₃×C₁₃₉⋊C₉	—	3	1	no	—
17	C₃×C₁₃₉⋊C₉	C₃²	1	3	yes	complemented
18	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
19	3₋¹⁺²×C₁₃₉	—	3	1	no	—
20	3₋¹⁺²×C₁₃₉	—	3	1	no	—
21	3₋¹⁺²×C₁₃₉	C₃²	1	3	yes	complemented
22	C₃×C₉×C₁₃₉	—	3	1	no	—
23	C₃²×C₁₃₉	—	9	1	no	—
24	C₃²×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
25	C₃²×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
26	C₃²×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
27	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
28	C₃×C₁₃₉⋊C₃	—	3	3	no	—
29	C₃×C₁₃₉⋊C₃	—	9	3	no	—
30	C₉×C₁₃₉	—	3	3	no	—
31	C₁₃₉⋊C₉	—	3	3	no	—
32	C₁₃₉⋊C₉	—	3	3	no	—
33	C₃×C₁₃₉	—	3	1	no	—
34	C₃×C₁₃₉	—	3	1	no	—
35	C₃×C₁₃₉	—	3	1	no	—
36	C₃×C₁₃₉	—	3	1	no	—
37	C₃×C₁₃₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₁₃₉⋊C₃	—	9	3	no	—
39	#6910	—	139	1	no	maximal, Sylow
40	C₁₃₉	#6910	1	1	yes	characteristic, complemented, Sylow
41	C₃×3₋¹⁺²	—	139	1	no	—
42	C₃×3₋¹⁺²	—	139	1	no	—
43	C₃×3₋¹⁺²	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
44	C₃×H(3,𝔽₃)	—	139	1	no	—
45	#731	—	139	9	no	—
46	C₃³	—	417	1	no	—
47	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
48	3₋¹⁺²	—	3	1	no	—
49	3₋¹⁺²	—	3	1	no	—
50	3₋¹⁺²	—	139	3	no	—
51	3₋¹⁺²	—	417	1	no	—
52	3₋¹⁺²	—	417	1	no	—
53	3₋¹⁺²	—	417	1	no	—
54	3₋¹⁺²	—	417	1	no	—
55	3₋¹⁺²	—	417	1	no	—
56	3₋¹⁺²	C₃×C₁₃₉⋊C₃	1	3	yes	complemented
57	H(3,𝔽₃)	—	139	3	no	—
58	H(3,𝔽₃)	—	417	1	no	—
59	H(3,𝔽₃)	—	417	1	no	—
60	C₃×C₉	—	3	1	no	—
61	C₃×C₉	—	139	3	no	—
62	C₃×C₉	—	417	1	no	—
63	C₃²	—	9	1	no	—
64	C₃²	—	417	3	no	—
65	C₃²	—	1251	3	no	—
66	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
67	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
68	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
69	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
70	C₉	—	3	3	no	—
71	C₉	—	417	3	no	—
72	C₉	—	417	3	no	—
73	C₃	—	3	1	no	—
74	C₃	—	3	1	no	—
75	C₃	—	3	1	no	—
76	C₃	—	3	1	no	—
77	C₃	—	1251	3	no	—
78	C₃	C₃×C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊(C₁₃₉⋊C₃)
commutator, cosocle	C₃²×C₁₃₉	C₃³
Frattini	C₃²	C₃²×C₁₃₉⋊C₃
Fitting	C₃×3₋¹⁺²×C₁₃₉	C₃
socle	C₃×C₁₃₉	C₃×H(3,𝔽₃)
prime radical	C₃×C₃²⋊(C₁₃₉⋊C₃)	C₃
hypercenter	C₃×3₋¹⁺²	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6910
LCS	G ▷ C₃²×C₁₃₉ ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. C₃×#16836730	C₃	semidirect
2. C₃×#16836730	C₃	semidirect
4. #26014615	C₃	semidirect
5. C₃×3₋¹⁺²×C₁₃₉	C₃	semidirect
12. #16836730	C₃²	semidirect
17. C₃×C₁₃₉⋊C₉	C₃²	semidirect
21. 3₋¹⁺²×C₁₃₉	C₃²	semidirect
40. C₁₃₉	#6910	semidirect
43. C₃×3₋¹⁺²	C₁₃₉⋊C₃	semidirect
56. 3₋¹⁺²	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
C₃×#16836730	3
C₃×C₃²⋊(C₁₃₉⋊C₃)	3
#26014615	3
C₃×3₋¹⁺²×C₁₃₉	3
#6910	139