Group #14564593 — subgroups

Subgroups — #14564593

Order 2432.

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

normal subgroups only

This group has 260 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⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	#11926306	C₂	1	2	yes	maximal
4	#11926306	C₂	1	2	yes	maximal
5	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#125	—	2	2	no	—
7	C₁₉×#125	C₄	1	4	yes	complemented
8	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
9	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
14	C₂×C₄×Dic₁₉	—	2	1	no	—
15	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
16	C₁₉⋊#95	—	2	1	no	—
17	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
18	C₂²×C₄×C₁₉	—	2	1	no	—
19	C₂²×C₄×C₁₉	—	2	1	no	—
20	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	—	2	4	no	—
25	C₄⋊C₄×C₁₉	—	2	4	no	—
26	C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
29	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
30	C₄²×C₁₉	C₂×C₄	1	2	yes	—
31	C₄²×C₁₉	D₄	1	2	yes	—
32	C₄⋊Dic₁₉	—	2	2	no	—
33	C₄⋊Dic₁₉	Q₈	1	4	yes	—
34	C₄×Dic₁₉	—	4	2	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂×C₁₉⋊C₈	—	2	4	no	—
37	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
51	C₂×C₄×C₁₉	#41	1	2	yes	—
52	C₂×Dic₁₉	—	2	4	no	—
53	C₂×Dic₁₉	—	4	2	no	—
54	C₂×Dic₁₉	—	4	2	no	—
55	C₁₉⋊C₈	—	4	2	no	—
56	#1989	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
59	C₂²×C₁₉	#135	1	2	yes	—
60	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
61	C₂²×C₁₉	#137	1	1	yes	characteristic
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	—	2	2	no	—
64	C₄×C₁₉	—	4	2	no	—
65	C₄×C₁₉	—	4	2	no	—
66	C₄×C₁₉	C₄×Q₈	1	2	yes	—
67	C₄×C₁₉	#124	1	1	yes	characteristic
68	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
69	Dic₁₉	—	4	4	no	—
70	C₂×#125	D₁₉	1	1	yes	characteristic
71	C₂×C₄⋊C₈	—	19	1	no	—
72	C₄×C₄⋊C₄	—	19	1	no	—
73	#340	—	19	2	no	—
74	#340	—	19	2	no	—
75	C₂×C₁₉	#391	1	1	yes	characteristic
76	C₂×C₁₉	#416	1	1	yes	characteristic
77	C₂×C₁₉	#417	1	1	yes	characteristic
78	C₂×C₁₉	#478	1	2	yes	—
79	C₂×C₁₉	#479	1	2	yes	—
80	C₂²×C₈	—	19	2	no	—
81	#125	—	2	2	no	—
82	#125	Dic₁₉	1	4	yes	complemented
83	C₂×C₄⋊C₄	—	2	1	no	—
84	C₂×C₄⋊C₄	—	2	1	no	—
85	C₂×C₄⋊C₄	—	19	2	no	—
86	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
87	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
88	C₂×C₄²	—	38	1	no	—
89	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
90	C₄⋊C₈	—	38	2	no	—
91	#95	—	38	1	no	—
92	C₁₉	#1989	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	2	1	no	—
95	C₂²×C₄	—	38	2	no	—
96	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
97	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
99	C₂×C₈	—	38	4	no	—
100	C₂×C₈	—	38	2	no	—
101	C₄⋊C₄	—	2	4	no	—
102	C₄⋊C₄	—	2	4	no	—
103	C₄⋊C₄	—	2	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	19	4	no	—
106	C₄⋊C₄	—	38	2	no	—
107	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
108	C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
109	C₄²	—	76	2	no	—
110	C₄²	C₂×Dic₁₉	1	2	yes	—
111	C₄²	C₂²⋊D₁₉	1	2	yes	—
112	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	4	1	no	—
121	C₂×C₄	—	38	4	no	—
122	C₂×C₄	—	76	2	no	—
123	C₂×C₄	—	76	2	no	—
124	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
125	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
126	C₂×C₄	Q₈×D₁₉	1	2	yes	—
127	C₂×C₄	#64545	1	2	yes	—
128	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
129	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
130	C₈	—	76	2	no	—
131	C₂²	#10597392	1	2	yes	—
132	C₂²	#10597395	1	1	yes	characteristic
133	C₂²	#10597396	1	2	yes	—
134	C₂²	#10597397	1	1	yes	characteristic
135	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
136	C₄	—	2	2	no	—
137	C₄	—	2	2	no	—
138	C₄	—	4	2	no	—
139	C₄	—	4	2	no	—
140	C₄	—	76	4	no	—
141	C₄	#10597390	1	1	yes	characteristic
142	C₄	Q₈×Dic₁₉	1	2	yes	—
143	C₄	#10597393	1	1	yes	characteristic
144	C₂	#11926451	1	1	yes	characteristic
145	C₂	#11926540	1	1	yes	characteristic
146	C₂	#11926545	1	1	yes	characteristic
147	C₂	#11926841	1	2	yes	—
148	C₂	#11926848	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₁₉⋊C₈)

C₂

yes

maximal, characteristic

C₄×C₄⋊Dic₁₉

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

#11926306

C₂

yes

maximal

C₂×C₁₉×#125

C₂

yes

maximal, characteristic

C₁₉×#125

—

C₁₉×#125

C₄

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉⋊#95

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

Q₈

yes

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×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

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1989

—

maximal, Sylow

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₂²×C₁₉

#135

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×Q₈

yes

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

C₂×#125

D₁₉

yes

characteristic

C₂×C₄⋊C₈

—

C₄×C₄⋊C₄

—

#340

—

#340

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#479

yes

—

C₂²×C₈

—

#125

—

#125

Dic₁₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

#95

—

C₁₉

#1989

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

C₂×Dic₁₉

yes

—

108

C₄⋊C₄

C₂×Dic₁₉

yes

—

109

C₄²

—

110

C₄²

C₂×Dic₁₉

yes

—

111

C₄²

C₂²⋊D₁₉

yes

—

112

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

C₂²⋊Dic₁₉

yes

—

125

C₂×C₄

C₂²⋊Dic₁₉

yes

—

126

C₂×C₄

Q₈×D₁₉

yes

—

127

C₂×C₄

#64545

yes

—

128

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

129

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

130

C₈

—

131

C₂²

#10597392

yes

—

132

C₂²

#10597395

yes

characteristic

133

C₂²

#10597396

yes

—

134

C₂²

#10597397

yes

characteristic

135

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

—

141

C₄

#10597390

yes

characteristic

142

C₄

Q₈×Dic₁₉

yes

—

143

C₄

#10597393

yes

characteristic

144

C₂

#11926451

yes

characteristic

145

C₂

#11926540

yes

characteristic

146

C₂

#11926545

yes

characteristic

147

C₂

#11926841

yes

—

148

C₂

#11926848

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#125	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#1989
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#125

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
7. C₁₉×#125	C₄	semidirect
82. #125	Dic₁₉	semidirect
92. C₁₉	#1989	semidirect

H ≅ G/N

type

7. C₁₉×#125

C₄

semidirect

82. #125

Dic₁₉

semidirect

92. C₁₉

#1989

semidirect

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

subgroup	index
C₂×C₄⋊(C₁₉⋊C₈)	2
C₄×C₄⋊Dic₁₉	2
#11926306	2
C₂×C₁₉×#125	2
#1989	19

subgroup

index

C₂×C₄⋊(C₁₉⋊C₈)

C₄×C₄⋊Dic₁₉

#11926306

C₂×C₁₉×#125

#1989

Subgroups — #14564593

Conjugacy classes of subgroups

Complements

Maximal subgroups