Group #14565308 — subgroups

Subgroups — #14565308

Order 2432.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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	#11927114	C₂	1	1	yes	maximal, characteristic
2	#11926516	C₂	1	2	yes	maximal
3	#11926339	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926338	C₂	1	2	yes	maximal, complemented
5	C₁₉×#354	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×D₁₉	C₄	1	1	yes	characteristic, complemented
7	C₂×#64543	C₂²	1	1	yes	characteristic
8	C₁₉×#124	C₂²	1	1	yes	characteristic
9	#10597390	C₄	1	1	yes	characteristic, complemented
10	#10597382	C₂²	1	1	yes	characteristic
11	#10597329	—	2	2	no	—
12	#10597324	—	2	2	no	—
13	#10597323	—	2	2	no	—
14	#10597318	C₄	1	1	yes	characteristic, complemented
15	#10597315	C₄	1	1	yes	characteristic, complemented
16	C₁₉×#99	C₂²	1	2	yes	—
17	#10597291	C₂²	1	2	yes	—
18	#10597263	—	2	2	no	—
19	C₂×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂×C₂²⋊D₁₉	D₄	1	2	yes	—
22	C₂²×Dic₁₉	D₄	1	2	yes	—
23	Q₈×D₁₉	—	4	2	no	—
24	#64543	—	4	2	no	—
25	C₂×C₄×D₁₉	—	2	1	no	—
26	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×Dic₃₈	—	2	1	no	—
28	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
29	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
30	C₂²⋊C₄×C₁₉	—	2	2	no	—
31	C₂²⋊C₄×C₁₉	—	2	2	no	—
32	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂²⋊Dic₁₉	—	2	2	no	—
34	C₂²⋊Dic₁₉	—	2	2	no	—
35	(C₂×D₁₉)⋊C₄	—	2	1	no	—
36	C₄⋊Dic₁₉	—	2	2	no	—
37	Dic₁₉⋊C₄	—	2	2	no	—
38	Dic₁₉⋊C₄	—	2	1	no	—
39	Dic₁₉⋊C₄	—	4	2	no	—
40	C₄×Dic₁₉	—	4	2	no	—
41	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₁₉	C₂×D₄	1	2	yes	—
43	C₂²×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	Q₈×C₁₉	—	4	1	no	—
45	D₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²⋊D₁₉	—	4	2	no	—
51	C₂×Dic₁₉	—	2	2	no	—
52	C₂×Dic₁₉	—	2	2	no	—
53	C₂×Dic₁₉	—	2	1	no	—
54	C₂×Dic₁₉	—	2	1	no	—
55	C₂×Dic₁₉	—	4	2	no	—
56	C₂×Dic₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
58	C₄×D₁₉	—	2	2	no	—
59	C₄×D₁₉	—	4	2	no	—
60	Dic₃₈	—	4	1	no	—
61	Dic₃₈	—	4	2	no	—
62	Dic₃₈	—	4	1	no	—
63	#2129	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	2	2	no	—
65	C₂²×C₁₉	—	4	2	no	—
66	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×D₁₉	—	2	1	no	—
68	C₂×D₁₉	—	4	1	no	—
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	4	1	no	—
71	C₄×C₁₉	—	4	1	no	—
72	C₄×C₁₉	—	8	2	no	—
73	Dic₁₉	—	2	2	no	—
74	Dic₁₉	—	4	1	no	—
75	Dic₁₉	—	4	1	no	—
76	Dic₁₉	—	8	2	no	—
77	Dic₁₉	#99	1	2	yes	—
78	#536	—	19	1	no	—
79	#410	—	19	2	no	—
80	#354	—	19	1	no	—
81	#354	—	19	2	no	—
82	#354	D₁₉	1	1	yes	characteristic, complemented
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	—	4	2	no	—
85	C₂×C₁₉	C₂×#99	1	1	yes	characteristic
86	D₁₉	—	4	1	no	—
87	C₂×#41	—	19	1	no	—
88	C₂²×Q₈	—	19	1	no	—
89	C₄⋊Q₈	—	19	1	no	—
90	C₄⋊Q₈	—	19	1	no	—
91	#124	—	19	1	no	—
92	#124	C₂×D₁₉	1	1	yes	characteristic
93	#123	—	38	2	no	—
94	C₂²⋊Q₈	—	38	2	no	—
95	#117	—	19	1	no	—
96	#117	—	38	2	no	—
97	#99	—	19	2	no	—
98	#99	—	38	2	no	—
99	#99	C₂×D₁₉	1	2	yes	—
100	C₁₉	#2129	1	1	yes	characteristic, complemented, Sylow
101	#41	—	76	2	no	—
102	C₂×Q₈	—	19	1	no	—
103	C₂×Q₈	—	19	1	no	—
104	C₂×Q₈	—	38	1	no	—
105	C₂×Q₈	—	76	2	no	—
106	C₂×Q₈	C₄×D₁₉	1	1	yes	characteristic
107	C₂×D₄	—	19	2	no	—
108	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
109	C₂²×C₄	—	19	2	no	—
110	C₂²×C₄	—	19	1	no	—
111	C₂²×C₄	—	38	1	no	—
112	C₄⋊C₄	—	38	1	no	—
113	C₄⋊C₄	—	38	2	no	—
114	C₄⋊C₄	—	38	2	no	—
115	C₄⋊C₄	—	76	2	no	—
116	C₂²⋊C₄	—	2	2	no	—
117	C₂²⋊C₄	—	2	2	no	—
118	C₂²⋊C₄	—	38	1	no	—
119	C₂²⋊C₄	—	38	2	no	—
120	C₂²⋊C₄	—	38	2	no	—
121	C₄²	—	19	1	no	—
122	C₄²	—	76	2	no	—
123	C₄²	C₄×D₁₉	1	1	yes	characteristic
124	C₂³	—	19	1	no	—
125	C₂³	D₄×D₁₉	1	2	yes	—
126	Q₈	—	4	1	no	—
127	Q₈	—	76	1	no	—
128	Q₈	—	76	1	no	—
129	Q₈	—	76	2	no	—
130	D₄	—	4	1	no	—
131	D₄	—	76	2	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	—	2	1	no	—
134	C₂×C₄	—	4	2	no	—
135	C₂×C₄	—	19	1	no	—
136	C₂×C₄	—	19	2	no	—
137	C₂×C₄	—	38	2	no	—
138	C₂×C₄	—	38	2	no	—
139	C₂×C₄	—	38	2	no	—
140	C₂×C₄	—	38	1	no	—
141	C₂×C₄	—	38	1	no	—
142	C₂×C₄	—	76	2	no	—
143	C₂×C₄	—	76	2	no	—
144	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
145	C₂²	—	2	2	no	—
146	C₂²	—	4	2	no	—
147	C₂²	—	38	1	no	—
148	C₂²	—	76	1	no	—
149	C₂²	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
150	C₄	—	2	1	no	—
151	C₄	—	4	1	no	—
152	C₄	—	4	1	no	—
153	C₄	—	8	2	no	—
154	C₄	—	19	2	no	—
155	C₄	—	38	2	no	—
156	C₄	—	76	1	no	—
157	C₄	—	76	1	no	—
158	C₄	—	152	2	no	—
159	C₂	—	2	1	no	—
160	C₂	—	4	2	no	—
161	C₂	—	76	1	no	—
162	C₂	#99×D₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927114

C₂

yes

maximal, characteristic

#11926516

C₂

yes

maximal

#11926339

C₂

yes

maximal, characteristic, complemented

#11926338

C₂

yes

maximal, complemented

C₁₉×#354

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₁₉

C₄

yes

characteristic, complemented

C₂×#64543

C₂²

yes

characteristic

C₁₉×#124

C₂²

yes

characteristic

#10597390

C₄

yes

characteristic, complemented

#10597382

C₂²

yes

—

—

—

C₄

yes

characteristic, complemented

#10597315

C₄

yes

characteristic, complemented

C₁₉×#99

C₂²

yes

—

#10597291

C₂²

yes

—

#10597263

—

C₂×Q₈×C₁₉

C₂×C₄

yes

characteristic

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

D₄

yes

—

C₂²×Dic₁₉

D₄

yes

—

Q₈×D₁₉

—

#64543

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

C₂×C₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

characteristic

C₂×Dic₃₈

C₂×C₄

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

—

C₂²×D₁₉

C₂²⋊C₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂²⋊C₄

yes

—

C₂×Dic₁₉

C₂²⋊C₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

#2129

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

#99

yes

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#99

yes

characteristic

D₁₉

—

C₂×#41

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#124

—

#124

C₂×D₁₉

yes

characteristic

#123

—

C₂²⋊Q₈

—

—

—

—

—

C₂×D₁₉

yes

—

100

C₁₉

#2129

yes

characteristic, complemented, Sylow

101

#41

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

C₄×D₁₉

yes

characteristic

107

C₂×D₄

—

108

C₂×D₄

C₂²×D₁₉

yes

characteristic

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₂²⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₄²

—

122

C₄²

—

123

C₄²

C₄×D₁₉

yes

characteristic

124

C₂³

—

125

C₂³

D₄×D₁₉

yes

—

126

Q₈

—

127

Q₈

—

128

Q₈

—

129

Q₈

—

130

D₄

—

131

D₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

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

C₂×C₄×D₁₉

yes

characteristic

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

—

149

C₂²

C₂²⋊C₄×D₁₉

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

158

C₄

—

152

—

159

C₂

—

160

C₂

—

161

C₂

—

162

C₂

#99×D₁₉

yes

characteristic

	subgroup	G/H
center	C₂	#99×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂×D₄	C₂²×D₁₉
Fitting	C₁₉×#354	C₂
socle	C₂×C₁₉	C₂×#99
prime radical	C₂×#64543	C₂²
cosocle	C₂×D₄×C₁₉	C₂³
hypercenter	#354	D₁₉
hypocenter	C₁₉	#2129
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #354

subgroup

G/H

center

C₂

#99×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂×D₄

C₂²×D₁₉

Fitting

C₁₉×#354

C₂

socle

C₂×C₁₉

C₂×#99

prime radical

C₂×#64543

C₂²

cosocle

C₂×D₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×D₄ ◁ #354

N	H ≅ G/N	type
3. #11926339	C₂	semidirect
4. #11926338	C₂	semidirect
5. C₁₉×#354	C₂	semidirect
6. C₂×Q₈×D₁₉	C₄	semidirect
9. #10597390	C₄	semidirect
14. #10597318	C₄	semidirect
15. #10597315	C₄	semidirect
82. #354	D₁₉	semidirect
100. C₁₉	#2129	semidirect

H ≅ G/N

type

3. #11926339

C₂

semidirect

4. #11926338

C₂

semidirect

5. C₁₉×#354

C₂

semidirect

6. C₂×Q₈×D₁₉

C₄

semidirect

9. #10597390

C₄

semidirect

14. #10597318

C₄

semidirect

15. #10597315

C₄

semidirect

82. #354

D₁₉

semidirect

100. C₁₉

#2129

semidirect

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

subgroup	index
#11927114	2
#11926516	2
#11926339	2
#11926338	2
C₁₉×#354	2
#2129	19

subgroup

index

C₁₉×#354

Subgroups — #14565308

Conjugacy classes of subgroups

Complements

Maximal subgroups