Group #14564183 — subgroups

Subgroups — #14564183

Order 2432.

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

normal subgroups only

This group has 340 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, complemented
2	#11926528	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597290	C₂	1	2	yes	maximal, complemented
4	#11926314	C₂	1	2	yes	maximal, complemented
5	C₁₉×#535	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#127	—	2	1	no	—
9	C₁₉×#124	—	2	1	no	—
10	C₁₉×#121	—	2	2	no	—
11	C₁₉×#120	C₄	1	4	yes	—
12	C₁₉×#117	C₂²	1	1	yes	characteristic
13	#10597394	—	2	4	no	—
14	C₂×#64520	—	2	2	no	—
15	C₂×#64520	C₂²	1	2	yes	—
16	C₂×#64520	C₂²	1	2	yes	—
17	#10597293	—	2	1	no	—
18	#10597290	—	2	1	no	—
19	#10597290	—	2	4	no	—
20	C₂⁴×C₁₉	C₂×C₄	1	2	yes	—
21	#41×C₁₉	—	2	2	no	—
22	#41×C₁₉	—	2	2	no	—
23	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×D₄×C₁₉	—	2	4	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×D₄×C₁₉	—	2	2	no	—
28	C₂×D₄×C₁₉	—	2	2	no	—
29	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₉	D₄	1	2	yes	—
32	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂²⋊C₄×C₁₉	—	2	4	no	—
35	C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
36	C₄²×C₁₉	—	2	1	no	—
37	#64520	—	2	4	no	—
38	#64520	—	2	2	no	—
39	#64520	—	2	2	no	—
40	#64520	—	2	2	no	—
41	#64520	D₄	1	4	yes	complemented
42	C₂×C₁₉⋊C₈	—	2	4	no	—
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂³×C₁₉	—	2	2	no	—
46	C₂³×C₁₉	—	2	4	no	—
47	C₂³×C₁₉	—	8	2	no	—
48	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	Q₈×C₁₉	—	2	2	no	—
51	D₄×C₁₉	—	2	4	no	—
52	D₄×C₁₉	—	2	2	no	—
53	D₄×C₁₉	—	4	1	no	—
54	D₄×C₁₉	—	4	2	no	—
55	D₄×C₁₉	—	4	1	no	—
56	D₄×C₁₉	—	8	4	no	—
57	C₂×C₄×C₁₉	—	2	2	no	—
58	C₂×C₄×C₁₉	—	2	2	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
61	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
62	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₉	#41	1	2	yes	—
65	C₁₉⋊C₈	—	2	4	no	—
66	C₁₉⋊C₈	—	4	2	no	—
67	#1914	—	19	1	no	maximal, Sylow
68	C₂²×C₁₉	—	2	2	no	—
69	C₂²×C₁₉	—	4	1	no	—
70	C₂²×C₁₉	—	4	2	no	—
71	C₂²×C₁₉	—	4	4	no	—
72	C₂²×C₁₉	—	4	2	no	—
73	C₂²×C₁₉	—	8	4	no	—
74	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₁₉	C₄×D₄	1	2	yes	—
76	C₄×C₁₉	—	2	2	no	—
77	C₄×C₁₉	—	4	2	no	—
78	C₄×C₁₉	#120	1	1	yes	characteristic
79	C₄×C₁₉	#121	1	2	yes	—
80	C₄×C₁₉	#123	1	1	yes	characteristic
81	#568	—	19	1	no	—
82	#535	D₁₉	1	1	yes	characteristic
83	#413	—	19	1	no	—
84	C₂×#100	—	19	2	no	—
85	#344	—	19	2	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	—	2	2	no	—
88	C₂×C₁₉	—	4	2	no	—
89	C₂×C₁₉	—	8	2	no	—
90	C₂×C₁₉	#386	1	1	yes	characteristic
91	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
92	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
93	#131	—	38	4	no	—
94	C₂×M₁₆	—	19	2	no	—
95	C₂×M₁₆	—	19	2	no	—
96	C₂×M₁₆	—	38	2	no	—
97	#127	—	2	1	no	—
98	#124	—	2	1	no	—
99	#121	—	2	2	no	—
100	#120	Dic₁₉	1	4	yes	—
101	#117	C₂×D₁₉	1	1	yes	characteristic
102	#101	—	38	1	no	—
103	#100	—	38	4	no	—
104	#100	—	38	1	no	—
105	C₁₉	#1914	1	1	yes	characteristic, complemented, Sylow
106	C₂⁴	C₂×Dic₁₉	1	2	yes	—
107	#41	—	2	2	no	—
108	#41	—	2	2	no	—
109	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂×D₄	—	2	4	no	—
111	C₂×D₄	—	2	2	no	—
112	C₂×D₄	—	2	2	no	—
113	C₂×D₄	—	2	1	no	—
114	C₂×D₄	—	2	1	no	—
115	C₂×D₄	C₂×Dic₁₉	1	2	yes	—
116	C₂×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
117	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
118	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
119	M₁₆	—	19	4	no	—
120	M₁₆	—	38	4	no	—
121	M₁₆	—	38	2	no	—
122	M₁₆	—	38	2	no	—
123	M₁₆	—	38	2	no	—
124	C₂×C₈	—	38	4	no	—
125	C₂×C₈	—	38	2	no	—
126	C₂×C₈	—	38	2	no	—
127	C₄⋊C₄	—	2	1	no	—
128	C₂²⋊C₄	—	2	4	no	—
129	C₂²⋊C₄	C₂×Dic₁₉	1	2	yes	—
130	C₄²	—	2	1	no	—
131	C₂³	—	2	2	no	—
132	C₂³	—	2	4	no	—
133	C₂³	—	8	2	no	—
134	C₂³	C₂²⋊Dic₁₉	1	2	yes	—
135	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
136	Q₈	—	2	2	no	—
137	D₄	—	2	4	no	—
138	D₄	—	2	2	no	—
139	D₄	—	4	1	no	—
140	D₄	—	4	1	no	—
141	D₄	—	4	2	no	—
142	D₄	—	8	4	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	2	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
147	C₂×C₄	D₄×D₁₉	1	2	yes	—
148	C₂×C₄	#64543	1	2	yes	—
149	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
150	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
151	C₈	—	38	4	no	—
152	C₈	—	76	2	no	—
153	C₂²	—	2	2	no	—
154	C₂²	—	4	1	no	—
155	C₂²	—	4	2	no	—
156	C₂²	—	4	4	no	—
157	C₂²	—	4	2	no	—
158	C₂²	—	8	4	no	—
159	C₂²	D₄×Dic₁₉	1	2	yes	—
160	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
161	C₄	—	2	2	no	—
162	C₄	—	4	2	no	—
163	C₄	#10597381	1	1	yes	characteristic
164	C₄	#10597383	1	1	yes	characteristic
165	C₄	#10597385	1	2	yes	—
166	C₂	—	2	1	no	—
167	C₂	—	2	2	no	—
168	C₂	—	4	2	no	—
169	C₂	—	8	2	no	—
170	C₂	#11926424	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927311

C₂

yes

maximal, characteristic, complemented

#11926528

C₂

yes

maximal, characteristic, complemented

C₂×#10597290

C₂

yes

maximal, complemented

#11926314

C₂

yes

maximal, complemented

C₁₉×#535

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₁₉×#127

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#120

C₄

yes

—

C₁₉×#117

C₂²

yes

—

—

C₂²

yes

—

C₂×#64520

C₂²

yes

—

#10597293

—

#10597290

—

#10597290

—

C₂⁴×C₁₉

C₂×C₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

—

—

—

—

—

D₄

yes

complemented

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1914

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#121

yes

—

C₄×C₁₉

yes

—

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#386

yes

characteristic

C₂×#41

C₂×D₁₉

yes

characteristic

C₂²×D₄

C₂×D₁₉

yes

characteristic

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

#127

—

#124

—

#121

—

100

#120

Dic₁₉

yes

—

101

#117

C₂×D₁₉

yes

characteristic

102

#101

—

103

#100

—

104

#100

—

105

C₁₉

#1914

yes

characteristic, complemented, Sylow

106

C₂⁴

C₂×Dic₁₉

yes

—

107

#41

—

108

#41

—

109

C₂×Q₈

C₂²⋊D₁₉

yes

characteristic

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

C₂×Dic₁₉

yes

—

116

C₂×D₄

C₂²⋊D₁₉

yes

characteristic

117

C₂²×C₄

C₂²⋊D₁₉

yes

—

118

C₂²×C₄

C₂²×D₁₉

yes

characteristic

119

M₁₆

—

120

M₁₆

—

121

M₁₆

—

122

M₁₆

—

123

M₁₆

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₄⋊C₄

—

128

C₂²⋊C₄

—

129

C₂²⋊C₄

C₂×Dic₁₉

yes

—

130

C₄²

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

C₂²⋊Dic₁₉

yes

—

135

C₂³

C₂²×Dic₁₉

yes

characteristic

136

Q₈

—

137

D₄

—

138

D₄

—

139

D₄

—

140

D₄

—

141

D₄

—

142

D₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

C₂²⋊Dic₁₉

yes

—

147

C₂×C₄

D₄×D₁₉

yes

—

148

C₂×C₄

#64543

yes

—

149

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

150

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

151

C₈

—

152

C₈

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

D₄×Dic₁₉

yes

—

160

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

161

C₄

—

162

C₄

—

163

C₄

#10597381

yes

characteristic

164

C₄

#10597383

yes

characteristic

165

C₄

#10597385

yes

—

166

C₂

—

167

C₂

—

168

C₂

—

169

C₂

—

170

C₂

#11926424

yes

characteristic

	subgroup	G/H
center	C₂	#11926424
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting, prime radical	C₁₉×#535	C₂
socle	C₂×C₁₉	#386
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#535	D₁₉
hypocenter	C₁₉	#1914
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #535

subgroup

G/H

center

C₂

#11926424

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting, prime radical

C₁₉×#535

C₂

socle

C₂×C₁₉

#386

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #535

N	H ≅ G/N	type
1. #11927311	C₂	semidirect
2. #11926528	C₂	semidirect
3. C₂×#10597290	C₂	semidirect
4. #11926314	C₂	semidirect
41. #64520	D₄	semidirect
105. C₁₉	#1914	semidirect

H ≅ G/N

type

1. #11927311

C₂

semidirect

2. #11926528

C₂

semidirect

3. C₂×#10597290

C₂

semidirect

4. #11926314

C₂

semidirect

41. #64520

D₄

semidirect

105. C₁₉

#1914

semidirect

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

subgroup	index
#11927311	2
#11926528	2
C₂×#10597290	2
#11926314	2
C₁₉×#535	2
#1914	19

subgroup

index

C₁₉×#535

Subgroups — #14564183

Conjugacy classes of subgroups

Complements

Maximal subgroups