Group #20287819 — subgroups

Subgroups — C₂×D₁₆×D₅₃ #20287819

Order 6784.

440 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 125 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	C₂×D₈×D₅₃	C₂	1	2	yes	maximal, complemented
2	C₂×D₈₄₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13133158	C₂	1	2	yes	maximal, complemented
4	D₁₆×D₅₃	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄×D₅₃	—	2	2	no	—
8	C₂×D₄₂₄	C₂²	1	2	yes	complemented
9	C₂×#11719922	—	2	2	no	—
10	D₈×D₅₃	—	2	4	no	—
11	D₈×D₅₃	C₂²	1	8	yes	complemented
12	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic
13	D₈₄₈	C₂²	1	4	yes	complemented
14	#13133158	C₂²	1	8	yes	complemented
15	C₂×#11719908	C₂²	1	1	yes	characteristic, complemented
16	C₁₆×D₅₃	C₂²	1	4	yes	complemented
17	C₂×D₈×C₅₃	C₂²	1	2	yes	complemented
18	D₁₆×C₅₃	C₂²	1	4	yes	complemented
19	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₅₃	—	4	2	no	—
21	C₂×D₄×C₅₃	—	2	2	no	—
22	C₂×C₂²⋊D₅₃	—	4	2	no	—
23	D₄×D₅₃	—	2	8	no	—
24	D₄×D₅₃	—	4	4	no	—
25	C₂×D₂₁₂	—	2	2	no	—
26	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
27	D₈×C₅₃	—	2	2	no	—
28	D₈×C₅₃	C₂³	1	4	yes	complemented
29	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
30	#11719922	—	2	8	no	—
31	C₂×#88322	D₄	1	1	yes	characteristic
32	D₄₂₄	—	2	2	no	—
33	D₄₂₄	C₂³	1	4	yes	complemented
34	C₈×D₅₃	D₄	1	2	yes	—
35	C₈×D₅₃	C₂³	1	2	yes	—
36	C₁₆×C₅₃	C₂³	1	2	yes	complemented
37	#11719908	C₂³	1	2	yes	complemented
38	C₂³×C₅₃	—	4	2	no	—
39	C₂²×D₅₃	—	4	2	no	—
40	C₂²×D₅₃	—	4	8	no	—
41	C₂²×D₅₃	—	8	8	no	—
42	C₂²×D₅₃	D₈	1	1	yes	characteristic
43	D₄×C₅₃	—	2	4	no	—
44	D₄×C₅₃	—	4	2	no	—
45	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
46	C₂²⋊D₅₃	—	4	8	no	—
47	C₂×Dic₅₃	D₈	1	1	yes	characteristic
48	D₂₁₂	—	2	4	no	—
49	D₂₁₂	—	4	2	no	—
50	C₄×D₅₃	D₈	1	2	yes	—
51	C₄×D₅₃	C₂×D₄	1	2	yes	—
52	C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
53	C₈×C₅₃	C₂⁴	1	1	yes	characteristic
54	#88322	C₂×D₄	1	2	yes	—
55	C₂²×C₅₃	—	4	4	no	—
56	C₂²×C₅₃	—	8	4	no	—
57	C₂²×C₅₃	C₂×D₈	1	1	yes	characteristic
58	C₂×D₅₃	—	4	4	no	—
59	C₂×D₅₃	—	8	4	no	—
60	C₂×D₅₃	—	8	16	no	—
61	C₂×D₅₃	D₁₆	1	4	yes	direct product factor
62	C₂×D₅₃	C₂×D₈	1	2	yes	—
63	C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
64	C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
65	Dic₅₃	C₂×D₈	1	2	yes	—
66	C₂²×D₁₆	—	53	1	no	maximal, Sylow
67	C₂×C₅₃	—	8	4	no	—
68	C₂×C₅₃	C₂×D₁₆	1	2	yes	complemented
69	C₂×C₅₃	C₂²×D₈	1	1	yes	characteristic
70	D₅₃	—	8	4	no	—
71	D₅₃	C₂×D₁₆	1	4	yes	direct product factor
72	C₂²×D₈	—	53	2	no	—
73	C₂×D₁₆	—	53	2	no	—
74	C₂×D₁₆	—	53	8	no	—
75	C₂×D₁₆	—	53	1	no	—
76	C₂×D₁₆	D₅₃	1	1	yes	characteristic, direct product factor
77	C₂²×C₁₆	—	53	1	no	—
78	C₅₃	C₂²×D₁₆	1	1	yes	characteristic, complemented, Sylow
79	C₂²×D₄	—	106	2	no	—
80	C₂×D₈	—	53	8	no	—
81	C₂×D₈	—	53	2	no	—
82	C₂×D₈	—	106	4	no	—
83	C₂×D₈	—	106	2	no	—
84	C₂×D₈	C₂×D₅₃	1	2	yes	complemented
85	C₂²×C₈	—	53	1	no	—
86	D₁₆	—	53	8	no	—
87	D₁₆	—	53	4	no	—
88	D₁₆	C₂×D₅₃	1	4	yes	direct product factor
89	C₂×C₁₆	—	53	1	no	—
90	C₂×C₁₆	—	53	4	no	—
91	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
92	C₂⁴	—	212	2	no	—
93	C₂×D₄	—	2	2	no	—
94	C₂×D₄	—	106	8	no	—
95	C₂×D₄	—	106	2	no	—
96	C₂×D₄	—	212	4	no	—
97	C₂×D₄	—	212	2	no	—
98	C₂²×C₄	—	53	1	no	—
99	D₈	—	2	2	no	—
100	D₈	—	53	4	no	—
101	D₈	—	106	8	no	—
102	D₈	—	106	2	no	—
103	D₈	C₂²×D₅₃	1	4	yes	complemented
104	C₂×C₈	—	53	1	no	—
105	C₂×C₈	—	53	2	no	—
106	C₂×C₈	—	53	2	no	—
107	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
108	C₁₆	—	53	2	no	—
109	C₁₆	C₂²×D₅₃	1	2	yes	complemented
110	C₂³	—	4	2	no	—
111	C₂³	—	53	1	no	—
112	C₂³	—	424	8	no	—
113	C₂³	—	212	8	no	—
114	C₂³	—	212	2	no	—
115	D₄	—	2	4	no	—
116	D₄	—	4	2	no	—
117	D₄	—	106	4	no	—
118	D₄	—	212	8	no	—
119	D₄	—	212	2	no	—
120	C₂×C₄	—	53	1	no	—
121	C₂×C₄	—	53	2	no	—
122	C₂×C₄	—	53	2	no	—
123	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
124	C₈	—	53	2	no	—
125	C₈	D₄×D₅₃	1	1	yes	characteristic
126	C₈	C₂³×D₅₃	1	1	yes	characteristic
127	C₂²	—	4	4	no	—
128	C₂²	—	8	4	no	—
129	C₂²	—	53	4	no	—
130	C₂²	—	53	2	no	—
131	C₂²	—	424	16	no	—
132	C₂²	—	424	4	no	—
133	C₂²	—	212	4	no	—
134	C₂²	D₈×D₅₃	1	1	yes	characteristic
135	C₄	—	53	2	no	—
136	C₄	D₈×D₅₃	1	1	yes	characteristic
137	C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
138	C₂	—	8	4	no	—
139	C₂	—	53	4	no	—
140	C₂	—	424	4	no	—
141	C₂	D₁₆×D₅₃	1	2	yes	direct product factor
142	C₂	C₂×D₈×D₅₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₈×D₅₃

C₂

yes

maximal, complemented

C₂×D₈₄₈

C₂

yes

maximal, characteristic, complemented

C₂×#13133158

C₂

yes

maximal, complemented

D₁₆×D₅₃

C₂

yes

maximal, direct product factor

C₂×C₁₆×D₅₃

C₂

yes

maximal, characteristic, complemented

C₂×D₁₆×C₅₃

C₂

yes

maximal, characteristic, complemented

C₂×D₄×D₅₃

—

C₂×D₄₂₄

C₂²

yes

complemented

C₂×#11719922

—

D₈×D₅₃

—

D₈×D₅₃

C₂²

yes

complemented

C₂×C₈×D₅₃

C₂²

yes

characteristic

D₈₄₈

C₂²

yes

complemented

#13133158

C₂²

yes

complemented

C₂×#11719908

C₂²

yes

characteristic, complemented

C₁₆×D₅₃

C₂²

yes

complemented

C₂×D₈×C₅₃

C₂²

yes

complemented

D₁₆×C₅₃

C₂²

yes

complemented

C₂×C₁₆×C₅₃

C₂²

yes

characteristic, complemented

C₂³×D₅₃

—

C₂×D₄×C₅₃

—

C₂×C₂²⋊D₅₃

—

D₄×D₅₃

—

D₄×D₅₃

—

C₂×D₂₁₂

—

C₂×C₄×D₅₃

D₄

yes

characteristic

D₈×C₅₃

—

D₈×C₅₃

C₂³

yes

complemented

C₂×C₈×C₅₃

C₂³

yes

characteristic

#11719922

—

C₂×#88322

D₄

yes

characteristic

D₄₂₄

—

D₄₂₄

C₂³

yes

complemented

C₈×D₅₃

D₄

yes

—

C₈×D₅₃

C₂³

yes

—

C₁₆×C₅₃

C₂³

yes

complemented

#11719908

C₂³

yes

complemented

C₂³×C₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

D₈

yes

characteristic

D₄×C₅₃

—

D₄×C₅₃

—

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²⋊D₅₃

—

C₂×Dic₅₃

D₈

yes

characteristic

D₂₁₂

—

D₂₁₂

—

C₄×D₅₃

D₈

yes

—

C₄×D₅₃

C₂×D₄

yes

—

C₈×C₅₃

C₂×D₄

yes

characteristic

C₈×C₅₃

C₂⁴

yes

characteristic

#88322

C₂×D₄

yes

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

C₂×D₈

yes

characteristic

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

D₁₆

yes

direct product factor

C₂×D₅₃

C₂×D₈

yes

—

C₄×C₅₃

C₂×D₈

yes

characteristic

C₄×C₅₃

C₂²×D₄

yes

characteristic

Dic₅₃

C₂×D₈

yes

—

C₂²×D₁₆

—

maximal, Sylow

C₂×C₅₃

—

C₂×C₅₃

C₂×D₁₆

yes

complemented

C₂×C₅₃

C₂²×D₈

yes

characteristic

D₅₃

—

D₅₃

C₂×D₁₆

yes

direct product factor

C₂²×D₈

—

C₂×D₁₆

—

C₂×D₁₆

—

C₂×D₁₆

—

C₂×D₁₆

D₅₃

yes

characteristic, direct product factor

C₂²×C₁₆

—

C₅₃

C₂²×D₁₆

yes

characteristic, complemented, Sylow

C₂²×D₄

—

106

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

106

—

C₂×D₈

—

106

—

C₂×D₈

C₂×D₅₃

yes

complemented

C₂²×C₈

—

D₁₆

—

D₁₆

—

D₁₆

C₂×D₅₃

yes

direct product factor

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₅₃

yes

characteristic, complemented

C₂⁴

—

212

—

C₂×D₄

—

C₂×D₄

—

106

—

C₂×D₄

—

106

—

C₂×D₄

—

212

—

C₂×D₄

—

212

—

C₂²×C₄

—

D₈

—

100

D₈

—

101

D₈

—

106

—

102

D₈

—

106

—

103

D₈

C₂²×D₅₃

yes

complemented

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

C₂²×D₅₃

yes

characteristic

108

C₁₆

—

109

C₁₆

C₂²×D₅₃

yes

complemented

110

C₂³

—

111

C₂³

—

112

C₂³

—

424

—

113

C₂³

—

212

—

114

C₂³

—

212

—

115

D₄

—

116

D₄

—

117

D₄

—

106

—

118

D₄

—

212

—

119

D₄

—

212

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

D₄×D₅₃

yes

characteristic

124

C₈

—

125

C₈

D₄×D₅₃

yes

characteristic

126

C₈

C₂³×D₅₃

yes

characteristic

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

424

—

132

C₂²

—

424

—

133

C₂²

—

212

—

134

C₂²

D₈×D₅₃

yes

characteristic

135

C₄

—

136

C₄

D₈×D₅₃

yes

characteristic

137

C₄

C₂×D₄×D₅₃

yes

characteristic

138

C₂

—

139

C₂

—

140

C₂

—

424

—

141

C₂

D₁₆×D₅₃

yes

direct product factor

142

C₂

C₂×D₈×D₅₃

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₅₃
commutator	C₈×C₅₃	C₂⁴
Frattini	C₈	C₂³×D₅₃
Fitting	C₂×D₁₆×C₅₃	C₂
socle	C₂²×C₅₃	C₂×D₈
hypercenter	C₂×D₁₆	D₅₃
hypocenter	C₅₃	C₂²×D₁₆
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₅₃

commutator

C₈×C₅₃

C₂⁴

Frattini

C₈

C₂³×D₅₃

Fitting

C₂×D₁₆×C₅₃

C₂

socle

C₂²×C₅₃

C₂×D₈

hypercenter

C₂×D₁₆

D₅₃

hypocenter

C₅₃

C₂²×D₁₆

LCS

G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. C₂×D₈×D₅₃	C₂	semidirect
2. C₂×D₈₄₈	C₂	semidirect
3. C₂×#13133158	C₂	semidirect
4. D₁₆×D₅₃	C₂	direct (N × H)
5. C₂×C₁₆×D₅₃	C₂	semidirect
6. C₂×D₁₆×C₅₃	C₂	semidirect
8. C₂×D₄₂₄	C₂²	semidirect
11. D₈×D₅₃	C₂²	semidirect
13. D₈₄₈	C₂²	semidirect
14. #13133158	C₂²	semidirect
15. C₂×#11719908	C₂²	semidirect
16. C₁₆×D₅₃	C₂²	semidirect
17. C₂×D₈×C₅₃	C₂²	semidirect
18. D₁₆×C₅₃	C₂²	semidirect
19. C₂×C₁₆×C₅₃	C₂²	semidirect
28. D₈×C₅₃	C₂³	semidirect
33. D₄₂₄	C₂³	semidirect
36. C₁₆×C₅₃	C₂³	semidirect
37. #11719908	C₂³	semidirect
61. C₂×D₅₃	D₁₆	direct (N × H)
68. C₂×C₅₃	C₂×D₁₆	semidirect
71. D₅₃	C₂×D₁₆	direct (N × H)
76. C₂×D₁₆	D₅₃	direct (N × H)
78. C₅₃	C₂²×D₁₆	semidirect
84. C₂×D₈	C₂×D₅₃	semidirect
88. D₁₆	C₂×D₅₃	direct (N × H)
91. C₂×C₁₆	C₂×D₅₃	semidirect
103. D₈	C₂²×D₅₃	semidirect
109. C₁₆	C₂²×D₅₃	semidirect
141. C₂	D₁₆×D₅₃	direct (N × H)

H ≅ G/N

type

1. C₂×D₈×D₅₃

C₂

semidirect

2. C₂×D₈₄₈

C₂

semidirect

3. C₂×#13133158

C₂

semidirect

4. D₁₆×D₅₃

C₂

direct (N × H)

5. C₂×C₁₆×D₅₃

C₂

semidirect

6. C₂×D₁₆×C₅₃

C₂

semidirect

8. C₂×D₄₂₄

C₂²

semidirect

11. D₈×D₅₃

C₂²

semidirect

13. D₈₄₈

C₂²

semidirect

14. #13133158

C₂²

semidirect

15. C₂×#11719908

C₂²

semidirect

16. C₁₆×D₅₃

C₂²

semidirect

17. C₂×D₈×C₅₃

C₂²

semidirect

18. D₁₆×C₅₃

C₂²

semidirect

19. C₂×C₁₆×C₅₃

C₂²

semidirect

28. D₈×C₅₃

C₂³

semidirect

33. D₄₂₄

C₂³

semidirect

36. C₁₆×C₅₃

C₂³

semidirect

37. #11719908

C₂³

semidirect

61. C₂×D₅₃

D₁₆

direct (N × H)

68. C₂×C₅₃

C₂×D₁₆

semidirect

71. D₅₃

C₂×D₁₆

direct (N × H)

76. C₂×D₁₆

D₅₃

direct (N × H)

78. C₅₃

C₂²×D₁₆

semidirect

84. C₂×D₈

C₂×D₅₃

semidirect

88. D₁₆

C₂×D₅₃

direct (N × H)

91. C₂×C₁₆

C₂×D₅₃

semidirect

103. D₈

C₂²×D₅₃

semidirect

109. C₁₆

C₂²×D₅₃

semidirect

141. C₂

D₁₆×D₅₃

direct (N × H)

Subgroups — C₂×D₁₆×D₅₃ #20287819

Conjugacy classes of subgroups

Complements

Subgroups — C2×D16×D53 #20287819

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₁₆×D₅₃ #20287819