Group #14562839 — subgroups

Subgroups — #14562839

Order 2432.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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	#11927255	C₂	1	1	yes	maximal, characteristic
2	#11926826	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926746	C₂	1	1	yes	maximal, characteristic
4	#11926293	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926276	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926273	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	#10597392	—	2	2	no	—
11	C₂×#64527	—	2	1	no	—
12	#10597343	—	2	1	no	—
13	#10597339	—	2	1	no	—
14	C₄⋊C₄×D₁₉	—	2	1	no	—
15	#10597336	—	2	1	no	—
16	C₄×D₇₆	C₂²	1	1	yes	characteristic
17	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
18	C₁₉×#103	—	2	2	no	—
19	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	#10597292	—	2	1	no	—
21	#10597267	—	2	1	no	—
22	#10597265	—	2	1	no	—
23	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×Q₈×C₁₉	—	2	1	no	—
26	C₂×Q₈×C₁₉	D₄	1	2	yes	—
27	C₂×D₇₆	D₄	1	1	yes	characteristic
28	C₂×C₄×D₁₉	—	2	1	no	—
29	C₂×C₄×D₁₉	—	2	2	no	—
30	C₂×Dic₃₈	D₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	—	2	1	no	—
32	C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	#64527	—	4	2	no	—
38	(C₂×D₁₉)⋊C₄	—	2	2	no	—
39	(C₂×D₁₉)⋊C₄	—	2	1	no	—
40	C₄⋊Dic₁₉	—	2	2	no	—
41	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
42	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
43	Dic₁₉⋊C₄	—	2	2	no	—
44	Dic₁₉⋊C₄	—	2	1	no	—
45	C₄×Dic₁₉	—	2	1	no	—
46	C₂×C₁₉⋊C₈	—	2	1	no	—
47	C₂×C₁₉⋊C₈	—	2	1	no	—
48	C₂²×D₁₉	—	2	1	no	—
49	Q₈×C₁₉	—	4	2	no	—
50	Q₈×C₁₉	—	4	1	no	—
51	Q₈×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	2	2	no	—
53	C₂×C₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×Dic₁₉	—	2	1	no	—
58	C₂×Dic₁₉	—	2	1	no	—
59	C₂×Dic₁₉	—	2	1	no	—
60	D₇₆	—	2	1	no	—
61	D₇₆	SD₁₆	1	2	yes	—
62	C₄×D₁₉	—	4	1	no	—
63	C₄×D₁₉	—	4	1	no	—
64	C₄×D₁₉	—	8	2	no	—
65	Dic₃₈	—	2	1	no	—
66	Dic₃₈	—	2	1	no	—
67	C₈×C₁₉	—	4	1	no	—
68	C₁₉⋊C₈	—	4	1	no	—
69	C₁₉⋊C₈	—	4	1	no	—
70	#1643	—	19	1	no	maximal, Sylow
71	C₂²×C₁₉	#120	1	1	yes	characteristic
72	C₂×D₁₉	—	2	2	no	—
73	C₂×D₁₉	—	4	1	no	—
74	C₂×D₁₉	—	4	1	no	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	4	2	no	—
77	C₄×C₁₉	—	8	1	no	—
78	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
79	C₄×C₁₉	#135	1	1	yes	characteristic
80	C₄×C₁₉	#137	1	1	yes	characteristic
81	C₄×C₁₉	#137	1	1	yes	characteristic
82	Dic₁₉	—	4	1	no	—
83	Dic₁₉	—	4	1	no	—
84	Dic₁₉	—	4	1	no	—
85	#554	—	19	1	no	—
86	#487	D₁₉	1	1	yes	characteristic, complemented
87	#475	—	19	1	no	—
88	#461	—	19	1	no	—
89	#333	—	19	1	no	—
90	Q₈⋊C₈	—	19	1	no	—
91	D₄⋊C₈	—	19	1	no	—
92	C₂×C₁₉	#448	1	1	yes	characteristic
93	C₂×C₁₉	#452	1	1	yes	characteristic
94	C₂×C₁₉	#455	1	1	yes	characteristic
95	D₁₉	—	4	2	no	—
96	C₂×SD₁₆	—	38	1	no	—
97	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
98	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
99	#125	—	38	1	no	—
100	C₂²⋊Q₈	—	38	1	no	—
101	C₂²⋊Q₈	—	38	2	no	—
102	C₄×Q₈	—	19	1	no	—
103	C₄×D₄	—	19	1	no	—
104	C₄×D₄	—	38	1	no	—
105	C₂×C₄⋊C₄	—	38	1	no	—
106	#106	—	38	1	no	—
107	C₄⋊C₈	—	19	1	no	—
108	C₄⋊C₈	—	19	1	no	—
109	#103	—	2	2	no	—
110	#103	—	38	1	no	—
111	#103	—	38	1	no	—
112	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
113	C₁₉	#1643	1	1	yes	characteristic, complemented, Sylow
114	C₂×Q₈	—	2	1	no	—
115	C₂×Q₈	—	19	1	no	—
116	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
117	C₂×D₄	—	19	1	no	—
118	C₂²×C₄	—	38	2	no	—
119	C₂²×C₄	—	38	1	no	—
120	SD₁₆	—	76	2	no	—
121	C₂×C₈	—	2	1	no	—
122	C₂×C₈	—	38	1	no	—
123	C₂×C₈	—	38	1	no	—
124	C₄⋊C₄	—	2	1	no	—
125	C₄⋊C₄	—	2	1	no	—
126	C₄⋊C₄	—	2	1	no	—
127	C₄⋊C₄	—	2	1	no	—
128	C₄⋊C₄	—	19	1	no	—
129	C₄⋊C₄	—	19	1	no	—
130	C₄⋊C₄	—	38	2	no	—
131	C₄⋊C₄	—	38	2	no	—
132	C₄⋊C₄	—	38	1	no	—
133	C₂²⋊C₄	—	38	2	no	—
134	C₂²⋊C₄	—	38	1	no	—
135	C₄²	—	38	1	no	—
136	C₄²	C₂²×D₁₉	1	1	yes	characteristic
137	C₂³	—	38	1	no	—
138	Q₈	—	4	2	no	—
139	Q₈	—	4	1	no	—
140	Q₈	—	4	1	no	—
141	Q₈	—	38	1	no	—
142	Q₈	—	38	1	no	—
143	D₄	—	19	2	no	—
144	D₄	—	38	1	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	4	1	no	—
147	C₂×C₄	—	38	1	no	—
148	C₂×C₄	—	38	1	no	—
149	C₂×C₄	—	38	1	no	—
150	C₂×C₄	—	76	1	no	—
151	C₂×C₄	—	76	1	no	—
152	C₂×C₄	—	152	2	no	—
153	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
154	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
155	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
156	C₈	—	4	1	no	—
157	C₈	—	76	1	no	—
158	C₈	—	76	1	no	—
159	C₂²	—	38	2	no	—
160	C₂²	—	76	1	no	—
161	C₂²	—	76	1	no	—
162	C₂²	#10597383	1	1	yes	characteristic
163	C₄	—	2	1	no	—
164	C₄	—	4	2	no	—
165	C₄	—	8	1	no	—
166	C₄	—	76	1	no	—
167	C₄	—	76	1	no	—
168	C₄	—	76	1	no	—
169	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
170	C₄	#10597361	1	1	yes	characteristic
171	C₄	#10597364	1	1	yes	characteristic
172	C₄	#10597365	1	1	yes	characteristic
173	C₂	—	76	2	no	—
174	C₂	#11926681	1	1	yes	characteristic
175	C₂	#11926705	1	1	yes	characteristic
176	C₂	#11926721	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927255

C₂

yes

maximal, characteristic

#11926826

C₂

yes

maximal, characteristic, complemented

#11926746

C₂

yes

maximal, characteristic

#11926293

C₂

yes

maximal, characteristic, complemented

#11926276

C₂

yes

maximal, characteristic, complemented

#11926273

C₂

yes

maximal, characteristic

C₁₉×#487

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

—

—

—

—

C₄⋊C₄×D₁₉

—

#10597336

—

C₄×D₇₆

C₂²

yes

characteristic

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

—

—

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64527

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×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

—

D₇₆

—

D₇₆

SD₁₆

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

#554

—

#487

D₁₉

yes

characteristic, complemented

#475

—

#461

—

#333

—

Q₈⋊C₈

—

D₄⋊C₈

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×SD₁₆

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#125

—

100

C₂²⋊Q₈

—

101

C₂²⋊Q₈

—

102

C₄×Q₈

—

103

C₄×D₄

—

104

C₄×D₄

—

105

C₂×C₄⋊C₄

—

106

#106

—

107

C₄⋊C₈

—

108

C₄⋊C₈

—

109

#103

—

110

#103

—

111

#103

—

112

C₄×C₈

C₂×D₁₉

yes

characteristic

113

C₁₉

#1643

yes

characteristic, complemented, Sylow

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

C₂²⋊D₁₉

yes

—

117

C₂×D₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

SD₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄⋊C₄

—

128

C₄⋊C₄

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₂²⋊C₄

—

134

C₂²⋊C₄

—

135

C₄²

—

136

C₄²

C₂²×D₁₉

yes

characteristic

137

C₂³

—

138

Q₈

—

139

Q₈

—

140

Q₈

—

141

Q₈

—

142

Q₈

—

143

D₄

—

144

D₄

—

145

C₂×C₄

—

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

D₄×D₁₉

yes

characteristic

154

C₂×C₄

D₄×D₁₉

yes

characteristic

155

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

156

C₈

—

157

C₈

—

158

C₈

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

#10597383

yes

characteristic

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

—

168

C₄

—

169

C₄

SD₁₆×D₁₉

yes

characteristic

170

C₄

#10597361

yes

characteristic

171

C₄

#10597364

yes

characteristic

172

C₄

#10597365

yes

characteristic

173

C₂

—

174

C₂

#11926681

yes

characteristic

175

C₂

#11926705

yes

characteristic

176

C₂

#11926721

yes

characteristic

	subgroup	G/H
center	C₂²	#10597383
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#487	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂×D₇₆	D₄
hypercenter	#487	D₁₉
hypocenter	C₁₉	#1643
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

#10597383

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#487

C₂

socle

C₂²×C₁₉

#120

prime radical

C₂×D₇₆

D₄

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
2. #11926826	C₂	semidirect
4. #11926293	C₂	semidirect
5. #11926276	C₂	semidirect
7. C₁₉×#487	C₂	semidirect
86. #487	D₁₉	semidirect
113. C₁₉	#1643	semidirect

H ≅ G/N

type

2. #11926826

C₂

semidirect

4. #11926293

C₂

semidirect

5. #11926276

C₂

semidirect

7. C₁₉×#487

C₂

semidirect

86. #487

D₁₉

semidirect

113. C₁₉

#1643

semidirect

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

subgroup	index
#11927255	2
#11926826	2
#11926746	2
#11926293	2
#11926276	2
#11926273	2
C₁₉×#487	2
#1643	19

subgroup

index

C₁₉×#487

Subgroups — #14562839

Conjugacy classes of subgroups

Complements

Maximal subgroups