Group #20244279 — subgroups

Subgroups — #20244279

Order 6016.

292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13094046	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093950	C₂	1	2	yes	maximal, complemented
3	#15689091	C₂	1	2	yes	maximal, complemented
4	C₂×#13093934	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#108×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625350	C₂²	1	2	yes	—
7	#13094046	—	2	2	no	—
8	#13094046	—	2	2	no	—
9	C₂×Dic₁₈₈	C₄	1	1	yes	characteristic, complemented
10	C₂×#10625325	C₄	1	2	yes	complemented
11	C₂×D₃₇₆	C₄	1	1	yes	characteristic, complemented
12	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
14	#13093950	—	2	4	no	—
15	(C₂×D₄₇)⋊C₈	—	2	4	no	—
16	#13093934	—	2	2	no	—
17	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	#108×C₄₇	—	2	2	no	—
20	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂×C₂²⋊D₄₇	—	2	2	no	—
22	C₂²×Dic₄₇	—	2	1	no	—
23	#10625350	—	2	2	no	—
24	#10625350	—	2	2	no	—
25	#10625350	—	2	2	no	—
26	#10625350	—	2	2	no	—
27	C₂×D₁₈₈	C₂×C₄	1	2	yes	—
28	C₂×C₄×D₄₇	—	2	2	no	—
29	C₂×Dic₉₄	C₂×C₄	1	2	yes	—
30	M₁₆×C₄₇	—	2	2	no	—
31	M₁₆×C₄₇	—	2	2	no	—
32	C₂×C₈×C₄₇	—	2	2	no	—
33	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₈×C₄₇	D₄	1	2	yes	—
36	C₂×C₈×C₄₇	D₄	1	2	yes	—
37	C₄×Dic₄₇	—	2	1	no	—
38	C₄×Dic₄₇	D₄	1	2	yes	—
39	C₂×C₄₇⋊C₈	—	2	1	no	—
40	C₂×C₄₇⋊C₈	—	2	1	no	—
41	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
42	Dic₁₈₈	—	2	2	no	—
43	D₃₇₆	—	2	2	no	—
44	#10625325	—	2	4	no	—
45	C₂³×C₄₇	#41	1	1	yes	characteristic
46	C₂²×D₄₇	—	2	2	no	—
47	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
53	C₂²⋊D₄₇	—	4	2	no	—
54	C₂²⋊D₄₇	—	4	2	no	—
55	C₂×Dic₄₇	—	2	2	no	—
56	C₂×Dic₄₇	—	2	2	no	—
57	C₂×Dic₄₇	—	4	2	no	—
58	D₁₈₈	—	2	2	no	—
59	D₁₈₈	—	2	2	no	—
60	C₄×D₄₇	—	4	2	no	—
61	C₄×D₄₇	—	4	2	no	—
62	Dic₉₄	—	2	2	no	—
63	Dic₉₄	—	2	2	no	—
64	C₈×C₄₇	—	4	2	no	—
65	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
66	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
67	C₄₇⋊C₈	—	2	2	no	—
68	C₂²×C₄₇	—	2	2	no	—
69	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
70	C₂²×C₄₇	#121	1	1	yes	characteristic
71	C₂²×C₄₇	#124	1	1	yes	characteristic
72	C₂×D₄₇	—	4	2	no	—
73	C₂×D₄₇	—	4	4	no	—
74	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
76	C₄×C₄₇	#121	1	1	yes	characteristic
77	C₄×C₄₇	#127	1	1	yes	characteristic
78	Dic₄₇	—	4	2	no	—
79	Dic₄₇	—	4	2	no	—
80	#1975	—	47	1	no	maximal, Sylow
81	C₂×C₄₇	—	2	1	no	—
82	C₂×C₄₇	—	2	1	no	—
83	C₂×C₄₇	#390	1	1	yes	characteristic
84	C₂×C₄₇	#444	1	2	yes	—
85	D₄₇	—	8	2	no	—
86	C₂×#135	—	47	1	no	—
87	C₂×#108	D₄₇	1	1	yes	characteristic, complemented
88	C₂×#104	—	47	2	no	—
89	#408	—	47	2	no	—
90	C₂×#97	—	47	1	no	—
91	C₄₇	#1975	1	1	yes	characteristic, complemented, Sylow
92	C₂×#41	—	47	2	no	—
93	#135	—	94	2	no	—
94	#135	—	94	2	no	—
95	C₂×Q₁₆	—	47	1	no	—
96	C₂×SD₁₆	—	47	2	no	—
97	C₂×D₈	—	47	1	no	—
98	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
99	C₂²×C₈	—	47	1	no	—
100	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
101	C₂×C₄²	—	47	1	no	—
102	#108	—	2	2	no	—
103	#104	—	94	4	no	—
104	C₂²⋊C₈	—	94	4	no	—
105	#97	—	94	2	no	—
106	#41	—	94	2	no	—
107	#41	—	94	2	no	—
108	#41	—	94	2	no	—
109	#41	—	94	2	no	—
110	C₂×Q₈	—	47	2	no	—
111	C₂×D₄	—	47	2	no	—
112	C₂×D₄	—	94	2	no	—
113	C₂²×C₄	—	94	1	no	—
114	C₂²×C₄	—	94	2	no	—
115	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
116	Q₁₆	—	94	2	no	—
117	SD₁₆	—	94	4	no	—
118	D₈	—	94	2	no	—
119	M₁₆	—	2	2	no	—
120	M₁₆	—	2	2	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	—	47	2	no	—
123	C₂×C₈	—	94	1	no	—
124	C₂×C₈	—	94	1	no	—
125	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
126	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
127	C₂×C₈	D₁₈₈	1	2	yes	—
128	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
129	C₄²	—	47	2	no	—
130	C₄²	—	94	1	no	—
131	C₂³	—	94	2	no	—
132	C₂³	#10625354	1	1	yes	characteristic
133	Q₈	—	94	2	no	—
134	Q₈	—	94	2	no	—
135	D₄	—	94	2	no	—
136	D₄	—	94	2	no	—
137	D₄	—	188	2	no	—
138	D₄	—	188	2	no	—
139	C₂×C₄	—	94	2	no	—
140	C₂×C₄	—	94	2	no	—
141	C₂×C₄	—	188	2	no	—
142	C₂×C₄	—	188	2	no	—
143	C₂×C₄	—	188	2	no	—
144	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
145	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
146	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
147	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
148	C₂×C₄	#10625354	1	1	yes	characteristic
149	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
150	C₈	—	4	2	no	—
151	C₈	—	94	2	no	—
152	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
153	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
154	C₂²	—	2	2	no	—
155	C₂²	—	188	4	no	—
156	C₂²	—	188	2	no	—
157	C₂²	#13093986	1	1	yes	characteristic
158	C₂²	#13093999	1	1	yes	characteristic
159	C₂²	#13094013	1	1	yes	characteristic
160	C₄	—	188	2	no	—
161	C₄	—	188	2	no	—
162	C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
163	C₄	#13093986	1	1	yes	characteristic
164	C₄	#13093999	1	1	yes	characteristic
165	C₄	#13094020	1	1	yes	characteristic
166	C₂	—	2	1	no	—
167	C₂	—	2	1	no	—
168	C₂	—	376	2	no	—
169	C₂	#15689024	1	1	yes	characteristic
170	C₂	#15689244	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094046

C₂

yes

maximal, characteristic

C₂×#13093950

C₂

yes

maximal, complemented

#15689091

C₂

yes

maximal, complemented

C₂×#13093934

C₂

yes

maximal, characteristic, complemented

C₂×#108×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×#10625350

C₂²

yes

—

#13094046

—

#13094046

—

C₂×Dic₁₈₈

C₄

yes

characteristic, complemented

C₂×#10625325

C₄

yes

complemented

C₂×D₃₇₆

C₄

yes

characteristic, complemented

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093950

—

(C₂×D₄₇)⋊C₈

—

#13093934

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#108×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂²×Dic₄₇

—

—

—

—

—

C₂×D₁₈₈

C₂×C₄

yes

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

C₂×C₄

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

Dic₁₈₈

—

D₃₇₆

—

#10625325

—

C₂³×C₄₇

#41

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂²⋊D₄₇

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄×D₄

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₄×D₄

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

#1975

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#390

yes

characteristic

C₂×C₄₇

#444

yes

—

D₄₇

—

C₂×#135

—

C₂×#108

D₄₇

yes

characteristic, complemented

C₂×#104

—

#408

—

C₂×#97

—

C₄₇

#1975

yes

characteristic, complemented, Sylow

C₂×#41

—

#135

—

#135

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

—

100

C₂²×C₈

C₂×D₄₇

yes

characteristic

101

C₂×C₄²

—

102

#108

—

103

#104

—

104

C₂²⋊C₈

—

105

#97

—

106

#41

—

107

#41

—

108

#41

—

109

#41

—

110

C₂×Q₈

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

C₂²×D₄₇

yes

characteristic

116

Q₁₆

—

117

SD₁₆

—

118

D₈

—

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₄×D₄₇

yes

characteristic

126

C₂×C₈

C₄×D₄₇

yes

characteristic

127

C₂×C₈

D₁₈₈

yes

—

128

C₂×C₈

C₂²⋊D₄₇

yes

—

129

C₄²

—

130

C₄²

—

131

C₂³

—

132

C₂³

#10625354

yes

characteristic

133

Q₈

—

134

Q₈

—

135

D₄

—

136

D₄

—

137

D₄

—

188

—

138

D₄

—

188

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

188

—

142

C₂×C₄

—

188

—

143

C₂×C₄

—

188

—

144

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

145

C₂×C₄

C₂×D₁₈₈

yes

characteristic

146

C₂×C₄

D₄×D₄₇

yes

characteristic

147

C₂×C₄

D₄×D₄₇

yes

characteristic

148

C₂×C₄

#10625354

yes

characteristic

149

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

150

C₈

—

151

C₈

—

152

C₈

(C₂×D₄₇)⋊C₄

yes

—

153

C₈

(C₂×D₄₇)⋊C₄

yes

—

154

C₂²

—

155

C₂²

—

188

—

156

C₂²

—

188

—

157

C₂²

#13093986

yes

characteristic

158

C₂²

#13093999

yes

characteristic

159

C₂²

#13094013

yes

characteristic

160

C₄

—

188

—

161

C₄

—

188

—

162

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

163

C₄

#13093986

yes

characteristic

164

C₄

#13093999

yes

characteristic

165

C₄

#13094020

yes

characteristic

166

C₂

—

167

C₂

—

168

C₂

—

376

—

169

C₂

#15689024

yes

characteristic

170

C₂

#15689244

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#108×C₄₇	C₂
socle	C₂²×C₄₇	C₄×D₄
hypercenter	C₂×#108	D₄₇
hypocenter	C₄₇	#1975
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#108×C₄₇

C₂

socle

C₂²×C₄₇

C₄×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
2. C₂×#13093950	C₂	semidirect
3. #15689091	C₂	semidirect
4. C₂×#13093934	C₂	semidirect
5. C₂×#108×C₄₇	C₂	semidirect
9. C₂×Dic₁₈₈	C₄	semidirect
10. C₂×#10625325	C₄	semidirect
11. C₂×D₃₇₆	C₄	semidirect
87. C₂×#108	D₄₇	semidirect
91. C₄₇	#1975	semidirect

H ≅ G/N

type

2. C₂×#13093950

C₂

semidirect

3. #15689091

C₂

semidirect

4. C₂×#13093934

C₂

semidirect

5. C₂×#108×C₄₇

C₂

semidirect

9. C₂×Dic₁₈₈

C₄

semidirect

10. C₂×#10625325

C₄

semidirect

11. C₂×D₃₇₆

C₄

semidirect

87. C₂×#108

D₄₇

semidirect

91. C₄₇

#1975

semidirect

Subgroups — #20244279

Conjugacy classes of subgroups

Complements