Group #20244788 — subgroups

Subgroups — #20244788

Order 6016.

196 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 65 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	#15689172	C₂	1	1	yes	maximal, characteristic
2	#15689171	C₂	1	1	yes	maximal, characteristic
3	C₂×#13093942	C₂	1	1	yes	maximal, characteristic
4	C₂×#13093942	C₂	1	1	yes	maximal, characteristic
5	C₂×#13093942	C₂	1	1	yes	maximal, characteristic
6	C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#430	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
9	C₂×#10625329	C₂²	1	1	yes	characteristic
10	C₂×#10625329	C₂²	1	1	yes	characteristic
11	C₂×#10625329	C₂²	1	1	yes	characteristic
12	#13093960	—	2	2	no	—
13	#13093959	—	2	2	no	—
14	#13093942	—	2	2	no	—
15	#13093942	—	2	2	no	—
16	#13093942	—	2	2	no	—
17	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	#108×C₄₇	—	2	2	no	—
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²×Dic₄₇	Q₈	1	2	yes	—
23	C₂×Dic₉₄	—	2	1	no	—
24	C₂×Dic₉₄	—	2	1	no	—
25	C₂×Dic₉₄	—	2	1	no	—
26	C₂×Dic₉₄	—	2	1	no	—
27	C₂×Dic₉₄	—	2	1	no	—
28	C₂×Dic₉₄	—	2	1	no	—
29	M₁₆×C₄₇	—	2	1	no	—
30	M₁₆×C₄₇	—	2	1	no	—
31	M₁₆×C₄₇	—	2	1	no	—
32	M₁₆×C₄₇	—	2	1	no	—
33	M₁₆×C₄₇	D₄	1	2	yes	—
34	M₁₆×C₄₇	D₄	1	2	yes	—
35	C₂×C₈×C₄₇	—	2	1	no	—
36	C₂×C₈×C₄₇	—	2	1	no	—
37	C₂×C₈×C₄₇	—	2	1	no	—
38	#10625329	—	2	1	no	—
39	#10625329	—	2	1	no	—
40	#10625329	—	2	1	no	—
41	#10625329	—	2	1	no	—
42	#10625329	—	2	1	no	—
43	#10625329	D₄	1	2	yes	—
44	C₂×C₄₇⋊C₈	—	2	1	no	—
45	C₂×C₄₇⋊C₈	—	2	1	no	—
46	C₂×C₄₇⋊C₈	—	2	1	no	—
47	C₂³×C₄₇	C₂×Q₈	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	#41	1	1	yes	characteristic
52	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
53	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
54	C₂×Dic₄₇	—	2	2	no	—
55	C₂×Dic₄₇	—	2	2	no	—
56	C₂×Dic₄₇	—	2	2	no	—
57	Dic₉₄	—	4	1	no	—
58	Dic₉₄	—	4	1	no	—
59	Dic₉₄	—	4	1	no	—
60	Dic₉₄	—	4	1	no	—
61	C₈×C₄₇	—	2	2	no	—
62	C₈×C₄₇	—	2	2	no	—
63	C₈×C₄₇	—	4	1	no	—
64	C₄₇⋊C₈	—	2	2	no	—
65	C₄₇⋊C₈	—	4	1	no	—
66	C₄₇⋊C₈	—	4	1	no	—
67	C₂²×C₄₇	—	4	1	no	—
68	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
69	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
70	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
71	C₄×C₄₇	#121	1	1	yes	characteristic
72	C₄×C₄₇	#121	1	1	yes	characteristic
73	C₄×C₄₇	#121	1	1	yes	characteristic
74	C₄×C₄₇	#126	1	1	yes	characteristic
75	Dic₄₇	—	4	2	no	—
76	#2070	—	47	1	no	maximal, Sylow
77	C₂×C₄₇	—	2	1	no	—
78	C₂×C₄₇	—	2	1	no	—
79	C₂×C₄₇	—	2	1	no	—
80	C₂×C₄₇	#396	1	1	yes	characteristic
81	#430	—	47	1	no	—
82	#430	—	47	1	no	—
83	#430	D₄₇	1	1	yes	characteristic
84	C₂×#101	—	47	1	no	—
85	C₂×#101	—	47	1	no	—
86	C₂×#101	—	47	1	no	—
87	#338	—	47	1	no	—
88	C₄₇	#2070	1	1	yes	characteristic, complemented, Sylow
89	C₂²×Q₈	—	47	1	no	—
90	C₂×M₁₆	—	47	1	no	—
91	C₂×M₁₆	—	47	1	no	—
92	C₂×M₁₆	—	47	1	no	—
93	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
94	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
95	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
96	#108	—	2	2	no	—
97	#108	—	94	2	no	—
98	#108	—	94	2	no	—
99	#101	—	94	2	no	—
100	#101	—	94	2	no	—
101	#101	—	94	2	no	—
102	C₂×Q₈	—	94	1	no	—
103	C₂×Q₈	—	94	1	no	—
104	C₂×Q₈	—	94	1	no	—
105	C₂×Q₈	—	94	1	no	—
106	C₂×Q₈	—	94	1	no	—
107	C₂×Q₈	—	94	1	no	—
108	C₂²×C₄	—	47	2	no	—
109	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
110	M₁₆	—	2	1	no	—
111	M₁₆	—	2	1	no	—
112	M₁₆	—	2	1	no	—
113	M₁₆	—	2	1	no	—
114	M₁₆	—	47	2	no	—
115	M₁₆	—	94	1	no	—
116	M₁₆	—	94	1	no	—
117	M₁₆	—	94	1	no	—
118	M₁₆	—	94	1	no	—
119	M₁₆	—	94	1	no	—
120	M₁₆	D₁₈₈	1	2	yes	—
121	M₁₆	C₂²⋊D₄₇	1	2	yes	—
122	C₂×C₈	—	2	1	no	—
123	C₂×C₈	—	2	1	no	—
124	C₂×C₈	—	2	1	no	—
125	C₂×C₈	—	94	1	no	—
126	C₂×C₈	—	94	1	no	—
127	C₂×C₈	—	94	1	no	—
128	C₂³	Q₈×D₄₇	1	1	yes	characteristic
129	Q₈	—	188	1	no	—
130	Q₈	—	188	1	no	—
131	Q₈	—	188	1	no	—
132	Q₈	—	188	1	no	—
133	C₂×C₄	—	94	2	no	—
134	C₂×C₄	—	94	2	no	—
135	C₂×C₄	—	94	2	no	—
136	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
137	C₂×C₄	#10625350	1	1	yes	characteristic
138	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
139	C₂×C₄	#10625352	1	1	yes	characteristic
140	C₂×C₄	#10625354	1	1	yes	characteristic
141	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
142	C₈	—	2	2	no	—
143	C₈	—	2	2	no	—
144	C₈	—	4	1	no	—
145	C₈	—	94	2	no	—
146	C₈	—	188	1	no	—
147	C₈	—	188	1	no	—
148	C₂²	—	4	1	no	—
149	C₂²	#13094000	1	1	yes	characteristic
150	C₂²	#13094002	1	1	yes	characteristic
151	C₂²	#13094004	1	1	yes	characteristic
152	C₄	—	188	2	no	—
153	C₄	#13093996	1	1	yes	characteristic
154	C₄	#13093998	1	1	yes	characteristic
155	C₄	#13093999	1	1	yes	characteristic
156	C₄	#13094019	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	—	2	1	no	—
160	C₂	#15689045	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689172

C₂

yes

maximal, characteristic

#15689171

C₂

yes

maximal, characteristic

C₂×#13093942

C₂

yes

maximal, characteristic

C₂×#13093942

C₂

yes

maximal, characteristic

C₂×#13093942

C₂

yes

maximal, characteristic

C₄₇⋊#338

C₂

yes

maximal, characteristic

C₄₇×#430

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

—

—

—

—

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#108×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

Q₈

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

D₄

yes

—

M₁₆×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

—

—

—

—

—

D₄

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₇

C₂²⋊Q₈

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#2070

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

D₄₇

yes

—

—

—

—

C₄₇

#2070

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂×M₁₆

C₂×D₄₇

yes

—

—

—

—

100

#101

—

101

#101

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂²×C₄

—

109

C₂²×C₄

C₂²×D₄₇

yes

characteristic

110

M₁₆

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

119

M₁₆

—

120

M₁₆

D₁₈₈

yes

—

121

M₁₆

C₂²⋊D₄₇

yes

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₂³

Q₈×D₄₇

yes

characteristic

129

Q₈

—

188

—

130

Q₈

—

188

—

131

Q₈

—

188

—

132

Q₈

—

188

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂×D₁₈₈

yes

characteristic

137

C₂×C₄

#10625350

yes

characteristic

138

C₂×C₄

D₄×D₄₇

yes

characteristic

139

C₂×C₄

#10625352

yes

characteristic

140

C₂×C₄

#10625354

yes

characteristic

141

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₈

—

188

—

147

C₈

—

188

—

148

C₂²

—

149

C₂²

#13094000

yes

characteristic

150

C₂²

#13094002

yes

characteristic

151

C₂²

#13094004

yes

characteristic

152

C₄

—

188

—

153

C₄

#13093996

yes

characteristic

154

C₄

#13093998

yes

characteristic

155

C₄

#13093999

yes

characteristic

156

C₄

#13094019

yes

characteristic

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#15689045

yes

characteristic

	subgroup	G/H
center	C₂	#15689045
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#430	C₂
socle	C₂×C₄₇	#396
hypercenter	#430	D₄₇
hypocenter	C₄₇	#2070
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #430

subgroup

G/H

center

C₂

#15689045

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#430

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #430

N	H ≅ G/N	type
88. C₄₇	#2070	semidirect

H ≅ G/N

type

88. C₄₇

#2070

semidirect

Subgroups — #20244788

Conjugacy classes of subgroups

Complements