Subgroups — C₂×#15692326 #20266191

Order 6464.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108084	C₂	1	2	yes	maximal
2	#15692326	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	#13108084	—	2	2	no	—
5	#13108084	C₂²	1	4	yes	—
6	C₂×#11717581	—	2	2	no	—
7	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
8	C₂×#11717579	C₄	1	1	yes	characteristic
9	C₈×D₁₀₁	C₄	1	2	yes	—
10	C₈×D₁₀₁	C₂²	1	2	yes	—
11	C₂×C₈×C₁₀₁	C₄	1	1	yes	characteristic
12	C₂²×D₁₀₁	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
15	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₄×D₁₀₁	D₄	1	1	yes	characteristic
17	C₄×D₁₀₁	Q₈	1	1	yes	characteristic
18	C₄×D₁₀₁	C₂³	1	1	yes	characteristic
19	#11717581	—	2	4	no	—
20	C₈×C₁₀₁	C₂×C₄	1	2	yes	—
21	#11717579	C₂×C₄	1	2	yes	—
22	C₂²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₁₀₁	—	2	2	no	—
24	C₂×D₁₀₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₁₀₁	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
28	Dic₁₀₁	C₄⋊C₄	1	1	yes	characteristic
29	Dic₁₀₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₁₀₁	#108	1	2	yes	complemented
31	C₂×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₁₀₁	—	2	1	no	—
33	D₁₀₁	—	2	1	no	—
34	C₁₀₁	C₂×#108	1	1	yes	characteristic, complemented, Sylow
35	C₂×#108	—	101	1	no	maximal, Sylow
36	C₂×M₁₆	—	101	2	no	—
37	C₂²×C₈	—	101	1	no	—
38	#108	—	101	4	no	—
39	C₂²×C₄	—	101	1	no	—
40	M₁₆	—	101	4	no	—
41	M₁₆	—	202	2	no	—
42	C₂×C₈	—	101	1	no	—
43	C₂×C₈	—	101	2	no	—
44	C₂×C₈	—	101	2	no	—
45	C₂×C₈	—	202	2	no	—
46	C₂×C₈	#87938	1	1	yes	characteristic
47	C₂³	—	101	1	no	—
48	C₂×C₄	—	101	1	no	—
49	C₂×C₄	—	101	1	no	—
50	C₂×C₄	—	101	1	no	—
51	C₂×C₄	—	101	1	no	—
52	C₂×C₄	—	101	1	no	—
53	C₂×C₄	C₂×#87938	1	1	yes	characteristic
54	C₈	—	101	2	no	—
55	C₈	—	202	4	no	—
56	C₈	C₂×#87938	1	2	yes	—
57	C₂²	—	101	1	no	—
58	C₂²	—	101	1	no	—
59	C₂²	—	202	2	no	—
60	C₂²	C₄⋊#87938	1	1	yes	characteristic
61	C₄	—	101	1	no	—
62	C₄	—	101	1	no	—
63	C₄	C₄⋊#87938	1	1	yes	characteristic
64	C₄	C₂²×#87938	1	1	yes	characteristic
65	C₂	—	202	1	no	—
66	C₂	—	202	1	no	—
67	C₂	#15692326	1	2	yes	direct product factor
68	C₂	C₂×C₄⋊#87938	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#87938
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₄	C₂²×#87938
Fitting	C₂×C₈×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₄⋊C₄
hypercenter	C₂×C₈	#87938
hypocenter	C₁₀₁	C₂×#108
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #15692326	C₂	direct (N × H)
30. C₂×C₁₀₁	#108	semidirect
34. C₁₀₁	C₂×#108	semidirect
67. C₂	#15692326	direct (N × H)

Subgroups — C2×#15692326 #20266191

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692326 #20266191