Group #20252963 — subgroups

Subgroups — C₂×#15689365 #20252963

Order 6016.

512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#13094004	C₂	1	2	yes	maximal
4	#15689365	C₂	1	8	yes	maximal, direct product factor
5	C₂×#13093947	C₂	1	2	yes	maximal, complemented
6	C₂×#107×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Dic₉₄	C₂²	1	2	yes	—
8	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₈₈	—	2	4	no	—
10	C₂×Dic₁₈₈	C₂²	1	4	yes	complemented
11	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₈×D₄₇	—	2	4	no	—
13	C₂×C₈×D₄₇	C₂²	1	4	yes	—
14	#13094004	—	2	4	no	—
15	#13094004	C₂²	1	8	yes	—
16	C₂×C₄⋊Dic₄₇	—	2	2	no	—
17	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
18	#13093947	C₂²	1	8	yes	complemented
19	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
21	#107×C₄₇	C₂²	1	4	yes	complemented
22	C₂³×D₄₇	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₇	—	2	2	no	—
24	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₇	—	2	2	no	—
26	C₂²×Dic₄₇	D₄	1	1	yes	characteristic
27	C₂×C₄×D₄₇	—	2	2	no	—
28	C₂×C₄×D₄₇	—	2	2	no	—
29	C₂×C₄×D₄₇	D₄	1	2	yes	—
30	C₂×C₄×D₄₇	C₂³	1	2	yes	—
31	C₂×Dic₉₄	—	2	4	no	—
32	C₂×Dic₉₄	—	2	4	no	—
33	C₂×Dic₉₄	—	2	2	no	—
34	C₂×Dic₉₄	C₂³	1	4	yes	—
35	C₂×C₈×C₄₇	D₄	1	4	yes	—
36	C₂×C₈×C₄₇	C₂³	1	2	yes	—
37	C₄⋊C₄×C₄₇	—	2	2	no	—
38	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
39	(C₂×D₄₇)⋊C₄	—	2	8	no	—
40	C₄⋊Dic₄₇	—	2	8	no	—
41	C₂×C₄₇⋊C₈	—	2	2	no	—
42	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
43	Dic₁₈₈	—	2	8	no	—
44	C₈×D₄₇	—	2	8	no	—
45	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂²×D₄₇	—	2	2	no	—
47	C₂²×D₄₇	—	2	2	no	—
48	C₂²×D₄₇	Q₁₆	1	4	yes	complemented
49	C₂²×D₄₇	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₄₇	—	2	4	no	—
51	C₂×C₄×C₄₇	—	4	4	no	—
52	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₄₇	#41	1	2	yes	—
55	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
56	C₂×Dic₄₇	—	2	2	no	—
57	C₂×Dic₄₇	—	2	4	no	—
58	C₂×Dic₄₇	—	4	4	no	—
59	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
60	C₄×D₄₇	—	2	4	no	—
61	C₄×D₄₇	—	2	2	no	—
62	C₄×D₄₇	—	2	2	no	—
63	Dic₉₄	—	2	4	no	—
64	Dic₉₄	—	2	4	no	—
65	Dic₉₄	—	4	4	no	—
66	C₈×C₄₇	C₂×D₄	1	4	yes	—
67	C₄₇⋊C₈	—	2	2	no	—
68	C₂²×C₄₇	#121	1	2	yes	—
69	C₂²×C₄₇	C₂×Q₁₆	1	2	yes	—
70	C₂²×C₄₇	#135	1	2	yes	—
71	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
72	C₂×D₄₇	—	2	2	no	—
73	C₂×D₄₇	—	2	2	no	—
74	C₂×D₄₇	—	2	8	no	—
75	C₂×D₄₇	C₂×Q₁₆	1	4	yes	complemented
76	C₄×C₄₇	—	4	4	no	—
77	C₄×C₄₇	#121	1	2	yes	—
78	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
79	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
80	Dic₄₇	—	2	2	no	—
81	Dic₄₇	—	4	4	no	—
82	C₂×#467	—	47	1	no	maximal, Sylow
83	C₂×C₄₇	#467	1	4	yes	complemented
84	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
85	C₂×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
86	C₂×C₄₇	C₂×#135	1	1	yes	characteristic
87	D₄₇	—	2	4	no	—
88	C₂²×Q₁₆	—	47	1	no	—
89	C₂³×C₈	—	47	1	no	—
90	C₂×C₂²⋊Q₈	—	47	2	no	—
91	#467	—	47	8	no	—
92	C₂×#107	D₄₇	1	1	yes	characteristic, complemented
93	C₂×#103	—	47	2	no	—
94	C₄₇	C₂×#467	1	1	yes	characteristic, complemented, Sylow
95	C₂²×Q₈	—	47	2	no	—
96	C₂³×C₄	—	47	1	no	—
97	C₂×Q₁₆	—	47	4	no	—
98	C₂×Q₁₆	—	94	4	no	—
99	C₂²×C₈	—	47	1	no	—
100	C₂²×C₈	—	47	4	no	—
101	C₂²×C₈	—	94	4	no	—
102	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
103	C₂²⋊Q₈	—	47	8	no	—
104	C₂²⋊Q₈	—	94	4	no	—
105	C₂×C₄⋊C₄	—	94	2	no	—
106	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
107	C₂×C₂²⋊C₄	—	94	2	no	—
108	#107	C₂×D₄₇	1	4	yes	complemented
109	#103	—	47	8	no	—
110	C₂⁴	—	47	1	no	—
111	C₂×Q₈	—	47	4	no	—
112	C₂×Q₈	—	94	2	no	—
113	C₂×Q₈	—	94	4	no	—
114	C₂×Q₈	—	94	4	no	—
115	C₂²×C₄	—	2	2	no	—
116	C₂²×C₄	—	47	1	no	—
117	C₂²×C₄	—	47	2	no	—
118	C₂²×C₄	—	47	2	no	—
119	C₂²×C₄	—	94	2	no	—
120	C₂²×C₄	—	94	2	no	—
121	C₂²×C₄	—	94	2	no	—
122	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
123	Q₁₆	—	94	8	no	—
124	C₂×C₈	—	47	2	no	—
125	C₂×C₈	—	94	2	no	—
126	C₂×C₈	—	94	8	no	—
127	C₂×C₈	D₁₈₈	1	4	yes	—
128	C₂×C₈	C₂²×D₄₇	1	2	yes	—
129	C₄⋊C₄	—	2	2	no	—
130	C₄⋊C₄	—	94	8	no	—
131	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
132	C₂²⋊C₄	—	94	8	no	—
133	C₂³	—	47	4	no	—
134	C₂³	—	47	2	no	—
135	C₂³	—	94	2	no	—
136	C₂³	—	94	2	no	—
137	C₂³	D₄×D₄₇	1	1	yes	characteristic
138	Q₈	—	94	4	no	—
139	Q₈	—	94	4	no	—
140	Q₈	—	188	4	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	4	4	no	—
143	C₂×C₄	—	47	2	no	—
144	C₂×C₄	—	94	2	no	—
145	C₂×C₄	—	94	4	no	—
146	C₂×C₄	—	94	2	no	—
147	C₂×C₄	—	94	2	no	—
148	C₂×C₄	—	94	4	no	—
149	C₂×C₄	—	188	4	no	—
150	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
151	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
152	C₂×C₄	#10625354	1	2	yes	—
153	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
154	C₈	—	94	2	no	—
155	C₈	C₂×D₁₈₈	1	4	yes	—
156	C₂²	—	47	4	no	—
157	C₂²	—	94	2	no	—
158	C₂²	—	94	8	no	—
159	C₂²	—	94	2	no	—
160	C₂²	#13093999	1	2	yes	—
161	C₂²	Q₁₆×D₄₇	1	2	yes	—
162	C₂²	#13094043	1	2	yes	—
163	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
164	C₄	—	4	4	no	—
165	C₄	—	94	2	no	—
166	C₄	—	188	4	no	—
167	C₄	#13093999	1	2	yes	—
168	C₄	C₂²×D₁₈₈	1	1	yes	characteristic
169	C₄	C₂×#10625354	1	1	yes	characteristic
170	C₂	—	94	4	no	—
171	C₂	#15689365	1	4	yes	direct product factor
172	C₂	C₂×#13093999	1	1	yes	characteristic
173	C₂	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
174	C₂	C₂×#13094043	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₈₈

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₄₇

C₂

yes

maximal, characteristic

C₂×#13094004

C₂

yes

maximal

#15689365

C₂

yes

maximal, direct product factor

C₂×#13093947

C₂

yes

maximal, complemented

C₂×#107×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₉₄

C₂²

yes

—

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂²

yes

complemented

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₄₇

—

C₂×C₈×D₄₇

C₂²

yes

—

#13094004

—

#13094004

C₂²

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×(C₂×D₄₇)⋊C₄

—

#13093947

C₂²

yes

complemented

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

#107×C₄₇

C₂²

yes

complemented

C₂³×D₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

D₄

yes

—

C₂×C₄×D₄₇

C₂³

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂³

yes

—

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂³

yes

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂³

yes

—

Dic₁₈₈

—

C₈×D₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

Q₁₆

yes

complemented

C₂²×D₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂×D₄

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

#121

yes

—

C₂²×C₄₇

C₂×Q₁₆

yes

—

C₂²×C₄₇

#135

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

C₂×Q₁₆

yes

complemented

C₄×C₄₇

—

C₄×C₄₇

#121

yes

—

C₄×C₄₇

C₂²×D₄

yes

characteristic

C₄×C₄₇

C₂×#41

yes

characteristic

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

C₂²×Q₁₆

yes

characteristic

C₂×C₄₇

C₂×#135

yes

characteristic

D₄₇

—

C₂²×Q₁₆

—

C₂³×C₈

—

C₂×C₂²⋊Q₈

—

#467

—

C₂×#107

D₄₇

yes

characteristic, complemented

C₂×#103

—

C₄₇

C₂×#467

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂³×C₄

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

—

100

C₂²×C₈

—

101

C₂²×C₈

—

102

C₂²×C₈

C₂×D₄₇

yes

characteristic

103

C₂²⋊Q₈

—

104

C₂²⋊Q₈

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

107

C₂×C₂²⋊C₄

—

108

#107

C₂×D₄₇

yes

complemented

109

#103

—

110

C₂⁴

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

C₂²×D₄₇

yes

characteristic

123

Q₁₆

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

D₁₈₈

yes

—

128

C₂×C₈

C₂²×D₄₇

yes

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

C₂²×D₄₇

yes

—

132

C₂²⋊C₄

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

D₄×D₄₇

yes

characteristic

138

Q₈

—

139

Q₈

—

140

Q₈

—

188

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

188

—

150

C₂×C₄

C₂×D₁₈₈

yes

—

151

C₂×C₄

D₄×D₄₇

yes

characteristic

152

C₂×C₄

#10625354

yes

—

153

C₂×C₄

C₂³×D₄₇

yes

characteristic

154

C₈

—

155

C₈

C₂×D₁₈₈

yes

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

#13093999

yes

—

161

C₂²

Q₁₆×D₄₇

yes

—

162

C₂²

#13094043

yes

—

163

C₂²

C₂×D₄×D₄₇

yes

characteristic

164

C₄

—

165

C₄

—

166

C₄

—

188

—

167

C₄

#13093999

yes

—

168

C₄

C₂²×D₁₈₈

yes

characteristic

169

C₄

C₂×#10625354

yes

characteristic

170

C₂

—

171

C₂

#15689365

yes

direct product factor

172

C₂

C₂×#13093999

yes

characteristic

173

C₂

C₂×Q₁₆×D₄₇

yes

characteristic

174

C₂

C₂×#13094043

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂×#107×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×#107	D₄₇
hypocenter	C₄₇	C₂×#467
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₂×#107×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
1. C₂²×Dic₁₈₈	C₂	semidirect
4. #15689365	C₂	direct (N × H)
5. C₂×#13093947	C₂	semidirect
6. C₂×#107×C₄₇	C₂	semidirect
10. C₂×Dic₁₈₈	C₂²	semidirect
18. #13093947	C₂²	semidirect
21. #107×C₄₇	C₂²	semidirect
48. C₂²×D₄₇	Q₁₆	semidirect
75. C₂×D₄₇	C₂×Q₁₆	semidirect
83. C₂×C₄₇	#467	semidirect
92. C₂×#107	D₄₇	semidirect
94. C₄₇	C₂×#467	semidirect
108. #107	C₂×D₄₇	semidirect
171. C₂	#15689365	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₁₈₈

C₂

semidirect

4. #15689365

C₂

direct (N × H)

5. C₂×#13093947

C₂

semidirect

6. C₂×#107×C₄₇

C₂

semidirect

10. C₂×Dic₁₈₈

C₂²

semidirect

18. #13093947

C₂²

semidirect

21. #107×C₄₇

C₂²

semidirect

48. C₂²×D₄₇

Q₁₆

semidirect

75. C₂×D₄₇

C₂×Q₁₆

semidirect

83. C₂×C₄₇

#467

semidirect

92. C₂×#107

D₄₇

semidirect

94. C₄₇

C₂×#467

semidirect

108. #107

C₂×D₄₇

semidirect

171. C₂

#15689365

direct (N × H)

Subgroups — C₂×#15689365 #20252963

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689365 #20252963

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689365 #20252963