Group #20244529 — subgroups

Subgroups — #20244529

Order 6016.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13094024	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093948	C₂	1	2	yes	maximal
3	#15688885	C₂	1	2	yes	maximal
4	#15688878	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₉₄	—	2	1	no	—
7	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
8	#13094024	—	2	4	no	—
9	C₂×C₄⋊Dic₄₇	—	2	1	no	—
10	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	#13093948	—	2	4	no	—
12	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	#95×C₄₇	—	2	1	no	—
16	#95×C₄₇	—	2	1	no	—
17	C₂×Q₈×C₄₇	—	2	1	no	—
18	C₂×Q₈×C₄₇	—	2	2	no	—
19	C₂×Q₈×C₄₇	—	2	2	no	—
20	C₂×Q₈×C₄₇	Q₈	1	2	yes	complemented
21	C₂²×C₄×C₄₇	—	2	1	no	—
22	C₂²×C₄×C₄₇	—	2	1	no	—
23	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₇	—	2	2	no	—
27	C₂×Dic₉₄	—	2	4	no	—
28	C₂×Dic₉₄	—	4	2	no	—
29	C₂×Dic₉₄	—	4	2	no	—
30	C₄⋊C₄×C₄₇	—	2	2	no	—
31	C₄²×C₄₇	—	2	2	no	—
32	C₄⋊Dic₄₇	—	2	4	no	—
33	C₄⋊Dic₄₇	—	2	2	no	—
34	C₄⋊Dic₄₇	D₄	1	4	yes	—
35	C₂×C₄₇⋊C₈	—	2	2	no	—
36	C₂×C₄₇⋊C₈	—	2	2	no	—
37	C₂×C₄₇⋊C₈	—	2	2	no	—
38	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
39	Q₈×C₄₇	—	2	4	no	—
40	Q₈×C₄₇	—	4	2	no	—
41	C₂×C₄×C₄₇	—	2	1	no	—
42	C₂×C₄×C₄₇	—	2	1	no	—
43	C₂×C₄×C₄₇	—	2	1	no	—
44	C₂×C₄×C₄₇	—	2	1	no	—
45	C₂×C₄×C₄₇	—	2	2	no	—
46	C₂×C₄×C₄₇	—	4	1	no	—
47	C₂×C₄×C₄₇	—	4	1	no	—
48	C₂×C₄×C₄₇	—	4	1	no	—
49	C₂×C₄×C₄₇	—	4	1	no	—
50	C₂×C₄×C₄₇	—	4	1	no	—
51	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
52	C₂×C₄×C₄₇	Q₁₆	1	2	yes	—
53	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
56	C₂×C₄×C₄₇	#41	1	2	yes	—
57	C₂×Dic₄₇	—	2	4	no	—
58	C₂×Dic₄₇	—	4	2	no	—
59	C₂×Dic₄₇	—	4	2	no	—
60	Dic₉₄	—	4	8	no	—
61	C₄₇⋊C₈	—	4	2	no	—
62	C₂²×C₄₇	#120	1	1	yes	characteristic
63	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
64	C₂²×C₄₇	#124	1	1	yes	characteristic
65	C₂²×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
66	C₂²×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
67	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
68	C₂²×C₄₇	#137	1	1	yes	characteristic
69	C₄×C₄₇	—	2	2	no	—
70	C₄×C₄₇	—	2	2	no	—
71	C₄×C₄₇	—	4	2	no	—
72	C₄×C₄₇	—	8	1	no	—
73	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
74	C₄×C₄₇	#124	1	2	yes	—
75	Dic₄₇	—	4	4	no	—
76	#2024	—	47	1	no	maximal, Sylow
77	C₂×C₄₇	#393	1	1	yes	characteristic
78	C₂×C₄₇	#450	1	1	yes	characteristic
79	C₂×C₄₇	#451	1	1	yes	characteristic
80	C₂×C₄₇	#475	1	1	yes	characteristic
81	C₂×C₄₇	#477	1	1	yes	characteristic
82	C₂×C₄₇	#487	1	1	yes	characteristic
83	C₂×C₄₇	#489	1	1	yes	characteristic
84	C₂×C₄⋊Q₈	—	47	1	no	—
85	C₂×#103	—	47	2	no	—
86	#391	D₄₇	1	1	yes	characteristic
87	#340	—	47	2	no	—
88	#336	—	47	1	no	—
89	C₄₇	#2024	1	1	yes	characteristic, complemented, Sylow
90	C₂²×Q₈	—	94	1	no	—
91	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
92	C₂²×C₈	—	47	2	no	—
93	C₄⋊Q₈	—	94	4	no	—
94	C₂×C₄⋊C₄	—	47	2	no	—
95	C₂×C₄⋊C₄	—	94	1	no	—
96	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
97	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
98	#103	—	94	4	no	—
99	#95	—	2	1	no	—
100	#95	—	2	1	no	—
101	C₂×Q₈	—	2	1	no	—
102	C₂×Q₈	—	2	2	no	—
103	C₂×Q₈	—	2	2	no	—
104	C₂×Q₈	—	94	4	no	—
105	C₂×Q₈	—	188	2	no	—
106	C₂×Q₈	—	188	2	no	—
107	C₂×Q₈	Dic₉₄	1	2	yes	complemented
108	C₂²×C₄	—	2	1	no	—
109	C₂²×C₄	—	2	1	no	—
110	C₂²×C₄	—	94	2	no	—
111	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
112	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
113	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
114	C₂×C₈	—	94	2	no	—
115	C₂×C₈	—	94	2	no	—
116	C₂×C₈	—	94	2	no	—
117	C₄⋊C₄	—	2	2	no	—
118	C₄⋊C₄	—	47	4	no	—
119	C₄⋊C₄	—	94	4	no	—
120	C₄⋊C₄	—	94	2	no	—
121	C₄²	—	2	2	no	—
122	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
123	Q₈	—	2	4	no	—
124	Q₈	—	4	2	no	—
125	Q₈	—	188	8	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	1	no	—
130	C₂×C₄	—	2	2	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	4	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	—	94	4	no	—
137	C₂×C₄	—	188	2	no	—
138	C₂×C₄	—	188	2	no	—
139	C₂×C₄	#10625336	1	2	yes	—
140	C₂×C₄	#10625337	1	2	yes	—
141	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
142	C₂×C₄	#10625350	1	1	yes	characteristic
143	C₂×C₄	D₄×D₄₇	1	2	yes	—
144	C₂×C₄	#10625352	1	2	yes	—
145	C₈	—	188	2	no	—
146	C₂²	#13093992	1	1	yes	characteristic
147	C₂²	#13094003	1	1	yes	characteristic
148	C₂²	#13094011	1	1	yes	characteristic
149	C₂²	C₂×#10625336	1	1	yes	characteristic
150	C₂²	C₂×#10625337	1	1	yes	characteristic
151	C₂²	#13094049	1	1	yes	characteristic
152	C₂²	#13094054	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	2	2	no	—
155	C₄	—	4	2	no	—
156	C₄	—	8	1	no	—
157	C₄	—	188	4	no	—
158	C₄	#13094001	1	2	yes	—
159	C₄	#13094010	1	2	yes	—
160	C₂	#15689035	1	1	yes	characteristic
161	C₂	#15689273	1	1	yes	characteristic
162	C₂	#15689278	1	1	yes	characteristic
163	C₂	#15689408	1	1	yes	characteristic
164	C₂	#15689418	1	1	yes	characteristic
165	C₂	#15689473	1	1	yes	characteristic
166	C₂	#15689482	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094024

C₂

yes

maximal, characteristic

C₂×#13093948

C₂

yes

maximal

#15688885

C₂

yes

maximal

#15688878

C₂

yes

maximal, characteristic

C₄₇×#391

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

—

C₂²×C₄₇⋊C₈

C₂²

yes

—

#13094024

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

#13093948

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#95×C₄₇

—

#95×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

Q₈

yes

complemented

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

SD₁₆

yes

—

C₂×C₄×C₄₇

Q₁₆

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

C₄₇⋊C₈

—

C₂²×C₄₇

#120

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₇

#124

yes

characteristic

C₂²×C₄₇

C₂×SD₁₆

yes

characteristic

C₂²×C₄₇

C₂×Q₁₆

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

—

C₄×C₄₇

#124

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄⋊Q₈

—

C₂×#103

—

#391

D₄₇

yes

characteristic

#340

—

#336

—

C₄₇

#2024

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

characteristic

#103

—

#95

—

100

#95

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

188

—

106

C₂×Q₈

—

188

—

107

C₂×Q₈

Dic₉₄

yes

complemented

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

112

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

113

C₂²×C₄

C₂²×D₄₇

yes

characteristic

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄²

—

122

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

123

Q₈

—

124

Q₈

—

125

Q₈

—

188

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

188

—

138

C₂×C₄

—

188

—

139

C₂×C₄

#10625336

yes

—

140

C₂×C₄

#10625337

yes

—

141

C₂×C₄

C₂×Dic₉₄

yes

characteristic

142

C₂×C₄

#10625350

yes

characteristic

143

C₂×C₄

D₄×D₄₇

yes

—

144

C₂×C₄

#10625352

yes

—

145

C₈

—

188

—

146

C₂²

#13093992

yes

characteristic

147

C₂²

#13094003

yes

characteristic

148

C₂²

#13094011

yes

characteristic

149

C₂²

C₂×#10625336

yes

characteristic

150

C₂²

C₂×#10625337

yes

characteristic

151

C₂²

#13094049

yes

characteristic

152

C₂²

#13094054

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

188

—

158

C₄

#13094001

yes

—

159

C₄

#13094010

yes

—

160

C₂

#15689035

yes

characteristic

161

C₂

#15689273

yes

characteristic

162

C₂

#15689278

yes

characteristic

163

C₂

#15689408

yes

characteristic

164

C₂

#15689418

yes

characteristic

165

C₂

#15689473

yes

characteristic

166

C₂

#15689482

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₇
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#391	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	#391	D₄₇
hypocenter	C₄₇	#2024
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₇

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#391

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
20. C₂×Q₈×C₄₇	Q₈	semidirect
89. C₄₇	#2024	semidirect
107. C₂×Q₈	Dic₉₄	semidirect

H ≅ G/N

type

20. C₂×Q₈×C₄₇

Q₈

semidirect

89. C₄₇

#2024

semidirect

107. C₂×Q₈

Dic₉₄

semidirect

Subgroups — #20244529

Conjugacy classes of subgroups

Complements