Group #21447653 — subgroups

Subgroups — #21447653

Order 7808.

146 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 63 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	#16840180	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840179	C₂	1	1	yes	maximal, characteristic, complemented
3	#16839877	C₂	1	1	yes	maximal, characteristic
4	#16839582	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839545	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#350	C₂	1	1	yes	maximal, characteristic, complemented
8	#14519797	C₄	1	1	yes	characteristic
9	#14519783	C₂²	1	1	yes	characteristic
10	#14519717	—	2	1	no	—
11	#14519717	C₂²	1	1	yes	characteristic
12	#14519716	—	2	1	no	—
13	C₂×#11758185	—	2	1	no	—
14	C₂×#11758185	C₂²	1	1	yes	characteristic
15	C₁₆×D₆₁	—	2	1	no	—
16	#14519712	C₄	1	1	yes	characteristic
17	#14519704	C₄	1	1	yes	characteristic
18	#14519703	C₄	1	1	yes	characteristic
19	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
20	#131×C₆₁	C₂²	1	1	yes	characteristic
21	M₃₂×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
23	#41×C₆₁	C₂×C₄	1	1	yes	characteristic
24	#11758222	C₂×C₄	1	1	yes	characteristic
25	M₁₆×C₆₁	—	2	1	no	—
26	M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₆₁	—	2	1	no	—
28	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
29	#11758202	C₈	1	1	yes	characteristic
30	#11758201	C₈	1	1	yes	characteristic
31	#11758200	C₈	1	1	yes	characteristic
32	#11758199	C₈	1	1	yes	characteristic
33	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
34	#11758194	C₂×C₄	1	1	yes	characteristic
35	C₂×#92418	C₂×C₄	1	1	yes	characteristic
36	#11758189	—	2	1	no	—
37	C₈×D₆₁	—	2	1	no	—
38	C₁₆×C₆₁	—	2	1	no	—
39	C₁₆×C₆₁	—	2	1	no	—
40	#11758185	—	2	1	no	—
41	#11758185	D₄	1	1	yes	characteristic
42	#11758185	D₄	1	1	yes	characteristic
43	Q₈×C₆₁	C₂×C₈	1	1	yes	characteristic
44	D₄×C₆₁	—	2	1	no	—
45	D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×C₆₁	—	2	1	no	—
47	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
48	C₂²⋊D₆₁	—	2	1	no	—
49	C₂×Dic₆₁	—	2	1	no	—
50	D₂₄₄	C₂×C₈	1	1	yes	characteristic
51	C₄×D₆₁	—	2	1	no	—
52	Dic₁₂₂	C₂×C₈	1	1	yes	characteristic
53	C₈×C₆₁	—	2	1	no	—
54	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
55	C₈×C₆₁	#41	1	1	yes	characteristic
56	#92418	—	2	1	no	—
57	#92418	C₂×C₈	1	1	yes	characteristic
58	#92418	C₂×C₈	1	1	yes	characteristic
59	C₂²×C₆₁	—	2	1	no	—
60	C₂²×C₆₁	#131	1	1	yes	characteristic
61	C₂×D₆₁	—	2	1	no	—
62	C₄×C₆₁	—	2	1	no	—
63	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
64	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
65	Dic₆₁	—	2	2	no	—
66	Dic₆₁	—	2	1	no	—
67	#2170	—	61	1	no	maximal, Sylow
68	C₂×C₆₁	—	2	1	no	—
69	C₂×C₆₁	—	4	1	no	—
70	C₂×C₆₁	C₈×D₄	1	1	yes	characteristic
71	D₆₁	—	4	1	no	—
72	#504	—	61	1	no	—
73	#504	—	61	1	no	—
74	#443	—	61	1	no	—
75	#364	—	61	1	no	—
76	#350	—	61	1	no	—
77	#350	D₆₁	1	1	yes	characteristic, complemented
78	C₄×C₁₆	—	61	1	no	—
79	C₆₁	#2170	1	1	yes	characteristic, complemented, Sylow
80	#135	—	61	1	no	—
81	#131	—	61	1	no	—
82	#131	C₂×D₆₁	1	1	yes	characteristic
83	M₃₂	—	61	1	no	—
84	M₃₂	—	122	1	no	—
85	M₃₂	—	122	1	no	—
86	M₃₂	C₂×D₆₁	1	1	yes	characteristic
87	C₂×C₁₆	—	61	1	no	—
88	C₂×C₁₆	—	122	1	no	—
89	C₂×C₁₆	—	122	1	no	—
90	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
91	#108	—	61	1	no	—
92	#104	—	61	1	no	—
93	#104	—	61	1	no	—
94	C₄×C₈	—	61	1	no	—
95	#41	—	61	1	no	—
96	#41	C₄×D₆₁	1	1	yes	characteristic
97	Q₁₆	—	61	1	no	—
98	SD₁₆	—	61	1	no	—
99	SD₁₆	—	61	1	no	—
100	D₈	—	61	1	no	—
101	M₁₆	—	2	1	no	—
102	M₁₆	—	61	1	no	—
103	M₁₆	—	122	1	no	—
104	M₁₆	C₄×D₆₁	1	1	yes	characteristic
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	61	1	no	—
107	C₂×C₈	—	122	1	no	—
108	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
109	C₄²	—	61	1	no	—
110	C₁₆	—	2	1	no	—
111	C₁₆	—	2	1	no	—
112	C₁₆	—	61	1	no	—
113	C₁₆	—	61	1	no	—
114	C₁₆	—	122	1	no	—
115	Q₈	—	61	1	no	—
116	Q₈	C₈×D₆₁	1	1	yes	characteristic
117	D₄	—	2	1	no	—
118	D₄	—	61	1	no	—
119	D₄	—	122	1	no	—
120	D₄	C₈×D₆₁	1	1	yes	characteristic
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	122	1	no	—
123	C₂×C₄	—	122	1	no	—
124	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	—	61	1	no	—
127	C₈	—	61	1	no	—
128	C₈	—	122	1	no	—
129	C₈	D₄×D₆₁	1	1	yes	characteristic
130	C₈	#11758224	1	1	yes	characteristic
131	C₂²	—	2	1	no	—
132	C₂²	—	122	1	no	—
133	C₂²	#14519785	1	1	yes	characteristic
134	C₄	—	2	1	no	—
135	C₄	—	122	2	no	—
136	C₄	—	122	1	no	—
137	C₄	#14519737	1	1	yes	characteristic
138	C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	1	no	—
141	C₂	—	244	1	no	—
142	C₂	#16839825	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840180

C₂

yes

maximal, characteristic, complemented

#16840179

C₂

yes

maximal, characteristic, complemented

#16839877

C₂

yes

maximal, characteristic

#16839582

C₂

yes

maximal, characteristic, complemented

#16839545

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₆₁

C₂

yes

maximal, characteristic, complemented

C₆₁×#350

C₂

yes

maximal, characteristic, complemented

#14519797

C₄

yes

characteristic

#14519783

C₂²

yes

characteristic

#14519717

—

#14519717

C₂²

yes

—

—

C₂²

yes

characteristic

C₁₆×D₆₁

—

#14519712

C₄

yes

characteristic

#14519704

C₄

yes

characteristic

#14519703

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

#131×C₆₁

C₂²

yes

characteristic

M₃₂×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

#41×C₆₁

C₂×C₄

yes

characteristic

#11758222

C₂×C₄

yes

characteristic

M₁₆×C₆₁

—

M₁₆×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

#11758202

C₈

yes

characteristic

#11758201

C₈

yes

characteristic

#11758200

C₈

yes

characteristic

#11758199

C₈

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

#11758194

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

C₈×D₆₁

—

C₁₆×C₆₁

—

C₁₆×C₆₁

—

#11758185

—

#11758185

D₄

yes

characteristic

#11758185

D₄

yes

characteristic

Q₈×C₆₁

C₂×C₈

yes

characteristic

D₄×C₆₁

—

D₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂²⋊D₆₁

—

C₂×Dic₆₁

—

D₂₄₄

C₂×C₈

yes

characteristic

C₄×D₆₁

—

Dic₁₂₂

C₂×C₈

yes

characteristic

C₈×C₆₁

—

C₈×C₆₁

C₂×D₄

yes

C₈×C₆₁

yes

—

C₂×C₈

yes

characteristic

#92418

C₂×C₈

yes

characteristic

C₂²×C₆₁

—

C₂²×C₆₁

#131

yes

characteristic

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

Dic₆₁

—

#2170

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

C₈×D₄

yes

characteristic

D₆₁

—

—

—

—

—

—

D₆₁

yes

characteristic, complemented

C₄×C₁₆

—

C₆₁

#2170

yes

characteristic, complemented, Sylow

#135

—

#131

—

#131

C₂×D₆₁

yes

characteristic

M₃₂

—

M₃₂

—

122

—

M₃₂

—

122

—

M₃₂

C₂×D₆₁

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

122

—

C₂×C₁₆

—

122

—

C₂×C₁₆

C₂×D₆₁

yes

—

—

—

C₄×C₈

—

#41

—

#41

C₄×D₆₁

yes

characteristic

Q₁₆

—

SD₁₆

—

SD₁₆

—

100

D₈

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

122

—

104

M₁₆

C₄×D₆₁

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

122

—

108

C₂×C₈

C₂²×D₆₁

yes

characteristic

109

C₄²

—

110

C₁₆

—

111

C₁₆

—

112

C₁₆

—

113

C₁₆

—

114

C₁₆

—

122

—

115

Q₈

—

116

Q₈

C₈×D₆₁

yes

characteristic

117

D₄

—

118

D₄

—

119

D₄

—

122

—

120

D₄

C₈×D₆₁

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

122

—

123

C₂×C₄

—

122

—

124

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

122

—

129

C₈

D₄×D₆₁

yes

characteristic

130

C₈

#11758224

yes

characteristic

131

C₂²

—

132

C₂²

—

122

—

133

C₂²

#14519785

yes

characteristic

134

C₄

—

135

C₄

—

122

—

136

C₄

—

122

—

137

C₄

#14519737

yes

characteristic

138

C₄

C₂×C₈×D₆₁

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

244

—

142

C₂

#16839825

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₆₁
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#350	C₂
socle	C₂×C₆₁	C₈×D₄
hypercenter	#350	D₆₁
hypocenter	C₆₁	#2170
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #350

subgroup

G/H

center

C₈

D₄×D₆₁

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#350

C₂

socle

C₂×C₆₁

C₈×D₄

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #350

N	H ≅ G/N	type
1. #16840180	C₂	semidirect
2. #16840179	C₂	semidirect
4. #16839582	C₂	semidirect
5. #16839545	C₂	semidirect
6. C₁₆×Dic₆₁	C₂	semidirect
7. C₆₁×#350	C₂	semidirect
77. #350	D₆₁	semidirect
79. C₆₁	#2170	semidirect

H ≅ G/N

type

1. #16840180

C₂

semidirect

2. #16840179

C₂

semidirect

4. #16839582

C₂

semidirect

5. #16839545

C₂

semidirect

6. C₁₆×Dic₆₁

C₂

semidirect

7. C₆₁×#350

C₂

semidirect

77. #350

D₆₁

semidirect

79. C₆₁

#2170

semidirect

Subgroups — #21447653

Conjugacy classes of subgroups

Complements