Group #14572713 — subgroups

Subgroups — #14572713

Order 2432.

402 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 161 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	#11927094	C₂	1	1	yes	maximal, characteristic
2	#11926621	C₂	1	2	yes	maximal, complemented
3	#11926617	C₂	1	4	yes	maximal, complemented
4	#11926609	C₂	1	2	yes	maximal, complemented
5	#11926597	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926509	C₂	1	4	yes	maximal, complemented
7	C₁₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#64541	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	#10597376	C₄	1	2	yes	—
11	#10597376	C₄	1	2	yes	—
12	C₂×#64515	C₂²	1	4	yes	—
13	C₂×C₈×D₁₉	C₂²	1	4	yes	—
14	#10597321	C₄	1	2	yes	—
15	#10597320	C₄	1	1	yes	characteristic
16	C₄×D₇₆	C₂²	1	2	yes	—
17	C₄×D₇₆	C₂²	1	2	yes	—
18	#10597315	C₄	1	1	yes	characteristic
19	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
20	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₁₉×#97	C₂²	1	2	yes	—
22	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
23	(C₂×D₁₉)⋊C₈	C₂²	1	4	yes	—
24	(C₂×D₁₉)⋊C₈	C₂²	1	4	yes	—
25	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
26	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
27	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×C₂²⋊D₁₉	C₂×C₄	1	4	yes	—
32	#64541	—	4	4	no	—
33	C₂×D₇₆	C₂×C₄	1	2	yes	—
34	C₂×D₇₆	C₂×C₄	1	2	yes	—
35	C₂×D₇₆	C₂×C₄	1	2	yes	—
36	C₂×C₄×D₁₉	C₂³	1	4	yes	—
37	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
38	C₂×C₈×C₁₉	C₂³	1	4	yes	—
39	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
41	C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	—
44	(C₂×D₁₉)⋊C₄	C₂×C₄	1	4	yes	—
45	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
46	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
47	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
48	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
49	#64515	—	4	4	no	—
50	C₈×D₁₉	—	4	4	no	—
51	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×D₁₉	C₂²×C₄	1	4	yes	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	4	1	no	—
56	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
62	C₂²⋊D₁₉	—	4	4	no	—
63	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
64	D₇₆	—	2	4	no	—
65	D₇₆	—	4	2	no	—
66	D₇₆	—	4	2	no	—
67	C₄×D₁₉	—	2	4	no	—
68	C₄×D₁₉	—	2	4	no	—
69	Dic₃₈	—	4	2	no	—
70	C₈×C₁₉	—	2	4	no	—
71	C₁₉⋊C₈	—	2	2	no	—
72	C₁₉⋊C₈	—	2	2	no	—
73	#2981	—	19	1	no	maximal, Sylow
74	C₂²×C₁₉	—	2	1	no	—
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	—	2	1	no	—
77	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
78	C₂×D₁₉	—	2	4	no	—
79	C₂×D₁₉	—	2	4	no	—
80	C₂×D₁₉	—	2	4	no	—
81	C₄×C₁₉	—	2	1	no	—
82	C₄×C₁₉	—	2	1	no	—
83	C₄×C₁₉	—	2	1	no	—
84	C₄×C₁₉	—	2	1	no	—
85	C₄×C₁₉	#131	1	2	yes	—
86	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
87	Dic₁₉	—	2	4	no	—
88	#532	—	19	1	no	—
89	#436	—	19	2	no	—
90	#435	—	19	4	no	—
91	C₈×D₄	—	19	2	no	—
92	#432	D₁₉	1	1	yes	characteristic, complemented
93	#431	—	19	1	no	—
94	#408	—	19	4	no	—
95	C₂×C₁₉	—	4	1	no	—
96	C₂×C₁₉	#518	1	1	yes	characteristic
97	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
98	C₂×C₁₉	#568	1	1	yes	characteristic
99	D₁₉	—	4	4	no	—
100	C₂×#41	—	19	2	no	—
101	C₂×M₁₆	—	19	4	no	—
102	C₂²×C₈	—	19	4	no	—
103	C₄⋊Q₈	—	19	1	no	—
104	#127	—	19	1	no	—
105	#124	—	19	2	no	—
106	#121	—	19	2	no	—
107	#121	—	19	2	no	—
108	C₄×D₄	—	19	2	no	—
109	C₄×D₄	—	19	2	no	—
110	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
111	C₄⋊C₈	—	19	2	no	—
112	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
113	C₂²⋊C₈	—	19	2	no	—
114	C₂²⋊C₈	—	19	4	no	—
115	C₂²⋊C₈	—	19	4	no	—
116	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
117	#97	C₂×D₁₉	1	2	yes	—
118	C₄×C₈	—	19	1	no	—
119	C₄×C₈	—	19	1	no	—
120	C₁₉	#2981	1	1	yes	characteristic, complemented, Sylow
121	#41	—	76	4	no	—
122	C₂×Q₈	—	19	2	no	—
123	C₂×D₄	—	19	4	no	—
124	C₂×D₄	—	19	2	no	—
125	C₂×D₄	—	19	2	no	—
126	C₂×D₄	—	19	2	no	—
127	C₂²×C₄	—	19	4	no	—
128	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
129	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
130	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
131	M₁₆	—	76	4	no	—
132	C₂×C₈	—	19	2	no	—
133	C₂×C₈	—	19	2	no	—
134	C₂×C₈	—	76	4	no	—
135	C₂×C₈	C₂²×D₁₉	1	4	yes	—
136	C₄⋊C₄	—	19	2	no	—
137	C₄⋊C₄	—	19	2	no	—
138	C₂²⋊C₄	—	19	4	no	—
139	C₂²⋊C₄	—	19	4	no	—
140	C₄²	C₄×D₁₉	1	1	yes	characteristic
141	C₄²	C₄×D₁₉	1	1	yes	characteristic
142	C₄²	C₂²×D₁₉	1	1	yes	characteristic
143	C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₂³	—	19	4	no	—
145	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
146	Q₈	—	76	2	no	—
147	D₄	—	38	4	no	—
148	D₄	—	76	2	no	—
149	D₄	—	76	2	no	—
150	D₄	—	76	4	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	4	1	no	—
154	C₂×C₄	—	19	4	no	—
155	C₂×C₄	—	38	4	no	—
156	C₂×C₄	—	38	4	no	—
157	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
158	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
159	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
160	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
161	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
162	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
163	C₈	—	2	4	no	—
164	C₈	—	38	2	no	—
165	C₈	—	38	2	no	—
166	C₂²	—	2	1	no	—
167	C₂²	—	2	1	no	—
168	C₂²	—	2	1	no	—
169	C₂²	—	38	4	no	—
170	C₂²	—	38	4	no	—
171	C₂²	—	38	4	no	—
172	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	—	2	1	no	—
176	C₄	—	2	1	no	—
177	C₄	—	38	4	no	—
178	C₄	#10597353	1	2	yes	—
179	C₄	#10597435	1	2	yes	—
180	C₂	—	4	1	no	—
181	C₂	—	76	4	no	—
182	C₂	#11927018	1	1	yes	characteristic
183	C₂	C₂×#10597353	1	1	yes	characteristic
184	C₂	#11927310	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927094

C₂

yes

maximal, characteristic

#11926621

C₂

yes

maximal, complemented

#11926617

C₂

yes

maximal, complemented

#11926609

C₂

yes

maximal, complemented

#11926597

C₂

yes

maximal, characteristic, complemented

#11926509

C₂

yes

maximal, complemented

C₁₉×#432

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597376

C₄

yes

—

#10597376

C₄

yes

—

C₂×#64515

C₂²

yes

—

C₂×C₈×D₁₉

C₂²

yes

—

#10597321

C₄

yes

—

#10597320

C₄

yes

characteristic

C₄×D₇₆

C₂²

yes

—

C₄×D₇₆

C₂²

yes

—

#10597315

C₄

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉×#97

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

(C₂×D₁₉)⋊C₈

C₂²

yes

—

(C₂×D₁₉)⋊C₈

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

C₂×C₄

yes

—

#64541

—

C₂×D₇₆

C₂×C₄

yes

—

C₂×D₇₆

C₂×C₄

yes

—

C₂×D₇₆

C₂×C₄

yes

—

C₂×C₄×D₁₉

C₂³

yes

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

C₂×C₄

yes

—

(C₂×D₁₉)⋊C₄

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

#64515

—

C₈×D₁₉

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂²×D₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

C₂²×C₄

yes

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2981

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#131

yes

—

C₄×C₁₉

H(5,𝔽₂)

yes

—

Dic₁₉

—

#532

—

#436

—

#435

—

C₈×D₄

—

#432

D₁₉

yes

characteristic, complemented

#431

—

#408

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

100

C₂×#41

—

101

C₂×M₁₆

—

102

C₂²×C₈

—

103

C₄⋊Q₈

—

104

#127

—

105

#124

—

106

#121

—

107

#121

—

108

C₄×D₄

—

109

C₄×D₄

—

110

C₂×C₄²

C₂×D₁₉

yes

characteristic

111

C₄⋊C₈

—

112

C₄⋊C₈

C₂×D₁₉

yes

—

113

C₂²⋊C₈

—

114

C₂²⋊C₈

—

115

C₂²⋊C₈

—

116

C₂²⋊C₈

C₂×D₁₉

yes

—

117

#97

C₂×D₁₉

yes

—

118

C₄×C₈

—

119

C₄×C₈

—

120

C₁₉

#2981

yes

characteristic, complemented, Sylow

121

#41

—

122

C₂×Q₈

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

—

127

C₂²×C₄

—

128

C₂²×C₄

C₄×D₁₉

yes

characteristic

129

C₂²×C₄

C₄×D₁₉

yes

characteristic

130

C₂²×C₄

C₂²×D₁₉

yes

characteristic

131

M₁₆

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

C₂²×D₁₉

yes

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₂²⋊C₄

—

139

C₂²⋊C₄

—

140

C₄²

C₄×D₁₉

yes

characteristic

141

C₄²

C₄×D₁₉

yes

characteristic

142

C₄²

C₂²×D₁₉

yes

characteristic

143

C₄²

C₂²×D₁₉

yes

characteristic

144

C₂³

—

145

C₂³

C₂×C₄×D₁₉

yes

characteristic

146

Q₈

—

147

D₄

—

148

D₄

—

149

D₄

—

150

D₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

158

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

159

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

160

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

161

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

162

C₂×C₄

C₂³×D₁₉

yes

characteristic

163

C₈

—

164

C₈

—

165

C₈

—

166

C₂²

—

167

C₂²

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

C₂²×C₄×D₁₉

yes

characteristic

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

—

178

C₄

#10597353

yes

—

179

C₄

#10597435

yes

—

180

C₂

—

181

C₂

—

182

C₂

#11927018

yes

characteristic

183

C₂

C₂×#10597353

yes

characteristic

184

C₂

#11927310

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#432	C₂
prime radical	#11927094	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#432	D₁₉
hypocenter	C₁₉	#2981
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #432

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₉

commutator, socle

C₂²×C₁₉

C₂³×C₄

Fitting

C₁₉×#432

C₂

prime radical

#11927094

C₂

cosocle

C₂×C₄×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #432

N	H ≅ G/N	type
2. #11926621	C₂	semidirect
3. #11926617	C₂	semidirect
4. #11926609	C₂	semidirect
5. #11926597	C₂	semidirect
6. #11926509	C₂	semidirect
7. C₁₉×#432	C₂	semidirect
92. #432	D₁₉	semidirect
120. C₁₉	#2981	semidirect

H ≅ G/N

type

2. #11926621

C₂

semidirect

3. #11926617

C₂

semidirect

4. #11926609

C₂

semidirect

5. #11926597

C₂

semidirect

6. #11926509

C₂

semidirect

7. C₁₉×#432

C₂

semidirect

92. #432

D₁₉

semidirect

120. C₁₉

#2981

semidirect

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

subgroup	index
#11927094	2
#11926621	2
#11926617	2
#11926609	2
#11926597	2
#11926509	2
C₁₉×#432	2
#2981	19

subgroup

index

C₁₉×#432

Subgroups — #14572713

Conjugacy classes of subgroups

Complements

Maximal subgroups