Group #14564997 — subgroups

Subgroups — #14564997

Order 2432.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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	#11926586	C₂	1	1	yes	maximal, characteristic
2	#11926570	C₂	1	1	yes	maximal, characteristic
3	#11926554	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597273	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597281	C₂	1	1	yes	maximal, characteristic
6	#11926312	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#108	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597372	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
14	C₂×#64520	C₂²	1	1	yes	characteristic
15	C₁₉×#108	—	2	2	no	—
16	#10597281	—	2	2	no	—
17	#10597275	—	2	1	no	—
18	#10597274	—	2	1	no	—
19	#10597273	—	2	2	no	—
20	#10597273	—	2	1	no	—
21	#10597273	—	2	1	no	—
22	Dic₁₉⋊C₈	—	2	2	no	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₉	—	2	1	no	—
25	C₂²×Dic₁₉	—	2	1	no	—
26	C₂×Dic₃₈	—	2	1	no	—
27	C₂×Dic₃₈	—	2	1	no	—
28	C₂×Dic₃₈	—	2	1	no	—
29	C₂×Dic₃₈	—	2	1	no	—
30	C₂×Dic₃₈	—	2	1	no	—
31	C₂×Dic₃₈	Q₈	1	2	yes	—
32	M₁₆×C₁₉	—	2	1	no	—
33	M₁₆×C₁₉	—	2	1	no	—
34	M₁₆×C₁₉	—	2	1	no	—
35	M₁₆×C₁₉	D₄	1	2	yes	—
36	C₂×C₈×C₁₉	—	2	1	no	—
37	C₂×C₈×C₁₉	—	2	1	no	—
38	C₂×C₈×C₁₉	—	2	1	no	—
39	C₂×C₈×C₁₉	—	2	1	no	—
40	C₂×C₈×C₁₉	D₄	1	2	yes	—
41	C₂²⋊Dic₁₉	—	2	1	no	—
42	C₄⋊Dic₁₉	—	2	1	no	—
43	C₄⋊Dic₁₉	—	2	1	no	—
44	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
45	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
46	C₄×Dic₁₉	—	2	1	no	—
47	#64520	—	2	1	no	—
48	#64520	—	2	1	no	—
49	C₂×C₁₉⋊C₈	—	2	1	no	—
50	C₂³×C₁₉	#41	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
57	C₂×Dic₁₉	—	2	1	no	—
58	C₂×Dic₁₉	—	2	1	no	—
59	C₂×Dic₁₉	—	2	2	no	—
60	C₂×Dic₁₉	—	4	1	no	—
61	C₂×Dic₁₉	—	4	1	no	—
62	C₂×Dic₁₉	—	4	1	no	—
63	C₂×Dic₁₉	—	8	1	no	—
64	Dic₃₈	—	2	2	no	—
65	Dic₃₈	—	2	2	no	—
66	Dic₃₈	—	4	1	no	—
67	Dic₃₈	—	4	1	no	—
68	C₈×C₁₉	—	2	2	no	—
69	C₈×C₁₉	—	2	2	no	—
70	C₈×C₁₉	—	4	1	no	—
71	C₁₉⋊C₈	—	4	1	no	—
72	#2064	—	19	1	no	maximal, Sylow
73	C₂²×C₁₉	—	2	1	no	—
74	C₂²×C₁₉	—	2	1	no	—
75	C₂²×C₁₉	#121	1	1	yes	characteristic
76	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
77	C₂²×C₁₉	#126	1	1	yes	characteristic
78	C₄×C₁₉	#121	1	1	yes	characteristic
79	C₄×C₁₉	#121	1	1	yes	characteristic
80	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
81	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
82	Dic₁₉	—	4	2	no	—
83	Dic₁₉	—	4	1	no	—
84	Dic₁₉	—	4	1	no	—
85	Dic₁₉	—	8	1	no	—
86	C₂×#108	D₁₉	1	1	yes	characteristic
87	#428	—	19	1	no	—
88	#424	—	19	1	no	—
89	#419	—	19	1	no	—
90	C₂×#103	—	19	1	no	—
91	C₂×#101	—	19	1	no	—
92	#343	—	19	1	no	—
93	C₂×C₁₉	—	2	1	no	—
94	C₂×C₁₉	—	2	1	no	—
95	C₂×C₁₉	#396	1	1	yes	characteristic
96	C₂×C₁₉	#471	1	1	yes	characteristic
97	C₂×C₁₉	#473	1	1	yes	characteristic
98	C₂²×Q₈	—	19	1	no	—
99	C₂×M₁₆	—	19	1	no	—
100	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
101	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
102	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
103	#117	—	19	1	no	—
104	C₂×C₄⋊C₄	—	19	1	no	—
105	#108	—	2	2	no	—
106	#107	—	38	1	no	—
107	#106	—	38	1	no	—
108	C₄⋊C₈	—	38	2	no	—
109	#103	—	38	1	no	—
110	#103	—	38	1	no	—
111	#103	—	38	2	no	—
112	#101	—	38	2	no	—
113	C₁₉	#2064	1	1	yes	characteristic, complemented, Sylow
114	C₂×Q₈	—	19	2	no	—
115	C₂×Q₈	—	38	1	no	—
116	C₂×Q₈	—	38	1	no	—
117	C₂×Q₈	—	38	1	no	—
118	C₂×Q₈	—	38	1	no	—
119	C₂×Q₈	—	38	1	no	—
120	C₂²×C₄	—	38	1	no	—
121	C₂²×C₄	—	38	1	no	—
122	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
123	M₁₆	—	2	1	no	—
124	M₁₆	—	2	1	no	—
125	M₁₆	—	2	1	no	—
126	M₁₆	—	38	1	no	—
127	M₁₆	—	38	1	no	—
128	M₁₆	C₂²⋊D₁₉	1	2	yes	—
129	C₂×C₈	—	2	1	no	—
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	—	2	1	no	—
132	C₂×C₈	—	2	1	no	—
133	C₂×C₈	—	38	1	no	—
134	C₂×C₈	D₇₆	1	2	yes	—
135	C₄⋊C₄	—	19	1	no	—
136	C₄⋊C₄	—	19	1	no	—
137	C₄⋊C₄	—	38	1	no	—
138	C₄⋊C₄	—	38	1	no	—
139	C₂²⋊C₄	—	38	1	no	—
140	C₄²	—	38	1	no	—
141	C₂³	#64545	1	1	yes	characteristic
142	Q₈	—	38	2	no	—
143	Q₈	—	38	2	no	—
144	Q₈	—	76	1	no	—
145	Q₈	—	76	1	no	—
146	C₂×C₄	—	38	2	no	—
147	C₂×C₄	—	38	1	no	—
148	C₂×C₄	—	38	1	no	—
149	C₂×C₄	—	76	1	no	—
150	C₂×C₄	—	76	1	no	—
151	C₂×C₄	—	76	1	no	—
152	C₂×C₄	—	152	1	no	—
153	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
154	C₂×C₄	#64541	1	1	yes	characteristic
155	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
156	C₂×C₄	#64543	1	1	yes	characteristic
157	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
158	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
159	C₈	—	2	2	no	—
160	C₈	—	2	2	no	—
161	C₈	—	4	1	no	—
162	C₈	—	76	1	no	—
163	C₂²	—	2	1	no	—
164	C₂²	—	2	1	no	—
165	C₂²	#10597341	1	1	yes	characteristic
166	C₂²	#10597344	1	1	yes	characteristic
167	C₂²	#10597392	1	1	yes	characteristic
168	C₄	—	76	1	no	—
169	C₄	—	76	1	no	—
170	C₄	—	76	2	no	—
171	C₄	—	152	1	no	—
172	C₄	#10597342	1	1	yes	characteristic
173	C₄	#10597343	1	1	yes	characteristic
174	C₄	#10597376	1	1	yes	characteristic
175	C₄	#10597385	1	1	yes	characteristic
176	C₂	—	2	1	no	—
177	C₂	—	2	1	no	—
178	C₂	#11926466	1	1	yes	characteristic
179	C₂	#11926808	1	1	yes	characteristic
180	C₂	#11926820	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926586

C₂

yes

maximal, characteristic

#11926570

C₂

yes

maximal, characteristic

#11926554

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal, characteristic

C₂×#10597281

C₂

yes

maximal, characteristic

#11926312

C₂

yes

maximal, characteristic

C₂×C₁₉×#108

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₁₉×#108

—

—

—

—

—

—

—

Dic₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2064

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#108

D₁₉

yes

—

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂×M₁₆

—

100

C₂×M₁₆

C₂×D₁₉

yes

characteristic

101

C₂×M₁₆

C₂×D₁₉

yes

characteristic

102

C₂²×C₈

C₂×D₁₉

yes

characteristic

103

#117

—

104

C₂×C₄⋊C₄

—

105

#108

—

106

#107

—

107

#106

—

108

C₄⋊C₈

—

109

#103

—

110

#103

—

111

#103

—

112

#101

—

113

C₁₉

#2064

yes

characteristic, complemented, Sylow

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

C₂²×D₁₉

yes

characteristic

123

M₁₆

—

124

M₁₆

—

125

M₁₆

—

126

M₁₆

—

127

M₁₆

—

128

M₁₆

C₂²⋊D₁₉

yes

—

129

C₂×C₈

—

130

C₂×C₈

—

131

C₂×C₈

—

132

C₂×C₈

—

133

C₂×C₈

—

134

C₂×C₈

D₇₆

yes

—

135

C₄⋊C₄

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₂²⋊C₄

—

140

C₄²

—

141

C₂³

#64545

yes

characteristic

142

Q₈

—

143

Q₈

—

144

Q₈

—

145

Q₈

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

152

—

153

C₂×C₄

C₂×D₇₆

yes

characteristic

154

C₂×C₄

#64541

yes

characteristic

155

C₂×C₄

D₄×D₁₉

yes

characteristic

156

C₂×C₄

#64543

yes

characteristic

157

C₂×C₄

Q₈×D₁₉

yes

characteristic

158

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

159

C₈

—

160

C₈

—

161

C₈

—

162

C₈

—

163

C₂²

—

164

C₂²

—

165

C₂²

#10597341

yes

characteristic

166

C₂²

#10597344

yes

characteristic

167

C₂²

#10597392

yes

characteristic

168

C₄

—

169

C₄

—

170

C₄

—

171

C₄

—

152

—

172

C₄

#10597342

yes

characteristic

173

C₄

#10597343

yes

characteristic

174

C₄

#10597376

yes

characteristic

175

C₄

#10597385

yes

characteristic

176

C₂

—

177

C₂

—

178

C₂

#11926466

yes

characteristic

179

C₂

#11926808

yes

characteristic

180

C₂

#11926820

yes

characteristic

	subgroup	G/H
center	C₂²	#10597341
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#108	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂³×C₁₉	#41
hypercenter	C₂×#108	D₁₉
hypocenter	C₁₉	#2064
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂²

#10597341

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#108

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
113. C₁₉	#2064	semidirect

H ≅ G/N

type

113. C₁₉

#2064

semidirect

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

subgroup	index
#11926586	2
#11926570	2
#11926554	2
C₂×#10597273	2
C₂×#10597281	2
#11926312	2
C₂×C₁₉×#108	2
#2064	19

subgroup

index

C₂×C₁₉×#108

Subgroups — #14564997

Conjugacy classes of subgroups

Complements

Maximal subgroups