Subgroups — A₄×#733 #11757812

Order 972.

145 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×3₋¹⁺²	C₃	1	3	yes	maximal
2	C₃×C₉×A₄	C₃	1	1	yes	maximal, characteristic
3	C₂²×#733	C₃	1	1	yes	maximal, characteristic, complemented
4	#66364	C₃	1	6	yes	maximal, complemented
5	#66359	C₃	1	2	yes	maximal, complemented
6	C₃×#733	—	4	1	no	maximal, Sylow
7	C₂×#733	—	3	1	no	—
8	C₃²×A₄	C₃²	1	1	yes	characteristic
9	C₂²×3₋¹⁺²	C₃²	1	3	yes	—
10	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
11	#1094	C₃²	1	6	yes	—
12	C₃×C₂²⋊C₉	C₃²	1	2	yes	—
13	C₉⋊A₄	—	3	6	no	—
14	C₉×A₄	—	3	2	no	—
15	C₉×A₄	—	3	1	no	—
16	C₉×A₄	—	3	3	no	—
17	C₃×3₋¹⁺²	—	4	3	no	—
18	C₃²×C₉	—	4	1	no	—
19	#733	—	4	6	no	—
20	#733	—	4	2	no	—
21	#733	A₄	1	1	yes	characteristic, direct product factor
22	C₂×3₋¹⁺²	—	3	3	no	—
23	C₂×C₃×C₉	—	3	1	no	—
24	C₂²×C₃²	C₃³	1	1	yes	characteristic
25	C₃×A₄	—	3	3	no	—
26	C₃×A₄	H(3,𝔽₃)	1	2	yes	—
27	C₃×A₄	H(3,𝔽₃)	1	1	yes	characteristic
28	C₂²×C₉	—	3	1	no	—
29	C₂²×C₉	—	3	3	no	—
30	C₂²⋊C₉	—	3	2	no	—
31	C₂²⋊C₉	—	3	6	no	—
32	C₃³	—	4	1	no	—
33	3₋¹⁺²	—	4	6	no	—
34	3₋¹⁺²	—	12	6	no	—
35	3₋¹⁺²	C₃×A₄	1	3	yes	—
36	C₃×C₉	—	4	2	no	—
37	C₃×C₉	—	12	1	no	—
38	C₃×C₉	—	12	2	no	—
39	C₃×C₉	—	12	3	no	—
40	C₃×C₉	C₃×A₄	1	1	yes	characteristic
41	C₂×C₃²	—	3	1	no	—
42	C₂×C₉	—	9	1	no	—
43	C₂×C₉	—	9	3	no	—
44	C₂²×C₃	—	3	1	no	—
45	C₂²×C₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
46	A₄	—	3	2	no	—
47	A₄	#733	1	3	yes	direct product factor
48	C₃²	—	4	1	no	—
49	C₃²	—	4	2	no	—
50	C₃²	—	12	3	no	—
51	C₃²	C₃²×A₄	1	1	yes	characteristic
52	C₉	—	3	1	no	—
53	C₉	—	3	3	no	—
54	C₉	—	12	2	no	—
55	C₉	—	12	6	no	—
56	C₂×C₃	—	3	1	no	—
57	C₂×C₃	—	9	1	no	—
58	C₂²	C₃×#733	1	1	yes	characteristic, complemented, Sylow
59	C₃	—	3	1	no	—
60	C₃	—	4	3	no	—
61	C₃	—	12	2	no	—
62	C₃	A₄×H(3,𝔽₃)	1	1	yes	characteristic
63	C₂	—	3	1	no	—

	subgroup	G/H
center	C₃	A₄×H(3,𝔽₃)
commutator, cosocle	C₂²×C₃²	C₃³
Frattini	C₃²	C₃²×A₄
Fitting	C₂²×#733	C₃
socle	C₂²×C₃	C₃×H(3,𝔽₃)
prime radical	C₃²×A₄	C₃²
hypercenter	#733	A₄
hypocenter	C₂²	C₃×#733
LCS	G ▷ C₂²×C₃² ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #733

Complements

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

N	H ≅ G/N	type
3. C₂²×#733	C₃	semidirect
4. #66364	C₃	semidirect
5. #66359	C₃	semidirect
21. #733	A₄	direct (N × H)
47. A₄	#733	direct (N × H)
58. C₂²	C₃×#733	semidirect

Maximal subgroups

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

subgroup	index
A₄×3₋¹⁺²	3
C₃×C₉×A₄	3
C₂²×#733	3
#66364	3
#66359	3
C₃×#733	4

Subgroups — A4×#733 #11757812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×#733 #11757812