Subgroups — C₃×#66436 #11758097

Order 972.

530 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₉	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂²⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₃×#1094	C₃	1	2	yes	maximal, complemented
4	#66436	C₃	1	27	yes	maximal, direct product factor
5	C₃×C₉⋊A₄	C₃	1	6	yes	maximal, complemented
6	C₃×C₉×A₄	C₃	1	3	yes	maximal, complemented
7	C₃×#737	—	4	1	no	maximal, Sylow
8	C₂×C₃²×C₉	—	3	1	no	—
9	C₂²×C₃³	C₃²	1	1	yes	characteristic
10	C₃²×A₄	C₃²	1	3	yes	—
11	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
12	C₂²×C₃×C₉	C₃²	1	2	yes	—
13	C₂²×C₃×C₉	C₃²	1	9	yes	complemented
14	C₂²⋊H(3,𝔽₃)	C₃²	1	9	yes	—
15	#1094	C₃²	1	18	yes	complemented
16	C₃×C₂²⋊C₉	C₃²	1	6	yes	—
17	C₉⋊A₄	C₃²	1	54	yes	complemented
18	C₉×A₄	C₃²	1	27	yes	complemented
19	#737	—	4	27	no	—
20	C₃×3₋¹⁺²	—	4	2	no	—
21	C₃×3₋¹⁺²	—	4	6	no	—
22	C₃×H(3,𝔽₃)	—	4	1	no	—
23	C₃²×C₉	—	4	3	no	—
24	C₃²×C₉	A₄	1	1	yes	characteristic, complemented
25	C₂×C₃³	—	3	1	no	—
26	C₂×C₃×C₉	—	3	2	no	—
27	C₂×C₃×C₉	—	3	1	no	—
28	C₂×C₃×C₉	—	3	9	no	—
29	C₂²×C₃²	—	3	3	no	—
30	C₂²×C₃²	C₃³	1	3	yes	—
31	C₂²×C₃²	C₃³	1	1	yes	characteristic
32	C₃×A₄	—	3	9	no	—
33	C₃×A₄	C₃³	1	9	yes	—
34	C₂²×C₉	C₃³	1	3	yes	—
35	C₂²×C₉	C₃³	1	6	yes	—
36	C₂²⋊C₉	C₃³	1	18	yes	—
37	C₃³	—	4	3	no	—
38	C₃³	C₃×A₄	1	1	yes	characteristic
39	3₋¹⁺²	—	4	18	no	—
40	3₋¹⁺²	—	4	54	no	—
41	H(3,𝔽₃)	—	4	9	no	—
42	C₃×C₉	—	4	6	no	—
43	C₃×C₉	—	4	27	no	—
44	C₃×C₉	C₃×A₄	1	2	yes	—
45	C₃×C₉	C₃×A₄	1	1	yes	characteristic
46	C₃×C₉	C₃×A₄	1	9	yes	complemented
47	C₂×C₃²	—	3	9	no	—
48	C₂×C₃²	—	3	3	no	—
49	C₂×C₃²	—	3	1	no	—
50	C₂×C₉	—	3	3	no	—
51	C₂×C₉	—	3	6	no	—
52	C₂²×C₃	—	3	3	no	—
53	C₂²×C₃	#737	1	3	yes	complemented
54	C₂²×C₃	C₃⁴	1	1	yes	characteristic
55	A₄	—	3	9	no	—
56	C₃²	—	3	3	no	—
57	C₃²	—	4	9	no	—
58	C₃²	—	12	9	no	—
59	C₃²	C₃²×A₄	1	3	yes	—
60	C₃²	C₃²×A₄	1	1	yes	characteristic
61	C₉	—	4	18	no	—
62	C₉	C₃²×A₄	1	3	yes	—
63	C₉	C₃²×A₄	1	6	yes	—
64	C₂×C₃	—	3	9	no	—
65	C₂×C₃	—	3	3	no	—
66	C₂×C₃	—	3	1	no	—
67	C₂²	C₃×#737	1	1	yes	characteristic, complemented, Sylow
68	C₃	—	3	3	no	—
69	C₃	—	12	9	no	—
70	C₃	#66436	1	3	yes	direct product factor
71	C₃	C₃³×A₄	1	1	yes	characteristic
72	C₂	—	3	1	no	—

	subgroup	G/H
center	C₃×C₉	C₃×A₄
commutator, cosocle	C₂²×C₃	C₃⁴
Frattini	C₃	C₃³×A₄
Fitting	C₂²×C₃²×C₉	C₃
socle	C₂²×C₃²	C₃³
prime radical	C₃×C₂²⋊H(3,𝔽₃)	C₃
hypercenter	C₃²×C₉	A₄
hypocenter	C₂²	C₃×#737
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×C₉	C₃	semidirect
3. C₃×#1094	C₃	semidirect
4. #66436	C₃	direct (N × H)
5. C₃×C₉⋊A₄	C₃	semidirect
6. C₃×C₉×A₄	C₃	semidirect
13. C₂²×C₃×C₉	C₃²	semidirect
15. #1094	C₃²	semidirect
17. C₉⋊A₄	C₃²	semidirect
18. C₉×A₄	C₃²	semidirect
24. C₃²×C₉	A₄	semidirect
46. C₃×C₉	C₃×A₄	semidirect
53. C₂²×C₃	#737	semidirect
67. C₂²	C₃×#737	semidirect
70. C₃	#66436	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×C₃²×C₉	3
C₃×C₂²⋊H(3,𝔽₃)	3
C₃×#1094	3
#66436	3
C₃×C₉⋊A₄	3
C₃×C₉×A₄	3
C₃×#737	4

Subgroups — C3×#66436 #11758097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#66436 #11758097