Group #14564947 — subgroups

Subgroups — #14564947

Order 2432.

360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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×D₁₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597266	C₂	1	2	yes	maximal, complemented
4	#11926445	C₂	1	2	yes	maximal, complemented
5	C₁₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
10	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
11	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×D₁₅₂	—	2	4	no	—
14	C₂×D₁₅₂	—	2	2	no	—
15	Dic₁₉⋊C₈	—	2	2	no	—
16	#10597266	—	2	4	no	—
17	C₂³×D₁₉	—	2	2	no	—
18	C₂²×C₄×C₁₉	—	2	2	no	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
21	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
22	C₂×D₇₆	—	2	2	no	—
23	C₂×D₇₆	—	2	2	no	—
24	C₂×D₇₆	—	2	2	no	—
25	C₂×D₇₆	—	2	2	no	—
26	C₂×D₇₆	—	2	2	no	—
27	C₂×D₇₆	D₄	1	4	yes	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	D₄	1	2	yes	—
30	C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₄⋊C₄×C₁₉	—	2	2	no	—
32	(C₂×D₁₉)⋊C₄	—	4	4	no	—
33	(C₂×D₁₉)⋊C₄	—	4	4	no	—
34	C₄×Dic₁₉	—	2	1	no	—
35	C₄×Dic₁₉	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	D₁₅₂	—	2	8	no	—
39	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂²×D₁₉	—	2	4	no	—
41	C₂²×D₁₉	—	4	2	no	—
42	C₂²×D₁₉	—	4	2	no	—
43	C₂²×D₁₉	—	4	2	no	—
44	C₂²×D₁₉	—	4	2	no	—
45	C₂²×D₁₉	—	4	2	no	—
46	C₂²×D₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₁₉	#41	1	2	yes	—
53	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂×Dic₁₉	—	2	1	no	—
55	C₂×Dic₁₉	—	2	1	no	—
56	C₂×Dic₁₉	—	2	1	no	—
57	C₂×Dic₁₉	—	2	2	no	—
58	C₂×Dic₁₉	D₈	1	2	yes	complemented
59	D₇₆	—	2	4	no	—
60	D₇₆	—	2	4	no	—
61	D₇₆	—	4	2	no	—
62	D₇₆	—	4	2	no	—
63	C₈×C₁₉	—	2	2	no	—
64	C₁₉⋊C₈	—	4	1	no	—
65	#2054	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	#121	1	2	yes	—
67	C₂²×C₁₉	#121	1	1	yes	characteristic
68	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
69	C₂²×C₁₉	#135	1	1	yes	characteristic
70	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
71	C₂×D₁₉	—	4	4	no	—
72	C₂×D₁₉	—	4	4	no	—
73	C₂×D₁₉	—	4	4	no	—
74	C₂×D₁₉	—	8	2	no	—
75	C₂×D₁₉	—	8	2	no	—
76	C₂×D₁₉	—	8	2	no	—
77	C₂×D₁₉	—	8	2	no	—
78	C₄×C₁₉	—	8	2	no	—
79	C₄×C₁₉	#120	1	1	yes	characteristic
80	C₄×C₁₉	#123	1	2	yes	—
81	C₄×C₁₉	#124	1	1	yes	characteristic
82	Dic₁₉	—	2	2	no	—
83	Dic₁₉	—	4	1	no	—
84	C₂²×D₈	—	19	1	no	—
85	C₂×C₄⋊C₈	—	19	1	no	—
86	C₂×#102	—	19	2	no	—
87	#390	—	19	2	no	—
88	#340	D₁₉	1	1	yes	characteristic, complemented
89	C₂×C₁₉	#394	1	1	yes	characteristic
90	C₂×C₁₉	#459	1	2	yes	—
91	C₂×C₁₉	#463	1	2	yes	—
92	C₂×C₁₉	#466	1	1	yes	characteristic
93	C₂×C₁₉	#469	1	1	yes	characteristic
94	D₁₉	—	8	4	no	—
95	C₂²×D₄	—	19	2	no	—
96	C₂×D₈	—	38	4	no	—
97	C₂×D₈	—	38	2	no	—
98	C₂²×C₈	—	19	1	no	—
99	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
100	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
101	C₂×C₂²⋊C₄	—	38	2	no	—
102	C₂×C₂²⋊C₄	—	38	2	no	—
103	C₂×C₄²	—	19	1	no	—
104	C₄⋊C₈	—	38	2	no	—
105	#102	—	38	4	no	—
106	C₁₉	#2054	1	1	yes	characteristic, complemented, Sylow
107	C₂⁴	—	38	2	no	—
108	C₂×D₄	—	19	4	no	—
109	C₂×D₄	—	38	2	no	—
110	C₂×D₄	—	38	2	no	—
111	C₂×D₄	—	38	2	no	—
112	C₂×D₄	—	38	2	no	—
113	C₂×D₄	—	38	2	no	—
114	C₂²×C₄	—	2	2	no	—
115	C₂²×C₄	—	19	1	no	—
116	C₂²×C₄	—	19	1	no	—
117	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
118	D₈	—	38	8	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	—	38	1	no	—
121	C₂×C₈	—	38	2	no	—
122	C₂×C₈	D₇₆	1	2	yes	—
123	C₄⋊C₄	—	2	2	no	—
124	C₄⋊C₄	—	2	2	no	—
125	C₂²⋊C₄	—	76	4	no	—
126	C₂²⋊C₄	—	76	4	no	—
127	C₄²	—	38	1	no	—
128	C₄²	—	38	1	no	—
129	C₂³	—	38	4	no	—
130	C₂³	—	76	2	no	—
131	C₂³	—	76	2	no	—
132	C₂³	—	76	2	no	—
133	C₂³	—	76	2	no	—
134	C₂³	—	76	2	no	—
135	C₂³	—	76	2	no	—
136	C₂³	D₄×D₁₉	1	1	yes	characteristic
137	D₄	—	38	4	no	—
138	D₄	—	38	4	no	—
139	D₄	—	76	2	no	—
140	D₄	—	76	2	no	—
141	C₂×C₄	—	4	2	no	—
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	4	2	no	—
144	C₂×C₄	—	19	2	no	—
145	C₂×C₄	—	38	1	no	—
146	C₂×C₄	—	38	1	no	—
147	C₂×C₄	—	38	1	no	—
148	C₂×C₄	—	38	2	no	—
149	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
150	C₂×C₄	#64541	1	2	yes	—
151	C₂×C₄	D₄×D₁₉	1	2	yes	—
152	C₂×C₄	#64545	1	1	yes	characteristic
153	C₈	—	2	2	no	—
154	C₈	—	76	1	no	—
155	C₂²	—	76	4	no	—
156	C₂²	—	76	4	no	—
157	C₂²	—	76	4	no	—
158	C₂²	—	152	2	no	—
159	C₂²	—	152	2	no	—
160	C₂²	—	152	2	no	—
161	C₂²	—	152	2	no	—
162	C₂²	#10597330	1	2	yes	—
163	C₂²	#10597341	1	1	yes	characteristic
164	C₂²	D₈×D₁₉	1	1	yes	characteristic
165	C₂²	#10597360	1	2	yes	—
166	C₂²	#10597365	1	1	yes	characteristic
167	C₄	—	8	2	no	—
168	C₄	—	38	2	no	—
169	C₄	—	76	1	no	—
170	C₄	#10597321	1	1	yes	characteristic
171	C₄	#10597328	1	1	yes	characteristic
172	C₄	#10597340	1	2	yes	—
173	C₂	—	152	4	no	—
174	C₂	#11926462	1	1	yes	characteristic
175	C₂	#11926738	1	2	yes	—
176	C₂	#11926762	1	2	yes	—
177	C₂	#11926781	1	1	yes	characteristic
178	C₂	#11926798	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₁₅₂

C₂

yes

maximal, characteristic

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂×#10597266

C₂

yes

maximal, complemented

#11926445

C₂

yes

maximal, complemented

C₁₉×#340

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×D₁₅₂

—

C₂×D₁₅₂

—

Dic₁₉⋊C₈

—

#10597266

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

complemented

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2054

—

maximal, Sylow

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₂×D₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#123

yes

—

C₄×C₁₉

#124

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂²×D₈

—

C₂×C₄⋊C₈

—

C₂×#102

—

#390

—

#340

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#394

yes

characteristic

C₂×C₁₉

#459

yes

—

C₂×C₁₉

#463

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

100

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

101

C₂×C₂²⋊C₄

—

102

C₂×C₂²⋊C₄

—

103

C₂×C₄²

—

104

C₄⋊C₈

—

105

#102

—

106

C₁₉

#2054

yes

characteristic, complemented, Sylow

107

C₂⁴

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

C₂²×D₁₉

yes

characteristic

118

D₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

D₇₆

yes

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₂²⋊C₄

—

126

C₂²⋊C₄

—

127

C₄²

—

128

C₄²

—

129

C₂³

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

D₄×D₁₉

yes

characteristic

137

D₄

—

138

D₄

—

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

—

149

C₂×C₄

C₂×D₇₆

yes

characteristic

150

C₂×C₄

#64541

yes

—

151

C₂×C₄

D₄×D₁₉

yes

—

152

C₂×C₄

#64545

yes

characteristic

153

C₈

—

154

C₈

—

155

C₂²

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

152

—

159

C₂²

—

152

—

160

C₂²

—

152

—

161

C₂²

—

152

—

162

C₂²

#10597330

yes

—

163

C₂²

#10597341

yes

characteristic

164

C₂²

D₈×D₁₉

yes

characteristic

165

C₂²

#10597360

yes

—

166

C₂²

#10597365

yes

characteristic

167

C₄

—

168

C₄

—

169

C₄

—

170

C₄

#10597321

yes

characteristic

171

C₄

#10597328

yes

characteristic

172

C₄

#10597340

yes

—

173

C₂

—

152

—

174

C₂

#11926462

yes

characteristic

175

C₂

#11926738

yes

—

176

C₂

#11926762

yes

—

177

C₂

#11926781

yes

characteristic

178

C₂

#11926798

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#340	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₁₅₂	C₂
hypercenter	#340	D₁₉
hypocenter	C₁₉	#2054
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#340

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₁₅₂

C₂

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
2. C₂×Dic₁₉⋊C₈	C₂	semidirect
3. C₂×#10597266	C₂	semidirect
4. #11926445	C₂	semidirect
5. C₁₉×#340	C₂	semidirect
58. C₂×Dic₁₉	D₈	semidirect
88. #340	D₁₉	semidirect
106. C₁₉	#2054	semidirect

H ≅ G/N

type

2. C₂×Dic₁₉⋊C₈

C₂

semidirect

3. C₂×#10597266

C₂

semidirect

4. #11926445

C₂

semidirect

5. C₁₉×#340

C₂

semidirect

58. C₂×Dic₁₉

D₈

semidirect

88. #340

D₁₉

semidirect

106. C₁₉

#2054

semidirect

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

subgroup	index
C₂²×D₁₅₂	2
C₂×Dic₁₉⋊C₈	2
C₂×#10597266	2
#11926445	2
C₁₉×#340	2
#2054	19

subgroup

index

C₂²×D₁₅₂

C₂×Dic₁₉⋊C₈

C₂×#10597266

#11926445

C₁₉×#340

#2054

Subgroups — #14564947

Conjugacy classes of subgroups

Complements

Maximal subgroups