Subgroups — #733×C₁₃₉⋊C₃ #46798630

Order 33777.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×C₁₃₉⋊C₃	C₃	1	3	yes	maximal
2	C₃×C₉×C₁₃₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#26014619	C₃	1	2	yes	maximal, complemented
4	#26014618	C₃	1	6	yes	maximal, complemented
5	#733×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₁₃₉⋊C₃	C₃²	1	1	yes	characteristic
7	#16836730	C₃²	1	6	yes	—
8	#16836729	—	3	3	no	—
9	#16836728	—	3	3	no	—
10	C₃×C₁₃₉⋊C₉	C₃²	1	2	yes	—
11	C₉×C₁₃₉⋊C₃	—	3	1	no	—
12	C₉×C₁₃₉⋊C₃	—	3	1	no	—
13	C₉×C₁₃₉⋊C₃	—	3	1	no	—
14	C₉×C₁₃₉⋊C₃	—	3	3	no	—
15	3₋¹⁺²×C₁₃₉	C₃²	1	3	yes	—
16	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
17	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
18	C₃×C₁₃₉⋊C₃	—	3	3	no	—
19	C₃×C₁₃₉⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃×C₁₃₉⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×C₁₃₉⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
22	C₉×C₁₃₉	—	3	1	no	—
23	C₉×C₁₃₉	—	3	3	no	—
24	C₁₃₉⋊C₉	—	3	2	no	—
25	C₁₃₉⋊C₉	—	3	6	no	—
26	C₃×C₁₃₉	—	3	1	no	—
27	C₃×C₁₃₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₁₃₉⋊C₃	—	3	1	no	—
29	C₁₃₉⋊C₃	—	3	1	no	—
30	C₁₃₉⋊C₃	#733	1	3	yes	direct product factor
31	C₃×#733	—	139	1	no	maximal, Sylow
32	C₁₃₉	C₃×#733	1	1	yes	characteristic, complemented, Sylow
33	C₃×3₋¹⁺²	—	139	3	no	—
34	C₃²×C₉	—	139	1	no	—
35	#733	—	139	6	no	—
36	#733	—	139	2	no	—
37	#733	C₁₃₉⋊C₃	1	1	yes	characteristic, direct product factor
38	C₃³	—	139	1	no	—
39	3₋¹⁺²	—	139	6	no	—
40	3₋¹⁺²	—	417	3	no	—
41	3₋¹⁺²	—	417	3	no	—
42	3₋¹⁺²	C₃×C₁₃₉⋊C₃	1	3	yes	—
43	C₃×C₉	—	139	2	no	—
44	C₃×C₉	—	417	1	no	—
45	C₃×C₉	—	417	1	no	—
46	C₃×C₉	—	417	1	no	—
47	C₃×C₉	—	417	3	no	—
48	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
49	C₃²	—	139	1	no	—
50	C₃²	—	139	1	no	—
51	C₃²	—	139	1	no	—
52	C₃²	—	417	3	no	—
53	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
54	C₉	—	3	1	no	—
55	C₉	—	3	3	no	—
56	C₉	—	417	2	no	—
57	C₉	—	417	6	no	—
58	C₃	—	3	1	no	—
59	C₃	—	139	3	no	—
60	C₃	—	417	1	no	—
61	C₃	—	417	1	no	—
62	C₃	H(3,𝔽₃)×C₁₃₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₁₃₉⋊C₃
commutator, cosocle	C₃²×C₁₃₉	C₃³
Frattini	C₃²	C₃²×C₁₃₉⋊C₃
Fitting	#733×C₁₃₉	C₃
socle	C₃×C₁₃₉	C₃×H(3,𝔽₃)
prime radical	C₃²×C₁₃₉⋊C₃	C₃²
hypercenter	#733	C₁₃₉⋊C₃
hypocenter	C₁₃₉	C₃×#733
LCS	G ▷ C₃²×C₁₃₉ ▷ C₃×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #733

Complements

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

N	H ≅ G/N	type
3. #26014619	C₃	semidirect
4. #26014618	C₃	semidirect
5. #733×C₁₃₉	C₃	semidirect
30. C₁₃₉⋊C₃	#733	direct (N × H)
32. C₁₃₉	C₃×#733	semidirect
37. #733	C₁₃₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
3₋¹⁺²×C₁₃₉⋊C₃	3
C₃×C₉×C₁₃₉⋊C₃	3
#26014619	3
#26014618	3
#733×C₁₃₉	3
C₃×#733	139

Subgroups — #733×C139⋊C3 #46798630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #733×C₁₃₉⋊C₃ #46798630