Group #14563658 — subgroups

Subgroups — #14563658

Order 2432.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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	C₂³×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597265	C₂	1	2	yes	maximal, complemented
3	#11926404	C₂	1	1	yes	maximal, characteristic
4	#11926306	C₂	1	2	yes	maximal, complemented
5	C₁₉×#380	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
9	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂²×C₁₉⋊C₈	—	2	4	no	—
12	C₂²×C₁₉⋊C₈	C₄	1	4	yes	complemented
13	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₁₉×#95	—	2	1	no	—
16	C₁₉⋊#95	—	2	1	no	—
17	#10597265	—	2	4	no	—
18	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	Q₈	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂²⋊C₄×C₁₉	—	4	2	no	—
30	C₂²⋊Dic₁₉	—	4	2	no	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	—	2	2	no	—
33	C₂×C₁₉⋊C₈	—	2	2	no	—
34	C₂×C₁₉⋊C₈	—	2	8	no	—
35	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
36	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
37	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
38	C₂³×C₁₉	—	2	2	no	—
39	C₂³×C₁₉	—	2	2	no	—
40	C₂³×C₁₉	C₄⋊C₄	1	2	yes	—
41	C₂³×C₁₉	SD₁₆	1	2	yes	—
42	C₂³×C₁₉	SD₁₆	1	2	yes	—
43	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	4	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	—	4	2	no	—
51	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
52	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#41	1	2	yes	—
56	C₂×Dic₁₉	—	4	2	no	—
57	C₂×Dic₁₉	—	4	2	no	—
58	C₂×Dic₁₉	—	4	2	no	—
59	C₁₉⋊C₈	—	2	2	no	—
60	C₁₉⋊C₈	C₂²⋊C₄	1	4	yes	complemented
61	#1807	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	2	2	no	—
63	C₂²×C₁₉	—	2	2	no	—
64	C₂²×C₁₉	—	2	4	no	—
65	C₂²×C₁₉	—	2	4	no	—
66	C₂²×C₁₉	#106	1	4	yes	complemented
67	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₁₉	#121	1	2	yes	—
69	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
70	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
71	C₂²×C₁₉	#135	1	2	yes	—
72	C₄×C₁₉	—	2	2	no	—
73	C₄×C₁₉	—	8	2	no	—
74	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₄×C₁₉	#117	1	1	yes	characteristic
76	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
77	Dic₁₉	—	8	2	no	—
78	C₂³×C₈	—	19	1	no	—
79	C₂×#106	—	19	2	no	—
80	#380	—	19	1	no	—
81	#380	D₁₉	1	1	yes	characteristic
82	#340	—	19	2	no	—
83	C₂×C₁₉	—	2	4	no	—
84	C₂×C₁₉	#380	1	1	yes	characteristic
85	C₂×C₁₉	C₂×#106	1	1	yes	characteristic
86	C₂×C₁₉	#427	1	1	yes	characteristic
87	C₂×C₁₉	#465	1	2	yes	—
88	C₂×C₁₉	#465	1	2	yes	—
89	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
90	C₂²×C₈	—	19	1	no	—
91	C₂²×C₈	—	19	4	no	—
92	C₂²×C₈	—	19	1	no	—
93	C₂²×C₈	—	38	4	no	—
94	C₂×C₄⋊C₄	—	19	2	no	—
95	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
96	C₂×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₂²⋊C₄	—	38	1	no	—
98	#106	—	38	4	no	—
99	#95	—	2	1	no	—
100	#95	—	38	1	no	—
101	C₁₉	#1807	1	1	yes	characteristic, complemented, Sylow
102	C₂⁴	C₂²⋊D₁₉	1	1	yes	characteristic
103	C₂²×C₄	—	2	2	no	—
104	C₂²×C₄	—	2	2	no	—
105	C₂²×C₄	—	2	2	no	—
106	C₂²×C₄	—	38	2	no	—
107	C₂²×C₄	Dic₃₈	1	2	yes	—
108	C₂²×C₄	C₄×D₁₉	1	2	yes	—
109	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
111	C₂×C₈	—	19	2	no	—
112	C₂×C₈	—	19	4	no	—
113	C₂×C₈	—	19	2	no	—
114	C₂×C₈	—	38	8	no	—
115	C₂×C₈	—	38	2	no	—
116	C₄⋊C₄	—	2	2	no	—
117	C₄⋊C₄	—	2	2	no	—
118	C₄⋊C₄	—	38	2	no	—
119	C₄⋊C₄	—	38	2	no	—
120	C₂²⋊C₄	—	4	2	no	—
121	C₂²⋊C₄	—	76	2	no	—
122	C₂³	—	2	2	no	—
123	C₂³	—	2	2	no	—
124	C₂³	Dic₁₉⋊C₄	1	2	yes	—
125	C₂³	#64526	1	2	yes	—
126	C₂³	#64527	1	2	yes	—
127	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	2	2	no	—
132	C₂×C₄	—	4	2	no	—
133	C₂×C₄	—	4	2	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	76	2	no	—
136	C₂×C₄	—	76	2	no	—
137	C₂×C₄	—	76	2	no	—
138	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
139	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
140	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
141	C₂×C₄	D₄×D₁₉	1	2	yes	—
142	C₂×C₄	#64543	1	2	yes	—
143	C₈	—	19	4	no	—
144	C₈	—	38	2	no	—
145	C₂²	—	2	2	no	—
146	C₂²	—	2	2	no	—
147	C₂²	—	2	4	no	—
148	C₂²	—	2	4	no	—
149	C₂²	#10597265	1	4	yes	complemented
150	C₂²	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
151	C₂²	C₂×#64526	1	1	yes	characteristic
152	C₂²	#10597385	1	2	yes	—
153	C₂²	C₂×#64527	1	1	yes	characteristic
154	C₂²	#10597396	1	2	yes	—
155	C₄	—	2	2	no	—
156	C₄	—	8	2	no	—
157	C₄	—	152	2	no	—
158	C₄	#10597323	1	1	yes	characteristic
159	C₄	#10597324	1	2	yes	—
160	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
161	C₂	—	2	4	no	—
162	C₂	#11926402	1	1	yes	characteristic
163	C₂	C₂×#10597265	1	1	yes	characteristic
164	C₂	#11926580	1	1	yes	characteristic
165	C₂	#11926771	1	2	yes	—
166	C₂	#11926775	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×#10597265

C₂

yes

maximal, complemented

#11926404

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal, complemented

C₁₉×#380

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₄

yes

complemented

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#95

—

C₁₉⋊#95

—

#10597265

—

C₂⁴×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄⋊C₄

yes

—

C₂³×C₁₉

SD₁₆

yes

—

C₂³×C₁₉

SD₁₆

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²⋊C₄

yes

complemented

#1807

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#106

yes

complemented

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

#135

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

—

Dic₁₉

—

C₂³×C₈

—

C₂×#106

—

#380

—

#380

D₁₉

yes

characteristic

#340

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#465

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#106

—

#95

—

100

#95

—

101

C₁₉

#1807

yes

characteristic, complemented, Sylow

102

C₂⁴

C₂²⋊D₁₉

yes

characteristic

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

Dic₃₈

yes

—

108

C₂²×C₄

C₄×D₁₉

yes

—

109

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

110

C₂²×C₄

C₂²×D₁₉

yes

characteristic

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₂³

—

123

C₂³

—

124

C₂³

Dic₁₉⋊C₄

yes

—

125

C₂³

#64526

yes

—

126

C₂³

#64527

yes

—

127

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

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

—

138

C₂×C₄

Dic₁₉⋊C₄

yes

—

139

C₂×C₄

C₂×Dic₃₈

yes

characteristic

140

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

141

C₂×C₄

D₄×D₁₉

yes

—

142

C₂×C₄

#64543

yes

—

143

C₈

—

144

C₈

—

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

#10597265

yes

complemented

150

C₂²

C₂×Dic₁₉⋊C₄

yes

characteristic

151

C₂²

C₂×#64526

yes

characteristic

152

C₂²

#10597385

yes

—

153

C₂²

C₂×#64527

yes

characteristic

154

C₂²

#10597396

yes

—

155

C₄

—

156

C₄

—

157

C₄

—

152

—

158

C₄

#10597323

yes

characteristic

159

C₄

#10597324

yes

—

160

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

161

C₂

—

162

C₂

#11926402

yes

characteristic

163

C₂

C₂×#10597265

yes

characteristic

164

C₂

#11926580

yes

characteristic

165

C₂

#11926771

yes

—

166

C₂

#11926775

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#380	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂⁴×C₁₉	D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#380	D₁₉
hypocenter	C₁₉	#1807
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#380

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂⁴×C₁₉

D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #380

N	H ≅ G/N	type
2. C₂×#10597265	C₂	semidirect
4. #11926306	C₂	semidirect
12. C₂²×C₁₉⋊C₈	C₄	semidirect
60. C₁₉⋊C₈	C₂²⋊C₄	semidirect
66. C₂²×C₁₉	#106	semidirect
101. C₁₉	#1807	semidirect
149. C₂²	#10597265	semidirect

H ≅ G/N

type

2. C₂×#10597265

C₂

semidirect

4. #11926306

C₂

semidirect

12. C₂²×C₁₉⋊C₈

C₄

semidirect

60. C₁₉⋊C₈

C₂²⋊C₄

semidirect

66. C₂²×C₁₉

#106

semidirect

101. C₁₉

#1807

semidirect

149. C₂²

#10597265

semidirect

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

subgroup	index
C₂³×C₁₉⋊C₈	2
C₂×#10597265	2
#11926404	2
#11926306	2
C₁₉×#380	2
#1807	19

subgroup

index

C₂³×C₁₉⋊C₈

C₁₉×#380

Subgroups — #14563658

Conjugacy classes of subgroups

Complements

Maximal subgroups