Group #14564158 — subgroups

Subgroups — #14564158

Order 2432.

312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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	#11927311	C₂	1	1	yes	maximal, characteristic
2	#11926553	C₂	1	2	yes	maximal, complemented
3	#11926518	C₂	1	1	yes	maximal, characteristic
4	#11926300	C₂	1	2	yes	maximal, complemented
5	C₁₉×#536	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×C₄⋊Q₈	C₄	1	2	yes	complemented
9	C₁₉×#124	C₄	1	2	yes	complemented
10	C₁₉×#123	—	2	2	no	—
11	C₁₉×C₂²⋊Q₈	—	2	2	no	—
12	C₁₉×#117	C₂²	1	1	yes	characteristic
13	#10597394	—	2	4	no	—
14	#10597372	C₂²	1	2	yes	—
15	C₂×#64520	—	2	2	no	—
16	C₂×#64520	C₂²	1	2	yes	—
17	#10597292	—	2	4	no	—
18	#10597291	—	2	2	no	—
19	#41×C₁₉	—	2	2	no	—
20	#41×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	—	2	1	no	—
22	C₂×Q₈×C₁₉	—	2	2	no	—
23	C₂×Q₈×C₁₉	—	2	2	no	—
24	C₂×Q₈×C₁₉	C₂×C₄	1	2	yes	—
25	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×D₄×C₁₉	D₄	1	2	yes	—
28	C₂²×C₄×C₁₉	—	2	1	no	—
29	C₂²×C₄×C₁₉	D₄	1	2	yes	—
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₄⋊C₄×C₁₉	—	2	4	no	—
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂²⋊C₄×C₁₉	—	2	4	no	—
34	C₂²⋊C₄×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	C₂×C₄	1	2	yes	—
36	C₂²⋊Dic₁₉	—	2	2	no	—
37	C₄⋊Dic₁₉	—	2	2	no	—
38	C₄×Dic₁₉	—	2	2	no	—
39	#64520	—	2	4	no	—
40	#64520	—	2	2	no	—
41	#64520	—	2	2	no	—
42	C₂×C₁₉⋊C₈	—	2	4	no	—
43	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
44	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
46	Q₈×C₁₉	—	2	2	no	—
47	Q₈×C₁₉	—	2	4	no	—
48	Q₈×C₁₉	—	4	1	no	—
49	Q₈×C₁₉	—	4	1	no	—
50	D₄×C₁₉	—	2	4	no	—
51	D₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	2	2	no	—
54	C₂×C₄×C₁₉	—	2	2	no	—
55	C₂×C₄×C₁₉	—	2	2	no	—
56	C₂×C₄×C₁₉	—	4	2	no	—
57	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
58	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₉	#41	1	2	yes	—
62	C₂×Dic₁₉	—	4	2	no	—
63	C₁₉⋊C₈	—	2	4	no	—
64	#1909	—	19	1	no	maximal, Sylow
65	C₂²×C₁₉	—	2	2	no	—
66	C₂²×C₁₉	—	4	1	no	—
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₁₉	#121	1	2	yes	—
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	4	2	no	—
72	C₄×C₁₉	—	4	2	no	—
73	C₄×C₁₉	C₄×D₄	1	2	yes	—
74	C₄×C₁₉	#120	1	1	yes	characteristic
75	C₄×C₁₉	#123	1	1	yes	characteristic
76	Dic₁₉	—	8	2	no	—
77	#568	—	19	1	no	—
78	#536	D₁₉	1	1	yes	characteristic
79	#419	—	19	2	no	—
80	#410	—	19	1	no	—
81	H(3,ℤ/4)	—	19	2	no	—
82	C₂×C₁₉	—	2	2	no	—
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	—	4	2	no	—
85	C₂×C₁₉	#386	1	1	yes	characteristic
86	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
87	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
88	#131	—	38	4	no	—
89	C₂×M₁₆	—	19	2	no	—
90	C₂×M₁₆	—	38	2	no	—
91	C₄⋊Q₈	Dic₁₉	1	2	yes	complemented
92	#124	Dic₁₉	1	2	yes	complemented
93	#123	—	2	2	no	—
94	C₂²⋊Q₈	—	2	2	no	—
95	#117	—	19	2	no	—
96	#117	C₂×D₁₉	1	1	yes	characteristic
97	#103	—	38	4	no	—
98	#99	—	38	2	no	—
99	C₁₉	#1909	1	1	yes	characteristic, complemented, Sylow
100	#41	—	2	2	no	—
101	#41	—	2	2	no	—
102	C₂×Q₈	—	2	1	no	—
103	C₂×Q₈	—	2	2	no	—
104	C₂×Q₈	—	2	2	no	—
105	C₂×Q₈	C₂×Dic₁₉	1	2	yes	—
106	C₂×Q₈	C₂×Dic₁₉	1	1	yes	characteristic
107	C₂×D₄	C₂×Dic₁₉	1	1	yes	characteristic
108	C₂×D₄	C₂²⋊D₁₉	1	2	yes	—
109	C₂²×C₄	—	2	1	no	—
110	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
111	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
112	M₁₆	—	38	4	no	—
113	M₁₆	—	38	2	no	—
114	M₁₆	—	38	2	no	—
115	C₂×C₈	—	19	4	no	—
116	C₂×C₈	—	38	4	no	—
117	C₄⋊C₄	—	2	4	no	—
118	C₄⋊C₄	—	2	1	no	—
119	C₄⋊C₄	—	38	2	no	—
120	C₂²⋊C₄	—	2	4	no	—
121	C₂²⋊C₄	—	2	1	no	—
122	C₂²⋊C₄	—	38	2	no	—
123	C₄²	—	38	2	no	—
124	C₄²	C₂×Dic₁₉	1	2	yes	—
125	C₂³	C₂²⋊Dic₁₉	1	2	yes	—
126	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
127	Q₈	—	2	2	no	—
128	Q₈	—	2	4	no	—
129	Q₈	—	4	1	no	—
130	Q₈	—	4	1	no	—
131	D₄	—	2	4	no	—
132	D₄	—	2	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	—	76	2	no	—
139	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
140	C₂×C₄	D₄×D₁₉	1	2	yes	—
141	C₂×C₄	#64543	1	2	yes	—
142	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
143	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
144	C₈	—	38	4	no	—
145	C₂²	—	2	2	no	—
146	C₂²	—	4	1	no	—
147	C₂²	—	4	2	no	—
148	C₂²	#10597385	1	2	yes	—
149	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
150	C₄	—	2	2	no	—
151	C₄	—	4	2	no	—
152	C₄	—	4	2	no	—
153	C₄	—	152	2	no	—
154	C₄	D₄×Dic₁₉	1	2	yes	—
155	C₄	#10597381	1	1	yes	characteristic
156	C₄	#10597383	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	2	no	—
159	C₂	—	4	2	no	—
160	C₂	#11926424	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927311

C₂

yes

maximal, characteristic

#11926553

C₂

yes

maximal, complemented

#11926518

C₂

yes

maximal, characteristic

#11926300

C₂

yes

maximal, complemented

C₁₉×#536

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₄

yes

complemented

C₁₉×#124

C₄

yes

complemented

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#117

C₂²

yes

characteristic

#10597394

—

#10597372

C₂²

yes

—

C₂×#64520

—

C₂×#64520

C₂²

yes

—

#10597292

—

#10597291

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1909

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#121

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#568

—

#536

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#386

yes

characteristic

C₂×#41

C₂×D₁₉

yes

characteristic

C₂²×Q₈

C₂×D₁₉

yes

characteristic

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

Dic₁₉

yes

complemented

#124

Dic₁₉

yes

complemented

#123

—

C₂²⋊Q₈

—

#117

—

#117

C₂×D₁₉

yes

characteristic

#103

—

#99

—

C₁₉

#1909

yes

characteristic, complemented, Sylow

100

#41

—

101

#41

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

C₂×Dic₁₉

yes

—

106

C₂×Q₈

C₂×Dic₁₉

yes

characteristic

107

C₂×D₄

C₂×Dic₁₉

yes

characteristic

108

C₂×D₄

C₂²⋊D₁₉

yes

—

109

C₂²×C₄

—

110

C₂²×C₄

C₂²⋊D₁₉

yes

—

111

C₂²×C₄

C₂²×D₁₉

yes

characteristic

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₂²⋊C₄

—

123

C₄²

—

124

C₄²

C₂×Dic₁₉

yes

—

125

C₂³

C₂²⋊Dic₁₉

yes

—

126

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

127

Q₈

—

128

Q₈

—

129

Q₈

—

130

Q₈

—

131

D₄

—

132

D₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

C₂²⋊Dic₁₉

yes

—

140

C₂×C₄

D₄×D₁₉

yes

—

141

C₂×C₄

#64543

yes

—

142

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

143

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

144

C₈

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

#10597385

yes

—

149

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

152

—

154

C₄

D₄×Dic₁₉

yes

—

155

C₄

#10597381

yes

characteristic

156

C₄

#10597383

yes

characteristic

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#11926424

yes

characteristic

	subgroup	G/H
center	C₂	#11926424
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#536	C₂
socle	C₂×C₁₉	#386
prime radical	C₂×#41×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#536	D₁₉
hypocenter	C₁₉	#1909
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #536

subgroup

G/H

center

C₂

#11926424

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#536

C₂

socle

C₂×C₁₉

#386

prime radical

C₂×#41×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #536

N	H ≅ G/N	type
2. #11926553	C₂	semidirect
4. #11926300	C₂	semidirect
8. C₁₉×C₄⋊Q₈	C₄	semidirect
9. C₁₉×#124	C₄	semidirect
91. C₄⋊Q₈	Dic₁₉	semidirect
92. #124	Dic₁₉	semidirect
99. C₁₉	#1909	semidirect

H ≅ G/N

type

2. #11926553

C₂

semidirect

4. #11926300

C₂

semidirect

8. C₁₉×C₄⋊Q₈

C₄

semidirect

9. C₁₉×#124

C₄

semidirect

91. C₄⋊Q₈

Dic₁₉

semidirect

92. #124

Dic₁₉

semidirect

99. C₁₉

#1909

semidirect

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

subgroup	index
#11927311	2
#11926553	2
#11926518	2
#11926300	2
C₁₉×#536	2
#1909	19

subgroup

index

C₁₉×#536

Subgroups — #14564158

Conjugacy classes of subgroups

Complements

Maximal subgroups