Group #14569402 — subgroups

Subgroups — #14569402

Order 2432.

528 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10597392	C₂	1	2	yes	maximal
2	C₂×#10597318	C₂	1	1	yes	maximal, characteristic
3	#11926475	C₂	1	4	yes	maximal, complemented
4	#11926470	C₂	1	4	yes	maximal
5	#11926451	C₂	1	2	yes	maximal, complemented
6	#11926410	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×C₄⋊Q₈	—	2	4	no	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	#10597392	—	2	8	no	—
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
15	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	4	yes	—
16	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
17	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
18	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
19	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
20	#10597318	—	2	4	no	—
21	C₁₉⋊#95	C₂²	1	4	yes	—
22	C₁₉⋊#95	C₂²	1	8	yes	—
23	C₂³×D₁₉	C₂³	1	1	yes	characteristic
24	C₂×Q₈×C₁₉	—	2	4	no	—
25	C₂×Q₈×C₁₉	—	2	4	no	—
26	C₂×Q₈×C₁₉	—	2	4	no	—
27	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
28	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
30	C₂²×Dic₁₉	C₂³	1	2	yes	—
31	C₂²×Dic₁₉	C₂³	1	4	yes	—
32	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
33	C₂×C₄×D₁₉	—	2	2	no	—
34	C₂×C₄×D₁₉	—	2	2	no	—
35	C₂×C₄×D₁₉	D₄	1	4	yes	—
36	C₄⋊C₄×C₁₉	—	2	8	no	—
37	C₄²×C₁₉	D₄	1	4	yes	—
38	(C₂×D₁₉)⋊C₄	—	2	8	no	—
39	(C₂×D₁₉)⋊C₄	—	2	4	no	—
40	C₄⋊Dic₁₉	—	2	4	no	—
41	Dic₁₉⋊C₄	—	2	4	no	—
42	Dic₁₉⋊C₄	—	2	8	no	—
43	C₄×Dic₁₉	—	2	2	no	—
44	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
45	C₂²×D₁₉	—	2	1	no	—
46	C₂²×D₁₉	—	2	1	no	—
47	C₂²×D₁₉	—	2	4	no	—
48	C₂²×D₁₉	C₂×D₄	1	2	yes	—
49	Q₈×C₁₉	—	4	8	no	—
50	C₂×C₄×C₁₉	—	2	4	no	—
51	C₂×C₄×C₁₉	—	2	4	no	—
52	C₂×C₄×C₁₉	—	2	4	no	—
53	C₂×C₄×C₁₉	—	2	4	no	—
54	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
56	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
57	C₂×C₄×C₁₉	#41	1	2	yes	—
58	C₂×Dic₁₉	—	2	1	no	—
59	C₂×Dic₁₉	—	2	1	no	—
60	C₂×Dic₁₉	—	2	2	no	—
61	C₂×Dic₁₉	—	2	4	no	—
62	C₂×Dic₁₉	—	2	4	no	—
63	C₂×Dic₁₉	—	2	8	no	—
64	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
65	C₄×D₁₉	—	2	8	no	—
66	#2621	—	19	1	no	maximal, Sylow
67	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
68	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
69	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
70	C₂²×C₁₉	2₋¹⁺⁴	1	4	yes	—
71	C₂×D₁₉	—	2	2	no	—
72	C₂×D₁₉	—	2	4	no	—
73	C₂×D₁₉	—	4	2	no	—
74	C₂×D₁₉	—	4	2	no	—
75	C₄×C₁₉	—	2	4	no	—
76	C₄×C₁₉	—	4	4	no	—
77	C₄×C₁₉	#121	1	4	yes	—
78	Dic₁₉	—	2	2	no	—
79	Dic₁₉	—	4	2	no	—
80	Dic₁₉	—	4	4	no	—
81	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic, complemented
82	C₂×C₂²⋊Q₈	—	19	2	no	—
83	C₂×#117	—	19	1	no	—
84	#398	—	19	4	no	—
85	#397	—	19	4	no	—
86	#391	—	19	2	no	—
87	#382	—	19	1	no	—
88	C₂×C₁₉	C₂×#121	1	1	yes	characteristic
89	C₂×C₁₉	#536	1	2	yes	—
90	C₂×C₁₉	#536	1	2	yes	—
91	C₂×C₁₉	#541	1	2	yes	—
92	D₁₉	—	4	2	no	—
93	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
94	C₂³×C₄	—	19	1	no	—
95	C₄⋊Q₈	—	2	4	no	—
96	C₂²⋊Q₈	—	38	8	no	—
97	#117	—	38	4	no	—
98	C₂×C₄⋊C₄	—	19	2	no	—
99	C₂×C₄⋊C₄	—	19	2	no	—
100	C₂×C₄⋊C₄	—	19	4	no	—
101	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
102	C₂×C₂²⋊C₄	—	19	2	no	—
103	C₂×C₂²⋊C₄	—	19	4	no	—
104	C₂×C₄²	—	19	1	no	—
105	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
106	#95	—	19	4	no	—
107	#95	—	19	8	no	—
108	C₁₉	#2621	1	1	yes	characteristic, complemented, Sylow
109	C₂⁴	—	19	1	no	—
110	C₂×Q₈	—	2	4	no	—
111	C₂×Q₈	—	2	4	no	—
112	C₂×Q₈	—	2	4	no	—
113	C₂²×C₄	—	19	1	no	—
114	C₂²×C₄	—	19	4	no	—
115	C₂²×C₄	—	19	2	no	—
116	C₂²×C₄	—	19	4	no	—
117	C₂²×C₄	—	38	2	no	—
118	C₂²×C₄	—	38	2	no	—
119	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
120	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
121	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
122	C₄⋊C₄	—	2	8	no	—
123	C₄⋊C₄	—	38	8	no	—
124	C₄⋊C₄	—	38	4	no	—
125	C₄⋊C₄	—	38	4	no	—
126	C₂²⋊C₄	—	38	8	no	—
127	C₂²⋊C₄	—	38	4	no	—
128	C₄²	—	38	2	no	—
129	C₄²	C₂²⋊D₁₉	1	4	yes	—
130	C₂³	—	19	2	no	—
131	C₂³	—	38	1	no	—
132	C₂³	—	38	4	no	—
133	C₂³	—	38	1	no	—
134	C₂³	C₂³×D₁₉	1	1	yes	characteristic
135	Q₈	—	4	8	no	—
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	19	2	no	—
141	C₂×C₄	—	38	1	no	—
142	C₂×C₄	—	38	1	no	—
143	C₂×C₄	—	38	8	no	—
144	C₂×C₄	—	38	4	no	—
145	C₂×C₄	—	38	4	no	—
146	C₂×C₄	—	38	8	no	—
147	C₂×C₄	—	38	2	no	—
148	C₂×C₄	D₄×D₁₉	1	2	yes	—
149	C₂×C₄	#64543	1	2	yes	—
150	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
151	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
152	C₂²	—	38	4	no	—
153	C₂²	—	38	2	no	—
154	C₂²	—	76	2	no	—
155	C₂²	—	76	2	no	—
156	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
157	C₂²	C₂×#64543	1	1	yes	characteristic
158	C₂²	#10597433	1	4	yes	—
159	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
160	C₄	—	2	4	no	—
161	C₄	—	4	4	no	—
162	C₄	—	38	2	no	—
163	C₄	—	76	2	no	—
164	C₄	—	76	4	no	—
165	C₄	#10597384	1	4	yes	—
166	C₂	—	76	2	no	—
167	C₂	C₂×#10597384	1	1	yes	characteristic
168	C₂	#11927118	1	2	yes	—
169	C₂	#11927119	1	2	yes	—
170	C₂	#11927155	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597392

C₂

yes

maximal

C₂×#10597318

C₂

yes

maximal, characteristic

#11926475

C₂

yes

maximal, complemented

#11926470

C₂

yes

maximal

#11926451

C₂

yes

maximal, complemented

#11926410

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic, complemented

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597392

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

#10597318

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₂×D₄

yes

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₄×D₁₉

—

#2621

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

characteristic, complemented

C₂×C₂²⋊Q₈

—

—

—

—

—

—

C₂×C₁₉

C₂×#121

yes

characteristic

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#541

yes

—

D₁₉

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₂³×C₄

—

C₄⋊Q₈

—

C₂²⋊Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

100

C₂×C₄⋊C₄

—

101

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

102

C₂×C₂²⋊C₄

—

103

C₂×C₂²⋊C₄

—

104

C₂×C₄²

—

105

C₂×C₄²

C₂×D₁₉

yes

characteristic

106

#95

—

107

#95

—

108

C₁₉

#2621

yes

characteristic, complemented, Sylow

109

C₂⁴

—

110

C₂×Q₈

—

111

C₂×Q₈

—

112

C₂×Q₈

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

C₂²×D₁₉

yes

—

120

C₂²×C₄

C₂²×D₁₉

yes

—

121

C₂²×C₄

C₂²×D₁₉

yes

characteristic

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₂²⋊C₄

—

127

C₂²⋊C₄

—

128

C₄²

—

129

C₄²

C₂²⋊D₁₉

yes

—

130

C₂³

—

131

C₂³

—

132

C₂³

—

133

C₂³

—

134

C₂³

C₂³×D₁₉

yes

characteristic

135

Q₈

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

D₄×D₁₉

yes

—

149

C₂×C₄

#64543

yes

—

150

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

151

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

152

C₂²

—

153

C₂²

—

154

C₂²

—

155

C₂²

—

156

C₂²

C₂×D₄×D₁₉

yes

characteristic

157

C₂²

C₂×#64543

yes

characteristic

158

C₂²

#10597433

yes

—

159

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

160

C₄

—

161

C₄

—

162

C₄

—

163

C₄

—

164

C₄

—

165

C₄

#10597384

yes

—

166

C₂

—

167

C₂

C₂×#10597384

yes

characteristic

168

C₂

#11927118

yes

—

169

C₂

#11927119

yes

—

170

C₂

#11927155

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
prime radical	C₂³×D₁₉	C₂³
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2621
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

prime radical

C₂³×D₁₉

C₂³

hypercenter

C₂×C₄⋊Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
3. #11926475	C₂	semidirect
5. #11926451	C₂	semidirect
6. #11926410	C₂	semidirect
7. C₂×C₁₉×C₄⋊Q₈	C₂	semidirect
81. C₂×C₄⋊Q₈	D₁₉	semidirect
108. C₁₉	#2621	semidirect

H ≅ G/N

type

3. #11926475

C₂

semidirect

5. #11926451

C₂

semidirect

6. #11926410

C₂

semidirect

7. C₂×C₁₉×C₄⋊Q₈

C₂

semidirect

81. C₂×C₄⋊Q₈

D₁₉

semidirect

108. C₁₉

#2621

semidirect

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

subgroup	index
C₂×#10597392	2
C₂×#10597318	2
#11926475	2
#11926470	2
#11926451	2
#11926410	2
C₂×C₁₉×C₄⋊Q₈	2
#2621	19

subgroup

index

C₂×C₁₉×C₄⋊Q₈

Subgroups — #14569402

Conjugacy classes of subgroups

Complements

Maximal subgroups