Group #20245462 — subgroups

Subgroups — #20245462

Order 6016.

170 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 45 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	#15689558	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689498	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689240	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688943	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688937	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#509	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
9	C₂×#10625334	—	2	1	no	—
10	#13094031	—	2	1	no	—
11	#13094020	—	2	1	no	—
12	#13093967	—	2	1	no	—
13	#13093965	—	2	1	no	—
14	#13093964	C₂²	1	1	yes	characteristic
15	#13093960	C₂²	1	1	yes	characteristic
16	#13093951	—	2	1	no	—
17	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
18	#135×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic
20	SD₃₂×C₄₇	—	2	1	no	—
21	D₁₆×C₄₇	—	2	1	no	—
22	M₃₂×C₄₇	C₂²	1	1	yes	characteristic
23	#41×C₄₇	—	2	1	no	—
24	C₂×D₄×C₄₇	—	2	1	no	—
25	C₂×C₂²⋊D₄₇	—	4	2	no	—
26	C₂×D₁₈₈	—	2	1	no	—
27	Q₁₆×C₄₇	D₄	1	1	yes	characteristic, complemented
28	SD₁₆×C₄₇	—	2	1	no	—
29	D₈×C₄₇	—	2	1	no	—
30	D₈×C₄₇	—	2	1	no	—
31	D₈×C₄₇	D₄	1	1	yes	characteristic, complemented
32	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
33	#10625334	—	4	1	no	—
34	#10625334	—	4	1	no	—
35	C₄×Dic₄₇	D₄	1	1	yes	characteristic
36	#10625329	—	2	1	no	—
37	#10625329	—	4	1	no	—
38	C₂×C₄₇⋊C₈	—	4	1	no	—
39	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
40	D₃₇₆	—	2	1	no	—
41	D₃₇₆	—	2	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	Q₈×C₄₇	—	2	1	no	—
47	D₄×C₄₇	—	2	1	no	—
48	D₄×C₄₇	—	4	1	no	—
49	D₄×C₄₇	—	4	1	no	—
50	D₄×C₄₇	—	4	1	no	—
51	C₂×C₄×C₄₇	—	4	1	no	—
52	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
53	C₂²⋊D₄₇	—	8	4	no	—
54	C₂×Dic₄₇	—	2	1	no	—
55	D₁₈₈	—	4	1	no	—
56	D₁₈₈	—	4	1	no	—
57	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₈×C₄₇	#41	1	1	yes	characteristic
59	C₄₇⋊C₈	—	4	1	no	—
60	C₄₇⋊C₈	D₈	1	1	yes	characteristic
61	C₄₇⋊C₈	D₈	1	1	yes	characteristic
62	C₂²×C₄₇	—	4	1	no	—
63	C₂²×C₄₇	—	8	2	no	—
64	C₂²×C₄₇	—	8	1	no	—
65	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
66	C₂×D₄₇	—	8	2	no	—
67	C₂×D₄₇	—	8	1	no	—
68	C₄×C₄₇	—	4	1	no	—
69	C₄×C₄₇	#121	1	1	yes	characteristic
70	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
71	Dic₄₇	—	2	2	no	—
72	#2213	—	47	1	no	maximal, Sylow
73	C₂×C₄₇	—	2	1	no	—
74	C₂×C₄₇	—	8	1	no	—
75	C₂×C₄₇	—	16	1	no	—
76	C₂×C₄₇	#459	1	1	yes	characteristic
77	D₄₇	—	16	1	no	—
78	#509	—	47	1	no	—
79	#509	D₄₇	1	1	yes	characteristic, complemented
80	#493	—	47	1	no	—
81	#443	—	47	1	no	—
82	#364	—	47	1	no	—
83	#361	—	47	1	no	—
84	#361	—	47	1	no	—
85	C₄₇	#2213	1	1	yes	characteristic, complemented, Sylow
86	#135	C₂×D₄₇	1	1	yes	characteristic
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	—	2	1	no	—
93	SD₃₂	—	94	1	no	—
94	D₁₆	—	2	1	no	—
95	D₁₆	—	94	1	no	—
96	M₃₂	—	47	1	no	—
97	M₃₂	C₂×D₄₇	1	1	yes	characteristic
98	#108	—	47	1	no	—
99	#104	—	94	1	no	—
100	C₄×C₈	—	47	1	no	—
101	#41	—	2	1	no	—
102	C₂×D₄	—	2	1	no	—
103	C₂×D₄	—	94	1	no	—
104	C₂×D₄	—	188	2	no	—
105	Q₁₆	C₂²⋊D₄₇	1	1	yes	characteristic, complemented
106	SD₁₆	—	2	1	no	—
107	D₈	—	2	1	no	—
108	D₈	—	2	1	no	—
109	D₈	—	94	1	no	—
110	D₈	—	94	1	no	—
111	D₈	—	188	1	no	—
112	D₈	—	188	1	no	—
113	D₈	C₂²⋊D₄₇	1	1	yes	characteristic, complemented
114	M₁₆	—	94	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	—	2	1	no	—
125	D₄	—	2	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	4	1	no	—
128	D₄	—	4	1	no	—
129	D₄	—	376	4	no	—
130	D₄	—	188	1	no	—
131	D₄	—	188	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	94	1	no	—
134	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
135	C₈	—	47	1	no	—
136	C₈	—	47	1	no	—
137	C₈	—	188	1	no	—
138	C₈	#10625352	1	1	yes	characteristic
139	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
140	C₂²	—	4	1	no	—
141	C₂²	—	8	2	no	—
142	C₂²	—	8	1	no	—
143	C₂²	—	376	2	no	—
144	C₂²	—	376	1	no	—
145	C₂²	#13094048	1	1	yes	characteristic
146	C₄	—	4	1	no	—
147	C₄	—	94	2	no	—
148	C₄	#13093996	1	1	yes	characteristic
149	C₄	D₈×D₄₇	1	1	yes	characteristic
150	C₂	—	2	1	no	—
151	C₂	—	8	1	no	—
152	C₂	—	16	1	no	—
153	C₂	—	752	1	no	—
154	C₂	#15689316	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689558

C₂

yes

maximal, characteristic, complemented

#15689498

C₂

yes

maximal, characteristic, complemented

#15689240

C₂

yes

maximal, characteristic, complemented

#15688943

C₂

yes

maximal, characteristic, complemented

#15688937

C₂

yes

maximal, characteristic, complemented

#15688936

C₂

yes

maximal, characteristic, complemented

C₄₇×#509

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

#13093960

C₂²

yes

characteristic

#13093951

—

C₈×Dic₄₇

C₂²

yes

characteristic

#135×C₄₇

C₂²

yes

characteristic

C₂×D₈×C₄₇

C₂²

yes

characteristic

SD₃₂×C₄₇

—

D₁₆×C₄₇

—

M₃₂×C₄₇

C₂²

yes

characteristic

#41×C₄₇

—

C₂×D₄×C₄₇

—

C₂×C₂²⋊D₄₇

—

C₂×D₁₈₈

—

Q₁₆×C₄₇

D₄

yes

characteristic, complemented

SD₁₆×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

D₄

yes

characteristic, complemented

C₂×C₈×C₄₇

C₂³

yes

characteristic

#10625334

—

#10625334

—

C₄×Dic₄₇

D₄

yes

characteristic

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

D₃₇₆

—

D₃₇₆

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₄₇⋊C₈

D₈

yes

characteristic

C₄₇⋊C₈

D₈

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#121

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

—

#2213

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#459

yes

characteristic

D₄₇

—

#509

—

#509

D₄₇

yes

characteristic, complemented

—

—

—

—

—

C₄₇

#2213

yes

characteristic, complemented, Sylow

#135

C₂×D₄₇

yes

characteristic

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₄₇

yes

characteristic

#131

—

#127

—

SD₃₂

—

SD₃₂

—

D₁₆

—

D₁₆

—

M₃₂

—

M₃₂

C₂×D₄₇

yes

characteristic

#108

—

#104

—

100

C₄×C₈

—

101

#41

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

188

—

105

Q₁₆

C₂²⋊D₄₇

yes

characteristic, complemented

106

SD₁₆

—

107

D₈

—

108

D₈

—

109

D₈

—

110

D₈

—

111

D₈

—

188

—

112

D₈

—

188

—

113

D₈

C₂²⋊D₄₇

yes

characteristic, complemented

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

—

129

D₄

—

376

—

130

D₄

—

188

—

131

D₄

—

188

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

D₄×D₄₇

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

188

—

138

C₈

#10625352

yes

characteristic

139

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

376

—

144

C₂²

—

376

—

145

C₂²

#13094048

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

#13093996

yes

characteristic

149

C₄

D₈×D₄₇

yes

characteristic

150

C₂

—

151

C₂

—

152

C₂

—

153

C₂

—

752

—

154

C₂

#15689316

yes

characteristic

	subgroup	G/H
center	C₂	#15689316
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#509	C₂
socle	C₂×C₄₇	#459
hypercenter	#509	D₄₇
hypocenter	C₄₇	#2213
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #509

subgroup

G/H

center

C₂

#15689316

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#509

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #509

N	H ≅ G/N	type
1. #15689558	C₂	semidirect
2. #15689498	C₂	semidirect
3. #15689240	C₂	semidirect
4. #15688943	C₂	semidirect
5. #15688937	C₂	semidirect
6. #15688936	C₂	semidirect
7. C₄₇×#509	C₂	semidirect
27. Q₁₆×C₄₇	D₄	semidirect
31. D₈×C₄₇	D₄	semidirect
79. #509	D₄₇	semidirect
85. C₄₇	#2213	semidirect
105. Q₁₆	C₂²⋊D₄₇	semidirect
113. D₈	C₂²⋊D₄₇	semidirect

H ≅ G/N

type

1. #15689558

C₂

semidirect

2. #15689498

C₂

semidirect

3. #15689240

C₂

semidirect

4. #15688943

C₂

semidirect

5. #15688937

C₂

semidirect

6. #15688936

C₂

semidirect

7. C₄₇×#509

C₂

semidirect

27. Q₁₆×C₄₇

D₄

semidirect

31. D₈×C₄₇

D₄

semidirect

79. #509

D₄₇

semidirect

85. C₄₇

#2213

semidirect

105. Q₁₆

C₂²⋊D₄₇

semidirect

113. D₈

C₂²⋊D₄₇

semidirect

Subgroups — #20245462

Conjugacy classes of subgroups

Complements