Group #14565104 — subgroups

Subgroups — #14565104

Order 2432.

184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11926592	C₂	1	1	yes	maximal, characteristic
2	#11926552	C₂	1	1	yes	maximal, characteristic
3	#11926552	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597281	C₂	1	1	yes	maximal, characteristic
5	#11926314	C₂	1	1	yes	maximal, characteristic
6	#11926314	C₂	1	1	yes	maximal, characteristic
7	C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#117	C₂²	1	1	yes	characteristic
11	C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂×#64520	C₂²	1	1	yes	characteristic
13	C₂×#64520	C₂²	1	1	yes	characteristic
14	C₂×#64520	C₂²	1	1	yes	characteristic
15	#10597281	—	2	2	no	—
16	#10597279	—	2	2	no	—
17	#10597267	—	2	2	no	—
18	#10597267	—	2	2	no	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₉	—	2	1	no	—
21	C₂×Dic₃₈	—	2	1	no	—
22	C₂×Dic₃₈	—	2	1	no	—
23	C₂×Dic₃₈	—	2	1	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	C₂×Dic₃₈	—	2	1	no	—
26	C₂×Dic₃₈	D₄	1	2	yes	—
27	M₁₆×C₁₉	—	2	1	no	—
28	M₁₆×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂²⋊C₄×C₁₉	—	2	1	no	—
33	C₂²⋊C₄×C₁₉	—	2	1	no	—
34	C₄²×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	#64520	—	2	1	no	—
37	#64520	—	2	1	no	—
38	#64520	—	2	1	no	—
39	#64520	—	2	1	no	—
40	#64520	—	2	1	no	—
41	#64520	—	2	1	no	—
42	C₂×C₁₉⋊C₈	—	2	1	no	—
43	C₂×C₁₉⋊C₈	—	2	1	no	—
44	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
45	C₂³×C₁₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂×Dic₁₉	—	2	2	no	—
55	C₂×Dic₁₉	—	4	1	no	—
56	C₂×Dic₁₉	—	4	1	no	—
57	Dic₃₈	—	2	2	no	—
58	Dic₃₈	—	2	2	no	—
59	Dic₃₈	—	4	1	no	—
60	Dic₃₈	—	4	1	no	—
61	C₈×C₁₉	—	4	1	no	—
62	C₁₉⋊C₈	—	2	2	no	—
63	C₁₉⋊C₈	—	4	1	no	—
64	C₁₉⋊C₈	—	4	1	no	—
65	#2082	—	19	1	no	maximal, Sylow
66	C₂²×C₁₉	—	4	1	no	—
67	C₂²×C₁₉	#123	1	1	yes	characteristic
68	C₂²×C₁₉	#124	1	1	yes	characteristic
69	C₂²×C₁₉	#126	1	1	yes	characteristic
70	C₄×C₁₉	—	8	1	no	—
71	C₄×C₁₉	—	8	1	no	—
72	C₄×C₁₉	#121	1	1	yes	characteristic
73	C₄×C₁₉	#123	1	1	yes	characteristic
74	C₄×C₁₉	#123	1	1	yes	characteristic
75	C₄×C₁₉	#126	1	1	yes	characteristic
76	Dic₁₉	—	4	2	no	—
77	#430	—	19	1	no	—
78	#419	—	19	1	no	—
79	#419	—	19	1	no	—
80	C₂×#101	—	19	1	no	—
81	#344	—	19	1	no	—
82	#344	—	19	1	no	—
83	H(3,ℤ/4)	D₁₉	1	1	yes	characteristic
84	C₂×C₁₉	—	2	1	no	—
85	C₂×C₁₉	—	2	1	no	—
86	C₂×C₁₉	—	2	1	no	—
87	C₂×C₁₉	#397	1	1	yes	characteristic
88	C₂²×Q₈	—	19	1	no	—
89	C₂×M₁₆	—	19	1	no	—
90	C₂×M₁₆	—	19	1	no	—
91	C₂×M₁₆	—	19	1	no	—
92	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
93	#117	C₂×D₁₉	1	1	yes	characteristic
94	#117	C₂×D₁₉	1	1	yes	characteristic
95	#108	—	38	2	no	—
96	#103	—	38	2	no	—
97	#103	—	38	2	no	—
98	#101	—	38	2	no	—
99	C₁₉	#2082	1	1	yes	characteristic, complemented, Sylow
100	C₂×Q₈	—	19	2	no	—
101	C₂×Q₈	—	38	1	no	—
102	C₂×Q₈	—	38	1	no	—
103	C₂×Q₈	—	38	1	no	—
104	C₂×Q₈	—	38	1	no	—
105	C₂×Q₈	—	38	1	no	—
106	C₂²×C₄	—	38	1	no	—
107	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
108	M₁₆	—	2	1	no	—
109	M₁₆	—	2	1	no	—
110	M₁₆	—	38	1	no	—
111	M₁₆	—	38	1	no	—
112	M₁₆	—	38	1	no	—
113	M₁₆	—	38	1	no	—
114	M₁₆	—	38	1	no	—
115	M₁₆	—	38	1	no	—
116	C₂×C₈	—	2	1	no	—
117	C₂×C₈	—	19	2	no	—
118	C₂×C₈	—	38	1	no	—
119	C₂×C₈	—	38	1	no	—
120	C₄⋊C₄	—	2	1	no	—
121	C₄⋊C₄	—	2	1	no	—
122	C₂²⋊C₄	—	2	1	no	—
123	C₂²⋊C₄	—	2	1	no	—
124	C₄²	—	2	1	no	—
125	C₄²	—	2	1	no	—
126	C₂³	#64543	1	1	yes	characteristic
127	Q₈	—	38	2	no	—
128	Q₈	—	38	2	no	—
129	Q₈	—	76	1	no	—
130	Q₈	—	76	1	no	—
131	C₂×C₄	—	4	1	no	—
132	C₂×C₄	—	4	1	no	—
133	C₂×C₄	—	38	2	no	—
134	C₂×C₄	—	76	1	no	—
135	C₂×C₄	—	76	1	no	—
136	C₂×C₄	#64541	1	1	yes	characteristic
137	C₂×C₄	#64541	1	1	yes	characteristic
138	C₂×C₄	#64541	1	1	yes	characteristic
139	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
140	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
141	C₂×C₄	#64545	1	1	yes	characteristic
142	C₈	—	4	1	no	—
143	C₈	—	38	2	no	—
144	C₈	—	76	1	no	—
145	C₈	—	76	1	no	—
146	C₂²	—	4	1	no	—
147	C₂²	#10597329	1	1	yes	characteristic
148	C₂²	#10597331	1	1	yes	characteristic
149	C₂²	#10597344	1	1	yes	characteristic
150	C₄	—	8	1	no	—
151	C₄	—	8	1	no	—
152	C₄	—	76	2	no	—
153	C₄	#10597322	1	1	yes	characteristic
154	C₄	#10597330	1	1	yes	characteristic
155	C₄	#10597340	1	1	yes	characteristic
156	C₄	#10597340	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	—	2	1	no	—
160	C₂	#11926473	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926592

C₂

yes

maximal, characteristic

#11926552

C₂

yes

maximal, characteristic

#11926552

C₂

yes

maximal, characteristic

C₂×#10597281

C₂

yes

maximal, characteristic

#11926314

C₂

yes

maximal, characteristic

#11926314

C₂

yes

maximal, characteristic

C₁₉×H(3,ℤ/4)

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

—

—

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

—

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2082

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#397

yes

characteristic

C₂²×Q₈

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

#117

C₂×D₁₉

yes

characteristic

#117

C₂×D₁₉

yes

—

—

—

—

C₁₉

#2082

yes

characteristic, complemented, Sylow

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂²×C₄

—

107

C₂²×C₄

C₂²×D₁₉

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

M₁₆

—

116

C₂×C₈

—

117

C₂×C₈

—

118

C₂×C₈

—

119

C₂×C₈

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₂²⋊C₄

—

123

C₂²⋊C₄

—

124

C₄²

—

125

C₄²

—

126

C₂³

#64543

yes

characteristic

127

Q₈

—

128

Q₈

—

129

Q₈

—

130

Q₈

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

#64541

yes

characteristic

137

C₂×C₄

#64541

yes

characteristic

138

C₂×C₄

#64541

yes

characteristic

139

C₂×C₄

D₄×D₁₉

yes

characteristic

140

C₂×C₄

D₄×D₁₉

yes

characteristic

141

C₂×C₄

#64545

yes

characteristic

142

C₈

—

143

C₈

—

144

C₈

—

145

C₈

—

146

C₂²

—

147

C₂²

#10597329

yes

characteristic

148

C₂²

#10597331

yes

characteristic

149

C₂²

#10597344

yes

characteristic

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

#10597322

yes

characteristic

154

C₄

#10597330

yes

characteristic

155

C₄

#10597340

yes

characteristic

156

C₄

#10597340

yes

characteristic

157

C₂

—

158

C₂

—

159

C₂

—

160

C₂

#11926473

yes

characteristic

	subgroup	G/H
center	C₂	#11926473
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×H(3,ℤ/4)	C₂
socle	C₂×C₁₉	#397
prime radical	C₂³×C₁₉	#41
hypercenter	H(3,ℤ/4)	D₁₉
hypocenter	C₁₉	#2082
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₂

#11926473

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×H(3,ℤ/4)

C₂

C₂×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
99. C₁₉	#2082	semidirect

H ≅ G/N

type

99. C₁₉

#2082

semidirect

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

subgroup	index
#11926592	2
#11926552	2
C₂×#10597281	2
#11926314	2
C₁₉×H(3,ℤ/4)	2
#2082	19

subgroup

index

C₁₉×H(3,ℤ/4)

Subgroups — #14565104

Conjugacy classes of subgroups

Complements

Maximal subgroups