Group #14564185 — subgroups

Subgroups — #14564185

Order 2432.

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

normal subgroups only

This group has 308 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	#11927311	C₂	1	1	yes	maximal, characteristic
2	#11927115	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597281	C₂	1	2	yes	maximal, complemented
4	#11926315	C₂	1	2	yes	maximal, complemented
5	C₁₉×#413	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
8	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
9	#10597394	—	2	4	no	—
10	#10597390	—	2	1	no	—
11	#10597382	—	2	1	no	—
12	#10597381	C₄	1	4	yes	—
13	#10597372	C₂²	1	1	yes	characteristic
14	#10597370	—	2	2	no	—
15	C₂×#64520	—	2	2	no	—
16	C₂×#64520	C₂²	1	2	yes	—
17	C₁₉×#101	—	2	1	no	—
18	C₁₉×#100	—	2	1	no	—
19	#10597281	—	2	4	no	—
20	#41×C₁₉	—	2	2	no	—
21	#41×C₁₉	—	2	2	no	—
22	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	D₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
28	C₂×Dic₃₈	—	2	1	no	—
29	C₂×Dic₃₈	—	2	2	no	—
30	C₂×Dic₃₈	—	2	1	no	—
31	C₂×Dic₃₈	—	2	2	no	—
32	M₁₆×C₁₉	—	2	2	no	—
33	M₁₆×C₁₉	—	2	2	no	—
34	C₂×C₈×C₁₉	—	2	2	no	—
35	C₂²⋊Dic₁₉	—	2	4	no	—
36	C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
37	C₄⋊Dic₁₉	—	2	1	no	—
38	Dic₁₉⋊C₄	—	2	4	no	—
39	C₄×Dic₁₉	—	2	1	no	—
40	#64520	—	2	4	no	—
41	#64520	—	2	2	no	—
42	#64520	D₄	1	4	yes	—
43	C₂×C₁₉⋊C₈	—	2	4	no	—
44	C₂×C₁₉⋊C₈	—	2	2	no	—
45	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
47	Q₈×C₁₉	—	2	2	no	—
48	D₄×C₁₉	—	2	4	no	—
49	D₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	2	2	no	—
52	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#41	1	2	yes	—
57	C₂×Dic₁₉	—	2	2	no	—
58	C₂×Dic₁₉	—	2	2	no	—
59	C₂×Dic₁₉	—	2	4	no	—
60	Dic₃₈	—	4	1	no	—
61	Dic₃₈	—	4	2	no	—
62	Dic₃₈	—	4	1	no	—
63	C₈×C₁₉	—	4	2	no	—
64	C₁₉⋊C₈	—	2	4	no	—
65	#1915	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	—	2	2	no	—
67	C₂²×C₁₉	—	4	1	no	—
68	C₂²×C₁₉	—	4	2	no	—
69	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₁₉	C₄×D₄	1	2	yes	—
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	#120	1	1	yes	characteristic
73	C₄×C₁₉	#121	1	2	yes	—
74	C₄×C₁₉	#123	1	1	yes	characteristic
75	Dic₁₉	—	4	2	no	—
76	Dic₁₉	—	4	2	no	—
77	#568	—	19	1	no	—
78	#536	—	19	1	no	—
79	#413	D₁₉	1	1	yes	characteristic
80	C₂×#101	—	19	2	no	—
81	#344	—	19	2	no	—
82	C₂×C₁₉	—	2	1	no	—
83	C₂×C₁₉	—	2	2	no	—
84	C₂×C₁₉	—	4	2	no	—
85	C₂×C₁₉	#386	1	1	yes	characteristic
86	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
87	C₂²×Q₈	—	19	1	no	—
88	#131	—	38	4	no	—
89	C₂×M₁₆	—	19	2	no	—
90	C₂×M₁₆	—	38	2	no	—
91	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
92	C₄⋊Q₈	—	38	1	no	—
93	#124	—	38	1	no	—
94	#123	—	19	4	no	—
95	C₂²⋊Q₈	—	38	2	no	—
96	#117	—	19	1	no	—
97	#101	—	2	1	no	—
98	#101	—	38	4	no	—
99	#100	—	2	1	no	—
100	C₁₉	#1915	1	1	yes	characteristic, complemented, Sylow
101	#41	—	2	2	no	—
102	#41	—	2	2	no	—
103	C₂×Q₈	—	38	1	no	—
104	C₂×Q₈	—	38	2	no	—
105	C₂×Q₈	—	38	2	no	—
106	C₂×Q₈	—	38	1	no	—
107	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
108	C₂×D₄	C₄×D₁₉	1	2	yes	—
109	C₂×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂²×C₄	—	19	2	no	—
111	C₂²×C₄	D₇₆	1	2	yes	—
112	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
113	M₁₆	—	2	2	no	—
114	M₁₆	—	2	2	no	—
115	M₁₆	—	19	4	no	—
116	M₁₆	—	38	4	no	—
117	M₁₆	—	38	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	38	4	no	—
120	C₂×C₈	—	38	2	no	—
121	C₄⋊C₄	—	38	4	no	—
122	C₄⋊C₄	—	38	1	no	—
123	C₂²⋊C₄	—	19	2	no	—
124	C₂²⋊C₄	—	38	4	no	—
125	C₄²	—	38	1	no	—
126	C₂³	(C₂×D₁₉)⋊C₄	1	2	yes	—
127	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
128	Q₈	—	2	2	no	—
129	Q₈	—	76	2	no	—
130	Q₈	—	76	1	no	—
131	Q₈	—	76	1	no	—
132	D₄	—	2	4	no	—
133	D₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	2	no	—
136	C₂×C₄	—	38	4	no	—
137	C₂×C₄	—	38	2	no	—
138	C₂×C₄	—	38	2	no	—
139	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
140	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
141	C₂×C₄	D₄×D₁₉	1	2	yes	—
142	C₂×C₄	#64543	1	2	yes	—
143	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
144	C₈	—	4	2	no	—
145	C₈	—	38	4	no	—
146	C₂²	—	2	2	no	—
147	C₂²	—	4	1	no	—
148	C₂²	—	4	2	no	—
149	C₂²	(C₂²⋊D₁₉)⋊C₄	1	2	yes	—
150	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	76	2	no	—
153	C₄	—	76	2	no	—
154	C₄	#10597328	1	1	yes	characteristic
155	C₄	#10597332	1	1	yes	characteristic
156	C₄	#10597385	1	2	yes	—
157	C₂	—	2	1	no	—
158	C₂	—	2	2	no	—
159	C₂	—	4	2	no	—
160	C₂	#11926421	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927311

C₂

yes

maximal, characteristic

#11927115

C₂

yes

maximal, characteristic

C₂×#10597281

C₂

yes

maximal, complemented

#11926315

C₂

yes

maximal, complemented

C₁₉×#413

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

—

—

—

C₄

yes

—

#10597372

C₂²

yes

—

—

C₂²

yes

—

C₁₉×#101

—

C₁₉×#100

—

#10597281

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

#64520

—

#64520

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1915

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#123

yes

characteristic

Dic₁₉

—

Dic₁₉

—

#568

—

#536

—

#413

D₁₉

yes

characteristic

C₂×#101

—

#344

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#386

yes

characteristic

C₂×#41

C₂×D₁₉

yes

characteristic

C₂²×Q₈

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₄⋊Q₈

—

#124

—

#123

—

C₂²⋊Q₈

—

—

—

—

—

100

C₁₉

#1915

yes

characteristic, complemented, Sylow

101

#41

—

102

#41

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

C₂²⋊D₁₉

yes

characteristic

108

C₂×D₄

C₄×D₁₉

yes

—

109

C₂×D₄

C₂²⋊D₁₉

yes

characteristic

110

C₂²×C₄

—

111

C₂²×C₄

D₇₆

yes

—

112

C₂²×C₄

C₂²×D₁₉

yes

characteristic

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

M₁₆

—

117

M₁₆

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₂×C₈

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₂²⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

—

126

C₂³

(C₂×D₁₉)⋊C₄

yes

—

127

C₂³

C₂×C₄×D₁₉

yes

characteristic

128

Q₈

—

129

Q₈

—

130

Q₈

—

131

Q₈

—

132

D₄

—

133

D₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

140

C₂×C₄

C₂×D₇₆

yes

characteristic

141

C₂×C₄

D₄×D₁₉

yes

—

142

C₂×C₄

#64543

yes

—

143

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

144

C₈

—

145

C₈

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

—

150

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

#10597328

yes

characteristic

155

C₄

#10597332

yes

characteristic

156

C₄

#10597385

yes

—

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#11926421

yes

characteristic

	subgroup	G/H
center	C₂	#11926421
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#413	C₂
socle	C₂×C₁₉	#386
prime radical	C₂×#41×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#413	D₁₉
hypocenter	C₁₉	#1915
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #413

subgroup

G/H

center

C₂

#11926421

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#413

C₂

socle

C₂×C₁₉

#386

prime radical

C₂×#41×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #413

N	H ≅ G/N	type
3. C₂×#10597281	C₂	semidirect
4. #11926315	C₂	semidirect
100. C₁₉	#1915	semidirect

H ≅ G/N

type

3. C₂×#10597281

C₂

semidirect

4. #11926315

C₂

semidirect

100. C₁₉

#1915

semidirect

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

subgroup	index
#11927311	2
#11927115	2
C₂×#10597281	2
#11926315	2
C₁₉×#413	2
#1915	19

subgroup

index

C₁₉×#413

Subgroups — #14564185

Conjugacy classes of subgroups

Complements

Maximal subgroups