Group #14563402 — subgroups

Subgroups — #14563402

Order 2432.

336 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 129 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×#10597318	C₂	1	1	yes	maximal, characteristic
2	C₂×(C₂×D₁₉)⋊C₈	C₂	1	2	yes	maximal
3	C₂×#10597260	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926298	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×(C₂×D₁₉)⋊C₄	C₄	1	2	yes	—
10	C₂×Dic₁₉⋊C₄	C₄	1	2	yes	—
11	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
13	#10597318	—	2	2	no	—
14	#10597318	—	2	2	no	—
15	C₄×C₈×C₁₉	—	2	2	no	—
16	(C₂×D₁₉)⋊C₈	C₄	1	8	yes	complemented
17	#10597260	—	2	2	no	—
18	C₂³×D₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
22	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₁₉	—	2	1	no	—
24	C₂×C₄×D₁₉	—	2	1	no	—
25	C₂×C₄×D₁₉	—	2	2	no	—
26	C₂×C₄×D₁₉	C₂×C₄	1	4	yes	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	C₂×C₄	1	4	yes	—
30	C₄²×C₁₉	D₄	1	2	yes	—
31	C₄²×C₁₉	D₄	1	2	yes	—
32	(C₂×D₁₉)⋊C₄	—	2	4	no	—
33	Dic₁₉⋊C₄	—	2	4	no	—
34	C₄×Dic₁₉	—	2	1	no	—
35	C₄×Dic₁₉	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂×C₁₉⋊C₈	—	2	2	no	—
38	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
39	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²×D₁₉	—	2	1	no	—
41	C₂²×D₁₉	—	2	1	no	—
42	C₂²×D₁₉	—	2	4	no	—
43	C₂²×D₁₉	C₄²	1	2	yes	—
44	C₂×C₄×C₁₉	—	2	4	no	—
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
46	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#41	1	2	yes	—
50	C₂×Dic₁₉	—	2	1	no	—
51	C₂×Dic₁₉	—	2	1	no	—
52	C₂×Dic₁₉	—	2	2	no	—
53	C₂×Dic₁₉	—	2	4	no	—
54	C₂×Dic₁₉	C₄²	1	2	yes	—
55	C₄×D₁₉	—	2	4	no	—
56	C₄×D₁₉	—	2	4	no	—
57	C₈×C₁₉	—	2	4	no	—
58	C₁₉⋊C₈	—	2	4	no	—
59	#1750	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	C₂×C₄²	1	1	yes	characteristic
61	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₁₉	#117	1	1	yes	characteristic
63	C₂²×C₁₉	#131	1	4	yes	—
64	C₂×D₁₉	—	2	2	no	—
65	C₂×D₁₉	—	2	4	no	—
66	C₂×D₁₉	—	4	2	no	—
67	C₂×D₁₉	—	4	2	no	—
68	C₄×C₁₉	—	2	4	no	—
69	C₄×C₁₉	C₄×D₄	1	2	yes	—
70	C₄×C₁₉	C₄×D₄	1	2	yes	—
71	Dic₁₉	—	2	2	no	—
72	Dic₁₉	—	4	2	no	—
73	C₂×#117	—	19	1	no	—
74	C₂×C₂²⋊C₈	—	19	2	no	—
75	C₂×#97	—	19	1	no	—
76	C₂×C₄×C₈	D₁₉	1	1	yes	characteristic, complemented
77	#336	—	19	2	no	—
78	C₂×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₁₉	#405	1	2	yes	—
80	C₂×C₁₉	#408	1	2	yes	—
81	C₂×C₁₉	#433	1	2	yes	—
82	D₁₉	—	4	2	no	—
83	C₂³×C₄	—	19	1	no	—
84	C₂²×C₈	—	19	2	no	—
85	C₂²×C₈	C₂×D₁₉	1	2	yes	—
86	#117	—	38	2	no	—
87	#117	—	38	2	no	—
88	C₂×C₄⋊C₄	—	19	2	no	—
89	C₂×C₂²⋊C₄	—	19	2	no	—
90	C₂×C₄²	—	19	1	no	—
91	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
92	C₂²⋊C₈	—	19	8	no	—
93	#97	—	38	2	no	—
94	C₄×C₈	—	2	2	no	—
95	C₁₉	#1750	1	1	yes	characteristic, complemented, Sylow
96	C₂⁴	—	19	1	no	—
97	C₂²×C₄	—	19	1	no	—
98	C₂²×C₄	—	19	4	no	—
99	C₂²×C₄	—	19	2	no	—
100	C₂²×C₄	—	38	1	no	—
101	C₂²×C₄	—	38	2	no	—
102	C₂²×C₄	—	38	1	no	—
103	C₂²×C₄	C₄×D₁₉	1	2	yes	—
104	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
105	C₂×C₈	—	2	2	no	—
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	19	4	no	—
108	C₂×C₈	—	38	2	no	—
109	C₂×C₈	—	38	2	no	—
110	C₂×C₈	C₄×D₁₉	1	4	yes	—
111	C₄⋊C₄	—	38	4	no	—
112	C₂²⋊C₄	—	38	4	no	—
113	C₄²	—	38	1	no	—
114	C₄²	—	38	1	no	—
115	C₄²	D₇₆	1	2	yes	—
116	C₄²	C₂²⋊D₁₉	1	2	yes	—
117	C₂³	—	19	2	no	—
118	C₂³	—	38	1	no	—
119	C₂³	—	38	4	no	—
120	C₂³	—	38	1	no	—
121	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	19	2	no	—
124	C₂×C₄	—	38	1	no	—
125	C₂×C₄	—	38	1	no	—
126	C₂×C₄	—	38	4	no	—
127	C₂×C₄	—	38	4	no	—
128	C₂×C₄	—	38	4	no	—
129	C₂×C₄	—	38	2	no	—
130	C₂×C₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
131	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
132	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
133	C₂×C₄	#64541	1	2	yes	—
134	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
135	C₈	—	2	4	no	—
136	C₈	—	38	4	no	—
137	C₂²	—	38	2	no	—
138	C₂²	—	38	4	no	—
139	C₂²	—	76	2	no	—
140	C₂²	—	76	2	no	—
141	C₂²	C₄²×D₁₉	1	1	yes	characteristic
142	C₂²	#10597318	1	1	yes	characteristic
143	C₂²	#10597347	1	4	yes	—
144	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
145	C₄	—	2	4	no	—
146	C₄	—	38	2	no	—
147	C₄	—	76	2	no	—
148	C₄	C₄×D₇₆	1	2	yes	—
149	C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
150	C₂	—	76	2	no	—
151	C₂	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
152	C₂	#11926498	1	2	yes	—
153	C₂	#11926510	1	2	yes	—
154	C₂	#11926603	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597318

C₂

yes

maximal, characteristic

C₂×(C₂×D₁₉)⋊C₈

C₂

yes

maximal

C₂×#10597260

C₂

yes

maximal, characteristic, complemented

#11926298

C₂

yes

maximal, complemented

C₂×C₄×C₈×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₄

yes

—

C₂×Dic₁₉⋊C₄

C₄

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597318

—

#10597318

—

C₄×C₈×C₁₉

—

(C₂×D₁₉)⋊C₈

C₄

yes

complemented

#10597260

—

C₂³×D₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂²×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

C₄²

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₄²

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1750

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄²

yes

characteristic

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

C₄×D₄

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×#117

—

C₂×C₂²⋊C₈

—

C₂×#97

—

C₂×C₄×C₈

D₁₉

yes

characteristic, complemented

#336

—

C₂×C₁₉

C₄×C₂²⋊C₄

yes

characteristic

C₂×C₁₉

#405

yes

—

C₂×C₁₉

#408

yes

—

C₂×C₁₉

#433

yes

—

D₁₉

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₁₉

#1750

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₄×D₁₉

yes

—

104

C₂²×C₄

C₂²×D₁₉

yes

characteristic

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

C₄×D₁₉

yes

—

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₄²

—

114

C₄²

—

115

C₄²

D₇₆

yes

—

116

C₄²

C₂²⋊D₁₉

yes

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

C₂×C₄×D₁₉

yes

characteristic

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

131

C₂×C₄

C₂×C₄×D₁₉

yes

—

132

C₂×C₄

C₂×D₇₆

yes

characteristic

133

C₂×C₄

#64541

yes

—

134

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

135

C₈

—

136

C₈

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

C₄²×D₁₉

yes

characteristic

142

C₂²

#10597318

yes

characteristic

143

C₂²

#10597347

yes

—

144

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

C₄×D₇₆

yes

—

149

C₄

C₄×C₂²⋊D₁₉

yes

—

150

C₂

—

151

C₂

C₄×(C₂×D₁₉)⋊C₄

yes

characteristic

152

C₂

#11926498

yes

—

153

C₂

#11926510

yes

—

154

C₂

#11926603

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂×C₄²
Fitting	C₂×C₄×C₈×C₁₉	C₂
socle	C₂³×C₁₉	C₂²×C₄
prime radical	C₂³×D₁₉	C₂×C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₈	D₁₉
hypocenter	C₁₉	#1750
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator

C₂²×C₁₉

C₂×C₄²

Fitting

C₂×C₄×C₈×C₁₉

C₂

socle

C₂³×C₁₉

C₂²×C₄

prime radical

C₂³×D₁₉

C₂×C₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×C₄×C₈

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
3. C₂×#10597260	C₂	semidirect
4. #11926298	C₂	semidirect
5. C₂×C₄×C₈×C₁₉	C₂	semidirect
16. (C₂×D₁₉)⋊C₈	C₄	semidirect
76. C₂×C₄×C₈	D₁₉	semidirect
95. C₁₉	#1750	semidirect

H ≅ G/N

type

3. C₂×#10597260

C₂

semidirect

4. #11926298

C₂

semidirect

5. C₂×C₄×C₈×C₁₉

C₂

semidirect

16. (C₂×D₁₉)⋊C₈

C₄

semidirect

76. C₂×C₄×C₈

D₁₉

semidirect

95. C₁₉

#1750

semidirect

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

subgroup	index
C₂×#10597318	2
C₂×(C₂×D₁₉)⋊C₈	2
C₂×#10597260	2
#11926298	2
C₂×C₄×C₈×C₁₉	2
#1750	19

subgroup

index

C₂×(C₂×D₁₉)⋊C₈

C₂×C₄×C₈×C₁₉

Subgroups — #14563402

Conjugacy classes of subgroups

Complements

Maximal subgroups