Group #14574175 — subgroups

Subgroups — #14574175

Order 2432.

340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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	#11927172	C₂	1	2	yes	maximal
2	#11926951	C₂	1	4	yes	maximal, complemented
3	#11926948	C₂	1	2	yes	maximal, complemented
4	#11926945	C₂	1	2	yes	maximal, complemented
5	#11926587	C₂	1	2	yes	maximal
6	C₂×#10597275	C₂	1	1	yes	maximal, characteristic
7	#11926499	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#427	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#117	C₂²	1	2	yes	—
11	#10597372	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
13	C₂×#64520	C₂²	1	1	yes	characteristic
14	#10597336	C₂²	1	4	yes	—
15	#10597334	C₂²	1	4	yes	—
16	#10597324	—	2	4	no	—
17	#10597316	—	2	2	no	—
18	#10597315	—	2	2	no	—
19	C₁₉×#107	C₂²	1	1	yes	characteristic
20	C₁₉×#107	C₂²	1	1	yes	characteristic
21	C₁₉×#106	C₂²	1	2	yes	—
22	#10597275	C₂²	1	2	yes	—
23	#10597275	C₂²	1	2	yes	—
24	#10597272	C₂²	1	2	yes	—
25	C₈×Dic₁₉	C₂²	1	2	yes	—
26	#10597265	C₂²	1	4	yes	—
27	#10597264	C₂²	1	4	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	2	2	no	—
30	C₂×Dic₃₈	—	2	4	no	—
31	C₂×C₈×C₁₉	Q₈	1	4	yes	complemented
32	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
35	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
36	C₂²⋊C₄×C₁₉	—	2	2	no	—
37	C₄²×C₁₉	—	2	2	no	—
38	C₂²⋊Dic₁₉	D₄	1	2	yes	—
39	C₄⋊Dic₁₉	—	2	2	no	—
40	C₄⋊Dic₁₉	—	2	4	no	—
41	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
42	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
43	C₄⋊Dic₁₉	C₂³	1	4	yes	—
44	Dic₁₉⋊C₄	—	2	4	no	—
45	Dic₁₉⋊C₄	—	2	4	no	—
46	C₄×Dic₁₉	C₂³	1	2	yes	—
47	#64520	Q₈	1	4	yes	complemented
48	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
49	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
55	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
56	C₂×Dic₁₉	—	2	4	no	—
57	C₂×Dic₁₉	—	8	2	no	—
58	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
59	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
60	Dic₃₈	—	8	4	no	—
61	C₈×C₁₉	C₂×Q₈	1	2	yes	—
62	C₈×C₁₉	C₂×Q₈	1	2	yes	—
63	C₁₉⋊C₈	C₂×Q₈	1	4	yes	—
64	#3164	—	19	1	no	maximal, Sylow
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	C₄⋊Q₈	1	2	yes	—
68	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
69	C₄×C₁₉	—	4	2	no	—
70	C₄×C₁₉	—	4	2	no	—
71	C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
72	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
73	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
74	Dic₁₉	—	2	2	no	—
75	Dic₁₉	—	2	2	no	—
76	Dic₁₉	—	4	4	no	—
77	#544	—	19	2	no	—
78	#501	—	19	4	no	—
79	#500	—	19	2	no	—
80	#499	—	19	2	no	—
81	#428	—	19	2	no	—
82	#427	D₁₉	1	1	yes	characteristic
83	C₂×#107	—	19	1	no	—
84	#405	—	19	1	no	—
85	C₂×C₁₉	—	2	2	no	—
86	C₂×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
87	C₂×C₁₉	#576	1	1	yes	characteristic
88	C₂×C₁₉	#578	1	1	yes	characteristic
89	C₂×M₁₆	—	19	1	no	—
90	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
91	C₄⋊Q₈	—	19	4	no	—
92	C₄⋊Q₈	—	38	2	no	—
93	#125	—	19	4	no	—
94	#125	—	38	2	no	—
95	C₂²⋊Q₈	—	38	4	no	—
96	#117	—	19	1	no	—
97	#117	C₂×D₁₉	1	2	yes	—
98	C₂×C₄⋊C₄	—	19	2	no	—
99	#107	—	19	2	no	—
100	#107	—	19	2	no	—
101	#107	—	19	4	no	—
102	#107	C₂×D₁₉	1	1	yes	characteristic
103	#107	C₂×D₁₉	1	1	yes	characteristic
104	#106	—	19	4	no	—
105	#106	C₂×D₁₉	1	2	yes	—
106	#97	—	19	2	no	—
107	C₄×C₈	—	19	2	no	—
108	C₁₉	#3164	1	1	yes	characteristic, complemented, Sylow
109	C₂×Q₈	—	38	4	no	—
110	C₂²×C₄	—	38	2	no	—
111	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
112	M₁₆	—	19	4	no	—
113	C₂×C₈	—	19	2	no	—
114	C₂×C₈	Dic₃₈	1	4	yes	complemented
115	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
116	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
117	C₄⋊C₄	—	19	1	no	—
118	C₄⋊C₄	—	19	1	no	—
119	C₄⋊C₄	—	19	4	no	—
120	C₄⋊C₄	—	38	4	no	—
121	C₄⋊C₄	—	38	4	no	—
122	C₄⋊C₄	—	38	4	no	—
123	C₄⋊C₄	—	38	2	no	—
124	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
125	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
126	C₂²⋊C₄	—	2	2	no	—
127	C₂²⋊C₄	—	19	2	no	—
128	C₄²	—	2	2	no	—
129	C₄²	—	19	2	no	—
130	C₂³	D₄×D₁₉	1	1	yes	characteristic
131	Q₈	—	152	4	no	—
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	19	2	no	—
135	C₂×C₄	—	19	2	no	—
136	C₂×C₄	—	38	4	no	—
137	C₂×C₄	—	152	2	no	—
138	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
139	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
140	C₂×C₄	Q₈×D₁₉	1	2	yes	—
141	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
142	C₈	—	19	4	no	—
143	C₈	C₂×Dic₃₈	1	2	yes	—
144	C₈	C₂×Dic₃₈	1	2	yes	—
145	C₂²	—	2	1	no	—
146	C₂²	—	2	1	no	—
147	C₂²	#10597334	1	2	yes	—
148	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
149	C₄	—	4	2	no	—
150	C₄	—	4	2	no	—
151	C₄	—	38	2	no	—
152	C₄	—	38	2	no	—
153	C₄	—	76	4	no	—
154	C₄	#10597334	1	2	yes	—
155	C₄	C₂²×Dic₃₈	1	1	yes	characteristic
156	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
157	C₂	—	2	2	no	—
158	C₂	C₂×#10597334	1	1	yes	characteristic
159	C₂	#11927346	1	1	yes	characteristic
160	C₂	#11927358	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927172

C₂

yes

maximal

#11926951

C₂

yes

maximal, complemented

#11926948

C₂

yes

maximal, complemented

#11926945

C₂

yes

maximal, complemented

#11926587

C₂

yes

maximal

C₂×#10597275

C₂

yes

maximal, characteristic

#11926499

C₂

yes

maximal, characteristic

C₁₉×#427

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

#10597372

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×#64520

C₂²

yes

characteristic

#10597336

C₂²

yes

—

#10597334

C₂²

yes

—

#10597324

—

#10597316

—

#10597315

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#106

C₂²

yes

—

#10597275

C₂²

yes

—

#10597275

C₂²

yes

—

#10597272

C₂²

yes

—

C₈×Dic₁₉

C₂²

yes

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

Q₈

yes

complemented

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

C₂³

yes

—

#64520

Q₈

yes

complemented

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

C₈×C₁₉

C₂×Q₈

yes

—

C₈×C₁₉

C₂×Q₈

yes

—

C₁₉⋊C₈

C₂×Q₈

yes

—

#3164

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄⋊Q₈

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄⋊Q₈

yes

—

C₄×C₁₉

C₂²×Q₈

yes

characteristic

C₄×C₁₉

C₂²×Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×#107

—

#405

—

C₂×C₁₉

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

#125

—

C₂²⋊Q₈

—

#117

—

#117

C₂×D₁₉

yes

—

C₂×C₄⋊C₄

—

#107

—

100

#107

—

101

#107

—

102

#107

C₂×D₁₉

yes

characteristic

103

#107

C₂×D₁₉

yes

characteristic

104

#106

—

105

#106

C₂×D₁₉

yes

—

106

#97

—

107

C₄×C₈

—

108

C₁₉

#3164

yes

characteristic, complemented, Sylow

109

C₂×Q₈

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²×D₁₉

yes

characteristic

112

M₁₆

—

113

C₂×C₈

—

114

C₂×C₈

Dic₃₈

yes

complemented

115

C₂×C₈

C₂²×D₁₉

yes

characteristic

116

C₂×C₈

C₂²×D₁₉

yes

characteristic

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

C₂²×D₁₉

yes

—

125

C₄⋊C₄

C₂²×D₁₉

yes

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₄²

—

130

C₂³

D₄×D₁₉

yes

characteristic

131

Q₈

—

152

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

152

—

138

C₂×C₄

C₂×Dic₃₈

yes

—

139

C₂×C₄

D₄×D₁₉

yes

characteristic

140

C₂×C₄

Q₈×D₁₉

yes

—

141

C₂×C₄

C₂³×D₁₉

yes

characteristic

142

C₈

—

143

C₈

C₂×Dic₃₈

yes

—

144

C₈

C₂×Dic₃₈

yes

—

145

C₂²

—

146

C₂²

—

147

C₂²

#10597334

yes

—

148

C₂²

C₂×D₄×D₁₉

yes

characteristic

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

#10597334

yes

—

155

C₄

C₂²×Dic₃₈

yes

characteristic

156

C₄

C₂×Q₈×D₁₉

yes

characteristic

157

C₂

—

158

C₂

C₂×#10597334

yes

characteristic

159

C₂

#11927346

yes

characteristic

160

C₂

#11927358

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#427	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#427	D₁₉
hypocenter	C₁₉	#3164
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #427

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#427

C₂

socle

C₂²×C₁₉

C₂²×D₄

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #427

N	H ≅ G/N	type
2. #11926951	C₂	semidirect
3. #11926948	C₂	semidirect
4. #11926945	C₂	semidirect
31. C₂×C₈×C₁₉	Q₈	semidirect
47. #64520	Q₈	semidirect
108. C₁₉	#3164	semidirect
114. C₂×C₈	Dic₃₈	semidirect

H ≅ G/N

type

2. #11926951

C₂

semidirect

3. #11926948

C₂

semidirect

4. #11926945

C₂

semidirect

31. C₂×C₈×C₁₉

Q₈

semidirect

47. #64520

Q₈

semidirect

108. C₁₉

#3164

semidirect

114. C₂×C₈

Dic₃₈

semidirect

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

subgroup	index
#11927172	2
#11926951	2
#11926948	2
#11926945	2
#11926587	2
C₂×#10597275	2
#11926499	2
C₁₉×#427	2
#3164	19

subgroup

index

C₁₉×#427

Subgroups — #14574175

Conjugacy classes of subgroups

Complements

Maximal subgroups