Subgroups — #46798447

Order 33777.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₁₃₉⋊C₃)	C₃	1	2	yes	maximal, complemented
2	C₃²⋊(C₁₃₉⋊C₉)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²⋊C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₁₃₉⋊C₃	—	3	2	no	—
5	C₃²⋊(C₁₃₉⋊C₃)	—	3	6	no	—
6	C₃×C₁₃₉⋊C₉	—	3	1	no	—
7	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
8	C₃×C₉×C₁₃₉	—	3	1	no	—
9	C₃²×C₁₃₉	—	3	2	no	—
10	C₃²×C₁₃₉	—	3	1	no	—
11	C₃²×C₁₃₉	—	3	1	no	—
12	C₃²×C₁₃₉	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₁₃₉⋊C₃	—	3	6	no	—
14	C₃×C₁₃₉⋊C₃	—	9	2	no	—
15	C₃×C₁₃₉⋊C₃	—	9	2	no	—
16	C₃×C₁₃₉⋊C₃	—	9	2	no	—
17	C₉×C₁₃₉	—	9	1	no	—
18	C₁₃₉⋊C₉	—	9	1	no	—
19	C₃×C₁₃₉	—	9	1	no	—
20	C₃×C₁₃₉	AΣL(1,𝔽₂₇)	1	2	yes	—
21	C₃×C₁₃₉	#732	1	1	yes	characteristic
22	C₃×C₁₃₉	#732	1	1	yes	characteristic
23	C₁₃₉⋊C₃	—	9	6	no	—
24	#6856	—	139	1	no	maximal, Sylow
25	C₁₃₉	#6856	1	1	yes	characteristic, complemented, Sylow
26	C₃×H(3,𝔽₃)	—	139	2	no	—
27	C₃²⋊C₉	—	139	1	no	—
28	C₃²⋊C₉	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
29	C₃³	—	417	2	no	—
30	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
31	H(3,𝔽₃)	—	417	6	no	—
32	C₃×C₉	—	3	1	no	—
33	C₃×C₉	—	417	1	no	—
34	C₃²	—	3	2	no	—
35	C₃²	—	3	1	no	—
36	C₃²	—	3	1	no	—
37	C₃²	—	417	6	no	—
38	C₃²	—	1251	2	no	—
39	C₃²	—	1251	2	no	—
40	C₃²	—	1251	2	no	—
41	C₃²	C₃²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic
42	C₉	—	9	1	no	—
43	C₉	—	1251	1	no	—
44	C₃	—	9	1	no	—
45	C₃	—	1251	6	no	—
46	C₃	#26014612	1	2	yes	—
47	C₃	#26014616	1	1	yes	characteristic
48	C₃	#26014617	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₃₉⋊C₃)
commutator, cosocle	C₃³×C₁₃₉	C₃²
Frattini	C₃³	C₃×C₁₃₉⋊C₃
Fitting	C₃²⋊C₉×C₁₃₉	C₃
socle	C₃²×C₁₃₉	H(3,𝔽₃)
hypercenter	C₃²⋊C₉	C₁₃₉⋊C₃
hypocenter	C₁₃₉	#6856
LCS	G ▷ C₃³×C₁₃₉ ▷ C₃²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₃²⋊(C₁₃₉⋊C₃)	C₃	semidirect
2. C₃²⋊(C₁₃₉⋊C₉)	C₃	semidirect
3. C₃²⋊C₉×C₁₃₉	C₃	semidirect
25. C₁₃₉	#6856	semidirect
28. C₃²⋊C₉	C₁₃₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃²⋊(C₁₃₉⋊C₃)	3
C₃²⋊(C₁₃₉⋊C₉)	3
C₃²⋊C₉×C₁₃₉	3
#6856	139