Group #14563839 — subgroups

Subgroups — #14563839

Order 2432.

278 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 93 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×#64520	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597279	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#11926308	C₂	1	2	yes	maximal, complemented
5	C₁₉×#407	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×#64520	—	2	1	no	—
10	C₂×#64520	—	2	4	no	—
11	C₂×#64520	C₂²	1	2	yes	—
12	C₂²×C₁₉⋊C₈	—	2	1	no	—
13	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
14	C₁₉×C₂²⋊C₈	—	2	1	no	—
15	C₁₉×C₂²⋊C₈	—	2	1	no	—
16	C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
17	C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
18	#10597279	—	2	4	no	—
19	C₂⁴×C₁₉	Q₈	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	M₁₆×C₁₉	—	2	2	no	—
29	M₁₆×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₂×C₈×C₁₉	—	2	1	no	—
32	#64520	—	2	4	no	—
33	#64520	—	2	2	no	—
34	#64520	D₄	1	4	yes	—
35	C₂×C₁₉⋊C₈	—	2	4	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
40	C₂³×C₁₉	—	2	2	no	—
41	C₂³×C₁₉	—	2	2	no	—
42	C₂³×C₁₉	—	4	1	no	—
43	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	2	1	no	—
53	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#41	1	2	yes	—
59	C₈×C₁₉	—	4	1	no	—
60	C₈×C₁₉	—	4	1	no	—
61	C₁₉⋊C₈	—	2	4	no	—
62	C₁₉⋊C₈	—	2	4	no	—
63	#1855	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	—	2	1	no	—
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	—	2	1	no	—
70	C₂²×C₁₉	—	2	1	no	—
71	C₂²×C₁₉	—	4	4	no	—
72	C₂²×C₁₉	#108	1	2	yes	complemented
73	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
75	C₄×C₁₉	—	2	1	no	—
76	C₄×C₁₉	—	2	1	no	—
77	C₄×C₁₉	C₄×D₄	1	2	yes	—
78	C₄×C₁₉	#120	1	1	yes	characteristic
79	C₄×C₁₉	#123	1	1	yes	characteristic
80	C₂²×M₁₆	—	19	1	no	—
81	C₂×#108	—	19	2	no	—
82	#407	D₁₉	1	1	yes	characteristic
83	C₂×C₂²⋊C₈	—	19	1	no	—
84	#341	—	19	2	no	—
85	C₂×C₁₉	—	2	2	no	—
86	C₂×C₁₉	—	2	2	no	—
87	C₂×C₁₉	—	4	1	no	—
88	C₂×C₁₉	#385	1	1	yes	characteristic
89	C₂×C₁₉	C₂×#108	1	1	yes	characteristic
90	C₂×C₁₉	#430	1	1	yes	characteristic
91	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
92	C₂×M₁₆	—	19	2	no	—
93	C₂×M₁₆	—	38	4	no	—
94	C₂×M₁₆	—	38	1	no	—
95	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
96	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
97	C₂²×C₈	—	19	2	no	—
98	C₂²×C₈	—	38	1	no	—
99	#108	—	38	4	no	—
100	C₂²⋊C₈	—	2	1	no	—
101	C₂²⋊C₈	—	2	1	no	—
102	C₂²⋊C₈	—	19	2	no	—
103	C₂²⋊C₈	—	19	2	no	—
104	C₁₉	#1855	1	1	yes	characteristic, complemented, Sylow
105	C₂⁴	Dic₃₈	1	1	yes	characteristic
106	C₂²×C₄	—	2	2	no	—
107	C₂²×C₄	—	2	2	no	—
108	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
109	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
110	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
111	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
113	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
114	M₁₆	—	2	2	no	—
115	M₁₆	—	2	2	no	—
116	M₁₆	—	19	4	no	—
117	M₁₆	—	38	4	no	—
118	M₁₆	—	38	2	no	—
119	C₂×C₈	—	2	1	no	—
120	C₂×C₈	—	2	1	no	—
121	C₂×C₈	—	19	4	no	—
122	C₂×C₈	—	38	4	no	—
123	C₂×C₈	—	38	2	no	—
124	C₂×C₈	—	38	2	no	—
125	C₂×C₈	—	38	2	no	—
126	C₂³	—	2	2	no	—
127	C₂³	—	2	2	no	—
128	C₂³	—	4	1	no	—
129	C₂³	Dic₁₉⋊C₄	1	1	yes	characteristic
130	C₂³	Dic₁₉⋊C₄	1	1	yes	characteristic
131	C₂³	C₂×Dic₃₈	1	1	yes	characteristic
132	C₂×C₄	—	2	2	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	2	1	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
140	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
141	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
142	C₂×C₄	D₄×D₁₉	1	2	yes	—
143	C₂×C₄	#64543	1	2	yes	—
144	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
145	C₈	—	4	1	no	—
146	C₈	—	4	1	no	—
147	C₈	—	38	4	no	—
148	C₈	—	38	4	no	—
149	C₂²	—	2	1	no	—
150	C₂²	—	2	1	no	—
151	C₂²	—	2	1	no	—
152	C₂²	—	2	1	no	—
153	C₂²	—	2	1	no	—
154	C₂²	—	2	1	no	—
155	C₂²	—	2	1	no	—
156	C₂²	—	4	4	no	—
157	C₂²	#10597279	1	2	yes	complemented
158	C₂²	#10597324	1	2	yes	—
159	C₂²	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
160	C₄	—	2	1	no	—
161	C₄	—	2	1	no	—
162	C₄	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
163	C₄	#10597381	1	1	yes	characteristic
164	C₄	#10597383	1	1	yes	characteristic
165	C₂	—	2	2	no	—
166	C₂	—	2	2	no	—
167	C₂	—	4	1	no	—
168	C₂	#11926416	1	1	yes	characteristic
169	C₂	C₂×#10597279	1	1	yes	characteristic
170	C₂	#11926592	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64520

C₂

yes

maximal, characteristic

C₂×#10597279

C₂

yes

maximal, complemented

C₂×C₂²⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

#11926308

C₂

yes

maximal, complemented

C₁₉×#407

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

—

C₂²

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

#10597279

—

C₂⁴×C₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

#64520

—

#64520

—

#64520

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄⋊C₄

yes

characteristic

C₂³×C₁₉

C₄⋊C₄

yes

characteristic

C₂³×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1855

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#108

yes

complemented

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂²×M₁₆

—

C₂×#108

—

#407

D₁₉

yes

characteristic

C₂×C₂²⋊C₈

—

#341

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

#108

—

100

C₂²⋊C₈

—

101

C₂²⋊C₈

—

102

C₂²⋊C₈

—

103

C₂²⋊C₈

—

104

C₁₉

#1855

yes

characteristic, complemented, Sylow

105

C₂⁴

Dic₃₈

yes

characteristic

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

Dic₃₈

yes

characteristic

109

C₂²×C₄

C₄×D₁₉

yes

characteristic

110

C₂²×C₄

C₄×D₁₉

yes

characteristic

111

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

112

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

113

C₂²×C₄

C₂²×D₁₉

yes

characteristic

114

M₁₆

—

115

M₁₆

—

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂³

—

127

C₂³

—

128

C₂³

—

129

C₂³

Dic₁₉⋊C₄

yes

characteristic

130

C₂³

Dic₁₉⋊C₄

yes

characteristic

131

C₂³

C₂×Dic₃₈

yes

characteristic

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

140

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

141

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

142

C₂×C₄

D₄×D₁₉

yes

—

143

C₂×C₄

#64543

yes

—

144

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

145

C₈

—

146

C₈

—

147

C₈

—

148

C₈

—

149

C₂²

—

150

C₂²

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

#10597279

yes

complemented

158

C₂²

#10597324

yes

—

159

C₂²

C₂×Dic₁₉⋊C₄

yes

characteristic

160

C₄

—

161

C₄

—

162

C₄

(C₂²⋊D₁₉)⋊C₄

yes

—

163

C₄

#10597381

yes

characteristic

164

C₄

#10597383

yes

characteristic

165

C₂

—

166

C₂

—

167

C₂

—

168

C₂

#11926416

yes

characteristic

169

C₂

C₂×#10597279

yes

characteristic

170

C₂

#11926592

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#407	C₂
socle	C₂²×C₁₉	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₉	Q₈
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#407	D₁₉
hypocenter	C₁₉	#1855
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#407

C₂

socle

C₂²×C₁₉

C₂×C₄⋊C₄

prime radical

C₂⁴×C₁₉

Q₈

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #407

N	H ≅ G/N	type
2. C₂×#10597279	C₂	semidirect
4. #11926308	C₂	semidirect
72. C₂²×C₁₉	#108	semidirect
104. C₁₉	#1855	semidirect
157. C₂²	#10597279	semidirect

H ≅ G/N

type

2. C₂×#10597279

C₂

semidirect

4. #11926308

C₂

semidirect

72. C₂²×C₁₉

#108

semidirect

104. C₁₉

#1855

semidirect

157. C₂²

#10597279

semidirect

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

subgroup	index
C₂²×#64520	2
C₂×#10597279	2
C₂×C₂²⋊(C₁₉⋊C₈)	2
#11926308	2
C₁₉×#407	2
#1855	19

subgroup

index

C₂²×#64520

C₂×#10597279

C₂×C₂²⋊(C₁₉⋊C₈)

#11926308

C₁₉×#407

#1855

Subgroups — #14563839

Conjugacy classes of subgroups

Complements

Maximal subgroups