Subgroups — C₂×C₃⋊SL(2,ℤ/4) #64268

Order 288.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×A₄	C₂	1	1	yes	maximal, characteristic
2	C₃⋊SL(2,ℤ/4)	C₂	1	2	yes	maximal, direct product factor
3	C₂×SL(2,ℤ/4)	—	3	3	no	maximal
4	C₂×#217	—	3	1	no	maximal
5	C₂×C₃×A₄	C₄	1	2	yes	complemented
6	C₂×C₃×A₄	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊Dic₃	—	4	1	no	maximal
8	C₂⁴×C₃	D₃	1	1	yes	characteristic
9	C₂²×A₄	D₃	1	3	yes	—
10	C₂²×Dic₃	—	3	1	no	—
11	C₂²×Dic₃	—	3	1	no	—
12	SL(2,ℤ/4)	—	3	6	no	—
13	#217	—	3	2	no	—
14	#217	—	3	2	no	—
15	C₂²×C₃²	—	4	1	no	—
16	C₃×A₄	C₂×C₄	1	1	yes	characteristic, complemented
17	C₃⋊Dic₃	—	4	2	no	—
18	C₂×C₂²⋊C₄	—	9	1	no	Sylow
19	C₂³×C₃	—	3	1	no	—
20	C₂³×C₃	—	3	1	no	—
21	C₂³×C₃	—	3	2	no	—
22	C₂³×C₃	Dic₃	1	2	yes	complemented
23	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
24	C₂×A₄	Dic₃	1	6	yes	complemented
25	C₂×A₄	C₂×D₃	1	3	yes	—
26	C₂×Dic₃	—	3	2	no	—
27	C₂×Dic₃	—	3	2	no	—
28	C₂×Dic₃	—	6	2	no	—
29	C₂×Dic₃	—	6	1	no	—
30	C₂×Dic₃	—	6	1	no	—
31	C₂×Dic₃	—	12	3	no	—
32	C₂×C₃²	—	4	2	no	—
33	C₂×C₃²	—	4	1	no	—
34	C₂⁴	C₃⋊D₃	1	1	yes	characteristic
35	C₂²×C₄	—	9	1	no	—
36	C₂²×C₄	—	9	1	no	—
37	C₂²⋊C₄	—	9	2	no	—
38	C₂²⋊C₄	—	9	2	no	—
39	C₂²×C₃	—	3	2	no	—
40	C₂²×C₃	—	3	1	no	—
41	C₂²×C₃	—	3	2	no	—
42	C₂²×C₃	—	3	2	no	—
43	C₂²×C₃	—	3	1	no	—
44	C₂²×C₃	—	3	1	no	—
45	C₂²×C₃	—	4	3	no	—
46	C₂²×C₃	—	6	1	no	—
47	C₂²×C₃	C₂×Dic₃	1	1	yes	characteristic, complemented
48	C₂²×C₃	S₄	1	1	yes	characteristic
49	A₄	C₂×Dic₃	1	3	yes	complemented
50	Dic₃	—	6	2	no	—
51	Dic₃	—	6	2	no	—
52	Dic₃	—	12	6	no	—
53	C₃²	—	4	1	no	Sylow
54	C₂³	—	3	1	no	—
55	C₂³	—	3	1	no	—
56	C₂³	—	3	2	no	—
57	C₂³	C₃⋊Dic₃	1	2	yes	complemented
58	C₂³	C₂×C₃⋊D₃	1	1	yes	characteristic
59	C₂×C₄	—	9	2	no	—
60	C₂×C₄	—	9	2	no	—
61	C₂×C₄	—	18	2	no	—
62	C₂×C₄	—	18	1	no	—
63	C₂×C₄	—	18	1	no	—
64	C₂×C₃	—	3	1	no	—
65	C₂×C₃	—	3	1	no	—
66	C₂×C₃	—	3	2	no	—
67	C₂×C₃	—	4	3	no	—
68	C₂×C₃	—	4	6	no	—
69	C₂×C₃	SL(2,ℤ/4)	1	2	yes	complemented
70	C₂×C₃	C₂×S₄	1	1	yes	characteristic
71	C₂²	—	3	2	no	—
72	C₂²	—	3	1	no	—
73	C₂²	—	3	1	no	—
74	C₂²	—	3	1	no	—
75	C₂²	—	3	2	no	—
76	C₂²	—	3	2	no	—
77	C₂²	—	6	1	no	—
78	C₂²	C₂×C₃⋊Dic₃	1	1	yes	characteristic, complemented
79	C₂²	C₃⋊S₄	1	1	yes	characteristic
80	C₄	—	18	2	no	—
81	C₄	—	18	2	no	—
82	C₃	—	4	3	no	—
83	C₃	C₂×SL(2,ℤ/4)	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	3	1	no	—
86	C₂	—	3	2	no	—
87	C₂	C₃⋊SL(2,ℤ/4)	1	2	yes	direct product factor
88	C₂	C₂×C₃⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊S₄
commutator, hypocenter	C₃×A₄	C₂×C₄
Frattini	C₂	C₂×C₃⋊S₄
Fitting, socle	C₂⁴×C₃	D₃
prime radical	C₂²×C₃×A₄	C₂
cosocle	C₂×C₃×A₄	C₂²
LCS	G ▷ C₃×A₄
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₃⋊SL(2,ℤ/4)	C₂	direct (N × H)
5. C₂×C₃×A₄	C₄	semidirect
16. C₃×A₄	C₂×C₄	semidirect
22. C₂³×C₃	Dic₃	semidirect
24. C₂×A₄	Dic₃	semidirect
47. C₂²×C₃	C₂×Dic₃	semidirect
49. A₄	C₂×Dic₃	semidirect
57. C₂³	C₃⋊Dic₃	semidirect
69. C₂×C₃	SL(2,ℤ/4)	semidirect
78. C₂²	C₂×C₃⋊Dic₃	semidirect
83. C₃	C₂×SL(2,ℤ/4)	semidirect
87. C₂	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
C₂²×C₃×A₄	2
C₃⋊SL(2,ℤ/4)	2
C₂×SL(2,ℤ/4)	3
C₂×#217	3
C₂×C₃⋊Dic₃	4

Subgroups — C2×C3⋊SL(2,ℤ/4) #64268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊SL(2,ℤ/4) #64268