Group #20245320 — subgroups

Subgroups — #20245320

Order 6016.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093970	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689361	C₂	1	1	yes	maximal, characteristic
4	#15688928	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688927	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×D₄₇)⋊C₁₆	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₄₇	—	2	1	no	—
9	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
10	C₂×#10625337	—	2	1	no	—
11	Q₁₆×D₄₇	—	2	2	no	—
12	Q₁₆×D₄₇	—	2	2	no	—
13	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	#13094000	—	2	1	no	—
15	#13093970	—	2	2	no	—
16	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
17	#13093958	C₂²	1	1	yes	characteristic
18	#13093948	—	2	1	no	—
19	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
21	Q₃₂×C₄₇	—	2	2	no	—
22	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₄₇	—	2	1	no	—
24	C₂×Q₈×C₄₇	—	2	1	no	—
25	Q₈×D₄₇	—	2	4	no	—
26	Q₈×D₄₇	—	4	2	no	—
27	C₂×C₄×D₄₇	—	4	1	no	—
28	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
29	C₂×Dic₉₄	—	2	1	no	—
30	C₂×Dic₉₄	—	4	1	no	—
31	Q₁₆×C₄₇	—	2	1	no	—
32	Q₁₆×C₄₇	—	2	1	no	—
33	Q₁₆×C₄₇	—	2	1	no	—
34	Q₁₆×C₄₇	D₄	1	2	yes	—
35	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
36	#10625337	—	2	4	no	—
37	(C₂×D₄₇)⋊C₄	—	4	1	no	—
38	C₄⋊Dic₄₇	—	2	1	no	—
39	Dic₄₇⋊C₄	—	4	1	no	—
40	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
41	Dic₁₈₈	—	2	1	no	—
42	Dic₁₈₈	D₄	1	2	yes	—
43	C₈×D₄₇	—	2	1	no	—
44	C₈×D₄₇	—	2	1	no	—
45	C₁₆×C₄₇	—	2	1	no	—
46	C₄₇⋊C₁₆	—	2	1	no	—
47	C₂²×D₄₇	D₈	1	1	yes	characteristic
48	Q₈×C₄₇	—	2	2	no	—
49	Q₈×C₄₇	—	4	1	no	—
50	Q₈×C₄₇	—	4	1	no	—
51	Q₈×C₄₇	—	4	1	no	—
52	C₂×C₄×C₄₇	—	4	1	no	—
53	C₂×C₄×C₄₇	—	4	1	no	—
54	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂×Dic₄₇	—	4	1	no	—
56	C₂×Dic₄₇	—	4	1	no	—
57	C₂×Dic₄₇	D₈	1	1	yes	characteristic
58	C₄×D₄₇	—	2	1	no	—
59	C₄×D₄₇	—	2	1	no	—
60	C₄×D₄₇	—	4	4	no	—
61	Dic₉₄	—	2	2	no	—
62	Dic₉₄	—	4	4	no	—
63	Dic₉₄	—	4	1	no	—
64	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₄₇⋊C₈	—	2	1	no	—
67	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
68	C₂×D₄₇	—	2	1	no	—
69	C₂×D₄₇	—	2	1	no	—
70	C₂×D₄₇	Q₃₂	1	2	yes	complemented
71	C₄×C₄₇	—	4	2	no	—
72	C₄×C₄₇	—	8	1	no	—
73	C₄×C₄₇	#120	1	1	yes	characteristic
74	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
75	Dic₄₇	—	2	1	no	—
76	Dic₄₇	—	4	2	no	—
77	Dic₄₇	—	8	1	no	—
78	#2188	—	47	1	no	maximal, Sylow
79	C₂×C₄₇	#447	1	1	yes	characteristic
80	C₂×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
81	C₂×C₄₇	#510	1	1	yes	characteristic
82	D₄₇	—	2	2	no	—
83	C₂²×Q₁₆	—	47	1	no	—
84	C₂×Q₃₂	—	47	1	no	—
85	C₂×Q₃₂	D₄₇	1	1	yes	characteristic, complemented
86	#467	—	47	1	no	—
87	#358	—	47	1	no	—
88	#358	—	47	1	no	—
89	C₂²⋊C₁₆	—	47	1	no	—
90	C₄₇	#2188	1	1	yes	characteristic, complemented, Sylow
91	C₂²×Q₈	—	94	1	no	—
92	C₂×Q₁₆	—	47	1	no	—
93	C₂×Q₁₆	—	94	1	no	—
94	C₂×Q₁₆	—	94	2	no	—
95	C₂×Q₁₆	—	94	2	no	—
96	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
97	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
98	C₂²×C₈	—	47	1	no	—
99	C₂²⋊Q₈	—	94	1	no	—
100	Q₃₂	—	2	2	no	—
101	Q₃₂	—	94	2	no	—
102	C₂×C₁₆	—	47	1	no	—
103	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
104	#107	—	47	1	no	—
105	#103	—	94	1	no	—
106	C₂×Q₈	—	2	1	no	—
107	C₂×Q₈	—	2	1	no	—
108	C₂×Q₈	—	94	4	no	—
109	C₂×Q₈	—	94	1	no	—
110	C₂×Q₈	—	188	1	no	—
111	C₂×Q₈	—	188	2	no	—
112	C₂²×C₄	—	47	1	no	—
113	C₂²×C₄	—	188	1	no	—
114	Q₁₆	—	2	1	no	—
115	Q₁₆	—	2	1	no	—
116	Q₁₆	—	2	1	no	—
117	Q₁₆	—	47	2	no	—
118	Q₁₆	—	94	4	no	—
119	Q₁₆	—	94	1	no	—
120	Q₁₆	C₂²⋊D₄₇	1	2	yes	—
121	C₂×C₈	—	47	1	no	—
122	C₂×C₈	—	94	1	no	—
123	C₂×C₈	—	94	1	no	—
124	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
125	C₄⋊C₄	—	94	1	no	—
126	C₄⋊C₄	—	188	1	no	—
127	C₂²⋊C₄	—	188	1	no	—
128	C₁₆	—	2	1	no	—
129	C₁₆	—	94	1	no	—
130	C₂³	—	47	1	no	—
131	Q₈	—	2	2	no	—
132	Q₈	—	4	1	no	—
133	Q₈	—	4	1	no	—
134	Q₈	—	4	1	no	—
135	Q₈	—	94	2	no	—
136	Q₈	—	188	4	no	—
137	Q₈	—	188	1	no	—
138	C₂×C₄	—	4	1	no	—
139	C₂×C₄	—	4	1	no	—
140	C₂×C₄	—	47	1	no	—
141	C₂×C₄	—	94	1	no	—
142	C₂×C₄	—	94	1	no	—
143	C₂×C₄	—	188	4	no	—
144	C₂×C₄	—	188	1	no	—
145	C₂×C₄	—	188	1	no	—
146	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
147	C₈	—	94	1	no	—
148	C₈	D₄×D₄₇	1	1	yes	characteristic
149	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
150	C₂²	—	47	2	no	—
151	C₂²	—	94	1	no	—
152	C₂²	—	94	1	no	—
153	C₂²	D₈×D₄₇	1	1	yes	characteristic
154	C₄	—	4	2	no	—
155	C₄	—	8	1	no	—
156	C₄	—	94	1	no	—
157	C₄	—	376	1	no	—
158	C₄	—	188	2	no	—
159	C₄	#13093992	1	1	yes	characteristic
160	C₄	#13094048	1	1	yes	characteristic
161	C₂	—	94	2	no	—
162	C₂	#15689255	1	1	yes	characteristic
163	C₂	Q₃₂×D₄₇	1	1	yes	characteristic
164	C₂	#15689565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×D₄₇

C₂

yes

maximal, characteristic

C₂×#13093970

C₂

yes

maximal, characteristic, complemented

#15689361

C₂

yes

maximal, characteristic

#15688928

C₂

yes

maximal, characteristic, complemented

#15688927

C₂

yes

maximal, characteristic, complemented

(C₂×D₄₇)⋊C₁₆

C₂

yes

maximal, characteristic

C₂×Q₃₂×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₇

—

C₂×Dic₁₈₈

C₂²

yes

characteristic

C₂×#10625337

—

Q₁₆×D₄₇

—

Q₁₆×D₄₇

—

C₂×C₈×D₄₇

C₂²

yes

characteristic

#13094000

—

#13093970

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093948

—

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

Q₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

Q₈×D₄₇

—

Q₈×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

D₄

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

#10625337

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

—

Dic₁₈₈

D₄

yes

—

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

D₈

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

Q₃₂

yes

complemented

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×Q₃₂

yes

characteristic

C₂×C₄₇

#510

yes

characteristic

D₄₇

—

C₂²×Q₁₆

—

C₂×Q₃₂

—

C₂×Q₃₂

D₄₇

yes

characteristic, complemented

#467

—

#358

—

#358

—

C₂²⋊C₁₆

—

C₄₇

#2188

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

C₂²⋊Q₈

—

100

Q₃₂

—

101

Q₃₂

—

102

C₂×C₁₆

—

103

C₂×C₁₆

C₂×D₄₇

yes

characteristic

104

#107

—

105

#103

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

188

—

111

C₂×Q₈

—

188

—

112

C₂²×C₄

—

113

C₂²×C₄

—

188

—

114

Q₁₆

—

115

Q₁₆

—

116

Q₁₆

—

117

Q₁₆

—

118

Q₁₆

—

119

Q₁₆

—

120

Q₁₆

C₂²⋊D₄₇

yes

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

C₂²×D₄₇

yes

characteristic

125

C₄⋊C₄

—

126

C₄⋊C₄

—

188

—

127

C₂²⋊C₄

—

188

—

128

C₁₆

—

129

C₁₆

—

130

C₂³

—

131

Q₈

—

132

Q₈

—

133

Q₈

—

134

Q₈

—

135

Q₈

—

136

Q₈

—

188

—

137

Q₈

—

188

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

188

—

144

C₂×C₄

—

188

—

145

C₂×C₄

—

188

—

146

C₂×C₄

D₄×D₄₇

yes

characteristic

147

C₈

—

148

C₈

D₄×D₄₇

yes

characteristic

149

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

D₈×D₄₇

yes

characteristic

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

376

—

158

C₄

—

188

—

159

C₄

#13093992

yes

characteristic

160

C₄

#13094048

yes

characteristic

161

C₂

—

162

C₂

#15689255

yes

characteristic

163

C₂

Q₃₂×D₄₇

yes

characteristic

164

C₂

#15689565

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×Q₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂×Q₃₂	D₄₇
hypocenter	C₄₇	#2188
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂×Q₃₂×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₂×Q₃₂

D₄₇

hypocenter

C₄₇

#2188

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
2. C₂×#13093970	C₂	semidirect
4. #15688928	C₂	semidirect
5. #15688927	C₂	semidirect
7. C₂×Q₃₂×C₄₇	C₂	semidirect
70. C₂×D₄₇	Q₃₂	semidirect
85. C₂×Q₃₂	D₄₇	semidirect
90. C₄₇	#2188	semidirect

H ≅ G/N

type

2. C₂×#13093970

C₂

semidirect

4. #15688928

C₂

semidirect

5. #15688927

C₂

semidirect

7. C₂×Q₃₂×C₄₇

C₂

semidirect

70. C₂×D₄₇

Q₃₂

semidirect

85. C₂×Q₃₂

D₄₇

semidirect

90. C₄₇

#2188

semidirect

Subgroups — #20245320

Conjugacy classes of subgroups

Complements