Group #21446940 — subgroups

Subgroups — #21446940

Order 7808.

342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14519807	C₂	1	2	yes	maximal
2	C₂²×Dic₂₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14519695	C₂	1	2	yes	maximal, complemented
4	#16839527	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#408	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₂₂	C₂²	1	2	yes	—
7	#14519807	—	2	4	no	—
8	#14519807	—	2	4	no	—
9	C₂×Dic₂₄₄	—	2	4	no	—
10	C₂×Dic₂₄₄	—	2	2	no	—
11	C₂×#11758202	—	2	2	no	—
12	C₂×#11758200	—	2	2	no	—
13	C₂×#11758194	C₂²	1	2	yes	—
14	#14519695	—	2	4	no	—
15	C₂×#41×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²⋊C₈×C₆₁	—	2	2	no	—
19	#41×C₆₁	—	2	2	no	—
20	#41×C₆₁	—	2	2	no	—
21	C₂×Q₈×C₆₁	D₄	1	1	yes	characteristic
22	C₂×D₄×C₆₁	—	2	1	no	—
23	C₂×D₄×C₆₁	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₆₁	—	2	1	no	—
25	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
26	C₂²×Dic₆₁	—	2	2	no	—
27	C₂×Dic₁₂₂	—	2	2	no	—
28	C₂×Dic₁₂₂	—	2	2	no	—
29	C₂×Dic₁₂₂	—	2	2	no	—
30	C₂×Dic₁₂₂	—	2	2	no	—
31	C₂×Dic₁₂₂	—	2	2	no	—
32	C₂×Dic₁₂₂	D₄	1	4	yes	—
33	M₁₆×C₆₁	—	2	2	no	—
34	C₂×C₈×C₆₁	—	2	2	no	—
35	C₂×C₈×C₆₁	—	2	1	no	—
36	C₂×C₈×C₆₁	D₄	1	2	yes	—
37	#11758202	—	2	8	no	—
38	#11758200	—	2	8	no	—
39	#11758194	—	2	2	no	—
40	#11758194	D₄	1	4	yes	—
41	C₂×#92418	—	2	2	no	—
42	Dic₂₄₄	—	2	8	no	—
43	C₂³×C₆₁	—	2	1	no	—
44	C₂³×C₆₁	#41	1	1	yes	characteristic
45	Q₈×C₆₁	—	2	2	no	—
46	D₄×C₆₁	—	2	2	no	—
47	D₄×C₆₁	—	4	2	no	—
48	C₂×C₄×C₆₁	—	2	1	no	—
49	C₂×C₄×C₆₁	—	4	1	no	—
50	C₂×C₄×C₆₁	—	4	1	no	—
51	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
55	C₂×Dic₆₁	—	2	4	no	—
56	C₂×Dic₆₁	—	4	2	no	—
57	C₂×Dic₆₁	—	4	2	no	—
58	Dic₁₂₂	—	2	4	no	—
59	Dic₁₂₂	—	2	4	no	—
60	Dic₁₂₂	—	4	2	no	—
61	Dic₁₂₂	—	4	2	no	—
62	C₈×C₆₁	—	2	2	no	—
63	C₈×C₆₁	—	4	1	no	—
64	#92418	—	2	4	no	—
65	C₂²×C₆₁	—	2	2	no	—
66	C₂²×C₆₁	—	4	1	no	—
67	C₂²×C₆₁	—	4	2	no	—
68	C₂²×C₆₁	#121	1	2	yes	—
69	C₂²×C₆₁	#121	1	1	yes	characteristic
70	C₄×C₆₁	—	4	1	no	—
71	C₄×C₆₁	#120	1	1	yes	characteristic
72	C₄×C₆₁	#120	1	2	yes	—
73	C₄×C₆₁	#127	1	1	yes	characteristic
74	Dic₆₁	—	4	4	no	—
75	#2020	—	61	1	no	maximal, Sylow
76	C₂×C₆₁	—	2	2	no	—
77	C₂×C₆₁	—	8	1	no	—
78	C₂×C₆₁	#392	1	1	yes	characteristic
79	C₂×C₆₁	#473	1	2	yes	—
80	C₂×#137	—	61	2	no	—
81	C₂²×Q₁₆	—	61	1	no	—
82	C₂×#101	—	61	2	no	—
83	#408	D₆₁	1	1	yes	characteristic
84	#341	—	61	1	no	—
85	C₆₁	#2020	1	1	yes	characteristic, complemented, Sylow
86	C₂×#41	C₂×D₆₁	1	1	yes	characteristic
87	C₂²×Q₈	—	61	2	no	—
88	#137	—	122	4	no	—
89	#137	—	122	4	no	—
90	C₂×Q₁₆	—	122	4	no	—
91	C₂×Q₁₆	—	122	2	no	—
92	C₂×Q₁₆	—	122	2	no	—
93	C₂×SD₁₆	—	122	2	no	—
94	C₂×M₁₆	—	61	2	no	—
95	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
96	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
97	#101	—	122	4	no	—
98	C₂²⋊C₈	—	2	2	no	—
99	#41	—	2	2	no	—
100	#41	—	2	2	no	—
101	C₂×Q₈	—	61	4	no	—
102	C₂×Q₈	—	122	2	no	—
103	C₂×Q₈	—	122	2	no	—
104	C₂×Q₈	—	122	2	no	—
105	C₂×Q₈	—	122	2	no	—
106	C₂×Q₈	—	122	2	no	—
107	C₂×Q₈	D₂₄₄	1	1	yes	characteristic
108	C₂×D₄	—	2	1	no	—
109	C₂×D₄	D₂₄₄	1	1	yes	characteristic
110	C₂²×C₄	—	2	1	no	—
111	C₂²×C₄	—	122	2	no	—
112	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
113	Q₁₆	—	122	8	no	—
114	Q₁₆	—	122	8	no	—
115	SD₁₆	—	122	8	no	—
116	M₁₆	—	2	2	no	—
117	M₁₆	—	61	4	no	—
118	M₁₆	—	122	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	2	1	no	—
121	C₂×C₈	—	122	2	no	—
122	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
123	C₂³	—	2	1	no	—
124	C₂³	#11758222	1	1	yes	characteristic
125	Q₈	—	2	2	no	—
126	Q₈	—	122	4	no	—
127	Q₈	—	122	4	no	—
128	Q₈	—	244	2	no	—
129	Q₈	—	244	2	no	—
130	D₄	—	2	2	no	—
131	D₄	—	4	2	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	122	4	no	—
136	C₂×C₄	—	244	2	no	—
137	C₂×C₄	—	244	2	no	—
138	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
139	C₂×C₄	D₄×D₆₁	1	2	yes	—
140	C₂×C₄	D₄×D₆₁	1	2	yes	—
141	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	4	1	no	—
144	C₈	—	122	4	no	—
145	C₂²	—	2	2	no	—
146	C₂²	—	4	2	no	—
147	C₂²	—	4	1	no	—
148	C₂²	#14519750	1	2	yes	—
149	C₂²	#14519751	1	1	yes	characteristic
150	C₄	—	4	1	no	—
151	C₄	—	244	4	no	—
152	C₄	#14519745	1	1	yes	characteristic
153	C₄	#14519747	1	2	yes	—
154	C₄	#14519773	1	1	yes	characteristic
155	C₂	—	2	2	no	—
156	C₂	—	8	1	no	—
157	C₂	#16839671	1	1	yes	characteristic
158	C₂	#16840037	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519807

C₂

yes

maximal

C₂²×Dic₂₄₄

C₂

yes

maximal, characteristic, complemented

C₂×#14519695

C₂

yes

maximal, complemented

#16839527

C₂

yes

maximal, characteristic, complemented

C₆₁×#408

C₂

yes

maximal, characteristic

C₂²×Dic₁₂₂

C₂²

yes

—

#14519807

—

#14519807

—

C₂×Dic₂₄₄

—

C₂×Dic₂₄₄

—

C₂×#11758202

—

C₂×#11758200

—

C₂×#11758194

C₂²

yes

—

#14519695

—

C₂×#41×C₆₁

C₂²

yes

characteristic

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂²⋊C₈×C₆₁

—

#41×C₆₁

—

#41×C₆₁

—

C₂×Q₈×C₆₁

D₄

yes

characteristic

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

D₄

yes

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

D₄

yes

—

—

—

—

D₄

yes

—

C₂×#92418

—

Dic₂₄₄

—

C₂³×C₆₁

—

C₂³×C₆₁

#41

yes

characteristic

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#121

yes

—

C₂²×C₆₁

#121

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

#120

yes

characteristic

C₄×C₆₁

#120

yes

—

C₄×C₆₁

#127

yes

characteristic

Dic₆₁

—

#2020

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#392

yes

characteristic

C₂×C₆₁

#473

yes

—

C₂×#137

—

C₂²×Q₁₆

—

C₂×#101

—

#408

D₆₁

yes

characteristic

#341

—

C₆₁

#2020

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₆₁

yes

characteristic

C₂²×Q₈

—

#137

—

122

—

#137

—

122

—

C₂×Q₁₆

—

122

—

C₂×Q₁₆

—

122

—

C₂×Q₁₆

—

122

—

C₂×SD₁₆

—

122

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

#101

—

122

—

C₂²⋊C₈

—

#41

—

100

#41

—

101

C₂×Q₈

—

102

C₂×Q₈

—

122

—

103

C₂×Q₈

—

122

—

104

C₂×Q₈

—

122

—

105

C₂×Q₈

—

122

—

106

C₂×Q₈

—

122

—

107

C₂×Q₈

D₂₄₄

yes

characteristic

108

C₂×D₄

—

109

C₂×D₄

D₂₄₄

yes

characteristic

110

C₂²×C₄

—

111

C₂²×C₄

—

122

—

112

C₂²×C₄

C₂²×D₆₁

yes

characteristic

113

Q₁₆

—

122

—

114

Q₁₆

—

122

—

115

SD₁₆

—

122

—

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

122

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

—

122

C₂×C₈

C₂²⋊D₆₁

yes

—

123

C₂³

—

124

C₂³

#11758222

yes

characteristic

125

Q₈

—

126

Q₈

—

122

—

127

Q₈

—

122

—

128

Q₈

—

244

—

129

Q₈

—

244

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

122

—

136

C₂×C₄

—

244

—

137

C₂×C₄

—

244

—

138

C₂×C₄

C₂×D₂₄₄

yes

characteristic

139

C₂×C₄

D₄×D₆₁

yes

—

140

C₂×C₄

D₄×D₆₁

yes

—

141

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

122

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

#14519750

yes

—

149

C₂²

#14519751

yes

characteristic

150

C₄

—

151

C₄

—

244

—

152

C₄

#14519745

yes

characteristic

153

C₄

#14519747

yes

—

154

C₄

#14519773

yes

characteristic

155

C₂

—

156

C₂

—

157

C₂

#16839671

yes

characteristic

158

C₂

#16840037

yes

—

	subgroup	G/H
center	C₂²	#14519751
commutator	C₂²×C₄×C₆₁	C₂³
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#408	C₂
socle	C₂²×C₆₁	#121
hypercenter	#408	D₆₁
hypocenter	C₆₁	#2020
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #408

subgroup

G/H

center

C₂²

#14519751

commutator

C₂²×C₄×C₆₁

C₂³

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#408

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #408

N	H ≅ G/N	type
2. C₂²×Dic₂₄₄	C₂	semidirect
3. C₂×#14519695	C₂	semidirect
4. #16839527	C₂	semidirect
85. C₆₁	#2020	semidirect

H ≅ G/N

type

2. C₂²×Dic₂₄₄

C₂

semidirect

3. C₂×#14519695

C₂

semidirect

4. #16839527

C₂

semidirect

85. C₆₁

#2020

semidirect

Subgroups — #21446940

Conjugacy classes of subgroups

Complements