Subgroups — C₂×#16810453 #20276507

Order 6784.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133153	C₂	1	2	yes	maximal
2	#16810453	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11719917	—	2	2	no	—
5	#13133153	—	2	2	no	—
6	#13133153	C₂²	1	4	yes	—
7	C₂²×C₈×C₅₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₅₃	C₄	1	2	yes	—
9	C₂×C₁₆×C₅₃	C₄	1	2	yes	—
10	C₂×C₁₆×C₅₃	C₂²	1	2	yes	—
11	C₂²×C₄×C₅₃	D₄	1	1	yes	characteristic
12	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₅₃	Q₈	1	1	yes	characteristic
16	C₂×C₈×C₅₃	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
18	#11719917	—	2	4	no	—
19	#11719917	—	4	2	no	—
20	C₂×#88322	—	4	2	no	—
21	C₁₆×C₅₃	C₂×C₄	1	4	yes	—
22	C₂³×C₅₃	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
26	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₅₃	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
29	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
30	C₈×C₅₃	C₄⋊C₄	1	1	yes	characteristic
31	C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
33	#88322	—	4	4	no	—
34	C₂²×C₅₃	—	2	2	no	—
35	C₂²×C₅₃	#107	1	1	yes	characteristic
36	C₂²×C₅₃	#107	1	1	yes	characteristic
37	C₂²×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
38	C₄×C₅₃	#107	1	1	yes	characteristic
39	C₄×C₅₃	#107	1	1	yes	characteristic
40	C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
42	C₂×#368	—	53	1	no	maximal, Sylow
43	C₂×C₅₃	—	2	1	no	—
44	C₂×C₅₃	—	2	1	no	—
45	C₂×C₅₃	#368	1	2	yes	complemented
46	C₂×C₅₃	C₂×#107	1	1	yes	characteristic
47	C₂²×C₁₆	D₅₃	1	1	yes	characteristic
48	C₂×#108	—	53	2	no	—
49	#368	—	53	4	no	—
50	C₅₃	C₂×#368	1	1	yes	characteristic, complemented, Sylow
51	C₂×M₁₆	—	106	2	no	—
52	C₂²×C₈	C₂×D₅₃	1	1	yes	characteristic
53	C₂×C₁₆	Dic₅₃	1	2	yes	—
54	C₂×C₁₆	Dic₅₃	1	2	yes	—
55	C₂×C₁₆	C₂×D₅₃	1	2	yes	—
56	#108	—	53	4	no	—
57	#108	—	106	2	no	—
58	C₂²×C₄	D₂₁₂	1	1	yes	characteristic
59	M₁₆	—	106	4	no	—
60	M₁₆	—	212	2	no	—
61	C₂×C₈	—	212	2	no	—
62	C₂×C₈	Dic₁₀₆	1	1	yes	characteristic
63	C₂×C₈	Dic₁₀₆	1	1	yes	characteristic
64	C₂×C₈	D₂₁₂	1	1	yes	characteristic
65	C₂×C₈	C₂×Dic₅₃	1	1	yes	characteristic
66	C₂×C₈	C₂×Dic₅₃	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
68	C₁₆	C₂×Dic₅₃	1	4	yes	—
69	C₂³	Dic₂₁₂	1	1	yes	characteristic
70	C₂×C₄	D₄₂₄	1	1	yes	characteristic
71	C₂×C₄	D₄₂₄	1	1	yes	characteristic
72	C₂×C₄	Dic₂₁₂	1	1	yes	characteristic
73	C₂×C₄	C₄⋊Dic₅₃	1	1	yes	characteristic
74	C₂×C₄	C₄⋊Dic₅₃	1	1	yes	characteristic
75	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
76	C₈	—	212	4	no	—
77	C₈	C₄⋊Dic₅₃	1	1	yes	characteristic
78	C₈	C₄⋊Dic₅₃	1	1	yes	characteristic
79	C₈	C₂×Dic₁₀₆	1	1	yes	characteristic
80	C₈	C₂²×Dic₅₃	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	#13133151	1	1	yes	characteristic
83	C₂²	#13133151	1	1	yes	characteristic
84	C₂²	C₂×Dic₂₁₂	1	1	yes	characteristic
85	C₄	#13133151	1	1	yes	characteristic
86	C₄	#13133151	1	1	yes	characteristic
87	C₄	C₂×C₄⋊Dic₅₃	1	1	yes	characteristic
88	C₄	C₂×D₄₂₄	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#16810453	1	2	yes	direct product factor
92	C₂	C₂×#13133151	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄₂₄
commutator	C₈×C₅₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅₃
Fitting	C₂²×C₁₆×C₅₃	C₂
socle	C₂²×C₅₃	#107
hypercenter	C₂²×C₁₆	D₅₃
hypocenter	C₅₃	C₂×#368
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #16810453	C₂	direct (N × H)
45. C₂×C₅₃	#368	semidirect
50. C₅₃	C₂×#368	semidirect
91. C₂	#16810453	direct (N × H)

Subgroups — C2×#16810453 #20276507

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16810453 #20276507