Subgroups — C₂×#16810461 #20277016

Order 6784.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₂₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#16810461	C₂	1	4	yes	maximal, direct product factor
3	C₂×#13133123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₁₂	—	2	1	no	—
6	Dic₄₂₄	—	2	1	no	—
7	Dic₄₂₄	C₂²	1	2	yes	complemented
8	#13133123	C₂²	1	2	yes	complemented
9	C₂×D₈×C₅₃	—	2	1	no	—
10	D₁₆×C₅₃	—	2	1	no	—
11	D₁₆×C₅₃	C₂²	1	2	yes	—
12	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₅₃	—	4	1	no	—
14	C₂×Dic₁₀₆	—	4	1	no	—
15	D₈×C₅₃	—	2	2	no	—
16	D₈×C₅₃	—	4	1	no	—
17	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
18	Dic₂₁₂	—	2	2	no	—
19	Dic₂₁₂	—	4	1	no	—
20	C₁₆×C₅₃	D₄	1	1	yes	characteristic
21	C₁₆×C₅₃	C₂³	1	1	yes	characteristic
22	C₂³×C₅₃	—	8	1	no	—
23	D₄×C₅₃	—	4	2	no	—
24	D₄×C₅₃	—	8	1	no	—
25	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
26	C₂×Dic₅₃	—	8	1	no	—
27	Dic₁₀₆	—	4	2	no	—
28	Dic₁₀₆	—	8	1	no	—
29	C₈×C₅₃	D₈	1	1	yes	characteristic
30	C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₅₃	—	8	2	no	—
32	C₂²×C₅₃	—	16	2	no	—
33	C₂²×C₅₃	D₁₆	1	1	yes	characteristic
34	C₄×C₅₃	D₁₆	1	1	yes	characteristic
35	C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
36	Dic₅₃	—	8	2	no	—
37	C₂×SD₆₄	—	53	1	no	maximal, Sylow
38	C₂×C₅₃	—	16	2	no	—
39	C₂×C₅₃	SD₆₄	1	2	yes	complemented
40	C₂×C₅₃	C₂×D₁₆	1	1	yes	characteristic
41	C₂×Q₃₂	—	53	1	no	—
42	C₂×D₁₆	D₅₃	1	1	yes	characteristic
43	SD₆₄	—	53	4	no	—
44	C₂×C₃₂	—	53	1	no	—
45	C₅₃	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	106	1	no	—
47	C₂×D₈	—	2	1	no	—
48	Q₃₂	—	53	2	no	—
49	Q₃₂	—	106	1	no	—
50	D₁₆	—	2	1	no	—
51	D₁₆	C₂×D₅₃	1	2	yes	—
52	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
53	C₃₂	—	53	2	no	—
54	C₂×Q₈	—	212	1	no	—
55	C₂×D₄	—	4	1	no	—
56	Q₁₆	—	106	2	no	—
57	Q₁₆	—	212	1	no	—
58	D₈	—	2	2	no	—
59	D₈	—	4	1	no	—
60	C₂×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
61	C₁₆	C₂²⋊D₅₃	1	1	yes	characteristic
62	C₁₆	C₂²×D₅₃	1	1	yes	characteristic
63	C₂³	—	8	1	no	—
64	Q₈	—	424	1	no	—
65	Q₈	—	212	2	no	—
66	D₄	—	4	2	no	—
67	D₄	—	8	1	no	—
68	C₂×C₄	—	424	1	no	—
69	C₂×C₄	#11719922	1	1	yes	characteristic
70	C₈	#11719922	1	1	yes	characteristic
71	C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
72	C₂²	—	8	2	no	—
73	C₂²	—	16	2	no	—
74	C₂²	#13133158	1	1	yes	characteristic
75	C₄	—	424	2	no	—
76	C₄	#13133158	1	1	yes	characteristic
77	C₄	C₂×#11719922	1	1	yes	characteristic
78	C₂	—	16	2	no	—
79	C₂	#16810461	1	2	yes	direct product factor
80	C₂	C₂×#13133158	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13133158
commutator	C₁₆×C₅₃	C₂³
Frattini	C₁₆	C₂²×D₅₃
Fitting	C₂×D₁₆×C₅₃	C₂
socle	C₂²×C₅₃	D₁₆
hypercenter	C₂×D₁₆	D₅₃
hypocenter	C₅₃	C₂×SD₆₄
LCS	G ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₄₂₄	C₂	semidirect
2. #16810461	C₂	direct (N × H)
3. C₂×#13133123	C₂	semidirect
7. Dic₄₂₄	C₂²	semidirect
8. #13133123	C₂²	semidirect
39. C₂×C₅₃	SD₆₄	semidirect
45. C₅₃	C₂×SD₆₄	semidirect
79. C₂	#16810461	direct (N × H)

Subgroups — C2×#16810461 #20277016

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16810461 #20277016