Subgroups — C₃×#66437 #11758098

Order 972.

536 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₃×#1094	C₃	1	8	yes	maximal, complemented
3	C₃²×C₂²⋊C₉	C₃	1	4	yes	maximal, complemented
4	#66437	C₃	1	27	yes	maximal, direct product factor
5	C₃×#737	—	4	1	no	maximal, Sylow
6	C₂×C₃×H(3,𝔽₃)	—	3	1	no	—
7	C₂²×C₃³	C₃²	1	4	yes	—
8	C₂²×H(3,𝔽₃)	C₃²	1	9	yes	—
9	#1094	C₃²	1	72	yes	complemented
10	C₃×C₂²⋊C₉	C₃²	1	1	yes	characteristic
11	C₃×C₂²⋊C₉	C₃²	1	8	yes	—
12	C₃×C₂²⋊C₉	C₃²	1	36	yes	complemented
13	#737	—	4	27	no	—
14	C₃×3₋¹⁺²	—	4	8	no	—
15	C₃×H(3,𝔽₃)	A₄	1	1	yes	characteristic
16	C₃²×C₉	—	4	4	no	—
17	C₂×C₃³	—	3	4	no	—
18	C₂×H(3,𝔽₃)	—	3	9	no	—
19	C₂²×C₃²	—	3	12	no	—
20	C₂²×C₃²	C₃³	1	12	yes	—
21	C₂²×C₃²	C₃³	1	1	yes	characteristic
22	C₂²⋊C₉	C₃³	1	3	yes	—
23	C₂²⋊C₉	C₃³	1	24	yes	—
24	C₃³	C₃×A₄	1	4	yes	—
25	3₋¹⁺²	—	4	72	no	—
26	H(3,𝔽₃)	C₃×A₄	1	9	yes	—
27	C₃×C₉	—	4	36	no	—
28	C₃×C₉	—	4	1	no	—
29	C₃×C₉	—	4	8	no	—
30	C₂×C₃²	—	3	1	no	—
31	C₂×C₃²	—	3	12	no	—
32	C₂×C₃²	—	9	12	no	—
33	C₂²×C₃	—	3	12	no	—
34	C₂²×C₃	#737	1	3	yes	complemented
35	C₂²×C₃	C₃⁴	1	1	yes	characteristic
36	C₃²	—	3	12	no	—
37	C₃²	C₃²×A₄	1	12	yes	—
38	C₃²	C₃²×A₄	1	1	yes	characteristic
39	C₉	—	4	3	no	—
40	C₉	—	4	24	no	—
41	C₂×C₃	—	3	3	no	—
42	C₂×C₃	—	3	1	no	—
43	C₂×C₃	—	9	12	no	—
44	C₂²	C₃×#737	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	3	12	no	—
46	C₃	#66437	1	3	yes	direct product factor
47	C₃	C₃³×A₄	1	1	yes	characteristic
48	C₂	—	3	1	no	—

	subgroup	G/H
center	C₃²	C₃²×A₄
commutator, cosocle	C₂²×C₃	C₃⁴
Frattini	C₃	C₃³×A₄
Fitting, prime radical	C₂²×C₃×H(3,𝔽₃)	C₃
socle	C₂²×C₃²	C₃³
hypercenter	C₃×H(3,𝔽₃)	A₄
hypocenter	C₂²	C₃×#737
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
2. C₃×#1094	C₃	semidirect
3. C₃²×C₂²⋊C₉	C₃	semidirect
4. #66437	C₃	direct (N × H)
9. #1094	C₃²	semidirect
12. C₃×C₂²⋊C₉	C₃²	semidirect
34. C₂²×C₃	#737	semidirect
44. C₂²	C₃×#737	semidirect
46. C₃	#66437	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×H(3,𝔽₃)	3
C₃×#1094	3
C₃²×C₂²⋊C₉	3
#66437	3
C₃×#737	4

Subgroups — C3×#66437 #11758098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#66437 #11758098