Subgroups — A₄×C₂₇⋊C₃ #11757796

Order 972.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×A₄	C₃	1	1	yes	maximal, characteristic
2	C₂²×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#66353	C₃	1	2	yes	maximal, complemented
4	C₂₇⋊A₄	C₃	1	6	yes	maximal, complemented
5	A₄×C₂₇	C₃	1	3	yes	maximal, complemented
6	C₃×C₂₇⋊C₃	—	4	1	no	maximal, Sylow
7	C₂×C₂₇⋊C₃	—	3	1	no	—
8	C₃²×A₄	C₉	1	1	yes	characteristic
9	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
10	C₃×C₂²⋊C₉	C₉	1	2	yes	—
11	C₉×A₄	C₉	1	4	yes	—
12	C₉×A₄	C₉	1	2	yes	—
13	C₉×A₄	C₃²	1	1	yes	characteristic
14	C₉×A₄	C₃²	1	2	yes	—
15	C₂²×C₂₇	C₃²	1	3	yes	complemented
16	C₂²⋊C₂₇	C₃²	1	6	yes	complemented
17	C₃²×C₉	—	4	1	no	—
18	C₂₇⋊C₃	—	4	2	no	—
19	C₂₇⋊C₃	—	4	6	no	—
20	C₂₇⋊C₃	A₄	1	1	yes	characteristic, direct product factor
21	C₃×C₂₇	—	4	3	no	—
22	C₂×C₃×C₉	—	3	1	no	—
23	C₂×C₂₇	—	3	3	no	—
24	C₂²×C₃²	C₃×C₉	1	1	yes	characteristic
25	C₃×A₄	—	3	3	no	—
26	C₃×A₄	C₃×C₉	1	2	yes	—
27	C₃×A₄	C₃×C₉	1	1	yes	characteristic
28	C₂²×C₉	C₃×C₉	1	2	yes	—
29	C₂²×C₉	C₃³	1	1	yes	characteristic
30	C₂²⋊C₉	C₃×C₉	1	2	yes	—
31	C₂²⋊C₉	C₃×C₉	1	4	yes	—
32	C₃³	—	4	1	no	—
33	C₃×C₉	—	4	2	no	—
34	C₃×C₉	—	4	2	no	—
35	C₃×C₉	—	4	4	no	—
36	C₃×C₉	—	4	1	no	—
37	C₃×C₉	—	4	2	no	—
38	C₃×C₉	C₃×A₄	1	1	yes	characteristic
39	C₂₇	—	4	6	no	—
40	C₂₇	C₃×A₄	1	3	yes	complemented
41	C₂×C₃²	—	3	1	no	—
42	C₂×C₉	—	3	2	no	—
43	C₂×C₉	—	3	1	no	—
44	C₂²×C₃	—	3	1	no	—
45	C₂²×C₃	C₃²×C₉	1	1	yes	characteristic
46	A₄	—	3	2	no	—
47	A₄	C₂₇⋊C₃	1	3	yes	direct product factor
48	C₃²	—	4	1	no	—
49	C₃²	—	4	2	no	—
50	C₃²	—	12	3	no	—
51	C₃²	C₉×A₄	1	1	yes	characteristic
52	C₉	—	4	2	no	—
53	C₉	—	4	4	no	—
54	C₉	C₉×A₄	1	2	yes	—
55	C₉	C₃²×A₄	1	1	yes	characteristic
56	C₂×C₃	—	3	1	no	—
57	C₂×C₃	—	9	1	no	—
58	C₂²	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
59	C₃	—	3	1	no	—
60	C₃	—	4	3	no	—
61	C₃	—	12	2	no	—
62	C₃	C₃×C₉×A₄	1	1	yes	characteristic
63	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini	C₉	C₃²×A₄
commutator, socle	C₂²×C₃	C₃²×C₉
Fitting	C₂²×C₂₇⋊C₃	C₃
prime radical	C₃²×A₄	C₉
cosocle	C₂²×C₉	C₃³
hypercenter	C₂₇⋊C₃	A₄
hypocenter	C₂²	C₃×C₂₇⋊C₃
LCS	G ▷ C₂²×C₃ ▷ C₂²
UCS	C₁ ◁ C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂₇⋊C₃	C₃	semidirect
3. #66353	C₃	semidirect
4. C₂₇⋊A₄	C₃	semidirect
5. A₄×C₂₇	C₃	semidirect
15. C₂²×C₂₇	C₃²	semidirect
16. C₂²⋊C₂₇	C₃²	semidirect
20. C₂₇⋊C₃	A₄	direct (N × H)
40. C₂₇	C₃×A₄	semidirect
47. A₄	C₂₇⋊C₃	direct (N × H)
58. C₂²	C₃×C₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×A₄	3
C₂²×C₂₇⋊C₃	3
#66353	3
C₂₇⋊A₄	3
A₄×C₂₇	3
C₃×C₂₇⋊C₃	4

Subgroups — A4×C27⋊C3 #11757796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — A₄×C₂₇⋊C₃ #11757796