Group #14562679 — subgroups

Subgroups — #14562679

Order 2432.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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	#11927175	C₂	1	1	yes	maximal, characteristic
2	#11926880	C₂	1	2	yes	maximal
3	#11926483	C₂	1	1	yes	maximal, characteristic
4	#11926282	C₂	1	2	yes	maximal
5	C₁₉×#324	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
7	#10597372	—	2	1	no	—
8	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
9	#10597370	—	2	1	no	—
10	#10597370	C₂²	1	2	yes	—
11	#10597336	—	2	2	no	—
12	#10597334	—	2	2	no	—
13	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
14	C₁₉⋊#95	—	2	1	no	—
15	C₁₉⋊#95	—	2	1	no	—
16	C₁₉⋊#95	C₂²	1	1	yes	characteristic
17	#10597275	—	2	2	no	—
18	#10597273	—	2	2	no	—
19	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₁₉	—	2	1	no	—
23	C₂²×Dic₁₉	—	2	1	no	—
24	C₂×Dic₃₈	—	2	1	no	—
25	C₂×Dic₃₈	D₄	1	2	yes	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂²⋊Dic₁₉	—	2	2	no	—
29	C₄⋊Dic₁₉	—	2	1	no	—
30	C₄⋊Dic₁₉	—	2	1	no	—
31	C₄⋊Dic₁₉	—	2	1	no	—
32	C₄⋊Dic₁₉	—	2	2	no	—
33	C₄⋊Dic₁₉	D₄	1	2	yes	—
34	Dic₁₉⋊C₄	—	2	2	no	—
35	Dic₁₉⋊C₄	—	2	2	no	—
36	C₄×Dic₁₉	—	2	2	no	—
37	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	4	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×Dic₁₉	—	2	2	no	—
46	C₂×Dic₁₉	—	2	2	no	—
47	C₂×Dic₁₉	—	4	1	no	—
48	C₂×Dic₁₉	—	4	1	no	—
49	C₂×Dic₁₉	—	4	2	no	—
50	C₂×Dic₁₉	—	4	1	no	—
51	C₂×Dic₁₉	—	4	1	no	—
52	Dic₃₈	—	4	2	no	—
53	Dic₃₈	—	8	1	no	—
54	C₈×C₁₉	—	4	2	no	—
55	#1617	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	#120	1	1	yes	characteristic
59	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
60	C₂²×C₁₉	#137	1	1	yes	characteristic
61	C₄×C₁₉	—	2	2	no	—
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	—	4	1	no	—
64	Dic₁₉	—	4	2	no	—
65	Dic₁₉	—	4	2	no	—
66	Dic₁₉	—	8	1	no	—
67	Dic₁₉	—	8	1	no	—
68	#544	—	19	1	no	—
69	#484	—	19	2	no	—
70	#400	—	19	1	no	—
71	#328	—	19	2	no	—
72	#324	D₁₉	1	1	yes	characteristic
73	C₂×C₁₉	—	2	1	no	—
74	C₂×C₁₉	—	2	1	no	—
75	C₂×C₁₉	#451	1	1	yes	characteristic
76	C₂×C₁₉	#454	1	1	yes	characteristic
77	C₂×C₁₉	#458	1	1	yes	characteristic
78	C₄⋊Q₈	—	38	2	no	—
79	#125	—	38	2	no	—
80	C₂²⋊Q₈	—	19	2	no	—
81	C₂²⋊Q₈	—	38	1	no	—
82	#117	—	38	1	no	—
83	C₂×C₄⋊C₄	—	19	1	no	—
84	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
85	#107	—	38	2	no	—
86	#103	—	38	2	no	—
87	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
88	#95	—	19	1	no	—
89	#95	—	38	1	no	—
90	#95	—	38	1	no	—
91	C₁₉	#1617	1	1	yes	characteristic, complemented, Sylow
92	C₂×Q₈	—	19	2	no	—
93	C₂×Q₈	—	38	1	no	—
94	C₂²×C₄	—	38	1	no	—
95	C₂²×C₄	—	38	1	no	—
96	C₂²×C₄	D₇₆	1	1	yes	characteristic
97	C₂²×C₄	D₇₆	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
99	C₂×C₈	—	2	2	no	—
100	C₄⋊C₄	—	2	2	no	—
101	C₄⋊C₄	—	19	2	no	—
102	C₄⋊C₄	—	38	2	no	—
103	C₄⋊C₄	—	38	1	no	—
104	C₄⋊C₄	—	38	1	no	—
105	C₄⋊C₄	—	38	1	no	—
106	C₄⋊C₄	—	38	2	no	—
107	C₄⋊C₄	—	38	2	no	—
108	C₂²⋊C₄	—	38	2	no	—
109	C₄²	—	38	2	no	—
110	C₂³	C₂×D₇₆	1	1	yes	characteristic
111	Q₈	—	76	2	no	—
112	Q₈	—	152	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	38	2	no	—
119	C₂×C₄	—	38	2	no	—
120	C₂×C₄	—	76	1	no	—
121	C₂×C₄	—	76	1	no	—
122	C₂×C₄	—	76	2	no	—
123	C₂×C₄	—	76	1	no	—
124	C₂×C₄	—	76	1	no	—
125	C₂×C₄	Dic₇₆	1	2	yes	—
126	C₂×C₄	D₄×D₁₉	1	2	yes	—
127	C₈	—	4	2	no	—
128	C₂²	—	2	1	no	—
129	C₂²	—	2	1	no	—
130	C₂²	#10597328	1	1	yes	characteristic
131	C₂²	C₂×Dic₇₆	1	1	yes	characteristic
132	C₂²	#10597355	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	2	2	no	—
135	C₄	—	4	1	no	—
136	C₄	—	76	2	no	—
137	C₄	—	76	2	no	—
138	C₄	—	152	1	no	—
139	C₄	—	152	1	no	—
140	C₂	—	2	1	no	—
141	C₂	—	2	1	no	—
142	C₂	#11926702	1	1	yes	characteristic
143	C₂	#11926719	1	1	yes	characteristic
144	C₂	#11926735	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927175

C₂

yes

maximal, characteristic

#11926880

C₂

yes

maximal

#11926483

C₂

yes

maximal, characteristic

#11926282

C₂

yes

maximal

C₁₉×#324

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

#10597370

—

#10597370

C₂²

yes

—

#10597336

—

#10597334

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂²

yes

characteristic

#10597275

—

#10597273

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

#1617

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#120

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

characteristic

C₂²×C₁₉

#137

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

#107

—

#103

—

C₂²⋊C₈

C₂×D₁₉

yes

—

#95

—

#95

—

#95

—

C₁₉

#1617

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₂³

C₂×D₇₆

yes

characteristic

111

Q₈

—

112

Q₈

—

152

—

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

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

Dic₇₆

yes

—

126

C₂×C₄

D₄×D₁₉

yes

—

127

C₈

—

128

C₂²

—

129

C₂²

—

130

C₂²

#10597328

yes

characteristic

131

C₂²

C₂×Dic₇₆

yes

characteristic

132

C₂²

#10597355

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

152

—

139

C₄

—

152

—

140

C₂

—

141

C₂

—

142

C₂

#11926702

yes

characteristic

143

C₂

#11926719

yes

characteristic

144

C₂

#11926735

yes

characteristic

	subgroup	G/H
center	C₂²	#10597328
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#324	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#324	D₁₉
hypocenter	C₁₉	#1617
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #324

subgroup

G/H

center

C₂²

#10597328

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#324

C₂

socle

C₂²×C₁₉

#120

prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #324

N	H ≅ G/N	type
91. C₁₉	#1617	semidirect

H ≅ G/N

type

91. C₁₉

#1617

semidirect

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

subgroup	index
#11927175	2
#11926880	2
#11926483	2
#11926282	2
C₁₉×#324	2
#1617	19

subgroup

index

C₁₉×#324

Subgroups — #14562679

Conjugacy classes of subgroups

Complements

Maximal subgroups