Subgroups — C₃×C₃⋊SL(2,ℤ/4) #88971

Order 432.

136 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	1	yes	maximal, characteristic, direct product factor
3	C₃×SL(2,ℤ/4)	—	3	3	no	maximal
4	C₃×#217	—	3	1	no	maximal
5	C₃²×A₄	C₄	1	1	yes	characteristic, complemented
6	C₃×C₃⋊Dic₃	—	4	1	no	maximal
7	C₂³×C₃²	D₃	1	1	yes	characteristic
8	C₂×C₃×A₄	—	2	1	no	—
9	C₂×C₃×A₄	—	2	3	no	—
10	C₂×C₃×A₄	D₃	1	3	yes	—
11	C₂×C₃×A₄	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃×Dic₃	—	3	1	no	—
13	C₂×C₃×Dic₃	—	3	1	no	—
14	C₂×C₃³	—	4	1	no	—
15	SL(2,ℤ/4)	—	3	3	no	—
16	C₃×C₂²⋊C₄	—	9	1	no	—
17	#217	—	3	1	no	—
18	C₂²×C₃²	—	3	1	no	—
19	C₂²×C₃²	—	3	1	no	—
20	C₂²×C₃²	Dic₃	1	1	yes	characteristic, complemented
21	C₃×A₄	—	2	1	no	—
22	C₃×A₄	—	2	3	no	—
23	C₃×A₄	Dic₃	1	3	yes	complemented
24	C₃×A₄	C₃×C₄	1	1	yes	characteristic, complemented
25	C₃⋊Dic₃	—	4	1	no	—
26	C₃×Dic₃	—	6	1	no	—
27	C₃×Dic₃	—	6	1	no	—
28	C₃×Dic₃	—	12	3	no	—
29	C₃³	—	4	1	no	Sylow
30	C₂³×C₃	—	2	1	no	—
31	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
32	C₂³×C₃	C₃⋊D₃	1	1	yes	characteristic
33	C₂×A₄	—	2	3	no	—
34	C₂×A₄	C₃×D₃	1	3	yes	—
35	C₂×C₃×C₄	—	9	1	no	—
36	C₂×C₃×C₄	—	9	1	no	—
37	C₂×Dic₃	—	3	1	no	—
38	C₂×Dic₃	—	3	1	no	—
39	C₂×C₃²	—	3	1	no	—
40	C₂×C₃²	—	3	1	no	—
41	C₂×C₃²	—	4	1	no	—
42	C₂×C₃²	—	4	3	no	—
43	C₂×C₃²	—	8	3	no	—
44	C₂×C₃²	—	8	1	no	—
45	C₂×C₃²	S₄	1	1	yes	characteristic
46	C₂²⋊C₄	—	9	1	no	Sylow
47	C₂²×C₃	—	2	1	no	—
48	C₂²×C₃	—	3	1	no	—
49	C₂²×C₃	—	3	1	no	—
50	C₂²×C₃	—	3	1	no	—
51	C₂²×C₃	—	3	1	no	—
52	C₂²×C₃	—	6	1	no	—
53	C₂²×C₃	—	6	1	no	—
54	C₂²×C₃	C₃×Dic₃	1	1	yes	characteristic, complemented
55	C₂²×C₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented
56	A₄	—	2	3	no	—
57	A₄	C₃×Dic₃	1	3	yes	complemented
58	C₃×C₄	—	18	1	no	—
59	C₃×C₄	—	18	1	no	—
60	Dic₃	—	6	1	no	—
61	Dic₃	—	6	1	no	—
62	Dic₃	—	12	3	no	—
63	C₃²	—	4	1	no	—
64	C₃²	—	4	3	no	—
65	C₃²	—	8	3	no	—
66	C₃²	—	8	1	no	—
67	C₃²	SL(2,ℤ/4)	1	1	yes	characteristic, complemented
68	C₂³	C₃×C₃⋊D₃	1	1	yes	characteristic
69	C₂×C₄	—	9	1	no	—
70	C₂×C₄	—	9	1	no	—
71	C₂×C₃	—	2	1	no	—
72	C₂×C₃	—	3	1	no	—
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	3	1	no	—
75	C₂×C₃	—	3	1	no	—
76	C₂×C₃	—	4	3	no	—
77	C₂×C₃	—	6	1	no	—
78	C₂×C₃	—	6	1	no	—
79	C₂×C₃	—	8	3	no	—
80	C₂×C₃	C₃×S₄	1	1	yes	characteristic
81	C₂×C₃	C₃⋊S₄	1	1	yes	characteristic
82	C₂²	—	3	1	no	—
83	C₂²	—	3	1	no	—
84	C₂²	C₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented
85	C₄	—	18	1	no	—
86	C₄	—	18	1	no	—
87	C₃	—	2	1	no	—
88	C₃	—	4	3	no	—
89	C₃	—	8	3	no	—
90	C₃	C₃×SL(2,ℤ/4)	1	1	yes	characteristic, complemented
91	C₃	C₃⋊SL(2,ℤ/4)	1	1	yes	characteristic, direct product factor
92	C₂	—	3	1	no	—
93	C₂	—	3	1	no	—
94	C₂	C₃×C₃⋊S₄	1	1	yes	characteristic

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

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)
5. C₃²×A₄	C₄	semidirect
20. C₂²×C₃²	Dic₃	semidirect
23. C₃×A₄	Dic₃	semidirect
24. C₃×A₄	C₃×C₄	semidirect
54. C₂²×C₃	C₃×Dic₃	semidirect
55. C₂²×C₃	C₃⋊Dic₃	semidirect
57. A₄	C₃×Dic₃	semidirect
67. C₃²	SL(2,ℤ/4)	semidirect
84. C₂²	C₃×C₃⋊Dic₃	semidirect
90. C₃	C₃×SL(2,ℤ/4)	semidirect
91. 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
C₃×SL(2,ℤ/4)	3
C₃×#217	3
C₃×C₃⋊Dic₃	4

Subgroups — C3×C3⋊SL(2,ℤ/4) #88971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊SL(2,ℤ/4) #88971