Subgroups — C₉×3₋¹⁺²×C₁₃₉ #46798412

Order 33777.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²×C₁₃₉	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic
3	C₉⋊C₉×C₁₃₉	C₃	1	6	yes	maximal, complemented
4	C₃²⋊C₉×C₁₃₉	C₃	1	2	yes	maximal
5	C₉²×C₁₃₉	C₃	1	3	yes	maximal, complemented
6	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
7	3₋¹⁺²×C₁₃₉	C₉	1	9	yes	direct product factor
8	C₃×C₉×C₁₃₉	—	3	3	no	—
9	C₃×C₉×C₁₃₉	C₃²	1	6	yes	—
10	C₃×C₉×C₁₃₉	C₃²	1	2	yes	—
11	C₃×C₉×C₁₃₉	C₃²	1	3	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	6	no	—
19	C₉×C₁₃₉	C₃×C₉	1	9	yes	complemented
20	C₉×C₁₃₉	3₋¹⁺²	1	3	yes	direct product factor
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	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₁₃₉	C₉×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
27	C₃×3₋¹⁺²	C₃×C₁₃₉	1	1	yes	characteristic
28	C₃²×C₉	C₃×C₁₃₉	1	1	yes	characteristic
29	C₉⋊C₉	C₃×C₁₃₉	1	6	yes	complemented
30	C₃²⋊C₉	C₃×C₁₃₉	1	2	yes	—
31	C₉²	C₃×C₁₃₉	1	3	yes	complemented
32	C₃³	C₃²×C₁₃₉	1	1	yes	characteristic
33	3₋¹⁺²	C₉×C₁₃₉	1	9	yes	direct product factor
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	C₃²×C₁₃₉	1	6	yes	—
36	C₃×C₉	C₃²×C₁₃₉	1	2	yes	—
37	C₃×C₉	C₃²×C₁₃₉	1	3	yes	—
38	C₃×C₉	C₃²×C₁₃₉	1	1	yes	characteristic
39	C₃²	—	3	1	no	—
40	C₃²	—	3	2	no	—
41	C₃²	C₃×C₉×C₁₃₉	1	3	yes	—
42	C₃²	C₃³×C₁₃₉	1	1	yes	characteristic
43	C₉	—	3	2	no	—
44	C₉	—	3	6	no	—
45	C₉	C₃×C₉×C₁₃₉	1	9	yes	complemented
46	C₉	3₋¹⁺²×C₁₃₉	1	3	yes	direct product factor
47	C₃	—	3	3	no	—
48	C₃	C₃²×C₉×C₁₃₉	1	1	yes	characteristic
49	C₃	C₃×3₋¹⁺²×C₁₃₉	1	1	yes	characteristic
50	C₃	#737×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₃×C₉×C₁₃₉	C₃²
commutator	C₃	C₃²×C₉×C₁₃₉
Frattini, cosocle	C₃²	C₃³×C₁₃₉
socle	C₃²×C₁₃₉	C₃³
prime radical	C₃³×C₁₃₉	C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉⋊C₉×C₁₃₉	C₃	semidirect
5. C₉²×C₁₃₉	C₃	semidirect
7. 3₋¹⁺²×C₁₃₉	C₉	direct (N × H)
19. C₉×C₁₃₉	C₃×C₉	semidirect
20. C₉×C₁₃₉	3₋¹⁺²	direct (N × H)
25. C₉×3₋¹⁺²	C₁₃₉	direct (N × H)
26. C₁₃₉	C₉×3₋¹⁺²	direct (N × H)
29. C₉⋊C₉	C₃×C₁₃₉	semidirect
31. C₉²	C₃×C₁₃₉	semidirect
33. 3₋¹⁺²	C₉×C₁₃₉	direct (N × H)
45. C₉	C₃×C₉×C₁₃₉	semidirect
46. C₉	3₋¹⁺²×C₁₃₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×3₋¹⁺²×C₁₃₉	3
C₃²×C₉×C₁₃₉	3
C₉⋊C₉×C₁₃₉	3
C₃²⋊C₉×C₁₃₉	3
C₉²×C₁₃₉	3
C₉×3₋¹⁺²	139

Subgroups — C9×3−1+2×C139 #46798412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×3₋¹⁺²×C₁₃₉ #46798412