Subgroups — C₂×#15692184 #20265197

Order 6464.

138 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	#15692184	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₀₁	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₀₁	C₄	1	1	yes	characteristic
7	C₂×#11717579	—	2	2	no	—
8	C₂×#11717579	C₂²	1	2	yes	—
9	C₄×Dic₁₀₁	C₄	1	2	yes	—
10	C₄×Dic₁₀₁	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₁	—	2	2	no	—
13	C₂×C₈×C₁₀₁	C₂²	1	2	yes	—
14	C₂³×C₁₀₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
17	C₂×C₄×C₁₀₁	Q₈	1	2	yes	—
18	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₁	—	2	2	no	—
20	C₂×Dic₁₀₁	C₈	1	4	yes	complemented
21	C₂×Dic₁₀₁	C₂×C₄	1	2	yes	—
22	C₂×Dic₁₀₁	C₂×C₄	1	2	yes	—
23	C₈×C₁₀₁	—	2	2	no	—
24	#11717579	—	2	2	no	—
25	C₂²×C₁₀₁	C₄⋊C₄	1	2	yes	—
26	C₂²×C₁₀₁	C₂×C₈	1	2	yes	—
27	C₂²×C₁₀₁	M₁₆	1	2	yes	—
28	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₁₀₁	C₄⋊C₄	1	2	yes	—
30	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
32	Dic₁₀₁	—	2	2	no	—
33	Dic₁₀₁	C₂×C₈	1	4	yes	complemented
34	C₂×C₁₀₁	C₄⋊C₈	1	4	yes	complemented
35	C₂×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₁₀₁	C₂²×C₈	1	1	yes	characteristic
37	C₂×C₁₀₁	C₂×M₁₆	1	1	yes	characteristic
38	C₁₀₁	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₄⋊C₈	—	101	1	no	maximal, Sylow
40	C₂²×C₈	—	101	1	no	—
41	C₂²×C₈	D₁₀₁	1	1	yes	characteristic
42	C₂×C₄²	—	101	1	no	—
43	C₄⋊C₈	—	101	4	no	—
44	C₂²×C₄	—	101	1	no	—
45	C₂²×C₄	—	101	1	no	—
46	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
47	C₂×C₈	—	2	2	no	—
48	C₂×C₈	—	101	2	no	—
49	C₂×C₈	—	202	2	no	—
50	C₂×C₈	C₂×D₁₀₁	1	2	yes	—
51	C₄²	—	101	2	no	—
52	C₄²	—	101	2	no	—
53	C₂³	C₄×D₁₀₁	1	1	yes	characteristic
54	C₂×C₄	—	101	4	no	—
55	C₂×C₄	—	101	2	no	—
56	C₂×C₄	—	101	2	no	—
57	C₂×C₄	—	202	2	no	—
58	C₂×C₄	Dic₂₀₂	1	2	yes	—
59	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
60	C₂×C₄	C₂²⋊D₁₀₁	1	2	yes	—
61	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
62	C₈	—	2	2	no	—
63	C₈	—	202	2	no	—
64	C₂²	#13108053	1	2	yes	—
65	C₂²	C₈×D₁₀₁	1	2	yes	—
66	C₂²	#13108057	1	2	yes	—
67	C₂²	C₂×C₄×D₁₀₁	1	1	yes	characteristic
68	C₄	—	101	4	no	—
69	C₄	—	202	2	no	—
70	C₄	#13108053	1	2	yes	—
71	C₄	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
72	C₄	C₂×Dic₂₀₂	1	1	yes	characteristic
73	C₂	#15692184	1	4	yes	direct product factor
74	C₂	C₂×#13108053	1	1	yes	characteristic
75	C₂	C₂×C₈×D₁₀₁	1	1	yes	characteristic
76	C₂	C₂×#13108057	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₀₁
commutator	C₂×C₁₀₁	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₂²×C₈×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂×C₄
hypercenter	C₂²×C₈	D₁₀₁
hypocenter	C₁₀₁	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #15692184	C₂	direct (N × H)
20. C₂×Dic₁₀₁	C₈	semidirect
33. Dic₁₀₁	C₂×C₈	semidirect
34. C₂×C₁₀₁	C₄⋊C₈	semidirect
38. C₁₀₁	C₂×C₄⋊C₈	semidirect
73. C₂	#15692184	direct (N × H)

Subgroups — C2×#15692184 #20265197

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692184 #20265197