Group #14565092 — subgroups

Subgroups — #14565092

Order 2432.

204 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 61 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	#11926593	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926549	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597290	C₂	1	1	yes	maximal, characteristic
4	#11926315	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926314	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926300	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#418	C₂	1	1	yes	maximal, characteristic
8	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#117	C₂²	1	1	yes	characteristic
11	#10597372	C₂²	1	1	yes	characteristic
12	C₂×#64520	C₂²	1	1	yes	characteristic
13	C₂×#64520	C₂²	1	1	yes	characteristic
14	C₂×#64520	C₂²	1	1	yes	characteristic
15	C₁₉×#102	—	2	2	no	—
16	#10597290	—	2	2	no	—
17	#10597289	—	2	2	no	—
18	#10597276	—	2	2	no	—
19	C₂⁴×C₁₉	—	2	1	no	—
20	C₂×D₄×C₁₉	—	2	1	no	—
21	C₂×D₄×C₁₉	—	2	1	no	—
22	C₂×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	D₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	M₁₆×C₁₉	—	2	1	no	—
28	M₁₆×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	D₄	1	2	yes	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₂²⋊C₄×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	—	2	1	no	—
33	C₂²⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄×Dic₁₉	—	2	1	no	—
36	#64520	—	2	1	no	—
37	#64520	—	2	1	no	—
38	#64520	—	2	1	no	—
39	#64520	—	2	1	no	—
40	#64520	—	2	1	no	—
41	#64520	—	2	1	no	—
42	C₂×C₁₉⋊C₈	—	2	1	no	—
43	C₂×C₁₉⋊C₈	—	2	1	no	—
44	C₂×C₁₉⋊C₈	—	2	1	no	—
45	C₂³×C₁₉	—	2	2	no	—
46	C₂³×C₁₉	—	4	1	no	—
47	C₂³×C₁₉	—	4	1	no	—
48	C₂³×C₁₉	—	8	2	no	—
49	C₂³×C₁₉	#41	1	1	yes	characteristic
50	D₄×C₁₉	—	2	2	no	—
51	D₄×C₁₉	—	2	2	no	—
52	D₄×C₁₉	—	4	1	no	—
53	D₄×C₁₉	—	4	1	no	—
54	C₂×C₄×C₁₉	—	4	1	no	—
55	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
58	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
59	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
60	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
61	C₂×Dic₁₉	—	4	1	no	—
62	C₈×C₁₉	—	2	2	no	—
63	C₁₉⋊C₈	—	4	1	no	—
64	C₁₉⋊C₈	—	4	1	no	—
65	C₁₉⋊C₈	—	4	1	no	—
66	#2081	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	—	4	1	no	—
68	C₂²×C₁₉	—	4	2	no	—
69	C₂²×C₁₉	—	8	2	no	—
70	C₂²×C₁₉	—	8	2	no	—
71	C₂²×C₁₉	—	8	2	no	—
72	C₂²×C₁₉	#123	1	1	yes	characteristic
73	C₂²×C₁₉	#124	1	1	yes	characteristic
74	C₂²×C₁₉	#126	1	1	yes	characteristic
75	C₄×C₁₉	—	8	1	no	—
76	C₄×C₁₉	#121	1	1	yes	characteristic
77	C₄×C₁₉	#123	1	1	yes	characteristic
78	C₄×C₁₉	#123	1	1	yes	characteristic
79	C₄×C₁₉	#126	1	1	yes	characteristic
80	Dic₁₉	—	8	1	no	—
81	#430	—	19	1	no	—
82	#418	—	19	1	no	—
83	#418	D₁₉	1	1	yes	characteristic
84	C₂×#100	—	19	1	no	—
85	#344	—	19	1	no	—
86	#344	—	19	1	no	—
87	H(3,ℤ/4)	—	19	1	no	—
88	C₂×C₁₉	—	2	1	no	—
89	C₂×C₁₉	—	2	1	no	—
90	C₂×C₁₉	—	2	1	no	—
91	C₂×C₁₉	—	8	2	no	—
92	C₂×C₁₉	#397	1	1	yes	characteristic
93	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
94	C₂×M₁₆	—	19	1	no	—
95	C₂×M₁₆	—	19	1	no	—
96	C₂×M₁₆	—	19	1	no	—
97	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
98	#117	—	19	1	no	—
99	#117	C₂×D₁₉	1	1	yes	characteristic
100	#108	—	38	2	no	—
101	#102	—	2	2	no	—
102	#102	—	38	2	no	—
103	#100	—	38	2	no	—
104	C₁₉	#2081	1	1	yes	characteristic, complemented, Sylow
105	C₂⁴	—	2	1	no	—
106	C₂×D₄	—	2	1	no	—
107	C₂×D₄	—	2	1	no	—
108	C₂×D₄	—	2	1	no	—
109	C₂×D₄	—	2	1	no	—
110	C₂×D₄	—	2	1	no	—
111	C₂×D₄	D₇₆	1	2	yes	—
112	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
113	M₁₆	—	2	1	no	—
114	M₁₆	—	2	1	no	—
115	M₁₆	—	38	1	no	—
116	M₁₆	—	38	1	no	—
117	M₁₆	—	38	1	no	—
118	M₁₆	—	38	1	no	—
119	M₁₆	—	38	1	no	—
120	M₁₆	—	38	1	no	—
121	C₂×C₈	—	38	1	no	—
122	C₂×C₈	—	38	1	no	—
123	C₂×C₈	—	38	1	no	—
124	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
125	C₄⋊C₄	—	2	1	no	—
126	C₄⋊C₄	—	38	1	no	—
127	C₂²⋊C₄	—	2	1	no	—
128	C₂²⋊C₄	—	38	1	no	—
129	C₄²	—	2	1	no	—
130	C₄²	—	38	1	no	—
131	C₂³	—	2	2	no	—
132	C₂³	—	4	1	no	—
133	C₂³	—	4	1	no	—
134	C₂³	—	8	2	no	—
135	C₂³	#64543	1	1	yes	characteristic
136	D₄	—	2	2	no	—
137	D₄	—	2	2	no	—
138	D₄	—	4	1	no	—
139	D₄	—	4	1	no	—
140	C₂×C₄	—	4	1	no	—
141	C₂×C₄	—	76	1	no	—
142	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
143	C₂×C₄	#64541	1	1	yes	characteristic
144	C₂×C₄	#64543	1	1	yes	characteristic
145	C₂×C₄	#64543	1	1	yes	characteristic
146	C₂×C₄	#64543	1	1	yes	characteristic
147	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
148	C₈	—	2	2	no	—
149	C₈	—	76	1	no	—
150	C₈	—	76	1	no	—
151	C₈	—	76	1	no	—
152	C₂²	—	4	1	no	—
153	C₂²	—	4	2	no	—
154	C₂²	—	8	2	no	—
155	C₂²	—	8	2	no	—
156	C₂²	—	8	2	no	—
157	C₂²	#10597325	1	1	yes	characteristic
158	C₂²	#10597332	1	1	yes	characteristic
159	C₂²	#10597382	1	1	yes	characteristic
160	C₄	—	8	1	no	—
161	C₄	—	152	1	no	—
162	C₄	#10597325	1	1	yes	characteristic
163	C₄	#10597332	1	1	yes	characteristic
164	C₄	#10597376	1	1	yes	characteristic
165	C₄	#10597381	1	1	yes	characteristic
166	C₂	—	2	1	no	—
167	C₂	—	2	1	no	—
168	C₂	—	2	1	no	—
169	C₂	—	8	2	no	—
170	C₂	#11926469	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926593

C₂

yes

maximal, characteristic, complemented

#11926549

C₂

yes

maximal, characteristic

C₂×#10597290

C₂

yes

maximal, characteristic

#11926315

C₂

yes

maximal, characteristic, complemented

#11926314

C₂

yes

maximal, characteristic, complemented

#11926300

C₂

yes

maximal, characteristic, complemented

C₁₉×#418

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₁₉×#102

—

#10597290

—

#10597289

—

#10597276

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

—

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#41

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2081

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#430

—

#418

—

#418

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#397

yes

characteristic

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

#117

—

#117

C₂×D₁₉

yes

characteristic

100

#108

—

101

#102

—

102

#102

—

103

#100

—

104

C₁₉

#2081

yes

characteristic, complemented, Sylow

105

C₂⁴

—

106

C₂×D₄

—

107

C₂×D₄

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

D₇₆

yes

—

112

C₂²×C₄

C₂²×D₁₉

yes

characteristic

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

M₁₆

—

117

M₁₆

—

118

M₁₆

—

119

M₁₆

—

120

M₁₆

—

121

C₂×C₈

—

122

C₂×C₈

—

123

C₂×C₈

—

124

C₂×C₈

C₂²⋊D₁₉

yes

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₂²⋊C₄

—

128

C₂²⋊C₄

—

129

C₄²

—

130

C₄²

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

—

135

C₂³

#64543

yes

characteristic

136

D₄

—

137

D₄

—

138

D₄

—

139

D₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

C₂×D₇₆

yes

characteristic

143

C₂×C₄

#64541

yes

characteristic

144

C₂×C₄

#64543

yes

characteristic

145

C₂×C₄

#64543

yes

characteristic

146

C₂×C₄

#64543

yes

characteristic

147

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

148

C₈

—

149

C₈

—

150

C₈

—

151

C₈

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

—

157

C₂²

#10597325

yes

characteristic

158

C₂²

#10597332

yes

characteristic

159

C₂²

#10597382

yes

characteristic

160

C₄

—

161

C₄

—

152

—

162

C₄

#10597325

yes

characteristic

163

C₄

#10597332

yes

characteristic

164

C₄

#10597376

yes

characteristic

165

C₄

#10597381

yes

characteristic

166

C₂

—

167

C₂

—

168

C₂

—

169

C₂

—

170

C₂

#11926469

yes

characteristic

	subgroup	G/H
center	C₂	#11926469
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#418	C₂
socle	C₂×C₁₉	#397
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	#418	D₁₉
hypocenter	C₁₉	#2081
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #418

subgroup

G/H

center

C₂

#11926469

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#418

C₂

socle

C₂×C₁₉

#397

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #418

N	H ≅ G/N	type
1. #11926593	C₂	semidirect
4. #11926315	C₂	semidirect
5. #11926314	C₂	semidirect
6. #11926300	C₂	semidirect
104. C₁₉	#2081	semidirect

H ≅ G/N

type

1. #11926593

C₂

semidirect

4. #11926315

C₂

semidirect

5. #11926314

C₂

semidirect

6. #11926300

C₂

semidirect

104. C₁₉

#2081

semidirect

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

subgroup	index
#11926593	2
#11926549	2
C₂×#10597290	2
#11926315	2
#11926314	2
#11926300	2
C₁₉×#418	2
#2081	19

subgroup

index

C₁₉×#418

Subgroups — #14565092

Conjugacy classes of subgroups

Complements

Maximal subgroups