Subgroups — C₂²×C₃⋊Dic₉ #88749

Order 432.

270 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊Dic₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃⋊Dic₃	—	3	1	no	maximal
4	C₂²×Dic₉	—	3	3	no	maximal
5	C₂²×C₃×C₉	C₄	1	4	yes	complemented
6	C₂²×C₃×C₉	C₂²	1	3	yes	—
7	C₃⋊Dic₉	C₂²	1	4	yes	direct product factor
8	C₂³×C₃²	D₃	1	1	yes	characteristic
9	C₂×C₃⋊Dic₃	—	3	6	no	—
10	C₂³×C₉	D₃	1	3	yes	—
11	C₂×Dic₉	—	3	18	no	—
12	C₂×C₃×C₉	C₂×C₄	1	6	yes	complemented
13	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
14	C₂²×Dic₃	—	9	3	no	—
15	C₂²×Dic₃	—	9	1	no	—
16	C₂²×C₃²	Dic₃	1	4	yes	—
17	C₂²×C₃²	C₂×D₃	1	3	yes	—
18	C₃⋊Dic₃	—	3	4	no	—
19	C₂²×C₉	Dic₃	1	12	yes	complemented
20	C₂²×C₉	C₂×D₃	1	9	yes	—
21	Dic₉	—	3	12	no	—
22	C₃×C₉	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
23	C₂³×C₃	D₉	1	3	yes	—
24	C₂³×C₃	C₃⋊D₃	1	1	yes	characteristic
25	C₂×Dic₃	—	9	18	no	—
26	C₂×Dic₃	—	9	6	no	—
27	C₂×C₃²	C₂×Dic₃	1	6	yes	—
28	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
29	C₂×C₉	C₂×Dic₃	1	18	yes	complemented
30	C₂×C₉	C₂²×D₃	1	3	yes	—
31	C₂²×C₄	—	27	1	no	Sylow
32	C₂²×C₃	Dic₉	1	12	yes	complemented
33	C₂²×C₃	C₂×D₉	1	9	yes	—
34	C₂²×C₃	C₃⋊Dic₃	1	4	yes	—
35	C₂²×C₃	C₂×C₃⋊D₃	1	3	yes	—
36	Dic₃	—	9	12	no	—
37	Dic₃	—	9	4	no	—
38	C₃²	C₂²×Dic₃	1	1	yes	characteristic
39	C₉	C₂²×Dic₃	1	3	yes	complemented
40	C₂³	C₃⋊D₉	1	1	yes	characteristic
41	C₂×C₄	—	27	6	no	—
42	C₂×C₃	C₂×Dic₉	1	18	yes	complemented
43	C₂×C₃	C₂²×D₉	1	3	yes	—
44	C₂×C₃	C₂×C₃⋊Dic₃	1	6	yes	—
45	C₂×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
46	C₂²	C₃⋊Dic₉	1	4	yes	direct product factor
47	C₂²	C₂×C₃⋊D₉	1	3	yes	—
48	C₄	—	27	4	no	—
49	C₃	C₂²×Dic₉	1	3	yes	complemented
50	C₃	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
51	C₂	C₂×C₃⋊Dic₉	1	6	yes	direct product factor
52	C₂	C₂²×C₃⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	C₃⋊D₉
commutator, hypocenter	C₃×C₉	C₂²×C₄
Frattini	C₂×C₃	C₂²×C₃⋊D₃
Fitting	C₂³×C₃×C₉	C₂
socle, prime radical	C₂³×C₃²	D₃
cosocle	C₂×C₃×C₉	C₂³
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊Dic₉	C₂	direct (N × H)
5. C₂²×C₃×C₉	C₄	semidirect
7. C₃⋊Dic₉	C₂²	direct (N × H)
12. C₂×C₃×C₉	C₂×C₄	semidirect
19. C₂²×C₉	Dic₃	semidirect
22. C₃×C₉	C₂²×C₄	semidirect
29. C₂×C₉	C₂×Dic₃	semidirect
32. C₂²×C₃	Dic₉	semidirect
39. C₉	C₂²×Dic₃	semidirect
42. C₂×C₃	C₂×Dic₉	semidirect
46. C₂²	C₃⋊Dic₉	direct (N × H)
49. C₃	C₂²×Dic₉	semidirect
51. C₂	C₂×C₃⋊Dic₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₉	2
C₂×C₃⋊Dic₉	2
C₂²×C₃⋊Dic₃	3
C₂²×Dic₉	3

Subgroups — C22×C3⋊Dic9 #88749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃⋊Dic₉ #88749