Group #14573403 — subgroups

Subgroups — C₂×#11926836 #14573403

Order 2432.

416 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 173 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×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	#11926836	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10597264	C₂	1	2	yes	maximal
4	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597267	C₂	1	2	yes	maximal
6	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₁₉	—	2	1	no	—
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₁₉×C₄⋊Q₈	—	2	2	no	—
10	C₁₉×C₄⋊Q₈	C₂²	1	4	yes	—
11	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
12	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₉⋊C₄	—	2	1	no	—
16	C₂×C₄×Dic₁₉	—	2	1	no	—
17	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
18	C₄×Dic₃₈	—	2	2	no	—
19	C₄×Dic₃₈	C₂²	1	4	yes	—
20	#10597267	C₂²	1	8	yes	—
21	#10597264	C₂²	1	8	yes	—
22	C₄⋊(C₁₉⋊C₈)	C₂²	1	4	yes	—
23	C₂×Q₈×C₁₉	—	2	4	no	—
24	C₂×Q₈×C₁₉	—	4	4	no	—
25	C₂²×C₄×C₁₉	—	2	2	no	—
26	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	2	1	no	—
30	C₂²×Dic₁₉	—	2	1	no	—
31	C₂×Dic₃₈	—	2	1	no	—
32	C₂×Dic₃₈	—	2	2	no	—
33	C₂×Dic₃₈	Q₈	1	4	yes	complemented
34	C₂×Dic₃₈	C₂³	1	2	yes	—
35	C₄⋊C₄×C₁₉	—	2	4	no	—
36	C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
38	C₄²×C₁₉	D₄	1	2	yes	—
39	C₄²×C₁₉	C₂³	1	2	yes	—
40	C₄⋊Dic₁₉	—	2	1	no	—
41	C₄⋊Dic₁₉	C₂³	1	2	yes	—
42	Dic₁₉⋊C₄	—	2	4	no	—
43	C₄×Dic₁₉	—	2	4	no	—
44	C₂×C₁₉⋊C₈	—	2	4	no	—
45	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
46	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
47	Q₈×C₁₉	—	4	8	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	2	4	no	—
50	C₂×C₄×C₁₉	—	4	4	no	—
51	C₂×C₄×C₁₉	Q₁₆	1	4	yes	—
52	C₂×C₄×C₁₉	C₂×D₄	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×Q₈	1	2	yes	—
56	C₂×C₄×C₁₉	#41	1	2	yes	—
57	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
58	C₂×Dic₁₉	—	2	4	no	—
59	C₂×Dic₁₉	—	2	2	no	—
60	C₂×Dic₁₉	—	2	2	no	—
61	C₂×Dic₁₉	—	4	2	no	—
62	Dic₃₈	—	2	4	no	—
63	Dic₃₈	—	2	2	no	—
64	Dic₃₈	C₂×Q₈	1	4	yes	complemented
65	C₁₉⋊C₈	—	2	4	no	—
66	C₂×#477	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
68	C₂²×C₁₉	C₂×Q₁₆	1	2	yes	—
69	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
70	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
71	C₄×C₁₉	—	2	2	no	—
72	C₄×C₁₉	—	4	4	no	—
73	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
74	C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
75	C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
76	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
77	Dic₁₉	—	2	4	no	—
78	Dic₁₉	—	4	2	no	—
79	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
80	C₂×C₄×Q₈	—	19	1	no	—
81	#477	—	19	8	no	—
82	C₂×#107	—	19	2	no	—
83	C₂×C₄⋊C₈	—	19	1	no	—
84	C₂×#103	—	19	2	no	—
85	C₂×C₁₉	#477	1	4	yes	complemented
86	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₁₉	C₂²×Q₁₆	1	1	yes	characteristic
88	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
89	C₂²×Q₈	—	2	1	no	—
90	C₂²×Q₈	—	19	1	no	—
91	C₂²×C₈	—	19	2	no	—
92	C₄⋊Q₈	—	2	2	no	—
93	C₄⋊Q₈	C₂×D₁₉	1	4	yes	—
94	C₄×Q₈	—	19	4	no	—
95	C₄×Q₈	—	38	2	no	—
96	C₂×C₄⋊C₄	—	2	1	no	—
97	C₂×C₄⋊C₄	—	19	1	no	—
98	C₂×C₄⋊C₄	—	38	1	no	—
99	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
100	C₂×C₄²	—	38	1	no	—
101	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
102	#107	—	19	8	no	—
103	C₄⋊C₈	—	19	4	no	—
104	#103	—	19	8	no	—
105	C₁₉	C₂×#477	1	1	yes	characteristic, complemented, Sylow
106	C₂×Q₈	—	2	4	no	—
107	C₂×Q₈	—	4	4	no	—
108	C₂×Q₈	—	19	4	no	—
109	C₂×Q₈	—	19	2	no	—
110	C₂×Q₈	—	38	2	no	—
111	C₂×Q₈	—	38	1	no	—
112	C₂²×C₄	—	2	2	no	—
113	C₂²×C₄	—	38	1	no	—
114	C₂²×C₄	—	38	1	no	—
115	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
116	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
117	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
118	C₂×C₈	—	19	4	no	—
119	C₂×C₈	—	38	4	no	—
120	C₄⋊C₄	—	2	4	no	—
121	C₄⋊C₄	—	2	2	no	—
122	C₄⋊C₄	—	19	2	no	—
123	C₄⋊C₄	—	38	4	no	—
124	C₄⋊C₄	—	38	1	no	—
125	C₄⋊C₄	C₂²×D₁₉	1	4	yes	—
126	C₄²	—	38	4	no	—
127	C₄²	C₂²⋊D₁₉	1	2	yes	—
128	C₄²	C₂²×D₁₉	1	2	yes	—
129	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
130	Q₈	—	4	8	no	—
131	Q₈	—	19	4	no	—
132	Q₈	—	38	4	no	—
133	Q₈	—	38	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	2	4	no	—
136	C₂×C₄	—	4	4	no	—
137	C₂×C₄	—	38	4	no	—
138	C₂×C₄	—	38	2	no	—
139	C₂×C₄	—	38	2	no	—
140	C₂×C₄	—	76	2	no	—
141	C₂×C₄	#64528	1	4	yes	—
142	C₂×C₄	Q₈×D₁₉	1	2	yes	—
143	C₂×C₄	#64545	1	2	yes	—
144	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
145	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
146	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
147	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
148	C₈	—	38	4	no	—
149	C₂²	#10597378	1	2	yes	—
150	C₂²	C₂×#64528	1	2	yes	—
151	C₂²	#10597392	1	2	yes	—
152	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	—	4	4	no	—
155	C₄	—	38	4	no	—
156	C₄	—	76	2	no	—
157	C₄	C₂×#64528	1	4	yes	—
158	C₄	#10597392	1	2	yes	—
159	C₄	C₂×Q₈×D₁₉	1	1	yes	characteristic
160	C₄	C₂×#64545	1	1	yes	characteristic
161	C₂	#11926836	1	4	yes	direct product factor
162	C₂	C₂×#10597392	1	1	yes	characteristic
163	C₂	C₂²×#64528	1	1	yes	characteristic
164	C₂	C₂×#10597378	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₃₈

C₂

yes

maximal, characteristic

#11926836

C₂

yes

maximal, direct product factor

C₂×#10597264

C₂

yes

maximal

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

—

C₂²×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂²

yes

—

#10597267

C₂²

yes

—

#10597264

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

Q₈

yes

complemented

C₂×Dic₃₈

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

C₂×Q₈

yes

complemented

C₁₉⋊C₈

—

C₂×#477

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

C₂×Q₁₆

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

C₂×Q₁₆

yes

—

C₄×C₁₉

C₂²×Q₈

yes

characteristic

C₄×C₁₉

C₂×#41

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

characteristic

C₂×C₄×Q₈

—

#477

—

C₂×#107

—

C₂×C₄⋊C₈

—

C₂×#103

—

C₂×C₁₉

#477

yes

complemented

C₂×C₁₉

C₂×C₂²⋊Q₈

yes

characteristic

C₂×C₁₉

C₂²×Q₁₆

yes

characteristic

C₂×C₁₉

C₂×AGL(1,ℤ/8)

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

100

C₂×C₄²

—

101

C₂×C₄²

C₂×D₁₉

yes

characteristic

102

#107

—

103

C₄⋊C₈

—

104

#103

—

105

C₁₉

C₂×#477

yes

characteristic, complemented, Sylow

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂×Q₈

—

109

C₂×Q₈

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

116

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

117

C₂²×C₄

C₂²×D₁₉

yes

characteristic

118

C₂×C₈

—

119

C₂×C₈

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

C₂²×D₁₉

yes

—

126

C₄²

—

127

C₄²

C₂²⋊D₁₉

yes

—

128

C₄²

C₂²×D₁₉

yes

—

129

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

130

Q₈

—

131

Q₈

—

132

Q₈

—

133

Q₈

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

#64528

yes

—

142

C₂×C₄

Q₈×D₁₉

yes

—

143

C₂×C₄

#64545

yes

—

144

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

145

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

146

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

147

C₂×C₄

C₂³×D₁₉

yes

characteristic

148

C₈

—

149

C₂²

#10597378

yes

—

150

C₂²

C₂×#64528

yes

—

151

C₂²

#10597392

yes

—

152

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

C₂×#64528

yes

—

158

C₄

#10597392

yes

—

159

C₄

C₂×Q₈×D₁₉

yes

characteristic

160

C₄

C₂×#64545

yes

characteristic

161

C₂

#11926836

yes

direct product factor

162

C₂

C₂×#10597392

yes

characteristic

163

C₂

C₂²×#64528

yes

characteristic

164

C₂

C₂×#10597378

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	C₂×#477
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

C₂×#477

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
2. #11926836	C₂	direct (N × H)
33. C₂×Dic₃₈	Q₈	semidirect
64. Dic₃₈	C₂×Q₈	semidirect
85. C₂×C₁₉	#477	semidirect
105. C₁₉	C₂×#477	semidirect
161. C₂	#11926836	direct (N × H)

H ≅ G/N

type

2. #11926836

C₂

direct (N × H)

33. C₂×Dic₃₈

Q₈

semidirect

64. Dic₃₈

C₂×Q₈

semidirect

85. C₂×C₁₉

#477

semidirect

105. C₁₉

C₂×#477

semidirect

161. C₂

#11926836

direct (N × H)

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

subgroup	index
C₂×C₄×Dic₃₈	2
#11926836	2
C₂×#10597264	2
C₂×C₄⋊(C₁₉⋊C₈)	2
C₂×#10597267	2
C₂×C₁₉×C₄⋊Q₈	2
C₂×#477	19

subgroup

index

C₂×C₄×Dic₃₈

C₂×C₄⋊(C₁₉⋊C₈)

C₂×C₁₉×C₄⋊Q₈

Subgroups — C₂×#11926836 #14573403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926836 #14573403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926836 #14573403