Subgroups — 3₋¹⁺²⋊(C₁₃₉⋊C₉) #46798483

Order 33777.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊(C₁₃₉⋊C₉)	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊(C₁₃₉⋊C₉)	C₃	1	1	yes	maximal, characteristic
4	C₃×3₋¹⁺²×C₁₃₉	C₃	1	1	yes	maximal, characteristic
5	C₃×C₁₃₉⋊C₉	—	3	1	no	—
6	C₃×C₁₃₉⋊C₉	—	3	3	no	—
7	C₃×C₁₃₉⋊C₉	—	3	1	no	—
8	C₃×C₁₃₉⋊C₉	—	3	1	no	—
9	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
10	3₋¹⁺²×C₁₃₉	—	3	2	no	—
11	3₋¹⁺²×C₁₃₉	C₉	1	3	yes	complemented
12	C₃×C₉×C₁₃₉	—	3	1	no	—
13	C₃²×C₁₃₉	—	3	1	no	—
14	C₃²×C₁₃₉	—	3	1	no	—
15	C₃²×C₁₃₉	—	3	1	no	—
16	C₃²×C₁₃₉	C₃×C₉	1	1	yes	characteristic
17	C₃²×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃²×C₁₃₉	3₋¹⁺²	1	2	yes	—
19	C₉×C₁₃₉	—	3	3	no	—
20	C₁₃₉⋊C₉	—	3	3	no	—
21	C₁₃₉⋊C₉	—	9	1	no	—
22	C₁₃₉⋊C₉	—	9	1	no	—
23	C₃×C₁₃₉	—	3	1	no	—
24	C₃×C₁₃₉	—	3	2	no	—
25	C₃×C₁₃₉	C₃²⋊C₉	1	1	yes	characteristic
26	C₃×C₁₃₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
27	C₃×C₁₃₉	#731	1	1	yes	characteristic
28	C₃×C₁₃₉	#733	1	1	yes	characteristic
29	3₋¹⁺²⋊C₉	—	139	1	no	maximal, Sylow
30	C₁₃₉	3₋¹⁺²⋊C₉	1	1	yes	characteristic, complemented, Sylow
31	C₃×3₋¹⁺²	C₁₃₉⋊C₃	1	1	yes	characteristic
32	C₃²×C₉	—	139	1	no	—
33	C₃²⋊C₉	—	139	1	no	—
34	C₃²⋊C₉	—	139	1	no	—
35	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
36	3₋¹⁺²	—	3	2	no	—
37	3₋¹⁺²	C₁₃₉⋊C₉	1	3	yes	complemented
38	C₃×C₉	—	3	1	no	—
39	C₃×C₉	—	417	1	no	—
40	C₃×C₉	—	417	3	no	—
41	C₃×C₉	—	417	1	no	—
42	C₃×C₉	—	417	1	no	—
43	C₃²	—	3	1	no	—
44	C₃²	—	3	1	no	—
45	C₃²	—	3	1	no	—
46	C₃²	C₃×C₁₃₉⋊C₉	1	1	yes	characteristic
47	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
48	C₃²	#16836730	1	2	yes	—
49	C₉	—	3	3	no	—
50	C₉	—	417	3	no	—
51	C₉	—	1251	1	no	—
52	C₉	—	1251	1	no	—
53	C₃	—	3	1	no	—
54	C₃	—	3	2	no	—
55	C₃	C₃²⋊(C₁₃₉⋊C₉)	1	1	yes	characteristic
56	C₃	#26014612	1	1	yes	characteristic
57	C₃	#26014615	1	1	yes	characteristic
58	C₃	#26014618	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₃₉⋊C₃)
commutator	C₃²×C₁₃₉	C₃×C₉
Frattini	C₃³	C₃×C₁₃₉⋊C₃
Fitting	C₃×3₋¹⁺²×C₁₃₉	C₃
socle	C₃²×C₁₃₉	H(3,𝔽₃)
prime radical, cosocle	C₃³×C₁₃₉	C₃²
hypercenter	C₃×3₋¹⁺²	C₁₃₉⋊C₃
hypocenter	C₁₃₉	3₋¹⁺²⋊C₉
LCS	G ▷ C₃²×C₁₃₉ ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
11. 3₋¹⁺²×C₁₃₉	C₉	semidirect
30. C₁₃₉	3₋¹⁺²⋊C₉	semidirect
37. 3₋¹⁺²	C₁₃₉⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₃₉⋊C₉	3
C₃²⋊(C₁₃₉⋊C₉)	3
C₃×3₋¹⁺²×C₁₃₉	3
3₋¹⁺²⋊C₉	139

Subgroups — 3−1+2⋊(C139⋊C9) #46798483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — 3₋¹⁺²⋊(C₁₃₉⋊C₉) #46798483