Group #14564745 — subgroups

Subgroups — #14564745

Order 2432.

382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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	C₂×#10597354	C₂	1	2	yes	maximal, complemented
2	C₂²×D₁₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597280	C₂	1	2	yes	maximal, complemented
4	#11926510	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	C₂²	1	1	yes	characteristic
7	C₂²×D₇₆	C₂²	1	2	yes	—
8	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×#64520	C₂²	1	1	yes	characteristic
11	#10597354	—	2	4	no	—
12	#10597354	—	2	4	no	—
13	C₂×D₁₅₂	—	2	4	no	—
14	C₂×D₁₅₂	—	2	2	no	—
15	C₂×D₁₅₂	—	2	2	no	—
16	C₂×#64516	—	2	2	no	—
17	#10597280	—	2	4	no	—
18	(C₂×D₁₉)⋊C₈	—	2	2	no	—
19	C₂³×D₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₂²⋊D₁₉	—	2	1	no	—
22	#64541	—	2	2	no	—
23	#64541	—	2	2	no	—
24	C₂×D₇₆	—	2	2	no	—
25	C₂×D₇₆	—	2	2	no	—
26	C₂×D₇₆	—	2	2	no	—
27	C₂×D₇₆	—	2	2	no	—
28	C₂×D₇₆	—	2	2	no	—
29	C₂×D₇₆	D₄	1	4	yes	—
30	C₂×D₇₆	D₄	1	1	yes	characteristic
31	C₂×C₄×D₁₉	—	2	1	no	—
32	C₂×Dic₃₈	D₄	1	1	yes	characteristic
33	M₁₆×C₁₉	—	2	2	no	—
34	M₁₆×C₁₉	D₄	1	4	yes	—
35	C₂×C₈×C₁₉	—	2	2	no	—
36	C₂×C₈×C₁₉	—	2	2	no	—
37	C₂×C₈×C₁₉	D₄	1	2	yes	—
38	#64520	—	2	2	no	—
39	C₂×C₁₉⋊C₈	—	2	1	no	—
40	D₁₅₂	—	2	8	no	—
41	D₁₅₂	—	2	8	no	—
42	#64516	—	2	8	no	—
43	C₂³×C₁₉	#41	1	1	yes	characteristic
44	C₂²×D₁₉	—	2	1	no	—
45	C₂²×D₁₉	—	2	4	no	—
46	C₂²×D₁₉	—	4	2	no	—
47	C₂²×D₁₉	—	4	2	no	—
48	C₂²×D₁₉	—	8	4	no	—
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
53	C₂²⋊D₁₉	—	4	2	no	—
54	C₂×Dic₁₉	—	2	1	no	—
55	D₇₆	—	2	4	no	—
56	D₇₆	—	2	4	no	—
57	D₇₆	—	2	2	no	—
58	D₇₆	—	4	2	no	—
59	D₇₆	—	4	2	no	—
60	C₄×D₁₉	—	4	1	no	—
61	C₄×D₁₉	—	4	1	no	—
62	Dic₃₈	—	2	2	no	—
63	C₈×C₁₉	—	2	4	no	—
64	C₈×C₁₉	—	2	2	no	—
65	C₁₉⋊C₈	—	4	1	no	—
66	#2018	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	—	2	2	no	—
68	C₂²×C₁₉	#121	1	2	yes	—
69	C₂²×C₁₉	#121	1	1	yes	characteristic
70	C₂×D₁₉	—	4	1	no	—
71	C₂×D₁₉	—	4	4	no	—
72	C₂×D₁₉	—	4	2	no	—
73	C₂×D₁₉	—	8	4	no	—
74	C₂×D₁₉	—	8	4	no	—
75	C₂×D₁₉	—	8	4	no	—
76	C₄×C₁₉	#120	1	2	yes	—
77	C₄×C₁₉	#120	1	1	yes	characteristic
78	C₄×C₁₉	#127	1	1	yes	characteristic
79	Dic₁₉	—	4	1	no	—
80	C₂×AGL(1,ℤ/8)	—	19	2	no	—
81	C₂²×D₈	—	19	1	no	—
82	C₂×#100	—	19	2	no	—
83	#408	—	19	1	no	—
84	#341	D₁₉	1	1	yes	characteristic, complemented
85	C₂×C₁₉	—	2	2	no	—
86	C₂×C₁₉	#392	1	1	yes	characteristic
87	C₂×C₁₉	#472	1	2	yes	—
88	D₁₉	—	8	1	no	—
89	D₁₉	—	8	4	no	—
90	C₂×#41	—	19	1	no	—
91	C₂²×D₄	—	19	2	no	—
92	AGL(1,ℤ/8)	—	38	4	no	—
93	AGL(1,ℤ/8)	—	38	4	no	—
94	C₂×SD₁₆	—	38	2	no	—
95	C₂×D₈	—	38	4	no	—
96	C₂×D₈	—	38	2	no	—
97	C₂×D₈	—	38	2	no	—
98	C₂×M₁₆	—	19	1	no	—
99	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
100	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
101	#100	—	38	4	no	—
102	C₂²⋊C₈	—	38	2	no	—
103	C₁₉	#2018	1	1	yes	characteristic, complemented, Sylow
104	C₂⁴	—	38	2	no	—
105	#41	—	38	2	no	—
106	#41	—	38	2	no	—
107	C₂×Q₈	—	19	1	no	—
108	C₂×D₄	—	19	1	no	—
109	C₂×D₄	—	19	4	no	—
110	C₂×D₄	—	38	1	no	—
111	C₂×D₄	—	38	2	no	—
112	C₂×D₄	—	38	2	no	—
113	C₂×D₄	—	38	2	no	—
114	C₂×D₄	—	38	2	no	—
115	C₂×D₄	—	38	2	no	—
116	C₂²×C₄	—	38	1	no	—
117	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
118	SD₁₆	—	38	8	no	—
119	D₈	—	38	8	no	—
120	D₈	—	38	8	no	—
121	M₁₆	—	2	2	no	—
122	M₁₆	—	38	2	no	—
123	M₁₆	D₇₆	1	4	yes	—
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	—	38	1	no	—
127	C₂×C₈	D₇₆	1	2	yes	—
128	C₂³	—	38	1	no	—
129	C₂³	—	38	4	no	—
130	C₂³	—	76	2	no	—
131	C₂³	—	76	2	no	—
132	C₂³	—	152	4	no	—
133	C₂³	#64545	1	1	yes	characteristic
134	Q₈	—	38	2	no	—
135	D₄	—	38	4	no	—
136	D₄	—	38	2	no	—
137	D₄	—	38	4	no	—
138	D₄	—	76	2	no	—
139	D₄	—	76	2	no	—
140	D₄	—	76	2	no	—
141	C₂×C₄	—	38	1	no	—
142	C₂×C₄	—	76	1	no	—
143	C₂×C₄	—	76	1	no	—
144	C₂×C₄	C₂×D₇₆	1	2	yes	—
145	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
146	C₂×C₄	D₄×D₁₉	1	2	yes	—
147	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
148	C₈	—	2	2	no	—
149	C₈	—	2	4	no	—
150	C₈	—	76	1	no	—
151	C₂²	—	2	2	no	—
152	C₂²	—	76	2	no	—
153	C₂²	—	76	1	no	—
154	C₂²	—	76	4	no	—
155	C₂²	—	152	4	no	—
156	C₂²	—	152	4	no	—
157	C₂²	—	152	4	no	—
158	C₂²	#10597341	1	2	yes	—
159	C₂²	#10597341	1	1	yes	characteristic
160	C₄	—	76	1	no	—
161	C₄	#10597320	1	1	yes	characteristic
162	C₄	#10597328	1	1	yes	characteristic
163	C₄	#10597328	1	2	yes	—
164	C₂	—	2	2	no	—
165	C₂	—	152	1	no	—
166	C₂	—	152	4	no	—
167	C₂	#11926454	1	1	yes	characteristic
168	C₂	#11926815	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597354

C₂

yes

maximal, complemented

C₂²×D₁₅₂

C₂

yes

maximal, characteristic, complemented

C₂×#10597280

C₂

yes

maximal, complemented

#11926510

C₂

yes

maximal, characteristic, complemented

C₁₉×#341

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

characteristic

C₂²×D₇₆

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

#10597354

—

#10597354

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×D₁₅₂

—

C₂×#64516

—

#10597280

—

(C₂×D₁₉)⋊C₈

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

D₄

yes

—

C₂×D₇₆

D₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×Dic₃₈

D₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

D₁₅₂

—

#64516

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2018

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

#121

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

#120

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×AGL(1,ℤ/8)

—

C₂²×D₈

—

C₂×#100

—

#408

—

#341

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

#392

yes

characteristic

C₂×C₁₉

#472

yes

—

D₁₉

—

D₁₉

—

C₂×#41

—

C₂²×D₄

—

AGL(1,ℤ/8)

—

AGL(1,ℤ/8)

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

100

C₂²×C₈

C₂×D₁₉

yes

characteristic

101

#100

—

102

C₂²⋊C₈

—

103

C₁₉

#2018

yes

characteristic, complemented, Sylow

104

C₂⁴

—

105

#41

—

106

#41

—

107

C₂×Q₈

—

108

C₂×D₄

—

109

C₂×D₄

—

110

C₂×D₄

—

111

C₂×D₄

—

112

C₂×D₄

—

113

C₂×D₄

—

114

C₂×D₄

—

115

C₂×D₄

—

116

C₂²×C₄

—

117

C₂²×C₄

C₂²×D₁₉

yes

characteristic

118

SD₁₆

—

119

D₈

—

120

D₈

—

121

M₁₆

—

122

M₁₆

—

123

M₁₆

D₇₆

yes

—

124

C₂×C₈

—

125

C₂×C₈

—

126

C₂×C₈

—

127

C₂×C₈

D₇₆

yes

—

128

C₂³

—

129

C₂³

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

152

—

133

C₂³

#64545

yes

characteristic

134

Q₈

—

135

D₄

—

136

D₄

—

137

D₄

—

138

D₄

—

139

D₄

—

140

D₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

C₂×D₇₆

yes

—

145

C₂×C₄

C₂×D₇₆

yes

characteristic

146

C₂×C₄

D₄×D₁₉

yes

—

147

C₂×C₄

D₄×D₁₉

yes

characteristic

148

C₈

—

149

C₈

—

150

C₈

—

151

C₂²

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

152

—

156

C₂²

—

152

—

157

C₂²

—

152

—

158

C₂²

#10597341

yes

—

159

C₂²

#10597341

yes

characteristic

160

C₄

—

161

C₄

#10597320

yes

characteristic

162

C₄

#10597328

yes

characteristic

163

C₄

#10597328

yes

—

164

C₂

—

165

C₂

—

152

—

166

C₂

—

152

—

167

C₂

#11926454

yes

characteristic

168

C₂

#11926815

yes

—

	subgroup	G/H
center	C₂²	#10597341
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#341	C₂
socle	C₂²×C₁₉	#121
hypercenter	#341	D₁₉
hypocenter	C₁₉	#2018
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#10597341

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#341

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
1. C₂×#10597354	C₂	semidirect
2. C₂²×D₁₅₂	C₂	semidirect
3. C₂×#10597280	C₂	semidirect
4. #11926510	C₂	semidirect
5. C₁₉×#341	C₂	semidirect
84. #341	D₁₉	semidirect
103. C₁₉	#2018	semidirect

H ≅ G/N

type

1. C₂×#10597354

C₂

semidirect

2. C₂²×D₁₅₂

C₂

semidirect

3. C₂×#10597280

C₂

semidirect

4. #11926510

C₂

semidirect

5. C₁₉×#341

C₂

semidirect

84. #341

D₁₉

semidirect

103. C₁₉

#2018

semidirect

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

subgroup	index
C₂×#10597354	2
C₂²×D₁₅₂	2
C₂×#10597280	2
#11926510	2
C₁₉×#341	2
#2018	19

subgroup

index

C₂²×D₁₅₂

C₁₉×#341

Subgroups — #14564745

Conjugacy classes of subgroups

Complements

Maximal subgroups