Subgroups — Dic₉⋊A₄ #88618

Order 432.

61 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉⋊A₄	C₂	1	1	yes	maximal, characteristic
2	Dic₃×A₄	—	3	1	no	maximal
3	C₂²×Dic₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₉⋊A₄	C₄	1	1	yes	characteristic, complemented
5	3₋¹⁺²⋊C₄	—	4	1	no	maximal
6	C₂×C₃×A₄	D₃	1	1	yes	characteristic
7	C₂³×C₉	C₂×C₃	1	1	yes	characteristic
8	C₂×C₂²⋊C₉	—	2	1	no	—
9	C₂×Dic₉	—	3	1	no	—
10	C₂×Dic₉	—	3	1	no	—
11	C₂×3₋¹⁺²	—	4	1	no	—
12	C₂²×Dic₃	—	3	1	no	—
13	C₄×A₄	—	9	1	no	—
14	C₃×A₄	Dic₃	1	1	yes	characteristic
15	C₃×Dic₃	—	12	1	no	—
16	C₂²×C₉	—	3	1	no	—
17	C₂²×C₉	—	3	1	no	—
18	C₂²×C₉	C₃×C₄	1	1	yes	characteristic, complemented
19	C₂²⋊C₉	—	2	1	no	—
20	Dic₉	—	3	1	no	—
21	Dic₉	A₄	1	1	yes	characteristic, complemented
22	3₋¹⁺²	—	4	1	no	Sylow
23	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
24	C₂×A₄	—	3	1	no	—
25	C₂×Dic₃	—	9	1	no	—
26	C₂×Dic₃	—	9	1	no	—
27	C₂×C₃²	—	4	1	no	—
28	C₂×C₉	—	3	1	no	—
29	C₂×C₉	—	3	1	no	—
30	C₂×C₉	—	8	1	no	—
31	C₂×C₉	C₂×A₄	1	1	yes	characteristic
32	C₂²×C₄	—	9	1	no	Sylow
33	C₂²×C₃	—	3	1	no	—
34	C₂²×C₃	—	3	1	no	—
35	C₂²×C₃	C₃×Dic₃	1	1	yes	characteristic
36	A₄	—	3	1	no	—
37	C₃×C₄	—	36	1	no	—
38	Dic₃	—	3	1	no	—
39	Dic₃	—	9	1	no	—
40	C₃²	—	4	1	no	—
41	C₉	—	8	1	no	—
42	C₉	C₄×A₄	1	1	yes	characteristic, complemented
43	C₂³	AGL(1,ℤ/9)	1	1	yes	characteristic
44	C₂×C₄	—	27	1	no	—
45	C₂×C₄	—	27	1	no	—
46	C₂×C₃	—	3	1	no	—
47	C₂×C₃	—	3	1	no	—
48	C₂×C₃	—	12	1	no	—
49	C₂×C₃	D₃×A₄	1	1	yes	characteristic
50	C₂²	—	3	1	no	—
51	C₂²	—	3	1	no	—
52	C₂²	3₋¹⁺²⋊C₄	1	1	yes	characteristic, complemented
53	C₄	—	9	1	no	—
54	C₄	—	27	1	no	—
55	C₃	—	12	1	no	—
56	C₃	Dic₃×A₄	1	1	yes	characteristic
57	C₂	—	3	1	no	—
58	C₂	—	3	1	no	—
59	C₂	D₉⋊A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₉⋊A₄
commutator, hypocenter	C₂²×C₉	C₃×C₄
Frattini	C₂×C₃	D₃×A₄
Fitting, cosocle	C₂³×C₉	C₂×C₃
socle	C₂³×C₃	C₃×D₃
prime radical	C₂×C₃×A₄	D₃
LCS	G ▷ C₂²×C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₂²×Dic₉	C₃	semidirect
4. C₉⋊A₄	C₄	semidirect
18. C₂²×C₉	C₃×C₄	semidirect
21. Dic₉	A₄	semidirect
42. C₉	C₄×A₄	semidirect
52. C₂²	3₋¹⁺²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉⋊A₄	2
Dic₃×A₄	3
C₂²×Dic₉	3
3₋¹⁺²⋊C₄	4

Subgroups — Dic9⋊A4 #88618

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₉⋊A₄ #88618