Subgroups — #23782043

Order 10432.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579689	C₂	1	2	yes	maximal
3	#19104733	C₂	1	2	yes	maximal
4	C₈×Dic₁₆₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₁₆₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₂₆	C₂²	1	2	yes	—
7	Dic₆₅₂	—	2	2	no	—
8	#14579689	—	2	4	no	—
9	C₂×C₁₆₃⋊C₈	C₂²	1	1	yes	characteristic
10	Dic₁₆₃⋊C₄	—	2	4	no	—
11	C₄×Dic₁₆₃	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₁₆₃	C₂²	1	2	yes	—
13	Q₁₆×C₁₆₃	—	2	2	no	—
14	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
15	Dic₃₂₆	—	2	2	no	—
16	Dic₃₂₆	—	2	2	no	—
17	C₂×Dic₁₆₃	—	2	2	no	—
18	C₂×Dic₁₆₃	D₄	1	2	yes	—
19	C₁₆₃⋊C₈	D₄	1	2	yes	—
20	Q₈×C₁₆₃	—	2	2	no	—
21	Q₈×C₁₆₃	—	2	2	no	—
22	C₂×C₄×C₁₆₃	—	2	2	no	—
23	C₂×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
24	C₈×C₁₆₃	D₄	1	2	yes	—
25	C₂²×C₁₆₃	C₂×D₄	1	1	yes	characteristic
26	C₄×C₁₆₃	—	4	2	no	—
27	C₄×C₁₆₃	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₆₃	C₂×D₄	1	1	yes	characteristic
29	Dic₁₆₃	—	4	2	no	—
30	Dic₁₆₃	Q₁₆	1	4	yes	complemented
31	C₂×C₁₆₃	#127	1	1	yes	characteristic
32	C₂×C₁₆₃	C₂×Q₁₆	1	2	yes	—
33	C₁₆₃	#494	1	1	yes	characteristic, complemented, Sylow
34	#494	—	163	1	no	maximal, Sylow
35	C₂×Q₁₆	—	163	2	no	—
36	C₂×Q₁₆	—	163	1	no	—
37	C₂×Q₁₆	D₁₆₃	1	1	yes	characteristic
38	C₄⋊Q₈	—	163	2	no	—
39	C₄×C₈	—	163	1	no	—
40	C₂×Q₈	—	163	2	no	—
41	C₂×Q₈	C₂×D₁₆₃	1	2	yes	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	326	4	no	—
44	Q₁₆	—	326	2	no	—
45	C₂×C₈	—	163	1	no	—
46	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
47	C₄⋊C₄	—	326	4	no	—
48	C₄²	—	163	1	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	326	2	no	—
52	Q₈	—	326	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	326	2	no	—
55	C₂×C₄	—	163	2	no	—
56	C₂×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
57	C₈	—	163	2	no	—
58	C₈	C₂²⋊D₁₆₃	1	2	yes	—
59	C₂²	D₄×D₁₆₃	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	652	2	no	—
62	C₄	—	163	4	no	—
63	C₄	D₄×D₁₆₃	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₁₆₃	1	1	yes	characteristic
65	C₂	#19104731	1	1	yes	characteristic
66	C₂	Q₁₆×D₁₆₃	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₆₃
commutator, cosocle	C₂×C₄×C₁₆₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₆₃
Fitting	C₂×Q₁₆×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	C₂×D₄
hypercenter	C₂×Q₁₆	D₁₆₃
hypocenter	C₁₆₃	#494
LCS	G ▷ C₂×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
30. Dic₁₆₃	Q₁₆	semidirect
33. C₁₆₃	#494	semidirect