Group #20245791 — subgroups

Subgroups — #20245791

Order 6016.

656 conjugacy classes of subgroups; only the 285 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 285 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×#13093983	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#15688992	C₂	1	2	yes	maximal, complemented
4	#15688988	C₂	1	2	yes	maximal, complemented
5	#15688981	C₂	1	4	yes	maximal
6	C₄×Dic₄₇⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₂×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₄₇	C₂²	1	2	yes	—
9	#13093983	—	2	4	no	—
10	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	C₂×Dic₄₇⋊C₄	C₂²	1	8	yes	—
12	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
13	C₂×C₄×Dic₄₇	C₄	1	8	yes	complemented
14	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
15	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
16	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
18	C₄₇⋊#95	C₂²	1	8	yes	—
19	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
20	#117×C₄₇	—	2	4	no	—
21	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
23	C₂×C₄²×C₄₇	C₂²	1	2	yes	—
24	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
26	C₂²×C₄×C₄₇	D₄	1	4	yes	—
27	C₂²×C₄×C₄₇	Q₈	1	4	yes	—
28	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
29	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
31	C₂²×Dic₄₇	—	2	8	no	—
32	C₂²×Dic₄₇	C₂×C₄	1	8	yes	—
33	C₂²×Dic₄₇	C₂³	1	4	yes	—
34	C₂²×Dic₄₇	C₂³	1	2	yes	—
35	C₂²×Dic₄₇	C₂³	1	2	yes	—
36	C₄⋊C₄×C₄₇	—	2	4	no	—
37	C₂²⋊C₄×C₄₇	—	2	4	no	—
38	C₄²×C₄₇	—	2	4	no	—
39	C₂²⋊Dic₄₇	—	2	4	no	—
40	C₄⋊Dic₄₇	—	2	4	no	—
41	Dic₄₇⋊C₄	—	2	16	no	—
42	C₄×Dic₄₇	—	2	4	no	—
43	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
44	C₄×Dic₄₇	C₂×C₄	1	8	yes	—
45	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
46	C₂³×C₄₇	—	2	4	no	—
47	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
48	C₂³×C₄₇	C₂×D₄	1	2	yes	—
49	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
50	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
51	C₂×C₄×C₄₇	—	2	4	no	—
52	C₂×C₄×C₄₇	—	2	8	no	—
53	C₂×C₄×C₄₇	C₄⋊C₄	1	16	yes	complemented
54	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
56	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
59	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
60	C₂×Dic₄₇	—	2	4	no	—
61	C₂×Dic₄₇	—	2	16	no	—
62	C₂×Dic₄₇	—	2	4	no	—
63	C₂×Dic₄₇	—	2	8	no	—
64	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
65	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
66	C₂×Dic₄₇	#41	1	8	yes	—
67	C₂²×C₄₇	—	2	4	no	—
68	C₂²×C₄₇	—	2	4	no	—
69	C₂²×C₄₇	—	2	4	no	—
70	C₂²×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
71	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
72	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
73	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
74	C₂²×C₄₇	C₂×#41	1	4	yes	—
75	C₄×C₄₇	—	4	4	no	—
76	C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
77	C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
78	Dic₄₇	—	2	4	no	—
79	Dic₄₇	—	4	4	no	—
80	Dic₄₇	#117	1	8	yes	complemented
81	#2285	—	47	1	no	maximal, Sylow
82	C₂×C₄₇	—	2	4	no	—
83	C₂×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄₇	C₂×#117	1	2	yes	—
85	C₂×C₄₇	#532	1	2	yes	—
86	C₂×C₄₇	#533	1	2	yes	—
87	C₂×#117	—	47	1	no	—
88	C₂×#117	D₄₇	1	1	yes	characteristic
89	C₂²×C₄²	—	47	1	no	—
90	#384	—	47	2	no	—
91	#382	—	47	2	no	—
92	#380	—	47	4	no	—
93	C₄×C₄⋊C₄	—	47	4	no	—
94	C₄₇	#2285	1	1	yes	characteristic, complemented, Sylow
95	C₂³×C₄	—	47	2	no	—
96	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
97	#117	—	2	4	no	—
98	#117	—	94	4	no	—
99	C₂×C₄⋊C₄	—	47	2	no	—
100	C₂×C₄⋊C₄	—	47	8	no	—
101	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
102	C₂×C₂²⋊C₄	—	47	2	no	—
103	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
104	C₂×C₄²	—	47	8	no	—
105	C₂×C₄²	—	47	1	no	—
106	C₂×C₄²	—	47	1	no	—
107	C₂×C₄²	—	47	2	no	—
108	C₂×C₄²	—	47	2	no	—
109	C₂×C₄²	C₂×D₄₇	1	2	yes	—
110	#95	—	47	8	no	—
111	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
112	C₂²×C₄	—	47	2	no	—
113	C₂²×C₄	—	47	8	no	—
114	C₂²×C₄	—	47	2	no	—
115	C₂²×C₄	—	47	4	no	—
116	C₂²×C₄	—	94	8	no	—
117	C₂²×C₄	Dic₉₄	1	4	yes	—
118	C₂²×C₄	C₄×D₄₇	1	4	yes	—
119	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
120	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
121	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
122	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
123	C₄⋊C₄	—	2	4	no	—
124	C₄⋊C₄	—	94	16	no	—
125	C₄⋊C₄	—	94	4	no	—
126	C₂²⋊C₄	—	2	4	no	—
127	C₂²⋊C₄	—	94	4	no	—
128	C₄²	—	2	4	no	—
129	C₄²	—	47	4	no	—
130	C₄²	—	47	8	no	—
131	C₄²	—	47	4	no	—
132	C₄²	—	94	4	no	—
133	C₂³	—	2	4	no	—
134	C₂³	C₂×Dic₉₄	1	2	yes	—
135	C₂³	C₂×C₄×D₄₇	1	2	yes	—
136	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
137	C₂³	C₂³×D₄₇	1	1	yes	characteristic
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	8	no	—
140	C₂×C₄	—	47	4	no	—
141	C₂×C₄	—	47	8	no	—
142	C₂×C₄	—	47	4	no	—
143	C₂×C₄	—	94	16	no	—
144	C₂×C₄	—	94	4	no	—
145	C₂×C₄	—	94	4	no	—
146	C₂×C₄	—	94	8	no	—
147	C₂×C₄	Dic₄₇⋊C₄	1	16	yes	complemented
148	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
149	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
150	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
151	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
152	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
153	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
154	C₂²	—	2	4	no	—
155	C₂²	—	2	4	no	—
156	C₂²	—	2	4	no	—
157	C₂²	C₂×Dic₄₇⋊C₄	1	4	yes	—
158	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
159	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
160	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
161	C₂²	#41×D₄₇	1	4	yes	—
162	C₄	—	4	4	no	—
163	C₄	—	47	8	no	—
164	C₄	—	94	4	no	—
165	C₄	—	188	4	no	—
166	C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
167	C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
168	C₂	—	2	4	no	—
169	C₂	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
170	C₂	#117×D₄₇	1	2	yes	—
171	C₂	#15689669	1	2	yes	—
172	C₂	#15689676	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093983

C₂

yes

maximal, characteristic

C₂²×C₄×Dic₄₇

C₂

yes

maximal, characteristic

#15688992

C₂

yes

maximal, complemented

#15688988

C₂

yes

maximal, complemented

#15688981

C₂

yes

maximal

C₄×Dic₄₇⋊C₄

C₂

yes

maximal, complemented

C₂×#117×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

—

#13093983

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₄

yes

complemented

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₄₇⋊#95

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

#117×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²×C₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

complemented

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

yes

—

C₂×C₄₇

—

C₂×C₄₇

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₄₇

C₂×#117

yes

—

C₂×C₄₇

#532

yes

—

C₂×C₄₇

#533

yes

—

C₂×#117

—

C₂×#117

D₄₇

yes

characteristic

C₂²×C₄²

—

#384

—

#382

—

#380

—

C₄×C₄⋊C₄

—

C₄₇

#2285

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

#117

—

#117

—

C₂×C₄⋊C₄

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

102

C₂×C₂²⋊C₄

—

103

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

104

C₂×C₄²

—

105

C₂×C₄²

—

106

C₂×C₄²

—

107

C₂×C₄²

—

108

C₂×C₄²

—

109

C₂×C₄²

C₂×D₄₇

yes

—

110

#95

—

111

C₂⁴

C₂²×D₄₇

yes

characteristic

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

Dic₉₄

yes

—

118

C₂²×C₄

C₄×D₄₇

yes

—

119

C₂²×C₄

C₂²⋊D₄₇

yes

—

120

C₂²×C₄

C₂²×D₄₇

yes

—

121

C₂²×C₄

C₂²×D₄₇

yes

characteristic

122

C₂²×C₄

C₂²×D₄₇

yes

characteristic

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₄²

—

130

C₄²

—

131

C₄²

—

132

C₄²

—

133

C₂³

—

134

C₂³

C₂×Dic₉₄

yes

—

135

C₂³

C₂×C₄×D₄₇

yes

—

136

C₂³

C₂×C₂²⋊D₄₇

yes

—

137

C₂³

C₂³×D₄₇

yes

characteristic

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

Dic₄₇⋊C₄

yes

complemented

148

C₂×C₄

C₂×Dic₉₄

yes

—

149

C₂×C₄

C₂×Dic₉₄

yes

—

150

C₂×C₄

C₂×C₄×D₄₇

yes

—

151

C₂×C₄

C₂×C₄×D₄₇

yes

—

152

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

153

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

C₂×Dic₄₇⋊C₄

yes

—

158

C₂²

C₂²×C₄×D₄₇

yes

characteristic

159

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

160

C₂²

C₂²×Dic₉₄

yes

characteristic

161

C₂²

#41×D₄₇

yes

—

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

—

188

—

166

C₄

C₂×Dic₄₇⋊C₄

yes

—

167

C₄

C₂×Dic₄₇⋊C₄

yes

—

168

C₂

—

169

C₂

C₂²×Dic₄₇⋊C₄

yes

characteristic

170

C₂

#117×D₄₇

yes

—

171

C₂

#15689669

yes

—

172

C₂

#15689676

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂×#117×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×#117	D₄₇
hypocenter	C₄₇	#2285
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#117

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Frattini

C₂³

C₂³×D₄₇

Fitting

C₂×#117×C₄₇

C₂

socle

C₂³×C₄₇

C₂⁴

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ C₂×#117

N	H ≅ G/N	type
3. #15688992	C₂	semidirect
4. #15688988	C₂	semidirect
6. C₄×Dic₄₇⋊C₄	C₂	semidirect
13. C₂×C₄×Dic₄₇	C₄	semidirect
53. C₂×C₄×C₄₇	C₄⋊C₄	semidirect
80. Dic₄₇	#117	semidirect
94. C₄₇	#2285	semidirect
147. C₂×C₄	Dic₄₇⋊C₄	semidirect

H ≅ G/N

type

3. #15688992

C₂

semidirect

4. #15688988

C₂

semidirect

6. C₄×Dic₄₇⋊C₄

C₂

semidirect

13. C₂×C₄×Dic₄₇

C₄

semidirect

53. C₂×C₄×C₄₇

C₄⋊C₄

semidirect

80. Dic₄₇

#117

semidirect

94. C₄₇

#2285

semidirect

147. C₂×C₄

Dic₄₇⋊C₄

semidirect

Subgroups — #20245791

Conjugacy classes of subgroups

Complements