Group #14562677 — subgroups

Subgroups — #14562677

Order 2432.

202 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11926877	C₂	1	2	yes	maximal
2	#11926483	C₂	1	1	yes	maximal, characteristic
3	#11926281	C₂	1	2	yes	maximal
4	#11926270	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#544	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊Q₈	—	2	2	no	—
7	C₁₉×#125	—	2	2	no	—
8	C₁₉×C₂²⋊Q₈	—	2	1	no	—
9	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
10	C₁₉×#117	—	2	1	no	—
11	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
13	#10597292	—	2	2	no	—
14	C₁₉⋊#95	—	2	1	no	—
15	C₁₉⋊#95	—	2	1	no	—
16	C₁₉⋊#95	C₂²	1	1	yes	characteristic
17	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
18	#10597264	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	1	no	—
20	C₂×Q₈×C₁₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₉	—	2	1	no	—
25	C₂²×Dic₁₉	—	2	1	no	—
26	C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₄⋊C₄×C₁₉	D₄	1	2	yes	—
33	C₂²⋊C₄×C₁₉	—	2	2	no	—
34	C₄²×C₁₉	—	2	2	no	—
35	C₄⋊Dic₁₉	—	2	2	no	—
36	C₂×C₁₉⋊C₈	—	2	2	no	—
37	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
38	Q₈×C₁₉	—	4	2	no	—
39	Q₈×C₁₉	—	8	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
48	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂×Dic₁₉	—	4	1	no	—
50	C₂×Dic₁₉	—	4	1	no	—
51	C₂×Dic₁₉	—	4	2	no	—
52	C₂×Dic₁₉	—	4	1	no	—
53	C₂×Dic₁₉	—	4	1	no	—
54	C₁₉⋊C₈	—	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	2	no	—
64	C₄×C₁₉	—	4	1	no	—
65	C₄×C₁₉	—	4	2	no	—
66	Dic₁₉	—	8	1	no	—
67	Dic₁₉	—	8	1	no	—
68	#544	D₁₉	1	1	yes	characteristic
69	#484	—	19	2	no	—
70	#400	—	19	1	no	—
71	#328	—	19	2	no	—
72	#324	—	19	1	no	—
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	—	2	2	no	—
79	#125	—	2	2	no	—
80	C₂²⋊Q₈	—	2	1	no	—
81	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
82	#117	—	2	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	—	19	2	no	—
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	—	2	1	no	—
93	C₂×Q₈	C₂²⋊D₁₉	1	2	yes	—
94	C₂²×C₄	—	38	1	no	—
95	C₂²×C₄	—	38	1	no	—
96	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
97	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
99	C₂×C₈	—	38	2	no	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	2	2	no	—
105	C₄⋊C₄	—	2	2	no	—
106	C₄⋊C₄	—	38	2	no	—
107	C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
108	C₂²⋊C₄	—	2	2	no	—
109	C₄²	—	2	2	no	—
110	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
111	Q₈	—	4	2	no	—
112	Q₈	—	8	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	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	#64528	1	2	yes	—
126	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
127	C₈	—	76	2	no	—
128	C₂²	—	2	1	no	—
129	C₂²	—	2	1	no	—
130	C₂²	#10597388	1	1	yes	characteristic
131	C₂²	C₂×#64528	1	1	yes	characteristic
132	C₂²	#10597399	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	2	2	no	—
135	C₄	—	4	2	no	—
136	C₄	—	4	1	no	—
137	C₄	—	4	2	no	—
138	C₄	—	152	1	no	—
139	C₄	—	152	1	no	—
140	C₂	—	2	1	no	—
141	C₂	—	2	1	no	—
142	C₂	#11926700	1	1	yes	characteristic
143	C₂	#11926717	1	1	yes	characteristic
144	C₂	#11926734	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926877

C₂

yes

maximal

#11926483

C₂

yes

maximal, characteristic

#11926281

C₂

yes

maximal

#11926270

C₂

yes

maximal, characteristic

C₁₉×#544

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

C₂²

yes

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

#10597292

—

C₁₉⋊#95

—

C₁₉⋊#95

—

C₁₉⋊#95

C₂²

yes

characteristic

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

#10597264

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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

—

C₁₉⋊C₈

—

#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

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#544

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

C₂×D₁₉

yes

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

#107

—

#103

—

C₂²⋊C₈

—

#95

—

#95

—

#95

—

C₁₉

#1617

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

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

C₂²⋊D₁₉

yes

—

108

C₂²⋊C₄

—

109

C₄²

—

110

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

111

Q₈

—

112

Q₈

—

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

#64528

yes

—

126

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

127

C₈

—

128

C₂²

—

129

C₂²

—

130

C₂²

#10597388

yes

characteristic

131

C₂²

C₂×#64528

yes

characteristic

132

C₂²

#10597399

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

152

—

139

C₄

—

152

—

140

C₂

—

141

C₂

—

142

C₂

#11926700

yes

characteristic

143

C₂

#11926717

yes

characteristic

144

C₂

#11926734

yes

characteristic

	subgroup	G/H
center	C₂²	#10597399
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#544	C₂
socle	C₂²×C₁₉	#120
prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#544	D₁₉
hypocenter	C₁₉	#1617
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #544

subgroup

G/H

center

C₂²

#10597399

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#544

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 ◁ #544

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
#11926877	2
#11926483	2
#11926281	2
#11926270	2
C₁₉×#544	2
#1617	19

subgroup

index

C₁₉×#544

Subgroups — #14562677

Conjugacy classes of subgroups

Complements

Maximal subgroups