Group #14564551 — subgroups

Subgroups — #14564551

Order 2432.

276 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 97 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×#10597276	C₂	1	1	yes	maximal, characteristic
2	#11926553	C₂	1	2	yes	maximal
3	C₂×#10597293	C₂	1	2	yes	maximal
4	#11926499	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	1	no	—
8	C₂×Q₁₆×C₁₉	—	2	1	no	—
9	C₂×Q₁₆×C₁₉	—	2	2	no	—
10	C₂×Q₁₆×C₁₉	C₄	1	4	yes	complemented
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597372	C₂²	1	1	yes	characteristic
13	C₂×#64520	C₂²	1	2	yes	—
14	C₂×#64520	C₂²	1	1	yes	characteristic
15	#10597293	—	2	4	no	—
16	#10597292	—	2	4	no	—
17	#10597276	—	2	2	no	—
18	#10597272	—	2	1	no	—
19	C₈×Dic₁₉	—	2	1	no	—
20	C₂×Q₈×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	—	2	2	no	—
22	C₂×Q₈×C₁₉	—	2	2	no	—
23	C₂×Q₈×C₁₉	—	2	2	no	—
24	C₂×Q₈×C₁₉	—	2	2	no	—
25	C₂×Q₈×C₁₉	C₂×C₄	1	4	yes	—
26	C₂²×C₄×C₁₉	—	2	2	no	—
27	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	Q₁₆×C₁₉	—	2	4	no	—
29	Q₁₆×C₁₉	—	2	4	no	—
30	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₈×C₁₉	D₄	1	2	yes	—
34	C₂²⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	D₄	1	2	yes	—
36	C₄×Dic₁₉	—	2	1	no	—
37	#64520	—	2	1	no	—
38	#64520	—	2	2	no	—
39	#64520	—	2	2	no	—
40	#64520	D₄	1	2	yes	—
41	C₂×C₁₉⋊C₈	—	2	1	no	—
42	C₂×C₁₉⋊C₈	—	2	2	no	—
43	C₂³×C₁₉	#41	1	1	yes	characteristic
44	Q₈×C₁₉	—	2	4	no	—
45	Q₈×C₁₉	—	2	4	no	—
46	Q₈×C₁₉	—	4	2	no	—
47	Q₈×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	—	2	4	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	—	4	2	no	—
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	1	yes	characteristic
54	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
57	C₂×Dic₁₉	—	2	2	no	—
58	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
59	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
60	C₁₉⋊C₈	—	2	2	no	—
61	C₁₉⋊C₈	—	4	2	no	—
62	#1979	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	—	2	2	no	—
64	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
65	C₂²×C₁₉	#121	1	1	yes	characteristic
66	C₂²×C₁₉	#124	1	1	yes	characteristic
67	C₄×C₁₉	—	4	4	no	—
68	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
70	C₄×C₁₉	#121	1	1	yes	characteristic
71	C₄×C₁₉	#127	1	1	yes	characteristic
72	Dic₁₉	—	4	2	no	—
73	C₂²×Q₁₆	D₁₉	1	1	yes	characteristic
74	C₂×#108	—	19	1	no	—
75	#419	—	19	2	no	—
76	C₂×#101	—	19	2	no	—
77	#405	—	19	1	no	—
78	C₂×C₁₉	—	2	1	no	—
79	C₂×C₁₉	—	2	1	no	—
80	C₂×C₁₉	#390	1	1	yes	characteristic
81	C₂×C₁₉	#473	1	2	yes	—
82	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
83	C₂×Q₁₆	—	2	1	no	—
84	C₂×Q₁₆	—	2	1	no	—
85	C₂×Q₁₆	—	2	2	no	—
86	C₂×Q₁₆	Dic₁₉	1	4	yes	complemented
87	C₂×M₁₆	—	19	1	no	—
88	C₂×M₁₆	—	19	2	no	—
89	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
90	#117	—	19	1	no	—
91	#108	—	38	2	no	—
92	#103	—	38	4	no	—
93	#101	—	38	4	no	—
94	#97	—	38	1	no	—
95	C₄×C₈	—	38	1	no	—
96	C₁₉	#1979	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	2	2	no	—
98	C₂×Q₈	—	2	2	no	—
99	C₂×Q₈	—	2	2	no	—
100	C₂×Q₈	—	2	2	no	—
101	C₂×Q₈	—	2	2	no	—
102	C₂×Q₈	C₂×Dic₁₉	1	4	yes	—
103	C₂²×C₄	—	2	2	no	—
104	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
105	Q₁₆	—	2	4	no	—
106	Q₁₆	—	2	4	no	—
107	M₁₆	—	19	2	no	—
108	M₁₆	—	38	1	no	—
109	M₁₆	—	38	2	no	—
110	M₁₆	—	38	2	no	—
111	C₂×C₈	—	38	1	no	—
112	C₂×C₈	—	38	2	no	—
113	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
114	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
115	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
116	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
117	C₄⋊C₄	—	19	2	no	—
118	C₂²⋊C₄	—	38	1	no	—
119	C₄²	—	38	1	no	—
120	C₂³	#64543	1	1	yes	characteristic
121	Q₈	—	2	4	no	—
122	Q₈	—	2	4	no	—
123	Q₈	—	4	2	no	—
124	Q₈	—	4	2	no	—
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	4	2	no	—
127	C₂×C₄	—	4	2	no	—
128	C₂×C₄	—	38	2	no	—
129	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
130	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
131	C₂×C₄	#64543	1	1	yes	characteristic
132	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
133	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
134	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
135	C₈	—	38	2	no	—
136	C₈	—	76	2	no	—
137	C₈	C₂²⋊Dic₁₉	1	2	yes	—
138	C₈	C₂²⋊Dic₁₉	1	2	yes	—
139	C₂²	—	2	2	no	—
140	C₂²	D₄×Dic₁₉	1	1	yes	characteristic
141	C₂²	#10597382	1	1	yes	characteristic
142	C₂²	#10597384	1	1	yes	characteristic
143	C₄	—	4	4	no	—
144	C₄	—	76	2	no	—
145	C₄	D₄×Dic₁₉	1	1	yes	characteristic
146	C₄	#10597384	1	1	yes	characteristic
147	C₄	#10597386	1	1	yes	characteristic
148	C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
149	C₂	—	2	1	no	—
150	C₂	—	2	1	no	—
151	C₂	#11926447	1	1	yes	characteristic
152	C₂	#11926816	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597276

C₂

yes

maximal, characteristic

#11926553

C₂

yes

maximal

C₂×#10597293

C₂

yes

maximal

#11926499

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

C₄

yes

complemented

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

—

—

—

—

C₈×Dic₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

C₄×Dic₁₉

—

—

—

—

D₄

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

#41

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

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×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1979

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂²×Q₁₆

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

#473

yes

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

Dic₁₉

yes

complemented

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₁₉

#1979

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂×Q₈

C₂×Dic₁₉

yes

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂²×D₁₉

yes

characteristic

105

Q₁₆

—

106

Q₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

—

110

M₁₆

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

C₂×Dic₁₉

yes

—

114

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

115

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

116

C₂×C₈

C₂²⋊D₁₉

yes

—

117

C₄⋊C₄

—

118

C₂²⋊C₄

—

119

C₄²

—

120

C₂³

#64543

yes

characteristic

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

D₄×D₁₉

yes

characteristic

130

C₂×C₄

D₄×D₁₉

yes

characteristic

131

C₂×C₄

#64543

yes

characteristic

132

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

133

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

134

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

C₂²⋊Dic₁₉

yes

—

138

C₈

C₂²⋊Dic₁₉

yes

—

139

C₂²

—

140

C₂²

D₄×Dic₁₉

yes

characteristic

141

C₂²

#10597382

yes

characteristic

142

C₂²

#10597384

yes

characteristic

143

C₄

—

144

C₄

—

145

C₄

D₄×Dic₁₉

yes

characteristic

146

C₄

#10597384

yes

characteristic

147

C₄

#10597386

yes

characteristic

148

C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

149

C₂

—

150

C₂

—

151

C₂

#11926447

yes

characteristic

152

C₂

#11926816

yes

—

	subgroup	G/H
center	C₂²	#10597384
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂²×Q₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#121
prime radical	C₂³×C₁₉	#41
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂²×Q₁₆	D₁₉
hypocenter	C₁₉	#1979
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

#10597384

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂²×Q₁₆×C₁₉

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂²×Q₁₆

D₁₉

hypocenter

C₁₉

#1979

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
10. C₂×Q₁₆×C₁₉	C₄	semidirect
86. C₂×Q₁₆	Dic₁₉	semidirect
96. C₁₉	#1979	semidirect

H ≅ G/N

type

10. C₂×Q₁₆×C₁₉

C₄

semidirect

86. C₂×Q₁₆

Dic₁₉

semidirect

96. C₁₉

#1979

semidirect

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

subgroup	index
C₂×#10597276	2
#11926553	2
C₂×#10597293	2
#11926499	2
C₂²×Q₁₆×C₁₉	2
#1979	19

subgroup

index

C₂²×Q₁₆×C₁₉

Subgroups — #14564551

Conjugacy classes of subgroups

Complements

Maximal subgroups