Subgroups — #23782032

Order 10432.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19104733	C₂	1	1	yes	maximal, characteristic
2	#19104726	C₂	1	1	yes	maximal, characteristic
3	#19104660	C₂	1	1	yes	maximal, characteristic
4	#19104659	C₂	1	1	yes	maximal, characteristic
5	#19104658	C₂	1	1	yes	maximal, characteristic
6	#19104645	C₂	1	1	yes	maximal, characteristic
7	#103×C₁₆₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₂₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₆₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₆₃	—	2	1	no	—
11	C₄⋊Dic₁₆₃	C₂²	1	1	yes	characteristic
12	Dic₁₆₃⋊C₄	—	2	1	no	—
13	Dic₁₆₃⋊C₄	—	2	1	no	—
14	Dic₁₆₃⋊C₄	—	2	1	no	—
15	C₄×Dic₁₆₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₆₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₆₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₆₃	C₂²	1	1	yes	characteristic
19	Dic₃₂₆	—	2	1	no	—
20	Dic₃₂₆	—	2	1	no	—
21	C₂×Dic₁₆₃	—	2	1	no	—
22	C₂×Dic₁₆₃	—	2	1	no	—
23	C₂×Dic₁₆₃	D₄	1	1	yes	characteristic
24	C₂×Dic₁₆₃	D₄	1	1	yes	characteristic
25	C₁₆₃⋊C₈	—	2	1	no	—
26	Q₈×C₁₆₃	—	2	1	no	—
27	Q₈×C₁₆₃	—	2	1	no	—
28	C₂×C₄×C₁₆₃	—	2	1	no	—
29	C₂×C₄×C₁₆₃	—	2	1	no	—
30	C₂×C₄×C₁₆₃	C₂³	1	1	yes	characteristic
31	C₈×C₁₆₃	—	2	1	no	—
32	C₂²×C₁₆₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₆₃	—	4	1	no	—
34	C₄×C₁₆₃	—	4	1	no	—
35	C₄×C₁₆₃	#41	1	1	yes	characteristic
36	C₄×C₁₆₃	#41	1	1	yes	characteristic
37	Dic₁₆₃	—	2	1	no	—
38	Dic₁₆₃	—	2	1	no	—
39	Dic₁₆₃	—	4	1	no	—
40	Dic₁₆₃	—	4	1	no	—
41	C₂×C₁₆₃	#124	1	1	yes	characteristic
42	C₂×C₁₆₃	#137	1	1	yes	characteristic
43	C₂×C₁₆₃	#137	1	1	yes	characteristic
44	C₁₆₃	#491	1	1	yes	characteristic, complemented, Sylow
45	#491	—	163	1	no	maximal, Sylow
46	C₄⋊Q₈	—	163	1	no	—
47	#125	—	163	1	no	—
48	#103	—	163	1	no	—
49	#103	—	163	1	no	—
50	#103	—	163	1	no	—
51	#103	D₁₆₃	1	1	yes	characteristic
52	#97	—	163	1	no	—
53	C₂×Q₈	—	163	1	no	—
54	C₂×Q₈	C₂×D₁₆₃	1	1	yes	characteristic
55	C₂×C₈	—	163	1	no	—
56	C₂×C₈	C₂×D₁₆₃	1	1	yes	characteristic
57	C₄⋊C₄	—	326	1	no	—
58	C₄⋊C₄	—	326	1	no	—
59	C₄⋊C₄	—	326	1	no	—
60	C₄⋊C₄	—	326	1	no	—
61	C₄⋊C₄	—	163	1	no	—
62	C₄⋊C₄	C₂×D₁₆₃	1	1	yes	characteristic
63	C₄²	—	163	1	no	—
64	Q₈	—	2	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	326	1	no	—
67	Q₈	—	326	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	326	1	no	—
71	C₂×C₄	—	326	1	no	—
72	C₂×C₄	—	163	1	no	—
73	C₂×C₄	—	163	1	no	—
74	C₂×C₄	C₂²×D₁₆₃	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	326	1	no	—
77	C₂²	D₄×D₁₆₃	1	1	yes	characteristic
78	C₄	—	4	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	326	1	no	—
81	C₄	—	326	1	no	—
82	C₄	—	652	1	no	—
83	C₄	—	652	1	no	—
84	C₄	#14579698	1	1	yes	characteristic
85	C₄	#14579699	1	1	yes	characteristic
86	C₂	#19104721	1	1	yes	characteristic
87	C₂	#19104764	1	1	yes	characteristic
88	C₂	#19104767	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₆₃
commutator, cosocle	C₂×C₄×C₁₆₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₆₃
Fitting	#103×C₁₆₃	C₂
socle, prime radical	C₂²×C₁₆₃	C₂×D₄
hypercenter	#103	D₁₆₃
hypocenter	C₁₆₃	#491
LCS	G ▷ C₂×C₄×C₁₆₃ ▷ C₂×C₁₆₃ ▷ C₁₆₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
44. C₁₆₃	#491	semidirect