Subgroups — #46798655

Order 33777.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16836730	C₃	1	2	yes	maximal
2	C₃×#16836730	C₃	1	1	yes	maximal, characteristic
3	#26014618	C₃	1	9	yes	maximal, complemented
4	C₃×3₋¹⁺²×C₁₃₉	C₃	1	1	yes	maximal, characteristic
5	#16836730	—	3	2	no	—
6	#16836730	—	3	2	no	—
7	#16836730	—	3	1	no	—
8	#16836730	—	3	2	no	—
9	#16836730	C₃²	1	6	yes	—
10	C₃×C₁₃₉⋊C₉	—	3	2	no	—
11	C₃×C₁₃₉⋊C₉	C₃²	1	3	yes	—
12	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
13	3₋¹⁺²×C₁₃₉	—	3	2	no	—
14	3₋¹⁺²×C₁₃₉	C₃²	1	3	yes	—
15	C₃×C₉×C₁₃₉	—	3	1	no	—
16	C₃²×C₁₃₉	—	9	1	no	—
17	C₃²×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃²×C₁₃₉	H(3,𝔽₃)	1	2	yes	—
19	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
20	C₉×C₁₃₉	—	3	3	no	—
21	C₁₃₉⋊C₉	—	3	6	no	—
22	C₁₃₉⋊C₉	—	3	3	no	—
23	C₃×C₁₃₉	—	3	1	no	—
24	C₃×C₁₃₉	—	3	2	no	—
25	C₃×C₁₃₉	—	3	1	no	—
26	C₃×C₁₃₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
27	#6912	—	139	1	no	maximal, Sylow
28	C₁₃₉	#6912	1	1	yes	characteristic, complemented, Sylow
29	C₃×3₋¹⁺²	—	139	1	no	—
30	C₃×3₋¹⁺²	—	139	2	no	—
31	C₃×3₋¹⁺²	C₁₃₉⋊C₃	1	1	yes	characteristic
32	#733	—	139	9	no	—
33	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
34	3₋¹⁺²	—	3	2	no	—
35	3₋¹⁺²	—	139	6	no	—
36	3₋¹⁺²	—	417	1	no	—
37	3₋¹⁺²	—	417	2	no	—
38	3₋¹⁺²	—	417	2	no	—
39	3₋¹⁺²	—	417	2	no	—
40	3₋¹⁺²	C₃×C₁₃₉⋊C₃	1	3	yes	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	139	3	no	—
43	C₃×C₉	—	417	2	no	—
44	C₃²	—	9	1	no	—
45	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
46	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	2	yes	—
47	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
48	C₉	—	3	3	no	—
49	C₉	—	417	3	no	—
50	C₉	—	417	6	no	—
51	C₃	—	3	1	no	—
52	C₃	—	3	2	no	—
53	C₃	—	3	1	no	—
54	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	C₃³×C₁₃₉	C₃²
hypercenter	C₃×3₋¹⁺²	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6912
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
3. #26014618	C₃	semidirect
28. C₁₃₉	#6912	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
#26014618	3
C₃×3₋¹⁺²×C₁₃₉	3
#6912	139