Group #19143267 — subgroups

Subgroups — C₂×#14582964 #19143267

Order 5504.

616 conjugacy classes of subgroups; only the 253 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 253 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×C₈×D₄₃	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	#14582964	C₂	1	8	yes	maximal, direct product factor
4	C₂×(C₂×D₄₃)⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₁₇₂	C₄	1	1	yes	characteristic
8	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
9	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₈×D₄₃	—	2	8	no	—
12	C₂×C₈×D₄₃	C₂²	1	8	yes	complemented
13	C₄×D₁₇₂	C₄	1	4	yes	—
14	C₄×D₁₇₂	C₂²	1	4	yes	—
15	C₂×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
16	C₂×(C₂×D₄₃)⋊C₄	C₄	1	2	yes	—
17	(C₂×D₄₃)⋊C₈	C₂²	1	8	yes	complemented
18	C₄×C₄₃⋊C₈	C₂²	1	4	yes	complemented
19	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄⋊C₈×C₄₃	C₂²	1	4	yes	complemented
22	C₂³×D₄₃	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₃	C₂×C₄	1	2	yes	—
27	C₂×D₁₇₂	C₈	1	8	yes	complemented
28	C₂×D₁₇₂	C₂×C₄	1	4	yes	—
29	C₂×C₄×D₄₃	—	2	4	no	—
30	C₂×C₄×D₄₃	—	2	4	no	—
31	C₂×C₄×D₄₃	C₂×C₄	1	4	yes	—
32	C₂×C₄×D₄₃	C₂³	1	4	yes	—
33	C₂×C₈×C₄₃	—	2	4	no	—
34	C₂×C₈×C₄₃	C₂³	1	4	yes	—
35	C₄²×C₄₃	C₂×C₄	1	2	yes	—
36	C₄²×C₄₃	C₂³	1	2	yes	—
37	(C₂×D₄₃)⋊C₄	C₂×C₄	1	8	yes	—
38	C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
39	C₂×C₄₃⋊C₈	—	2	2	no	—
40	C₂×C₄₃⋊C₈	D₄	1	4	yes	complemented
41	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
42	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
43	C₈×D₄₃	—	2	16	no	—
44	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×D₄₃	—	2	4	no	—
46	C₂²×D₄₃	—	2	4	no	—
47	C₂²×D₄₃	C₂×C₈	1	8	yes	complemented
48	C₂²×D₄₃	C₂²×C₄	1	4	yes	—
49	C₂×C₄×C₄₃	—	2	2	no	—
50	C₂×C₄×C₄₃	C₂×C₈	1	4	yes	complemented
51	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
52	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
54	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₄₃	#41	1	2	yes	—
56	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
57	C₂×Dic₄₃	—	2	4	no	—
58	C₂×Dic₄₃	C₂²×C₄	1	4	yes	—
59	D₁₇₂	C₂×C₈	1	16	yes	complemented
60	C₄×D₄₃	—	2	8	no	—
61	C₄×D₄₃	—	2	4	no	—
62	C₄×D₄₃	—	2	4	no	—
63	C₈×C₄₃	—	2	4	no	—
64	C₄₃⋊C₈	—	2	2	no	—
65	C₄₃⋊C₈	C₂×D₄	1	4	yes	complemented
66	C₂²×C₄₃	C₄×D₄	1	2	yes	—
67	C₂²×C₄₃	C₂²×C₈	1	2	yes	—
68	C₂²×C₄₃	#131	1	2	yes	—
69	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
70	C₂×D₄₃	—	2	4	no	—
71	C₂×D₄₃	—	2	4	no	—
72	C₂×D₄₃	—	2	16	no	—
73	C₂×D₄₃	C₂²×C₈	1	8	yes	complemented
74	C₄×C₄₃	—	2	2	no	—
75	C₄×C₄₃	C₄×D₄	1	2	yes	—
76	C₄×C₄₃	C₂²×C₈	1	4	yes	complemented
77	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
78	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
79	Dic₄₃	—	2	4	no	—
80	C₂×C₈×D₄	—	43	1	no	maximal, Sylow
81	C₂×C₄₃	C₈×D₄	1	4	yes	complemented
82	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
83	C₂×C₄₃	C₂³×C₈	1	1	yes	characteristic
84	C₂×C₄₃	C₂×#131	1	1	yes	characteristic
85	D₄₃	—	2	8	no	—
86	C₂³×C₈	—	43	2	no	—
87	C₂×C₄×D₄	—	43	1	no	—
88	C₈×D₄	—	43	8	no	—
89	C₂×C₄⋊C₈	D₄₃	1	1	yes	characteristic, complemented
90	C₂×C₂²⋊C₈	—	43	2	no	—
91	C₂×C₄×C₈	—	43	1	no	—
92	C₄₃	C₂×C₈×D₄	1	1	yes	characteristic, complemented, Sylow
93	C₂²×D₄	—	43	1	no	—
94	C₂³×C₄	—	43	2	no	—
95	C₂²×C₈	—	43	1	no	—
96	C₂²×C₈	—	43	1	no	—
97	C₂²×C₈	—	43	8	no	—
98	C₂²×C₈	—	86	8	no	—
99	C₂²×C₈	C₂×D₄₃	1	2	yes	—
100	C₄×D₄	—	43	4	no	—
101	C₄×D₄	—	43	4	no	—
102	C₂×C₄⋊C₄	—	43	1	no	—
103	C₂×C₂²⋊C₄	—	43	2	no	—
104	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
105	C₄⋊C₈	C₂×D₄₃	1	4	yes	complemented
106	C₂²⋊C₈	—	43	8	no	—
107	C₄×C₈	—	43	4	no	—
108	C₂⁴	—	43	2	no	—
109	C₂×D₄	—	43	8	no	—
110	C₂×D₄	—	43	4	no	—
111	C₂²×C₄	—	43	2	no	—
112	C₂²×C₄	—	43	4	no	—
113	C₂²×C₄	—	43	4	no	—
114	C₂²×C₄	—	86	4	no	—
115	C₂²×C₄	—	86	4	no	—
116	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
117	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
118	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
119	C₂×C₈	—	2	4	no	—
120	C₂×C₈	—	43	4	no	—
121	C₂×C₈	—	43	2	no	—
122	C₂×C₈	—	43	2	no	—
123	C₂×C₈	—	86	16	no	—
124	C₂×C₈	—	86	2	no	—
125	C₂×C₈	C₂²×D₄₃	1	4	yes	—
126	C₄⋊C₄	—	43	4	no	—
127	C₂²⋊C₄	—	43	8	no	—
128	C₄²	C₄×D₄₃	1	2	yes	—
129	C₄²	C₂²×D₄₃	1	2	yes	—
130	C₂³	—	43	8	no	—
131	C₂³	—	43	4	no	—
132	C₂³	—	86	4	no	—
133	C₂³	—	86	4	no	—
134	C₂³	C₂×C₄×D₄₃	1	1	yes	characteristic
135	D₄	—	43	16	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	43	4	no	—
138	C₂×C₄	—	86	4	no	—
139	C₂×C₄	—	86	8	no	—
140	C₂×C₄	—	86	4	no	—
141	C₂×C₄	—	86	4	no	—
142	C₂×C₄	C₈×D₄₃	1	4	yes	complemented
143	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
144	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
145	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
146	C₂×C₄	D₄×D₄₃	1	2	yes	—
147	C₂×C₄	#10621902	1	2	yes	—
148	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
149	C₈	—	2	4	no	—
150	C₈	—	43	4	no	—
151	C₈	—	86	2	no	—
152	C₂²	—	43	8	no	—
153	C₂²	—	86	4	no	—
154	C₂²	—	86	4	no	—
155	C₂²	—	86	16	no	—
156	C₂²	#13063287	1	2	yes	—
157	C₂²	C₂×C₈×D₄₃	1	2	yes	—
158	C₂²	#13063333	1	2	yes	—
159	C₂²	C₂²×C₄×D₄₃	1	1	yes	characteristic
160	C₄	—	2	2	no	—
161	C₄	—	86	4	no	—
162	C₄	#13063287	1	2	yes	—
163	C₄	C₂×C₈×D₄₃	1	4	yes	complemented
164	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
165	C₄	C₂×#10621902	1	1	yes	characteristic
166	C₂	—	86	8	no	—
167	C₂	#14582964	1	4	yes	direct product factor
168	C₂	C₂×#13063287	1	1	yes	characteristic
169	C₂	C₂²×C₈×D₄₃	1	1	yes	characteristic
170	C₂	C₂×#13063333	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₈×D₄₃

C₂

yes

maximal, complemented

C₂×C₄×D₁₇₂

C₂

yes

maximal, characteristic

#14582964

C₂

yes

maximal, direct product factor

C₂×(C₂×D₄₃)⋊C₈

C₂

yes

maximal, complemented

C₂×C₄×C₄₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×C₄⋊C₈×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₄

yes

characteristic

C₂²×C₄×D₄₃

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×C₈×D₄₃

—

C₂×C₈×D₄₃

C₂²

yes

complemented

C₄×D₁₇₂

C₄

yes

—

C₄×D₁₇₂

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₄

yes

characteristic

C₂×(C₂×D₄₃)⋊C₄

C₄

yes

—

(C₂×D₄₃)⋊C₈

C₂²

yes

complemented

C₄×C₄₃⋊C₈

C₂²

yes

complemented

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₂²

yes

complemented

C₂³×D₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂×D₁₇₂

C₈

yes

complemented

C₂×D₁₇₂

C₂×C₄

yes

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

—

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₄×D₄₃

C₂³

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂³

yes

—

(C₂×D₄₃)⋊C₄

C₂×C₄

yes

—

C₄⋊Dic₄₃

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

complemented

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₈×D₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₂×C₈

yes

complemented

C₂²×D₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₈

yes

complemented

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

D₁₇₂

C₂×C₈

yes

complemented

C₄×D₄₃

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

C₂×D₄

yes

complemented

C₂²×C₄₃

C₄×D₄

yes

—

C₂²×C₄₃

C₂²×C₈

yes

—

C₂²×C₄₃

#131

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

C₂²×C₈

yes

complemented

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

C₂²×C₈

yes

complemented

C₄×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

C₂×#41

yes

characteristic

Dic₄₃

—

C₂×C₈×D₄

—

maximal, Sylow

C₂×C₄₃

C₈×D₄

yes

complemented

C₂×C₄₃

C₂×C₄×D₄

yes

characteristic

C₂×C₄₃

C₂³×C₈

yes

characteristic

C₂×C₄₃

C₂×#131

yes

characteristic

D₄₃

—

C₂³×C₈

—

C₂×C₄×D₄

—

C₈×D₄

—

C₂×C₄⋊C₈

D₄₃

yes

characteristic, complemented

C₂×C₂²⋊C₈

—

C₂×C₄×C₈

—

C₄₃

C₂×C₈×D₄

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

—

100

C₄×D₄

—

101

C₄×D₄

—

102

C₂×C₄⋊C₄

—

103

C₂×C₂²⋊C₄

—

104

C₂×C₄²

C₂×D₄₃

yes

characteristic

105

C₄⋊C₈

C₂×D₄₃

yes

complemented

106

C₂²⋊C₈

—

107

C₄×C₈

—

108

C₂⁴

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

C₄×D₄₃

yes

characteristic

117

C₂²×C₄

C₄×D₄₃

yes

characteristic

118

C₂²×C₄

C₂²×D₄₃

yes

characteristic

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

C₂²×D₄₃

yes

—

126

C₄⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

C₄×D₄₃

yes

—

129

C₄²

C₂²×D₄₃

yes

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

C₂×C₄×D₄₃

yes

characteristic

135

D₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

C₈×D₄₃

yes

complemented

143

C₂×C₄

C₂×C₄×D₄₃

yes

—

144

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

145

C₂×C₄

C₂×C₄×D₄₃

yes

—

146

C₂×C₄

D₄×D₄₃

yes

—

147

C₂×C₄

#10621902

yes

—

148

C₂×C₄

C₂³×D₄₃

yes

characteristic

149

C₈

—

150

C₈

—

151

C₈

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

#13063287

yes

—

157

C₂²

C₂×C₈×D₄₃

yes

—

158

C₂²

#13063333

yes

—

159

C₂²

C₂²×C₄×D₄₃

yes

characteristic

160

C₄

—

161

C₄

—

162

C₄

#13063287

yes

—

163

C₄

C₂×C₈×D₄₃

yes

complemented

164

C₄

C₂×D₄×D₄₃

yes

characteristic

165

C₄

C₂×#10621902

yes

characteristic

166

C₂

—

167

C₂

#14582964

yes

direct product factor

168

C₂

C₂×#13063287

yes

characteristic

169

C₂

C₂²×C₈×D₄₃

yes

characteristic

170

C₂

C₂×#13063333

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator	C₂×C₄₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×C₄⋊C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	C₂×C₄⋊C₈	D₄₃
hypocenter	C₄₃	C₂×C₈×D₄
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₃

commutator

C₂×C₄₃

C₂³×C₈

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×C₄⋊C₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂²×C₄

hypercenter

C₂×C₄⋊C₈

D₄₃

hypocenter

C₄₃

C₂×C₈×D₄

LCS

G ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
1. C₂²×C₈×D₄₃	C₂	semidirect
3. #14582964	C₂	direct (N × H)
4. C₂×(C₂×D₄₃)⋊C₈	C₂	semidirect
5. C₂×C₄×C₄₃⋊C₈	C₂	semidirect
6. C₂×C₄⋊C₈×C₄₃	C₂	semidirect
12. C₂×C₈×D₄₃	C₂²	semidirect
17. (C₂×D₄₃)⋊C₈	C₂²	semidirect
18. C₄×C₄₃⋊C₈	C₂²	semidirect
21. C₄⋊C₈×C₄₃	C₂²	semidirect
27. C₂×D₁₇₂	C₈	semidirect
40. C₂×C₄₃⋊C₈	D₄	semidirect
47. C₂²×D₄₃	C₂×C₈	semidirect
50. C₂×C₄×C₄₃	C₂×C₈	semidirect
59. D₁₇₂	C₂×C₈	semidirect
65. C₄₃⋊C₈	C₂×D₄	semidirect
73. C₂×D₄₃	C₂²×C₈	semidirect
76. C₄×C₄₃	C₂²×C₈	semidirect
81. C₂×C₄₃	C₈×D₄	semidirect
89. C₂×C₄⋊C₈	D₄₃	semidirect
92. C₄₃	C₂×C₈×D₄	semidirect
105. C₄⋊C₈	C₂×D₄₃	semidirect
142. C₂×C₄	C₈×D₄₃	semidirect
163. C₄	C₂×C₈×D₄₃	semidirect
167. C₂	#14582964	direct (N × H)

H ≅ G/N

type

1. C₂²×C₈×D₄₃

C₂

semidirect

3. #14582964

C₂

direct (N × H)

4. C₂×(C₂×D₄₃)⋊C₈

C₂

semidirect

5. C₂×C₄×C₄₃⋊C₈

C₂

semidirect

6. C₂×C₄⋊C₈×C₄₃

C₂

semidirect

12. C₂×C₈×D₄₃

C₂²

semidirect

17. (C₂×D₄₃)⋊C₈

C₂²

semidirect

18. C₄×C₄₃⋊C₈

C₂²

semidirect

21. C₄⋊C₈×C₄₃

C₂²

semidirect

27. C₂×D₁₇₂

C₈

semidirect

40. C₂×C₄₃⋊C₈

D₄

semidirect

47. C₂²×D₄₃

C₂×C₈

semidirect

50. C₂×C₄×C₄₃

C₂×C₈

semidirect

59. D₁₇₂

C₂×C₈

semidirect

65. C₄₃⋊C₈

C₂×D₄

semidirect

73. C₂×D₄₃

C₂²×C₈

semidirect

76. C₄×C₄₃

C₂²×C₈

semidirect

81. C₂×C₄₃

C₈×D₄

semidirect

89. C₂×C₄⋊C₈

D₄₃

semidirect

92. C₄₃

C₂×C₈×D₄

semidirect

105. C₄⋊C₈

C₂×D₄₃

semidirect

142. C₂×C₄

C₈×D₄₃

semidirect

163. C₄

C₂×C₈×D₄₃

semidirect

167. C₂

#14582964

direct (N × H)

Subgroups — C₂×#14582964 #19143267

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14582964 #19143267

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582964 #19143267