Subgroups — #23781920

Order 10432.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14579682	C₂	1	1	yes	maximal, characteristic
2	#19104711	C₂	1	2	yes	maximal
3	#19104667	C₂	1	1	yes	maximal, characteristic, complemented
4	#19104659	C₂	1	2	yes	maximal, complemented
5	C₂×Q₁₆×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₆₃	C₂²	1	1	yes	characteristic
7	#14579682	—	2	2	no	—
8	C₂×C₁₆₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₆₃	C₂²	1	2	yes	—
10	Dic₁₆₃⋊C₄	—	2	2	no	—
11	(C₂×D₁₆₃)⋊C₄	—	2	2	no	—
12	C₂×Q₈×C₁₆₃	C₂²	1	2	yes	—
13	Q₁₆×C₁₆₃	—	2	2	no	—
14	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
15	C₂²×D₁₆₃	D₄	1	1	yes	characteristic
16	C₂×Dic₁₆₃	—	2	2	no	—
17	C₂×Dic₁₆₃	D₄	1	1	yes	characteristic
18	C₄×D₁₆₃	—	2	1	no	—
19	C₄×D₁₆₃	—	2	1	no	—
20	C₁₆₃⋊C₈	—	2	1	no	—
21	Q₈×C₁₆₃	—	2	2	no	—
22	Q₈×C₁₆₃	—	2	2	no	—
23	C₂×C₄×C₁₆₃	—	2	2	no	—
24	C₂×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
25	C₈×C₁₆₃	D₄	1	2	yes	—
26	C₂²×C₁₆₃	C₂×D₄	1	1	yes	characteristic
27	C₂×D₁₆₃	—	2	1	no	—
28	C₂×D₁₆₃	—	2	2	no	—
29	C₄×C₁₆₃	—	4	2	no	—
30	C₄×C₁₆₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₆₃	#41	1	1	yes	characteristic
32	Dic₁₆₃	—	2	1	no	—
33	Dic₁₆₃	—	4	2	no	—
34	C₂×C₁₆₃	#121	1	1	yes	characteristic
35	C₂×C₁₆₃	#137	1	2	yes	—
36	D₁₆₃	—	4	1	no	—
37	C₁₆₃	#470	1	1	yes	characteristic, complemented, Sylow
38	#470	—	163	1	no	maximal, Sylow
39	C₂×Q₁₆	D₁₆₃	1	1	yes	characteristic, complemented
40	C₂×M₁₆	—	163	1	no	—
41	C₂²⋊Q₈	—	163	2	no	—
42	#106	—	163	1	no	—
43	#103	—	163	2	no	—
44	C₂×Q₈	C₂×D₁₆₃	1	2	yes	—
45	C₂²×C₄	—	163	1	no	—
46	Q₁₆	—	2	2	no	—
47	M₁₆	—	326	2	no	—
48	C₂×C₈	—	163	1	no	—
49	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
50	C₄⋊C₄	—	326	2	no	—
51	C₄⋊C₄	—	163	2	no	—
52	C₂²⋊C₄	—	326	2	no	—
53	C₂³	—	163	1	no	—
54	Q₈	—	2	2	no	—
55	Q₈	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	326	1	no	—
58	C₂×C₄	—	326	1	no	—
59	C₂×C₄	—	326	2	no	—
60	C₂×C₄	—	163	1	no	—
61	C₂×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
62	C₈	—	326	1	no	—
63	C₈	C₂²⋊D₁₆₃	1	2	yes	—
64	C₂²	—	326	1	no	—
65	C₂²	—	326	2	no	—
66	C₂²	D₄×D₁₆₃	1	1	yes	characteristic
67	C₄	—	4	2	no	—
68	C₄	—	326	1	no	—
69	C₄	—	652	2	no	—
70	C₄	C₂×C₂²⋊D₁₆₃	1	1	yes	characteristic
71	C₄	#14579698	1	1	yes	characteristic
72	C₂	—	652	1	no	—
73	C₂	#19104706	1	1	yes	characteristic
74	C₂	#19104767	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	C₂²×C₁₆₃	C₂×D₄
prime radical	C₂²×D₁₆₃	D₄
hypercenter	C₂×Q₁₆	D₁₆₃
hypocenter	C₁₆₃	#470
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
3. #19104667	C₂	semidirect
4. #19104659	C₂	semidirect
5. C₂×Q₁₆×C₁₆₃	C₂	semidirect
37. C₁₆₃	#470	semidirect
39. C₂×Q₁₆	D₁₆₃	semidirect