Group #14564382 — subgroups

Subgroups — #14564382

Order 2432.

208 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 83 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×#10597279	C₂	1	1	yes	maximal, characteristic
2	#11926580	C₂	1	1	yes	maximal, characteristic
3	#11926572	C₂	1	1	yes	maximal, characteristic
4	#11926571	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#11926304	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	#10597372	C₂²	1	1	yes	characteristic
12	C₂×#64520	C₂²	1	1	yes	characteristic
13	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	#10597279	—	2	2	no	—
16	Dic₁₉⋊C₈	—	2	2	no	—
17	#10597265	C₄	1	2	yes	complemented
18	#10597264	C₄	1	2	yes	complemented
19	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
20	C₄×C₁₉⋊C₈	—	2	2	no	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	M₁₆×C₁₉	—	2	1	no	—
24	M₁₆×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂²⋊C₄×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	Q₈	1	2	yes	—
31	C₂²⋊Dic₁₉	—	2	1	no	—
32	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
33	C₄×Dic₁₉	—	2	1	no	—
34	#64520	—	2	1	no	—
35	#64520	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	1	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
42	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
43	C₂×C₁₉⋊C₈	Q₈	1	2	yes	—
44	C₂³×C₁₉	#41	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	2	2	no	—
47	C₂×C₄×C₁₉	—	2	2	no	—
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×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂×Dic₁₉	—	2	2	no	—
55	C₈×C₁₉	—	4	1	no	—
56	C₁₉⋊C₈	—	2	2	no	—
57	C₁₉⋊C₈	—	4	1	no	—
58	C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
59	C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
60	#1945	—	19	1	no	maximal, Sylow
61	C₂²×C₁₉	—	2	2	no	—
62	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
63	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
64	C₂²×C₁₉	#125	1	1	yes	characteristic
65	C₄×C₁₉	—	2	4	no	—
66	C₄×C₁₉	—	4	2	no	—
67	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
69	C₄×C₁₉	#121	1	1	yes	characteristic
70	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
71	Dic₁₉	—	4	2	no	—
72	C₂×#108	—	19	1	no	—
73	#427	—	19	1	no	—
74	#424	—	19	1	no	—
75	#424	—	19	1	no	—
76	C₂×C₄×C₈	—	19	1	no	—
77	#339	—	19	1	no	—
78	#339	D₁₉	1	1	yes	characteristic
79	C₂×C₁₉	—	2	1	no	—
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	#389	1	1	yes	characteristic
82	C₂×C₁₉	#443	1	2	yes	—
83	C₂×M₁₆	—	19	1	no	—
84	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
85	C₂²×C₈	—	19	1	no	—
86	C₂²×C₈	—	19	1	no	—
87	#117	—	19	1	no	—
88	#117	C₂×D₁₉	1	1	yes	characteristic
89	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
90	#108	—	38	2	no	—
91	#107	—	19	2	no	—
92	#106	—	19	2	no	—
93	C₄⋊C₈	—	38	2	no	—
94	C₄⋊C₈	—	38	2	no	—
95	C₄×C₈	—	38	2	no	—
96	C₁₉	#1945	1	1	yes	characteristic, complemented, Sylow
97	C₂²×C₄	—	2	1	no	—
98	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
99	M₁₆	—	2	1	no	—
100	M₁₆	—	2	1	no	—
101	M₁₆	—	38	1	no	—
102	M₁₆	—	38	1	no	—
103	C₂×C₈	—	2	1	no	—
104	C₂×C₈	—	19	1	no	—
105	C₂×C₈	—	19	1	no	—
106	C₂×C₈	—	19	2	no	—
107	C₂×C₈	—	19	2	no	—
108	C₂×C₈	—	19	2	no	—
109	C₂×C₈	—	38	1	no	—
110	C₂×C₈	—	38	1	no	—
111	C₂×C₈	—	38	1	no	—
112	C₄⋊C₄	—	19	2	no	—
113	C₄⋊C₄	C₄×D₁₉	1	2	yes	—
114	C₂²⋊C₄	—	2	1	no	—
115	C₂²⋊C₄	—	38	1	no	—
116	C₄²	—	2	1	no	—
117	C₄²	—	2	1	no	—
118	C₄²	—	38	1	no	—
119	C₄²	Dic₃₈	1	2	yes	—
120	C₂³	#64543	1	1	yes	characteristic
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	38	2	no	—
125	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
126	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
127	C₂×C₄	#64541	1	1	yes	characteristic
128	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
129	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
130	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
131	C₈	—	4	1	no	—
132	C₈	—	19	2	no	—
133	C₈	—	19	2	no	—
134	C₈	—	38	2	no	—
135	C₈	—	76	1	no	—
136	C₂²	—	2	2	no	—
137	C₂²	#10597324	1	1	yes	characteristic
138	C₂²	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
139	C₂²	#10597335	1	1	yes	characteristic
140	C₄	—	2	4	no	—
141	C₄	—	4	2	no	—
142	C₄	—	76	2	no	—
143	C₄	C₄×Dic₃₈	1	1	yes	characteristic
144	C₄	#10597330	1	1	yes	characteristic
145	C₄	#10597334	1	1	yes	characteristic
146	C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
147	C₂	—	2	1	no	—
148	C₂	—	2	1	no	—
149	C₂	#11926441	1	1	yes	characteristic
150	C₂	#11926658	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597279

C₂

yes

maximal, characteristic

#11926580

C₂

yes

maximal, characteristic

#11926572

C₂

yes

maximal, characteristic

#11926571

C₂

yes

maximal, characteristic

C₂×C₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#11926304

C₂

yes

maximal, characteristic

C₁₉×#339

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597279

—

Dic₁₉⋊C₈

—

#10597265

C₄

yes

complemented

#10597264

C₄

yes

complemented

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

Q₈

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₄⋊C₄

yes

—

C₁₉⋊C₈

C₄⋊C₄

yes

—

#1945

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₉

#125

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₄×Q₈

yes

characteristic

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

Dic₁₉

—

—

—

—

—

C₂×C₄×C₈

—

#339

—

#339

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#389

yes

characteristic

C₂×C₁₉

#443

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

#117

—

#117

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₁₉

#1945

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

100

M₁₆

—

101

M₁₆

—

102

M₁₆

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₄⋊C₄

—

113

C₄⋊C₄

C₄×D₁₉

yes

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

116

C₄²

—

117

C₄²

—

118

C₄²

—

119

C₄²

Dic₃₈

yes

—

120

C₂³

#64543

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₂×Dic₃₈

yes

characteristic

126

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

127

C₂×C₄

#64541

yes

characteristic

128

C₂×C₄

D₄×D₁₉

yes

characteristic

129

C₂×C₄

D₄×D₁₉

yes

characteristic

130

C₂×C₄

Q₈×D₁₉

yes

characteristic

131

C₈

—

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

136

C₂²

—

137

C₂²

#10597324

yes

characteristic

138

C₂²

(C₂²⋊D₁₉)⋊C₄

yes

characteristic

139

C₂²

#10597335

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

C₄×Dic₃₈

yes

characteristic

144

C₄

#10597330

yes

characteristic

145

C₄

#10597334

yes

characteristic

146

C₄

C₄⋊C₄×D₁₉

yes

characteristic

147

C₂

—

148

C₂

—

149

C₂

#11926441

yes

characteristic

150

C₂

#11926658

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#339	C₂
socle	C₂²×C₁₉	C₄×D₄
prime radical	C₂³×C₁₉	#41
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#339	D₁₉
hypocenter	C₁₉	#1945
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #339

subgroup

G/H

center

C₂×C₄

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#339

C₂

socle

C₂²×C₁₉

C₄×D₄

prime radical

C₂³×C₁₉

#41

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #339

N	H ≅ G/N	type
17. #10597265	C₄	semidirect
18. #10597264	C₄	semidirect
96. C₁₉	#1945	semidirect

H ≅ G/N

type

17. #10597265

C₄

semidirect

18. #10597264

C₄

semidirect

96. C₁₉

#1945

semidirect

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

subgroup	index
C₂×#10597279	2
#11926580	2
#11926572	2
#11926571	2
C₂×C₄×C₁₉⋊C₈	2
#11926304	2
C₁₉×#339	2
#1945	19

subgroup

index

C₂×C₄×C₁₉⋊C₈

C₁₉×#339

Subgroups — #14564382

Conjugacy classes of subgroups

Complements

Maximal subgroups