Group #14564167 — subgroups

Subgroups — #14564167

Order 2432.

362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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	#11927111	C₂	1	1	yes	maximal, characteristic
2	#11926562	C₂	1	2	yes	maximal, complemented
3	C₂×#10597290	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926300	C₂	1	2	yes	maximal, complemented
5	C₁₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×#64541	C₂²	1	1	yes	characteristic
8	C₄×D₄×C₁₉	—	2	4	no	—
9	C₁₉×#117	C₂²	1	2	yes	—
10	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
11	#10597399	—	2	2	no	—
12	#10597386	C₄	1	2	yes	complemented
13	#10597384	—	2	2	no	—
14	#10597382	C₄	1	2	yes	complemented
15	#10597372	C₂²	1	1	yes	characteristic
16	C₂×#64520	C₂²	1	2	yes	—
17	#10597290	—	2	2	no	—
18	#10597262	—	2	4	no	—
19	C₂⁴×C₁₉	D₄	1	2	yes	—
20	C₂×D₄×C₁₉	—	2	2	no	—
21	C₂×D₄×C₁₉	—	2	2	no	—
22	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×D₄×C₁₉	D₄	1	2	yes	—
24	C₂²×C₄×C₁₉	—	2	4	no	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂×C₂²⋊D₁₉	—	2	1	no	—
27	C₂×C₂²⋊D₁₉	—	2	4	no	—
28	#64541	—	2	2	no	—
29	#64541	—	2	2	no	—
30	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic, complemented
31	C₂×C₄×D₁₉	—	2	1	no	—
32	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic, complemented
33	C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₂²⋊C₄×C₁₉	—	2	4	no	—
35	C₂²⋊C₄×C₁₉	—	2	2	no	—
36	C₄²×C₁₉	D₄	1	4	yes	complemented
37	C₂²⋊Dic₁₉	—	2	4	no	—
38	C₂²⋊Dic₁₉	—	2	1	no	—
39	C₄⋊Dic₁₉	—	2	1	no	—
40	C₄×Dic₁₉	C₂×C₄	1	2	yes	complemented
41	#64520	—	2	2	no	—
42	#64520	—	2	2	no	—
43	C₂×C₁₉⋊C₈	—	2	2	no	—
44	C₂³×C₁₉	—	2	2	no	—
45	C₂³×C₁₉	—	2	2	no	—
46	C₂³×C₁₉	—	8	2	no	—
47	C₂³×C₁₉	C₂²⋊C₄	1	4	yes	—
48	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂²×D₁₉	—	2	1	no	—
50	D₄×C₁₉	—	2	4	no	—
51	D₄×C₁₉	—	2	4	no	—
52	C₂×C₄×C₁₉	—	2	4	no	—
53	C₂×C₄×C₁₉	—	8	4	no	—
54	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	#41	1	2	yes	—
58	C₂²⋊D₁₉	—	4	1	no	—
59	C₂²⋊D₁₉	—	4	1	no	—
60	C₂²⋊D₁₉	—	8	4	no	—
61	C₂×Dic₁₉	—	2	2	no	—
62	C₂×Dic₁₉	—	2	1	no	—
63	D₇₆	—	2	2	no	—
64	C₄×D₁₉	—	4	2	no	—
65	Dic₃₈	—	2	2	no	—
66	C₁₉⋊C₈	—	4	2	no	—
67	#1911	—	19	1	no	maximal, Sylow
68	C₂²×C₁₉	—	2	4	no	—
69	C₂²×C₁₉	—	4	1	no	—
70	C₂²×C₁₉	—	4	4	no	—
71	C₂²×C₁₉	—	4	4	no	—
72	C₂²×C₁₉	—	8	2	no	—
73	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₁₉	#120	1	1	yes	characteristic
75	C₂²×C₁₉	#123	1	1	yes	characteristic
76	C₂×D₁₉	—	4	2	no	—
77	C₂×D₁₉	—	4	1	no	—
78	C₄×C₁₉	—	4	4	no	—
79	C₄×C₁₉	C₄×D₄	1	2	yes	—
80	C₄×C₁₉	#121	1	2	yes	—
81	Dic₁₉	—	4	2	no	—
82	Dic₁₉	—	4	1	no	—
83	#535	—	19	1	no	—
84	#518	D₁₉	1	1	yes	characteristic, complemented
85	#421	—	19	2	no	—
86	C₂×#100	—	19	1	no	—
87	H(3,ℤ/4)	—	19	2	no	—
88	C₂×C₁₉	—	2	1	no	—
89	C₂×C₁₉	—	2	1	no	—
90	C₂×C₁₉	—	2	1	no	—
91	C₂×C₁₉	—	4	4	no	—
92	C₂×C₁₉	#386	1	1	yes	characteristic
93	D₁₉	—	8	1	no	—
94	C₂×#41	—	19	1	no	—
95	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
96	C₂×M₁₆	—	19	2	no	—
97	#127	—	19	2	no	—
98	#124	—	19	2	no	—
99	#121	—	38	2	no	—
100	#120	—	38	2	no	—
101	C₄×D₄	—	2	4	no	—
102	#117	—	19	1	no	—
103	#117	C₂×D₁₉	1	2	yes	—
104	C₂×C₂²⋊C₄	—	2	2	no	—
105	#104	—	38	4	no	—
106	#100	—	38	2	no	—
107	C₁₉	#1911	1	1	yes	characteristic, complemented, Sylow
108	C₂⁴	C₂²⋊D₁₉	1	2	yes	—
109	#41	—	38	2	no	—
110	#41	—	38	2	no	—
111	C₂×Q₈	—	19	1	no	—
112	C₂×D₄	—	2	2	no	—
113	C₂×D₄	—	2	2	no	—
114	C₂×D₄	—	19	1	no	—
115	C₂×D₄	—	38	1	no	—
116	C₂×D₄	—	38	4	no	—
117	C₂×D₄	C₄×D₁₉	1	2	yes	—
118	C₂×D₄	D₇₆	1	2	yes	—
119	C₂²×C₄	—	2	4	no	—
120	C₂²×C₄	—	38	1	no	—
121	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
122	M₁₆	—	38	2	no	—
123	M₁₆	—	38	2	no	—
124	C₂×C₈	—	38	2	no	—
125	C₄⋊C₄	—	2	2	no	—
126	C₄⋊C₄	—	38	1	no	—
127	C₂²⋊C₄	—	2	4	no	—
128	C₂²⋊C₄	—	2	2	no	—
129	C₂²⋊C₄	—	38	4	no	—
130	C₂²⋊C₄	—	38	1	no	—
131	C₄²	—	19	2	no	—
132	C₄²	C₂²⋊D₁₉	1	4	yes	complemented
133	C₂³	—	2	2	no	—
134	C₂³	—	2	2	no	—
135	C₂³	—	8	2	no	—
136	C₂³	—	38	1	no	—
137	C₂³	(C₂×D₁₉)⋊C₄	1	4	yes	—
138	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
139	Q₈	—	38	2	no	—
140	D₄	—	2	4	no	—
141	D₄	—	2	4	no	—
142	D₄	—	38	2	no	—
143	D₄	—	76	1	no	—
144	D₄	—	76	1	no	—
145	D₄	—	152	4	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	8	4	no	—
148	C₂×C₄	—	38	2	no	—
149	C₂×C₄	—	38	1	no	—
150	C₂×C₄	—	76	2	no	—
151	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
152	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
153	C₂×C₄	#64541	1	2	yes	—
154	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
155	C₈	—	76	2	no	—
156	C₂²	—	2	4	no	—
157	C₂²	—	4	1	no	—
158	C₂²	—	4	4	no	—
159	C₂²	—	4	4	no	—
160	C₂²	—	8	2	no	—
161	C₂²	—	76	2	no	—
162	C₂²	—	76	1	no	—
163	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
164	C₂²	#10597375	1	1	yes	characteristic
165	C₂²	#10597399	1	1	yes	characteristic
166	C₄	—	4	4	no	—
167	C₄	—	76	2	no	—
168	C₄	—	76	1	no	—
169	C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
170	C₄	#10597376	1	2	yes	—
171	C₂	—	2	1	no	—
172	C₂	—	2	1	no	—
173	C₂	—	2	1	no	—
174	C₂	—	4	4	no	—
175	C₂	—	152	1	no	—
176	C₂	#11926423	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927111

C₂

yes

maximal, characteristic

#11926562

C₂

yes

maximal, complemented

C₂×#10597290

C₂

yes

maximal, characteristic, complemented

#11926300

C₂

yes

maximal, complemented

C₁₉×#518

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂×#64541

C₂²

yes

characteristic

C₄×D₄×C₁₉

—

C₁₉×#117

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

—

#10597399

—

#10597386

C₄

yes

complemented

#10597384

—

#10597382

C₄

yes

complemented

#10597372

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

#10597290

—

#10597262

—

C₂⁴×C₁₉

D₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

C₂×C₄

yes

characteristic, complemented

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₂×C₄

yes

characteristic, complemented

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

complemented

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

C₂×C₄

yes

complemented

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

#1911

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

Dic₁₉

—

#535

—

#518

D₁₉

yes

characteristic, complemented

#421

—

C₂×#100

—

H(3,ℤ/4)

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#386

yes

characteristic

D₁₉

—

C₂×#41

—

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

#127

—

#124

—

#121

—

100

#120

—

101

C₄×D₄

—

102

#117

—

103

#117

C₂×D₁₉

yes

—

104

C₂×C₂²⋊C₄

—

105

#104

—

106

#100

—

107

C₁₉

#1911

yes

characteristic, complemented, Sylow

108

C₂⁴

C₂²⋊D₁₉

yes

—

109

#41

—

110

#41

—

111

C₂×Q₈

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂×D₄

—

117

C₂×D₄

C₄×D₁₉

yes

—

118

C₂×D₄

D₇₆

yes

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

C₂²×D₁₉

yes

characteristic

122

M₁₆

—

123

M₁₆

—

124

C₂×C₈

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₂²⋊C₄

—

128

C₂²⋊C₄

—

129

C₂²⋊C₄

—

130

C₂²⋊C₄

—

131

C₄²

—

132

C₄²

C₂²⋊D₁₉

yes

complemented

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

(C₂×D₁₉)⋊C₄

yes

—

138

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

139

Q₈

—

140

D₄

—

141

D₄

—

142

D₄

—

143

D₄

—

144

D₄

—

145

D₄

—

152

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

152

C₂×C₄

C₂×D₇₆

yes

characteristic

153

C₂×C₄

#64541

yes

—

154

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

155

C₈

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

—

161

C₂²

—

162

C₂²

—

163

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

164

C₂²

#10597375

yes

characteristic

165

C₂²

#10597399

yes

characteristic

166

C₄

—

167

C₄

—

168

C₄

—

169

C₄

C₄×C₂²⋊D₁₉

yes

—

170

C₄

#10597376

yes

—

171

C₂

—

172

C₂

—

173

C₂

—

174

C₂

—

175

C₂

—

152

—

176

C₂

#11926423

yes

characteristic

	subgroup	G/H
center	C₂	#11926423
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#518	C₂
socle	C₂×C₁₉	#386
prime radical	#11927111	C₂
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#518	D₁₉
hypocenter	C₁₉	#1911
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #518

subgroup

G/H

center

C₂

#11926423

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#518

C₂

C₂×C₁₉

C₂

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #518

N	H ≅ G/N	type
2. #11926562	C₂	semidirect
3. C₂×#10597290	C₂	semidirect
4. #11926300	C₂	semidirect
5. C₁₉×#518	C₂	semidirect
12. #10597386	C₄	semidirect
14. #10597382	C₄	semidirect
30. C₂×D₇₆	C₂×C₄	semidirect
32. C₂×Dic₃₈	C₂×C₄	semidirect
36. C₄²×C₁₉	D₄	semidirect
40. C₄×Dic₁₉	C₂×C₄	semidirect
84. #518	D₁₉	semidirect
107. C₁₉	#1911	semidirect
132. C₄²	C₂²⋊D₁₉	semidirect

H ≅ G/N

type

2. #11926562

C₂

semidirect

3. C₂×#10597290

C₂

semidirect

4. #11926300

C₂

semidirect

5. C₁₉×#518

C₂

semidirect

12. #10597386

C₄

semidirect

14. #10597382

C₄

semidirect

30. C₂×D₇₆

C₂×C₄

semidirect

32. C₂×Dic₃₈

C₂×C₄

semidirect

36. C₄²×C₁₉

D₄

semidirect

40. C₄×Dic₁₉

C₂×C₄

semidirect

84. #518

D₁₉

semidirect

107. C₁₉

#1911

semidirect

132. C₄²

C₂²⋊D₁₉

semidirect

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

subgroup	index
#11927111	2
#11926562	2
C₂×#10597290	2
#11926300	2
C₁₉×#518	2
#1911	19

subgroup

index

C₁₉×#518

Subgroups — #14564167

Conjugacy classes of subgroups

Complements

Maximal subgroups