Subgroups — C₉⋊SL(2,ℤ/4) #88607

Order 432.

81 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	C₃⋊SL(2,ℤ/4)	—	3	1	no	maximal
3	(C₂²⋊C₉)⋊C₄	—	3	2	no	maximal
4	#3676	—	3	1	no	maximal
5	C₉×A₄	C₄	1	1	yes	characteristic, complemented
6	C₃⋊Dic₉	—	4	1	no	maximal
7	C₂×C₃×A₄	D₃	1	1	yes	characteristic
8	C₂³×C₉	D₃	1	1	yes	characteristic
9	C₂×C₂²⋊C₉	D₃	1	2	yes	—
10	C₂×Dic₉	—	3	1	no	—
11	C₂×Dic₉	—	3	1	no	—
12	C₂×C₃×C₉	—	4	1	no	—
13	SL(2,ℤ/4)	—	9	3	no	—
14	#217	—	9	1	no	—
15	C₃×A₄	Dic₃	1	1	yes	characteristic
16	C₃⋊Dic₃	—	12	1	no	—
17	C₂²×C₉	—	3	1	no	—
18	C₂²×C₉	—	3	1	no	—
19	C₂²×C₉	Dic₃	1	1	yes	characteristic, complemented
20	C₂²⋊C₉	Dic₃	1	2	yes	complemented
21	Dic₉	—	6	1	no	—
22	Dic₉	—	6	1	no	—
23	Dic₉	—	12	2	no	—
24	C₃×C₉	—	4	1	no	Sylow
25	C₂³×C₃	C₃⋊D₃	1	1	yes	characteristic
26	C₂×A₄	D₉	1	3	yes	—
27	C₂×Dic₃	—	9	1	no	—
28	C₂×Dic₃	—	9	1	no	—
29	C₂×C₃²	—	4	1	no	—
30	C₂×C₉	—	3	1	no	—
31	C₂×C₉	—	3	1	no	—
32	C₂×C₉	—	4	2	no	—
33	C₂×C₉	S₄	1	1	yes	characteristic
34	C₂²⋊C₄	—	27	1	no	Sylow
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	—	3	1	no	—
37	C₂²×C₃	C₃⋊Dic₃	1	1	yes	characteristic
38	A₄	Dic₉	1	3	yes	complemented
39	Dic₃	—	18	1	no	—
40	Dic₃	—	18	1	no	—
41	Dic₃	—	36	3	no	—
42	C₃²	—	4	1	no	—
43	C₉	—	4	2	no	—
44	C₉	SL(2,ℤ/4)	1	1	yes	characteristic, complemented
45	C₂³	C₃⋊D₉	1	1	yes	characteristic
46	C₂×C₄	—	27	1	no	—
47	C₂×C₄	—	27	1	no	—
48	C₂×C₃	—	3	1	no	—
49	C₂×C₃	—	3	1	no	—
50	C₂×C₃	—	4	3	no	—
51	C₂×C₃	C₃⋊S₄	1	1	yes	characteristic
52	C₂²	—	3	1	no	—
53	C₂²	—	3	1	no	—
54	C₂²	C₃⋊Dic₉	1	1	yes	characteristic, complemented
55	C₄	—	54	1	no	—
56	C₄	—	54	1	no	—
57	C₃	—	4	3	no	—
58	C₃	C₃⋊SL(2,ℤ/4)	1	1	yes	characteristic
59	C₂	—	3	1	no	—
60	C₂	—	3	1	no	—
61	C₂	C₉⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	C₉⋊S₄
commutator, hypocenter	C₉×A₄	C₄
Frattini	C₂×C₃	C₃⋊S₄
Fitting	C₂³×C₉	D₃
socle	C₂³×C₃	C₃⋊D₃
prime radical	C₂×C₃×A₄	D₃
cosocle	C₂×C₉×A₄	C₂
LCS	G ▷ C₉×A₄
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
5. C₉×A₄	C₄	semidirect
19. C₂²×C₉	Dic₃	semidirect
20. C₂²⋊C₉	Dic₃	semidirect
38. A₄	Dic₉	semidirect
44. C₉	SL(2,ℤ/4)	semidirect
54. C₂²	C₃⋊Dic₉	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
C₃⋊SL(2,ℤ/4)	3
(C₂²⋊C₉)⋊C₄	3
#3676	3
C₃⋊Dic₉	4

Subgroups — C9⋊SL(2,ℤ/4) #88607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊SL(2,ℤ/4) #88607