Subgroups — Q₃₂×D₁₆₃ #23782091

Order 10432.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₁₆×D₁₆₃	C₂	1	2	yes	maximal
2	Dic₁₃₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#19104681	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₁₆₃	C₂	1	1	yes	maximal, characteristic
5	Q₃₂×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×D₁₆₃	—	2	2	no	—
7	Dic₆₅₂	C₂²	1	2	yes	—
8	#14579689	—	2	2	no	—
9	C₈×D₁₆₃	C₂²	1	1	yes	characteristic
10	C₁₆₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	Q₁₆×C₁₆₃	C₂²	1	2	yes	—
12	C₁₆×C₁₆₃	C₂²	1	1	yes	characteristic
13	Dic₃₂₆	—	2	2	no	—
14	Dic₃₂₆	—	4	2	no	—
15	C₄×D₁₆₃	—	4	2	no	—
16	C₄×D₁₆₃	D₄	1	1	yes	characteristic
17	C₁₆₃⋊C₈	D₄	1	1	yes	characteristic
18	Q₈×C₁₆₃	—	2	2	no	—
19	C₈×C₁₆₃	C₂³	1	1	yes	characteristic
20	C₂×D₁₆₃	D₈	1	1	yes	characteristic
21	C₄×C₁₆₃	—	4	2	no	—
22	C₄×C₁₆₃	C₂×D₄	1	1	yes	characteristic
23	Dic₁₆₃	—	4	2	no	—
24	Dic₁₆₃	D₈	1	1	yes	characteristic
25	C₂×C₁₆₃	C₂×D₈	1	1	yes	characteristic
26	D₁₆₃	Q₃₂	1	2	yes	direct product factor
27	C₁₆₃	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₃₂	—	163	1	no	maximal, Sylow
29	C₂×Q₁₆	—	163	2	no	—
30	Q₃₂	—	163	2	no	—
31	Q₃₂	—	163	1	no	—
32	Q₃₂	D₁₆₃	1	1	yes	characteristic, direct product factor
33	C₂×C₁₆	—	163	1	no	—
34	C₂×Q₈	—	326	2	no	—
35	Q₁₆	—	326	2	no	—
36	Q₁₆	—	163	2	no	—
37	Q₁₆	C₂×D₁₆₃	1	2	yes	—
38	C₂×C₈	—	163	1	no	—
39	C₁₆	—	163	1	no	—
40	C₁₆	C₂×D₁₆₃	1	1	yes	characteristic
41	Q₈	—	2	2	no	—
42	Q₈	—	326	2	no	—
43	Q₈	—	652	2	no	—
44	C₂×C₄	—	652	2	no	—
45	C₂×C₄	—	163	1	no	—
46	C₈	—	163	1	no	—
47	C₈	C₂²×D₁₆₃	1	1	yes	characteristic
48	C₂²	—	163	1	no	—
49	C₄	—	4	2	no	—
50	C₄	—	652	2	no	—
51	C₄	—	163	1	no	—
52	C₄	D₄×D₁₆₃	1	1	yes	characteristic
53	C₂	—	163	2	no	—
54	C₂	D₈×D₁₆₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₆₃
commutator, cosocle	C₈×C₁₆₃	C₂³
Frattini	C₈	C₂²×D₁₆₃
Fitting	Q₃₂×C₁₆₃	C₂
socle	C₂×C₁₆₃	C₂×D₈
prime radical	C₂×D₁₆₃	D₈
hypercenter	Q₃₂	D₁₆₃
hypocenter	C₁₆₃	C₂×Q₃₂
LCS	G ▷ C₈×C₁₆₃ ▷ C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₁₃₀₄	C₂	semidirect
3. #19104681	C₂	semidirect
5. Q₃₂×C₁₆₃	C₂	semidirect
26. D₁₆₃	Q₃₂	direct (N × H)
27. C₁₆₃	C₂×Q₃₂	semidirect
32. Q₃₂	D₁₆₃	direct (N × H)

Subgroups — Q32×D163 #23782091

Conjugacy classes of subgroups

Complements

Subgroups — Q₃₂×D₁₆₃ #23782091