Subgroups — Q₆₄×D₄₇ #20245691

Order 6016.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₄₇	C₂	1	2	yes	maximal
2	Dic₇₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688963	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₄₇	—	2	2	no	—
7	Dic₃₇₆	C₂²	1	2	yes	—
8	#13093970	—	2	2	no	—
9	C₁₆×D₄₇	C₂²	1	1	yes	characteristic
10	C₄₇⋊C₃₂	C₂²	1	1	yes	characteristic
11	Q₃₂×C₄₇	C₂²	1	2	yes	—
12	C₃₂×C₄₇	C₂²	1	1	yes	characteristic
13	Q₈×D₄₇	—	4	2	no	—
14	Q₁₆×C₄₇	—	2	2	no	—
15	#10625337	—	4	2	no	—
16	Dic₁₈₈	—	2	2	no	—
17	C₈×D₄₇	D₄	1	1	yes	characteristic
18	C₁₆×C₄₇	C₂³	1	1	yes	characteristic
19	C₄₇⋊C₁₆	D₄	1	1	yes	characteristic
20	Q₈×C₄₇	—	4	2	no	—
21	C₄×D₄₇	—	8	2	no	—
22	C₄×D₄₇	D₈	1	1	yes	characteristic
23	Dic₉₄	—	4	2	no	—
24	Dic₉₄	—	8	2	no	—
25	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
26	C₄₇⋊C₈	D₈	1	1	yes	characteristic
27	C₂×D₄₇	D₁₆	1	1	yes	characteristic
28	C₄×C₄₇	—	8	2	no	—
29	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
30	Dic₄₇	—	8	2	no	—
31	Dic₄₇	D₁₆	1	1	yes	characteristic
32	C₂×Q₆₄	—	47	1	no	maximal, Sylow
33	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
34	D₄₇	Q₆₄	1	2	yes	direct product factor
35	C₂×Q₃₂	—	47	2	no	—
36	Q₆₄	—	47	2	no	—
37	Q₆₄	—	47	1	no	—
38	Q₆₄	D₄₇	1	1	yes	characteristic, direct product factor
39	C₂×C₃₂	—	47	1	no	—
40	C₄₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₁₆	—	94	2	no	—
42	Q₃₂	—	47	2	no	—
43	Q₃₂	—	94	2	no	—
44	Q₃₂	C₂×D₄₇	1	2	yes	—
45	C₂×C₁₆	—	47	1	no	—
46	C₃₂	—	47	1	no	—
47	C₃₂	C₂×D₄₇	1	1	yes	characteristic
48	C₂×Q₈	—	188	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	94	2	no	—
51	Q₁₆	—	188	2	no	—
52	C₂×C₈	—	47	1	no	—
53	C₁₆	—	47	1	no	—
54	C₁₆	C₂²×D₄₇	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	376	2	no	—
57	Q₈	—	188	2	no	—
58	C₂×C₄	—	47	1	no	—
59	C₂×C₄	—	376	2	no	—
60	C₈	—	47	1	no	—
61	C₈	D₄×D₄₇	1	1	yes	characteristic
62	C₂²	—	47	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	47	1	no	—
65	C₄	—	376	2	no	—
66	C₄	D₈×D₄₇	1	1	yes	characteristic
67	C₂	—	47	2	no	—
68	C₂	D₁₆×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₄₇
commutator	C₁₆×C₄₇	C₂³
Frattini	C₁₆	C₂²×D₄₇
Fitting	C₄₇×Q₆₄	C₂
socle	C₂×C₄₇	C₂×D₁₆
hypercenter	Q₆₄	D₄₇
hypocenter	C₄₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₇₅₂	C₂	semidirect
3. #15688963	C₂	semidirect
5. C₄₇×Q₆₄	C₂	semidirect
34. D₄₇	Q₆₄	direct (N × H)
38. Q₆₄	D₄₇	direct (N × H)
40. C₄₇	C₂×Q₆₄	semidirect

Subgroups — Q64×D47 #20245691

Conjugacy classes of subgroups

Complements

Subgroups — Q₆₄×D₄₇ #20245691