Subgroups — C₂²×Q₈×Dic₅₃ #20287891

Order 6784.

1664 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₅₃	C₂	1	24	yes	maximal, direct product factor
2	C₂²×C₄⋊Dic₅₃	C₂	1	3	yes	maximal
3	C₂²×C₄×Dic₅₃	C₂	1	3	yes	maximal
4	C₂³×Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₅₃	C₂²	1	3	yes	—
6	C₂³×Dic₅₃	C₂²	1	1	yes	characteristic
7	Q₈×Dic₅₃	C₂²	1	64	yes	direct product factor
8	C₂×C₄⋊Dic₅₃	C₂²	1	36	yes	—
9	C₂×C₄×Dic₅₃	C₂²	1	36	yes	—
10	C₂²×Q₈×C₅₃	C₄	1	16	yes	complemented
11	C₂²×Q₈×C₅₃	C₂²	1	12	yes	—
12	C₂³×C₄×C₅₃	C₂²	1	3	yes	—
13	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
14	C₂×Q₈×C₅₃	C₂×C₄	1	96	yes	complemented
15	C₂×Q₈×C₅₃	C₂³	1	16	yes	—
16	C₂²×C₄×C₅₃	C₂×C₄	1	24	yes	—
17	C₂²×C₄×C₅₃	C₂³	1	18	yes	—
18	C₂²×Dic₅₃	—	2	12	no	—
19	C₂²×Dic₅₃	Q₈	1	8	yes	direct product factor
20	C₂²×Dic₅₃	C₂³	1	18	yes	—
21	C₂²×Dic₅₃	C₂³	1	6	yes	—
22	C₄⋊Dic₅₃	C₂³	1	48	yes	—
23	C₄×Dic₅₃	C₂³	1	48	yes	—
24	C₂³×C₅₃	C₂²×C₄	1	4	yes	—
25	C₂³×C₅₃	C₂×Q₈	1	4	yes	—
26	C₂³×C₅₃	#41	1	4	yes	—
27	C₂³×C₅₃	C₂⁴	1	3	yes	—
28	Q₈×C₅₃	C₂²×C₄	1	64	yes	complemented
29	C₂×C₄×C₅₃	C₂²×C₄	1	72	yes	—
30	C₂×C₄×C₅₃	C₂⁴	1	12	yes	—
31	C₂×Dic₅₃	—	2	36	no	—
32	C₂×Dic₅₃	C₂×Q₈	1	24	yes	direct product factor
33	C₂×Dic₅₃	C₂⁴	1	12	yes	—
34	C₂×Dic₅₃	C₂⁴	1	4	yes	—
35	C₂²×C₅₃	C₄×Q₈	1	16	yes	complemented
36	C₂²×C₅₃	C₂³×C₄	1	6	yes	—
37	C₂²×C₅₃	C₂²×Q₈	1	6	yes	—
38	C₂²×C₅₃	C₂×#41	1	6	yes	—
39	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
40	C₄×C₅₃	C₂³×C₄	1	24	yes	—
41	Dic₅₃	—	2	12	no	—
42	Dic₅₃	C₂²×Q₈	1	8	yes	direct product factor
43	C₂²×C₄×Q₈	—	53	1	no	maximal, Sylow
44	C₂×C₅₃	C₂×C₄×Q₈	1	12	yes	complemented
45	C₂×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
46	C₂×C₅₃	C₂³×Q₈	1	1	yes	characteristic
47	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
48	C₂³×Q₈	D₅₃	1	1	yes	characteristic
49	C₂×C₄×Q₈	—	53	24	no	—
50	C₂²×C₄⋊C₄	—	53	3	no	—
51	C₂²×C₄²	—	53	3	no	—
52	C₅₃	C₂²×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
53	C₂²×Q₈	Dic₅₃	1	16	yes	direct product factor
54	C₂²×Q₈	C₂×D₅₃	1	12	yes	—
55	C₂³×C₄	—	53	1	no	—
56	C₂³×C₄	—	53	3	no	—
57	C₂³×C₄	C₂×D₅₃	1	3	yes	—
58	C₄×Q₈	—	53	64	no	—
59	C₂×C₄⋊C₄	—	53	36	no	—
60	C₂×C₄²	—	53	36	no	—
61	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
62	C₂×Q₈	C₂×Dic₅₃	1	96	yes	direct product factor
63	C₂×Q₈	C₂²×D₅₃	1	16	yes	—
64	C₂²×C₄	—	53	8	no	—
65	C₂²×C₄	—	53	6	no	—
66	C₂²×C₄	—	53	18	no	—
67	C₂²×C₄	—	106	12	no	—
68	C₂²×C₄	C₂×Dic₅₃	1	24	yes	—
69	C₂²×C₄	C₂²×D₅₃	1	18	yes	—
70	C₄⋊C₄	—	53	48	no	—
71	C₄²	—	53	48	no	—
72	C₂³	Q₈×D₅₃	1	4	yes	—
73	C₂³	#11719949	1	4	yes	—
74	C₂³	C₂²×Dic₅₃	1	4	yes	—
75	C₂³	C₂³×D₅₃	1	3	yes	—
76	Q₈	C₂²×Dic₅₃	1	64	yes	direct product factor
77	C₂×C₄	—	53	24	no	—
78	C₂×C₄	—	53	4	no	—
79	C₂×C₄	—	53	12	no	—
80	C₂×C₄	—	106	36	no	—
81	C₂×C₄	C₂²×Dic₅₃	1	72	yes	—
82	C₂×C₄	C₂³×D₅₃	1	12	yes	—
83	C₂²	Q₈×Dic₅₃	1	16	yes	direct product factor
84	C₂²	C₂³×Dic₅₃	1	6	yes	—
85	C₂²	C₂×Q₈×D₅₃	1	6	yes	—
86	C₂²	C₂×#11719949	1	6	yes	—
87	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
88	C₄	—	53	8	no	—
89	C₄	—	106	12	no	—
90	C₄	C₂³×Dic₅₃	1	24	yes	—
91	C₂	C₂×Q₈×Dic₅₃	1	12	yes	direct product factor
92	C₂	C₂⁴×Dic₅₃	1	1	yes	characteristic
93	C₂	C₂²×Q₈×D₅₃	1	1	yes	characteristic
94	C₂	C₂²×#11719949	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₅₃
commutator	C₂×C₅₃	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₅₃
Fitting	C₂³×Q₈×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂³
hypercenter	C₂³×Q₈	D₅₃
hypocenter	C₅₃	C₂²×C₄×Q₈
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×Dic₅₃	C₂	direct (N × H)
7. Q₈×Dic₅₃	C₂²	direct (N × H)
10. C₂²×Q₈×C₅₃	C₄	semidirect
14. C₂×Q₈×C₅₃	C₂×C₄	semidirect
19. C₂²×Dic₅₃	Q₈	direct (N × H)
28. Q₈×C₅₃	C₂²×C₄	semidirect
32. C₂×Dic₅₃	C₂×Q₈	direct (N × H)
35. C₂²×C₅₃	C₄×Q₈	semidirect
42. Dic₅₃	C₂²×Q₈	direct (N × H)
44. C₂×C₅₃	C₂×C₄×Q₈	semidirect
52. C₅₃	C₂²×C₄×Q₈	semidirect
53. C₂²×Q₈	Dic₅₃	direct (N × H)
62. C₂×Q₈	C₂×Dic₅₃	direct (N × H)
76. Q₈	C₂²×Dic₅₃	direct (N × H)
83. C₂²	Q₈×Dic₅₃	direct (N × H)
91. C₂	C₂×Q₈×Dic₅₃	direct (N × H)

Subgroups — C22×Q8×Dic53 #20287891

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×Q₈×Dic₅₃ #20287891