Group #20277014 — subgroups

Subgroups — SD₆₄×D₅₃ #20277014

Order 6784.

112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#16810462	C₂	1	1	yes	maximal, characteristic, complemented
4	#16810461	C₂	1	1	yes	maximal, characteristic, complemented
5	#16810460	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₂×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×SD₆₄	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₁₆×D₅₃	—	2	1	no	—
9	D₈×D₅₃	—	2	1	no	—
10	Dic₄₂₄	C₂²	1	1	yes	characteristic, complemented
11	#13133163	—	2	1	no	—
12	D₈₄₈	C₂²	1	1	yes	characteristic
13	#13133158	—	2	1	no	—
14	C₁₆×D₅₃	C₂²	1	1	yes	characteristic
15	#13133123	C₂²	1	1	yes	characteristic, complemented
16	Q₃₂×C₅₃	C₂²	1	1	yes	characteristic, complemented
17	D₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₃₂×C₅₃	C₂²	1	1	yes	characteristic, complemented
19	Q₈×D₅₃	—	4	1	no	—
20	D₄×D₅₃	—	4	1	no	—
21	Q₁₆×C₅₃	—	2	1	no	—
22	D₈×C₅₃	—	2	1	no	—
23	#11719925	—	4	1	no	—
24	#11719922	—	4	1	no	—
25	Dic₂₁₂	—	2	1	no	—
26	D₄₂₄	—	2	1	no	—
27	C₈×D₅₃	D₄	1	1	yes	characteristic
28	C₁₆×C₅₃	C₂³	1	1	yes	characteristic
29	#11719908	D₄	1	1	yes	characteristic
30	C₂²×D₅₃	—	8	1	no	—
31	Q₈×C₅₃	—	4	1	no	—
32	D₄×C₅₃	—	4	1	no	—
33	C₂²⋊D₅₃	—	8	1	no	—
34	D₂₁₂	—	4	1	no	—
35	C₄×D₅₃	—	8	1	no	—
36	C₄×D₅₃	D₈	1	1	yes	characteristic
37	Dic₁₀₆	—	4	1	no	—
38	Dic₁₀₆	—	8	1	no	—
39	C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
40	#88322	D₈	1	1	yes	characteristic
41	C₂²×C₅₃	—	8	1	no	—
42	C₂×D₅₃	—	8	1	no	—
43	C₂×D₅₃	—	16	2	no	—
44	C₂×D₅₃	D₁₆	1	1	yes	characteristic
45	C₄×C₅₃	—	8	1	no	—
46	C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
47	Dic₅₃	—	8	1	no	—
48	Dic₅₃	D₁₆	1	1	yes	characteristic
49	C₂×SD₆₄	—	53	1	no	maximal, Sylow
50	C₂×C₅₃	—	16	1	no	—
51	C₂×C₅₃	C₂×D₁₆	1	1	yes	characteristic
52	D₅₃	—	16	1	no	—
53	D₅₃	SD₆₄	1	2	yes	direct product factor
54	C₂×Q₃₂	—	53	1	no	—
55	C₂×D₁₆	—	53	1	no	—
56	SD₆₄	—	53	1	no	—
57	SD₆₄	—	53	1	no	—
58	SD₆₄	—	53	1	no	—
59	SD₆₄	D₅₃	1	1	yes	characteristic, direct product factor
60	C₂×C₃₂	—	53	1	no	—
61	C₅₃	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₁₆	—	106	1	no	—
63	C₂×D₈	—	106	1	no	—
64	Q₃₂	—	53	1	no	—
65	Q₃₂	—	106	1	no	—
66	Q₃₂	C₂×D₅₃	1	1	yes	characteristic, complemented
67	D₁₆	—	53	1	no	—
68	D₁₆	—	106	1	no	—
69	D₁₆	C₂×D₅₃	1	1	yes	characteristic
70	C₂×C₁₆	—	53	1	no	—
71	C₃₂	—	53	1	no	—
72	C₃₂	C₂×D₅₃	1	1	yes	characteristic, complemented
73	C₂×Q₈	—	212	1	no	—
74	C₂×D₄	—	212	1	no	—
75	Q₁₆	—	2	1	no	—
76	Q₁₆	—	106	1	no	—
77	Q₁₆	—	212	1	no	—
78	D₈	—	2	1	no	—
79	D₈	—	106	1	no	—
80	D₈	—	212	1	no	—
81	C₂×C₈	—	53	1	no	—
82	C₁₆	—	53	1	no	—
83	C₁₆	C₂²×D₅₃	1	1	yes	characteristic
84	C₂³	—	424	1	no	—
85	Q₈	—	4	1	no	—
86	Q₈	—	424	1	no	—
87	Q₈	—	212	1	no	—
88	D₄	—	4	1	no	—
89	D₄	—	424	1	no	—
90	D₄	—	212	1	no	—
91	C₂×C₄	—	53	1	no	—
92	C₂×C₄	—	424	1	no	—
93	C₈	—	53	1	no	—
94	C₈	D₄×D₅₃	1	1	yes	characteristic
95	C₂²	—	8	1	no	—
96	C₂²	—	53	1	no	—
97	C₂²	—	848	2	no	—
98	C₂²	—	424	1	no	—
99	C₄	—	8	1	no	—
100	C₄	—	53	1	no	—
101	C₄	—	424	1	no	—
102	C₄	D₈×D₅₃	1	1	yes	characteristic
103	C₂	—	16	1	no	—
104	C₂	—	53	2	no	—
105	C₂	—	848	1	no	—
106	C₂	D₁₆×D₅₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₃₂×D₅₃

C₂

yes

maximal, characteristic, complemented

D₁₆×D₅₃

C₂

yes

maximal, characteristic

#16810462

C₂

yes

maximal, characteristic, complemented

#16810461

C₂

yes

maximal, characteristic, complemented

#16810460

C₂

yes

maximal, characteristic, complemented

C₃₂×D₅₃

C₂

yes

maximal, characteristic, complemented

C₅₃×SD₆₄

C₂

yes

maximal, characteristic, complemented

Q₁₆×D₅₃

—

D₈×D₅₃

—

Dic₄₂₄

C₂²

yes

characteristic, complemented

#13133163

—

D₈₄₈

C₂²

yes

characteristic

#13133158

—

C₁₆×D₅₃

C₂²

yes

characteristic

#13133123

C₂²

yes

characteristic, complemented

Q₃₂×C₅₃

C₂²

yes

characteristic, complemented

D₁₆×C₅₃

C₂²

yes

characteristic

C₃₂×C₅₃

C₂²

yes

characteristic, complemented

Q₈×D₅₃

—

D₄×D₅₃

—

Q₁₆×C₅₃

—

D₈×C₅₃

—

#11719925

—

#11719922

—

Dic₂₁₂

—

D₄₂₄

—

C₈×D₅₃

D₄

yes

characteristic

C₁₆×C₅₃

C₂³

yes

characteristic

#11719908

D₄

yes

characteristic

C₂²×D₅₃

—

Q₈×C₅₃

—

D₄×C₅₃

—

C₂²⋊D₅₃

—

D₂₁₂

—

C₄×D₅₃

—

C₄×D₅₃

D₈

yes

characteristic

Dic₁₀₆

—

Dic₁₀₆

—

C₈×C₅₃

C₂×D₄

yes

characteristic

#88322

D₈

yes

characteristic

C₂²×C₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

D₁₆

yes

characteristic

C₄×C₅₃

—

C₄×C₅₃

C₂×D₈

yes

characteristic

Dic₅₃

—

Dic₅₃

D₁₆

yes

characteristic

C₂×SD₆₄

—

maximal, Sylow

C₂×C₅₃

—

C₂×C₅₃

C₂×D₁₆

yes

characteristic

D₅₃

—

D₅₃

SD₆₄

yes

direct product factor

C₂×Q₃₂

—

C₂×D₁₆

—

SD₆₄

—

SD₆₄

—

SD₆₄

—

SD₆₄

D₅₃

yes

characteristic, direct product factor

C₂×C₃₂

—

C₅₃

C₂×SD₆₄

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

106

—

C₂×D₈

—

106

—

Q₃₂

—

Q₃₂

—

106

—

Q₃₂

C₂×D₅₃

yes

characteristic, complemented

D₁₆

—

D₁₆

—

106

—

D₁₆

C₂×D₅₃

yes

characteristic

C₂×C₁₆

—

C₃₂

—

C₃₂

C₂×D₅₃

yes

characteristic, complemented

C₂×Q₈

—

212

—

C₂×D₄

—

212

—

Q₁₆

—

Q₁₆

—

106

—

Q₁₆

—

212

—

D₈

—

D₈

—

106

—

D₈

—

212

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂²×D₅₃

yes

characteristic

C₂³

—

424

—

Q₈

—

Q₈

—

424

—

Q₈

—

212

—

D₄

—

D₄

—

424

—

D₄

—

212

—

C₂×C₄

—

C₂×C₄

—

424

—

C₈

—

C₈

D₄×D₅₃

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

848

—

C₂²

—

424

—

C₄

—

100

C₄

—

101

C₄

—

424

—

102

C₄

D₈×D₅₃

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

—

848

—

106

C₂

D₁₆×D₅₃

yes

characteristic

	subgroup	G/H
center	C₂	D₁₆×D₅₃
commutator	C₁₆×C₅₃	C₂³
Frattini	C₁₆	C₂²×D₅₃
Fitting	C₅₃×SD₆₄	C₂
socle	C₂×C₅₃	C₂×D₁₆
hypercenter	SD₆₄	D₅₃
hypocenter	C₅₃	C₂×SD₆₄
LCS	G ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

subgroup

G/H

center

C₂

D₁₆×D₅₃

commutator

C₁₆×C₅₃

C₂³

Frattini

C₁₆

C₂²×D₅₃

Fitting

C₅₃×SD₆₄

C₂

socle

C₂×C₅₃

C₂×D₁₆

hypercenter

SD₆₄

D₅₃

hypocenter

C₅₃

C₂×SD₆₄

LCS

G ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

N	H ≅ G/N	type
1. Q₃₂×D₅₃	C₂	semidirect
3. #16810462	C₂	semidirect
4. #16810461	C₂	semidirect
5. #16810460	C₂	semidirect
6. C₃₂×D₅₃	C₂	semidirect
7. C₅₃×SD₆₄	C₂	semidirect
10. Dic₄₂₄	C₂²	semidirect
15. #13133123	C₂²	semidirect
16. Q₃₂×C₅₃	C₂²	semidirect
18. C₃₂×C₅₃	C₂²	semidirect
53. D₅₃	SD₆₄	direct (N × H)
59. SD₆₄	D₅₃	direct (N × H)
61. C₅₃	C₂×SD₆₄	semidirect
66. Q₃₂	C₂×D₅₃	semidirect
72. C₃₂	C₂×D₅₃	semidirect

H ≅ G/N

type

1. Q₃₂×D₅₃

C₂

semidirect

3. #16810462

C₂

semidirect

4. #16810461

C₂

semidirect

5. #16810460

C₂

semidirect

6. C₃₂×D₅₃

C₂

semidirect

7. C₅₃×SD₆₄

C₂

semidirect

10. Dic₄₂₄

C₂²

semidirect

15. #13133123

C₂²

semidirect

16. Q₃₂×C₅₃

C₂²

semidirect

18. C₃₂×C₅₃

C₂²

semidirect

53. D₅₃

SD₆₄

direct (N × H)

59. SD₆₄

D₅₃

direct (N × H)

61. C₅₃

C₂×SD₆₄

semidirect

66. Q₃₂

C₂×D₅₃

semidirect

72. C₃₂

C₂×D₅₃

semidirect

Subgroups — SD₆₄×D₅₃ #20277014

Conjugacy classes of subgroups

Complements

Subgroups — SD64×D53 #20277014

Conjugacy classes of subgroups

Complements

Subgroups — SD₆₄×D₅₃ #20277014