Subgroups — C₄×C₃⋊Dic₉ #88533

Order 432.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊Dic₉	C₂	1	2	yes	maximal
3	C₄×C₃⋊Dic₃	—	3	1	no	maximal
4	C₄×Dic₉	—	3	3	no	maximal
5	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₉	C₄	1	2	yes	complemented
7	C₃⋊Dic₉	C₄	1	4	yes	direct product factor
8	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
9	C₂×C₃⋊Dic₃	—	3	2	no	—
10	C₂×C₄×C₉	D₃	1	3	yes	—
11	C₂×Dic₉	—	3	6	no	—
12	C₂×C₃×C₉	C₂×C₄	1	2	yes	—
13	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
14	C₄×Dic₃	—	9	3	no	—
15	C₄×Dic₃	—	9	1	no	—
16	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
17	C₃²×C₄	Dic₃	1	2	yes	—
18	C₃⋊Dic₃	—	3	4	no	—
19	C₂²×C₉	C₂×D₃	1	3	yes	—
20	C₄×C₉	Dic₃	1	6	yes	complemented
21	Dic₉	—	3	12	no	—
22	C₃×C₉	C₄²	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃×C₄	D₉	1	3	yes	—
24	C₂×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
25	C₂×Dic₃	—	9	6	no	—
26	C₂×Dic₃	—	9	2	no	—
27	C₂×C₃²	C₄×D₃	1	2	yes	—
28	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
29	C₂×C₉	C₄×D₃	1	6	yes	—
30	C₂×C₉	C₂×Dic₃	1	3	yes	—
31	C₄²	—	27	1	no	Sylow
32	C₂²×C₃	C₂×D₉	1	3	yes	—
33	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
34	C₃×C₄	Dic₉	1	6	yes	complemented
35	C₃×C₄	C₃⋊Dic₃	1	2	yes	—
36	Dic₃	—	9	12	no	—
37	Dic₃	—	9	4	no	—
38	C₃²	C₄×Dic₃	1	1	yes	characteristic
39	C₉	C₄×Dic₃	1	3	yes	complemented
40	C₂×C₄	—	27	2	no	—
41	C₂×C₄	C₃⋊D₉	1	1	yes	characteristic
42	C₂×C₃	C₄×D₉	1	6	yes	—
43	C₂×C₃	C₂×Dic₉	1	3	yes	—
44	C₂×C₃	C₄×C₃⋊D₃	1	2	yes	—
45	C₂×C₃	C₂×C₃⋊Dic₃	1	1	yes	characteristic
46	C₂²	C₂×C₃⋊D₉	1	1	yes	characteristic
47	C₄	—	27	4	no	—
48	C₄	C₃⋊Dic₉	1	2	yes	direct product factor
49	C₃	C₄×Dic₉	1	3	yes	complemented
50	C₃	C₄×C₃⋊Dic₃	1	1	yes	characteristic
51	C₂	C₄×C₃⋊D₉	1	2	yes	—
52	C₂	C₂×C₃⋊Dic₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	C₃⋊D₉
commutator, hypocenter	C₃×C₉	C₄²
Frattini	C₂²×C₃	C₂×C₃⋊D₃
Fitting	C₂×C₃×C₄×C₉	C₂
socle, prime radical	C₂²×C₃²	C₂×D₃
cosocle	C₂²×C₃×C₉	C₂²
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
6. C₃×C₄×C₉	C₄	semidirect
7. C₃⋊Dic₉	C₄	direct (N × H)
20. C₄×C₉	Dic₃	semidirect
22. C₃×C₉	C₄²	semidirect
34. C₃×C₄	Dic₉	semidirect
39. C₉	C₄×Dic₃	semidirect
48. C₄	C₃⋊Dic₉	direct (N × H)
49. C₃	C₄×Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₉	2
C₂×C₃⋊Dic₉	2
C₄×C₃⋊Dic₃	3
C₄×Dic₉	3

Subgroups — C4×C3⋊Dic9 #88533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃⋊Dic₉ #88533