Group #14572732 — subgroups

Subgroups — #14572732

Order 2432.

322 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 161 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	#11927101	C₂	1	1	yes	maximal, characteristic
2	#11926672	C₂	1	4	yes	maximal, complemented
3	#11926671	C₂	1	2	yes	maximal, complemented
4	#11926668	C₂	1	2	yes	maximal, complemented
5	#11926602	C₂	1	4	yes	maximal
6	#11926597	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#432	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	#10597372	C₂²	1	2	yes	—
10	#10597370	C₄	1	2	yes	—
11	#10597370	C₄	1	2	yes	—
12	#10597316	C₄	1	2	yes	—
13	#10597315	C₄	1	1	yes	characteristic
14	#10597315	C₄	1	1	yes	characteristic
15	C₄×Dic₃₈	C₂²	1	2	yes	—
16	C₄×Dic₃₈	C₂²	1	2	yes	—
17	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₁₉×#97	C₂²	1	2	yes	—
20	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
21	#10597272	C₂²	1	4	yes	—
22	Dic₁₉⋊C₈	C₂²	1	4	yes	—
23	Dic₁₉⋊C₈	C₂²	1	4	yes	—
24	C₈×Dic₁₉	C₂²	1	4	yes	—
25	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
26	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
27	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
31	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
32	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
33	C₂×C₈×C₁₉	C₂³	1	4	yes	—
34	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
36	C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	—
39	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
40	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
41	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
42	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
43	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	—
44	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	—
45	C₄×Dic₁₉	C₂³	1	4	yes	—
46	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
47	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
48	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	—	2	2	no	—
50	C₂×C₄×C₁₉	—	2	2	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
58	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
59	C₂×Dic₁₉	C₂²×C₄	1	4	yes	—
60	Dic₃₈	—	2	4	no	—
61	Dic₃₈	—	4	2	no	—
62	C₈×C₁₉	—	2	4	no	—
63	C₁₉⋊C₈	—	2	2	no	—
64	C₁₉⋊C₈	—	2	2	no	—
65	#2985	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	—	2	1	no	—
67	C₂²×C₁₉	—	2	1	no	—
68	C₂²×C₁₉	—	2	1	no	—
69	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	2	1	no	—
72	C₄×C₁₉	—	2	1	no	—
73	C₄×C₁₉	—	2	1	no	—
74	C₄×C₁₉	#131	1	2	yes	—
75	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
76	Dic₁₉	—	2	4	no	—
77	Dic₁₉	—	2	4	no	—
78	#533	—	19	1	no	—
79	#446	—	19	2	no	—
80	#446	—	19	4	no	—
81	C₈×Q₈	—	19	2	no	—
82	#433	—	19	4	no	—
83	#432	D₁₉	1	1	yes	characteristic
84	#431	—	19	1	no	—
85	C₂×C₁₉	—	4	1	no	—
86	C₂×C₁₉	#519	1	1	yes	characteristic
87	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
88	C₂×C₁₉	#568	1	1	yes	characteristic
89	C₄⋊Q₈	—	19	1	no	—
90	C₄⋊Q₈	—	19	1	no	—
91	#125	—	19	2	no	—
92	C₂²⋊Q₈	—	19	2	no	—
93	C₂²⋊Q₈	—	19	2	no	—
94	C₄×Q₈	—	19	2	no	—
95	C₄×Q₈	—	19	2	no	—
96	#117	—	19	2	no	—
97	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
98	C₄⋊C₈	—	19	4	no	—
99	C₄⋊C₈	—	19	4	no	—
100	C₄⋊C₈	—	19	2	no	—
101	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
102	C₂²⋊C₈	—	19	2	no	—
103	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
104	#97	—	19	4	no	—
105	#97	C₂×D₁₉	1	2	yes	—
106	C₄×C₈	—	19	4	no	—
107	C₄×C₈	—	19	1	no	—
108	C₄×C₈	—	19	1	no	—
109	C₁₉	#2985	1	1	yes	characteristic, complemented, Sylow
110	C₂×Q₈	—	19	2	no	—
111	C₂×Q₈	—	19	2	no	—
112	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
113	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
114	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
115	C₂×C₈	—	19	2	no	—
116	C₂×C₈	—	19	2	no	—
117	C₂×C₈	C₂²×D₁₉	1	4	yes	—
118	C₄⋊C₄	—	19	4	no	—
119	C₄⋊C₄	—	19	4	no	—
120	C₄⋊C₄	—	19	2	no	—
121	C₄⋊C₄	—	19	2	no	—
122	C₄⋊C₄	—	19	2	no	—
123	C₄⋊C₄	—	19	2	no	—
124	C₂²⋊C₄	—	19	4	no	—
125	C₄²	—	19	4	no	—
126	C₄²	C₄×D₁₉	1	1	yes	characteristic
127	C₄²	C₄×D₁₉	1	1	yes	characteristic
128	C₄²	C₂²×D₁₉	1	1	yes	characteristic
129	C₄²	C₂²×D₁₉	1	1	yes	characteristic
130	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
131	Q₈	—	38	4	no	—
132	Q₈	—	76	2	no	—
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	—	2	2	no	—
135	C₂×C₄	—	4	1	no	—
136	C₂×C₄	—	19	4	no	—
137	C₂×C₄	—	19	4	no	—
138	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
139	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
140	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
141	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
142	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
143	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
144	C₈	—	2	4	no	—
145	C₈	—	38	2	no	—
146	C₈	—	38	2	no	—
147	C₂²	—	2	1	no	—
148	C₂²	—	2	1	no	—
149	C₂²	—	2	1	no	—
150	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
151	C₄	—	2	1	no	—
152	C₄	—	2	1	no	—
153	C₄	—	2	1	no	—
154	C₄	—	2	1	no	—
155	C₄	—	38	4	no	—
156	C₄	—	38	4	no	—
157	C₄	#10597353	1	2	yes	—
158	C₄	#10597436	1	2	yes	—
159	C₂	—	4	1	no	—
160	C₂	#11927021	1	1	yes	characteristic
161	C₂	C₂×#10597353	1	1	yes	characteristic
162	C₂	#11927310	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927101

C₂

yes

maximal, characteristic

#11926672

C₂

yes

maximal, complemented

#11926671

C₂

yes

maximal, complemented

#11926668

C₂

yes

maximal, complemented

#11926602

C₂

yes

maximal

#11926597

C₂

yes

maximal, characteristic

C₁₉×#432

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

—

#10597370

C₄

yes

—

#10597370

C₄

yes

—

#10597316

C₄

yes

—

#10597315

C₄

yes

characteristic

#10597315

C₄

yes

characteristic

C₄×Dic₃₈

C₂²

yes

—

C₄×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉×#97

C₂²

yes

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597272

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

C₈×Dic₁₉

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

C₂×C₄

yes

—

Dic₁₉⋊C₄

C₂×C₄

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

C₂²×C₄

yes

—

C₂×Dic₁₉

C₂²×C₄

yes

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2985

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂³×C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#131

yes

—

C₄×C₁₉

2₋¹⁺⁴

yes

—

Dic₁₉

—

Dic₁₉

—

#533

—

#446

—

#446

—

C₈×Q₈

—

#433

—

#432

D₁₉

yes

characteristic

#431

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

100

C₄⋊C₈

—

101

C₄⋊C₈

C₂×D₁₉

yes

—

102

C₂²⋊C₈

—

103

C₂²⋊C₈

C₂×D₁₉

yes

—

104

#97

—

105

#97

C₂×D₁₉

yes

—

106

C₄×C₈

—

107

C₄×C₈

—

108

C₄×C₈

—

109

C₁₉

#2985

yes

characteristic, complemented, Sylow

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂²×C₄

C₄×D₁₉

yes

characteristic

113

C₂²×C₄

C₄×D₁₉

yes

characteristic

114

C₂²×C₄

C₂²×D₁₉

yes

characteristic

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

C₂²×D₁₉

yes

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₂²⋊C₄

—

125

C₄²

—

126

C₄²

C₄×D₁₉

yes

characteristic

127

C₄²

C₄×D₁₉

yes

characteristic

128

C₄²

C₂²×D₁₉

yes

characteristic

129

C₄²

C₂²×D₁₉

yes

characteristic

130

C₂³

C₂×C₄×D₁₉

yes

characteristic

131

Q₈

—

132

Q₈

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

139

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

140

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

141

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

142

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

143

C₂×C₄

C₂³×D₁₉

yes

characteristic

144

C₈

—

145

C₈

—

146

C₈

—

147

C₂²

—

148

C₂²

—

149

C₂²

—

150

C₂²

C₂²×C₄×D₁₉

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

#10597353

yes

—

158

C₄

#10597436

yes

—

159

C₂

—

160

C₂

#11927021

yes

characteristic

161

C₂

C₂×#10597353

yes

characteristic

162

C₂

#11927310

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#432	C₂
prime radical	C₂³×C₁₉	C₂²×C₄
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#432	D₁₉
hypocenter	C₁₉	#2985
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #432

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₁₉

commutator, socle

C₂²×C₁₉

C₂³×C₄

Fitting

C₁₉×#432

C₂

prime radical

C₂³×C₁₉

C₂²×C₄

cosocle

C₂×C₄×C₁₉

C₂⁴

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₄ ◁ #432

N	H ≅ G/N	type
2. #11926672	C₂	semidirect
3. #11926671	C₂	semidirect
4. #11926668	C₂	semidirect
109. C₁₉	#2985	semidirect

H ≅ G/N

type

2. #11926672

C₂

semidirect

3. #11926671

C₂

semidirect

4. #11926668

C₂

semidirect

109. C₁₉

#2985

semidirect

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

subgroup	index
#11927101	2
#11926672	2
#11926671	2
#11926668	2
#11926602	2
#11926597	2
C₁₉×#432	2
#2985	19

subgroup

index

C₁₉×#432

Subgroups — #14572732

Conjugacy classes of subgroups

Complements

Maximal subgroups