Group #19139081 — subgroups

Subgroups — #19139081

Order 5504.

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×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	#14582838	C₂	1	4	yes	maximal, complemented
3	#14582806	C₂	1	2	yes	maximal, complemented
4	#14582764	C₂	1	2	yes	maximal, complemented
5	#14582760	C₂	1	4	yes	maximal
6	C₄×C₂²⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
7	C₂×C₂²⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₄₃	C₂²	1	2	yes	—
9	C₂×C₄⋊Dic₄₃	—	2	4	no	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
13	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
14	C₄₃⋊#95	C₂²	1	8	yes	—
15	C₄₃⋊#95	C₂²	1	2	yes	—
16	C₄₃⋊#95	C₂²	1	8	yes	—
17	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²⋊Q₈×C₄₃	—	2	4	no	—
20	C₂×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
23	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
24	C₂×Q₈×C₄₃	—	2	2	no	—
25	C₂×Q₈×C₄₃	—	2	4	no	—
26	C₂²×C₄×C₄₃	—	2	4	no	—
27	C₂²×C₄×C₄₃	D₄	1	4	yes	—
28	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
29	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
30	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂²×Dic₄₃	—	2	4	no	—
33	C₂²×Dic₄₃	—	2	8	no	—
34	C₂²×Dic₄₃	C₂³	1	4	yes	—
35	C₂²×Dic₄₃	C₂³	1	4	yes	—
36	C₄⋊C₄×C₄₃	—	2	2	no	—
37	C₄⋊C₄×C₄₃	—	2	4	no	—
38	C₂²⋊C₄×C₄₃	—	2	4	no	—
39	C₂²⋊Dic₄₃	—	2	4	no	—
40	C₄⋊Dic₄₃	—	2	4	no	—
41	C₄⋊Dic₄₃	—	2	4	no	—
42	C₄×Dic₄₃	—	2	4	no	—
43	C₂³×C₄₃	—	2	2	no	—
44	C₂³×C₄₃	—	2	2	no	—
45	C₂³×C₄₃	C₂×D₄	1	2	yes	—
46	C₂³×C₄₃	#41	1	4	yes	—
47	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
48	Q₈×C₄₃	—	4	4	no	—
49	C₂×C₄×C₄₃	—	2	2	no	—
50	C₂×C₄×C₄₃	—	2	8	no	—
51	C₂×C₄×C₄₃	—	2	2	no	—
52	C₂×C₄×C₄₃	—	2	2	no	—
53	C₂×C₄×C₄₃	—	2	4	no	—
54	C₂×C₄×C₄₃	—	2	4	no	—
55	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₄₃	#41	1	4	yes	—
58	C₂×Dic₄₃	—	2	4	no	—
59	C₂×Dic₄₃	—	2	4	no	—
60	C₂×Dic₄₃	—	2	4	no	—
61	C₂×Dic₄₃	—	2	8	no	—
62	C₂×Dic₄₃	—	2	4	no	—
63	C₂×Dic₄₃	—	4	8	no	—
64	C₂²×C₄₃	—	2	2	no	—
65	C₂²×C₄₃	—	2	2	no	—
66	C₂²×C₄₃	—	2	8	no	—
67	C₂²×C₄₃	#124	1	4	yes	—
68	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
69	C₂²×C₄₃	C₂×#41	1	2	yes	—
70	C₂²×C₄₃	C₂×#41	1	2	yes	—
71	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
72	C₄×C₄₃	—	2	2	no	—
73	C₄×C₄₃	—	4	2	no	—
74	C₄×C₄₃	—	4	2	no	—
75	C₄×C₄₃	#123	1	4	yes	—
76	Dic₄₃	—	4	4	no	—
77	Dic₄₃	—	4	4	no	—
78	#2503	—	43	1	no	maximal, Sylow
79	C₂×C₄₃	—	2	4	no	—
80	C₂×C₄₃	C₂×#123	1	1	yes	characteristic
81	C₂×C₄₃	C₂×#124	1	1	yes	characteristic
82	C₂×C₄₃	#536	1	1	yes	characteristic
83	C₂×C₄₃	#552	1	4	yes	—
84	C₂×C₂²⋊Q₈	D₄₃	1	1	yes	characteristic
85	C₂²×C₄⋊C₄	—	43	1	no	—
86	#400	—	43	4	no	—
87	#391	—	43	2	no	—
88	#382	—	43	2	no	—
89	#381	—	43	4	no	—
90	C₄×C₂²⋊C₄	—	43	1	no	—
91	C₄₃	#2503	1	1	yes	characteristic, complemented, Sylow
92	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
93	C₂³×C₄	—	43	2	no	—
94	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
95	C₂²⋊Q₈	—	2	4	no	—
96	C₂×C₄⋊C₄	—	43	2	no	—
97	C₂×C₄⋊C₄	—	43	2	no	—
98	C₂×C₄⋊C₄	—	86	4	no	—
99	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
100	C₂×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
101	C₂×C₂²⋊C₄	—	43	2	no	—
102	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
103	C₂×C₄²	—	43	2	no	—
104	#95	—	43	2	no	—
105	#95	—	43	8	no	—
106	#95	—	43	8	no	—
107	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
108	C₂×Q₈	—	2	4	no	—
109	C₂×Q₈	—	2	2	no	—
110	C₂²×C₄	—	2	4	no	—
111	C₂²×C₄	—	43	4	no	—
112	C₂²×C₄	—	43	4	no	—
113	C₂²×C₄	—	86	8	no	—
114	C₂²×C₄	—	86	4	no	—
115	C₂²×C₄	C₂²⋊D₄₃	1	4	yes	—
116	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
117	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
118	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
119	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
120	C₄⋊C₄	—	2	2	no	—
121	C₄⋊C₄	—	2	4	no	—
122	C₄⋊C₄	—	86	4	no	—
123	C₄⋊C₄	—	86	4	no	—
124	C₂²⋊C₄	—	2	4	no	—
125	C₂²⋊C₄	—	86	4	no	—
126	C₄²	—	86	4	no	—
127	C₂³	—	2	2	no	—
128	C₂³	—	2	2	no	—
129	C₂³	#10621902	1	4	yes	—
130	C₂³	C₂×C₂²⋊D₄₃	1	2	yes	—
131	C₂³	C₂³×D₄₃	1	1	yes	characteristic
132	Q₈	—	4	4	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	8	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	86	4	no	—
140	C₂×C₄	—	86	4	no	—
141	C₂×C₄	—	86	4	no	—
142	C₂×C₄	—	86	8	no	—
143	C₂×C₄	—	86	4	no	—
144	C₂×C₄	—	172	8	no	—
145	C₂×C₄	#10621900	1	4	yes	—
146	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
147	C₂×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
148	C₂²	—	2	8	no	—
149	C₂²	—	2	2	no	—
150	C₂²	—	2	2	no	—
151	C₂²	#13063314	1	4	yes	—
152	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
153	C₂²	C₂×#10621900	1	2	yes	—
154	C₂²	C₂×#10621902	1	2	yes	—
155	C₂²	#13063372	1	2	yes	—
156	C₄	—	2	2	no	—
157	C₄	—	4	2	no	—
158	C₄	—	4	2	no	—
159	C₄	—	172	4	no	—
160	C₄	—	172	4	no	—
161	C₄	#13063306	1	4	yes	—
162	C₂	—	2	4	no	—
163	C₂	C₂×#13063306	1	1	yes	characteristic
164	C₂	C₂×#13063314	1	1	yes	characteristic
165	C₂	#14583470	1	1	yes	characteristic
166	C₂	#14583591	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic

#14582838

C₂

yes

maximal, complemented

#14582806

C₂

yes

maximal, complemented

#14582764

C₂

yes

maximal, complemented

#14582760

C₂

yes

maximal

C₄×C₂²⋊Dic₄₃

C₂

yes

maximal, characteristic

C₂×C₂²⋊Q₈×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂²⋊Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

#41

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

Q₈×C₄₃

—

C₂×C₄×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×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#124

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

2₋¹⁺⁴

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#123

yes

—

Dic₄₃

—

Dic₄₃

—

#2503

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₂²⋊Q₈

D₄₃

yes

characteristic

C₂²×C₄⋊C₄

—

—

—

—

—

C₄×C₂²⋊C₄

—

C₄₃

#2503

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂³×C₄

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

100

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

101

C₂×C₂²⋊C₄

—

102

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

103

C₂×C₄²

—

104

#95

—

105

#95

—

106

#95

—

107

C₂⁴

C₂²×D₄₃

yes

characteristic

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

C₂²⋊D₄₃

yes

—

116

C₂²×C₄

C₂²×D₄₃

yes

—

117

C₂²×C₄

C₂²×D₄₃

yes

—

118

C₂²×C₄

C₂²×D₄₃

yes

characteristic

119

C₂²×C₄

C₂²×D₄₃

yes

characteristic

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₂²⋊C₄

—

125

C₂²⋊C₄

—

126

C₄²

—

127

C₂³

—

128

C₂³

—

129

C₂³

#10621902

yes

—

130

C₂³

C₂×C₂²⋊D₄₃

yes

—

131

C₂³

C₂³×D₄₃

yes

characteristic

132

Q₈

—

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

—

144

C₂×C₄

—

172

—

145

C₂×C₄

#10621900

yes

—

146

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

147

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

148

C₂²

—

149

C₂²

—

150

C₂²

—

151

C₂²

#13063314

yes

—

152

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

153

C₂²

C₂×#10621900

yes

—

154

C₂²

C₂×#10621902

yes

—

155

C₂²

#13063372

yes

—

156

C₄

—

157

C₄

—

158

C₄

—

159

C₄

—

172

—

160

C₄

—

172

—

161

C₄

#13063306

yes

—

162

C₂

—

163

C₂

C₂×#13063306

yes

characteristic

164

C₂

C₂×#13063314

yes

characteristic

165

C₂

#14583470

yes

characteristic

166

C₂

#14583591

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₂×C₂²⋊Q₈×C₄₃	C₂
hypercenter	C₂×C₂²⋊Q₈	D₄₃
hypocenter	C₄₃	#2503
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₂×C₂²⋊Q₈×C₄₃

C₂

hypercenter

C₂×C₂²⋊Q₈

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

N	H ≅ G/N	type
2. #14582838	C₂	semidirect
3. #14582806	C₂	semidirect
4. #14582764	C₂	semidirect
91. C₄₃	#2503	semidirect

H ≅ G/N

type

2. #14582838

C₂

semidirect

3. #14582806

C₂

semidirect

4. #14582764

C₂

semidirect

91. C₄₃

#2503

semidirect

Subgroups — #19139081

Conjugacy classes of subgroups

Complements