Subgroups — #20265452

Order 6464.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692285	C₂	1	2	yes	maximal
2	C₂×Dic₄₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692191	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692173	C₂	1	2	yes	maximal, complemented
5	#131×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₀₂	C₂²	1	2	yes	—
7	Dic₄₀₄	—	2	1	no	—
8	Dic₄₀₄	—	2	1	no	—
9	#13108064	—	2	2	no	—
10	#13108062	—	2	2	no	—
11	#13108058	C₂²	1	2	yes	—
12	#41×C₁₀₁	C₂²	1	1	yes	characteristic
13	M₁₆×C₁₀₁	—	2	1	no	—
14	M₁₆×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₁₀₁	—	2	1	no	—
16	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
17	Q₈×C₁₀₁	D₄	1	1	yes	characteristic
18	D₄×C₁₀₁	—	2	1	no	—
19	D₄×C₁₀₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₁	—	2	1	no	—
21	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₀₁	—	2	2	no	—
23	Dic₂₀₂	—	2	2	no	—
24	Dic₂₀₂	—	2	2	no	—
25	C₈×C₁₀₁	—	2	1	no	—
26	C₈×C₁₀₁	D₄	1	1	yes	characteristic
27	C₈×C₁₀₁	D₄	1	1	yes	characteristic
28	#11717579	—	2	2	no	—
29	C₂²×C₁₀₁	—	2	1	no	—
30	C₂²×C₁₀₁	#41	1	1	yes	characteristic
31	C₄×C₁₀₁	—	2	1	no	—
32	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
34	Dic₁₀₁	—	4	2	no	—
35	C₂×C₁₀₁	—	2	1	no	—
36	C₂×C₁₀₁	—	4	1	no	—
37	C₂×C₁₀₁	#121	1	1	yes	characteristic
38	C₁₀₁	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	101	1	no	maximal, Sylow
40	#137	—	101	2	no	—
41	C₂×Q₁₆	—	101	1	no	—
42	#131	D₁₀₁	1	1	yes	characteristic
43	#108	—	101	1	no	—
44	#101	—	101	2	no	—
45	#41	C₂×D₁₀₁	1	1	yes	characteristic
46	C₂×Q₈	—	101	2	no	—
47	Q₁₆	—	202	2	no	—
48	Q₁₆	—	202	1	no	—
49	Q₁₆	—	202	1	no	—
50	SD₁₆	—	202	2	no	—
51	M₁₆	—	2	1	no	—
52	M₁₆	—	101	2	no	—
53	M₁₆	C₂×D₁₀₁	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
56	Q₈	—	202	2	no	—
57	Q₈	—	202	2	no	—
58	Q₈	D₄₀₄	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	D₄₀₄	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	202	2	no	—
63	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	—	202	2	no	—
66	C₈	C₂²⋊D₁₀₁	1	1	yes	characteristic
67	C₈	C₂²⋊D₁₀₁	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	#13108074	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	404	2	no	—
72	C₄	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
73	C₄	C₂×D₄₀₄	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#15692229	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692229
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#131×C₁₀₁	C₂
socle	C₂×C₁₀₁	#121
hypercenter	#131	D₁₀₁
hypocenter	C₁₀₁	#473
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₄₀₄	C₂	semidirect
3. #15692191	C₂	semidirect
4. #15692173	C₂	semidirect
38. C₁₀₁	#473	semidirect