Subgroups — C₂×#16839595 #21448110

Order 7808.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
2	#16839595	C₂	1	4	yes	maximal, direct product factor
3	C₂×#14519683	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
6	C₂×#11758185	C₄	1	1	yes	characteristic
7	C₁₆×D₆₁	C₄	1	2	yes	—
8	C₁₆×D₆₁	C₂²	1	2	yes	—
9	#14519683	C₂²	1	2	yes	complemented
10	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
11	C₃₂×C₆₁	C₂²	1	2	yes	complemented
12	C₂×C₄×D₆₁	C₈	1	1	yes	characteristic
13	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×#92418	C₈	1	1	yes	characteristic
15	C₈×D₆₁	C₈	1	2	yes	—
16	C₈×D₆₁	C₂×C₄	1	2	yes	—
17	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₆₁	C₂³	1	1	yes	characteristic
19	#11758185	C₂×C₄	1	2	yes	—
20	C₂²×D₆₁	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₆₁	C₁₆	1	1	yes	characteristic
23	C₄×D₆₁	C₁₆	1	2	yes	—
24	C₄×D₆₁	C₂×C₈	1	2	yes	—
25	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
26	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
27	#92418	C₂×C₈	1	2	yes	—
28	C₂²×C₆₁	C₂×C₁₆	1	1	yes	characteristic
29	C₂×D₆₁	—	2	2	no	—
30	C₂×D₆₁	C₂×C₁₆	1	2	yes	—
31	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
32	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
33	Dic₆₁	C₂×C₁₆	1	2	yes	—
34	C₂×M₆₄	—	61	1	no	maximal, Sylow
35	C₂×C₆₁	M₆₄	1	2	yes	complemented
36	C₂×C₆₁	C₂²×C₁₆	1	1	yes	characteristic
37	D₆₁	—	2	2	no	—
38	C₂²×C₁₆	—	61	1	no	—
39	M₆₄	—	61	4	no	—
40	C₂×C₃₂	—	61	1	no	—
41	C₂×C₃₂	D₆₁	1	1	yes	characteristic, complemented
42	C₆₁	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₈	—	61	1	no	—
44	C₂×C₁₆	—	61	1	no	—
45	C₂×C₁₆	—	61	2	no	—
46	C₂×C₁₆	—	61	2	no	—
47	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
48	C₃₂	—	61	2	no	—
49	C₃₂	C₂×D₆₁	1	2	yes	complemented
50	C₂²×C₄	—	61	1	no	—
51	C₂×C₈	—	61	1	no	—
52	C₂×C₈	—	61	2	no	—
53	C₂×C₈	—	61	2	no	—
54	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
55	C₁₆	—	61	2	no	—
56	C₁₆	C₄×D₆₁	1	1	yes	characteristic
57	C₁₆	C₂²×D₆₁	1	1	yes	characteristic
58	C₂³	—	61	1	no	—
59	C₂×C₄	—	61	1	no	—
60	C₂×C₄	—	61	2	no	—
61	C₂×C₄	—	61	2	no	—
62	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
63	C₈	—	61	2	no	—
64	C₈	C₈×D₆₁	1	1	yes	characteristic
65	C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
66	C₂²	—	61	2	no	—
67	C₂²	—	122	2	no	—
68	C₂²	C₁₆×D₆₁	1	1	yes	characteristic
69	C₄	—	61	2	no	—
70	C₄	C₁₆×D₆₁	1	1	yes	characteristic
71	C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
72	C₂	—	122	2	no	—
73	C₂	#16839595	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₆₁
commutator	C₂×C₆₁	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₆₁
Fitting	C₂×C₃₂×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₁₆
hypercenter	C₂×C₃₂	D₆₁
hypocenter	C₆₁	C₂×M₆₄
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #16839595	C₂	direct (N × H)
3. C₂×#14519683	C₂	semidirect
4. C₂×C₃₂×C₆₁	C₂	semidirect
9. #14519683	C₂²	semidirect
11. C₃₂×C₆₁	C₂²	semidirect
35. C₂×C₆₁	M₆₄	semidirect
41. C₂×C₃₂	D₆₁	semidirect
42. C₆₁	C₂×M₆₄	semidirect
49. C₃₂	C₂×D₆₁	semidirect
73. C₂	#16839595	direct (N × H)

Subgroups — C2×#16839595 #21448110

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16839595 #21448110