Subgroups — #20265906

Order 6464.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692255	C₂	1	3	yes	maximal
2	#15692246	C₂	1	6	yes	maximal
3	Q₈×Dic₁₀₁	C₂	1	2	yes	maximal
4	C₄×Dic₂₀₂	C₂	1	3	yes	maximal
5	C₄×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₀₂	C₂²	1	3	yes	—
7	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₁₀₁	C₂²	1	6	yes	—
9	C₄⋊Dic₁₀₁	C₂²	1	6	yes	—
10	#13108053	C₂²	1	6	yes	—
11	C₄×Dic₁₀₁	C₂²	1	6	yes	—
12	C₂×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₀₁	C₂²	1	3	yes	—
14	C₄²×C₁₀₁	C₂²	1	3	yes	—
15	Q₈×C₁₀₁	Q₈	1	4	yes	complemented
16	C₂×C₄×C₁₀₁	C₂³	1	3	yes	—
17	C₂×C₄×C₁₀₁	C₂³	1	3	yes	—
18	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₁	C₂³	1	2	yes	—
20	C₂×Dic₁₀₁	C₂³	1	6	yes	—
21	Dic₂₀₂	—	2	6	no	—
22	C₂²×C₁₀₁	C₂⁴	1	1	yes	characteristic
23	C₄×C₁₀₁	—	2	3	no	—
24	C₄×C₁₀₁	C₂×Q₈	1	6	yes	—
25	C₄×C₁₀₁	#41	1	2	yes	—
26	Dic₁₀₁	—	2	6	no	—
27	Dic₁₀₁	—	2	2	no	—
28	C₂×C₁₀₁	C₂²×Q₈	1	1	yes	characteristic
29	C₂×C₁₀₁	C₂×#41	1	1	yes	characteristic
30	C₂×C₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
31	C₁₀₁	#557	1	1	yes	characteristic, complemented, Sylow
32	#557	—	101	1	no	maximal, Sylow
33	C₄⋊Q₈	—	101	3	no	—
34	#125	—	101	6	no	—
35	C₄×Q₈	—	101	2	no	—
36	C₄×Q₈	—	101	3	no	—
37	C₄×Q₈	D₁₀₁	1	1	yes	characteristic
38	C₂×Q₈	—	101	3	no	—
39	C₂×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
40	C₄⋊C₄	—	101	6	no	—
41	C₄⋊C₄	—	101	1	no	—
42	C₄⋊C₄	—	101	6	no	—
43	C₄⋊C₄	—	101	6	no	—
44	C₄⋊C₄	C₂×D₁₀₁	1	3	yes	—
45	C₄²	—	101	6	no	—
46	C₄²	C₂×D₁₀₁	1	3	yes	—
47	Q₈	—	202	6	no	—
48	Q₈	Dic₂₀₂	1	4	yes	complemented
49	C₂×C₄	—	101	2	no	—
50	C₂×C₄	—	101	6	no	—
51	C₂×C₄	C₂²×D₁₀₁	1	3	yes	—
52	C₂×C₄	C₂²×D₁₀₁	1	3	yes	—
53	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
54	C₂²	C₂³×D₁₀₁	1	1	yes	characteristic
55	C₄	—	2	3	no	—
56	C₄	—	202	6	no	—
57	C₄	—	202	2	no	—
58	C₄	C₂×Dic₂₀₂	1	6	yes	—
59	C₄	#13108075	1	2	yes	—
60	C₂	C₂²×Dic₂₀₂	1	1	yes	characteristic
61	C₂	C₂×#13108075	1	1	yes	characteristic
62	C₂	#15692302	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₀₁
commutator, socle	C₂²×C₁₀₁	C₂⁴
Fitting	C₄×Q₈×C₁₀₁	C₂
hypercenter	C₄×Q₈	D₁₀₁
hypocenter	C₁₀₁	#557
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
15. Q₈×C₁₀₁	Q₈	semidirect
31. C₁₀₁	#557	semidirect
48. Q₈	Dic₂₀₂	semidirect