Subgroups — C₄⋊(C₃⋊Dic₉) #88535

Order 432.

130 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	—	2	2	no	—
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	1	yes	characteristic
13	C₂×C₃×C₉	D₄	1	1	yes	characteristic
14	C₂×C₃×C₉	Q₈	1	1	yes	characteristic
15	C₄⋊Dic₃	—	9	3	no	—
16	C₄⋊Dic₃	—	9	1	no	—
17	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
18	C₃²×C₄	Dic₃	1	2	yes	—
19	C₃⋊Dic₃	—	6	2	no	—
20	C₂²×C₉	C₂×D₃	1	3	yes	—
21	C₄×C₉	Dic₃	1	6	yes	complemented
22	Dic₉	—	6	6	no	—
23	C₃×C₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃×C₄	D₉	1	3	yes	—
25	C₂×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
26	C₂×Dic₃	—	9	6	no	—
27	C₂×Dic₃	—	9	2	no	—
28	C₂×C₃²	Dic₆	1	1	yes	characteristic
29	C₂×C₃²	D₁₂	1	1	yes	characteristic
30	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
31	C₂×C₉	Dic₆	1	3	yes	—
32	C₂×C₉	D₁₂	1	3	yes	—
33	C₂×C₉	C₂×Dic₃	1	3	yes	—
34	C₄⋊C₄	—	27	1	no	Sylow
35	C₂²×C₃	C₂×D₉	1	3	yes	—
36	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
37	C₃×C₄	Dic₉	1	6	yes	complemented
38	C₃×C₄	C₃⋊Dic₃	1	2	yes	—
39	Dic₃	—	18	6	no	—
40	Dic₃	—	18	2	no	—
41	C₃²	C₄⋊Dic₃	1	1	yes	characteristic
42	C₉	C₄⋊Dic₃	1	3	yes	complemented
43	C₂×C₄	—	27	2	no	—
44	C₂×C₄	C₃⋊D₉	1	1	yes	characteristic
45	C₂×C₃	Dic₁₈	1	3	yes	—
46	C₂×C₃	D₃₆	1	3	yes	—
47	C₂×C₃	C₂×Dic₉	1	3	yes	—
48	C₂×C₃	#634	1	1	yes	characteristic
49	C₂×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
50	C₂×C₃	C₂×C₃⋊Dic₃	1	1	yes	characteristic
51	C₂²	C₂×C₃⋊D₉	1	1	yes	characteristic
52	C₄	—	54	2	no	—
53	C₄	C₃⋊Dic₉	1	2	yes	complemented
54	C₃	C₄⋊Dic₉	1	3	yes	complemented
55	C₃	C₄⋊(C₃⋊Dic₃)	1	1	yes	characteristic
56	C₂	#6226	1	1	yes	characteristic
57	C₂	C₄⋊(C₃⋊D₉)	1	1	yes	characteristic
58	C₂	C₂×C₃⋊Dic₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₃×C₄×C₉	C₄	semidirect
21. C₄×C₉	Dic₃	semidirect
23. C₃×C₉	C₄⋊C₄	semidirect
37. C₃×C₄	Dic₉	semidirect
42. C₉	C₄⋊Dic₃	semidirect
53. C₄	C₃⋊Dic₉	semidirect
54. 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) #88535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₃⋊Dic₉) #88535