Subgroups — #20266113

Order 6464.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#87938	C₂	1	2	yes	maximal
2	(C₂×#87938)⋊C₄	C₂	1	4	yes	maximal
3	C₄²×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#87938	C₂²	1	4	yes	—
5	C₄×#87938	C₄	1	8	yes	complemented
6	C₂×C₄×D₁₀₁	C₂²	1	2	yes	—
7	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
8	C₄×Dic₁₀₁	C₄	1	2	yes	complemented
9	C₄×Dic₁₀₁	C₄	1	1	yes	characteristic, complemented
10	C₄²×C₁₀₁	C₄	1	1	yes	characteristic, complemented
11	C₂²×D₁₀₁	C₂³	1	1	yes	characteristic
12	C₂×#87938	—	2	8	no	—
13	C₂×#87938	C₂×C₄	1	8	yes	—
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	2	yes	—
17	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
18	C₄×D₁₀₁	—	2	4	no	—
19	C₄×D₁₀₁	C₂×C₄	1	4	yes	—
20	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₁₀₁	C₂²×C₄	1	2	yes	—
22	C₂×D₁₀₁	#41	1	4	yes	—
23	#87938	—	2	8	no	—
24	C₄×C₁₀₁	—	2	2	no	—
25	C₄×C₁₀₁	C₄²	1	2	yes	—
26	Dic₁₀₁	—	2	2	no	—
27	Dic₁₀₁	C₄²	1	2	yes	—
28	C₂×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
29	C₂×C₁₀₁	#117	1	2	yes	—
30	D₁₀₁	#117	1	4	yes	—
31	C₁₀₁	#376	1	1	yes	characteristic, complemented, Sylow
32	#376	—	101	1	no	maximal, Sylow
33	C₂×C₄²	—	101	2	no	—
34	C₂×C₄²	—	101	1	no	—
35	#95	—	101	4	no	—
36	C₂²×C₄	—	101	1	no	—
37	C₂²×C₄	—	101	4	no	—
38	C₂²×C₄	—	101	2	no	—
39	C₄²	—	101	8	no	—
40	C₄²	—	101	2	no	—
41	C₄²	—	101	1	no	—
42	C₄²	#87938	1	1	yes	characteristic, complemented
43	C₂³	—	101	1	no	—
44	C₂×C₄	—	101	1	no	—
45	C₂×C₄	—	101	4	no	—
46	C₂×C₄	—	101	8	no	—
47	C₂×C₄	—	101	2	no	—
48	C₂×C₄	—	202	4	no	—
49	C₂×C₄	—	202	8	no	—
50	C₂×C₄	C₂×#87938	1	2	yes	—
51	C₂×C₄	C₂×#87938	1	1	yes	characteristic
52	C₂²	—	101	2	no	—
53	C₂²	—	101	4	no	—
54	C₂²	C₂²×#87938	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	—	101	2	no	—
57	C₄	—	202	8	no	—
58	C₄	—	202	2	no	—
59	C₄	C₄×#87938	1	2	yes	—
60	C₂	—	101	4	no	—
61	C₂	C₂×C₄×#87938	1	1	yes	characteristic
62	C₂	#15692334	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#87938
commutator	C₂×C₁₀₁	C₂×C₄²
Frattini	C₂²	C₂²×#87938
Fitting	C₄²×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂²×C₄
hypercenter	C₄²	#87938
hypocenter	C₁₀₁	#376
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
5. C₄×#87938	C₄	semidirect
8. C₄×Dic₁₀₁	C₄	semidirect
9. C₄×Dic₁₀₁	C₄	semidirect
10. C₄²×C₁₀₁	C₄	semidirect
31. C₁₀₁	#376	semidirect
42. C₄²	#87938	semidirect