Subgroups — (C₃⋊SL(2,ℤ/4))⋊C₃ #88604

Order 432.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₃⋊SL(2,ℤ/4)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#217	—	3	1	no	maximal
4	C₂²⋊H(3,𝔽₃)	C₄	1	1	yes	characteristic, complemented
5	(C₃⋊Dic₃)⋊C₃	—	4	1	no	maximal
6	C₂³×C₃²	D₃	1	1	yes	characteristic
7	C₂×C₃×A₄	—	2	1	no	—
8	C₂×C₃×A₄	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×Dic₃	—	3	1	no	—
10	C₂×C₃×Dic₃	—	3	1	no	—
11	C₂×H(3,𝔽₃)	—	4	1	no	—
12	SL(2,ℤ/4)	—	9	1	no	—
13	C₃×C₂²⋊C₄	—	9	1	no	—
14	#217	—	3	1	no	—
15	C₂²×C₃²	—	3	1	no	—
16	C₂²×C₃²	—	3	1	no	—
17	C₂²×C₃²	Dic₃	1	1	yes	characteristic, complemented
18	C₃×A₄	—	2	1	no	—
19	C₃×A₄	C₃×C₄	1	1	yes	characteristic, complemented
20	C₃⋊Dic₃	—	4	1	no	—
21	C₃×Dic₃	—	6	1	no	—
22	C₃×Dic₃	—	6	1	no	—
23	H(3,𝔽₃)	—	4	1	no	Sylow
24	C₂³×C₃	—	3	1	no	—
25	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
26	C₂×A₄	—	3	1	no	—
27	C₂×A₄	—	6	1	no	—
28	C₂×C₃×C₄	—	9	1	no	—
29	C₂×C₃×C₄	—	9	1	no	—
30	C₂×Dic₃	—	3	1	no	—
31	C₂×Dic₃	—	3	1	no	—
32	C₂×C₃²	—	3	1	no	—
33	C₂×C₃²	—	3	1	no	—
34	C₂×C₃²	—	4	1	no	—
35	C₂×C₃²	—	8	1	no	—
36	C₂×C₃²	S₄	1	1	yes	characteristic
37	C₂²⋊C₄	—	9	1	no	Sylow
38	C₂²×C₃	—	3	1	no	—
39	C₂²×C₃	—	3	1	no	—
40	C₂²×C₃	—	3	1	no	—
41	C₂²×C₃	—	3	1	no	—
42	C₂²×C₃	—	3	1	no	—
43	C₂²×C₃	—	6	1	no	—
44	C₂²×C₃	—	6	1	no	—
45	C₂²×C₃	C₃×Dic₃	1	1	yes	characteristic
46	A₄	—	3	1	no	—
47	A₄	—	6	1	no	—
48	C₃×C₄	—	18	1	no	—
49	C₃×C₄	—	18	1	no	—
50	Dic₃	—	6	1	no	—
51	Dic₃	—	6	1	no	—
52	Dic₃	—	36	1	no	—
53	C₃²	—	4	1	no	—
54	C₃²	—	8	1	no	—
55	C₃²	SL(2,ℤ/4)	1	1	yes	characteristic, complemented
56	C₂³	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
57	C₂×C₄	—	9	1	no	—
58	C₂×C₄	—	9	1	no	—
59	C₂×C₃	—	3	1	no	—
60	C₂×C₃	—	3	1	no	—
61	C₂×C₃	—	3	1	no	—
62	C₂×C₃	—	3	1	no	—
63	C₂×C₃	—	3	1	no	—
64	C₂×C₃	—	6	1	no	—
65	C₂×C₃	—	6	1	no	—
66	C₂×C₃	—	12	1	no	—
67	C₂×C₃	—	24	1	no	—
68	C₂×C₃	C₃×S₄	1	1	yes	characteristic
69	C₂²	—	3	1	no	—
70	C₂²	—	3	1	no	—
71	C₂²	(C₃⋊Dic₃)⋊C₃	1	1	yes	characteristic, complemented
72	C₄	—	18	1	no	—
73	C₄	—	18	1	no	—
74	C₃	—	3	1	no	—
75	C₃	—	12	1	no	—
76	C₃	—	24	1	no	—
77	C₃	C₃×SL(2,ℤ/4)	1	1	yes	characteristic
78	C₂	—	3	1	no	—
79	C₂	—	3	1	no	—
80	C₂	(C₃⋊S₄)⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	(C₃⋊S₄)⋊C₃
commutator, hypocenter	C₃×A₄	C₃×C₄
Frattini	C₂×C₃	C₃×S₄
Fitting	C₂³×C₃²	D₃
socle	C₂³×C₃	C₃×D₃
prime radical	C₂×C₂²⋊H(3,𝔽₃)	C₂
cosocle	C₂×C₃×A₄	C₂×C₃
LCS	G ▷ C₃×A₄
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊SL(2,ℤ/4)	C₃	semidirect
4. C₂²⋊H(3,𝔽₃)	C₄	semidirect
17. C₂²×C₃²	Dic₃	semidirect
19. C₃×A₄	C₃×C₄	semidirect
55. C₃²	SL(2,ℤ/4)	semidirect
71. C₂²	(C₃⋊Dic₃)⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊H(3,𝔽₃)	2
C₃⋊SL(2,ℤ/4)	3
C₃×#217	3
(C₃⋊Dic₃)⋊C₃	4

Subgroups — (C3⋊SL(2,ℤ/4))⋊C3 #88604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊SL(2,ℤ/4))⋊C₃ #88604