Group #14563627 — subgroups

Subgroups — #14563627

Order 2432.

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

normal subgroups only

This group has 336 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	#11926568	C₂	1	2	yes	maximal, complemented
2	C₂×#10597290	C₂	1	2	yes	maximal
3	#11926313	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂³×C₄×C₁₉	C₄	1	2	yes	—
7	C₄×D₄×C₁₉	—	2	2	no	—
8	C₄×D₄×C₁₉	—	2	2	no	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊C₄×C₁₉	C₄	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×#64520	C₂²	1	4	yes	—
13	#10597290	—	2	4	no	—
14	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
15	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
16	C₂⁴×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×D₄×C₁₉	—	2	2	no	—
18	C₂×D₄×C₁₉	—	2	2	no	—
19	C₂×D₄×C₁₉	D₄	1	2	yes	—
20	C₂×D₄×C₁₉	Q₈	1	2	yes	—
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	4	4	no	—
24	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂²⋊C₄×C₁₉	—	2	4	no	—
30	C₄²×C₁₉	D₄	1	2	yes	—
31	C₄²×C₁₉	D₄	1	2	yes	—
32	#64520	—	2	4	no	—
33	#64520	—	2	4	no	—
34	C₂×C₁₉⋊C₈	—	2	4	no	—
35	C₂³×C₁₉	—	2	2	no	—
36	C₂³×C₁₉	—	2	2	no	—
37	C₂³×C₁₉	—	4	2	no	—
38	C₂³×C₁₉	—	4	2	no	—
39	C₂³×C₁₉	C₄⋊C₄	1	4	yes	—
40	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	D₄×C₁₉	—	2	4	no	—
42	D₄×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	4	4	no	—
47	C₂×C₄×C₁₉	—	4	4	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	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	C₁₉⋊C₈	—	4	4	no	—
57	#1800	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	—	2	1	no	—
59	C₂²×C₁₉	—	2	1	no	—
60	C₂²×C₁₉	—	2	4	no	—
61	C₂²×C₁₉	—	4	4	no	—
62	C₂²×C₁₉	—	4	4	no	—
63	C₂²×C₁₉	—	4	2	no	—
64	C₂²×C₁₉	—	4	2	no	—
65	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₁₉	#117	1	1	yes	characteristic
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	2	2	no	—
70	C₄×C₁₉	—	4	2	no	—
71	C₄×C₁₉	#100	1	2	yes	complemented
72	C₄×C₁₉	#121	1	2	yes	—
73	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
74	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic
75	#423	—	19	2	no	—
76	C₂×#100	—	19	2	no	—
77	#343	—	19	2	no	—
78	C₂×C₁₉	—	2	1	no	—
79	C₂×C₁₉	—	2	1	no	—
80	C₂×C₁₉	—	4	4	no	—
81	C₂×C₁₉	#380	1	1	yes	characteristic
82	C₂×C₁₉	C₂×#100	1	1	yes	characteristic
83	C₂×C₁₉	#413	1	1	yes	characteristic
84	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
85	C₂³×C₄	Dic₁₉	1	2	yes	—
86	C₂×M₁₆	—	19	4	no	—
87	C₄×D₄	—	2	2	no	—
88	C₄×D₄	—	2	2	no	—
89	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
90	C₂×C₂²⋊C₄	Dic₁₉	1	2	yes	—
91	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
92	C₄⋊C₈	—	38	2	no	—
93	C₄⋊C₈	—	38	2	no	—
94	#100	—	38	4	no	—
95	C₁₉	#1800	1	1	yes	characteristic, complemented, Sylow
96	C₂⁴	C₂×Dic₁₉	1	2	yes	—
97	C₂×D₄	—	2	2	no	—
98	C₂×D₄	—	2	2	no	—
99	C₂×D₄	Dic₃₈	1	2	yes	—
100	C₂×D₄	D₇₆	1	2	yes	—
101	C₂²×C₄	—	2	2	no	—
102	C₂²×C₄	—	2	2	no	—
103	C₂²×C₄	—	4	4	no	—
104	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
105	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
106	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
107	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
108	M₁₆	—	38	4	no	—
109	M₁₆	—	38	4	no	—
110	C₂×C₈	—	38	4	no	—
111	C₄⋊C₄	—	2	2	no	—
112	C₂²⋊C₄	—	2	4	no	—
113	C₄²	C₂²⋊D₁₉	1	2	yes	—
114	C₄²	C₂²⋊D₁₉	1	2	yes	—
115	C₂³	—	2	2	no	—
116	C₂³	—	2	2	no	—
117	C₂³	—	4	2	no	—
118	C₂³	—	4	2	no	—
119	C₂³	C₄⋊Dic₁₉	1	4	yes	—
120	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
121	D₄	—	2	4	no	—
122	D₄	—	2	4	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	4	4	no	—
127	C₂×C₄	—	4	4	no	—
128	C₂×C₄	—	4	2	no	—
129	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
130	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
131	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
132	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
133	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
134	C₂×C₄	#64541	1	2	yes	—
135	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
136	C₈	—	76	4	no	—
137	C₂²	—	2	1	no	—
138	C₂²	—	2	1	no	—
139	C₂²	—	2	4	no	—
140	C₂²	—	4	4	no	—
141	C₂²	—	4	4	no	—
142	C₂²	—	4	2	no	—
143	C₂²	—	4	2	no	—
144	C₂²	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
145	C₂²	#10597372	1	1	yes	characteristic
146	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
147	C₄	—	2	2	no	—
148	C₄	—	2	1	no	—
149	C₄	—	4	2	no	—
150	C₄	#10597290	1	2	yes	complemented
151	C₄	#10597370	1	2	yes	—
152	C₄	#10597376	1	2	yes	—
153	C₂	—	2	1	no	—
154	C₂	—	2	1	no	—
155	C₂	—	4	4	no	—
156	C₂	#11926404	1	1	yes	characteristic
157	C₂	C₂×#10597290	1	1	yes	characteristic
158	C₂	#11926528	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926568

C₂

yes

maximal, complemented

C₂×#10597290

C₂

yes

maximal

#11926313

C₂

yes

maximal, complemented

C₂×C₄×D₄×C₁₉

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂³×C₄×C₁₉

C₄

yes

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₄

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

#10597290

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂×D₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

D₄

yes

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₄⋊C₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₁₉⋊C₈

—

#1800

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

#117

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#100

yes

complemented

C₄×C₁₉

#121

yes

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×D₄

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂³×C₄

Dic₁₉

yes

—

C₂×M₁₆

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₄

Dic₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#100

—

C₁₉

#1800

yes

characteristic, complemented, Sylow

C₂⁴

C₂×Dic₁₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

Dic₃₈

yes

—

100

C₂×D₄

D₇₆

yes

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

105

C₂²×C₄

C₂×Dic₁₉

yes

—

106

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

107

C₂²×C₄

C₂²×D₁₉

yes

characteristic

108

M₁₆

—

109

M₁₆

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₄²

C₂²⋊D₁₉

yes

—

114

C₄²

C₂²⋊D₁₉

yes

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₄⋊Dic₁₉

yes

—

120

C₂³

C₂²×Dic₁₉

yes

characteristic

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂²⋊Dic₁₉

yes

—

130

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

131

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

132

C₂×C₄

C₂×Dic₃₈

yes

characteristic

133

C₂×C₄

C₂×D₇₆

yes

characteristic

134

C₂×C₄

#64541

yes

—

135

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

136

C₈

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

C₂×C₄⋊Dic₁₉

yes

characteristic

145

C₂²

#10597372

yes

characteristic

146

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

#10597290

yes

complemented

151

C₄

#10597370

yes

—

152

C₄

#10597376

yes

—

153

C₂

—

154

C₂

—

155

C₂

—

156

C₂

#11926404

yes

characteristic

157

C₂

C₂×#10597290

yes

characteristic

158

C₂

#11926528

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₄×D₄×C₁₉	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	#1800
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×D₄

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₁₉

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₄×D₄×C₁₉

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₄×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×C₄×D₄

D₁₉

hypocenter

C₁₉

#1800

LCS

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×D₄

N	H ≅ G/N	type
1. #11926568	C₂	semidirect
3. #11926313	C₂	semidirect
71. C₄×C₁₉	#100	semidirect
95. C₁₉	#1800	semidirect
150. C₄	#10597290	semidirect

H ≅ G/N

type

1. #11926568

C₂

semidirect

3. #11926313

C₂

semidirect

71. C₄×C₁₉

#100

semidirect

95. C₁₉

#1800

semidirect

150. C₄

#10597290

semidirect

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

subgroup	index
#11926568	2
C₂×#10597290	2
#11926313	2
C₂×C₄×D₄×C₁₉	2
#1800	19

subgroup

index

C₂×C₄×D₄×C₁₉

Subgroups — #14563627

Conjugacy classes of subgroups

Complements

Maximal subgroups