Group #14564734 — subgroups

Subgroups — #14564734

Order 2432.

370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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×#64528	C₂	1	2	yes	maximal
2	C₂×#10597315	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597267	C₂	1	2	yes	maximal
4	#11926299	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₈	C₂²	1	2	yes	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×#64528	—	2	4	no	—
11	C₂×#64528	—	2	4	no	—
12	C₂×#64528	—	2	4	no	—
13	C₂×C₄⋊Dic₁₉	—	2	2	no	—
14	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
15	#10597315	—	2	4	no	—
16	C₁₉×#95	—	2	2	no	—
17	#10597267	—	2	4	no	—
18	C₂×Q₈×C₁₉	—	2	1	no	—
19	C₂×Q₈×C₁₉	—	2	2	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	D₄	1	2	yes	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	D₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	2	2	no	—
27	C₂×Dic₃₈	—	2	2	no	—
28	C₂×Dic₃₈	—	2	2	no	—
29	C₂×Dic₃₈	—	2	2	no	—
30	C₂×Dic₃₈	—	2	2	no	—
31	C₂×Dic₃₈	—	2	2	no	—
32	C₂×Dic₃₈	D₄	1	4	yes	—
33	C₄⋊C₄×C₁₉	—	2	2	no	—
34	C₄²×C₁₉	—	2	2	no	—
35	#64528	—	2	16	no	—
36	C₄⋊Dic₁₉	—	2	8	no	—
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
40	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
41	Q₈×C₁₉	—	2	4	no	—
42	Q₈×C₁₉	—	4	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	Q₁₆	1	4	yes	complemented
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂×Dic₁₉	—	2	4	no	—
56	C₂×Dic₁₉	—	4	2	no	—
57	C₂×Dic₁₉	—	4	2	no	—
58	Dic₃₈	—	2	4	no	—
59	Dic₃₈	—	2	4	no	—
60	Dic₃₈	—	4	2	no	—
61	Dic₃₈	—	4	2	no	—
62	C₁₉⋊C₈	—	2	4	no	—
63	#2016	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	#120	1	1	yes	characteristic
65	C₂²×C₁₉	#121	1	1	yes	characteristic
66	C₂²×C₁₉	#127	1	1	yes	characteristic
67	C₂²×C₁₉	C₂×Q₁₆	1	2	yes	—
68	C₂²×C₁₉	#137	1	2	yes	—
69	C₄×C₁₉	—	2	4	no	—
70	C₄×C₁₉	—	4	2	no	—
71	C₄×C₁₉	—	8	1	no	—
72	C₄×C₁₉	#120	1	2	yes	—
73	C₄×C₁₉	#121	1	2	yes	—
74	Dic₁₉	—	4	4	no	—
75	C₂²×Q₁₆	—	19	2	no	—
76	C₂×C₄⋊Q₈	—	19	1	no	—
77	C₂×#103	—	19	2	no	—
78	#391	D₁₉	1	1	yes	characteristic
79	#336	—	19	1	no	—
80	C₂×C₁₉	#392	1	1	yes	characteristic
81	C₂×C₁₉	#451	1	2	yes	—
82	C₂×C₁₉	#462	1	2	yes	—
83	C₂×C₁₉	#494	1	1	yes	characteristic
84	C₂×C₁₉	#497	1	1	yes	characteristic
85	C₂²×Q₈	—	19	2	no	—
86	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
87	C₂×Q₁₆	—	38	4	no	—
88	C₂×Q₁₆	—	38	4	no	—
89	C₂×Q₁₆	—	38	4	no	—
90	C₂²×C₈	—	19	2	no	—
91	C₄⋊Q₈	—	38	4	no	—
92	C₂×C₄⋊C₄	—	38	2	no	—
93	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
94	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
95	#103	—	38	4	no	—
96	#95	—	2	2	no	—
97	C₁₉	#2016	1	1	yes	characteristic, complemented, Sylow
98	C₂×Q₈	—	2	1	no	—
99	C₂×Q₈	—	2	2	no	—
100	C₂×Q₈	—	2	2	no	—
101	C₂×Q₈	—	19	4	no	—
102	C₂×Q₈	—	38	2	no	—
103	C₂×Q₈	—	38	2	no	—
104	C₂×Q₈	—	38	2	no	—
105	C₂×Q₈	—	38	2	no	—
106	C₂×Q₈	—	38	2	no	—
107	C₂×Q₈	D₇₆	1	2	yes	—
108	C₂²×C₄	—	2	1	no	—
109	C₂²×C₄	—	2	1	no	—
110	C₂²×C₄	—	38	2	no	—
111	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
112	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
113	Q₁₆	—	38	16	no	—
114	C₂×C₈	—	19	4	no	—
115	C₂×C₈	—	38	2	no	—
116	C₂×C₈	—	38	2	no	—
117	C₄⋊C₄	—	2	2	no	—
118	C₄⋊C₄	—	38	8	no	—
119	C₄²	—	2	2	no	—
120	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
121	Q₈	—	2	4	no	—
122	Q₈	—	4	2	no	—
123	Q₈	—	38	4	no	—
124	Q₈	—	38	4	no	—
125	Q₈	—	76	2	no	—
126	Q₈	—	76	2	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	4	1	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	38	4	no	—
135	C₂×C₄	—	76	2	no	—
136	C₂×C₄	—	76	2	no	—
137	C₂×C₄	#64528	1	4	yes	complemented
138	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
139	C₂×C₄	#64541	1	1	yes	characteristic
140	C₂×C₄	D₄×D₁₉	1	2	yes	—
141	C₂×C₄	D₄×D₁₉	1	2	yes	—
142	C₈	—	38	4	no	—
143	C₂²	#10597376	1	1	yes	characteristic
144	C₂²	#10597383	1	1	yes	characteristic
145	C₂²	#10597386	1	1	yes	characteristic
146	C₂²	C₂×#64528	1	2	yes	—
147	C₂²	#10597397	1	2	yes	—
148	C₄	—	2	4	no	—
149	C₄	—	4	2	no	—
150	C₄	—	8	1	no	—
151	C₄	—	76	4	no	—
152	C₄	#10597328	1	2	yes	—
153	C₄	#10597330	1	2	yes	—
154	C₂	#11926453	1	1	yes	characteristic
155	C₂	#11926699	1	2	yes	—
156	C₂	#11926754	1	2	yes	—
157	C₂	#11926923	1	1	yes	characteristic
158	C₂	#11926939	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#64528

C₂

yes

maximal

C₂×#10597315

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal

#11926299

C₂

yes

maximal, characteristic

C₁₉×#391

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

—

—

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597315

—

C₁₉×#95

—

#10597267

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

#64528

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

Q₁₆

yes

complemented

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×Q₁₆

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

—

C₂×#103

—

#391

D₁₉

yes

characteristic

#336

—

C₂×C₁₉

#392

yes

characteristic

C₂×C₁₉

#451

yes

—

C₂×C₁₉

#462

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

#103

—

#95

—

C₁₉

#2016

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

D₇₆

yes

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

C₂²⋊D₁₉

yes

—

112

C₂²×C₄

C₂²×D₁₉

yes

characteristic

113

Q₁₆

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄²

—

120

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

125

Q₈

—

126

Q₈

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

#64528

yes

complemented

138

C₂×C₄

C₂×D₇₆

yes

characteristic

139

C₂×C₄

#64541

yes

characteristic

140

C₂×C₄

D₄×D₁₉

yes

—

141

C₂×C₄

D₄×D₁₉

yes

—

142

C₈

—

143

C₂²

#10597376

yes

characteristic

144

C₂²

#10597383

yes

characteristic

145

C₂²

#10597386

yes

characteristic

146

C₂²

C₂×#64528

yes

—

147

C₂²

#10597397

yes

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

#10597328

yes

—

153

C₄

#10597330

yes

—

154

C₂

#11926453

yes

characteristic

155

C₂

#11926699

yes

—

156

C₂

#11926754

yes

—

157

C₂

#11926923

yes

characteristic

158

C₂

#11926939

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#391	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2016
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#391

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
50. C₂×C₄×C₁₉	Q₁₆	semidirect
97. C₁₉	#2016	semidirect
137. C₂×C₄	#64528	semidirect

H ≅ G/N

type

50. C₂×C₄×C₁₉

Q₁₆

semidirect

97. C₁₉

#2016

semidirect

137. C₂×C₄

#64528

semidirect

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

subgroup	index
C₂²×#64528	2
C₂×#10597315	2
C₂×#10597267	2
#11926299	2
C₁₉×#391	2
#2016	19

subgroup

index

C₂²×#64528

C₁₉×#391

Subgroups — #14564734

Conjugacy classes of subgroups

Complements

Maximal subgroups