Group #14574530 — subgroups

Subgroups — #14574530

Order 2432.

378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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	#11927115	C₂	1	2	yes	maximal
2	#11926886	C₂	1	4	yes	maximal, complemented
3	#11926802	C₂	1	2	yes	maximal, complemented
4	#11926785	C₂	1	2	yes	maximal, complemented
5	#11926702	C₂	1	4	yes	maximal, complemented
6	C₁₉×#408	C₂	1	1	yes	maximal, characteristic
7	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃₈	C₂²	1	2	yes	—
9	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597390	—	2	2	no	—
12	#10597382	—	2	2	no	—
13	#10597381	—	2	2	no	—
14	#10597381	—	2	2	no	—
15	#10597372	C₂²	1	2	yes	—
16	#10597370	C₂²	1	4	yes	—
17	#10597370	C₂²	1	4	yes	—
18	C₂×Dic₇₆	C₂²	1	2	yes	—
19	C₂×Dic₇₆	C₂²	1	2	yes	—
20	C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
21	#10597275	C₂²	1	2	yes	—
22	#10597274	C₂²	1	2	yes	—
23	#10597273	C₂²	1	4	yes	—
24	#10597273	C₂²	1	4	yes	—
25	#41×C₁₉	—	4	1	no	—
26	#41×C₁₉	—	4	1	no	—
27	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
29	C₂×D₄×C₁₉	D₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
32	C₂²×Dic₁₉	—	2	2	no	—
33	C₂×Dic₃₈	—	2	2	no	—
34	C₂×Dic₃₈	—	4	2	no	—
35	C₂×Dic₃₈	—	4	2	no	—
36	C₂×Dic₃₈	C₂³	1	4	yes	—
37	M₁₆×C₁₉	—	4	1	no	—
38	C₂×C₈×C₁₉	—	4	1	no	—
39	C₂×C₈×C₁₉	C₂³	1	2	yes	—
40	C₂×C₈×C₁₉	C₂³	1	2	yes	—
41	C₂²⋊Dic₁₉	—	2	2	no	—
42	C₂²⋊Dic₁₉	—	2	4	no	—
43	C₂²⋊Dic₁₉	—	2	4	no	—
44	C₄⋊Dic₁₉	C₂³	1	4	yes	—
45	Dic₁₉⋊C₄	—	2	4	no	—
46	Dic₁₉⋊C₄	—	2	4	no	—
47	C₄×Dic₁₉	—	2	2	no	—
48	Dic₇₆	—	4	2	no	—
49	Dic₇₆	—	4	2	no	—
50	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂³×C₁₉	C₂×D₄	1	2	yes	—
52	Q₈×C₁₉	—	4	1	no	—
53	D₄×C₁₉	—	4	2	no	—
54	D₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	—	2	1	no	—
56	C₂×C₄×C₁₉	—	2	1	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
62	C₂×Dic₁₉	—	2	4	no	—
63	C₂×Dic₁₉	—	2	4	no	—
64	C₂×Dic₁₉	—	4	4	no	—
65	Dic₃₈	—	2	4	no	—
66	Dic₃₈	—	2	4	no	—
67	Dic₃₈	—	4	4	no	—
68	C₈×C₁₉	—	2	2	no	—
69	C₈×C₁₉	—	2	2	no	—
70	#3202	—	19	1	no	maximal, Sylow
71	C₂²×C₁₉	—	2	2	no	—
72	C₂²×C₁₉	—	2	1	no	—
73	C₂²×C₁₉	—	2	2	no	—
74	C₂²×C₁₉	—	2	4	no	—
75	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
79	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
80	Dic₁₉	—	4	4	no	—
81	Dic₁₉	—	4	4	no	—
82	#536	—	19	2	no	—
83	#485	—	19	4	no	—
84	#470	—	19	2	no	—
85	#467	—	19	2	no	—
86	#451	—	19	4	no	—
87	#408	D₁₉	1	1	yes	characteristic
88	C₂×C₁₉	—	4	2	no	—
89	C₂×C₁₉	—	4	1	no	—
90	C₂×C₁₉	#534	1	1	yes	characteristic
91	C₂×C₁₉	#578	1	2	yes	—
92	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
93	C₂²×Q₈	—	19	2	no	—
94	C₂×Q₁₆	—	19	2	no	—
95	C₂×Q₁₆	—	19	2	no	—
96	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
97	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
98	C₄⋊Q₈	—	38	2	no	—
99	#124	—	38	2	no	—
100	#123	—	38	2	no	—
101	#123	—	38	2	no	—
102	C₂²⋊Q₈	—	19	4	no	—
103	C₂²⋊Q₈	—	19	4	no	—
104	#117	—	19	2	no	—
105	#107	—	19	2	no	—
106	#106	—	19	2	no	—
107	#103	—	19	4	no	—
108	#103	—	19	4	no	—
109	C₂²⋊C₈	C₂×D₁₉	1	4	yes	—
110	C₁₉	#3202	1	1	yes	characteristic, complemented, Sylow
111	#41	—	4	1	no	—
112	#41	—	4	1	no	—
113	C₂×Q₈	—	19	4	no	—
114	C₂×Q₈	—	38	2	no	—
115	C₂×Q₈	—	76	2	no	—
116	C₂×Q₈	—	76	2	no	—
117	C₂×Q₈	D₇₆	1	1	yes	characteristic
118	C₂×D₄	D₇₆	1	1	yes	characteristic
119	C₂×D₄	D₇₆	1	2	yes	—
120	C₂²×C₄	—	38	2	no	—
121	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
122	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
123	Q₁₆	—	76	2	no	—
124	Q₁₆	—	76	2	no	—
125	M₁₆	—	4	1	no	—
126	C₂×C₈	—	4	1	no	—
127	C₂×C₈	C₂²×D₁₉	1	2	yes	—
128	C₂×C₈	C₂²×D₁₉	1	2	yes	—
129	C₄⋊C₄	—	19	4	no	—
130	C₄⋊C₄	—	38	4	no	—
131	C₄⋊C₄	—	38	4	no	—
132	C₂²⋊C₄	—	38	2	no	—
133	C₂²⋊C₄	—	38	4	no	—
134	C₂²⋊C₄	—	38	4	no	—
135	C₄²	—	38	2	no	—
136	C₂³	C₂×D₇₆	1	1	yes	characteristic
137	C₂³	C₂×D₇₆	1	2	yes	—
138	Q₈	—	4	1	no	—
139	Q₈	—	38	4	no	—
140	Q₈	—	38	4	no	—
141	Q₈	—	76	4	no	—
142	D₄	—	4	2	no	—
143	D₄	—	4	1	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	38	4	no	—
149	C₂×C₄	—	38	4	no	—
150	C₂×C₄	—	76	4	no	—
151	C₂×C₄	C₂×D₇₆	1	2	yes	—
152	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
153	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
154	C₈	—	2	2	no	—
155	C₈	—	2	2	no	—
156	C₂²	—	2	2	no	—
157	C₂²	—	2	4	no	—
158	C₂²	—	2	2	no	—
159	C₂²	—	2	1	no	—
160	C₂²	C₂²×D₇₆	1	1	yes	characteristic
161	C₄	—	2	2	no	—
162	C₄	—	2	1	no	—
163	C₄	—	76	4	no	—
164	C₄	—	76	4	no	—
165	C₄	#10597430	1	1	yes	characteristic
166	C₄	#10597430	1	1	yes	characteristic
167	C₂	—	4	2	no	—
168	C₂	—	4	1	no	—
169	C₂	#11927106	1	1	yes	characteristic
170	C₂	#11927361	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927115

C₂

yes

maximal

#11926886

C₂

yes

maximal, complemented

#11926802

C₂

yes

maximal, complemented

#11926785

C₂

yes

maximal, complemented

#11926702

C₂

yes

maximal, complemented

C₁₉×#408

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

—

—

—

—

C₂²

yes

—

#10597370

C₂²

yes

—

#10597370

C₂²

yes

—

C₂×Dic₇₆

C₂²

yes

—

C₂×Dic₇₆

C₂²

yes

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

#10597275

C₂²

yes

—

#10597274

C₂²

yes

—

#10597273

C₂²

yes

—

#10597273

C₂²

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

Dic₇₆

—

Dic₇₆

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

#3202

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#534

yes

characteristic

C₂×C₁₉

#578

yes

—

C₂×#41

C₂×D₁₉

yes

characteristic

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

#124

—

100

#123

—

101

#123

—

102

C₂²⋊Q₈

—

103

C₂²⋊Q₈

—

104

#117

—

105

#107

—

106

#106

—

107

#103

—

108

#103

—

109

C₂²⋊C₈

C₂×D₁₉

yes

—

110

C₁₉

#3202

yes

characteristic, complemented, Sylow

111

#41

—

112

#41

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

D₇₆

yes

characteristic

118

C₂×D₄

D₇₆

yes

characteristic

119

C₂×D₄

D₇₆

yes

—

120

C₂²×C₄

—

121

C₂²×C₄

C₂²×D₁₉

yes

—

122

C₂²×C₄

C₂²×D₁₉

yes

characteristic

123

Q₁₆

—

124

Q₁₆

—

125

M₁₆

—

126

C₂×C₈

—

127

C₂×C₈

C₂²×D₁₉

yes

—

128

C₂×C₈

C₂²×D₁₉

yes

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₂²⋊C₄

—

133

C₂²⋊C₄

—

134

C₂²⋊C₄

—

135

C₄²

—

136

C₂³

C₂×D₇₆

yes

characteristic

137

C₂³

C₂×D₇₆

yes

—

138

Q₈

—

139

Q₈

—

140

Q₈

—

141

Q₈

—

142

D₄

—

143

D₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

C₂×D₇₆

yes

—

152

C₂×C₄

C₂×D₇₆

yes

characteristic

153

C₂×C₄

C₂³×D₁₉

yes

characteristic

154

C₈

—

155

C₈

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

C₂²×D₇₆

yes

characteristic

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

#10597430

yes

characteristic

166

C₄

#10597430

yes

characteristic

167

C₂

—

168

C₂

—

169

C₂

#11927106

yes

characteristic

170

C₂

#11927361

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₇₆
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#408	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂×#41×C₁₉	C₂²
hypercenter	#408	D₁₉
hypocenter	C₁₉	#3202
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ #408

subgroup

G/H

center

C₂²

C₂²×D₇₆

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#408

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂×#41×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×#41 ◁ #408

N	H ≅ G/N	type
2. #11926886	C₂	semidirect
3. #11926802	C₂	semidirect
4. #11926785	C₂	semidirect
5. #11926702	C₂	semidirect
110. C₁₉	#3202	semidirect

H ≅ G/N

type

2. #11926886

C₂

semidirect

3. #11926802

C₂

semidirect

4. #11926785

C₂

semidirect

5. #11926702

C₂

semidirect

110. C₁₉

#3202

semidirect

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

subgroup	index
#11927115	2
#11926886	2
#11926802	2
#11926785	2
#11926702	2
C₁₉×#408	2
#3202	19

subgroup

index

C₁₉×#408

Subgroups — #14574530

Conjugacy classes of subgroups

Complements

Maximal subgroups