Subgroups — C₃×A₄⋊Q₈ #64248

Order 288.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×A₄	C₂	1	1	yes	maximal, characteristic
2	C₃×SL(2,ℤ/4)	C₂	1	2	yes	maximal
3	A₄⋊Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₂²⋊Q₈	—	3	1	no	maximal
5	C₂×C₃×A₄	C₂²	1	1	yes	characteristic
6	C₃×Dic₆	—	4	1	no	maximal
7	C₂×C₃×Q₈	—	3	1	no	—
8	C₂²×C₃×C₄	D₃	1	1	yes	characteristic
9	C₄×A₄	—	2	1	no	—
10	C₄×A₄	C₂×C₃	1	1	yes	characteristic
11	SL(2,ℤ/4)	C₂×C₃	1	2	yes	—
12	C₃×C₄⋊C₄	—	3	1	no	—
13	C₃×C₄⋊C₄	—	3	2	no	—
14	C₃×C₂²⋊C₄	—	3	2	no	—
15	C₃×A₄	Q₈	1	1	yes	characteristic, complemented
16	C₃²×C₄	—	4	1	no	—
17	C₃×Dic₃	—	4	2	no	—
18	C₂²⋊Q₈	—	3	1	no	Sylow
19	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
20	C₂×A₄	—	2	1	no	—
21	C₂×A₄	C₂²×C₃	1	1	yes	characteristic
22	C₃×Q₈	—	6	1	no	—
23	C₃×Q₈	—	6	1	no	—
24	C₂×C₃×C₄	—	3	1	no	—
25	C₂×C₃×C₄	—	3	1	no	—
26	C₂×C₃×C₄	—	3	2	no	—
27	C₂×C₃×C₄	—	3	2	no	—
28	Dic₆	—	4	1	no	—
29	C₂×C₃²	—	4	1	no	—
30	C₂×Q₈	—	3	1	no	—
31	C₂²×C₄	C₃×D₃	1	1	yes	characteristic
32	C₄⋊C₄	—	3	1	no	—
33	C₄⋊C₄	—	3	2	no	—
34	C₂²⋊C₄	—	3	2	no	—
35	C₂²×C₃	—	3	1	no	—
36	C₂²×C₃	—	3	1	no	—
37	C₂²×C₃	Dic₆	1	1	yes	characteristic, complemented
38	A₄	—	2	1	no	—
39	A₄	C₃×Q₈	1	1	yes	characteristic, complemented
40	C₃×C₄	—	3	1	no	—
41	C₃×C₄	—	4	1	no	—
42	C₃×C₄	—	6	2	no	—
43	C₃×C₄	—	6	2	no	—
44	C₃×C₄	—	8	1	no	—
45	C₃×C₄	S₄	1	1	yes	characteristic
46	Dic₃	—	4	2	no	—
47	C₃²	—	4	1	no	Sylow
48	C₂³	C₂×C₃×D₃	1	1	yes	characteristic
49	Q₈	—	6	1	no	—
50	Q₈	—	6	1	no	—
51	C₂×C₄	—	3	1	no	—
52	C₂×C₄	—	3	1	no	—
53	C₂×C₄	—	3	2	no	—
54	C₂×C₄	—	3	2	no	—
55	C₂×C₃	—	3	1	no	—
56	C₂×C₃	—	3	1	no	—
57	C₂×C₃	—	4	1	no	—
58	C₂×C₃	—	8	1	no	—
59	C₂×C₃	C₂×S₄	1	1	yes	characteristic
60	C₂²	—	3	1	no	—
61	C₂²	—	3	1	no	—
62	C₂²	C₃×Dic₆	1	1	yes	characteristic, complemented
63	C₄	—	3	1	no	—
64	C₄	—	6	2	no	—
65	C₄	—	6	2	no	—
66	C₄	C₃×S₄	1	1	yes	characteristic
67	C₃	—	4	1	no	—
68	C₃	—	8	1	no	—
69	C₃	A₄⋊Q₈	1	1	yes	characteristic, direct product factor
70	C₂	—	3	1	no	—
71	C₂	—	3	1	no	—
72	C₂	C₂×C₃×S₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×S₄
commutator, cosocle	C₂×A₄	C₂²×C₃
Frattini	C₂	C₂×C₃×S₄
Fitting	C₂²×C₃×C₄	D₃
socle	C₂³×C₃	C₂×D₃
prime radical	C₂×C₃×A₄	C₂²
hypercenter	C₃×C₄	S₄
hypocenter	A₄	C₃×Q₈
LCS	G ▷ C₂×A₄ ▷ A₄
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
3. A₄⋊Q₈	C₃	direct (N × H)
15. C₃×A₄	Q₈	semidirect
37. C₂²×C₃	Dic₆	semidirect
39. A₄	C₃×Q₈	semidirect
62. C₂²	C₃×Dic₆	semidirect
69. C₃	A₄⋊Q₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×A₄	2
C₃×SL(2,ℤ/4)	2
A₄⋊Q₈	3
C₃×C₂²⋊Q₈	3
C₃×Dic₆	4

Subgroups — C3×A4⋊Q8 #64248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×A₄⋊Q₈ #64248