Subgroups — #46798638

Order 33777.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26014630	C₃	1	3	yes	maximal, complemented
2	C₃×C₉×C₁₃₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#26014619	C₃	1	1	yes	maximal, characteristic, complemented
4	#26014617	C₃	1	1	yes	maximal, characteristic, complemented
5	#26014615	C₃	1	3	yes	maximal, complemented
6	#26014612	C₃	1	3	yes	maximal, complemented
7	#733×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₁₃₉⋊C₃	C₃²	1	1	yes	characteristic
9	#16836730	C₃²	1	3	yes	—
10	#16836729	—	3	3	no	—
11	#16836728	—	3	3	no	—
12	C₃²⋊(C₁₃₉⋊C₃)	C₃²	1	3	yes	—
13	C₃×C₁₃₉⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₁₃₉⋊C₉	C₃²	1	1	yes	characteristic
15	C₉×C₁₃₉⋊C₃	—	3	1	no	—
16	C₉×C₁₃₉⋊C₃	—	3	1	no	—
17	C₉×C₁₃₉⋊C₃	—	3	1	no	—
18	C₉×C₁₃₉⋊C₃	—	3	3	no	—
19	3₋¹⁺²×C₁₃₉	C₃²	1	3	yes	—
20	C₃×C₉×C₁₃₉	C₃²	1	1	yes	characteristic
21	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
22	C₃×C₁₃₉⋊C₃	—	3	1	no	—
23	C₃×C₁₃₉⋊C₃	—	3	3	no	—
24	C₃×C₁₃₉⋊C₃	—	3	3	no	—
25	C₉×C₁₃₉	—	3	1	no	—
26	C₉×C₁₃₉	—	3	3	no	—
27	C₁₃₉⋊C₉	—	3	1	no	—
28	C₁₃₉⋊C₉	—	3	3	no	—
29	C₁₃₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
30	C₁₃₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
31	C₁₃₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
32	C₃×C₁₃₉	—	3	1	no	—
33	C₃×C₁₃₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₁₃₉⋊C₃	—	3	3	no	—
35	C₁₃₉⋊C₃	—	9	3	no	—
36	#6908	—	139	1	no	maximal, Sylow
37	C₁₃₉	#6908	1	1	yes	characteristic, complemented, Sylow
38	#737	—	139	3	no	—
39	C₃²×C₉	—	139	1	no	—
40	#733	—	139	1	no	—
41	#733	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
42	#732	—	139	1	no	—
43	#731	—	139	3	no	—
44	AΣL(1,𝔽₂₇)	—	139	3	no	—
45	C₃³	—	139	1	no	—
46	3₋¹⁺²	—	139	3	no	—
47	3₋¹⁺²	—	417	3	no	—
48	3₋¹⁺²	—	417	3	no	—
49	3₋¹⁺²	C₃×C₁₃₉⋊C₃	1	3	yes	—
50	H(3,𝔽₃)	—	139	3	no	—
51	C₃×C₉	—	139	1	no	—
52	C₃×C₉	—	139	1	no	—
53	C₃×C₉	—	417	1	no	—
54	C₃×C₉	—	417	1	no	—
55	C₃×C₉	—	417	1	no	—
56	C₃×C₉	—	417	3	no	—
57	C₃×C₉	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
58	C₃²	—	417	3	no	—
59	C₃²	—	417	1	no	—
60	C₃²	—	417	3	no	—
61	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
62	C₉	—	3	1	no	—
63	C₉	—	3	3	no	—
64	C₉	—	139	1	no	—
65	C₉	—	139	1	no	—
66	C₉	—	139	1	no	—
67	C₉	—	417	1	no	—
68	C₉	—	417	3	no	—
69	C₃	—	3	1	no	—
70	C₃	—	417	3	no	—
71	C₃	—	1251	3	no	—
72	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)
hypercenter	#733	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6908
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
1. #26014630	C₃	semidirect
2. C₃×C₉×C₁₃₉⋊C₃	C₃	semidirect
3. #26014619	C₃	semidirect
4. #26014617	C₃	semidirect
5. #26014615	C₃	semidirect
6. #26014612	C₃	semidirect
7. #733×C₁₃₉	C₃	semidirect
37. C₁₃₉	#6908	semidirect
41. #733	C₁₃₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#26014630	3
C₃×C₉×C₁₃₉⋊C₃	3
#26014619	3
#26014617	3
#26014615	3
#26014612	3
#733×C₁₃₉	3
#6908	139