Group #19139766 — subgroups

Subgroups — #19139766

Order 5504.

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

normal subgroups only

This group has 564 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	C₂×#13063324	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#14582811	C₂	1	4	yes	maximal, complemented
4	#14582802	C₂	1	1	yes	maximal, characteristic
5	#14582765	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582764	C₂	1	1	yes	maximal, characteristic, complemented
7	#14582757	C₂	1	4	yes	maximal, complemented
8	C₄×Dic₄₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#390	C₂	1	1	yes	maximal, characteristic
10	C₂²×Dic₈₆	C₂²	1	2	yes	—
11	C₂³×Dic₄₃	C₂²	1	2	yes	—
12	#13063324	—	2	4	no	—
13	D₄×Dic₄₃	—	2	4	no	—
14	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
17	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
18	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊Dic₄₃	C₂²	1	4	yes	—
20	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
22	C₄₃⋊#95	C₂²	1	2	yes	—
23	C₄₃⋊#95	C₂²	1	4	yes	—
24	C₄₃⋊#95	C₂²	1	4	yes	—
25	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
28	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
29	C₂⁴×C₄₃	C₂³	1	2	yes	—
30	C₂×D₄×C₄₃	—	2	2	no	—
31	C₂×D₄×C₄₃	—	2	2	no	—
32	C₂×D₄×C₄₃	Q₈	1	4	yes	complemented
33	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
34	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
35	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂²×Dic₄₃	—	2	4	no	—
37	C₂²×Dic₄₃	—	2	8	no	—
38	C₂²×Dic₄₃	C₂³	1	2	yes	—
39	C₂²×Dic₄₃	C₂³	1	2	yes	—
40	C₂²×Dic₄₃	C₂³	1	2	yes	—
41	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
42	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
43	C₂×Dic₈₆	—	2	4	no	—
44	C₂×Dic₈₆	—	4	4	no	—
45	C₄⋊C₄×C₄₃	—	2	2	no	—
46	C₂²⋊C₄×C₄₃	—	4	4	no	—
47	C₄²×C₄₃	—	2	2	no	—
48	C₂²⋊Dic₄₃	—	2	4	no	—
49	C₂²⋊Dic₄₃	—	4	4	no	—
50	C₄⋊Dic₄₃	—	2	2	no	—
51	C₄⋊Dic₄₃	—	2	2	no	—
52	Dic₄₃⋊C₄	—	2	4	no	—
53	Dic₄₃⋊C₄	—	2	4	no	—
54	C₄×Dic₄₃	—	2	2	no	—
55	C₄×Dic₄₃	D₄	1	4	yes	—
56	C₂³×C₄₃	—	2	2	no	—
57	C₂³×C₄₃	—	2	4	no	—
58	C₂³×C₄₃	—	2	2	no	—
59	C₂³×C₄₃	—	2	4	no	—
60	C₂³×C₄₃	C₂×Q₈	1	4	yes	—
61	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
62	D₄×C₄₃	—	2	8	no	—
63	C₂×C₄×C₄₃	—	2	2	no	—
64	C₂×C₄×C₄₃	—	2	2	no	—
65	C₂×C₄×C₄₃	—	2	2	no	—
66	C₂×C₄×C₄₃	—	2	2	no	—
67	C₂×C₄×C₄₃	—	2	4	no	—
68	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
70	C₂×C₄×C₄₃	#41	1	2	yes	—
71	C₂×Dic₄₃	—	2	2	no	—
72	C₂×Dic₄₃	—	2	2	no	—
73	C₂×Dic₄₃	—	2	2	no	—
74	C₂×Dic₄₃	—	2	2	no	—
75	C₂×Dic₄₃	—	2	2	no	—
76	C₂×Dic₄₃	—	2	4	no	—
77	C₂×Dic₄₃	—	2	2	no	—
78	C₂×Dic₄₃	—	2	4	no	—
79	C₂×Dic₄₃	—	4	8	no	—
80	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
81	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
82	C₂×Dic₄₃	#41	1	4	yes	—
83	Dic₈₆	—	4	8	no	—
84	C₂²×C₄₃	—	2	4	no	—
85	C₂²×C₄₃	—	2	8	no	—
86	C₂²×C₄₃	—	4	2	no	—
87	C₂²×C₄₃	—	4	2	no	—
88	C₂²×C₄₃	—	4	4	no	—
89	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
90	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
91	C₂²×C₄₃	C₂×#41	1	2	yes	—
92	C₂²×C₄₃	C₂×#41	1	1	yes	characteristic
93	C₂²×C₄₃	H(5,𝔽₂)	1	2	yes	—
94	C₄×C₄₃	—	4	2	no	—
95	C₄×C₄₃	—	4	2	no	—
96	C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
97	Dic₄₃	—	2	2	no	—
98	Dic₄₃	—	4	2	no	—
99	Dic₄₃	—	4	2	no	—
100	Dic₄₃	—	4	2	no	—
101	Dic₄₃	#124	1	4	yes	—
102	#2563	—	43	1	no	maximal, Sylow
103	C₂×C₄₃	—	4	4	no	—
104	C₂×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
105	C₂×C₄₃	C₂×#124	1	1	yes	characteristic
106	C₂×C₄₃	#535	1	1	yes	characteristic
107	C₂×C₄₃	#554	1	2	yes	—
108	C₂×C₄₃	#555	1	2	yes	—
109	C₂×C₄⋊Q₈	—	43	1	no	—
110	C₂×C₄×D₄	—	43	1	no	—
111	#393	—	43	4	no	—
112	#390	—	43	1	no	—
113	#390	D₄₃	1	1	yes	characteristic
114	#382	—	43	1	no	—
115	#382	—	43	1	no	—
116	#380	—	43	4	no	—
117	C₄×C₄⋊C₄	—	43	1	no	—
118	C₄₃	#2563	1	1	yes	characteristic, complemented, Sylow
119	C₂²×Q₈	—	43	2	no	—
120	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
121	C₂³×C₄	—	43	2	no	—
122	C₄⋊Q₈	—	86	4	no	—
123	C₄×D₄	—	86	4	no	—
124	C₂×C₄⋊C₄	—	43	1	no	—
125	C₂×C₄⋊C₄	—	43	2	no	—
126	C₂×C₄⋊C₄	—	43	1	no	—
127	C₂×C₄⋊C₄	—	43	2	no	—
128	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
129	C₂×C₂²⋊C₄	—	43	2	no	—
130	C₂×C₂²⋊C₄	—	43	4	no	—
131	C₂×C₂²⋊C₄	C₂×D₄₃	1	4	yes	—
132	C₂×C₄²	—	43	1	no	—
133	C₂×C₄²	—	43	1	no	—
134	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
135	#95	—	43	2	no	—
136	#95	—	43	4	no	—
137	#95	—	43	4	no	—
138	C₂⁴	C₂²×D₄₃	1	2	yes	—
139	C₂×Q₈	—	86	4	no	—
140	C₂×Q₈	—	172	4	no	—
141	C₂×D₄	—	2	2	no	—
142	C₂×D₄	—	2	2	no	—
143	C₂×D₄	Dic₈₆	1	4	yes	complemented
144	C₂²×C₄	—	43	1	no	—
145	C₂²×C₄	—	43	1	no	—
146	C₂²×C₄	—	43	2	no	—
147	C₂²×C₄	—	43	2	no	—
148	C₂²×C₄	—	43	2	no	—
149	C₂²×C₄	—	86	4	no	—
150	C₂²×C₄	—	86	8	no	—
151	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
152	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
153	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
154	C₄⋊C₄	—	2	2	no	—
155	C₄⋊C₄	—	86	4	no	—
156	C₄⋊C₄	—	86	4	no	—
157	C₄⋊C₄	—	86	2	no	—
158	C₄⋊C₄	—	86	2	no	—
159	C₂²⋊C₄	—	4	4	no	—
160	C₂²⋊C₄	—	86	4	no	—
161	C₂²⋊C₄	—	172	4	no	—
162	C₄²	—	2	2	no	—
163	C₄²	—	43	4	no	—
164	C₄²	—	86	2	no	—
165	C₂³	—	2	2	no	—
166	C₂³	—	2	4	no	—
167	C₂³	—	2	2	no	—
168	C₂³	—	2	4	no	—
169	C₂³	C₂×Dic₈₆	1	4	yes	—
170	C₂³	C₂³×D₄₃	1	1	yes	characteristic
171	Q₈	—	172	8	no	—
172	D₄	—	2	8	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	43	2	no	—
179	C₂×C₄	—	43	4	no	—
180	C₂×C₄	—	43	2	no	—
181	C₂×C₄	—	86	2	no	—
182	C₂×C₄	—	86	2	no	—
183	C₂×C₄	—	86	2	no	—
184	C₂×C₄	—	86	2	no	—
185	C₂×C₄	—	86	4	no	—
186	C₂×C₄	—	86	2	no	—
187	C₂×C₄	—	86	2	no	—
188	C₂×C₄	—	86	4	no	—
189	C₂×C₄	—	172	8	no	—
190	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
191	C₂×C₄	D₄×D₄₃	1	2	yes	—
192	C₂×C₄	#10621900	1	2	yes	—
193	C₂²	—	2	8	no	—
194	C₂²	—	2	4	no	—
195	C₂²	—	4	4	no	—
196	C₂²	—	4	2	no	—
197	C₂²	—	4	2	no	—
198	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
199	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
200	C₂²	#41×D₄₃	1	2	yes	—
201	C₂²	C₂×#10621900	1	1	yes	characteristic
202	C₂²	#13063370	1	2	yes	—
203	C₄	—	4	2	no	—
204	C₄	—	4	2	no	—
205	C₄	—	43	4	no	—
206	C₄	—	86	2	no	—
207	C₄	—	172	2	no	—
208	C₄	—	172	2	no	—
209	C₄	—	172	2	no	—
210	C₄	#13063302	1	4	yes	—
211	C₂	—	4	4	no	—
212	C₂	C₂×#13063302	1	1	yes	characteristic
213	C₂	#124×D₄₃	1	1	yes	characteristic
214	C₂	#14583462	1	1	yes	characteristic
215	C₂	#14583608	1	2	yes	—
216	C₂	#14583613	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063324

C₂

yes

maximal, characteristic, complemented

C₂×D₄×Dic₄₃

C₂

yes

maximal, characteristic

#14582811

C₂

yes

maximal, complemented

#14582802

C₂

yes

maximal, characteristic

#14582765

C₂

yes

maximal, characteristic, complemented

#14582764

C₂

yes

maximal, characteristic, complemented

#14582757

C₂

yes

maximal, complemented

C₄×Dic₄₃⋊C₄

C₂

yes

maximal, characteristic, complemented

C₄₃×#390

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

C₂³×Dic₄₃

C₂²

yes

—

#13063324

—

D₄×Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂²×D₄×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂⁴×C₄₃

C₂³

yes

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

Q₈

yes

complemented

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

#41

yes

—

Dic₈₆

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

100

Dic₄₃

—

101

Dic₄₃

#124

yes

—

102

#2563

—

maximal, Sylow

103

C₂×C₄₃

—

104

C₂×C₄₃

C₂×C₂²⋊Q₈

yes

characteristic

105

C₂×C₄₃

C₂×#124

yes

characteristic

106

C₂×C₄₃

#535

yes

characteristic

107

C₂×C₄₃

#554

yes

—

108

C₂×C₄₃

#555

yes

—

109

C₂×C₄⋊Q₈

—

110

C₂×C₄×D₄

—

111

#393

—

112

#390

—

113

#390

D₄₃

yes

characteristic

114

#382

—

115

#382

—

116

#380

—

117

C₄×C₄⋊C₄

—

118

C₄₃

#2563

yes

characteristic, complemented, Sylow

119

C₂²×Q₈

—

120

C₂²×D₄

C₂×D₄₃

yes

characteristic

121

C₂³×C₄

—

122

C₄⋊Q₈

—

123

C₄×D₄

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

129

C₂×C₂²⋊C₄

—

130

C₂×C₂²⋊C₄

—

131

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

132

C₂×C₄²

—

133

C₂×C₄²

—

134

C₂×C₄²

C₂×D₄₃

yes

characteristic

135

#95

—

136

#95

—

137

#95

—

138

C₂⁴

C₂²×D₄₃

yes

—

139

C₂×Q₈

—

140

C₂×Q₈

—

172

—

141

C₂×D₄

—

142

C₂×D₄

—

143

C₂×D₄

Dic₈₆

yes

complemented

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

C₂²×D₄₃

yes

—

152

C₂²×C₄

C₂²×D₄₃

yes

—

153

C₂²×C₄

C₂²×D₄₃

yes

characteristic

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₂²⋊C₄

—

160

C₂²⋊C₄

—

161

C₂²⋊C₄

—

172

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₂³

—

166

C₂³

—

167

C₂³

—

168

C₂³

—

169

C₂³

C₂×Dic₈₆

yes

—

170

C₂³

C₂³×D₄₃

yes

characteristic

171

Q₈

—

172

—

172

D₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

172

—

190

C₂×C₄

C₂×Dic₈₆

yes

—

191

C₂×C₄

D₄×D₄₃

yes

—

192

C₂×C₄

#10621900

yes

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

C₂×D₄×D₄₃

yes

characteristic

199

C₂²

C₂²×Dic₈₆

yes

characteristic

200

C₂²

#41×D₄₃

yes

—

201

C₂²

C₂×#10621900

yes

characteristic

202

C₂²

#13063370

yes

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

—

172

—

208

C₄

—

172

—

209

C₄

—

172

—

210

C₄

#13063302

yes

—

211

C₂

—

212

C₂

C₂×#13063302

yes

characteristic

213

C₂

#124×D₄₃

yes

characteristic

214

C₂

#14583462

yes

characteristic

215

C₂

#14583608

yes

—

216

C₂

#14583613

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#390	C₂
hypercenter	#390	D₄₃
hypocenter	C₄₃	#2563
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #390

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#390

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #390

N	H ≅ G/N	type
1. C₂×#13063324	C₂	semidirect
3. #14582811	C₂	semidirect
5. #14582765	C₂	semidirect
6. #14582764	C₂	semidirect
7. #14582757	C₂	semidirect
8. C₄×Dic₄₃⋊C₄	C₂	semidirect
32. C₂×D₄×C₄₃	Q₈	semidirect
118. C₄₃	#2563	semidirect
143. C₂×D₄	Dic₈₆	semidirect

H ≅ G/N

type

1. C₂×#13063324

C₂

semidirect

3. #14582811

C₂

semidirect

5. #14582765

C₂

semidirect

6. #14582764

C₂

semidirect

7. #14582757

C₂

semidirect

8. C₄×Dic₄₃⋊C₄

C₂

semidirect

32. C₂×D₄×C₄₃

Q₈

semidirect

118. C₄₃

#2563

semidirect

143. C₂×D₄

Dic₈₆

semidirect

Subgroups — #19139766

Conjugacy classes of subgroups

Complements