Group #14564681 — subgroups

Subgroups — #14564681

Order 2432.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#10597388	C₂	1	2	yes	maximal, complemented
2	#11927125	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597262	C₂	1	2	yes	maximal, complemented
4	#11926313	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×#64541	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×#64528	—	2	2	no	—
11	#10597388	—	2	4	no	—
12	#10597388	—	2	4	no	—
13	C₂×#64527	—	2	2	no	—
14	#10597376	—	2	2	no	—
15	C₂×#64520	C₂²	1	2	yes	—
16	#10597343	—	2	2	no	—
17	#10597341	—	2	2	no	—
18	C₁₉×#95	—	2	2	no	—
19	#10597262	—	2	4	no	—
20	C₂×Q₈×C₁₉	—	2	1	no	—
21	C₂×Q₈×C₁₉	—	2	2	no	—
22	C₂×Q₈×C₁₉	—	2	2	no	—
23	C₂×Q₈×C₁₉	D₄	1	2	yes	complemented
24	C₂²×C₄×C₁₉	—	2	1	no	—
25	C₂²×C₄×C₁₉	—	2	1	no	—
26	C₂²×C₄×C₁₉	D₄	1	2	yes	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂×C₂²⋊D₁₉	—	2	2	no	—
29	#64541	—	2	2	no	—
30	#64541	—	2	2	no	—
31	#64541	—	2	2	no	—
32	#64541	—	2	2	no	—
33	C₂×D₇₆	—	2	2	no	—
34	C₂×D₇₆	D₄	1	2	yes	—
35	C₂×C₄×D₁₉	—	2	2	no	—
36	C₂×Dic₃₈	D₄	1	2	yes	—
37	C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₄²×C₁₉	—	2	2	no	—
39	#64528	—	2	8	no	—
40	#64527	—	2	8	no	—
41	(C₂×D₁₉)⋊C₄	—	2	4	no	—
42	C₄⋊Dic₁₉	—	2	2	no	—
43	#64520	—	2	2	no	—
44	#64520	D₄	1	4	yes	complemented
45	C₂×C₁₉⋊C₈	—	2	2	no	—
46	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×D₁₉	—	2	2	no	—
48	Q₈×C₁₉	—	2	4	no	—
49	Q₈×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	—	4	1	no	—
57	C₂×C₄×C₁₉	—	4	2	no	—
58	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
62	C₂²⋊D₁₉	—	4	2	no	—
63	C₂²⋊D₁₉	—	4	2	no	—
64	C₂×Dic₁₉	—	2	2	no	—
65	D₇₆	—	2	2	no	—
66	D₇₆	—	2	2	no	—
67	D₇₆	—	8	2	no	—
68	C₄×D₁₉	—	4	2	no	—
69	C₄×D₁₉	—	4	2	no	—
70	Dic₃₈	—	2	2	no	—
71	Dic₃₈	—	2	2	no	—
72	C₁₉⋊C₈	—	2	4	no	—
73	#2007	—	19	1	no	maximal, Sylow
74	C₂²×C₁₉	—	2	1	no	—
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	#120	1	1	yes	characteristic
77	C₂²×C₁₉	#121	1	1	yes	characteristic
78	C₂²×C₁₉	#127	1	1	yes	characteristic
79	C₂×D₁₉	—	4	2	no	—
80	C₂×D₁₉	—	4	2	no	—
81	C₂×D₁₉	—	4	2	no	—
82	C₄×C₁₉	—	4	2	no	—
83	C₄×C₁₉	—	4	2	no	—
84	C₄×C₁₉	—	4	2	no	—
85	C₄×C₁₉	#120	1	2	yes	—
86	C₄×C₁₉	#121	1	2	yes	—
87	Dic₁₉	—	4	2	no	—
88	C₂×#137	—	19	2	no	—
89	#537	—	19	1	no	—
90	C₂×#104	—	19	2	no	—
91	#391	D₁₉	1	1	yes	characteristic, complemented
92	#343	—	19	1	no	—
93	C₂×C₁₉	—	2	1	no	—
94	C₂×C₁₉	—	2	1	no	—
95	C₂×C₁₉	#392	1	1	yes	characteristic
96	C₂×C₁₉	#455	1	1	yes	characteristic
97	C₂×C₁₉	#456	1	1	yes	characteristic
98	D₁₉	—	8	2	no	—
99	C₂×#41	—	19	2	no	—
100	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
101	#137	—	38	4	no	—
102	#137	—	38	4	no	—
103	C₂×Q₁₆	—	38	2	no	—
104	C₂×SD₁₆	—	38	2	no	—
105	C₂×M₁₆	—	19	2	no	—
106	C₂²⋊Q₈	—	38	2	no	—
107	#121	—	38	2	no	—
108	#121	—	38	2	no	—
109	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
110	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
111	#104	—	38	4	no	—
112	#95	—	2	2	no	—
113	C₁₉	#2007	1	1	yes	characteristic, complemented, Sylow
114	#41	—	38	2	no	—
115	#41	—	38	2	no	—
116	#41	—	38	2	no	—
117	#41	—	38	2	no	—
118	C₂×Q₈	—	2	1	no	—
119	C₂×Q₈	—	2	2	no	—
120	C₂×Q₈	—	2	2	no	—
121	C₂×Q₈	—	19	2	no	—
122	C₂×Q₈	D₇₆	1	2	yes	complemented
123	C₂×D₄	—	19	2	no	—
124	C₂×D₄	—	38	2	no	—
125	C₂×D₄	—	38	2	no	—
126	C₂²×C₄	—	2	1	no	—
127	C₂²×C₄	—	2	1	no	—
128	C₂²×C₄	—	38	2	no	—
129	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
130	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
131	Q₁₆	—	38	8	no	—
132	SD₁₆	—	38	8	no	—
133	M₁₆	—	19	4	no	—
134	M₁₆	—	38	2	no	—
135	C₂×C₈	—	38	2	no	—
136	C₄⋊C₄	—	2	2	no	—
137	C₄⋊C₄	—	38	2	no	—
138	C₂²⋊C₄	—	38	4	no	—
139	C₄²	—	2	2	no	—
140	C₂³	—	38	2	no	—
141	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
142	Q₈	—	2	4	no	—
143	Q₈	—	4	2	no	—
144	Q₈	—	38	2	no	—
145	Q₈	—	38	2	no	—
146	D₄	—	38	2	no	—
147	D₄	—	38	2	no	—
148	D₄	—	76	2	no	—
149	D₄	—	76	2	no	—
150	D₄	—	152	2	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	4	1	no	—
155	C₂×C₄	—	4	1	no	—
156	C₂×C₄	—	4	1	no	—
157	C₂×C₄	—	4	1	no	—
158	C₂×C₄	—	4	2	no	—
159	C₂×C₄	—	38	2	no	—
160	C₂×C₄	—	76	2	no	—
161	C₂×C₄	—	76	2	no	—
162	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
163	C₂×C₄	#64541	1	1	yes	characteristic
164	C₂×C₄	D₄×D₁₉	1	2	yes	—
165	C₂×C₄	D₄×D₁₉	1	2	yes	—
166	C₈	—	38	4	no	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	1	no	—
169	C₂²	—	76	2	no	—
170	C₂²	—	76	2	no	—
171	C₂²	—	76	2	no	—
172	C₂²	#10597376	1	1	yes	characteristic
173	C₂²	#10597383	1	1	yes	characteristic
174	C₂²	#10597386	1	1	yes	characteristic
175	C₄	—	4	2	no	—
176	C₄	—	4	2	no	—
177	C₄	—	4	2	no	—
178	C₄	—	76	2	no	—
179	C₄	#10597328	1	2	yes	—
180	C₄	#10597330	1	2	yes	—
181	C₂	—	2	1	no	—
182	C₂	—	2	1	no	—
183	C₂	—	152	2	no	—
184	C₂	#11926453	1	1	yes	characteristic
185	C₂	#11926721	1	1	yes	characteristic
186	C₂	#11926726	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597388

C₂

yes

maximal, complemented

#11927125

C₂

yes

maximal, characteristic

C₂×#10597262

C₂

yes

maximal, complemented

#11926313

C₂

yes

maximal, characteristic, complemented

C₁₉×#391

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂×#64541

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

—

—

—

—

—

C₂²

yes

—

#10597343

—

#10597341

—

C₁₉×#95

—

#10597262

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

—

—

—

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

#64528

—

#64527

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

#64520

D₄

yes

complemented

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

#2007

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic, complemented

#343

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×#41

—

100

C₂²×Q₈

C₂×D₁₉

yes

characteristic

101

#137

—

102

#137

—

103

C₂×Q₁₆

—

104

C₂×SD₁₆

—

105

C₂×M₁₆

—

106

C₂²⋊Q₈

—

107

#121

—

108

#121

—

109

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

110

C₂×C₄²

C₂×D₁₉

yes

characteristic

111

#104

—

112

#95

—

113

C₁₉

#2007

yes

characteristic, complemented, Sylow

114

#41

—

115

#41

—

116

#41

—

117

#41

—

118

C₂×Q₈

—

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×Q₈

D₇₆

yes

complemented

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

C₂²⋊D₁₉

yes

—

130

C₂²×C₄

C₂²×D₁₉

yes

characteristic

131

Q₁₆

—

132

SD₁₆

—

133

M₁₆

—

134

M₁₆

—

135

C₂×C₈

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₂²⋊C₄

—

139

C₄²

—

140

C₂³

—

141

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

142

Q₈

—

143

Q₈

—

144

Q₈

—

145

Q₈

—

146

D₄

—

147

D₄

—

148

D₄

—

149

D₄

—

150

D₄

—

152

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

C₂×D₇₆

yes

characteristic

163

C₂×C₄

#64541

yes

characteristic

164

C₂×C₄

D₄×D₁₉

yes

—

165

C₂×C₄

D₄×D₁₉

yes

—

166

C₈

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

#10597376

yes

characteristic

173

C₂²

#10597383

yes

characteristic

174

C₂²

#10597386

yes

characteristic

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

#10597328

yes

—

180

C₄

#10597330

yes

—

181

C₂

—

182

C₂

—

183

C₂

—

152

—

184

C₂

#11926453

yes

characteristic

185

C₂

#11926721

yes

characteristic

186

C₂

#11926726

yes

characteristic

	subgroup	G/H
center	C₂²	#10597383
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#391	C₂
socle	C₂²×C₁₉	#120
prime radical	#11927125	C₂
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2007
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #391

subgroup

G/H

center

C₂²

#10597383

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#391

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #391

N	H ≅ G/N	type
1. C₂×#10597388	C₂	semidirect
3. C₂×#10597262	C₂	semidirect
4. #11926313	C₂	semidirect
5. C₁₉×#391	C₂	semidirect
23. C₂×Q₈×C₁₉	D₄	semidirect
44. #64520	D₄	semidirect
91. #391	D₁₉	semidirect
113. C₁₉	#2007	semidirect
122. C₂×Q₈	D₇₆	semidirect

H ≅ G/N

type

1. C₂×#10597388

C₂

semidirect

3. C₂×#10597262

C₂

semidirect

4. #11926313

C₂

semidirect

5. C₁₉×#391

C₂

semidirect

23. C₂×Q₈×C₁₉

D₄

semidirect

44. #64520

D₄

semidirect

91. #391

D₁₉

semidirect

113. C₁₉

#2007

semidirect

122. C₂×Q₈

D₇₆

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10597388	2
#11927125	2
C₂×#10597262	2
#11926313	2
C₁₉×#391	2
#2007	19

subgroup

index

C₁₉×#391

Subgroups — #14564681

Conjugacy classes of subgroups

Complements

Maximal subgroups