Group #20245463 — subgroups

Subgroups — #20245463

Order 6016.

170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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	#15689561	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689559	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689498	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689239	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688943	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#361	C₂	1	1	yes	maximal, characteristic, complemented
8	#13094046	C₂²	1	1	yes	characteristic
9	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
10	C₂×#10625334	—	2	1	no	—
11	#13094032	—	2	1	no	—
12	#13094020	—	2	1	no	—
13	#13093969	—	2	1	no	—
14	#13093968	—	2	1	no	—
15	D₇₅₂	—	2	1	no	—
16	#13093965	—	2	1	no	—
17	#13093964	C₂²	1	1	yes	characteristic
18	#13093950	—	2	1	no	—
19	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic
21	M₃₂×C₄₇	C₂²	1	1	yes	characteristic
22	#108×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×D₄×C₄₇	—	2	1	no	—
24	C₂×C₂²⋊D₄₇	—	4	2	no	—
25	#10625350	—	2	1	no	—
26	C₂×D₁₈₈	—	2	1	no	—
27	D₈×C₄₇	—	2	1	no	—
28	D₈×C₄₇	—	2	1	no	—
29	M₁₆×C₄₇	—	2	1	no	—
30	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
31	#10625334	—	4	1	no	—
32	#10625334	—	4	1	no	—
33	C₄×Dic₄₇	D₄	1	1	yes	characteristic
34	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
35	Dic₁₈₈	D₄	1	1	yes	characteristic, complemented
36	D₃₇₆	—	2	1	no	—
37	D₃₇₆	—	2	1	no	—
38	D₃₇₆	D₄	1	1	yes	characteristic, complemented
39	#10625325	—	2	1	no	—
40	#10625324	—	4	1	no	—
41	C₈×D₄₇	—	4	1	no	—
42	C₁₆×C₄₇	—	2	1	no	—
43	C₄₇⋊C₁₆	—	2	1	no	—
44	C₂³×C₄₇	—	4	1	no	—
45	C₂²×D₄₇	—	4	1	no	—
46	D₄×C₄₇	—	4	1	no	—
47	D₄×C₄₇	—	4	1	no	—
48	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂²⋊D₄₇	—	4	1	no	—
50	C₂²⋊D₄₇	—	8	4	no	—
51	C₂×Dic₄₇	—	2	1	no	—
52	D₁₈₈	—	2	1	no	—
53	D₁₈₈	—	4	1	no	—
54	D₁₈₈	—	4	1	no	—
55	C₄×D₄₇	—	4	1	no	—
56	Dic₉₄	—	2	1	no	—
57	C₈×C₄₇	—	4	1	no	—
58	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₈×C₄₇	#41	1	1	yes	characteristic
60	C₄₇⋊C₈	D₈	1	1	yes	characteristic
61	C₄₇⋊C₈	D₈	1	1	yes	characteristic
62	C₂²×C₄₇	—	8	2	no	—
63	C₂²×C₄₇	—	8	1	no	—
64	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂×D₄₇	—	4	1	no	—
66	C₂×D₄₇	—	8	2	no	—
67	C₂×D₄₇	—	8	1	no	—
68	C₄×C₄₇	#121	1	1	yes	characteristic
69	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
70	Dic₄₇	—	2	2	no	—
71	Dic₄₇	—	4	1	no	—
72	#2213	—	47	1	no	maximal, Sylow
73	C₂×C₄₇	—	2	1	no	—
74	C₂×C₄₇	—	16	1	no	—
75	C₂×C₄₇	#459	1	1	yes	characteristic
76	D₄₇	—	8	1	no	—
77	D₄₇	—	16	1	no	—
78	#509	—	47	1	no	—
79	#509	—	47	1	no	—
80	#493	—	47	1	no	—
81	#443	—	47	1	no	—
82	#364	—	47	1	no	—
83	#361	—	47	1	no	—
84	#361	D₄₇	1	1	yes	characteristic, complemented
85	C₄₇	#2213	1	1	yes	characteristic, complemented, Sylow
86	#135	—	47	1	no	—
87	C₂×D₈	—	47	1	no	—
88	C₂×D₈	—	94	1	no	—
89	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic
90	#131	—	94	1	no	—
91	#127	—	94	1	no	—
92	SD₃₂	—	94	1	no	—
93	SD₃₂	—	94	1	no	—
94	D₁₆	—	94	1	no	—
95	D₁₆	—	94	1	no	—
96	M₃₂	—	47	1	no	—
97	M₃₂	C₂×D₄₇	1	1	yes	characteristic
98	#108	C₂×D₄₇	1	1	yes	characteristic
99	#104	—	94	1	no	—
100	C₄×C₈	—	47	1	no	—
101	#41	—	94	1	no	—
102	C₂×D₄	—	2	1	no	—
103	C₂×D₄	—	94	1	no	—
104	C₂×D₄	—	188	2	no	—
105	Q₁₆	—	47	1	no	—
106	SD₁₆	—	94	1	no	—
107	D₈	—	2	1	no	—
108	D₈	—	2	1	no	—
109	D₈	—	47	1	no	—
110	D₈	—	94	1	no	—
111	D₈	—	94	1	no	—
112	D₈	—	188	1	no	—
113	D₈	—	188	1	no	—
114	M₁₆	—	2	1	no	—
115	M₁₆	—	188	1	no	—
116	C₂×C₈	—	47	1	no	—
117	C₂×C₈	—	188	1	no	—
118	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
119	C₄²	—	47	1	no	—
120	C₁₆	—	2	1	no	—
121	C₁₆	—	94	1	no	—
122	C₂³	—	4	1	no	—
123	C₂³	—	188	1	no	—
124	Q₈	—	94	1	no	—
125	D₄	—	4	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	94	1	no	—
128	D₄	—	376	4	no	—
129	D₄	—	188	1	no	—
130	D₄	—	188	1	no	—
131	D₄	—	188	1	no	—
132	C₂×C₄	—	94	1	no	—
133	C₂×C₄	—	188	1	no	—
134	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
135	C₈	—	4	1	no	—
136	C₈	—	47	1	no	—
137	C₈	—	47	1	no	—
138	C₈	#10625350	1	1	yes	characteristic
139	C₈	D₄×D₄₇	1	1	yes	characteristic
140	C₂²	—	8	2	no	—
141	C₂²	—	8	1	no	—
142	C₂²	—	376	2	no	—
143	C₂²	—	376	1	no	—
144	C₂²	—	188	1	no	—
145	C₂²	#13094051	1	1	yes	characteristic
146	C₄	—	94	2	no	—
147	C₄	—	188	1	no	—
148	C₄	#13093997	1	1	yes	characteristic
149	C₄	D₈×D₄₇	1	1	yes	characteristic
150	C₂	—	2	1	no	—
151	C₂	—	16	1	no	—
152	C₂	—	376	1	no	—
153	C₂	—	752	1	no	—
154	C₂	#15689317	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689561

C₂

yes

maximal, characteristic, complemented

#15689559

C₂

yes

maximal, characteristic, complemented

#15689498

C₂

yes

maximal, characteristic, complemented

#15689239

C₂

yes

maximal, characteristic, complemented

#15688943

C₂

yes

maximal, characteristic, complemented

#15688935

C₂

yes

maximal, characteristic, complemented

C₄₇×#361

C₂

yes

maximal, characteristic, complemented

#13094046

C₂²

yes

characteristic

C₂×D₃₇₆

C₂²

yes

—

—

—

—

—

D₇₅₂

—

#13093965

—

#13093964

C₂²

yes

characteristic

#13093950

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×D₈×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

C₂²

yes

characteristic

#108×C₄₇

C₂²

yes

characteristic

C₂×D₄×C₄₇

—

C₂×C₂²⋊D₄₇

—

#10625350

—

C₂×D₁₈₈

—

D₈×C₄₇

—

D₈×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

#10625334

—

#10625334

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

D₄

yes

characteristic, complemented

D₃₇₆

—

D₃₇₆

—

D₃₇₆

D₄

yes

characteristic, complemented

#10625325

—

#10625324

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂²×D₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

D₈

yes

characteristic

C₄₇⋊C₈

D₈

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

#121

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2213

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#459

yes

characteristic

D₄₇

—

D₄₇

—

—

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2213

yes

characteristic, complemented, Sylow

#135

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₄₇

yes

characteristic

#131

—

#127

—

SD₃₂

—

SD₃₂

—

D₁₆

—

D₁₆

—

M₃₂

—

M₃₂

C₂×D₄₇

yes

characteristic

#108

C₂×D₄₇

yes

characteristic

#104

—

100

C₄×C₈

—

101

#41

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

188

—

105

Q₁₆

—

106

SD₁₆

—

107

D₈

—

108

D₈

—

109

D₈

—

110

D₈

—

111

D₈

—

112

D₈

—

188

—

113

D₈

—

188

—

114

M₁₆

—

115

M₁₆

—

188

—

116

C₂×C₈

—

117

C₂×C₈

—

188

—

118

C₂×C₈

C₂²×D₄₇

yes

characteristic

119

C₄²

—

120

C₁₆

—

121

C₁₆

—

122

C₂³

—

123

C₂³

—

188

—

124

Q₈

—

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

376

—

129

D₄

—

188

—

130

D₄

—

188

—

131

D₄

—

188

—

132

C₂×C₄

—

133

C₂×C₄

—

188

—

134

C₂×C₄

D₄×D₄₇

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

#10625350

yes

characteristic

139

C₈

D₄×D₄₇

yes

characteristic

140

C₂²

—

141

C₂²

—

142

C₂²

—

376

—

143

C₂²

—

376

—

144

C₂²

—

188

—

145

C₂²

#13094051

yes

characteristic

146

C₄

—

147

C₄

—

188

—

148

C₄

#13093997

yes

characteristic

149

C₄

D₈×D₄₇

yes

characteristic

150

C₂

—

151

C₂

—

152

C₂

—

376

—

153

C₂

—

752

—

154

C₂

#15689317

yes

characteristic

	subgroup	G/H
center	C₂	#15689317
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#361	C₂
socle	C₂×C₄₇	#459
hypercenter	#361	D₄₇
hypocenter	C₄₇	#2213
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #361

subgroup

G/H

center

C₂

#15689317

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#361

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #361

N	H ≅ G/N	type
1. #15689561	C₂	semidirect
2. #15689559	C₂	semidirect
3. #15689498	C₂	semidirect
4. #15689239	C₂	semidirect
5. #15688943	C₂	semidirect
6. #15688935	C₂	semidirect
7. C₄₇×#361	C₂	semidirect
35. Dic₁₈₈	D₄	semidirect
38. D₃₇₆	D₄	semidirect
84. #361	D₄₇	semidirect
85. C₄₇	#2213	semidirect

H ≅ G/N

type

1. #15689561

C₂

semidirect

2. #15689559

C₂

semidirect

3. #15689498

C₂

semidirect

4. #15689239

C₂

semidirect

5. #15688943

C₂

semidirect

6. #15688935

C₂

semidirect

7. C₄₇×#361

C₂

semidirect

35. Dic₁₈₈

D₄

semidirect

38. D₃₇₆

D₄

semidirect

84. #361

D₄₇

semidirect

85. C₄₇

#2213

semidirect

Subgroups — #20245463

Conjugacy classes of subgroups

Complements