Subgroups — C₂×#15692186 #20265207

Order 6464.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11717579	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#15692186	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₀₁	—	2	1	no	—
6	C₂×#11717579	C₄	1	4	yes	complemented
7	C₂×#11717579	C₂²	1	2	yes	—
8	C₄⋊Dic₁₀₁	—	2	1	no	—
9	C₄⋊Dic₁₀₁	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₀₁	—	2	1	no	—
11	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₀₁	—	2	1	no	—
13	C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
14	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₁	—	2	2	no	—
16	C₂×C₄×C₁₀₁	—	4	2	no	—
17	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₁	Q₈	1	2	yes	—
20	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₀₁	—	2	2	no	—
22	C₂×Dic₁₀₁	—	4	2	no	—
23	#11717579	C₂×C₄	1	4	yes	complemented
24	C₂²×C₁₀₁	C₄⋊C₄	1	2	yes	—
25	C₂²×C₁₀₁	SD₁₆	1	2	yes	—
26	C₂²×C₁₀₁	SD₁₆	1	2	yes	—
27	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₀₁	—	4	2	no	—
29	C₄×C₁₀₁	C₄⋊C₄	1	2	yes	—
30	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
32	Dic₁₀₁	—	4	2	no	—
33	C₂×C₁₀₁	#106	1	4	yes	complemented
34	C₂×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
36	C₂×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
37	C₁₀₁	C₂×#106	1	1	yes	characteristic, complemented, Sylow
38	C₂×#106	—	101	1	no	maximal, Sylow
39	C₂²×C₈	—	101	1	no	—
40	C₂×C₄⋊C₄	—	101	1	no	—
41	C₂×C₄⋊C₄	D₁₀₁	1	1	yes	characteristic
42	#106	—	101	4	no	—
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	202	1	no	—
45	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
46	C₂×C₈	—	101	4	no	—
47	C₂×C₈	—	101	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	101	2	no	—
50	C₄⋊C₄	—	202	1	no	—
51	C₄⋊C₄	C₂×D₁₀₁	1	2	yes	—
52	C₂³	C₂²⋊D₁₀₁	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	404	2	no	—
56	C₂×C₄	—	202	2	no	—
57	C₂×C₄	Dic₂₀₂	1	2	yes	—
58	C₂×C₄	C₄×D₁₀₁	1	2	yes	—
59	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
61	C₈	—	101	4	no	—
62	C₂²	#13108053	1	2	yes	—
63	C₂²	#13108061	1	2	yes	—
64	C₂²	#13108062	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	404	2	no	—
68	C₄	#13108053	1	2	yes	—
69	C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
70	C₄	C₂×Dic₂₀₂	1	1	yes	characteristic
71	C₂	#15692186	1	4	yes	direct product factor
72	C₂	C₂×#13108053	1	1	yes	characteristic
73	C₂	C₂×#13108061	1	1	yes	characteristic
74	C₂	C₂×#13108062	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₀₁
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₂×C₄⋊C₄×C₁₀₁	C₂
socle	C₂³×C₁₀₁	D₄
hypercenter	C₂×C₄⋊C₄	D₁₀₁
hypocenter	C₁₀₁	C₂×#106
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #15692186	C₂	direct (N × H)
6. C₂×#11717579	C₄	semidirect
23. #11717579	C₂×C₄	semidirect
33. C₂×C₁₀₁	#106	semidirect
37. C₁₀₁	C₂×#106	semidirect
71. C₂	#15692186	direct (N × H)

Subgroups — C2×#15692186 #20265207

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692186 #20265207