Subgroups — #20289773

Order 6784.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133286	C₂	1	2	yes	maximal
2	C₂×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊#6157	—	2	2	no	—
4	#13133286	—	2	2	no	—
5	#13133286	C₄	1	4	yes	complemented
6	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic
7	C₂×#11719908	C₄	1	1	yes	characteristic, complemented
8	C₁₆×D₅₃	—	2	2	no	—
9	C₂×C₁₆×C₅₃	C₄	1	1	yes	characteristic, complemented
10	C₂²×#6157	—	4	2	no	—
11	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
12	C₄⋊#6157	—	2	4	no	—
13	C₄⋊#6157	—	4	2	no	—
14	C₂×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
15	C₂×#88322	Q₈	1	1	yes	characteristic
16	C₈×D₅₃	C₂×C₄	1	2	yes	—
17	C₈×D₅₃	D₄	1	2	yes	—
18	C₁₆×C₅₃	—	2	1	no	—
19	#11719908	—	2	1	no	—
20	C₂²×D₅₃	D₈	1	1	yes	characteristic
21	C₂×#6157	—	4	4	no	—
22	C₂×#6157	—	8	2	no	—
23	C₂×#6157	—	8	2	no	—
24	C₂×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×Dic₅₃	Q₁₆	1	1	yes	characteristic
26	C₄×D₅₃	C₂²⋊C₄	1	2	yes	—
27	C₄×D₅₃	SD₁₆	1	2	yes	—
28	C₈×C₅₃	C₄²	1	1	yes	characteristic
29	C₈×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
30	#88322	C₄⋊C₄	1	2	yes	—
31	C₂²×C₅₃	#107	1	1	yes	characteristic
32	C₂×D₅₃	#102	1	2	yes	—
33	C₂×D₅₃	D₁₆	1	1	yes	characteristic
34	C₂×D₅₃	SD₃₂	1	2	yes	—
35	C₂×D₅₃	Q₃₂	1	1	yes	characteristic
36	#6157	—	8	4	no	—
37	C₄×C₅₃	#95	1	1	yes	characteristic
38	C₄×C₅₃	#106	1	1	yes	characteristic
39	Dic₅₃	#103	1	2	yes	—
40	#1380	—	53	1	no	maximal, Sylow
41	C₂×C₅₃	#340	1	1	yes	characteristic
42	C₂×C₅₃	#366	1	1	yes	characteristic
43	C₂×C₅₃	#367	1	1	yes	characteristic
44	D₅₃	#357	1	2	yes	—
45	D₅₃	#358	1	2	yes	—
46	C₂²×C₁₆	—	53	1	no	—
47	C₂×#107	—	53	2	no	—
48	C₅₃	#1380	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₈	—	53	1	no	—
50	C₂×C₄⋊C₄	—	106	2	no	—
51	C₂×C₁₆	—	53	1	no	—
52	C₂×C₁₆	—	106	2	no	—
53	C₂×C₁₆	#6157	1	1	yes	characteristic, complemented
54	#107	—	53	4	no	—
55	#107	—	106	2	no	—
56	C₂²×C₄	—	53	1	no	—
57	C₂²×C₄	—	212	2	no	—
58	C₂×C₈	—	53	1	no	—
59	C₂×C₈	—	53	2	no	—
60	C₂×C₈	—	53	2	no	—
61	C₂×C₈	C₂×#6157	1	1	yes	characteristic
62	C₄⋊C₄	—	106	4	no	—
63	C₄⋊C₄	—	212	2	no	—
64	C₁₆	—	2	1	no	—
65	C₁₆	—	106	1	no	—
66	C₂³	—	53	1	no	—
67	C₂×C₄	—	53	1	no	—
68	C₂×C₄	—	53	2	no	—
69	C₂×C₄	—	53	2	no	—
70	C₂×C₄	—	424	2	no	—
71	C₂×C₄	—	424	2	no	—
72	C₂×C₄	—	212	4	no	—
73	C₂×C₄	C₄⋊#6157	1	1	yes	characteristic
74	C₈	—	53	2	no	—
75	C₈	C₄×#6157	1	1	yes	characteristic
76	C₈	C₂²⋊#6157	1	1	yes	characteristic
77	C₂²	—	53	1	no	—
78	C₂²	—	53	1	no	—
79	C₂²	—	53	2	no	—
80	C₂²	—	53	2	no	—
81	C₂²	#13133286	1	1	yes	characteristic
82	C₄	—	53	2	no	—
83	C₄	—	424	4	no	—
84	C₄	(C₂×#6157)⋊C₄	1	1	yes	characteristic
85	C₄	#13133285	1	1	yes	characteristic
86	C₂	—	53	2	no	—
87	C₂	—	53	2	no	—
88	C₂	#16811497	1	1	yes	characteristic
89	C₂	#16811549	1	1	yes	characteristic
90	C₂	#16811550	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13133286
commutator	C₈×C₅₃	C₄²
Frattini	C₂×C₈	C₂×#6157
Fitting	C₂×C₁₆×C₅₃	C₄
socle	C₂²×C₅₃	#107
hypercenter	C₂×C₁₆	#6157
hypocenter	C₅₃	#1380
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
5. #13133286	C₄	semidirect
7. C₂×#11719908	C₄	semidirect
9. C₂×C₁₆×C₅₃	C₄	semidirect
48. C₅₃	#1380	semidirect
53. C₂×C₁₆	#6157	semidirect