Subgroups — C₂×#16810451 #20276495

Order 6784.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133151	C₂	1	2	yes	maximal
2	#16810451	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₅₃	—	2	2	no	—
5	#13133151	—	2	2	no	—
6	#13133151	C₂²	1	4	yes	—
7	C₂²×C₈×C₅₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₅₃	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₅₃	C₂²	1	2	yes	—
10	C₂²×C₄×C₅₃	D₄	1	1	yes	characteristic
11	C₂²×Dic₅₃	—	4	2	no	—
12	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₅₃	Q₈	1	2	yes	—
15	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
16	C₄⋊Dic₅₃	—	2	4	no	—
17	C₄⋊Dic₅₃	—	4	2	no	—
18	C₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
19	C₂³×C₅₃	D₈	1	1	yes	characteristic
20	C₂×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
22	C₂×C₄×C₅₃	Q₁₆	1	2	yes	—
23	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₅₃	—	4	4	no	—
25	C₂×Dic₅₃	—	8	4	no	—
26	C₈×C₅₃	C₄⋊C₄	1	2	yes	—
27	C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₅₃	#107	1	2	yes	—
30	C₂²×C₅₃	SD₃₂	1	4	yes	—
31	C₂²×C₅₃	C₂×D₈	1	1	yes	characteristic
32	C₄×C₅₃	#107	1	2	yes	—
33	C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₄×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
35	Dic₅₃	—	8	4	no	—
36	C₂×#367	—	53	1	no	maximal, Sylow
37	C₂×C₅₃	#367	1	4	yes	complemented
38	C₂×C₅₃	C₂×#107	1	1	yes	characteristic
39	C₂×C₅₃	C₂×SD₃₂	1	2	yes	—
40	C₂²×C₁₆	D₅₃	1	1	yes	characteristic
41	C₂×#107	—	53	2	no	—
42	#367	—	53	4	no	—
43	C₅₃	C₂×#367	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₈	C₂×D₅₃	1	1	yes	characteristic
45	C₂×C₄⋊C₄	—	106	2	no	—
46	C₂×C₁₆	Dic₅₃	1	4	yes	complemented
47	C₂×C₁₆	C₂×D₅₃	1	2	yes	—
48	#107	—	53	4	no	—
49	#107	—	106	2	no	—
50	C₂²×C₄	—	212	2	no	—
51	C₂²×C₄	D₂₁₂	1	1	yes	characteristic
52	C₂×C₈	Dic₁₀₆	1	2	yes	—
53	C₂×C₈	D₂₁₂	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₅₃	1	2	yes	—
55	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
56	C₄⋊C₄	—	106	4	no	—
57	C₄⋊C₄	—	212	2	no	—
58	C₁₆	C₂×Dic₅₃	1	4	yes	complemented
59	C₂³	D₄₂₄	1	1	yes	characteristic
60	C₂×C₄	—	424	4	no	—
61	C₂×C₄	—	212	4	no	—
62	C₂×C₄	D₄₂₄	1	1	yes	characteristic
63	C₂×C₄	Dic₂₁₂	1	2	yes	—
64	C₂×C₄	C₄⋊Dic₅₃	1	2	yes	—
65	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
66	C₈	C₄⋊Dic₅₃	1	2	yes	—
67	C₈	C₂×Dic₁₀₆	1	1	yes	characteristic
68	C₈	C₂²×Dic₅₃	1	1	yes	characteristic
69	C₂²	#13133151	1	2	yes	—
70	C₂²	#13133162	1	4	yes	—
71	C₂²	C₂×D₄₂₄	1	1	yes	characteristic
72	C₄	—	424	4	no	—
73	C₄	#13133151	1	2	yes	—
74	C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
75	C₄	C₂×Dic₂₁₂	1	1	yes	characteristic
76	C₂	#16810451	1	4	yes	direct product factor
77	C₂	C₂×#13133151	1	1	yes	characteristic
78	C₂	C₂×#13133162	1	2	yes	—

	subgroup	G/H
center	C₂³	D₄₂₄
commutator	C₈×C₅₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅₃
Fitting	C₂²×C₁₆×C₅₃	C₂
socle	C₂³×C₅₃	D₈
hypercenter	C₂²×C₁₆	D₅₃
hypocenter	C₅₃	C₂×#367
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #16810451	C₂	direct (N × H)
8. C₂×C₁₆×C₅₃	C₄	semidirect
18. C₁₆×C₅₃	C₂×C₄	semidirect
37. C₂×C₅₃	#367	semidirect
43. C₅₃	C₂×#367	semidirect
46. C₂×C₁₆	Dic₅₃	semidirect
58. C₁₆	C₂×Dic₅₃	semidirect
76. C₂	#16810451	direct (N × H)

Subgroups — C2×#16810451 #20276495

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16810451 #20276495