Subgroups — C₄×C₃⋊S₄ #64260

Order 288.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊S₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×A₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊SL(2,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×S₄	—	3	3	no	maximal
5	C₄×#67	—	3	1	no	maximal
6	C₂×C₃×A₄	C₂²	1	1	yes	characteristic
7	C₃⋊S₄	C₄	1	2	yes	direct product factor
8	C₄×C₃⋊D₃	—	4	1	no	maximal
9	C₂×S₄	—	3	3	no	—
10	C₂²×C₃×C₄	D₃	1	1	yes	characteristic, complemented
11	C₂×#67	—	3	1	no	—
12	C₂×C₄×D₃	—	3	1	no	—
13	C₄×A₄	D₃	1	3	yes	complemented
14	SL(2,ℤ/4)	—	3	3	no	—
15	#217	—	3	1	no	—
16	(C₂×D₃)⋊C₄	—	3	1	no	—
17	Dic₃⋊C₄	—	3	1	no	—
18	C₄×Dic₃	—	3	1	no	—
19	C₂×C₃⋊D₃	—	4	1	no	—
20	C₃×A₄	C₂×C₄	1	1	yes	characteristic, complemented
21	C₃²×C₄	—	4	1	no	—
22	C₃⋊Dic₃	—	4	1	no	—
23	C₄×D₄	—	9	1	no	Sylow
24	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
25	C₂²×D₃	—	3	1	no	—
26	C₂×A₄	C₂×D₃	1	3	yes	—
27	S₄	—	3	6	no	—
28	C₂×C₃×C₄	—	3	1	no	—
29	C₂×C₃×C₄	—	3	1	no	—
30	#67	—	3	2	no	—
31	#67	—	3	2	no	—
32	C₂×Dic₃	—	3	1	no	—
33	C₂×Dic₃	—	3	1	no	—
34	C₂×Dic₃	—	3	1	no	—
35	C₄×D₃	—	6	1	no	—
36	C₄×D₃	—	6	1	no	—
37	C₄×D₃	—	12	3	no	—
38	C₂×C₃²	—	4	1	no	—
39	C₃⋊D₃	—	4	2	no	—
40	C₂×D₄	—	9	1	no	—
41	C₂²×C₄	—	9	1	no	—
42	C₂²×C₄	C₃⋊D₃	1	1	yes	characteristic, complemented
43	C₄⋊C₄	—	9	1	no	—
44	C₂²⋊C₄	—	9	1	no	—
45	C₂²⋊C₄	—	9	1	no	—
46	C₄²	—	9	1	no	—
47	C₂²×C₃	—	3	1	no	—
48	C₂²×C₃	—	3	1	no	—
49	C₂²×C₃	C₄×D₃	1	1	yes	characteristic, complemented
50	C₂×D₃	—	3	2	no	—
51	C₂×D₃	—	6	1	no	—
52	C₂×D₃	—	6	1	no	—
53	C₂×D₃	—	12	3	no	—
54	A₄	C₄×D₃	1	3	yes	complemented
55	C₃×C₄	—	3	1	no	—
56	C₃×C₄	—	4	3	no	—
57	C₃×C₄	S₄	1	1	yes	characteristic, complemented
58	Dic₃	—	3	2	no	—
59	Dic₃	—	6	1	no	—
60	Dic₃	—	6	1	no	—
61	Dic₃	—	12	3	no	—
62	C₃²	—	4	1	no	Sylow
63	C₂³	—	9	1	no	—
64	C₂³	C₂×C₃⋊D₃	1	1	yes	characteristic
65	D₄	—	9	2	no	—
66	D₄	—	9	2	no	—
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	9	1	no	—
70	C₂×C₄	—	9	1	no	—
71	C₂×C₄	—	9	1	no	—
72	C₂×C₄	—	18	1	no	—
73	C₂×C₄	—	18	1	no	—
74	C₂×C₃	—	3	1	no	—
75	C₂×C₃	—	3	1	no	—
76	C₂×C₃	—	4	3	no	—
77	C₂×C₃	C₂×S₄	1	1	yes	characteristic
78	D₃	—	6	2	no	—
79	D₃	—	12	6	no	—
80	C₂²	—	3	1	no	—
81	C₂²	—	3	1	no	—
82	C₂²	—	9	2	no	—
83	C₂²	—	18	1	no	—
84	C₂²	—	18	1	no	—
85	C₂²	C₄×C₃⋊D₃	1	1	yes	characteristic, complemented
86	C₄	—	3	1	no	—
87	C₄	—	9	2	no	—
88	C₄	—	18	1	no	—
89	C₄	—	18	1	no	—
90	C₄	C₃⋊S₄	1	1	yes	characteristic, direct product factor
91	C₃	—	4	3	no	—
92	C₃	C₄×S₄	1	1	yes	characteristic, complemented
93	C₂	—	3	1	no	—
94	C₂	—	3	1	no	—
95	C₂	—	18	2	no	—
96	C₂	C₂×C₃⋊S₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×A₄	C₂	semidirect
3. C₃⋊SL(2,ℤ/4)	C₂	semidirect
7. C₃⋊S₄	C₄	direct (N × H)
10. C₂²×C₃×C₄	D₃	semidirect
13. C₄×A₄	D₃	semidirect
20. C₃×A₄	C₂×C₄	semidirect
42. C₂²×C₄	C₃⋊D₃	semidirect
49. C₂²×C₃	C₄×D₃	semidirect
54. A₄	C₄×D₃	semidirect
57. C₃×C₄	S₄	semidirect
85. C₂²	C₄×C₃⋊D₃	semidirect
90. C₄	C₃⋊S₄	direct (N × H)
92. C₃	C₄×S₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊S₄	2
C₃×C₄×A₄	2
C₃⋊SL(2,ℤ/4)	2
C₄×S₄	3
C₄×#67	3
C₄×C₃⋊D₃	4

Subgroups — C4×C3⋊S4 #64260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃⋊S₄ #64260