Subgroups — C₃⋊(C₃⋊SL(2,ℤ/4)) #88974

Order 432.

210 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)	—	3	12	no	maximal
3	#3757	—	3	1	no	maximal
4	C₃²×A₄	C₄	1	1	yes	characteristic, complemented
5	C₃⋊(C₃⋊Dic₃)	—	4	1	no	maximal
6	C₂³×C₃²	D₃	1	1	yes	characteristic
7	C₂×C₃×A₄	D₃	1	12	yes	—
8	C₂×C₃⋊Dic₃	—	3	1	no	—
9	C₂×C₃⋊Dic₃	—	3	1	no	—
10	C₂×C₃³	—	4	1	no	—
11	SL(2,ℤ/4)	—	9	9	no	—
12	#217	—	9	4	no	—
13	C₂²×C₃²	—	3	1	no	—
14	C₂²×C₃²	—	3	1	no	—
15	C₂²×C₃²	Dic₃	1	1	yes	characteristic, complemented
16	C₃×A₄	Dic₃	1	12	yes	complemented
17	C₃⋊Dic₃	—	6	1	no	—
18	C₃⋊Dic₃	—	6	1	no	—
19	C₃⋊Dic₃	—	12	12	no	—
20	C₃³	—	4	1	no	Sylow
21	C₂³×C₃	C₃⋊D₃	1	4	yes	—
22	C₂×A₄	C₃⋊D₃	1	9	yes	—
23	C₂×Dic₃	—	9	4	no	—
24	C₂×Dic₃	—	9	4	no	—
25	C₂×C₃²	—	3	1	no	—
26	C₂×C₃²	—	3	1	no	—
27	C₂×C₃²	—	4	12	no	—
28	C₂×C₃²	S₄	1	1	yes	characteristic
29	C₂²⋊C₄	—	27	1	no	Sylow
30	C₂²×C₃	—	3	4	no	—
31	C₂²×C₃	—	3	4	no	—
32	C₂²×C₃	C₃⋊Dic₃	1	4	yes	complemented
33	A₄	C₃⋊Dic₃	1	9	yes	complemented
34	Dic₃	—	18	4	no	—
35	Dic₃	—	18	4	no	—
36	Dic₃	—	36	9	no	—
37	C₃²	—	4	12	no	—
38	C₃²	SL(2,ℤ/4)	1	1	yes	characteristic, complemented
39	C₂³	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
40	C₂×C₄	—	27	1	no	—
41	C₂×C₄	—	27	1	no	—
42	C₂×C₃	—	3	4	no	—
43	C₂×C₃	—	3	4	no	—
44	C₂×C₃	—	4	9	no	—
45	C₂×C₃	C₃⋊S₄	1	4	yes	—
46	C₂²	—	3	1	no	—
47	C₂²	—	3	1	no	—
48	C₂²	C₃⋊(C₃⋊Dic₃)	1	1	yes	characteristic, complemented
49	C₄	—	54	1	no	—
50	C₄	—	54	1	no	—
51	C₃	—	4	9	no	—
52	C₃	C₃⋊SL(2,ℤ/4)	1	4	yes	complemented
53	C₂	—	3	1	no	—
54	C₂	—	3	1	no	—
55	C₂	C₃⋊(C₃⋊S₄)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₃⋊S₄)
commutator, hypocenter	C₃²×A₄	C₄
Fitting, socle	C₂³×C₃²	D₃
prime radical, cosocle	C₂×C₃²×A₄	C₂
LCS	G ▷ C₃²×A₄
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
4. C₃²×A₄	C₄	semidirect
15. C₂²×C₃²	Dic₃	semidirect
16. C₃×A₄	Dic₃	semidirect
32. C₂²×C₃	C₃⋊Dic₃	semidirect
33. A₄	C₃⋊Dic₃	semidirect
38. C₃²	SL(2,ℤ/4)	semidirect
48. C₂²	C₃⋊(C₃⋊Dic₃)	semidirect
52. C₃	C₃⋊SL(2,ℤ/4)	semidirect

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
#3757	3
C₃⋊(C₃⋊Dic₃)	4

Subgroups — C3⋊(C3⋊SL(2,ℤ/4)) #88974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊SL(2,ℤ/4)) #88974