Group #14573210 — subgroups

Subgroups — C₂×#11926786 #14573210

Order 2432.

512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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×Dic₇₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597343	C₂	1	2	yes	maximal
4	#11926786	C₂	1	8	yes	maximal, direct product factor
5	C₂×#10597267	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃₈	C₂²	1	2	yes	—
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
12	C₂×C₄⋊Dic₁₉	—	2	2	no	—
13	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×Dic₇₆	—	2	4	no	—
15	C₂×Dic₇₆	C₂²	1	4	yes	complemented
16	C₂×C₈×D₁₉	—	2	4	no	—
17	C₂×C₈×D₁₉	C₂²	1	4	yes	—
18	#10597343	—	2	4	no	—
19	#10597343	C₂²	1	8	yes	—
20	C₁₉×#107	C₂²	1	4	yes	complemented
21	#10597267	C₂²	1	8	yes	complemented
22	C₂³×D₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	—	2	2	no	—
26	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
27	C₂×C₄×D₁₉	—	2	2	no	—
28	C₂×C₄×D₁₉	—	2	2	no	—
29	C₂×C₄×D₁₉	D₄	1	2	yes	—
30	C₂×C₄×D₁₉	C₂³	1	2	yes	—
31	C₂×Dic₃₈	—	2	4	no	—
32	C₂×Dic₃₈	—	2	4	no	—
33	C₂×Dic₃₈	—	2	2	no	—
34	C₂×Dic₃₈	C₂³	1	4	yes	—
35	C₂×C₈×C₁₉	D₄	1	4	yes	—
36	C₂×C₈×C₁₉	C₂³	1	2	yes	—
37	C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
39	(C₂×D₁₉)⋊C₄	—	2	8	no	—
40	C₄⋊Dic₁₉	—	2	8	no	—
41	C₂×C₁₉⋊C₈	—	2	2	no	—
42	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
43	Dic₇₆	—	2	8	no	—
44	C₈×D₁₉	—	2	8	no	—
45	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×D₁₉	—	2	2	no	—
47	C₂²×D₁₉	—	2	2	no	—
48	C₂²×D₁₉	Q₁₆	1	4	yes	complemented
49	C₂²×D₁₉	C₂×D₄	1	2	yes	—
50	C₂×C₄×C₁₉	—	2	4	no	—
51	C₂×C₄×C₁₉	—	4	4	no	—
52	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#41	1	2	yes	—
55	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
56	C₂×Dic₁₉	—	2	2	no	—
57	C₂×Dic₁₉	—	2	4	no	—
58	C₂×Dic₁₉	—	4	4	no	—
59	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
60	C₄×D₁₉	—	2	4	no	—
61	C₄×D₁₉	—	2	2	no	—
62	C₄×D₁₉	—	2	2	no	—
63	Dic₃₈	—	2	4	no	—
64	Dic₃₈	—	2	4	no	—
65	Dic₃₈	—	4	4	no	—
66	C₈×C₁₉	C₂×D₄	1	4	yes	—
67	C₁₉⋊C₈	—	2	2	no	—
68	C₂×#467	—	19	1	no	maximal, Sylow
69	C₂²×C₁₉	#121	1	2	yes	—
70	C₂²×C₁₉	C₂×Q₁₆	1	2	yes	—
71	C₂²×C₁₉	#135	1	2	yes	—
72	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
73	C₂×D₁₉	—	2	2	no	—
74	C₂×D₁₉	—	2	2	no	—
75	C₂×D₁₉	—	2	8	no	—
76	C₂×D₁₉	C₂×Q₁₆	1	4	yes	complemented
77	C₄×C₁₉	—	4	4	no	—
78	C₄×C₁₉	#121	1	2	yes	—
79	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
80	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
81	Dic₁₉	—	2	2	no	—
82	Dic₁₉	—	4	4	no	—
83	C₂²×Q₁₆	—	19	1	no	—
84	C₂³×C₈	—	19	1	no	—
85	C₂×C₂²⋊Q₈	—	19	2	no	—
86	#467	—	19	8	no	—
87	C₂×#107	D₁₉	1	1	yes	characteristic, complemented
88	C₂×#103	—	19	2	no	—
89	C₂×C₁₉	#467	1	4	yes	complemented
90	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
91	C₂×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
92	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
93	D₁₉	—	2	4	no	—
94	C₂²×Q₈	—	19	2	no	—
95	C₂³×C₄	—	19	1	no	—
96	C₂×Q₁₆	—	19	4	no	—
97	C₂×Q₁₆	—	38	4	no	—
98	C₂²×C₈	—	19	1	no	—
99	C₂²×C₈	—	19	4	no	—
100	C₂²×C₈	—	38	4	no	—
101	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
102	C₂²⋊Q₈	—	19	8	no	—
103	C₂²⋊Q₈	—	38	4	no	—
104	C₂×C₄⋊C₄	—	38	2	no	—
105	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
106	C₂×C₂²⋊C₄	—	38	2	no	—
107	#107	C₂×D₁₉	1	4	yes	complemented
108	#103	—	19	8	no	—
109	C₁₉	C₂×#467	1	1	yes	characteristic, complemented, Sylow
110	C₂⁴	—	19	1	no	—
111	C₂×Q₈	—	19	4	no	—
112	C₂×Q₈	—	38	2	no	—
113	C₂×Q₈	—	38	4	no	—
114	C₂×Q₈	—	38	4	no	—
115	C₂²×C₄	—	2	2	no	—
116	C₂²×C₄	—	19	1	no	—
117	C₂²×C₄	—	19	2	no	—
118	C₂²×C₄	—	19	2	no	—
119	C₂²×C₄	—	38	2	no	—
120	C₂²×C₄	—	38	2	no	—
121	C₂²×C₄	—	38	2	no	—
122	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
123	Q₁₆	—	38	8	no	—
124	C₂×C₈	—	19	2	no	—
125	C₂×C₈	—	38	2	no	—
126	C₂×C₈	—	38	8	no	—
127	C₂×C₈	D₇₆	1	4	yes	—
128	C₂×C₈	C₂²×D₁₉	1	2	yes	—
129	C₄⋊C₄	—	2	2	no	—
130	C₄⋊C₄	—	38	8	no	—
131	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
132	C₂²⋊C₄	—	38	8	no	—
133	C₂³	—	19	2	no	—
134	C₂³	—	19	4	no	—
135	C₂³	—	38	2	no	—
136	C₂³	—	38	2	no	—
137	C₂³	D₄×D₁₉	1	1	yes	characteristic
138	Q₈	—	38	4	no	—
139	Q₈	—	38	4	no	—
140	Q₈	—	76	4	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	—	4	4	no	—
143	C₂×C₄	—	19	2	no	—
144	C₂×C₄	—	38	2	no	—
145	C₂×C₄	—	38	2	no	—
146	C₂×C₄	—	38	2	no	—
147	C₂×C₄	—	38	4	no	—
148	C₂×C₄	—	38	4	no	—
149	C₂×C₄	—	76	4	no	—
150	C₂×C₄	C₂×D₇₆	1	2	yes	—
151	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
152	C₂×C₄	#64545	1	2	yes	—
153	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
154	C₈	—	38	2	no	—
155	C₈	C₂×D₇₆	1	4	yes	—
156	C₂²	—	19	4	no	—
157	C₂²	—	38	8	no	—
158	C₂²	—	38	2	no	—
159	C₂²	—	38	2	no	—
160	C₂²	#10597341	1	2	yes	—
161	C₂²	#10597358	1	2	yes	—
162	C₂²	Q₁₆×D₁₉	1	2	yes	—
163	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
164	C₄	—	4	4	no	—
165	C₄	—	38	2	no	—
166	C₄	—	76	4	no	—
167	C₄	#10597341	1	2	yes	—
168	C₄	C₂²×D₇₆	1	1	yes	characteristic
169	C₄	C₂×#64545	1	1	yes	characteristic
170	C₂	—	38	4	no	—
171	C₂	#11926786	1	4	yes	direct product factor
172	C₂	C₂×#10597341	1	1	yes	characteristic
173	C₂	C₂×Q₁₆×D₁₉	1	1	yes	characteristic
174	C₂	C₂×#10597358	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₆

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₁₉

C₂

yes

maximal, characteristic

C₂×#10597343

C₂

yes

maximal

#11926786

C₂

yes

maximal, direct product factor

C₂×#10597267

C₂

yes

maximal, complemented

C₂×C₁₉×#107

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Dic₇₆

—

C₂×Dic₇₆

C₂²

yes

complemented

C₂×C₈×D₁₉

—

C₂×C₈×D₁₉

C₂²

yes

—

#10597343

—

#10597343

C₂²

yes

—

C₁₉×#107

C₂²

yes

complemented

#10597267

C₂²

yes

complemented

C₂³×D₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

—

C₂×C₄×D₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂³

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

Dic₇₆

—

C₈×D₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

Q₁₆

yes

complemented

C₂²×D₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

C₂×D₄

yes

—

C₁₉⋊C₈

—

C₂×#467

—

maximal, Sylow

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

C₂×Q₁₆

yes

—

C₂²×C₁₉

#135

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

C₂×Q₁₆

yes

complemented

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂²×Q₁₆

—

C₂³×C₈

—

C₂×C₂²⋊Q₈

—

#467

—

C₂×#107

D₁₉

yes

characteristic, complemented

C₂×#103

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

C₂²×Q₁₆

yes

characteristic

C₂×C₁₉

C₂×#135

yes

characteristic

D₁₉

—

C₂²×Q₈

—

C₂³×C₄

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

—

C₂²×C₈

—

100

C₂²×C₈

—

101

C₂²×C₈

C₂×D₁₉

yes

characteristic

102

C₂²⋊Q₈

—

103

C₂²⋊Q₈

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

106

C₂×C₂²⋊C₄

—

107

#107

C₂×D₁₉

yes

complemented

108

#103

—

109

C₁₉

C₂×#467

yes

characteristic, complemented, Sylow

110

C₂⁴

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

C₂²×D₁₉

yes

characteristic

123

Q₁₆

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

D₇₆

yes

—

128

C₂×C₈

C₂²×D₁₉

yes

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

C₂²×D₁₉

yes

—

132

C₂²⋊C₄

—

133

C₂³

—

134

C₂³

—

135

C₂³

—

136

C₂³

—

137

C₂³

D₄×D₁₉

yes

characteristic

138

Q₈

—

139

Q₈

—

140

Q₈

—

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

—

150

C₂×C₄

C₂×D₇₆

yes

—

151

C₂×C₄

D₄×D₁₉

yes

characteristic

152

C₂×C₄

#64545

yes

—

153

C₂×C₄

C₂³×D₁₉

yes

characteristic

154

C₈

—

155

C₈

C₂×D₇₆

yes

—

156

C₂²

—

157

C₂²

—

158

C₂²

—

159

C₂²

—

160

C₂²

#10597341

yes

—

161

C₂²

#10597358

yes

—

162

C₂²

Q₁₆×D₁₉

yes

—

163

C₂²

C₂×D₄×D₁₉

yes

characteristic

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

#10597341

yes

—

168

C₄

C₂²×D₇₆

yes

characteristic

169

C₄

C₂×#64545

yes

characteristic

170

C₂

—

171

C₂

#11926786

yes

direct product factor

172

C₂

C₂×#10597341

yes

characteristic

173

C₂

C₂×Q₁₆×D₁₉

yes

characteristic

174

C₂

C₂×#10597358

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×#107	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂³×D₁₉	D₄
hypercenter	C₂×#107	D₁₉
hypocenter	C₁₉	C₂×#467
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×#107

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂³×D₁₉

D₄

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
1. C₂²×Dic₇₆	C₂	semidirect
4. #11926786	C₂	direct (N × H)
5. C₂×#10597267	C₂	semidirect
6. C₂×C₁₉×#107	C₂	semidirect
15. C₂×Dic₇₆	C₂²	semidirect
20. C₁₉×#107	C₂²	semidirect
21. #10597267	C₂²	semidirect
48. C₂²×D₁₉	Q₁₆	semidirect
76. C₂×D₁₉	C₂×Q₁₆	semidirect
87. C₂×#107	D₁₉	semidirect
89. C₂×C₁₉	#467	semidirect
107. #107	C₂×D₁₉	semidirect
109. C₁₉	C₂×#467	semidirect
171. C₂	#11926786	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₇₆

C₂

semidirect

4. #11926786

C₂

direct (N × H)

5. C₂×#10597267

C₂

semidirect

6. C₂×C₁₉×#107

C₂

semidirect

15. C₂×Dic₇₆

C₂²

semidirect

20. C₁₉×#107

C₂²

semidirect

21. #10597267

C₂²

semidirect

48. C₂²×D₁₉

Q₁₆

semidirect

76. C₂×D₁₉

C₂×Q₁₆

semidirect

87. C₂×#107

D₁₉

semidirect

89. C₂×C₁₉

#467

semidirect

107. #107

C₂×D₁₉

semidirect

109. C₁₉

C₂×#467

semidirect

171. C₂

#11926786

direct (N × H)

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

subgroup	index
C₂²×Dic₇₆	2
C₂²×C₈×D₁₉	2
C₂×#10597343	2
#11926786	2
C₂×#10597267	2
C₂×C₁₉×#107	2
C₂×#467	19

subgroup

index

C₂²×Dic₇₆

C₂²×C₈×D₁₉

C₂×C₁₉×#107

Subgroups — C₂×#11926786 #14573210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926786 #14573210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926786 #14573210