Group #20245333 — subgroups

Subgroups — #20245333

Order 6016.

226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 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	#15689923	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689559	C₂	1	2	yes	maximal, complemented
3	#15688932	C₂	1	2	yes	maximal, complemented
4	#15688905	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625350	—	2	1	no	—
7	#13094057	—	2	2	no	—
8	#13094052	—	2	2	no	—
9	#13094046	—	2	1	no	—
10	#13094046	C₂²	1	2	yes	—
11	#13093968	—	2	2	no	—
12	#13093965	—	2	2	no	—
13	#13093964	C₂²	1	2	yes	complemented
14	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
15	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
16	#121×C₄₇	—	2	1	no	—
17	#106×C₄₇	C₂²	1	1	yes	characteristic, complemented
18	#102×C₄₇	—	2	1	no	—
19	C₂×D₄×C₄₇	—	2	1	no	—
20	C₂×D₄×C₄₇	—	4	1	no	—
21	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
22	C₂×C₂²⋊D₄₇	—	4	1	no	—
23	#10625350	—	2	2	no	—
24	#10625350	—	2	2	no	—
25	#10625350	—	4	1	no	—
26	#10625350	—	4	1	no	—
27	C₂×D₁₈₈	—	2	1	no	—
28	C₂×C₄×D₄₇	—	4	1	no	—
29	C₂×Dic₉₄	—	2	1	no	—
30	D₈×C₄₇	—	2	2	no	—
31	M₁₆×C₄₇	—	2	2	no	—
32	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
33	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×C₄₇	—	2	1	no	—
35	C₂²⋊C₄×C₄₇	—	4	1	no	—
36	Dic₁₈₈	—	2	1	no	—
37	Dic₁₈₈	D₄	1	2	yes	complemented
38	D₃₇₆	—	2	1	no	—
39	D₃₇₆	D₄	1	2	yes	complemented
40	#10625325	—	2	2	no	—
41	#10625325	—	2	2	no	—
42	C₄₇⋊C₁₆	—	2	2	no	—
43	C₂³×C₄₇	—	4	1	no	—
44	C₂³×C₄₇	D₈	1	1	yes	characteristic
45	C₂²×D₄₇	—	4	1	no	—
46	D₄×C₄₇	—	4	1	no	—
47	D₄×C₄₇	—	4	1	no	—
48	D₄×C₄₇	—	8	2	no	—
49	C₂×C₄×C₄₇	—	2	1	no	—
50	C₂×C₄×C₄₇	—	2	1	no	—
51	C₂×C₄×C₄₇	—	4	1	no	—
52	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
53	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂²⋊D₄₇	—	4	2	no	—
55	C₂²⋊D₄₇	—	4	2	no	—
56	C₂×Dic₄₇	—	4	1	no	—
57	D₁₈₈	—	2	2	no	—
58	D₁₈₈	—	4	1	no	—
59	C₄×D₄₇	—	4	2	no	—
60	C₄×D₄₇	—	4	2	no	—
61	Dic₉₄	—	2	2	no	—
62	Dic₉₄	—	4	1	no	—
63	C₈×C₄₇	—	2	1	no	—
64	C₈×C₄₇	C₂×D₄	1	2	yes	—
65	C₂²×C₄₇	—	2	1	no	—
66	C₂²×C₄₇	—	4	1	no	—
67	C₂²×C₄₇	—	8	1	no	—
68	C₂²×C₄₇	—	8	1	no	—
69	C₂²×C₄₇	—	8	1	no	—
70	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
71	C₂×D₄₇	—	4	2	no	—
72	C₂×D₄₇	—	8	2	no	—
73	C₄×C₄₇	—	2	1	no	—
74	C₄×C₄₇	—	8	1	no	—
75	C₄×C₄₇	#120	1	1	yes	characteristic
76	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
77	Dic₄₇	—	4	2	no	—
78	#2190	—	47	1	no	maximal, Sylow
79	C₂×C₄₇	—	2	1	no	—
80	C₂×C₄₇	—	4	1	no	—
81	C₂×C₄₇	—	16	1	no	—
82	C₂×C₄₇	#447	1	1	yes	characteristic
83	D₄₇	—	8	2	no	—
84	#575	—	47	1	no	—
85	#509	—	47	2	no	—
86	#469	D₄₇	1	1	yes	characteristic, complemented
87	#360	—	47	2	no	—
88	#349	—	47	1	no	—
89	C₄₇	#2190	1	1	yes	characteristic, complemented, Sylow
90	C₂×#41	—	94	1	no	—
91	#137	—	94	2	no	—
92	AGL(1,ℤ/8)	—	94	2	no	—
93	#135	—	47	2	no	—
94	#135	—	94	1	no	—
95	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
96	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
97	#121	—	2	1	no	—
98	SD₃₂	—	94	2	no	—
99	D₁₆	—	94	2	no	—
100	M₃₂	—	47	2	no	—
101	#106	C₂×D₄₇	1	1	yes	characteristic, complemented
102	#102	—	2	1	no	—
103	#41	—	94	2	no	—
104	#41	—	94	2	no	—
105	#41	—	188	1	no	—
106	#41	—	188	1	no	—
107	C₂×Q₈	—	94	1	no	—
108	C₂×D₄	—	2	1	no	—
109	C₂×D₄	—	4	1	no	—
110	C₂×D₄	—	94	1	no	—
111	C₂×D₄	—	188	1	no	—
112	C₂²×C₄	—	188	1	no	—
113	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
114	Q₁₆	—	47	2	no	—
115	Q₁₆	—	94	1	no	—
116	SD₁₆	—	94	2	no	—
117	SD₁₆	—	94	2	no	—
118	D₈	—	2	2	no	—
119	D₈	—	47	2	no	—
120	D₈	—	94	1	no	—
121	M₁₆	—	2	2	no	—
122	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
123	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
124	C₄⋊C₄	—	2	1	no	—
125	C₂²⋊C₄	—	4	1	no	—
126	C₁₆	—	94	2	no	—
127	C₂³	—	4	1	no	—
128	C₂³	—	188	1	no	—
129	C₂³	#10625334	1	1	yes	characteristic
130	Q₈	—	94	2	no	—
131	Q₈	—	188	1	no	—
132	D₄	—	4	1	no	—
133	D₄	—	4	1	no	—
134	D₄	—	8	2	no	—
135	D₄	—	94	2	no	—
136	D₄	—	188	1	no	—
137	D₄	—	188	2	no	—
138	D₄	—	188	2	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	4	1	no	—
142	C₂×C₄	—	188	2	no	—
143	C₂×C₄	—	188	1	no	—
144	C₂×C₄	—	188	2	no	—
145	C₂×C₄	#10625334	1	1	yes	characteristic
146	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
147	C₈	—	2	1	no	—
148	C₈	D₄×D₄₇	1	2	yes	—
149	C₂²	—	2	1	no	—
150	C₂²	—	4	1	no	—
151	C₂²	—	8	1	no	—
152	C₂²	—	8	1	no	—
153	C₂²	—	8	1	no	—
154	C₂²	—	376	2	no	—
155	C₂²	—	188	2	no	—
156	C₂²	C₂×#10625334	1	1	yes	characteristic
157	C₄	—	2	1	no	—
158	C₄	—	8	1	no	—
159	C₄	—	188	2	no	—
160	C₄	#13093992	1	1	yes	characteristic
161	C₄	#13094049	1	1	yes	characteristic
162	C₂	—	2	1	no	—
163	C₂	—	4	1	no	—
164	C₂	—	16	1	no	—
165	C₂	—	376	2	no	—
166	C₂	#15689256	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689923

C₂

yes

maximal, characteristic, complemented

#15689559

C₂

yes

maximal, complemented

#15688932

C₂

yes

maximal, complemented

#15688905

C₂

yes

maximal, characteristic, complemented

C₄₇×#469

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

—

#13093968

—

#13093965

—

#13093964

C₂²

yes

complemented

C₂×D₈×C₄₇

C₂²

yes

characteristic, complemented

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#121×C₄₇

—

#106×C₄₇

C₂²

yes

characteristic, complemented

#102×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

—

—

—

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

D₈×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

Dic₁₈₈

—

Dic₁₈₈

D₄

yes

complemented

D₃₇₆

—

D₃₇₆

D₄

yes

complemented

#10625325

—

#10625325

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂³×C₄₇

D₈

yes

characteristic

C₂²×D₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂×D₄

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#2190

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#447

yes

characteristic

D₄₇

—

#575

—

#509

—

#469

D₄₇

yes

characteristic, complemented

#360

—

#349

—

C₄₇

#2190

yes

characteristic, complemented, Sylow

C₂×#41

—

—

—

—

—

C₂×D₈

C₂×D₄₇

yes

characteristic, complemented

C₂×M₁₆

C₂×D₄₇

yes

characteristic

#121

—

SD₃₂

—

D₁₆

—

100

M₃₂

—

101

#106

C₂×D₄₇

yes

characteristic, complemented

102

#102

—

103

#41

—

104

#41

—

105

#41

—

188

—

106

#41

—

188

—

107

C₂×Q₈

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

188

—

112

C₂²×C₄

—

188

—

113

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

114

Q₁₆

—

115

Q₁₆

—

116

SD₁₆

—

117

SD₁₆

—

118

D₈

—

119

D₈

—

120

D₈

—

121

M₁₆

—

122

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

123

C₂×C₈

C₂²×D₄₇

yes

characteristic

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

126

C₁₆

—

127

C₂³

—

128

C₂³

—

188

—

129

C₂³

#10625334

yes

characteristic

130

Q₈

—

131

Q₈

—

188

—

132

D₄

—

133

D₄

—

134

D₄

—

135

D₄

—

136

D₄

—

188

—

137

D₄

—

188

—

138

D₄

—

188

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

188

—

143

C₂×C₄

—

188

—

144

C₂×C₄

—

188

—

145

C₂×C₄

#10625334

yes

characteristic

146

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

147

C₈

—

148

C₈

D₄×D₄₇

yes

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

376

—

155

C₂²

—

188

—

156

C₂²

C₂×#10625334

yes

characteristic

157

C₄

—

158

C₄

—

159

C₄

—

188

—

160

C₄

#13093992

yes

characteristic

161

C₄

#13094049

yes

characteristic

162

C₂

—

163

C₂

—

164

C₂

—

165

C₂

—

376

—

166

C₂

#15689256

yes

characteristic

	subgroup	G/H
center	C₂	#15689256
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#469	C₂
socle	C₂×C₄₇	#447
hypercenter	#469	D₄₇
hypocenter	C₄₇	#2190
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

subgroup

G/H

center

C₂

#15689256

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#469

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #469

N	H ≅ G/N	type
1. #15689923	C₂	semidirect
2. #15689559	C₂	semidirect
3. #15688932	C₂	semidirect
4. #15688905	C₂	semidirect
5. C₄₇×#469	C₂	semidirect
13. #13093964	C₂²	semidirect
14. C₂×D₈×C₄₇	C₂²	semidirect
17. #106×C₄₇	C₂²	semidirect
37. Dic₁₈₈	D₄	semidirect
39. D₃₇₆	D₄	semidirect
86. #469	D₄₇	semidirect
89. C₄₇	#2190	semidirect
95. C₂×D₈	C₂×D₄₇	semidirect
101. #106	C₂×D₄₇	semidirect

H ≅ G/N

type

1. #15689923

C₂

semidirect

2. #15689559

C₂

semidirect

3. #15688932

C₂

semidirect

4. #15688905

C₂

semidirect

5. C₄₇×#469

C₂

semidirect

13. #13093964

C₂²

semidirect

14. C₂×D₈×C₄₇

C₂²

semidirect

17. #106×C₄₇

C₂²

semidirect

37. Dic₁₈₈

D₄

semidirect

39. D₃₇₆

D₄

semidirect

86. #469

D₄₇

semidirect

89. C₄₇

#2190

semidirect

95. C₂×D₈

C₂×D₄₇

semidirect

101. #106

C₂×D₄₇

semidirect

Subgroups — #20245333

Conjugacy classes of subgroups

Complements