Subgroups — C₃×#66353 #11757815

Order 972.

170 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
2	#66353	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₂²⋊C₂₇	C₃	1	3	yes	maximal, complemented
4	C₃×C₂₇⋊C₃	—	4	1	no	maximal, Sylow
5	C₂×C₃²×C₉	—	3	1	no	—
6	C₂²×C₃³	C₉	1	1	yes	characteristic
7	C₂²×C₃×C₉	C₉	1	6	yes	—
8	C₂²×C₃×C₉	C₉	1	2	yes	—
9	C₂²×C₃×C₉	C₃²	1	1	yes	characteristic
10	C₂²×C₃×C₉	C₃²	1	3	yes	—
11	C₂²⋊C₂₇	C₃²	1	9	yes	complemented
12	C₃²×C₉	A₄	1	1	yes	characteristic
13	C₂₇⋊C₃	—	4	9	no	—
14	C₃×C₂₇	—	4	3	no	—
15	C₂×C₃³	—	3	1	no	—
16	C₂×C₃×C₉	—	3	2	no	—
17	C₂×C₃×C₉	—	3	6	no	—
18	C₂×C₃×C₉	—	3	3	no	—
19	C₂×C₃×C₉	—	3	1	no	—
20	C₂²×C₃²	—	3	3	no	—
21	C₂²×C₃²	C₃×C₉	1	3	yes	—
22	C₂²×C₃²	C₃×C₉	1	1	yes	characteristic
23	C₂²×C₉	C₃×C₉	1	2	yes	—
24	C₂²×C₉	C₃×C₉	1	6	yes	—
25	C₂²×C₉	C₃³	1	1	yes	characteristic
26	C₃³	C₂²⋊C₉	1	1	yes	characteristic
27	C₃×C₉	C₂²⋊C₉	1	2	yes	—
28	C₃×C₉	C₂²⋊C₉	1	6	yes	—
29	C₃×C₉	C₃×A₄	1	3	yes	—
30	C₃×C₉	C₃×A₄	1	1	yes	characteristic
31	C₂₇	—	4	9	no	—
32	C₂×C₃²	—	3	9	no	—
33	C₂×C₃²	—	3	3	no	—
34	C₂×C₃²	—	3	1	no	—
35	C₂×C₉	—	3	6	no	—
36	C₂×C₉	—	3	2	no	—
37	C₂×C₉	—	3	1	no	—
38	C₂²×C₃	—	3	3	no	—
39	C₂²×C₃	C₂₇⋊C₃	1	3	yes	complemented
40	C₂²×C₃	C₃²×C₉	1	1	yes	characteristic
41	C₃²	—	3	3	no	—
42	C₃²	C₃×C₂²⋊C₉	1	3	yes	—
43	C₃²	C₃×C₂²⋊C₉	1	1	yes	characteristic
44	C₉	C₃×C₂²⋊C₉	1	6	yes	—
45	C₉	C₃×C₂²⋊C₉	1	2	yes	—
46	C₉	C₃²×A₄	1	1	yes	characteristic
47	C₂×C₃	—	3	9	no	—
48	C₂×C₃	—	3	3	no	—
49	C₂×C₃	—	3	1	no	—
50	C₂²	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
51	C₃	—	3	3	no	—
52	C₃	#66353	1	3	yes	direct product factor
53	C₃	C₃²×C₂²⋊C₉	1	1	yes	characteristic
54	C₂	—	3	1	no	—

	subgroup	G/H
center	C₃×C₉	C₃×A₄
commutator	C₂²×C₃	C₃²×C₉
Frattini	C₉	C₃²×A₄
Fitting	C₂²×C₃²×C₉	C₃
socle	C₂²×C₃²	C₃×C₉
prime radical	C₂²×C₃³	C₉
cosocle	C₂²×C₉	C₃³
hypercenter	C₃²×C₉	A₄
hypocenter	C₂²	C₃×C₂₇⋊C₃
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
2. #66353	C₃	direct (N × H)
3. C₃×C₂²⋊C₂₇	C₃	semidirect
11. C₂²⋊C₂₇	C₃²	semidirect
39. C₂²×C₃	C₂₇⋊C₃	semidirect
50. C₂²	C₃×C₂₇⋊C₃	semidirect
52. C₃	#66353	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
#66353	3
C₃×C₂²⋊C₂₇	3
C₃×C₂₇⋊C₃	4

Subgroups — C3×#66353 #11757815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#66353 #11757815