Group #14574781 — subgroups

Subgroups — #14574781

Order 2432.

360 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 141 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	#11927101	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597315	C₂	1	1	yes	maximal, characteristic
3	#11926942	C₂	1	2	yes	maximal, complemented
4	#11926895	C₂	1	2	yes	maximal, complemented
5	#11926875	C₂	1	4	yes	maximal
6	#11926830	C₂	1	4	yes	maximal, complemented
7	C₁₉×#431	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	—	2	1	no	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	#10597372	—	2	1	no	—
11	C₂×C₄⋊Dic₁₉	—	2	1	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	#10597370	—	2	1	no	—
14	#10597370	C₂²	1	2	yes	—
15	#10597316	—	2	1	no	—
16	#10597315	—	2	1	no	—
17	#10597315	—	2	1	no	—
18	#10597315	C₂²	1	1	yes	characteristic
19	#10597315	C₂²	1	2	yes	—
20	#10597315	C₂²	1	2	yes	—
21	#10597315	C₂²	1	1	yes	characteristic
22	C₄×Dic₃₈	—	2	1	no	—
23	C₄×Dic₃₈	C₂²	1	2	yes	—
24	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
25	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₄×C₈×C₁₉	C₂²	1	2	yes	—
27	#10597274	C₂²	1	8	yes	—
28	#10597273	C₂²	1	8	yes	—
29	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₉	—	2	2	no	—
33	C₂×Dic₃₈	—	2	2	no	—
34	C₂×Dic₃₈	—	2	2	no	—
35	C₂×Dic₃₈	—	2	1	no	—
36	C₂×Dic₃₈	—	4	4	no	—
37	C₂×Dic₃₈	C₂³	1	2	yes	—
38	C₂×C₈×C₁₉	C₂³	1	4	yes	—
39	C₄²×C₁₉	D₄	1	1	yes	characteristic
40	C₄²×C₁₉	D₄	1	1	yes	characteristic
41	C₄²×C₁₉	C₂³	1	1	yes	characteristic
42	C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²⋊Dic₁₉	—	2	2	no	—
44	C₄⋊Dic₁₉	—	2	1	no	—
45	C₄⋊Dic₁₉	—	2	2	no	—
46	C₄⋊Dic₁₉	—	2	2	no	—
47	C₄⋊Dic₁₉	—	2	2	no	—
48	C₄⋊Dic₁₉	—	2	1	no	—
49	C₄⋊Dic₁₉	—	2	1	no	—
50	C₄⋊Dic₁₉	C₂³	1	4	yes	—
51	C₄⋊Dic₁₉	C₂³	1	2	yes	—
52	Dic₁₉⋊C₄	—	2	2	no	—
53	Dic₁₉⋊C₄	—	2	2	no	—
54	C₄×Dic₁₉	—	2	2	no	—
55	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	SD₁₆	1	4	yes	—
59	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
65	C₂×Dic₁₉	—	2	2	no	—
66	C₂×Dic₁₉	—	2	2	no	—
67	C₂×Dic₁₉	—	2	4	no	—
68	C₂×Dic₁₉	—	4	4	no	—
69	Dic₃₈	—	2	4	no	—
70	Dic₃₈	—	4	4	no	—
71	Dic₃₈	—	4	4	no	—
72	Dic₃₈	—	4	2	no	—
73	C₈×C₁₉	—	2	4	no	—
74	#3229	—	19	1	no	maximal, Sylow
75	C₂²×C₁₉	—	2	1	no	—
76	C₂²×C₁₉	—	2	1	no	—
77	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
78	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
79	C₄×C₁₉	—	2	1	no	—
80	C₄×C₁₉	—	2	1	no	—
81	C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
82	C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
83	C₄×C₁₉	#137	1	2	yes	—
84	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
85	Dic₁₉	—	4	2	no	—
86	Dic₁₉	—	4	4	no	—
87	Dic₁₉	—	4	2	no	—
88	#533	—	19	1	no	—
89	C₂×C₄⋊Q₈	—	19	1	no	—
90	#498	—	19	2	no	—
91	#487	—	19	2	no	—
92	#483	—	19	4	no	—
93	#475	—	19	4	no	—
94	#431	D₁₉	1	1	yes	characteristic
95	C₂×C₁₉	—	2	2	no	—
96	C₂×C₁₉	#536	1	1	yes	characteristic
97	C₂×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
98	C₂×C₁₉	C₂×#137	1	1	yes	characteristic
99	C₂²×Q₈	—	38	1	no	—
100	C₄⋊Q₈	—	19	2	no	—
101	C₄⋊Q₈	—	19	2	no	—
102	C₄⋊Q₈	—	19	1	no	—
103	C₄⋊Q₈	—	19	1	no	—
104	C₄⋊Q₈	—	38	1	no	—
105	C₄⋊Q₈	—	38	1	no	—
106	#125	—	38	1	no	—
107	C₂²⋊Q₈	—	19	2	no	—
108	C₂²⋊Q₈	—	38	1	no	—
109	C₄×Q₈	—	19	2	no	—
110	C₄×Q₈	—	38	1	no	—
111	#117	—	38	1	no	—
112	C₂×C₄⋊C₄	—	19	2	no	—
113	C₂×C₄⋊C₄	—	38	1	no	—
114	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
115	#106	—	19	8	no	—
116	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
117	#103	—	19	8	no	—
118	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
119	C₄×C₈	C₂×D₁₉	1	2	yes	—
120	C₁₉	#3229	1	1	yes	characteristic, complemented, Sylow
121	C₂×Q₈	—	19	2	no	—
122	C₂×Q₈	—	38	1	no	—
123	C₂×Q₈	—	38	2	no	—
124	C₂×Q₈	—	38	2	no	—
125	C₂×Q₈	—	76	4	no	—
126	C₂²×C₄	—	38	2	no	—
127	C₂²×C₄	D₇₆	1	1	yes	characteristic
128	C₂²×C₄	D₇₆	1	1	yes	characteristic
129	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
130	C₂×C₈	C₂²×D₁₉	1	4	yes	—
131	C₄⋊C₄	—	19	4	no	—
132	C₄⋊C₄	—	19	2	no	—
133	C₄⋊C₄	—	38	2	no	—
134	C₄⋊C₄	—	38	2	no	—
135	C₄⋊C₄	—	38	2	no	—
136	C₄⋊C₄	—	38	2	no	—
137	C₄⋊C₄	—	38	2	no	—
138	C₄⋊C₄	—	38	1	no	—
139	C₄⋊C₄	—	38	1	no	—
140	C₄⋊C₄	—	38	1	no	—
141	C₂²⋊C₄	—	38	2	no	—
142	C₄²	—	38	2	no	—
143	C₄²	D₇₆	1	1	yes	characteristic
144	C₄²	D₇₆	1	1	yes	characteristic
145	C₄²	C₂²×D₁₉	1	1	yes	characteristic
146	C₄²	C₂²×D₁₉	1	1	yes	characteristic
147	C₂³	C₂×D₇₆	1	1	yes	characteristic
148	Q₈	—	38	4	no	—
149	Q₈	—	76	4	no	—
150	Q₈	—	76	4	no	—
151	Q₈	—	76	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	38	2	no	—
155	C₂×C₄	—	38	2	no	—
156	C₂×C₄	—	38	4	no	—
157	C₂×C₄	—	76	4	no	—
158	C₂×C₄	#64516	1	4	yes	—
159	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
160	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
161	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
162	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
163	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
164	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
165	C₈	—	2	4	no	—
166	C₂²	—	2	1	no	—
167	C₂²	—	2	1	no	—
168	C₂²	C₂×#64516	1	2	yes	—
169	C₂²	C₂²×D₇₆	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	1	no	—
172	C₄	—	76	4	no	—
173	C₄	—	76	2	no	—
174	C₄	—	76	2	no	—
175	C₄	C₂×#64516	1	2	yes	—
176	C₄	C₂×#64516	1	2	yes	—
177	C₄	#10597355	1	2	yes	—
178	C₄	#10597436	1	2	yes	—
179	C₂	—	2	2	no	—
180	C₂	#11927120	1	1	yes	characteristic
181	C₂	C₂²×#64516	1	1	yes	characteristic
182	C₂	C₂×#10597355	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic

C₂×#10597315

C₂

yes

maximal, characteristic

#11926942

C₂

yes

maximal, complemented

#11926895

C₂

yes

maximal, complemented

#11926875

C₂

yes

maximal

#11926830

C₂

yes

maximal, complemented

C₁₉×#431

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

#10597370

—

#10597370

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

#10597315

C₂²

yes

—

#10597315

C₂²

yes

—

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

—

#10597274

C₂²

yes

—

#10597273

C₂²

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#3229

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

—

C₄×C₁₉

C₂×SD₁₆

yes

—

C₄×C₁₉

#137

yes

—

C₄×C₁₉

2₋¹⁺⁴

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#533

—

C₂×C₄⋊Q₈

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#536

yes

characteristic

C₂×C₁₉

C₂²×SD₁₆

yes

characteristic

C₂×C₁₉

C₂×#137

yes

characteristic

C₂²×Q₈

—

100

C₄⋊Q₈

—

101

C₄⋊Q₈

—

102

C₄⋊Q₈

—

103

C₄⋊Q₈

—

104

C₄⋊Q₈

—

105

C₄⋊Q₈

—

106

#125

—

107

C₂²⋊Q₈

—

108

C₂²⋊Q₈

—

109

C₄×Q₈

—

110

C₄×Q₈

—

111

#117

—

112

C₂×C₄⋊C₄

—

113

C₂×C₄⋊C₄

—

114

C₂×C₄²

C₂×D₁₉

yes

characteristic

115

#106

—

116

C₄⋊C₈

C₂×D₁₉

yes

—

117

#103

—

118

C₂²⋊C₈

C₂×D₁₉

yes

—

119

C₄×C₈

C₂×D₁₉

yes

—

120

C₁₉

#3229

yes

characteristic, complemented, Sylow

121

C₂×Q₈

—

122

C₂×Q₈

—

123

C₂×Q₈

—

124

C₂×Q₈

—

125

C₂×Q₈

—

126

C₂²×C₄

—

127

C₂²×C₄

D₇₆

yes

characteristic

128

C₂²×C₄

D₇₆

yes

characteristic

129

C₂²×C₄

C₂²×D₁₉

yes

characteristic

130

C₂×C₈

C₂²×D₁₉

yes

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₂²⋊C₄

—

142

C₄²

—

143

C₄²

D₇₆

yes

characteristic

144

C₄²

D₇₆

yes

characteristic

145

C₄²

C₂²×D₁₉

yes

characteristic

146

C₄²

C₂²×D₁₉

yes

characteristic

147

C₂³

C₂×D₇₆

yes

characteristic

148

Q₈

—

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

#64516

yes

—

159

C₂×C₄

C₂×D₇₆

yes

characteristic

160

C₂×C₄

C₂×D₇₆

yes

characteristic

161

C₂×C₄

C₂×D₇₆

yes

characteristic

162

C₂×C₄

C₂×D₇₆

yes

characteristic

163

C₂×C₄

C₂×D₇₆

yes

characteristic

164

C₂×C₄

C₂³×D₁₉

yes

characteristic

165

C₈

—

166

C₂²

—

167

C₂²

—

168

C₂²

C₂×#64516

yes

—

169

C₂²

C₂²×D₇₆

yes

characteristic

170

C₄

—

171

C₄

—

172

C₄

—

173

C₄

—

174

C₄

—

175

C₄

C₂×#64516

yes

—

176

C₄

C₂×#64516

yes

—

177

C₄

#10597355

yes

—

178

C₄

#10597436

yes

—

179

C₂

—

180

C₂

#11927120

yes

characteristic

181

C₂

C₂²×#64516

yes

characteristic

182

C₂

C₂×#10597355

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#431	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#431	D₁₉
hypocenter	C₁₉	#3229
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#431

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
3. #11926942	C₂	semidirect
4. #11926895	C₂	semidirect
6. #11926830	C₂	semidirect
120. C₁₉	#3229	semidirect

H ≅ G/N

type

3. #11926942

C₂

semidirect

4. #11926895

C₂

semidirect

6. #11926830

C₂

semidirect

120. C₁₉

#3229

semidirect

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

subgroup	index
#11927101	2
C₂×#10597315	2
#11926942	2
#11926895	2
#11926875	2
#11926830	2
C₁₉×#431	2
#3229	19

subgroup

index

C₁₉×#431

Subgroups — #14574781

Conjugacy classes of subgroups

Complements

Maximal subgroups