Group #14564955 — subgroups

Subgroups — #14564955

Order 2432.

288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597292	C₂	1	2	yes	maximal
3	#11926451	C₂	1	2	yes	maximal
4	#11926307	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
7	C₂×Q₁₆×C₁₉	—	2	4	no	—
8	C₂×Q₁₆×C₁₉	—	2	2	no	—
9	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#10597292	—	2	4	no	—
14	C₁₉⋊#95	—	2	2	no	—
15	C₁₉⋊#95	—	2	2	no	—
16	Dic₁₉⋊C₈	—	2	2	no	—
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	2	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	—	2	2	no	—
22	C₂×Q₈×C₁₉	D₄	1	4	yes	—
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₉	—	2	2	no	—
26	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
27	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
28	Q₁₆×C₁₉	—	2	8	no	—
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₂×C₈×C₁₉	D₄	1	2	yes	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	—	2	2	no	—
33	C₄×Dic₁₉	—	2	1	no	—
34	C₄×Dic₁₉	—	2	1	no	—
35	C₂×C₁₉⋊C₈	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
38	Q₈×C₁₉	—	2	4	no	—
39	Q₈×C₁₉	—	2	4	no	—
40	Q₈×C₁₉	—	4	2	no	—
41	Q₈×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	—	2	4	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#41	1	2	yes	—
49	C₂×Dic₁₉	—	2	1	no	—
50	C₂×Dic₁₉	—	2	1	no	—
51	C₂×Dic₁₉	—	2	1	no	—
52	C₂×Dic₁₉	—	2	2	no	—
53	C₂×Dic₁₉	—	4	2	no	—
54	C₂×Dic₁₉	—	4	2	no	—
55	C₂×Dic₁₉	—	4	2	no	—
56	C₂×Dic₁₉	Q₁₆	1	2	yes	complemented
57	C₈×C₁₉	—	2	2	no	—
58	C₁₉⋊C₈	—	4	1	no	—
59	#2056	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	#121	1	1	yes	characteristic
61	C₂²×C₁₉	#121	1	2	yes	—
62	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
63	C₂²×C₁₉	#135	1	1	yes	characteristic
64	C₂²×C₁₉	#137	1	2	yes	—
65	C₄×C₁₉	—	4	4	no	—
66	C₄×C₁₉	#120	1	1	yes	characteristic
67	C₄×C₁₉	#123	1	2	yes	—
68	C₄×C₁₉	#124	1	1	yes	characteristic
69	Dic₁₉	—	2	2	no	—
70	Dic₁₉	—	4	1	no	—
71	Dic₁₉	—	8	2	no	—
72	C₂²×Q₁₆	D₁₉	1	1	yes	characteristic
73	C₂×C₄⋊C₈	—	19	1	no	—
74	C₂×#103	—	19	2	no	—
75	#391	—	19	2	no	—
76	#340	—	19	1	no	—
77	C₂×C₁₉	#394	1	1	yes	characteristic
78	C₂×C₁₉	#462	1	2	yes	—
79	C₂×C₁₉	#464	1	2	yes	—
80	C₂×C₁₉	#467	1	1	yes	characteristic
81	C₂×C₁₉	#470	1	1	yes	characteristic
82	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
83	C₂×Q₁₆	—	2	4	no	—
84	C₂×Q₁₆	—	2	2	no	—
85	C₂²×C₈	—	19	1	no	—
86	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
87	C₂×C₄⋊C₄	—	19	2	no	—
88	C₂×C₄²	—	19	1	no	—
89	C₄⋊C₈	—	38	2	no	—
90	#103	—	38	4	no	—
91	#95	—	38	2	no	—
92	#95	—	38	2	no	—
93	C₁₉	#2056	1	1	yes	characteristic, complemented, Sylow
94	C₂×Q₈	—	2	2	no	—
95	C₂×Q₈	—	2	2	no	—
96	C₂×Q₈	—	2	2	no	—
97	C₂×Q₈	—	2	2	no	—
98	C₂×Q₈	—	2	2	no	—
99	C₂×Q₈	C₂²⋊D₁₉	1	4	yes	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	—	19	1	no	—
102	C₂²×C₄	—	19	1	no	—
103	C₂²×C₄	—	38	2	no	—
104	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
105	Q₁₆	—	2	8	no	—
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	—	38	2	no	—
108	C₂×C₈	—	38	1	no	—
109	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
110	C₄⋊C₄	—	38	2	no	—
111	C₄⋊C₄	—	38	2	no	—
112	C₄²	—	38	1	no	—
113	C₄²	—	38	1	no	—
114	C₂³	D₄×D₁₉	1	1	yes	characteristic
115	Q₈	—	2	4	no	—
116	Q₈	—	2	4	no	—
117	Q₈	—	4	2	no	—
118	Q₈	—	4	2	no	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	4	2	no	—
121	C₂×C₄	—	4	2	no	—
122	C₂×C₄	—	19	2	no	—
123	C₂×C₄	—	38	1	no	—
124	C₂×C₄	—	38	1	no	—
125	C₂×C₄	—	38	1	no	—
126	C₂×C₄	—	38	2	no	—
127	C₂×C₄	—	76	2	no	—
128	C₂×C₄	—	76	2	no	—
129	C₂×C₄	—	76	2	no	—
130	C₂×C₄	#64543	1	1	yes	characteristic
131	C₂×C₄	#64543	1	2	yes	—
132	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
133	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
134	C₈	—	2	2	no	—
135	C₈	—	76	1	no	—
136	C₂²	Q₁₆×D₁₉	1	1	yes	characteristic
137	C₂²	#10597364	1	2	yes	—
138	C₂²	#10597365	1	1	yes	characteristic
139	C₂²	#10597384	1	1	yes	characteristic
140	C₂²	#10597385	1	2	yes	—
141	C₄	—	4	4	no	—
142	C₄	—	38	2	no	—
143	C₄	—	76	1	no	—
144	C₄	—	152	2	no	—
145	C₄	#10597381	1	2	yes	—
146	C₄	#10597382	1	1	yes	characteristic
147	C₄	#10597399	1	1	yes	characteristic
148	C₂	#11926458	1	1	yes	characteristic
149	C₂	#11926752	1	2	yes	—
150	C₂	#11926768	1	2	yes	—
151	C₂	#11926782	1	1	yes	characteristic
152	C₂	#11926799	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₁₉⋊C₈

C₂

yes

maximal, characteristic

C₂×#10597292

C₂

yes

maximal

#11926451

C₂

yes

maximal

#11926307

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

#10597292

—

C₁₉⋊#95

—

C₁₉⋊#95

—

Dic₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

D₄

yes

characteristic

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

Q₁₆

yes

complemented

C₈×C₁₉

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#123

yes

—

C₄×C₁₉

#124

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂²×Q₁₆

D₁₉

yes

characteristic

C₂×C₄⋊C₈

—

C₂×#103

—

#391

—

#340

—

C₂×C₁₉

#394

yes

characteristic

C₂×C₁₉

#462

yes

—

C₂×C₁₉

#464

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂×D₁₉

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

#103

—

#95

—

#95

—

C₁₉

#2056

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₁₉

yes

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂²×D₁₉

yes

characteristic

105

Q₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

C₂²⋊D₁₉

yes

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄²

—

113

C₄²

—

114

C₂³

D₄×D₁₉

yes

characteristic

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

#64543

yes

characteristic

131

C₂×C₄

#64543

yes

—

132

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

133

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

134

C₈

—

135

C₈

—

136

C₂²

Q₁₆×D₁₉

yes

characteristic

137

C₂²

#10597364

yes

—

138

C₂²

#10597365

yes

characteristic

139

C₂²

#10597384

yes

characteristic

140

C₂²

#10597385

yes

—

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

152

—

145

C₄

#10597381

yes

—

146

C₄

#10597382

yes

characteristic

147

C₄

#10597399

yes

characteristic

148

C₂

#11926458

yes

characteristic

149

C₂

#11926752

yes

—

150

C₂

#11926768

yes

—

151

C₂

#11926782

yes

characteristic

152

C₂

#11926799

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂²×Q₁₆×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂²×Q₁₆	D₁₉
hypocenter	C₁₉	#2056
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂²×Q₁₆×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

hypercenter

C₂²×Q₁₆

D₁₉

hypocenter

C₁₉

#2056

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
56. C₂×Dic₁₉	Q₁₆	semidirect
93. C₁₉	#2056	semidirect

H ≅ G/N

type

56. C₂×Dic₁₉

Q₁₆

semidirect

93. C₁₉

#2056

semidirect

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

subgroup	index
C₂×Dic₁₉⋊C₈	2
C₂×#10597292	2
#11926451	2
#11926307	2
C₂²×Q₁₆×C₁₉	2
#2056	19

subgroup

index

C₂×Dic₁₉⋊C₈

C₂²×Q₁₆×C₁₉

Subgroups — #14564955

Conjugacy classes of subgroups

Complements

Maximal subgroups