Group #14565197 — subgroups

Subgroups — #14565197

Order 2432.

214 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 87 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	#11926442	C₂	1	1	yes	maximal, characteristic
2	#11926306	C₂	1	2	yes	maximal
3	#11926306	C₂	1	2	yes	maximal
4	#11926299	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#384	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
7	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
8	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₉⋊C₄	—	2	1	no	—
13	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
14	C₁₉⋊#95	—	2	1	no	—
15	C₂²×C₄×C₁₉	—	2	2	no	—
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	—	2	1	no	—
20	C₂²×Dic₁₉	—	2	1	no	—
21	C₄⋊C₄×C₁₉	—	2	4	no	—
22	C₄⋊C₄×C₁₉	—	4	2	no	—
23	C₄⋊C₄×C₁₉	—	4	2	no	—
24	C₄²×C₁₉	—	2	2	no	—
25	C₄⋊Dic₁₉	—	2	1	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	C₄⋊Dic₁₉	Q₈	1	2	yes	—
28	Dic₁₉⋊C₄	—	4	2	no	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂×C₁₉⋊C₈	—	2	2	no	—
32	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	4	2	no	—
38	C₂×C₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
41	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
42	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#41	1	2	yes	—
44	C₂×C₄×C₁₉	#41	1	2	yes	—
45	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
46	C₂×Dic₁₉	—	2	2	no	—
47	C₂×Dic₁₉	—	4	1	no	—
48	C₂×Dic₁₉	—	4	1	no	—
49	C₂×Dic₁₉	—	4	1	no	—
50	C₂×Dic₁₉	—	4	1	no	—
51	C₂×Dic₁₉	—	4	1	no	—
52	C₁₉⋊C₈	—	4	2	no	—
53	#2100	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
55	C₂²×C₁₉	#123	1	1	yes	characteristic
56	C₂²×C₁₉	#124	1	1	yes	characteristic
57	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
58	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
59	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
60	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
61	C₄×C₁₉	—	2	2	no	—
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	—	8	2	no	—
64	C₄×C₁₉	#125	1	2	yes	—
65	C₄×C₁₉	#126	1	2	yes	—
66	Dic₁₉	—	4	2	no	—
67	Dic₁₉	—	8	1	no	—
68	#389	—	19	1	no	—
69	#384	D₁₉	1	1	yes	characteristic
70	#340	—	19	2	no	—
71	#340	—	19	2	no	—
72	#336	—	19	1	no	—
73	C₂×C₁₉	#400	1	1	yes	characteristic
74	C₂×C₁₉	#476	1	1	yes	characteristic
75	C₂×C₁₉	#477	1	1	yes	characteristic
76	C₂×C₁₉	#481	1	1	yes	characteristic
77	C₂×C₁₉	#484	1	1	yes	characteristic
78	C₂×C₁₉	#487	1	1	yes	characteristic
79	C₂×C₁₉	#490	1	1	yes	characteristic
80	C₂²×C₈	—	19	2	no	—
81	C₂×C₄⋊C₄	—	2	1	no	—
82	C₂×C₄⋊C₄	—	2	1	no	—
83	C₂×C₄⋊C₄	—	19	1	no	—
84	C₂×C₄⋊C₄	—	19	1	no	—
85	C₂×C₄⋊C₄	—	38	1	no	—
86	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
87	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
88	#95	—	38	1	no	—
89	C₁₉	#2100	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₄	—	2	2	no	—
91	C₂²×C₄	—	38	1	no	—
92	C₂²×C₄	—	38	1	no	—
93	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
94	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
95	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
96	C₂×C₈	—	38	2	no	—
97	C₂×C₈	—	38	2	no	—
98	C₂×C₈	—	38	2	no	—
99	C₄⋊C₄	—	2	4	no	—
100	C₄⋊C₄	—	4	2	no	—
101	C₄⋊C₄	—	4	2	no	—
102	C₄⋊C₄	—	19	2	no	—
103	C₄⋊C₄	—	38	1	no	—
104	C₄⋊C₄	—	38	2	no	—
105	C₄⋊C₄	—	76	2	no	—
106	C₄²	—	2	2	no	—
107	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	—	4	2	no	—
113	C₂×C₄	—	4	2	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	38	2	no	—
116	C₂×C₄	—	76	1	no	—
117	C₂×C₄	—	76	1	no	—
118	C₂×C₄	—	76	1	no	—
119	C₂×C₄	—	76	1	no	—
120	C₂×C₄	—	76	1	no	—
121	C₂×C₄	#64527	1	2	yes	—
122	C₂×C₄	#64528	1	2	yes	—
123	C₂×C₄	#64541	1	2	yes	—
124	C₂×C₄	#64543	1	2	yes	—
125	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
126	C₂×C₄	#64545	1	1	yes	characteristic
127	C₈	—	76	2	no	—
128	C₂²	#10597375	1	1	yes	characteristic
129	C₂²	#10597378	1	1	yes	characteristic
130	C₂²	#10597378	1	1	yes	characteristic
131	C₂²	#10597382	1	1	yes	characteristic
132	C₂²	C₂×#64527	1	1	yes	characteristic
133	C₂²	C₂×#64528	1	1	yes	characteristic
134	C₂²	#10597392	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	2	2	no	—
137	C₄	—	8	2	no	—
138	C₄	—	76	2	no	—
139	C₄	—	152	1	no	—
140	C₄	#10597335	1	2	yes	—
141	C₄	#10597344	1	2	yes	—
142	C₂	#11926482	1	1	yes	characteristic
143	C₂	#11926831	1	1	yes	characteristic
144	C₂	#11926836	1	1	yes	characteristic
145	C₂	#11926862	1	1	yes	characteristic
146	C₂	#11926879	1	1	yes	characteristic
147	C₂	#11926894	1	1	yes	characteristic
148	C₂	#11926908	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926442

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

#11926306

C₂

yes

maximal

#11926299

C₂

yes

maximal, characteristic

C₁₉×#384

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉⋊#95

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

Q₈

yes

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

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

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#2100

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#125

yes

—

C₄×C₁₉

#126

yes

—

Dic₁₉

—

Dic₁₉

—

#389

—

#384

D₁₉

yes

—

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

—

C₁₉

#2100

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

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

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

#64527

yes

—

122

C₂×C₄

#64528

yes

—

123

C₂×C₄

#64541

yes

—

124

C₂×C₄

#64543

yes

—

125

C₂×C₄

Q₈×D₁₉

yes

characteristic

126

C₂×C₄

#64545

yes

characteristic

127

C₈

—

128

C₂²

#10597375

yes

characteristic

129

C₂²

#10597378

yes

characteristic

130

C₂²

#10597378

yes

characteristic

131

C₂²

#10597382

yes

characteristic

132

C₂²

C₂×#64527

yes

characteristic

133

C₂²

C₂×#64528

yes

characteristic

134

C₂²

#10597392

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

152

—

140

C₄

#10597335

yes

—

141

C₄

#10597344

yes

—

142

C₂

#11926482

yes

characteristic

143

C₂

#11926831

yes

characteristic

144

C₂

#11926836

yes

characteristic

145

C₂

#11926862

yes

characteristic

146

C₂

#11926879

yes

characteristic

147

C₂

#11926894

yes

characteristic

148

C₂

#11926908

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#384	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#384	D₁₉
hypocenter	C₁₉	#2100
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#384

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #384

N	H ≅ G/N	type
89. C₁₉	#2100	semidirect

H ≅ G/N

type

89. C₁₉

#2100

semidirect

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

subgroup	index
#11926442	2
#11926306	2
#11926299	2
C₁₉×#384	2
#2100	19

subgroup

index

C₁₉×#384

Subgroups — #14565197

Conjugacy classes of subgroups

Complements

Maximal subgroups