Subgroups — C₃²×SL(2,ℤ/4) #88968

Order 432.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×A₄	C₂	1	1	yes	maximal, characteristic
2	C₃×SL(2,ℤ/4)	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₂²⋊C₄	—	3	1	no	maximal
4	C₃²×A₄	C₄	1	1	yes	characteristic, complemented
5	C₃²×Dic₃	—	4	1	no	maximal
6	C₂³×C₃²	D₃	1	1	yes	characteristic
7	C₂×C₃×A₄	—	2	4	no	—
8	C₂×C₃×A₄	C₂×C₃	1	4	yes	—
9	C₂×C₃²×C₄	—	3	1	no	—
10	C₂×C₃²×C₄	—	3	1	no	—
11	C₂×C₃³	—	4	1	no	—
12	SL(2,ℤ/4)	C₃²	1	1	yes	characteristic, direct product factor
13	C₃×C₂²⋊C₄	—	3	4	no	—
14	C₂²×C₃²	—	3	1	no	—
15	C₂²×C₃²	—	3	1	no	—
16	C₂²×C₃²	Dic₃	1	1	yes	characteristic, complemented
17	C₃×A₄	—	2	4	no	—
18	C₃×A₄	C₃×C₄	1	4	yes	complemented
19	C₃²×C₄	—	6	1	no	—
20	C₃²×C₄	—	6	1	no	—
21	C₃×Dic₃	—	4	4	no	—
22	C₃³	—	4	1	no	Sylow
23	C₂³×C₃	C₃×D₃	1	4	yes	—
24	C₂×A₄	—	2	4	no	—
25	C₂×A₄	C₂×C₃²	1	1	yes	characteristic
26	C₂×C₃×C₄	—	3	4	no	—
27	C₂×C₃×C₄	—	3	4	no	—
28	C₂×C₃²	—	3	1	no	—
29	C₂×C₃²	—	3	1	no	—
30	C₂×C₃²	—	4	4	no	—
31	C₂×C₃²	—	8	4	no	—
32	C₂×C₃²	S₄	1	1	yes	characteristic
33	C₂²⋊C₄	—	3	1	no	Sylow
34	C₂²×C₃	—	3	4	no	—
35	C₂²×C₃	—	3	4	no	—
36	C₂²×C₃	C₃×Dic₃	1	4	yes	complemented
37	A₄	—	2	4	no	—
38	A₄	C₃²×C₄	1	1	yes	characteristic, complemented
39	C₃×C₄	—	6	4	no	—
40	C₃×C₄	—	6	4	no	—
41	Dic₃	—	4	1	no	—
42	C₃²	—	4	4	no	—
43	C₃²	—	8	4	no	—
44	C₃²	SL(2,ℤ/4)	1	1	yes	characteristic, direct product factor
45	C₂³	C₃²×D₃	1	1	yes	characteristic
46	C₂×C₄	—	3	1	no	—
47	C₂×C₄	—	3	1	no	—
48	C₂×C₃	—	3	4	no	—
49	C₂×C₃	—	3	4	no	—
50	C₂×C₃	—	4	1	no	—
51	C₂×C₃	—	8	4	no	—
52	C₂×C₃	C₃×S₄	1	4	yes	—
53	C₂²	—	3	1	no	—
54	C₂²	—	3	1	no	—
55	C₂²	C₃²×Dic₃	1	1	yes	characteristic, complemented
56	C₄	—	6	1	no	—
57	C₄	—	6	1	no	—
58	C₃	—	4	1	no	—
59	C₃	—	8	4	no	—
60	C₃	C₃×SL(2,ℤ/4)	1	4	yes	direct product factor
61	C₂	—	3	1	no	—
62	C₂	—	3	1	no	—
63	C₂	C₃²×S₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃²	S₄
commutator, hypocenter	A₄	C₃²×C₄
Frattini	C₂	C₃²×S₄
Fitting, socle	C₂³×C₃²	D₃
prime radical	C₂×C₃²×A₄	C₂
cosocle	C₂×A₄	C₂×C₃²
LCS	G ▷ A₄
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
2. C₃×SL(2,ℤ/4)	C₃	direct (N × H)
4. C₃²×A₄	C₄	semidirect
12. SL(2,ℤ/4)	C₃²	direct (N × H)
16. C₂²×C₃²	Dic₃	semidirect
18. C₃×A₄	C₃×C₄	semidirect
36. C₂²×C₃	C₃×Dic₃	semidirect
38. A₄	C₃²×C₄	semidirect
44. C₃²	SL(2,ℤ/4)	direct (N × H)
55. C₂²	C₃²×Dic₃	semidirect
60. C₃	C₃×SL(2,ℤ/4)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×A₄	2
C₃×SL(2,ℤ/4)	3
C₃²×C₂²⋊C₄	3
C₃²×Dic₃	4

Subgroups — C32×SL(2,ℤ/4) #88968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×SL(2,ℤ/4) #88968