Group #14564506 — subgroups

Subgroups — #14564506

Order 2432.

304 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 109 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	C₂²×Dic₇₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597274	C₂	1	1	yes	maximal, characteristic
3	C₂×#10597273	C₂	1	2	yes	maximal
4	#11926450	C₂	1	2	yes	maximal
5	C₂×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×Dic₇₆	—	2	2	no	—
12	C₂×Dic₇₆	—	2	2	no	—
13	C₂×Dic₇₆	C₄	1	4	yes	complemented
14	C₁₉×#97	—	2	2	no	—
15	C₁₉⋊#95	—	2	4	no	—
16	#10597274	—	2	2	no	—
17	#10597273	—	2	4	no	—
18	C₂²×C₄×C₁₉	D₄	1	2	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₉	—	2	2	no	—
21	C₂²×Dic₁₉	—	2	2	no	—
22	C₂×Dic₃₈	—	2	2	no	—
23	C₂×Dic₃₈	—	2	2	no	—
24	C₂×Dic₃₈	—	2	2	no	—
25	C₂×Dic₃₈	—	2	2	no	—
26	C₂×Dic₃₈	—	2	2	no	—
27	C₂×Dic₃₈	C₂×C₄	1	4	yes	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
31	C₂×C₈×C₁₉	D₄	1	2	yes	—
32	C₂×C₈×C₁₉	D₄	1	2	yes	—
33	C₂×C₈×C₁₉	D₄	1	2	yes	—
34	C₄²×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	C₄⋊Dic₁₉	—	2	2	no	—
37	C₄⋊Dic₁₉	—	2	2	no	—
38	Dic₇₆	—	2	8	no	—
39	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	4	no	—
42	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
48	C₂×Dic₁₉	—	2	4	no	—
49	C₂×Dic₁₉	—	4	2	no	—
50	C₂×Dic₁₉	—	4	2	no	—
51	C₂×Dic₁₉	—	4	2	no	—
52	C₂×Dic₁₉	—	4	4	no	—
53	Dic₃₈	—	2	4	no	—
54	Dic₃₈	—	2	4	no	—
55	Dic₃₈	—	4	2	no	—
56	Dic₃₈	—	4	2	no	—
57	C₈×C₁₉	—	2	2	no	—
58	C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
59	#1971	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
61	C₂²×C₁₉	#121	1	1	yes	characteristic
62	C₂²×C₁₉	#127	1	1	yes	characteristic
63	C₂²×C₁₉	#137	1	4	yes	—
64	C₄×C₁₉	—	4	2	no	—
65	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
67	C₄×C₁₉	#121	1	1	yes	characteristic
68	C₄×C₁₉	#124	1	1	yes	characteristic
69	Dic₁₉	—	4	4	no	—
70	Dic₁₉	—	8	2	no	—
71	C₂²×Q₁₆	—	19	1	no	—
72	C₂×#106	—	19	1	no	—
73	C₂×#103	—	19	2	no	—
74	C₂×#97	D₁₉	1	1	yes	characteristic
75	#391	—	19	2	no	—
76	C₂×C₁₉	#390	1	1	yes	characteristic
77	C₂×C₁₉	#441	1	2	yes	—
78	C₂×C₁₉	#470	1	2	yes	—
79	C₂×C₁₉	#497	1	2	yes	—
80	C₂²×Q₈	—	19	2	no	—
81	C₂×Q₁₆	—	19	4	no	—
82	C₂×Q₁₆	—	38	2	no	—
83	C₂×Q₁₆	—	38	2	no	—
84	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
85	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
86	C₂×C₄⋊C₄	—	19	2	no	—
87	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
88	#106	—	38	2	no	—
89	#103	—	38	4	no	—
90	#97	—	2	2	no	—
91	#95	—	38	4	no	—
92	C₁₉	#1971	1	1	yes	characteristic, complemented, Sylow
93	C₂×Q₈	—	19	4	no	—
94	C₂×Q₈	—	38	2	no	—
95	C₂×Q₈	—	38	2	no	—
96	C₂×Q₈	—	38	2	no	—
97	C₂×Q₈	—	38	2	no	—
98	C₂×Q₈	—	38	2	no	—
99	C₂²×C₄	—	38	2	no	—
100	C₂²×C₄	—	38	2	no	—
101	C₂²×C₄	D₇₆	1	2	yes	—
102	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
103	Q₁₆	—	38	8	no	—
104	C₂×C₈	—	2	1	no	—
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	C₄×D₁₉	1	2	yes	—
107	C₂×C₈	D₇₆	1	2	yes	—
108	C₂×C₈	D₇₆	1	2	yes	—
109	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
110	C₄⋊C₄	—	38	2	no	—
111	C₄⋊C₄	—	38	2	no	—
112	C₄²	—	2	1	no	—
113	C₄²	—	2	1	no	—
114	C₂³	C₂×D₇₆	1	1	yes	characteristic
115	Q₈	—	38	4	no	—
116	Q₈	—	38	4	no	—
117	Q₈	—	76	2	no	—
118	Q₈	—	76	2	no	—
119	C₂×C₄	—	2	2	no	—
120	C₂×C₄	—	2	4	no	—
121	C₂×C₄	—	38	4	no	—
122	C₂×C₄	—	76	2	no	—
123	C₂×C₄	—	76	2	no	—
124	C₂×C₄	—	76	2	no	—
125	C₂×C₄	—	76	4	no	—
126	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
127	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
128	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
129	C₂×C₄	#64541	1	1	yes	characteristic
130	C₂×C₄	#64541	1	1	yes	characteristic
131	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
132	C₈	—	2	2	no	—
133	C₈	(C₂×D₁₉)⋊C₄	1	4	yes	—
134	C₂²	C₄×D₇₆	1	1	yes	characteristic
135	C₂²	#10597320	1	1	yes	characteristic
136	C₂²	#10597355	1	4	yes	—
137	C₂²	#10597376	1	1	yes	characteristic
138	C₄	—	4	2	no	—
139	C₄	—	76	4	no	—
140	C₄	—	152	2	no	—
141	C₄	C₄×D₇₆	1	1	yes	characteristic
142	C₄	#10597321	1	1	yes	characteristic
143	C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
144	C₄	#10597376	1	1	yes	characteristic
145	C₂	#11926446	1	1	yes	characteristic
146	C₂	#11926652	1	2	yes	—
147	C₂	#11926802	1	2	yes	—
148	C₂	#11926938	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₆

C₂

yes

maximal, characteristic

C₂×#10597274

C₂

yes

maximal, characteristic

C₂×#10597273

C₂

yes

maximal

#11926450

C₂

yes

maximal

C₂×C₁₉×#97

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₇₆

—

C₂×Dic₇₆

—

C₂×Dic₇₆

C₄

yes

complemented

C₁₉×#97

—

C₁₉⋊#95

—

#10597274

—

#10597273

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₇₆

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

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

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

—

#1971

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

C₂²×C₁₉

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

—

Dic₁₉

—

C₂²×Q₁₆

—

C₂×#106

—

C₂×#103

—

C₂×#97

D₁₉

yes

characteristic

#391

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

#441

yes

—

C₂×C₁₉

#470

yes

—

C₂×C₁₉

#497

yes

—

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

—

C₁₉

#1971

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

D₇₆

yes

—

102

C₂²×C₄

C₂²×D₁₉

yes

characteristic

103

Q₁₆

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₄×D₁₉

yes

—

107

C₂×C₈

D₇₆

yes

—

108

C₂×C₈

D₇₆

yes

—

109

C₂×C₈

C₂²⋊D₁₉

yes

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄²

—

113

C₄²

—

114

C₂³

C₂×D₇₆

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

C₂×C₄×D₁₉

yes

characteristic

127

C₂×C₄

C₂×D₇₆

yes

characteristic

128

C₂×C₄

C₂×D₇₆

yes

characteristic

129

C₂×C₄

#64541

yes

characteristic

130

C₂×C₄

#64541

yes

characteristic

131

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

132

C₈

—

133

C₈

(C₂×D₁₉)⋊C₄

yes

—

134

C₂²

C₄×D₇₆

yes

characteristic

135

C₂²

#10597320

yes

characteristic

136

C₂²

#10597355

yes

—

137

C₂²

#10597376

yes

characteristic

138

C₄

—

139

C₄

—

140

C₄

—

152

—

141

C₄

C₄×D₇₆

yes

characteristic

142

C₄

#10597321

yes

characteristic

143

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

144

C₄

#10597376

yes

characteristic

145

C₂

#11926446

yes

characteristic

146

C₂

#11926652

yes

—

147

C₂

#11926802

yes

—

148

C₂

#11926938

yes

—

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#97	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#97	D₁₉
hypocenter	C₁₉	#1971
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#97

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×#97

D₁₉

hypocenter

C₁₉

#1971

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
13. C₂×Dic₇₆	C₄	semidirect
92. C₁₉	#1971	semidirect

H ≅ G/N

type

13. C₂×Dic₇₆

C₄

semidirect

92. C₁₉

#1971

semidirect

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

subgroup	index
C₂²×Dic₇₆	2
C₂×#10597274	2
C₂×#10597273	2
#11926450	2
C₂×C₁₉×#97	2
#1971	19

subgroup

index

C₂²×Dic₇₆

C₂×C₁₉×#97

Subgroups — #14564506

Conjugacy classes of subgroups

Complements

Maximal subgroups