Subgroups — Dic₁₆₃⋊C₁₆ #23781483

Order 10432.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₁₆₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₆₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆₃⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₁₆₃	C₄	1	1	yes	characteristic
6	C₁₆₃⋊C₁₆	—	2	1	no	—
7	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₆₃	—	2	1	no	—
9	C₂×Dic₁₆₃	C₈	1	1	yes	characteristic
10	C₂×Dic₁₆₃	C₈	1	1	yes	characteristic
11	C₁₆₃⋊C₈	—	2	1	no	—
12	C₂×C₄×C₁₆₃	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₆₃	D₄	1	1	yes	characteristic
14	C₈×C₁₆₃	Q₈	1	1	yes	characteristic
15	C₂²×C₁₆₃	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₆₃	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₆₃	M₁₆	1	1	yes	characteristic
18	Dic₁₆₃	—	2	1	no	—
19	Dic₁₆₃	C₁₆	1	2	yes	complemented
20	C₂×C₁₆₃	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₁₆₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₆₃	M₃₂	1	1	yes	characteristic
23	C₁₆₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	163	1	no	maximal, Sylow
25	C₂×C₁₆	—	163	1	no	—
26	C₂×C₁₆	D₁₆₃	1	1	yes	characteristic
27	C₄×C₈	—	163	1	no	—
28	C₂×C₈	—	163	1	no	—
29	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
30	C₄²	—	163	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	326	1	no	—
33	C₂×C₄	—	163	1	no	—
34	C₂×C₄	—	163	1	no	—
35	C₂×C₄	C₄×D₁₆₃	1	1	yes	characteristic
36	C₈	—	326	1	no	—
37	C₈	C₂²⋊D₁₆₃	1	1	yes	characteristic
38	C₈	Dic₃₂₆	1	1	yes	characteristic
39	C₂²	C₈×D₁₆₃	1	1	yes	characteristic
40	C₄	—	326	1	no	—
41	C₄	—	163	2	no	—
42	C₄	Dic₁₆₃⋊C₄	1	1	yes	characteristic
43	C₄	#14579682	1	1	yes	characteristic
44	C₂	Dic₁₆₃⋊C₈	1	1	yes	characteristic
45	C₂	C₁₆×D₁₆₃	1	1	yes	characteristic
46	C₂	#19104674	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₆₃
commutator	C₂×C₁₆₃	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	C₂×C₈
cosocle	C₂×C₈×C₁₆₃	C₂²
hypercenter	C₂×C₁₆	D₁₆₃
hypocenter	C₁₆₃	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₁₆₃	C₁₆	semidirect
23. C₁₆₃	C₄⋊C₁₆	semidirect

Subgroups — Dic163⋊C16 #23781483

Conjugacy classes of subgroups

Complements

Subgroups — Dic₁₆₃⋊C₁₆ #23781483