Subgroups — C₃×A₄×C₂₇ #11757793

Order 972.

158 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×C₃×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂²⋊C₂₇	C₃	1	2	yes	maximal, complemented
4	A₄×C₂₇	C₃	1	9	yes	maximal, direct product factor
5	C₃²×C₂₇	—	4	1	no	maximal, Sylow
6	C₂×C₃×C₂₇	—	3	1	no	—
7	C₃²×A₄	C₉	1	1	yes	characteristic
8	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
9	C₃×C₂²⋊C₉	C₉	1	2	yes	—
10	C₉×A₄	C₉	1	6	yes	—
11	C₉×A₄	C₃²	1	3	yes	—
12	C₂²×C₂₇	C₃²	1	3	yes	complemented
13	C₂²⋊C₂₇	C₃²	1	6	yes	complemented
14	C₃²×C₉	—	4	1	no	—
15	C₃×C₂₇	—	4	2	no	—
16	C₃×C₂₇	—	4	9	no	—
17	C₃×C₂₇	A₄	1	1	yes	characteristic, direct product factor
18	C₂×C₃×C₉	—	3	1	no	—
19	C₂×C₂₇	—	3	3	no	—
20	C₂²×C₃²	C₃×C₉	1	1	yes	characteristic
21	C₃×A₄	C₂₇	1	9	yes	direct product factor
22	C₃×A₄	C₃×C₉	1	3	yes	—
23	C₂²×C₉	C₃×C₉	1	2	yes	—
24	C₂²×C₉	C₃³	1	1	yes	characteristic
25	C₂²⋊C₉	C₃×C₉	1	6	yes	—
26	C₃³	—	4	1	no	—
27	C₃×C₉	—	4	2	no	—
28	C₃×C₉	—	4	6	no	—
29	C₃×C₉	—	4	3	no	—
30	C₃×C₉	C₃×A₄	1	1	yes	characteristic
31	C₂₇	—	4	6	no	—
32	C₂₇	C₃×A₄	1	3	yes	direct product factor
33	C₂×C₃²	—	3	1	no	—
34	C₂×C₉	—	3	2	no	—
35	C₂×C₉	—	3	1	no	—
36	C₂²×C₃	C₃×C₂₇	1	3	yes	complemented
37	C₂²×C₃	C₃²×C₉	1	1	yes	characteristic
38	A₄	C₃×C₂₇	1	9	yes	direct product factor
39	C₃²	—	4	9	no	—
40	C₃²	—	4	3	no	—
41	C₃²	C₉×A₄	1	1	yes	characteristic
42	C₉	—	4	6	no	—
43	C₉	C₉×A₄	1	2	yes	—
44	C₉	C₃²×A₄	1	1	yes	characteristic
45	C₂×C₃	—	3	3	no	—
46	C₂×C₃	—	3	1	no	—
47	C₂²	C₃²×C₂₇	1	1	yes	characteristic, complemented, Sylow
48	C₃	—	4	9	no	—
49	C₃	A₄×C₂₇	1	3	yes	direct product factor
50	C₃	C₃×C₉×A₄	1	1	yes	characteristic
51	C₂	—	3	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₂₇	C₃	semidirect
3. C₃×C₂²⋊C₂₇	C₃	semidirect
4. A₄×C₂₇	C₃	direct (N × H)
12. C₂²×C₂₇	C₃²	semidirect
13. C₂²⋊C₂₇	C₃²	semidirect
17. C₃×C₂₇	A₄	direct (N × H)
21. C₃×A₄	C₂₇	direct (N × H)
32. C₂₇	C₃×A₄	direct (N × H)
36. C₂²×C₃	C₃×C₂₇	semidirect
38. A₄	C₃×C₂₇	direct (N × H)
47. C₂²	C₃²×C₂₇	semidirect
49. C₃	A₄×C₂₇	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×C₉×A₄	3
C₂²×C₃×C₂₇	3
C₃×C₂²⋊C₂₇	3
A₄×C₂₇	3
C₃²×C₂₇	4

Subgroups — C3×A4×C27 #11757793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×A₄×C₂₇ #11757793