Subgroups — C₂×C₉×C₃⋊(C₃⋊D₃) #11758131

Order 972.

732 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₃⋊(C₃⋊D₃)	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉×C₃⋊D₃	—	3	13	no	maximal
5	C₃³×C₉	C₂²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₃⁴	C₂×C₃	1	1	yes	characteristic
7	C₃×C₃⋊(C₃⋊D₃)	C₂×C₃	1	2	yes	—
8	C₂×C₃²×C₉	—	2	13	no	—
9	C₂×C₃²×C₉	D₃	1	13	yes	complemented
10	C₉×C₃⋊D₃	—	3	26	no	—
11	C₂×C₃⋊(C₃⋊D₃)	C₉	1	1	yes	characteristic, direct product factor
12	C₂×C₃×C₃⋊D₃	—	3	13	no	—
13	C₂×D₃×C₉	—	9	13	no	—
14	C₃⁴	C₂²×C₃	1	1	yes	characteristic
15	C₃²×C₉	—	2	13	no	—
16	C₃²×C₉	C₂×D₃	1	13	yes	complemented
17	C₂×C₃³	—	2	13	no	—
18	C₂×C₃³	C₂×C₉	1	1	yes	characteristic, complemented
19	C₂×C₃³	C₃×D₃	1	13	yes	—
20	C₃⋊(C₃⋊D₃)	C₂×C₉	1	2	yes	direct product factor
21	C₃×C₃⋊D₃	—	3	26	no	—
22	C₂×C₃×C₉	—	2	52	no	—
23	C₂×C₃×C₉	C₃⋊D₃	1	13	yes	complemented
24	D₃×C₉	—	9	26	no	—
25	C₂×C₃⋊D₃	—	3	13	no	—
26	C₂×C₃×D₃	—	9	13	no	—
27	C₂²×C₉	—	27	1	no	—
28	C₃³	—	2	13	no	—
29	C₃³	C₂²×C₉	1	1	yes	characteristic, complemented
30	C₃³	C₂×C₃×D₃	1	13	yes	—
31	C₃×C₉	—	2	52	no	—
32	C₃×C₉	C₂×C₃⋊D₃	1	13	yes	complemented
33	C₂×C₃²	—	2	52	no	—
34	C₂×C₃²	D₃×C₉	1	13	yes	complemented
35	C₂×C₃²	C₃×C₃⋊D₃	1	13	yes	—
36	C₃⋊D₃	—	3	26	no	—
37	C₃×D₃	—	9	26	no	—
38	C₂×C₉	—	2	13	no	—
39	C₂×C₉	—	27	2	no	—
40	C₂×C₉	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
41	C₂²×C₃	—	27	1	no	—
42	C₂×D₃	—	9	13	no	—
43	C₃²	—	2	52	no	—
44	C₃²	C₂×D₃×C₉	1	13	yes	complemented
45	C₃²	C₂×C₃×C₃⋊D₃	1	13	yes	—
46	C₉	—	2	13	no	—
47	C₉	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
48	C₂×C₃	—	2	13	no	—
49	C₂×C₃	—	27	2	no	—
50	C₂×C₃	C₉×C₃⋊D₃	1	13	yes	complemented
51	C₂×C₃	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
52	D₃	—	9	26	no	—
53	C₂²	—	27	1	no	Sylow
54	C₃	—	2	13	no	—
55	C₃	C₂×C₉×C₃⋊D₃	1	13	yes	complemented
56	C₃	C₂×C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
57	C₂	—	27	2	no	—
58	C₂	C₉×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉	C₃⋊(C₃⋊D₃)
commutator, hypocenter	C₃³	C₂²×C₉
Frattini	C₃	C₂×C₃×C₃⋊(C₃⋊D₃)
Fitting	C₂×C₃³×C₉	C₂
socle	C₂×C₃⁴	C₂×C₃
prime radical	C₂×C₃×C₃⋊(C₃⋊D₃)	C₃
cosocle	C₃⁴	C₂²×C₃
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×C₉	C₂	semidirect
2. C₉×C₃⋊(C₃⋊D₃)	C₂	direct (N × H)
5. C₃³×C₉	C₂²	semidirect
9. C₂×C₃²×C₉	D₃	semidirect
11. C₂×C₃⋊(C₃⋊D₃)	C₉	direct (N × H)
16. C₃²×C₉	C₂×D₃	semidirect
18. C₂×C₃³	C₂×C₉	semidirect
20. C₃⋊(C₃⋊D₃)	C₂×C₉	direct (N × H)
23. C₂×C₃×C₉	C₃⋊D₃	semidirect
29. C₃³	C₂²×C₉	semidirect
32. C₃×C₉	C₂×C₃⋊D₃	semidirect
34. C₂×C₃²	D₃×C₉	semidirect
40. C₂×C₉	C₃⋊(C₃⋊D₃)	direct (N × H)
44. C₃²	C₂×D₃×C₉	semidirect
47. C₉	C₂×C₃⋊(C₃⋊D₃)	direct (N × H)
50. C₂×C₃	C₉×C₃⋊D₃	semidirect
55. C₃	C₂×C₉×C₃⋊D₃	semidirect
58. C₂	C₉×C₃⋊(C₃⋊D₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×C₉	2
C₉×C₃⋊(C₃⋊D₃)	2
C₂×C₃×C₃⋊(C₃⋊D₃)	3
C₂×C₉×C₃⋊D₃	3

Subgroups — C2×C9×C3⋊(C3⋊D3) #11758131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₃⋊(C₃⋊D₃) #11758131