Subgroups — #20266226

Order 6464.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692322	C₂	1	2	yes	maximal
2	C₄⋊#11717581	C₂	1	1	yes	maximal, characteristic
3	C₄×#11717581	C₂	1	1	yes	maximal, characteristic
4	C₄×#11717581	C₂	1	2	yes	maximal
5	#15692220	C₂	1	1	yes	maximal, characteristic
6	C₂×#11717581	C₂²	1	2	yes	—
7	C₂×#11717581	C₂²	1	1	yes	characteristic
8	C₂×#11717581	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₀₂	C₄	1	1	yes	characteristic
10	#13108053	C₄	1	2	yes	—
11	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
12	C₄×Dic₁₀₁	C₂²	1	2	yes	—
13	C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₀₁	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₀₁	C₂³	1	1	yes	characteristic
19	Dic₂₀₂	C₈	1	4	yes	complemented
20	#11717581	—	2	2	no	—
21	#11717581	—	2	1	no	—
22	#11717581	Q₈	1	2	yes	complemented
23	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₀₁	—	2	2	no	—
25	C₄×C₁₀₁	C₂×C₈	1	2	yes	—
26	Dic₁₀₁	—	2	1	no	—
27	Dic₁₀₁	C₂×C₈	1	4	yes	—
28	Dic₁₀₁	C₂×Q₈	1	1	yes	characteristic
29	Dic₁₀₁	#41	1	1	yes	characteristic
30	C₂×C₁₀₁	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₁₀₁	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₁₀₁	#131	1	1	yes	characteristic
33	C₁₀₁	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
34	C₈×Q₈	—	101	1	no	maximal, Sylow
35	C₄×Q₈	—	101	1	no	—
36	C₄⋊C₈	—	101	1	no	—
37	C₄⋊C₈	—	101	2	no	—
38	C₄×C₈	—	101	2	no	—
39	C₄×C₈	—	101	1	no	—
40	C₂×Q₈	—	101	1	no	—
41	C₂×C₈	—	101	1	no	—
42	C₂×C₈	—	101	2	no	—
43	C₂×C₈	—	101	1	no	—
44	C₄⋊C₄	—	101	2	no	—
45	C₄⋊C₄	#87938	1	1	yes	characteristic
46	C₄²	—	101	2	no	—
47	C₄²	—	101	1	no	—
48	Q₈	—	101	4	no	—
49	C₂×C₄	—	101	1	no	—
50	C₂×C₄	—	101	2	no	—
51	C₂×C₄	—	101	1	no	—
52	C₂×C₄	C₂×#87938	1	2	yes	—
53	C₂×C₄	C₂×#87938	1	1	yes	characteristic
54	C₈	—	101	2	no	—
55	C₈	—	202	2	no	—
56	C₈	—	202	1	no	—
57	C₂²	C₂²×#87938	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	101	1	no	—
60	C₄	—	101	1	no	—
61	C₄	—	101	4	no	—
62	C₄	—	202	1	no	—
63	C₄	D₁₀₁⋊C₈	1	2	yes	—
64	C₂	Q₈×#87938	1	1	yes	characteristic
65	C₂	C₂×D₁₀₁⋊C₈	1	1	yes	characteristic
66	C₂	#15692342	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#87938
commutator	C₂×C₁₀₁	C₂²×C₈
Fitting	C₄⋊C₄×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂²×C₄
hypercenter	C₄⋊C₄	#87938
hypocenter	C₁₀₁	C₈×Q₈
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
19. Dic₂₀₂	C₈	semidirect
22. #11717581	Q₈	semidirect
33. C₁₀₁	C₈×Q₈	semidirect