Subgroups — #23781772

Order 10432.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₁₆₃	C₂	1	2	yes	maximal
2	#19104667	C₂	1	1	yes	maximal, characteristic
3	#19104659	C₂	1	2	yes	maximal
4	#19104645	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₁₆₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₆₃⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₁₆₃	—	2	2	no	—
8	C₄⋊Dic₁₆₃	C₂²	1	2	yes	—
9	C₄×Dic₁₆₃	—	2	2	no	—
10	C₄×Dic₁₆₃	C₂²	1	1	yes	characteristic
11	C₂×Q₈×C₁₆₃	C₂²	1	2	yes	—
12	Q₁₆×C₁₆₃	C₄	1	4	yes	complemented
13	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₁₆₃	—	2	2	no	—
15	C₂×Dic₁₆₃	D₄	1	2	yes	—
16	C₁₆₃⋊C₈	—	2	1	no	—
17	Q₈×C₁₆₃	—	2	2	no	—
18	Q₈×C₁₆₃	C₂×C₄	1	4	yes	—
19	C₂×C₄×C₁₆₃	—	2	2	no	—
20	C₂×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
21	C₈×C₁₆₃	C₂×C₄	1	2	yes	—
22	C₂²×C₁₆₃	C₂×D₄	1	1	yes	characteristic
23	C₄×C₁₆₃	—	2	4	no	—
24	C₄×C₁₆₃	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₁₆₃	#41	1	1	yes	characteristic
26	Dic₁₆₃	—	2	2	no	—
27	Dic₁₆₃	—	4	2	no	—
28	C₂×C₁₆₃	C₄×D₄	1	1	yes	characteristic
29	C₂×C₁₆₃	#137	1	2	yes	—
30	C₁₆₃	#441	1	1	yes	characteristic, complemented, Sylow
31	#441	—	163	1	no	maximal, Sylow
32	C₂×Q₁₆	D₁₆₃	1	1	yes	characteristic
33	C₄×Q₈	—	163	2	no	—
34	#106	—	163	1	no	—
35	#103	—	163	2	no	—
36	#97	—	163	1	no	—
37	C₂×Q₈	C₂×D₁₆₃	1	2	yes	—
38	Q₁₆	Dic₁₆₃	1	4	yes	complemented
39	C₂×C₈	—	163	1	no	—
40	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
41	C₄⋊C₄	—	326	2	no	—
42	C₄⋊C₄	—	163	2	no	—
43	C₄²	—	326	2	no	—
44	C₄²	—	163	1	no	—
45	Q₈	—	2	2	no	—
46	Q₈	C₂×Dic₁₆₃	1	4	yes	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	326	2	no	—
49	C₂×C₄	—	163	2	no	—
50	C₂×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
51	C₈	—	326	1	no	—
52	C₈	C₂×Dic₁₆₃	1	2	yes	—
53	C₂²	D₄×D₁₆₃	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	326	2	no	—
56	C₄	—	652	2	no	—
57	C₄	C₂²×Dic₁₆₃	1	1	yes	characteristic
58	C₄	#14579698	1	1	yes	characteristic
59	C₂	D₄×Dic₁₆₃	1	1	yes	characteristic
60	C₂	#19104767	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₆₃
commutator	C₄×C₁₆₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₆₃
Fitting	C₂×Q₁₆×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	C₂×D₄
cosocle	C₂×C₄×C₁₆₃	C₂³
hypercenter	C₂×Q₁₆	D₁₆₃
hypocenter	C₁₆₃	#441
LCS	G ▷ C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
12. Q₁₆×C₁₆₃	C₄	semidirect
30. C₁₆₃	#441	semidirect
38. Q₁₆	Dic₁₆₃	semidirect