Subgroups — C₉×#16836730 #46798548

Order 33777.

148 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
2	(C₁₃₉⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
3	C₃²⋊(C₁₃₉⋊C₉)	C₃	1	2	yes	maximal
4	C₉×C₁₃₉⋊C₉	C₃	1	3	yes	maximal, complemented
5	C₃²×C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic
6	#16836730	C₉	1	9	yes	direct product factor
7	C₃×C₁₃₉⋊C₉	C₃²	1	6	yes	—
8	C₃×C₁₃₉⋊C₉	C₃²	1	3	yes	—
9	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
10	C₃×C₉×C₁₃₉	—	3	3	no	—
11	C₃×C₉×C₁₃₉	C₃²	1	2	yes	—
12	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
13	C₃²×C₁₃₉	—	3	1	no	—
14	C₃²×C₁₃₉	—	3	2	no	—
15	C₃²×C₁₃₉	C₃×C₉	1	3	yes	—
16	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
17	C₉×C₁₃₉	—	3	2	no	—
18	C₉×C₁₃₉	3₋¹⁺²	1	3	yes	complemented
19	C₁₃₉⋊C₉	—	3	6	no	—
20	C₁₃₉⋊C₉	C₃×C₉	1	9	yes	complemented
21	C₃×C₁₃₉	—	3	3	no	—
22	C₃×C₁₃₉	C₃²×C₉	1	1	yes	characteristic
23	C₃×C₁₃₉	C₃×3₋¹⁺²	1	1	yes	characteristic
24	C₃×C₁₃₉	#737	1	2	yes	—
25	C₉×3₋¹⁺²	—	139	1	no	maximal, Sylow
26	C₁₃₉	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
27	C₃×3₋¹⁺²	—	139	1	no	—
28	C₃²×C₉	C₁₃₉⋊C₃	1	1	yes	characteristic
29	C₉⋊C₉	—	139	6	no	—
30	C₃²⋊C₉	—	139	2	no	—
31	C₉²	—	139	3	no	—
32	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
33	3₋¹⁺²	—	139	9	no	—
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	—	139	3	no	—
36	C₃×C₉	—	139	6	no	—
37	C₃×C₉	C₃×C₁₃₉⋊C₃	1	2	yes	—
38	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
39	C₃²	—	3	1	no	—
40	C₃²	—	3	2	no	—
41	C₃²	C₉×C₁₃₉⋊C₃	1	3	yes	—
42	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
43	C₉	—	3	2	no	—
44	C₉	—	139	9	no	—
45	C₉	—	417	6	no	—
46	C₉	#16836730	1	3	yes	direct product factor
47	C₃	—	3	3	no	—
48	C₃	C₃×C₉×C₁₃₉⋊C₃	1	1	yes	characteristic
49	C₃	C₃×#16836730	1	1	yes	characteristic
50	C₃	#26014629	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. (C₁₃₉⋊C₉)⋊C₉	C₃	semidirect
4. C₉×C₁₃₉⋊C₉	C₃	semidirect
6. #16836730	C₉	direct (N × H)
18. C₉×C₁₃₉	3₋¹⁺²	semidirect
20. C₁₃₉⋊C₉	C₃×C₉	semidirect
26. C₁₃₉	C₉×3₋¹⁺²	semidirect
46. C₉	#16836730	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#16836730	3
(C₁₃₉⋊C₉)⋊C₉	3
C₃²⋊(C₁₃₉⋊C₉)	3
C₉×C₁₃₉⋊C₉	3
C₃²×C₉×C₁₃₉	3
C₉×3₋¹⁺²	139

Subgroups — C9×#16836730 #46798548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#16836730 #46798548