Subgroups — D₃×Q₆₄ #69382

Order 384.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×Q₃₂	C₂	1	2	yes	maximal
2	C₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#4522	C₂	1	2	yes	maximal, complemented
4	Dic₄₈	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₆₄	—	3	1	no	maximal, Sylow
7	D₃×Q₁₆	—	2	2	no	—
8	C₃×Q₃₂	C₂²	1	2	yes	—
9	#829	—	2	2	no	—
10	Dic₂₄	C₂²	1	2	yes	—
11	D₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₃×C₃₂	C₂²	1	1	yes	characteristic
13	C₃⋊C₃₂	C₂²	1	1	yes	characteristic
14	C₂×Q₃₂	—	3	2	no	—
15	Q₆₄	—	3	2	no	—
16	Q₆₄	—	3	1	no	—
17	Q₆₄	D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₃₂	—	3	1	no	—
19	D₃×Q₈	—	4	2	no	—
20	C₃×Q₁₆	—	2	2	no	—
21	#216	—	4	2	no	—
22	Dic₁₂	—	2	2	no	—
23	D₃×C₈	D₄	1	1	yes	characteristic
24	C₃×C₁₆	C₂³	1	1	yes	characteristic
25	C₃⋊C₁₆	D₄	1	1	yes	characteristic
26	C₂×Q₁₆	—	6	2	no	—
27	Q₃₂	—	3	2	no	—
28	Q₃₂	—	6	2	no	—
29	Q₃₂	C₂×D₃	1	2	yes	—
30	C₂×C₁₆	—	3	1	no	—
31	C₃₂	—	3	1	no	—
32	C₃₂	C₂×D₃	1	1	yes	characteristic
33	C₃×Q₈	—	4	2	no	—
34	C₄×D₃	—	8	2	no	—
35	C₄×D₃	D₈	1	1	yes	characteristic
36	Dic₆	—	4	2	no	—
37	Dic₆	—	8	2	no	—
38	C₃×C₈	C₂×D₄	1	1	yes	characteristic
39	C₃⋊C₈	D₈	1	1	yes	characteristic
40	C₂×Q₈	—	12	2	no	—
41	Q₁₆	—	2	2	no	—
42	Q₁₆	—	6	2	no	—
43	Q₁₆	—	12	2	no	—
44	C₂×C₈	—	3	1	no	—
45	C₁₆	—	3	1	no	—
46	C₁₆	C₂²×D₃	1	1	yes	characteristic
47	C₂×D₃	D₁₆	1	1	yes	characteristic
48	C₃×C₄	—	8	2	no	—
49	C₃×C₄	C₂×D₈	1	1	yes	characteristic
50	Dic₃	—	8	2	no	—
51	Dic₃	D₁₆	1	1	yes	characteristic
52	Q₈	—	4	2	no	—
53	Q₈	—	12	2	no	—
54	Q₈	—	24	2	no	—
55	C₂×C₄	—	3	1	no	—
56	C₂×C₄	—	24	2	no	—
57	C₈	—	3	1	no	—
58	C₈	D₃×D₄	1	1	yes	characteristic
59	C₂×C₃	C₂×D₁₆	1	1	yes	characteristic
60	D₃	Q₆₄	1	2	yes	direct product factor
61	C₂²	—	3	1	no	—
62	C₄	—	3	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	24	2	no	—
65	C₄	D₃×D₈	1	1	yes	characteristic
66	C₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
67	C₂	—	3	2	no	—
68	C₂	D₃×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×D₁₆
commutator, cosocle	C₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₃
Fitting	C₃×Q₆₄	C₂
socle	C₂×C₃	C₂×D₁₆
prime radical	C₂×D₃	D₁₆
hypercenter	Q₆₄	D₃
hypocenter	C₃	C₂×Q₆₄
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. C₃×Q₆₄	C₂	semidirect
3. #4522	C₂	semidirect
4. Dic₄₈	C₂	semidirect
17. Q₆₄	D₃	direct (N × H)
60. D₃	Q₆₄	direct (N × H)
66. C₃	C₂×Q₆₄	semidirect

Maximal subgroups

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

subgroup	index
D₃×Q₃₂	2
C₃×Q₆₄	2
#4522	2
Dic₄₈	2
D₃×C₃₂	2
C₂×Q₆₄	3

Subgroups — D3×Q64 #69382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×Q₆₄ #69382