Group #20244296 — subgroups

Subgroups — #20244296

Order 6016.

316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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	C₂²×D₃₇₆	C₂	1	1	yes	maximal, characteristic
2	#15689129	C₂	1	2	yes	maximal, complemented
3	C₂×#13093940	C₂	1	2	yes	maximal, complemented
4	#15689078	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#108×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₈₈	C₂²	1	2	yes	—
7	C₂×D₃₇₆	—	2	1	no	—
8	C₂×D₃₇₆	—	2	1	no	—
9	C₂×D₃₇₆	—	2	2	no	—
10	C₂×D₃₇₆	C₄	1	4	yes	complemented
11	C₂×#10625329	C₂²	1	1	yes	characteristic
12	#13093983	C₂²	1	1	yes	characteristic
13	#13093946	—	2	4	no	—
14	#13093940	—	2	4	no	—
15	#13093934	—	2	1	no	—
16	C₈×Dic₄₇	—	2	1	no	—
17	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	#108×C₄₇	—	2	2	no	—
20	C₂³×D₄₇	—	2	2	no	—
21	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂×D₁₈₈	—	2	2	no	—
23	C₂×D₁₈₈	—	2	2	no	—
24	C₂×D₁₈₈	—	2	2	no	—
25	C₂×D₁₈₈	—	2	2	no	—
26	C₂×D₁₈₈	—	2	2	no	—
27	C₂×D₁₈₈	C₂×C₄	1	4	yes	—
28	M₁₆×C₄₇	—	2	2	no	—
29	M₁₆×C₄₇	—	2	2	no	—
30	C₂×C₈×C₄₇	—	2	2	no	—
31	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
33	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
34	C₂×C₈×C₄₇	D₄	1	2	yes	—
35	C₂²⋊Dic₄₇	—	2	1	no	—
36	C₄⋊Dic₄₇	D₄	1	2	yes	—
37	C₄×Dic₄₇	—	2	1	no	—
38	#10625329	—	2	1	no	—
39	#10625329	D₄	1	2	yes	—
40	C₂×C₄₇⋊C₈	—	2	1	no	—
41	D₃₇₆	—	2	4	no	—
42	D₃₇₆	—	2	4	no	—
43	C₂³×C₄₇	#41	1	1	yes	characteristic
44	C₂²×D₄₇	—	2	4	no	—
45	C₂²×D₄₇	—	4	2	no	—
46	C₂²×D₄₇	—	4	2	no	—
47	C₂²×D₄₇	—	8	4	no	—
48	C₂×C₄×C₄₇	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
54	C₂×Dic₄₇	—	2	2	no	—
55	D₁₈₈	—	2	4	no	—
56	D₁₈₈	—	2	4	no	—
57	D₁₈₈	—	4	2	no	—
58	D₁₈₈	—	4	2	no	—
59	C₈×C₄₇	—	4	2	no	—
60	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
61	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
62	C₄₇⋊C₈	—	2	2	no	—
63	C₂²×C₄₇	—	2	2	no	—
64	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
65	C₂²×C₄₇	#121	1	1	yes	characteristic
66	C₂²×C₄₇	#124	1	1	yes	characteristic
67	C₂×D₄₇	—	4	4	no	—
68	C₂×D₄₇	—	8	4	no	—
69	C₂×D₄₇	—	8	4	no	—
70	C₂×D₄₇	—	8	4	no	—
71	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
73	C₄×C₄₇	#121	1	1	yes	characteristic
74	C₄×C₄₇	#127	1	1	yes	characteristic
75	Dic₄₇	—	4	2	no	—
76	#1978	—	47	1	no	maximal, Sylow
77	C₂×C₄₇	—	2	1	no	—
78	C₂×C₄₇	—	2	1	no	—
79	C₂×C₄₇	#390	1	1	yes	characteristic
80	C₂×C₄₇	#472	1	2	yes	—
81	D₄₇	—	8	4	no	—
82	C₂²×D₈	—	47	1	no	—
83	C₂×#108	D₄₇	1	1	yes	characteristic, complemented
84	#418	—	47	2	no	—
85	C₂×#100	—	47	2	no	—
86	#405	—	47	1	no	—
87	C₄₇	#1978	1	1	yes	characteristic, complemented, Sylow
88	C₂²×D₄	—	47	2	no	—
89	C₂×D₈	—	47	4	no	—
90	C₂×D₈	—	94	1	no	—
91	C₂×D₈	—	94	1	no	—
92	C₂×D₈	—	94	2	no	—
93	C₂×M₁₆	—	47	1	no	—
94	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
95	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
96	#117	—	47	1	no	—
97	#108	—	2	2	no	—
98	#102	—	94	4	no	—
99	#100	—	94	4	no	—
100	#97	—	94	1	no	—
101	C₄×C₈	—	94	1	no	—
102	C₂⁴	—	94	2	no	—
103	C₂×D₄	—	47	4	no	—
104	C₂×D₄	—	94	2	no	—
105	C₂×D₄	—	94	2	no	—
106	C₂×D₄	—	94	2	no	—
107	C₂×D₄	—	94	2	no	—
108	C₂×D₄	—	94	2	no	—
109	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
110	D₈	—	94	4	no	—
111	D₈	—	94	4	no	—
112	M₁₆	—	2	2	no	—
113	M₁₆	—	2	2	no	—
114	M₁₆	—	47	2	no	—
115	M₁₆	—	94	1	no	—
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	94	1	no	—
118	C₂×C₈	C₄×D₄₇	1	2	yes	—
119	C₂×C₈	D₁₈₈	1	1	yes	characteristic
120	C₂×C₈	D₁₈₈	1	1	yes	characteristic
121	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
122	C₄⋊C₄	—	47	2	no	—
123	C₂²⋊C₄	—	94	1	no	—
124	C₄²	—	94	1	no	—
125	C₂³	—	94	4	no	—
126	C₂³	—	376	4	no	—
127	C₂³	—	188	2	no	—
128	C₂³	—	188	2	no	—
129	C₂³	#10625354	1	1	yes	characteristic
130	D₄	—	94	4	no	—
131	D₄	—	94	4	no	—
132	D₄	—	188	2	no	—
133	D₄	—	188	2	no	—
134	C₂×C₄	—	94	2	no	—
135	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
136	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
137	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
138	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
139	C₂×C₄	#10625354	1	1	yes	characteristic
140	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
141	C₈	—	4	2	no	—
142	C₈	—	94	2	no	—
143	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
144	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
145	C₂²	—	2	2	no	—
146	C₂²	—	376	4	no	—
147	C₂²	—	376	4	no	—
148	C₂²	—	376	4	no	—
149	C₂²	—	188	4	no	—
150	C₂²	#13093986	1	1	yes	characteristic
151	C₂²	#13093999	1	1	yes	characteristic
152	C₂²	#13094013	1	1	yes	characteristic
153	C₄	—	188	2	no	—
154	C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
155	C₄	#13093986	1	1	yes	characteristic
156	C₄	#13093999	1	1	yes	characteristic
157	C₄	#13094020	1	1	yes	characteristic
158	C₂	—	2	1	no	—
159	C₂	—	2	1	no	—
160	C₂	—	376	4	no	—
161	C₂	#15689024	1	1	yes	characteristic
162	C₂	#15689394	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₃₇₆

C₂

yes

maximal, characteristic

#15689129

C₂

yes

maximal, complemented

C₂×#13093940

C₂

yes

maximal, complemented

#15689078

C₂

yes

maximal, characteristic, complemented

C₂×#108×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

C₄

yes

complemented

C₂×#10625329

C₂²

yes

characteristic

#13093983

C₂²

yes

—

—

—

C₈×Dic₄₇

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#108×C₄₇

—

C₂³×D₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂×C₄

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

—

C₄×Dic₄₇

—

#10625329

—

#10625329

D₄

yes

—

C₂×C₄₇⋊C₈

—

D₃₇₆

—

D₃₇₆

—

C₂³×C₄₇

#41

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄×D₄

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₄×D₄

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1978

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#390

yes

characteristic

C₂×C₄₇

#472

yes

—

D₄₇

—

C₂²×D₈

—

C₂×#108

D₄₇

yes

characteristic, complemented

#418

—

C₂×#100

—

#405

—

C₄₇

#1978

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

C₂×D₄₇

yes

—

—

—

—

100

#97

—

101

C₄×C₈

—

102

C₂⁴

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂²×C₄

C₂²×D₄₇

yes

characteristic

110

D₈

—

111

D₈

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

C₄×D₄₇

yes

—

119

C₂×C₈

D₁₈₈

yes

characteristic

120

C₂×C₈

D₁₈₈

yes

characteristic

121

C₂×C₈

C₂²⋊D₄₇

yes

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₂³

—

126

C₂³

—

376

—

127

C₂³

—

188

—

128

C₂³

—

188

—

129

C₂³

#10625354

yes

characteristic

130

D₄

—

131

D₄

—

132

D₄

—

188

—

133

D₄

—

188

—

134

C₂×C₄

—

135

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

136

C₂×C₄

C₂×D₁₈₈

yes

characteristic

137

C₂×C₄

D₄×D₄₇

yes

characteristic

138

C₂×C₄

D₄×D₄₇

yes

characteristic

139

C₂×C₄

#10625354

yes

characteristic

140

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

141

C₈

—

142

C₈

—

143

C₈

(C₂×D₄₇)⋊C₄

yes

—

144

C₈

(C₂×D₄₇)⋊C₄

yes

—

145

C₂²

—

146

C₂²

—

376

—

147

C₂²

—

376

—

148

C₂²

—

376

—

149

C₂²

—

188

—

150

C₂²

#13093986

yes

characteristic

151

C₂²

#13093999

yes

characteristic

152

C₂²

#13094013

yes

characteristic

153

C₄

—

188

—

154

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

155

C₄

#13093986

yes

characteristic

156

C₄

#13093999

yes

characteristic

157

C₄

#13094020

yes

characteristic

158

C₂

—

159

C₂

—

160

C₂

—

376

—

161

C₂

#15689024

yes

characteristic

162

C₂

#15689394

yes

—

	subgroup	G/H
center	C₂²	#13093999
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#108×C₄₇	C₂
socle	C₂²×C₄₇	#121
hypercenter	C₂×#108	D₄₇
hypocenter	C₄₇	#1978
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂²

#13093999

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#108×C₄₇

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
2. #15689129	C₂	semidirect
3. C₂×#13093940	C₂	semidirect
4. #15689078	C₂	semidirect
5. C₂×#108×C₄₇	C₂	semidirect
10. C₂×D₃₇₆	C₄	semidirect
83. C₂×#108	D₄₇	semidirect
87. C₄₇	#1978	semidirect

H ≅ G/N

type

2. #15689129

C₂

semidirect

3. C₂×#13093940

C₂

semidirect

4. #15689078

C₂

semidirect

5. C₂×#108×C₄₇

C₂

semidirect

10. C₂×D₃₇₆

C₄

semidirect

83. C₂×#108

D₄₇

semidirect

87. C₄₇

#1978

semidirect

Subgroups — #20244296

Conjugacy classes of subgroups

Complements