Group #14564717 — subgroups

Subgroups — #14564717

Order 2432.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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	C₂²×#64526	C₂	1	2	yes	maximal
2	C₂×#10597315	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597267	C₂	1	2	yes	maximal, complemented
4	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#390	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×#64526	—	2	4	no	—
12	C₂×#64526	—	2	4	no	—
13	C₂×#64526	—	2	4	no	—
14	C₂×C₄⋊Dic₁₉	—	2	2	no	—
15	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
16	#10597315	—	2	4	no	—
17	#10597267	—	2	4	no	—
18	C₂⁴×C₁₉	—	2	1	no	—
19	C₂×D₄×C₁₉	—	2	2	no	—
20	C₂×D₄×C₁₉	—	2	2	no	—
21	C₂×D₄×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	D₄	1	2	yes	—
23	C₂²×C₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	D₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	2	2	no	—
27	C₂×Dic₃₈	—	2	2	no	—
28	C₂×Dic₃₈	—	2	2	no	—
29	C₂×Dic₃₈	—	2	2	no	—
30	C₂×Dic₃₈	—	2	2	no	—
31	C₂×Dic₃₈	—	2	2	no	—
32	C₂×Dic₃₈	D₄	1	4	yes	—
33	C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂²⋊C₄×C₁₉	—	4	4	no	—
35	C₄²×C₁₉	—	2	2	no	—
36	#64526	—	2	16	no	—
37	C₄⋊Dic₁₉	—	2	8	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
41	C₂³×C₁₉	—	2	2	no	—
42	C₂³×C₁₉	—	4	1	no	—
43	C₂³×C₁₉	—	4	1	no	—
44	C₂³×C₁₉	—	4	2	no	—
45	C₂³×C₁₉	—	4	2	no	—
46	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
47	D₄×C₁₉	—	2	4	no	—
48	D₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	2	no	—
53	C₂×C₄×C₁₉	SD₁₆	1	4	yes	complemented
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
58	C₂×Dic₁₉	—	2	4	no	—
59	C₂×Dic₁₉	—	4	2	no	—
60	C₂×Dic₁₉	—	4	2	no	—
61	Dic₃₈	—	2	4	no	—
62	Dic₃₈	—	2	4	no	—
63	Dic₃₈	—	4	2	no	—
64	Dic₃₈	—	4	2	no	—
65	C₁₉⋊C₈	—	2	4	no	—
66	#2013	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	—	4	2	no	—
68	C₂²×C₁₉	—	4	4	no	—
69	C₂²×C₁₉	—	8	2	no	—
70	C₂²×C₁₉	—	8	1	no	—
71	C₂²×C₁₉	—	8	1	no	—
72	C₂²×C₁₉	#120	1	1	yes	characteristic
73	C₂²×C₁₉	#121	1	1	yes	characteristic
74	C₂²×C₁₉	#127	1	1	yes	characteristic
75	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	—
76	C₂²×C₁₉	#137	1	2	yes	—
77	C₄×C₁₉	—	2	4	no	—
78	C₄×C₁₉	—	8	1	no	—
79	C₄×C₁₉	#120	1	2	yes	—
80	C₄×C₁₉	#121	1	2	yes	—
81	Dic₁₉	—	4	4	no	—
82	C₂²×SD₁₆	—	19	2	no	—
83	C₂×C₄⋊Q₈	—	19	1	no	—
84	C₂×#103	—	19	2	no	—
85	#390	D₁₉	1	1	yes	characteristic
86	#336	—	19	1	no	—
87	C₂×C₁₉	—	8	2	no	—
88	C₂×C₁₉	#392	1	1	yes	characteristic
89	C₂×C₁₉	#448	1	2	yes	—
90	C₂×C₁₉	#461	1	2	yes	—
91	C₂×C₁₉	#492	1	1	yes	characteristic
92	C₂×C₁₉	#497	1	1	yes	characteristic
93	C₂²×Q₈	—	19	2	no	—
94	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
95	C₂×SD₁₆	—	38	4	no	—
96	C₂×SD₁₆	—	38	4	no	—
97	C₂×SD₁₆	—	38	4	no	—
98	C₂²×C₈	—	19	2	no	—
99	C₄⋊Q₈	—	38	4	no	—
100	C₂×C₄⋊C₄	—	38	2	no	—
101	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
102	C₂×C₂²⋊C₄	—	2	2	no	—
103	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
104	#103	—	38	4	no	—
105	C₁₉	#2013	1	1	yes	characteristic, complemented, Sylow
106	C₂⁴	—	2	1	no	—
107	C₂×Q₈	—	19	4	no	—
108	C₂×Q₈	—	38	2	no	—
109	C₂×Q₈	—	38	2	no	—
110	C₂×Q₈	—	38	2	no	—
111	C₂×Q₈	—	38	2	no	—
112	C₂×Q₈	—	38	2	no	—
113	C₂×D₄	—	2	1	no	—
114	C₂×D₄	—	2	2	no	—
115	C₂×D₄	—	2	2	no	—
116	C₂×D₄	D₇₆	1	2	yes	—
117	C₂²×C₄	—	2	1	no	—
118	C₂²×C₄	—	38	2	no	—
119	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
120	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
121	SD₁₆	—	38	16	no	—
122	C₂×C₈	—	19	4	no	—
123	C₂×C₈	—	38	2	no	—
124	C₂×C₈	—	38	2	no	—
125	C₄⋊C₄	—	2	2	no	—
126	C₄⋊C₄	—	38	8	no	—
127	C₂²⋊C₄	—	4	4	no	—
128	C₄²	—	2	2	no	—
129	C₂³	—	2	2	no	—
130	C₂³	—	4	2	no	—
131	C₂³	—	4	1	no	—
132	C₂³	—	4	1	no	—
133	C₂³	—	4	2	no	—
134	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
135	Q₈	—	38	4	no	—
136	Q₈	—	38	4	no	—
137	Q₈	—	76	2	no	—
138	Q₈	—	76	2	no	—
139	D₄	—	2	4	no	—
140	D₄	—	4	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	2	no	—
143	C₂×C₄	—	4	2	no	—
144	C₂×C₄	—	4	1	no	—
145	C₂×C₄	—	38	4	no	—
146	C₂×C₄	—	76	2	no	—
147	C₂×C₄	—	76	2	no	—
148	C₂×C₄	#64526	1	4	yes	complemented
149	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
150	C₂×C₄	#64541	1	1	yes	characteristic
151	C₂×C₄	D₄×D₁₉	1	2	yes	—
152	C₂×C₄	D₄×D₁₉	1	2	yes	—
153	C₈	—	38	4	no	—
154	C₂²	—	4	2	no	—
155	C₂²	—	4	4	no	—
156	C₂²	—	8	1	no	—
157	C₂²	—	8	2	no	—
158	C₂²	—	8	1	no	—
159	C₂²	#10597376	1	1	yes	characteristic
160	C₂²	C₂×#64526	1	2	yes	—
161	C₂²	#10597383	1	1	yes	characteristic
162	C₂²	#10597386	1	1	yes	characteristic
163	C₂²	#10597397	1	2	yes	—
164	C₄	—	2	4	no	—
165	C₄	—	8	1	no	—
166	C₄	—	76	4	no	—
167	C₄	#10597328	1	2	yes	—
168	C₄	#10597330	1	2	yes	—
169	C₂	—	8	2	no	—
170	C₂	#11926453	1	1	yes	characteristic
171	C₂	#11926682	1	2	yes	—
172	C₂	#11926749	1	2	yes	—
173	C₂	#11926916	1	1	yes	characteristic
174	C₂	#11926939	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64526

C₂

yes

maximal

C₂×#10597315

C₂

yes

maximal, characteristic, complemented

C₂×#10597267

C₂

yes

maximal, complemented

#11926299

C₂

yes

maximal, characteristic, complemented

C₁₉×#390

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

—

—

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597315

—

#10597267

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

#64526

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

complemented

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

#2013

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

C₂²×SD₁₆

—

C₂×C₄⋊Q₈

—

C₂×#103

—

#390

D₁₉

yes

characteristic

#336

—

C₂×C₁₉

—

C₂×C₁₉

#392

yes

characteristic

C₂×C₁₉

#448

yes

—

C₂×C₁₉

#461

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂×SD₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

102

C₂×C₂²⋊C₄

—

103

C₂×C₄²

C₂×D₁₉

yes

characteristic

104

#103

—

105

C₁₉

#2013

yes

characteristic, complemented, Sylow

106

C₂⁴

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

D₇₆

yes

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

C₂²⋊D₁₉

yes

—

120

C₂²×C₄

C₂²×D₁₉

yes

characteristic

121

SD₁₆

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₂³

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

135

Q₈

—

136

Q₈

—

137

Q₈

—

138

Q₈

—

139

D₄

—

140

D₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

#64526

yes

complemented

149

C₂×C₄

C₂×D₇₆

yes

characteristic

150

C₂×C₄

#64541

yes

characteristic

151

C₂×C₄

D₄×D₁₉

yes

—

152

C₂×C₄

D₄×D₁₉

yes

—

153

C₈

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

#10597376

yes

characteristic

160

C₂²

C₂×#64526

yes

—

161

C₂²

#10597383

yes

characteristic

162

C₂²

#10597386

yes

characteristic

163

C₂²

#10597397

yes

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

#10597328

yes

—

168

C₄

#10597330

yes

—

169

C₂

—

170

C₂

#11926453

yes

characteristic

171

C₂

#11926682

yes

—

172

C₂

#11926749

yes

—

173

C₂

#11926916

yes

characteristic

174

C₂

#11926939

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#390	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	#390	D₁₉
hypocenter	C₁₉	#2013
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#390

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

N	H ≅ G/N	type
2. C₂×#10597315	C₂	semidirect
3. C₂×#10597267	C₂	semidirect
4. #11926299	C₂	semidirect
53. C₂×C₄×C₁₉	SD₁₆	semidirect
105. C₁₉	#2013	semidirect
148. C₂×C₄	#64526	semidirect

H ≅ G/N

type

2. C₂×#10597315

C₂

semidirect

3. C₂×#10597267

C₂

semidirect

4. #11926299

C₂

semidirect

53. C₂×C₄×C₁₉

SD₁₆

semidirect

105. C₁₉

#2013

semidirect

148. C₂×C₄

#64526

semidirect

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

subgroup	index
C₂²×#64526	2
C₂×#10597315	2
C₂×#10597267	2
#11926299	2
C₁₉×#390	2
#2013	19

subgroup

index

C₂²×#64526

C₁₉×#390

Subgroups — #14564717

Conjugacy classes of subgroups

Complements

Maximal subgroups