Subgroups — C₃×C₉×C₂²⋊C₉ #11757816

Order 972.

302 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	C₃²×C₂²⋊C₉	C₃	1	3	yes	maximal
3	C₉×C₂²⋊C₉	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₉²	—	4	1	no	maximal, Sylow
5	C₂×C₃²×C₉	—	3	1	no	—
6	C₂²×C₃³	C₃²	1	1	yes	characteristic
7	C₂²×C₃×C₉	C₉	1	9	yes	complemented
8	C₂²×C₃×C₉	C₃²	1	3	yes	—
9	C₃×C₂²⋊C₉	C₉	1	27	yes	direct product factor
10	C₃×C₂²⋊C₉	C₃²	1	9	yes	—
11	C₃²×C₉	—	4	3	no	—
12	C₃²×C₉	A₄	1	1	yes	characteristic
13	C₉²	—	4	9	no	—
14	C₂×C₃³	—	3	1	no	—
15	C₂×C₃×C₉	—	3	9	no	—
16	C₂×C₃×C₉	—	3	3	no	—
17	C₂²×C₃²	C₃×C₉	1	9	yes	—
18	C₂²×C₃²	C₃×C₉	1	3	yes	—
19	C₂²×C₃²	C₃³	1	1	yes	characteristic
20	C₂²×C₉	C₃×C₉	1	9	yes	complemented
21	C₂²⋊C₉	C₃×C₉	1	27	yes	direct product factor
22	C₃³	C₃×A₄	1	1	yes	characteristic
23	C₃×C₉	—	4	27	no	—
24	C₃×C₉	—	4	9	no	—
25	C₃×C₉	C₂²⋊C₉	1	9	yes	direct product factor
26	C₃×C₉	C₃×A₄	1	3	yes	—
27	C₂×C₃²	—	3	9	no	—
28	C₂×C₃²	—	3	3	no	—
29	C₂×C₃²	—	3	1	no	—
30	C₂×C₉	—	3	9	no	—
31	C₂²×C₃	C₉²	1	9	yes	complemented
32	C₂²×C₃	C₃²×C₉	1	3	yes	—
33	C₂²×C₃	C₃²×C₉	1	1	yes	characteristic
34	C₃²	C₉×A₄	1	9	yes	—
35	C₃²	C₃×C₂²⋊C₉	1	3	yes	—
36	C₃²	C₃²×A₄	1	1	yes	characteristic
37	C₉	—	4	27	no	—
38	C₉	C₃×C₂²⋊C₉	1	9	yes	direct product factor
39	C₂×C₃	—	3	9	no	—
40	C₂×C₃	—	3	3	no	—
41	C₂×C₃	—	3	1	no	—
42	C₂²	C₃×C₉²	1	1	yes	characteristic, complemented, Sylow
43	C₃	C₉×C₂²⋊C₉	1	9	yes	direct product factor
44	C₃	C₃×C₉×A₄	1	3	yes	—
45	C₃	C₃²×C₂²⋊C₉	1	1	yes	characteristic
46	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₉	A₄
commutator, hypocenter	C₂²	C₃×C₉²
Frattini	C₃²	C₃²×A₄
Fitting	C₂²×C₃²×C₉	C₃
socle, prime radical	C₂²×C₃³	C₃²
cosocle	C₂²×C₃²	C₃³
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₂²⋊C₉	C₃	direct (N × H)
7. C₂²×C₃×C₉	C₉	semidirect
9. C₃×C₂²⋊C₉	C₉	direct (N × H)
20. C₂²×C₉	C₃×C₉	semidirect
21. C₂²⋊C₉	C₃×C₉	direct (N × H)
25. C₃×C₉	C₂²⋊C₉	direct (N × H)
31. C₂²×C₃	C₉²	semidirect
38. C₉	C₃×C₂²⋊C₉	direct (N × H)
42. C₂²	C₃×C₉²	semidirect
43. C₃	C₉×C₂²⋊C₉	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
C₃²×C₂²⋊C₉	3
C₉×C₂²⋊C₉	3
C₃×C₉²	4

Subgroups — C3×C9×C22⋊C9 #11757816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×C₂²⋊C₉ #11757816