Group #20243179 — subgroups

Subgroups — #20243179

Order 6016.

360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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×#13093986	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093940	C₂	1	2	yes	maximal
3	M₁₆×Dic₄₇	C₂	1	2	yes	maximal, complemented
4	#15688892	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#343	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄×D₄₇	C₄	1	2	yes	—
8	C₂×#10625329	C₂²	1	2	yes	—
9	#13093986	—	2	2	no	—
10	#13093986	—	2	2	no	—
11	C₂×(C₂×D₄₇)⋊C₄	C₄	1	2	yes	—
12	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	#13093940	C₄	1	8	yes	complemented
14	#13093934	—	2	2	no	—
15	C₈×Dic₄₇	—	2	2	no	—
16	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂³×D₄₇	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂×D₁₈₈	—	2	2	no	—
24	C₂×D₁₈₈	—	2	1	no	—
25	C₂×D₁₈₈	—	2	1	no	—
26	C₂×D₁₈₈	C₂×C₄	1	4	yes	—
27	C₂×C₄×D₄₇	—	2	2	no	—
28	C₂×C₄×D₄₇	—	2	2	no	—
29	C₂×C₄×D₄₇	—	4	4	no	—
30	M₁₆×C₄₇	—	2	2	no	—
31	M₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
32	C₂×C₈×C₄₇	—	2	2	no	—
33	C₄⋊C₄×C₄₇	—	2	2	no	—
34	(C₂×D₄₇)⋊C₄	—	2	4	no	—
35	C₄×Dic₄₇	D₄	1	2	yes	—
36	C₄×Dic₄₇	D₄	1	2	yes	—
37	#10625329	—	2	2	no	—
38	#10625329	C₂×C₄	1	4	yes	complemented
39	C₂×C₄₇⋊C₈	—	2	2	no	—
40	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₂²×D₄₇	—	2	2	no	—
42	C₂²×D₄₇	—	2	2	no	—
43	C₂²×D₄₇	—	4	2	no	—
44	C₂²×D₄₇	—	4	2	no	—
45	C₂²×D₄₇	C₄²	1	4	yes	—
46	C₂×C₄×C₄₇	—	2	2	no	—
47	C₂×C₄×C₄₇	—	4	2	no	—
48	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
49	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
51	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
52	C₂×Dic₄₇	—	2	2	no	—
53	C₂×Dic₄₇	—	4	1	no	—
54	C₂×Dic₄₇	C₂²⋊C₄	1	2	yes	—
55	C₂×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
57	D₁₈₈	—	2	4	no	—
58	D₁₈₈	—	2	4	no	—
59	C₄×D₄₇	—	4	4	no	—
60	C₄×D₄₇	—	4	4	no	—
61	C₈×C₄₇	—	2	4	no	—
62	C₄₇⋊C₈	—	2	4	no	—
63	C₂²×C₄₇	—	2	1	no	—
64	C₂²×C₄₇	—	2	1	no	—
65	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
66	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄₇	#117	1	1	yes	characteristic
68	C₂×D₄₇	—	2	4	no	—
69	C₂×D₄₇	—	4	4	no	—
70	C₂×D₄₇	—	4	2	no	—
71	C₂×D₄₇	—	4	2	no	—
72	C₂×D₄₇	—	4	4	no	—
73	C₄×C₄₇	—	4	2	no	—
74	C₄×C₄₇	C₄×D₄	1	2	yes	—
75	C₄×C₄₇	C₄×D₄	1	2	yes	—
76	Dic₄₇	—	2	1	no	—
77	Dic₄₇	—	2	2	no	—
78	Dic₄₇	#100	1	2	yes	complemented
79	C₄×#100	—	47	1	no	maximal, Sylow
80	C₂×C₄₇	—	2	1	no	—
81	C₂×C₄₇	—	2	1	no	—
82	C₂×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄₇	C₂×#100	1	1	yes	characteristic
84	C₂×C₄₇	#413	1	1	yes	characteristic
85	D₄₇	—	4	4	no	—
86	C₂×C₄×D₄	—	47	1	no	—
87	C₂×#100	—	47	2	no	—
88	C₄×M₁₆	—	47	2	no	—
89	#343	—	47	1	no	—
90	#343	D₄₇	1	1	yes	characteristic, complemented
91	C₄₇	C₄×#100	1	1	yes	characteristic, complemented, Sylow
92	C₂²×D₄	—	47	1	no	—
93	C₂³×C₄	—	47	2	no	—
94	C₂×M₁₆	—	47	2	no	—
95	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
96	C₄×D₄	—	94	2	no	—
97	C₄×D₄	—	94	2	no	—
98	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
99	C₂×C₂²⋊C₄	—	47	2	no	—
100	C₂×C₄²	—	47	1	no	—
101	#100	—	47	8	no	—
102	#97	—	94	2	no	—
103	C₄×C₈	—	94	2	no	—
104	C₂⁴	—	47	2	no	—
105	C₂×D₄	—	47	4	no	—
106	C₂×D₄	—	94	2	no	—
107	C₂×D₄	—	94	1	no	—
108	C₂×D₄	—	94	1	no	—
109	C₂²×C₄	—	47	1	no	—
110	C₂²×C₄	—	47	1	no	—
111	C₂²×C₄	—	94	2	no	—
112	C₂²×C₄	—	94	2	no	—
113	C₂²×C₄	—	188	4	no	—
114	C₂²×C₄	C₄×D₄₇	1	2	yes	—
115	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
116	M₁₆	—	2	2	no	—
117	M₁₆	—	47	4	no	—
118	M₁₆	—	94	2	no	—
119	M₁₆	C₄×D₄₇	1	4	yes	complemented
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	—	94	2	no	—
122	C₄⋊C₄	—	2	2	no	—
123	C₂²⋊C₄	—	94	4	no	—
124	C₄²	—	47	2	no	—
125	C₄²	—	47	2	no	—
126	C₂³	—	47	4	no	—
127	C₂³	—	94	2	no	—
128	C₂³	—	94	2	no	—
129	C₂³	—	188	2	no	—
130	C₂³	—	188	2	no	—
131	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
132	D₄	—	94	4	no	—
133	D₄	—	94	4	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	4	2	no	—
136	C₂×C₄	—	47	1	no	—
137	C₂×C₄	—	47	2	no	—
138	C₂×C₄	—	47	1	no	—
139	C₂×C₄	—	94	2	no	—
140	C₂×C₄	—	188	4	no	—
141	C₂×C₄	—	188	4	no	—
142	C₂×C₄	—	188	1	no	—
143	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
144	C₂×C₄	D₄×D₄₇	1	2	yes	—
145	C₂×C₄	#10625352	1	1	yes	characteristic
146	C₂×C₄	#10625354	1	1	yes	characteristic
147	C₈	—	2	4	no	—
148	C₈	—	94	4	no	—
149	C₂²	—	2	1	no	—
150	C₂²	—	2	1	no	—
151	C₂²	—	94	4	no	—
152	C₂²	—	188	4	no	—
153	C₂²	—	188	4	no	—
154	C₂²	—	188	2	no	—
155	C₂²	—	188	2	no	—
156	C₂²	C₄²×D₄₇	1	1	yes	characteristic
157	C₂²	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
158	C₂²	#13093982	1	1	yes	characteristic
159	C₄	—	4	2	no	—
160	C₄	—	47	2	no	—
161	C₄	—	94	1	no	—
162	C₄	—	94	2	no	—
163	C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
164	C₄	#13093986	1	2	yes	—
165	C₂	—	2	1	no	—
166	C₂	—	2	1	no	—
167	C₂	—	188	4	no	—
168	C₂	#15688970	1	1	yes	characteristic
169	C₂	#100×D₄₇	1	1	yes	characteristic
170	C₂	#15689106	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093986

C₂

yes

maximal, characteristic

C₂×#13093940

C₂

yes

maximal

M₁₆×Dic₄₇

C₂

yes

maximal, complemented

#15688892

C₂

yes

maximal, characteristic, complemented

C₄₇×#343

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

characteristic

C₂²×C₄×D₄₇

C₄

yes

—

C₂×#10625329

C₂²

yes

—

#13093986

—

#13093986

—

C₂×(C₂×D₄₇)⋊C₄

C₄

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093940

C₄

yes

complemented

#13093934

—

C₈×Dic₄₇

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂³×D₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂×C₄

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

C₂×C₄

yes

complemented

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄×Dic₄₇

D₄

yes

—

C₄×Dic₄₇

D₄

yes

—

#10625329

—

#10625329

C₂×C₄

yes

complemented

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₄²

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²⋊C₄

yes

—

C₂×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₇

C₂²⋊C₄

yes

characteristic

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄²

yes

characteristic

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

#117

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

—

C₄×C₄₇

C₄×D₄

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

yes

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

C₄×C₂²⋊C₄

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

C₂×C₄×D₄

—

C₂×#100

—

C₄×M₁₆

—

#343

—

#343

D₄₇

yes

characteristic, complemented

C₄₇

C₄×#100

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

C₂×C₂²⋊C₄

—

100

C₂×C₄²

—

101

#100

—

102

#97

—

103

C₄×C₈

—

104

C₂⁴

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

188

—

114

C₂²×C₄

C₄×D₄₇

yes

—

115

C₂²×C₄

C₂²×D₄₇

yes

characteristic

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

119

M₁₆

C₄×D₄₇

yes

complemented

120

C₂×C₈

—

121

C₂×C₈

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₄²

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

—

188

—

130

C₂³

—

188

—

131

C₂³

C₂×C₄×D₄₇

yes

characteristic

132

D₄

—

133

D₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

188

—

141

C₂×C₄

—

188

—

142

C₂×C₄

—

188

—

143

C₂×C₄

C₂×C₄×D₄₇

yes

—

144

C₂×C₄

D₄×D₄₇

yes

—

145

C₂×C₄

#10625352

yes

characteristic

146

C₂×C₄

#10625354

yes

characteristic

147

C₈

—

148

C₈

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

188

—

153

C₂²

—

188

—

154

C₂²

—

188

—

155

C₂²

—

188

—

156

C₂²

C₄²×D₄₇

yes

characteristic

157

C₂²

C₂²⋊C₄×D₄₇

yes

characteristic

158

C₂²

#13093982

yes

characteristic

159

C₄

—

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

164

C₄

#13093986

yes

—

165

C₂

—

166

C₂

—

167

C₂

—

188

—

168

C₂

#15688970

yes

characteristic

169

C₂

#100×D₄₇

yes

characteristic

170

C₂

#15689106

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#343	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	#343	D₄₇
hypocenter	C₄₇	C₄×#100
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₇

commutator

C₂²×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#343

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #343

N	H ≅ G/N	type
3. M₁₆×Dic₄₇	C₂	semidirect
4. #15688892	C₂	semidirect
5. C₄₇×#343	C₂	semidirect
13. #13093940	C₄	semidirect
31. M₁₆×C₄₇	C₂×C₄	semidirect
38. #10625329	C₂×C₄	semidirect
78. Dic₄₇	#100	semidirect
90. #343	D₄₇	semidirect
91. C₄₇	C₄×#100	semidirect
119. M₁₆	C₄×D₄₇	semidirect

H ≅ G/N

type

3. M₁₆×Dic₄₇

C₂

semidirect

4. #15688892

C₂

semidirect

5. C₄₇×#343

C₂

semidirect

13. #13093940

C₄

semidirect

31. M₁₆×C₄₇

C₂×C₄

semidirect

38. #10625329

C₂×C₄

semidirect

78. Dic₄₇

#100

semidirect

90. #343

D₄₇

semidirect

91. C₄₇

C₄×#100

semidirect

119. M₁₆

C₄×D₄₇

semidirect

Subgroups — #20243179

Conjugacy classes of subgroups

Complements