Group #14562801 — subgroups

Subgroups — #14562801

Order 2432.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11927209	C₂	1	1	yes	maximal, characteristic
2	#11926896	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926840	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926835	C₂	1	1	yes	maximal, characteristic
5	#11926274	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926271	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₁₉	—	2	1	no	—
9	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	#10597392	—	2	1	no	—
11	#10597342	—	2	2	no	—
12	#10597339	—	2	1	no	—
13	#10597334	—	2	1	no	—
14	C₄×D₇₆	C₂²	1	1	yes	characteristic
15	#10597315	C₂²	1	1	yes	characteristic
16	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	#10597278	—	2	1	no	—
20	#10597275	—	2	1	no	—
21	#10597274	—	2	1	no	—
22	#10597273	—	2	1	no	—
23	#10597267	—	2	2	no	—
24	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	Q₈×D₁₉	—	4	2	no	—
27	Q₈×D₁₉	—	4	2	no	—
28	C₂×D₇₆	D₄	1	1	yes	characteristic
29	C₂×C₄×D₁₉	—	2	2	no	—
30	C₂×C₄×D₁₉	—	2	1	no	—
31	C₂×Dic₃₈	—	2	2	no	—
32	C₂×Dic₃₈	—	2	1	no	—
33	C₂×Dic₃₈	D₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	—	2	1	no	—
35	C₂×C₈×C₁₉	—	2	1	no	—
36	C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
38	C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	(C₂×D₁₉)⋊C₄	—	2	2	no	—
40	(C₂×D₁₉)⋊C₄	—	2	1	no	—
41	C₄⋊Dic₁₉	—	2	1	no	—
42	C₄⋊Dic₁₉	—	2	1	no	—
43	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
44	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
45	Dic₁₉⋊C₄	—	2	2	no	—
46	Dic₁₉⋊C₄	—	2	1	no	—
47	C₄×Dic₁₉	—	2	1	no	—
48	C₂×C₁₉⋊C₈	—	2	1	no	—
49	C₂²×D₁₉	—	2	1	no	—
50	Q₈×C₁₉	—	4	1	no	—
51	Q₈×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂×Dic₁₉	—	2	1	no	—
57	C₂×Dic₁₉	—	2	1	no	—
58	C₂×Dic₁₉	—	2	1	no	—
59	C₂×Dic₁₉	—	4	1	no	—
60	D₇₆	—	2	1	no	—
61	D₇₆	Q₁₆	1	2	yes	—
62	C₄×D₁₉	—	4	4	no	—
63	C₄×D₁₉	—	4	1	no	—
64	C₄×D₁₉	—	4	1	no	—
65	Dic₃₈	—	2	1	no	—
66	Dic₃₈	—	4	4	no	—
67	Dic₃₈	—	4	2	no	—
68	Dic₃₈	SD₁₆	1	2	yes	—
69	C₈×C₁₉	—	4	1	no	—
70	C₈×C₁₉	—	4	1	no	—
71	C₁₉⋊C₈	—	4	1	no	—
72	#1637	—	19	1	no	maximal, Sylow
73	C₂²×C₁₉	#120	1	1	yes	characteristic
74	C₂×D₁₉	—	2	2	no	—
75	C₂×D₁₉	—	4	1	no	—
76	C₂×D₁₉	—	4	1	no	—
77	C₄×C₁₉	—	2	1	no	—
78	C₄×C₁₉	—	4	2	no	—
79	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
80	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
81	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
82	C₄×C₁₉	#137	1	1	yes	characteristic
83	Dic₁₉	—	2	2	no	—
84	Dic₁₉	—	4	1	no	—
85	Dic₁₉	—	4	1	no	—
86	Dic₁₉	—	8	1	no	—
87	D₄×Q₈	—	19	1	no	—
88	#487	—	19	1	no	—
89	#477	—	19	1	no	—
90	#476	—	19	1	no	—
91	#332	D₁₉	1	1	yes	characteristic, complemented
92	Q₈⋊C₈	—	19	1	no	—
93	D₄⋊C₈	—	19	1	no	—
94	C₂×C₁₉	#450	1	1	yes	characteristic
95	C₂×C₁₉	#451	1	1	yes	characteristic
96	C₂×C₁₉	#454	1	1	yes	characteristic
97	D₁₉	—	4	2	no	—
98	C₂²×Q₈	—	38	1	no	—
99	C₄⋊Q₈	—	19	1	no	—
100	C₄⋊Q₈	—	38	1	no	—
101	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
102	C₂²⋊Q₈	—	38	1	no	—
103	C₂²⋊Q₈	—	38	2	no	—
104	C₄×Q₈	—	19	1	no	—
105	C₄×D₄	—	19	1	no	—
106	C₄×D₄	—	38	1	no	—
107	#107	—	38	1	no	—
108	#106	—	38	1	no	—
109	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
110	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
111	#103	—	38	1	no	—
112	#103	—	38	2	no	—
113	#102	—	38	1	no	—
114	C₄×C₈	—	19	1	no	—
115	C₁₉	#1637	1	1	yes	characteristic, complemented, Sylow
116	C₂×Q₈	—	2	1	no	—
117	C₂×Q₈	—	19	1	no	—
118	C₂×Q₈	—	38	2	no	—
119	C₂×Q₈	—	38	1	no	—
120	C₂×Q₈	—	76	2	no	—
121	C₂×Q₈	—	76	2	no	—
122	C₂×D₄	—	19	1	no	—
123	C₂²×C₄	—	38	2	no	—
124	C₂²×C₄	—	38	1	no	—
125	C₂×C₈	—	2	1	no	—
126	C₂×C₈	—	2	1	no	—
127	C₂×C₈	—	38	1	no	—
128	C₄⋊C₄	—	2	1	no	—
129	C₄⋊C₄	—	19	1	no	—
130	C₄⋊C₄	—	19	1	no	—
131	C₄⋊C₄	—	38	2	no	—
132	C₄⋊C₄	—	38	1	no	—
133	C₄⋊C₄	—	38	1	no	—
134	C₄⋊C₄	—	38	1	no	—
135	C₄⋊C₄	D₇₆	1	2	yes	—
136	C₂²⋊C₄	—	38	2	no	—
137	C₂²⋊C₄	—	38	1	no	—
138	C₄²	—	38	1	no	—
139	C₄²	C₂²×D₁₉	1	1	yes	characteristic
140	C₂³	—	38	1	no	—
141	Q₈	—	4	1	no	—
142	Q₈	—	4	1	no	—
143	Q₈	—	19	2	no	—
144	Q₈	—	38	1	no	—
145	Q₈	—	76	2	no	—
146	Q₈	—	76	4	no	—
147	D₄	—	19	2	no	—
148	D₄	—	38	1	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	38	1	no	—
151	C₂×C₄	—	38	1	no	—
152	C₂×C₄	—	38	1	no	—
153	C₂×C₄	—	76	4	no	—
154	C₂×C₄	—	76	1	no	—
155	C₂×C₄	—	76	1	no	—
156	C₂×C₄	—	76	1	no	—
157	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
158	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
159	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
160	C₈	—	4	1	no	—
161	C₈	—	4	1	no	—
162	C₈	—	76	1	no	—
163	C₂²	—	38	2	no	—
164	C₂²	—	76	1	no	—
165	C₂²	—	76	1	no	—
166	C₂²	#10597328	1	1	yes	characteristic
167	C₄	—	2	1	no	—
168	C₄	—	4	2	no	—
169	C₄	—	38	2	no	—
170	C₄	—	76	1	no	—
171	C₄	—	76	1	no	—
172	C₄	—	152	1	no	—
173	C₄	#10597357	1	1	yes	characteristic
174	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
175	C₄	#10597361	1	1	yes	characteristic
176	C₄	Q₁₆×D₁₉	1	1	yes	characteristic
177	C₂	—	76	2	no	—
178	C₂	#11926696	1	1	yes	characteristic
179	C₂	#11926701	1	1	yes	characteristic
180	C₂	#11926719	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927209

C₂

yes

maximal, characteristic

#11926896

C₂

yes

maximal, characteristic, complemented

#11926840

C₂

yes

maximal, characteristic, complemented

#11926835

C₂

yes

maximal, characteristic

#11926274

C₂

yes

maximal, characteristic, complemented

#11926271

C₂

yes

maximal, characteristic

C₁₉×#332

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

—

—

—

C₄×D₇₆

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

—

—

—

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

Q₈×D₁₉

—

Q₈×D₁₉

—

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

Q₁₆

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

SD₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

D₄×Q₈

—

—

—

—

D₁₉

yes

characteristic, complemented

Q₈⋊C₈

—

D₄⋊C₈

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂²×Q₈

—

C₄⋊Q₈

—

100

C₄⋊Q₈

—

101

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

102

C₂²⋊Q₈

—

103

C₂²⋊Q₈

—

104

C₄×Q₈

—

105

C₄×D₄

—

106

C₄×D₄

—

107

#107

—

108

#106

—

109

C₄⋊C₈

C₂×D₁₉

yes

characteristic

110

C₄⋊C₈

C₂×D₁₉

yes

characteristic

111

#103

—

112

#103

—

113

#102

—

114

C₄×C₈

—

115

C₁₉

#1637

yes

characteristic, complemented, Sylow

116

C₂×Q₈

—

117

C₂×Q₈

—

118

C₂×Q₈

—

119

C₂×Q₈

—

120

C₂×Q₈

—

121

C₂×Q₈

—

122

C₂×D₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

D₇₆

yes

—

136

C₂²⋊C₄

—

137

C₂²⋊C₄

—

138

C₄²

—

139

C₄²

C₂²×D₁₉

yes

characteristic

140

C₂³

—

141

Q₈

—

142

Q₈

—

143

Q₈

—

144

Q₈

—

145

Q₈

—

146

Q₈

—

147

D₄

—

148

D₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

C₂×D₇₆

yes

characteristic

158

C₂×C₄

D₄×D₁₉

yes

characteristic

159

C₂×C₄

D₄×D₁₉

yes

characteristic

160

C₈

—

161

C₈

—

162

C₈

—

163

C₂²

—

164

C₂²

—

165

C₂²

—

166

C₂²

#10597328

yes

characteristic

167

C₄

—

168

C₄

—

169

C₄

—

170

C₄

—

171

C₄

—

172

C₄

—

152

—

173

C₄

#10597357

yes

characteristic

174

C₄

SD₁₆×D₁₉

yes

characteristic

175

C₄

#10597361

yes

characteristic

176

C₄

Q₁₆×D₁₉

yes

characteristic

177

C₂

—

178

C₂

#11926696

yes

characteristic

179

C₂

#11926701

yes

characteristic

180

C₂

#11926719

yes

characteristic

	subgroup	G/H
center	C₂²	#10597328
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#332	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂×D₇₆	D₄
hypercenter	#332	D₁₉
hypocenter	C₁₉	#1637
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #332

subgroup

G/H

center

C₂²

#10597328

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#332

C₂

socle

C₂²×C₁₉

#120

prime radical

C₂×D₇₆

D₄

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #332

N	H ≅ G/N	type
2. #11926896	C₂	semidirect
3. #11926840	C₂	semidirect
5. #11926274	C₂	semidirect
7. C₁₉×#332	C₂	semidirect
91. #332	D₁₉	semidirect
115. C₁₉	#1637	semidirect

H ≅ G/N

type

2. #11926896

C₂

semidirect

3. #11926840

C₂

semidirect

5. #11926274

C₂

semidirect

7. C₁₉×#332

C₂

semidirect

91. #332

D₁₉

semidirect

115. C₁₉

#1637

semidirect

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

subgroup	index
#11927209	2
#11926896	2
#11926840	2
#11926835	2
#11926274	2
#11926271	2
C₁₉×#332	2
#1637	19

subgroup

index

C₁₉×#332

Subgroups — #14562801

Conjugacy classes of subgroups

Complements

Maximal subgroups