Group #14564433 — subgroups

Subgroups — #14564433

Order 2432.

384 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 113 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×C₄×D₇₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₂×D₁₉)⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₇₆	C₄	1	1	yes	characteristic
6	C₂²×C₄×D₁₉	C₂²	1	2	yes	—
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×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
11	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
12	C₄×D₇₆	—	2	2	no	—
13	C₄×D₇₆	—	2	2	no	—
14	C₁₉×#97	—	2	2	no	—
15	(C₂×D₁₉)⋊C₈	—	2	8	no	—
16	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₂³×D₁₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
22	C₂×D₇₆	—	2	4	no	—
23	C₂×D₇₆	—	2	2	no	—
24	C₂×C₄×D₁₉	—	2	4	no	—
25	C₂×C₄×D₁₉	—	2	2	no	—
26	C₂×C₄×D₁₉	—	2	2	no	—
27	C₂×C₄×D₁₉	—	2	4	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	D₄	1	4	yes	complemented
31	C₄²×C₁₉	D₄	1	2	yes	—
32	C₄²×C₁₉	D₄	1	2	yes	—
33	(C₂×D₁₉)⋊C₄	—	2	4	no	—
34	C₄⋊Dic₁₉	—	2	2	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂×C₁₉⋊C₈	—	2	4	no	—
37	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂²×D₁₉	—	2	2	no	—
39	C₂²×D₁₉	—	2	4	no	—
40	C₂²×D₁₉	—	2	2	no	—
41	C₂²×D₁₉	—	2	4	no	—
42	C₂²×D₁₉	M₁₆	1	4	yes	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
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	2	yes	—
51	C₂×Dic₁₉	—	2	2	no	—
52	C₂×Dic₁₉	—	2	4	no	—
53	D₇₆	—	2	8	no	—
54	C₄×D₁₉	—	4	4	no	—
55	C₄×D₁₉	—	4	2	no	—
56	C₄×D₁₉	—	4	2	no	—
57	C₈×C₁₉	—	2	4	no	—
58	C₁₉⋊C₈	—	4	2	no	—
59	#1955	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₁₉	C₄×D₄	1	2	yes	—
62	C₂²×C₁₉	C₂×M₁₆	1	2	yes	—
63	C₂²×C₁₉	#131	1	2	yes	—
64	C₂×D₁₉	—	2	4	no	—
65	C₂×D₁₉	—	2	8	no	—
66	C₂×D₁₉	—	4	2	no	—
67	C₂×D₁₉	—	4	2	no	—
68	C₂×D₁₉	—	4	4	no	—
69	C₄×C₁₉	—	2	2	no	—
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	#121	1	2	yes	—
72	C₄×C₁₉	#124	1	1	yes	characteristic
73	C₄×C₁₉	#127	1	1	yes	characteristic
74	Dic₁₉	—	4	2	no	—
75	C₂×C₄×D₄	—	19	1	no	—
76	C₂×C₄⋊C₈	—	19	1	no	—
77	C₂×C₂²⋊C₈	—	19	4	no	—
78	C₂×#97	D₁₉	1	1	yes	characteristic, complemented
79	C₂×C₁₉	#390	1	1	yes	characteristic
80	C₂×C₁₉	#407	1	1	yes	characteristic
81	C₂×C₁₉	#408	1	1	yes	characteristic
82	C₂×C₁₉	#435	1	4	yes	—
83	D₁₉	—	4	4	no	—
84	C₂²×D₄	—	19	1	no	—
85	C₂³×C₄	—	19	2	no	—
86	C₂²×C₈	—	19	2	no	—
87	C₂²×C₈	C₂×D₁₉	1	2	yes	—
88	C₄×D₄	—	38	2	no	—
89	C₄×D₄	—	38	2	no	—
90	C₂×C₄⋊C₄	—	19	1	no	—
91	C₂×C₂²⋊C₄	—	19	2	no	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	C₄⋊C₈	—	38	2	no	—
94	C₂²⋊C₈	—	38	8	no	—
95	#97	—	2	2	no	—
96	C₁₉	#1955	1	1	yes	characteristic, complemented, Sylow
97	C₂⁴	—	19	2	no	—
98	C₂×D₄	—	38	4	no	—
99	C₂×D₄	—	38	2	no	—
100	C₂²×C₄	—	19	2	no	—
101	C₂²×C₄	—	38	4	no	—
102	C₂²×C₄	—	38	2	no	—
103	C₂²×C₄	—	38	4	no	—
104	C₂²×C₄	—	38	2	no	—
105	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
106	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
107	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	2	2	no	—
110	C₂×C₈	—	38	4	no	—
111	C₂×C₈	—	38	2	no	—
112	C₂×C₈	D₇₆	1	4	yes	complemented
113	C₄⋊C₄	—	38	2	no	—
114	C₂²⋊C₄	—	38	4	no	—
115	C₄²	D₇₆	1	2	yes	—
116	C₄²	C₂²⋊D₁₉	1	2	yes	—
117	C₂³	—	19	4	no	—
118	C₂³	—	38	4	no	—
119	C₂³	—	38	2	no	—
120	C₂³	—	38	4	no	—
121	C₂³	—	38	2	no	—
122	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
123	D₄	—	38	8	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	—	38	4	no	—
127	C₂×C₄	—	38	2	no	—
128	C₂×C₄	—	76	4	no	—
129	C₂×C₄	—	76	2	no	—
130	C₂×C₄	—	76	2	no	—
131	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
132	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
133	C₂×C₄	C₂×D₇₆	1	2	yes	—
134	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
135	C₂×C₄	#64541	1	2	yes	—
136	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
137	C₈	—	2	4	no	—
138	C₈	—	76	2	no	—
139	C₂²	—	38	8	no	—
140	C₂²	—	38	4	no	—
141	C₂²	—	76	4	no	—
142	C₂²	—	76	2	no	—
143	C₂²	—	76	2	no	—
144	C₂²	C₄×D₇₆	1	2	yes	—
145	C₂²	M₁₆×D₁₉	1	2	yes	—
146	C₂²	#10597353	1	2	yes	—
147	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
148	C₄	—	2	2	no	—
149	C₄	—	2	2	no	—
150	C₄	—	76	2	no	—
151	C₄	#10597320	1	1	yes	characteristic
152	C₄	#10597321	1	1	yes	characteristic
153	C₄	#10597376	1	2	yes	—
154	C₂	—	76	4	no	—
155	C₂	#11926446	1	1	yes	characteristic
156	C₂	#11926507	1	1	yes	characteristic
157	C₂	#11926512	1	1	yes	characteristic
158	C₂	#11926617	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×D₇₆

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic, complemented

C₂×(C₂×D₁₉)⋊C₈

C₂

yes

maximal, complemented

C₂×C₁₉×#97

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₄

yes

characteristic

C₂²×C₄×D₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₄

yes

—

C₂×C₄⋊Dic₁₉

C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₄×D₇₆

—

C₄×D₇₆

—

C₁₉×#97

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

C₂³×D₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

complemented

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1955

—

maximal, Sylow

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₂²×C₁₉

C₂×M₁₆

yes

—

C₂²×C₁₉

#131

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂×C₄×D₄

—

C₂×C₄⋊C₈

—

C₂×C₂²⋊C₈

—

C₂×#97

D₁₉

yes

characteristic, complemented

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

D₁₉

—

C₂²×D₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₁₉

#1955

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

C₄×D₁₉

yes

characteristic

106

C₂²×C₄

C₄×D₁₉

yes

characteristic

107

C₂²×C₄

C₂²×D₁₉

yes

characteristic

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

D₇₆

yes

complemented

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

115

C₄²

D₇₆

yes

—

116

C₄²

C₂²⋊D₁₉

yes

—

117

C₂³

—

118

C₂³

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

C₂×C₄×D₁₉

yes

characteristic

123

D₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

132

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

133

C₂×C₄

C₂×D₇₆

yes

—

134

C₂×C₄

C₂×D₇₆

yes

characteristic

135

C₂×C₄

#64541

yes

—

136

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

137

C₈

—

138

C₈

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

C₄×D₇₆

yes

—

145

C₂²

M₁₆×D₁₉

yes

—

146

C₂²

#10597353

yes

—

147

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

#10597320

yes

characteristic

152

C₄

#10597321

yes

characteristic

153

C₄

#10597376

yes

—

154

C₂

—

155

C₂

#11926446

yes

characteristic

156

C₂

#11926507

yes

characteristic

157

C₂

#11926512

yes

characteristic

158

C₂

#11926617

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₉
commutator, socle	C₂³×C₁₉	C₂²×C₄
Fitting	C₂×C₁₉×#97	C₂
prime radical	C₂²×D₇₆	C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#97	D₁₉
hypocenter	C₁₉	#1955
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₉

commutator, socle

C₂³×C₁₉

C₂²×C₄

Fitting

C₂×C₁₉×#97

C₂

prime radical

C₂²×D₇₆

C₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×#97

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
2. C₂×C₄⋊(C₁₉⋊C₈)	C₂	semidirect
3. C₂×(C₂×D₁₉)⋊C₈	C₂	semidirect
4. C₂×C₁₉×#97	C₂	semidirect
30. C₂×C₈×C₁₉	D₄	semidirect
78. C₂×#97	D₁₉	semidirect
96. C₁₉	#1955	semidirect
112. C₂×C₈	D₇₆	semidirect

H ≅ G/N

type

2. C₂×C₄⋊(C₁₉⋊C₈)

C₂

semidirect

3. C₂×(C₂×D₁₉)⋊C₈

C₂

semidirect

4. C₂×C₁₉×#97

C₂

semidirect

30. C₂×C₈×C₁₉

D₄

semidirect

78. C₂×#97

D₁₉

semidirect

96. C₁₉

#1955

semidirect

112. C₂×C₈

D₇₆

semidirect

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

subgroup	index
C₂×C₄×D₇₆	2
C₂×C₄⋊(C₁₉⋊C₈)	2
C₂×(C₂×D₁₉)⋊C₈	2
C₂×C₁₉×#97	2
#1955	19

subgroup

index

C₂×C₄×D₇₆

C₂×C₄⋊(C₁₉⋊C₈)

C₂×(C₂×D₁₉)⋊C₈

C₂×C₁₉×#97

#1955

Subgroups — #14564433

Conjugacy classes of subgroups

Complements

Maximal subgroups