Subgroups — #20265187

Order 6464.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₀₂	C₂	1	1	yes	maximal, characteristic
2	#15692214	C₂	1	1	yes	maximal, characteristic
3	#15692180	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₀₂	—	2	1	no	—
6	C₂×Dic₂₀₂	—	2	2	no	—
7	C₂×Dic₂₀₂	C₄	1	4	yes	complemented
8	C₂×Dic₂₀₂	C₂²	1	2	yes	—
9	C₂²×Dic₁₀₁	—	2	1	no	—
10	C₄⋊Dic₁₀₁	C₂²	1	2	yes	—
11	C₂²⋊Dic₁₀₁	—	2	1	no	—
12	C₄×Dic₁₀₁	—	2	1	no	—
13	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	M₁₆×C₁₀₁	—	2	2	no	—
15	C₂×C₈×C₁₀₁	C₂²	1	2	yes	—
16	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
20	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₀₁	—	2	4	no	—
22	C₂×Dic₁₀₁	—	2	2	no	—
23	C₂×Dic₁₀₁	—	2	2	no	—
24	Dic₂₀₂	—	2	4	no	—
25	Dic₂₀₂	—	2	2	no	—
26	Dic₂₀₂	C₂×C₄	1	4	yes	—
27	C₈×C₁₀₁	—	2	2	no	—
28	C₂²×C₁₀₁	—	2	2	no	—
29	C₂²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
32	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
34	Dic₁₀₁	—	2	4	no	—
35	Dic₁₀₁	—	4	2	no	—
36	C₂×C₁₀₁	—	2	2	no	—
37	C₂×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₁₀₁	#137	1	2	yes	—
39	C₁₀₁	#419	1	1	yes	characteristic, complemented, Sylow
40	#419	—	101	1	no	maximal, Sylow
41	C₂²×Q₈	—	101	1	no	—
42	C₂×M₁₆	D₁₀₁	1	1	yes	characteristic
43	#117	—	101	1	no	—
44	#103	—	101	4	no	—
45	C₂×Q₈	—	101	4	no	—
46	C₂×Q₈	—	101	2	no	—
47	C₂×Q₈	—	202	1	no	—
48	C₂×Q₈	—	202	2	no	—
49	C₂²×C₄	—	202	1	no	—
50	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
51	M₁₆	—	2	2	no	—
52	C₂×C₈	C₂×D₁₀₁	1	2	yes	—
53	C₄⋊C₄	—	101	2	no	—
54	C₂²⋊C₄	—	202	1	no	—
55	C₄²	—	202	1	no	—
56	C₂³	D₄₀₄	1	1	yes	characteristic
57	Q₈	—	101	4	no	—
58	Q₈	—	202	4	no	—
59	Q₈	—	202	2	no	—
60	C₂×C₄	—	202	2	no	—
61	C₂×C₄	—	202	4	no	—
62	C₂×C₄	—	202	2	no	—
63	C₂×C₄	C₄×D₁₀₁	1	2	yes	—
64	C₂×C₄	D₄₀₄	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊D₁₀₁	1	2	yes	—
66	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	#13108051	1	2	yes	—
70	C₂²	C₂×D₄₀₄	1	1	yes	characteristic
71	C₄	—	404	2	no	—
72	C₄	—	202	4	no	—
73	C₄	#13108051	1	2	yes	—
74	C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
75	C₄	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
76	C₂	—	2	2	no	—
77	C₂	C₂×#13108051	1	1	yes	characteristic
78	C₂	#15692288	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₀₄
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₂×M₁₆×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	C₂×M₁₆	D₁₀₁
hypocenter	C₁₀₁	#419
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #15692180	C₂	semidirect
7. C₂×Dic₂₀₂	C₄	semidirect
39. C₁₀₁	#419	semidirect