Subgroups — C₂×#16810460 #20277015

Order 6784.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₄₈	C₂	1	1	yes	maximal, characteristic
2	#16810460	C₂	1	4	yes	maximal, direct product factor
3	C₂×#13133123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄₂₄	—	2	1	no	—
6	D₈₄₈	—	2	1	no	—
7	D₈₄₈	C₂²	1	2	yes	—
8	#13133123	C₂²	1	2	yes	complemented
9	C₂×Q₁₆×C₅₃	—	2	1	no	—
10	Q₃₂×C₅₃	—	2	1	no	—
11	Q₃₂×C₅₃	C₂²	1	2	yes	complemented
12	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₅₃	—	4	1	no	—
14	C₂×D₂₁₂	—	4	1	no	—
15	Q₁₆×C₅₃	—	2	2	no	—
16	Q₁₆×C₅₃	—	4	1	no	—
17	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
18	D₄₂₄	—	2	2	no	—
19	D₄₂₄	—	4	1	no	—
20	C₁₆×C₅₃	D₄	1	1	yes	characteristic
21	C₁₆×C₅₃	C₂³	1	1	yes	characteristic
22	C₂²×D₅₃	—	8	1	no	—
23	Q₈×C₅₃	—	4	2	no	—
24	Q₈×C₅₃	—	8	1	no	—
25	C₂×C₄×C₅₃	—	8	1	no	—
26	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
27	D₂₁₂	—	4	2	no	—
28	D₂₁₂	—	8	1	no	—
29	C₈×C₅₃	D₈	1	1	yes	characteristic
30	C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₅₃	D₁₆	1	1	yes	characteristic
32	C₂×D₅₃	—	8	2	no	—
33	C₂×D₅₃	—	16	2	no	—
34	C₄×C₅₃	—	8	2	no	—
35	C₄×C₅₃	D₁₆	1	1	yes	characteristic
36	C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
37	C₂×SD₆₄	—	53	1	no	maximal, Sylow
38	C₂×C₅₃	SD₆₄	1	2	yes	complemented
39	C₂×C₅₃	C₂×D₁₆	1	1	yes	characteristic
40	D₅₃	—	16	2	no	—
41	C₂×Q₃₂	D₅₃	1	1	yes	characteristic, complemented
42	C₂×D₁₆	—	53	1	no	—
43	SD₆₄	—	53	4	no	—
44	C₂×C₃₂	—	53	1	no	—
45	C₅₃	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	2	1	no	—
47	C₂×D₈	—	106	1	no	—
48	Q₃₂	—	2	1	no	—
49	Q₃₂	C₂×D₅₃	1	2	yes	complemented
50	D₁₆	—	53	2	no	—
51	D₁₆	—	106	1	no	—
52	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
53	C₃₂	—	53	2	no	—
54	C₂×Q₈	—	4	1	no	—
55	C₂×D₄	—	212	1	no	—
56	Q₁₆	—	2	2	no	—
57	Q₁₆	—	4	1	no	—
58	D₈	—	106	2	no	—
59	D₈	—	212	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	—	424	1	no	—
64	Q₈	—	4	2	no	—
65	Q₈	—	8	1	no	—
66	D₄	—	424	1	no	—
67	D₄	—	212	2	no	—
68	C₂×C₄	—	8	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	—	848	2	no	—
73	C₂²	—	424	2	no	—
74	C₂²	#13133158	1	1	yes	characteristic
75	C₄	—	8	2	no	—
76	C₄	#13133158	1	1	yes	characteristic
77	C₄	C₂×#11719922	1	1	yes	characteristic
78	C₂	—	848	2	no	—
79	C₂	#16810460	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×Q₃₂×C₅₃	C₂
socle	C₂²×C₅₃	D₁₆
hypercenter	C₂×Q₃₂	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×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #16810460	C₂	direct (N × H)
3. C₂×#13133123	C₂	semidirect
4. C₂×Q₃₂×C₅₃	C₂	semidirect
8. #13133123	C₂²	semidirect
11. Q₃₂×C₅₃	C₂²	semidirect
38. C₂×C₅₃	SD₆₄	semidirect
41. C₂×Q₃₂	D₅₃	semidirect
45. C₅₃	C₂×SD₆₄	semidirect
49. Q₃₂	C₂×D₅₃	semidirect
79. C₂	#16810460	direct (N × H)

Subgroups — C2×#16810460 #20277015

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16810460 #20277015