Group #14567279 — subgroups

Subgroups — #14567279

Order 2432.

800 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 213 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	C₂³×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597315	C₂	1	2	yes	maximal, complemented
3	C₂×#10597370	C₂	1	1	yes	maximal, characteristic
4	#11926465	C₂	1	4	yes	maximal, complemented
5	#11926450	C₂	1	2	yes	maximal, complemented
6	#11926419	C₂	1	4	yes	maximal
7	C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×Dic₁₉	C₂²	1	2	yes	—
10	C₂²×Dic₃₈	—	2	4	no	—
11	C₂²×Dic₃₈	—	2	8	no	—
12	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
13	C₂²×Dic₃₈	C₂²	1	2	yes	—
14	C₂²×Dic₃₈	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₉	C₂²	1	8	yes	—
20	#10597370	—	2	4	no	—
21	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
22	#10597315	—	2	8	no	—
23	C₁₉×#95	C₂²	1	2	yes	—
24	C₁₉⋊#95	C₂²	1	8	yes	—
25	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	—	2	4	no	—
27	C₂²×C₄×C₁₉	D₄	1	4	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₁₉	—	2	4	no	—
32	C₂²×Dic₁₉	—	2	8	no	—
33	C₂²×Dic₁₉	C₂³	1	2	yes	—
34	C₂²×Dic₁₉	C₂³	1	2	yes	—
35	C₂²×Dic₁₉	C₂³	1	4	yes	—
36	C₂×Dic₃₈	—	2	32	no	—
37	C₂×Dic₃₈	—	2	4	no	—
38	C₂×Dic₃₈	—	2	4	no	—
39	C₂×Dic₃₈	—	2	4	no	—
40	C₂×Dic₃₈	—	2	8	no	—
41	C₂×Dic₃₈	—	2	4	no	—
42	C₂×Dic₃₈	—	2	2	no	—
43	C₂×Dic₃₈	D₄	1	8	yes	—
44	C₂²⋊C₄×C₁₉	Q₈	1	8	yes	complemented
45	C₄²×C₁₉	—	2	4	no	—
46	C₂²⋊Dic₁₉	—	2	4	no	—
47	C₄⋊Dic₁₉	—	2	2	no	—
48	C₄⋊Dic₁₉	—	2	16	no	—
49	Dic₁₉⋊C₄	—	2	4	no	—
50	C₂³×C₁₉	—	2	2	no	—
51	C₂³×C₁₉	—	2	2	no	—
52	C₂³×C₁₉	C₂×D₄	1	2	yes	—
53	C₂³×C₁₉	C₂×Q₈	1	4	yes	—
54	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
55	C₂×C₄×C₁₉	—	2	4	no	—
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	4	no	—
58	C₂×C₄×C₁₉	—	2	8	no	—
59	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
62	C₂×C₄×C₁₉	C₂×Q₈	1	8	yes	complemented
63	C₂×Dic₁₉	—	2	16	no	—
64	C₂×Dic₁₉	—	2	4	no	—
65	C₂×Dic₁₉	—	2	4	no	—
66	C₂×Dic₁₉	—	2	2	no	—
67	C₂×Dic₁₉	—	2	2	no	—
68	C₂×Dic₁₉	—	2	4	no	—
69	C₂×Dic₁₉	—	2	4	no	—
70	C₂×Dic₁₉	C₂×D₄	1	8	yes	—
71	Dic₃₈	—	2	16	no	—
72	Dic₃₈	—	2	16	no	—
73	Dic₃₈	—	4	4	no	—
74	#2434	—	19	1	no	maximal, Sylow
75	C₂²×C₁₉	—	2	2	no	—
76	C₂²×C₁₉	—	2	2	no	—
77	C₂²×C₁₉	—	2	8	no	—
78	C₂²×C₁₉	C₄⋊Q₈	1	4	yes	complemented
79	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
80	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
81	C₂²×C₁₉	C₂²×Q₈	1	2	yes	—
82	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
83	C₄×C₁₉	—	2	2	no	—
84	C₄×C₁₉	—	2	8	no	—
85	C₄×C₁₉	#120	1	4	yes	—
86	Dic₁₉	—	2	8	no	—
87	Dic₁₉	—	4	2	no	—
88	Dic₁₉	—	4	2	no	—
89	C₂³×Q₈	—	19	1	no	—
90	C₂×C₄⋊Q₈	—	19	2	no	—
91	C₂×C₂²⋊Q₈	—	19	1	no	—
92	#395	—	19	4	no	—
93	#391	—	19	2	no	—
94	#385	—	19	4	no	—
95	C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic
96	C₂×C₁₉	—	2	4	no	—
97	C₂×C₁₉	C₂×#120	1	1	yes	characteristic
98	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
99	C₂×C₁₉	#536	1	1	yes	characteristic
100	C₂×C₁₉	D₄×Q₈	1	4	yes	—
101	C₂²×Q₈	—	19	2	no	—
102	C₂²×Q₈	—	19	1	no	—
103	C₂²×Q₈	—	19	2	no	—
104	C₂²×Q₈	—	38	8	no	—
105	C₂²×Q₈	—	38	4	no	—
106	C₂³×C₄	—	19	2	no	—
107	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
108	C₄⋊Q₈	—	38	8	no	—
109	C₂²⋊Q₈	—	38	4	no	—
110	C₂×C₄⋊C₄	—	19	1	no	—
111	C₂×C₄⋊C₄	—	19	2	no	—
112	C₂×C₄⋊C₄	—	19	8	no	—
113	C₂×C₂²⋊C₄	—	19	2	no	—
114	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
115	C₂×C₄²	C₂×D₁₉	1	2	yes	—
116	#95	—	19	8	no	—
117	#95	C₂×D₁₉	1	2	yes	—
118	C₁₉	#2434	1	1	yes	characteristic, complemented, Sylow
119	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
120	C₂×Q₈	—	19	8	no	—
121	C₂×Q₈	—	38	8	no	—
122	C₂×Q₈	—	38	32	no	—
123	C₂×Q₈	—	38	4	no	—
124	C₂×Q₈	—	38	4	no	—
125	C₂×Q₈	—	38	2	no	—
126	C₂×Q₈	—	38	4	no	—
127	C₂×Q₈	—	38	4	no	—
128	C₂²×C₄	—	2	4	no	—
129	C₂²×C₄	—	19	4	no	—
130	C₂²×C₄	—	19	2	no	—
131	C₂²×C₄	—	19	2	no	—
132	C₂²×C₄	—	38	8	no	—
133	C₂²×C₄	—	38	4	no	—
134	C₂²×C₄	D₇₆	1	4	yes	—
135	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
136	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
137	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
138	C₄⋊C₄	—	38	16	no	—
139	C₄⋊C₄	—	38	4	no	—
140	C₄⋊C₄	—	38	2	no	—
141	C₂²⋊C₄	—	38	4	no	—
142	C₂²⋊C₄	Dic₃₈	1	8	yes	complemented
143	C₄²	—	2	4	no	—
144	C₂³	—	2	2	no	—
145	C₂³	—	2	2	no	—
146	C₂³	C₂×Dic₃₈	1	4	yes	—
147	C₂³	C₂×D₇₆	1	2	yes	—
148	C₂³	C₂³×D₁₉	1	1	yes	characteristic
149	Q₈	—	38	16	no	—
150	Q₈	—	38	16	no	—
151	Q₈	—	76	4	no	—
152	C₂×C₄	—	2	4	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	2	8	no	—
156	C₂×C₄	—	19	8	no	—
157	C₂×C₄	—	38	16	no	—
158	C₂×C₄	—	38	4	no	—
159	C₂×C₄	—	38	4	no	—
160	C₂×C₄	—	38	2	no	—
161	C₂×C₄	—	38	2	no	—
162	C₂×C₄	—	38	4	no	—
163	C₂×C₄	—	38	4	no	—
164	C₂×C₄	C₂×Dic₃₈	1	8	yes	complemented
165	C₂×C₄	C₂×D₇₆	1	2	yes	—
166	C₂×C₄	C₂×D₇₆	1	2	yes	—
167	C₂×C₄	D₄×D₁₉	1	4	yes	—
168	C₂²	—	2	2	no	—
169	C₂²	—	2	8	no	—
170	C₂²	—	2	2	no	—
171	C₂²	#10597315	1	4	yes	complemented
172	C₂²	C₂²×Dic₃₈	1	2	yes	—
173	C₂²	C₂²×D₇₆	1	1	yes	characteristic
174	C₂²	C₂×D₄×D₁₉	1	2	yes	—
175	C₂²	#10597436	1	2	yes	—
176	C₄	—	2	8	no	—
177	C₄	—	2	2	no	—
178	C₄	—	38	8	no	—
179	C₄	—	76	2	no	—
180	C₄	—	76	2	no	—
181	C₄	#10597328	1	4	yes	—
182	C₂	—	2	4	no	—
183	C₂	C₂×#10597328	1	1	yes	characteristic
184	C₂	C₂×#10597315	1	1	yes	characteristic
185	C₂	#11927120	1	1	yes	characteristic
186	C₂	D₄×Dic₃₈	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×Dic₃₈

C₂

yes

maximal, characteristic

C₂×#10597315

C₂

yes

maximal, complemented

C₂×#10597370

C₂

yes

maximal, characteristic

#11926465

C₂

yes

maximal, complemented

#11926450

C₂

yes

maximal, complemented

#11926419

C₂

yes

maximal

C₄×C₂²⋊C₄×C₁₉

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

C₂²

yes

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

—

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

#10597315

—

C₁₉×#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₂²⋊C₄×C₁₉

Q₈

yes

complemented

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

complemented

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

#2434

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄⋊Q₈

yes

complemented

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂³×Q₈

—

C₂×C₄⋊Q₈

—

C₂×C₂²⋊Q₈

—

#395

—

#391

—

#385

—

C₄×C₂²⋊C₄

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

C₂×#120

yes

characteristic

C₂×C₁₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₉

#536

yes

characteristic

100

C₂×C₁₉

D₄×Q₈

yes

—

101

C₂²×Q₈

—

102

C₂²×Q₈

—

103

C₂²×Q₈

—

104

C₂²×Q₈

—

105

C₂²×Q₈

—

106

C₂³×C₄

—

107

C₂³×C₄

C₂×D₁₉

yes

characteristic

108

C₄⋊Q₈

—

109

C₂²⋊Q₈

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

—

113

C₂×C₂²⋊C₄

—

114

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

115

C₂×C₄²

C₂×D₁₉

yes

—

116

#95

—

117

#95

C₂×D₁₉

yes

—

118

C₁₉

#2434

yes

characteristic, complemented, Sylow

119

C₂⁴

C₂²×D₁₉

yes

characteristic

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×Q₈

—

123

C₂×Q₈

—

124

C₂×Q₈

—

125

C₂×Q₈

—

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

D₇₆

yes

—

135

C₂²×C₄

C₂²×D₁₉

yes

—

136

C₂²×C₄

C₂²×D₁₉

yes

characteristic

137

C₂²×C₄

C₂²×D₁₉

yes

characteristic

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₂²⋊C₄

—

142

C₂²⋊C₄

Dic₃₈

yes

complemented

143

C₄²

—

144

C₂³

—

145

C₂³

—

146

C₂³

C₂×Dic₃₈

yes

—

147

C₂³

C₂×D₇₆

yes

—

148

C₂³

C₂³×D₁₉

yes

characteristic

149

Q₈

—

150

Q₈

—

151

Q₈

—

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

—

163

C₂×C₄

—

164

C₂×C₄

C₂×Dic₃₈

yes

complemented

165

C₂×C₄

C₂×D₇₆

yes

—

166

C₂×C₄

C₂×D₇₆

yes

—

167

C₂×C₄

D₄×D₁₉

yes

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

#10597315

yes

complemented

172

C₂²

C₂²×Dic₃₈

yes

—

173

C₂²

C₂²×D₇₆

yes

characteristic

174

C₂²

C₂×D₄×D₁₉

yes

—

175

C₂²

#10597436

yes

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

#10597328

yes

—

182

C₂

—

183

C₂

C₂×#10597328

yes

characteristic

184

C₂

C₂×#10597315

yes

characteristic

185

C₂

#11927120

yes

characteristic

186

C₂

D₄×Dic₃₈

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₄×C₂²⋊C₄×C₁₉	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₄×C₂²⋊C₄	D₁₉
hypocenter	C₁₉	#2434
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₄×C₂²⋊C₄×C₁₉

C₂

prime radical

C₂⁴×C₁₉

C₂³

hypercenter

C₄×C₂²⋊C₄

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

N	H ≅ G/N	type
2. C₂×#10597315	C₂	semidirect
4. #11926465	C₂	semidirect
5. #11926450	C₂	semidirect
44. C₂²⋊C₄×C₁₉	Q₈	semidirect
62. C₂×C₄×C₁₉	C₂×Q₈	semidirect
78. C₂²×C₁₉	C₄⋊Q₈	semidirect
118. C₁₉	#2434	semidirect
142. C₂²⋊C₄	Dic₃₈	semidirect
164. C₂×C₄	C₂×Dic₃₈	semidirect
171. C₂²	#10597315	semidirect

H ≅ G/N

type

2. C₂×#10597315

C₂

semidirect

4. #11926465

C₂

semidirect

5. #11926450

C₂

semidirect

44. C₂²⋊C₄×C₁₉

Q₈

semidirect

62. C₂×C₄×C₁₉

C₂×Q₈

semidirect

78. C₂²×C₁₉

C₄⋊Q₈

semidirect

118. C₁₉

#2434

semidirect

142. C₂²⋊C₄

Dic₃₈

semidirect

164. C₂×C₄

C₂×Dic₃₈

semidirect

171. C₂²

#10597315

semidirect

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

subgroup	index
C₂³×Dic₃₈	2
C₂×#10597315	2
C₂×#10597370	2
#11926465	2
#11926450	2
#11926419	2
C₄×C₂²⋊C₄×C₁₉	2
#2434	19

subgroup

index

C₂³×Dic₃₈

C₄×C₂²⋊C₄×C₁₉

Subgroups — #14567279

Conjugacy classes of subgroups

Complements

Maximal subgroups