Subgroups — C₃×#11760441 #15691643

Order 3159.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₁₃⋊C₃)	C₃	1	3	yes	maximal, complemented
2	#11760441	C₃	1	9	yes	maximal, direct product factor
3	C₃²×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₁₃	C₃²	1	1	yes	characteristic
5	C₃²×C₁₃⋊C₃	—	3	3	no	—
6	C₃×C₉×C₁₃	—	3	2	no	—
7	C₃×C₉×C₁₃	—	3	1	no	—
8	C₃×C₉×C₁₃	C₃²	1	3	yes	complemented
9	C₃²⋊(C₁₃⋊C₃)	—	3	6	no	—
10	C₃²⋊(C₁₃⋊C₃)	C₃²	1	9	yes	complemented
11	C₃×#732	—	13	1	no	maximal, Sylow
12	C₃²×C₁₃	—	3	3	no	—
13	C₃²×C₁₃	H(3,𝔽₃)	1	2	yes	—
14	C₃²×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃²×C₁₃	C₃³	1	1	yes	characteristic
16	C₃×C₁₃⋊C₃	—	3	9	no	—
17	C₃×C₁₃⋊C₃	—	9	9	no	—
18	C₉×C₁₃	—	3	3	no	—
19	C₃×H(3,𝔽₃)	—	13	3	no	—
20	C₃²×C₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
21	#732	—	13	9	no	—
22	C₃×C₁₃	—	3	2	no	—
23	C₃×C₁₃	—	3	1	no	—
24	C₃×C₁₃	#732	1	3	yes	complemented
25	C₃×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
26	C₁₃⋊C₃	—	9	9	no	—
27	C₃³	—	39	3	no	—
28	C₃³	C₃×C₁₃⋊C₃	1	1	yes	characteristic
29	H(3,𝔽₃)	—	13	9	no	—
30	H(3,𝔽₃)	—	39	6	no	—
31	C₃×C₉	—	3	2	no	—
32	C₃×C₉	—	3	1	no	—
33	C₃×C₉	C₃×C₁₃⋊C₃	1	3	yes	complemented
34	C₁₃	C₃×#732	1	1	yes	characteristic, complemented, Sylow
35	C₃²	—	3	3	no	—
36	C₃²	—	39	9	no	—
37	C₃²	—	117	9	no	—
38	C₃²	C₃²⋊(C₁₃⋊C₃)	1	2	yes	—
39	C₃²	C₃²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
40	C₃²	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
41	C₉	—	3	3	no	—
42	C₃	—	3	2	no	—
43	C₃	—	3	1	no	—
44	C₃	—	117	9	no	—
45	C₃	#11760441	1	3	yes	direct product factor
46	C₃	C₃×C₃²⋊(C₁₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₃⋊C₃)
commutator, cosocle	C₃²×C₁₃	C₃³
Frattini	C₃²	C₃²×C₁₃⋊C₃
Fitting	C₃²×C₉×C₁₃	C₃
socle	C₃²×C₁₃	H(3,𝔽₃)
hypercenter	C₃²×C₉	C₁₃⋊C₃
hypocenter	C₁₃	C₃×#732
LCS	G ▷ C₃²×C₁₃ ▷ C₃×C₁₃ ▷ C₁₃
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⋊(C₁₃⋊C₃)	C₃	semidirect
2. #11760441	C₃	direct (N × H)
3. C₃²×C₉×C₁₃	C₃	semidirect
8. C₃×C₉×C₁₃	C₃²	semidirect
10. C₃²⋊(C₁₃⋊C₃)	C₃²	semidirect
20. C₃²×C₉	C₁₃⋊C₃	semidirect
24. C₃×C₁₃	#732	semidirect
33. C₃×C₉	C₃×C₁₃⋊C₃	semidirect
34. C₁₃	C₃×#732	semidirect
45. C₃	#11760441	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×C₃²⋊(C₁₃⋊C₃)	3
#11760441	3
C₃²×C₉×C₁₃	3
C₃×#732	13

Subgroups — C3×#11760441 #15691643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#11760441 #15691643