Subgroups — #46798552

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	C₃²×C₁₃₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	(C₁₃₉⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
4	C₃²⋊(C₁₃₉⋊C₉)	C₃	1	1	yes	maximal, characteristic
5	C₉×C₁₃₉⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃²⋊C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic
7	#16836730	C₉	1	9	yes	complemented
8	C₃×C₁₃₉⋊C₉	—	3	3	no	—
9	C₃×C₁₃₉⋊C₉	C₃²	1	3	yes	—
10	C₃×C₁₃₉⋊C₉	C₃²	1	2	yes	—
11	C₃×C₁₃₉⋊C₉	C₃²	1	3	yes	—
12	C₃×C₁₃₉⋊C₉	C₃²	1	1	yes	characteristic
13	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
14	C₃×C₉×C₁₃₉	C₃²	1	3	yes	—
15	C₃²×C₁₃₉	—	3	1	no	—
16	C₃²×C₁₃₉	—	3	1	no	—
17	C₃²×C₁₃₉	—	3	1	no	—
18	C₃²×C₁₃₉	C₃×C₉	1	3	yes	—
19	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
20	C₉×C₁₃₉	—	3	3	no	—
21	C₁₃₉⋊C₉	—	3	2	no	—
22	C₁₃₉⋊C₉	—	3	3	no	—
23	C₁₃₉⋊C₉	C₃×C₉	1	9	yes	complemented
24	C₁₃₉⋊C₉	3₋¹⁺²	1	3	yes	complemented
25	C₃×C₁₃₉	—	3	3	no	—
26	C₃×C₁₃₉	C₃²×C₉	1	1	yes	characteristic
27	C₃×C₁₃₉	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₃×C₁₃₉	#737	1	1	yes	characteristic
29	C₃×C₁₃₉	#737	1	1	yes	characteristic
30	C₉×3₋¹⁺²	—	139	1	no	maximal, Sylow
31	C₁₃₉	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
32	C₃×3₋¹⁺²	—	139	1	no	—
33	C₃²×C₉	—	139	1	no	—
34	C₉⋊C₉	—	139	6	no	—
35	C₃²⋊C₉	—	139	1	no	—
36	C₃²⋊C₉	C₁₃₉⋊C₃	1	1	yes	characteristic
37	C₉²	—	139	3	no	—
38	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
39	3₋¹⁺²	—	139	9	no	—
40	C₃×C₉	—	139	1	no	—
41	C₃×C₉	—	139	3	no	—
42	C₃×C₉	—	139	3	no	—
43	C₃×C₉	—	139	2	no	—
44	C₃×C₉	—	417	3	no	—
45	C₃×C₉	C₃×C₁₃₉⋊C₃	1	3	yes	—
46	C₃²	—	3	1	no	—
47	C₃²	—	3	1	no	—
48	C₃²	—	3	1	no	—
49	C₃²	C₉×C₁₃₉⋊C₃	1	3	yes	—
50	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
51	C₉	—	3	3	no	—
52	C₉	—	139	9	no	—
53	C₉	—	139	3	no	—
54	C₉	—	417	2	no	—
55	C₉	—	417	3	no	—
56	C₃	—	3	3	no	—
57	C₃	C₃×C₉×C₁₃₉⋊C₃	1	1	yes	characteristic
58	C₃	3₋¹⁺²×C₁₃₉⋊C₃	1	1	yes	characteristic
59	C₃	#26014628	1	1	yes	characteristic
60	C₃	#26014630	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₁₃₉⋊C₃
commutator	C₃×C₁₃₉	C₃²×C₉
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 ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. (C₁₃₉⋊C₉)⋊C₉	C₃	semidirect
5. C₉×C₁₃₉⋊C₉	C₃	semidirect
7. #16836730	C₉	semidirect
23. C₁₃₉⋊C₉	C₃×C₉	semidirect
24. C₁₃₉⋊C₉	3₋¹⁺²	semidirect
31. C₁₃₉	C₉×3₋¹⁺²	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
C₃²×C₁₃₉⋊C₉	3
(C₁₃₉⋊C₉)⋊C₉	3
C₃²⋊(C₁₃₉⋊C₉)	3
C₉×C₁₃₉⋊C₉	3
C₃²⋊C₉×C₁₃₉	3
C₉×3₋¹⁺²	139