Group #14564162 — subgroups

Subgroups — #14564162

Order 2432.

344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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	#11927108	C₂	1	1	yes	maximal, characteristic
2	#11926550	C₂	1	2	yes	maximal, complemented
3	#11926518	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926301	C₂	1	2	yes	maximal, complemented
5	C₁₉×#568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×D₇₆	C₂²	1	1	yes	characteristic
8	C₁₉×#131	—	2	4	no	—
9	C₂×M₁₆×C₁₉	—	2	2	no	—
10	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
11	#10597393	C₄	1	2	yes	complemented
12	#10597386	C₄	1	2	yes	complemented
13	#10597383	—	2	2	no	—
14	#10597376	—	2	2	no	—
15	#10597372	C₂²	1	2	yes	—
16	#10597372	C₂²	1	1	yes	characteristic
17	#10597291	—	2	2	no	—
18	#10597278	—	2	4	no	—
19	C₂³×D₁₉	—	2	1	no	—
20	#41×C₁₉	—	2	2	no	—
21	#41×C₁₉	—	2	2	no	—
22	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×D₄×C₁₉	D₄	1	2	yes	—
25	C₂²×C₄×C₁₉	D₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂×C₂²⋊D₁₉	—	2	4	no	—
28	C₂×D₇₆	—	2	2	no	—
29	C₂×D₇₆	—	2	2	no	—
30	C₂×D₇₆	—	2	1	no	—
31	C₂×D₇₆	C₂×C₄	1	2	yes	—
32	M₁₆×C₁₉	—	2	4	no	—
33	M₁₆×C₁₉	—	2	2	no	—
34	M₁₆×C₁₉	—	2	2	no	—
35	C₂×C₈×C₁₉	—	2	4	no	—
36	C₂×C₈×C₁₉	D₄	1	4	yes	complemented
37	C₂²⋊Dic₁₉	—	2	1	no	—
38	C₂²⋊Dic₁₉	—	2	2	no	—
39	(C₂×D₁₉)⋊C₄	—	2	4	no	—
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	—	2	2	no	—
42	C₄×Dic₁₉	—	2	2	no	—
43	C₄×Dic₁₉	C₂×C₄	1	2	yes	—
44	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×D₁₉	—	2	2	no	—
47	C₂²×D₁₉	—	4	2	no	—
48	C₂²×D₁₉	—	8	2	no	—
49	Q₈×C₁₉	—	2	2	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	C₂²⋊C₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#41	1	2	yes	—
59	C₂²⋊D₁₉	—	8	4	no	—
60	C₂×Dic₁₉	—	2	2	no	—
61	C₂×Dic₁₉	—	4	2	no	—
62	D₇₆	—	2	4	no	—
63	D₇₆	—	4	1	no	—
64	D₇₆	—	4	1	no	—
65	C₈×C₁₉	—	2	4	no	—
66	#1910	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	—	2	2	no	—
68	C₂²×C₁₉	—	4	1	no	—
69	C₂²×C₁₉	—	4	2	no	—
70	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₁₉	#121	1	2	yes	—
72	C₂×D₁₉	—	4	4	no	—
73	C₂×D₁₉	—	4	2	no	—
74	C₂×D₁₉	—	8	4	no	—
75	C₄×C₁₉	—	2	2	no	—
76	C₄×C₁₉	C₄×D₄	1	2	yes	—
77	C₄×C₁₉	#120	1	1	yes	characteristic
78	C₄×C₁₉	#123	1	1	yes	characteristic
79	Dic₁₉	—	4	2	no	—
80	Dic₁₉	—	8	2	no	—
81	#568	D₁₉	1	1	yes	characteristic, complemented
82	#535	—	19	1	no	—
83	#418	—	19	2	no	—
84	#410	—	19	1	no	—
85	H(3,ℤ/4)	—	19	2	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	—	2	2	no	—
88	C₂×C₁₉	—	4	2	no	—
89	C₂×C₁₉	#386	1	1	yes	characteristic
90	D₁₉	—	8	2	no	—
91	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
92	C₂²×D₄	—	19	1	no	—
93	#131	—	2	4	no	—
94	C₂×M₁₆	—	2	2	no	—
95	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
96	#127	—	19	2	no	—
97	#124	—	19	2	no	—
98	#121	—	38	2	no	—
99	#120	—	38	2	no	—
100	#117	—	19	1	no	—
101	#117	—	19	2	no	—
102	#102	—	38	4	no	—
103	#99	—	38	2	no	—
104	C₁₉	#1910	1	1	yes	characteristic, complemented, Sylow
105	C₂⁴	—	38	1	no	—
106	#41	—	2	2	no	—
107	#41	—	2	2	no	—
108	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
109	C₂×D₄	—	19	2	no	—
110	C₂×D₄	—	38	4	no	—
111	C₂×D₄	—	38	2	no	—
112	C₂×D₄	—	38	2	no	—
113	C₂×D₄	—	38	1	no	—
114	C₂×D₄	C₄×D₁₉	1	1	yes	characteristic
115	C₂×D₄	D₇₆	1	2	yes	—
116	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
117	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
118	M₁₆	—	2	4	no	—
119	M₁₆	—	2	2	no	—
120	M₁₆	—	2	2	no	—
121	C₂×C₈	—	2	4	no	—
122	C₂×C₈	C₂²⋊D₁₉	1	4	yes	complemented
123	C₄⋊C₄	—	38	1	no	—
124	C₄⋊C₄	—	38	2	no	—
125	C₂²⋊C₄	—	38	1	no	—
126	C₂²⋊C₄	—	38	4	no	—
127	C₂²⋊C₄	—	38	2	no	—
128	C₄²	—	19	2	no	—
129	C₄²	—	38	2	no	—
130	C₂³	—	38	2	no	—
131	C₂³	—	76	2	no	—
132	C₂³	—	152	2	no	—
133	C₂³	(C₂×D₁₉)⋊C₄	1	2	yes	—
134	C₂³	C₂×D₇₆	1	1	yes	characteristic
135	Q₈	—	2	2	no	—
136	D₄	—	2	4	no	—
137	D₄	—	2	2	no	—
138	D₄	—	38	4	no	—
139	D₄	—	76	1	no	—
140	D₄	—	76	1	no	—
141	D₄	—	152	4	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	38	2	no	—
145	C₂×C₄	—	76	2	no	—
146	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
147	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
148	C₂×C₄	#64541	1	2	yes	—
149	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
150	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
151	C₈	—	2	4	no	—
152	C₂²	—	2	2	no	—
153	C₂²	—	4	1	no	—
154	C₂²	—	4	2	no	—
155	C₂²	—	76	4	no	—
156	C₂²	—	76	2	no	—
157	C₂²	—	152	4	no	—
158	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
159	C₂²	#10597376	1	2	yes	—
160	C₄	—	2	2	no	—
161	C₄	—	76	2	no	—
162	C₄	—	152	2	no	—
163	C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
164	C₄	#10597375	1	1	yes	characteristic
165	C₄	#10597399	1	1	yes	characteristic
166	C₂	—	2	1	no	—
167	C₂	—	2	2	no	—
168	C₂	—	4	2	no	—
169	C₂	—	152	2	no	—
170	C₂	#11926423	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927108

C₂

yes

maximal, characteristic

#11926550

C₂

yes

maximal, complemented

#11926518

C₂

yes

maximal, characteristic, complemented

#11926301

C₂

yes

maximal, complemented

C₁₉×#568

C₂

yes

maximal, characteristic, complemented

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂²×D₇₆

C₂²

yes

characteristic

C₁₉×#131

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂²

yes

—

#10597393

C₄

yes

complemented

#10597386

C₄

yes

—

—

C₂²

yes

—

#10597372

C₂²

yes

characteristic

#10597291

—

#10597278

—

C₂³×D₁₉

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

complemented

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂×C₄

yes

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×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

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

#1910

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#121

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

#568

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#386

yes

characteristic

D₁₉

—

C₂×#41

C₂×D₁₉

yes

characteristic

C₂²×D₄

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

—

—

—

—

100

#117

—

101

#117

—

102

#102

—

103

#99

—

104

C₁₉

#1910

yes

characteristic, complemented, Sylow

105

C₂⁴

—

106

#41

—

107

#41

—

108

C₂×Q₈

C₄×D₁₉

yes

characteristic

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

C₄×D₁₉

yes

characteristic

115

C₂×D₄

D₇₆

yes

—

116

C₂²×C₄

C₂²⋊D₁₉

yes

—

117

C₂²×C₄

C₂²×D₁₉

yes

characteristic

118

M₁₆

—

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

C₂²⋊D₁₉

yes

complemented

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₄²

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

152

—

133

C₂³

(C₂×D₁₉)⋊C₄

yes

—

134

C₂³

C₂×D₇₆

yes

characteristic

135

Q₈

—

136

D₄

—

137

D₄

—

138

D₄

—

139

D₄

—

140

D₄

—

141

D₄

—

152

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

147

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

148

C₂×C₄

#64541

yes

—

149

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

150

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

151

C₈

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

152

—

158

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

159

C₂²

#10597376

yes

—

160

C₄

—

161

C₄

—

162

C₄

—

152

—

163

C₄

C₄×C₂²⋊D₁₉

yes

—

164

C₄

#10597375

yes

characteristic

165

C₄

#10597399

yes

characteristic

166

C₂

—

167

C₂

—

168

C₂

—

169

C₂

—

152

—

170

C₂

#11926423

yes

characteristic

	subgroup	G/H
center	C₂	#11926423
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#568	C₂
socle	C₂×C₁₉	#386
prime radical	#11927108	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#568	D₁₉
hypocenter	C₁₉	#1910
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #568

subgroup

G/H

center

C₂

#11926423

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#568

C₂

C₂×C₁₉

C₂

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #568

N	H ≅ G/N	type
2. #11926550	C₂	semidirect
3. #11926518	C₂	semidirect
4. #11926301	C₂	semidirect
5. C₁₉×#568	C₂	semidirect
11. #10597393	C₄	semidirect
12. #10597386	C₄	semidirect
36. C₂×C₈×C₁₉	D₄	semidirect
81. #568	D₁₉	semidirect
104. C₁₉	#1910	semidirect
122. C₂×C₈	C₂²⋊D₁₉	semidirect

H ≅ G/N

type

2. #11926550

C₂

semidirect

3. #11926518

C₂

semidirect

4. #11926301

C₂

semidirect

5. C₁₉×#568

C₂

semidirect

11. #10597393

C₄

semidirect

12. #10597386

C₄

semidirect

36. C₂×C₈×C₁₉

D₄

semidirect

81. #568

D₁₉

semidirect

104. C₁₉

#1910

semidirect

122. C₂×C₈

C₂²⋊D₁₉

semidirect

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

subgroup	index
#11927108	2
#11926550	2
#11926518	2
#11926301	2
C₁₉×#568	2
#1910	19

subgroup

index

C₁₉×#568

Subgroups — #14564162

Conjugacy classes of subgroups

Complements

Maximal subgroups