Group #20246641 — subgroups

Subgroups — C₂×#15689063 #20246641

Order 6016.

604 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 237 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×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#15689063	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄₇⋊#95	C₂	1	2	yes	maximal
5	C₂×C₄₇⋊#95	C₂	1	2	yes	maximal
6	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂³×Dic₄₇	C₂²	1	2	yes	—
9	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₄₇	—	2	4	no	—
11	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
12	C₂×Dic₄₇⋊C₄	—	2	4	no	—
13	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	—
14	C₄₇⋊#95	C₂²	1	8	yes	—
15	C₄₇⋊#95	C₂²	1	8	yes	—
16	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
17	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
18	#95×C₄₇	C₂²	1	4	yes	—
19	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₄₇	—	2	4	no	—
21	C₂²×C₄×C₄₇	—	2	4	no	—
22	C₂²×C₄×C₄₇	—	2	4	no	—
23	C₂²×C₄×C₄₇	—	2	4	no	—
24	C₂²×C₄×C₄₇	D₄	1	4	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
26	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
27	C₂²×Dic₄₇	—	2	2	no	—
28	C₂²×Dic₄₇	—	2	2	no	—
29	C₂²×Dic₄₇	—	2	2	no	—
30	C₂²×Dic₄₇	—	2	4	no	—
31	C₂²×Dic₄₇	—	2	4	no	—
32	C₂²×Dic₄₇	—	2	8	no	—
33	C₂²×Dic₄₇	Q₈	1	4	yes	—
34	C₂²×Dic₄₇	C₂³	1	2	yes	—
35	C₂²×Dic₄₇	C₂³	1	4	yes	—
36	C₂²×Dic₄₇	C₂³	1	2	yes	—
37	C₄⋊Dic₄₇	—	2	8	no	—
38	Dic₄₇⋊C₄	—	2	8	no	—
39	C₂³×C₄₇	C₂×D₄	1	2	yes	—
40	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
41	C₂³×C₄₇	#41	1	4	yes	—
42	C₂³×C₄₇	#41	1	2	yes	—
43	C₂³×C₄₇	#41	1	4	yes	—
44	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
45	C₂×C₄×C₄₇	—	2	8	no	—
46	C₂×C₄×C₄₇	—	2	4	no	—
47	C₂×C₄×C₄₇	—	2	4	no	—
48	C₂×C₄×C₄₇	—	2	4	no	—
49	C₂×C₄×C₄₇	—	2	4	no	—
50	C₂×C₄×C₄₇	—	4	8	no	—
51	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
52	C₂×Dic₄₇	—	2	8	no	—
53	C₂×Dic₄₇	—	2	2	no	—
54	C₂×Dic₄₇	—	2	2	no	—
55	C₂×Dic₄₇	—	2	2	no	—
56	C₂×Dic₄₇	—	2	4	no	—
57	C₂×Dic₄₇	—	2	4	no	—
58	C₂×Dic₄₇	—	2	8	no	—
59	C₂×Dic₄₇	—	4	4	no	—
60	C₂×Dic₄₇	—	4	8	no	—
61	C₂×Dic₄₇	C₂×Q₈	1	4	yes	—
62	C₂²×C₄₇	C₂²⋊Q₈	1	4	yes	—
63	C₂²×C₄₇	#123	1	4	yes	—
64	C₂²×C₄₇	#124	1	4	yes	—
65	C₂²×C₄₇	#125	1	8	yes	—
66	C₂²×C₄₇	#126	1	8	yes	—
67	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
68	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
69	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
70	C₂²×C₄₇	C₂×#41	1	2	yes	—
71	C₂²×C₄₇	C₂×#41	1	2	yes	—
72	C₄×C₄₇	—	2	4	no	—
73	C₄×C₄₇	—	4	4	no	—
74	Dic₄₇	—	2	4	no	—
75	Dic₄₇	—	4	2	no	—
76	Dic₄₇	—	4	4	no	—
77	C₂×#400	—	47	1	no	maximal, Sylow
78	C₂×C₄₇	#400	1	8	yes	complemented
79	C₂×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
80	C₂×C₄₇	C₂×#123	1	1	yes	characteristic
81	C₂×C₄₇	C₂×#124	1	1	yes	characteristic
82	C₂×C₄₇	C₂×#125	1	2	yes	—
83	C₂×C₄₇	C₂×#126	1	2	yes	—
84	C₂²×C₄⋊C₄	—	47	1	no	—
85	C₂²×C₄⋊C₄	—	47	1	no	—
86	#400	—	47	8	no	—
87	C₂×#95	—	47	2	no	—
88	C₂×#95	—	47	2	no	—
89	C₂×#95	D₄₇	1	1	yes	characteristic
90	C₄₇	C₂×#400	1	1	yes	characteristic, complemented, Sylow
91	C₂³×C₄	—	47	1	no	—
92	C₂³×C₄	—	47	2	no	—
93	C₂³×C₄	—	47	1	no	—
94	C₂³×C₄	C₂×D₄₇	1	2	yes	—
95	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
96	C₂×C₄⋊C₄	—	47	4	no	—
97	C₂×C₄⋊C₄	—	47	4	no	—
98	C₂×C₄⋊C₄	—	94	4	no	—
99	C₂×C₄⋊C₄	—	94	4	no	—
100	#95	—	47	8	no	—
101	#95	—	47	8	no	—
102	#95	C₂×D₄₇	1	4	yes	—
103	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
104	C₂²×C₄	—	2	4	no	—
105	C₂²×C₄	—	2	4	no	—
106	C₂²×C₄	—	2	4	no	—
107	C₂²×C₄	—	2	4	no	—
108	C₂²×C₄	—	47	4	no	—
109	C₂²×C₄	—	47	2	no	—
110	C₂²×C₄	—	47	2	no	—
111	C₂²×C₄	—	47	4	no	—
112	C₂²×C₄	—	94	2	no	—
113	C₂²×C₄	—	94	2	no	—
114	C₂²×C₄	—	94	2	no	—
115	C₂²×C₄	—	94	4	no	—
116	C₂²×C₄	—	94	8	no	—
117	C₂²×C₄	—	94	4	no	—
118	C₂²×C₄	D₁₈₈	1	4	yes	—
119	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
120	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
121	C₄⋊C₄	—	94	8	no	—
122	C₄⋊C₄	—	94	8	no	—
123	C₂³	C₂×D₁₈₈	1	2	yes	—
124	C₂³	#10625350	1	4	yes	—
125	C₂³	#10625352	1	2	yes	—
126	C₂³	#10625352	1	4	yes	—
127	C₂³	Q₈×D₄₇	1	2	yes	—
128	C₂³	C₂³×D₄₇	1	1	yes	characteristic
129	C₂×C₄	—	2	8	no	—
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	2	4	no	—
132	C₂×C₄	—	2	4	no	—
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	4	8	no	—
135	C₂×C₄	—	47	4	no	—
136	C₂×C₄	—	94	8	no	—
137	C₂×C₄	—	94	2	no	—
138	C₂×C₄	—	94	2	no	—
139	C₂×C₄	—	94	2	no	—
140	C₂×C₄	—	94	4	no	—
141	C₂×C₄	—	94	4	no	—
142	C₂×C₄	—	94	8	no	—
143	C₂×C₄	—	188	4	no	—
144	C₂×C₄	—	188	8	no	—
145	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
146	C₂²	#13094004	1	4	yes	—
147	C₂²	#13094008	1	4	yes	—
148	C₂²	#13094012	1	4	yes	—
149	C₂²	#13094014	1	8	yes	—
150	C₂²	#13094017	1	8	yes	—
151	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
152	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
153	C₂²	C₂×#10625352	1	1	yes	characteristic
154	C₂²	C₂×#10625352	1	2	yes	—
155	C₂²	C₂×#10625350	1	2	yes	—
156	C₄	—	2	4	no	—
157	C₄	—	4	4	no	—
158	C₄	—	94	4	no	—
159	C₄	—	188	2	no	—
160	C₄	—	188	4	no	—
161	C₂	#15689063	1	8	yes	direct product factor
162	C₂	C₂×#13094004	1	1	yes	characteristic
163	C₂	C₂×#13094008	1	1	yes	characteristic
164	C₂	C₂×#13094012	1	1	yes	characteristic
165	C₂	C₂×#13094014	1	2	yes	—
166	C₂	C₂×#13094017	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₄₇⋊C₄

C₂

yes

maximal, characteristic

#15689063

C₂

yes

maximal, direct product factor

C₂×C₄₇⋊#95

C₂

yes

maximal

C₂×C₄₇⋊#95

C₂

yes

maximal

C₂×#95×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

Q₈

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×Q₈

yes

—

C₂²×C₄₇

C₂²⋊Q₈

yes

—

C₂²×C₄₇

#123

yes

—

C₂²×C₄₇

#124

yes

—

C₂²×C₄₇

#125

yes

—

C₂²×C₄₇

#126

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×C₂²⋊Q₈

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

C₂×#126

yes

—

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

—

#400

—

C₂×#95

—

C₂×#95

—

C₂×#95

D₄₇

yes

characteristic

C₄₇

C₂×#400

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

100

#95

—

101

#95

—

102

#95

C₂×D₄₇

yes

—

103

C₂⁴

C₂²×D₄₇

yes

characteristic

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

D₁₈₈

yes

—

119

C₂²×C₄

C₂²×D₄₇

yes

—

120

C₂²×C₄

C₂²×D₄₇

yes

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₂³

C₂×D₁₈₈

yes

—

124

C₂³

#10625350

yes

—

125

C₂³

#10625352

yes

—

126

C₂³

#10625352

yes

—

127

C₂³

Q₈×D₄₇

yes

—

128

C₂³

C₂³×D₄₇

yes

characteristic

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

188

—

144

C₂×C₄

—

188

—

145

C₂×C₄

C₂×D₁₈₈

yes

—

146

C₂²

#13094004

yes

—

147

C₂²

#13094008

yes

—

148

C₂²

#13094012

yes

—

149

C₂²

#13094014

yes

—

150

C₂²

#13094017

yes

—

151

C₂²

C₂²×D₁₈₈

yes

characteristic

152

C₂²

C₂×Q₈×D₄₇

yes

characteristic

153

C₂²

C₂×#10625352

yes

characteristic

154

C₂²

C₂×#10625352

yes

—

155

C₂²

C₂×#10625350

yes

—

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

188

—

160

C₄

—

188

—

161

C₂

#15689063

yes

direct product factor

162

C₂

C₂×#13094004

yes

characteristic

163

C₂

C₂×#13094008

yes

characteristic

164

C₂

C₂×#13094012

yes

characteristic

165

C₂

C₂×#13094014

yes

—

166

C₂

C₂×#13094017

yes

—

	subgroup	G/H
center	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂⁴
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂×#95×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	C₂×#400
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

subgroup

G/H

center

C₂⁴

C₂²×D₄₇

commutator

C₂³×C₄₇

C₂⁴

Frattini

C₂³

C₂³×D₄₇

Fitting

C₂×#95×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂×#95

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂×#95

N	H ≅ G/N	type
3. #15689063	C₂	direct (N × H)
78. C₂×C₄₇	#400	semidirect
90. C₄₇	C₂×#400	semidirect
161. C₂	#15689063	direct (N × H)

H ≅ G/N

type

3. #15689063

C₂

direct (N × H)

78. C₂×C₄₇

#400

semidirect

90. C₄₇

C₂×#400

semidirect

161. C₂

#15689063

direct (N × H)

Subgroups — C₂×#15689063 #20246641

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689063 #20246641

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689063 #20246641