Group #14563062 — subgroups

Subgroups — #14563062

Order 2432.

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

normal subgroups only

This group has 150 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	#11926826	C₂	1	1	yes	maximal, characteristic
2	#11926751	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₃₈	C₂	1	1	yes	maximal, characteristic
4	#11926295	C₂	1	1	yes	maximal, characteristic
5	#11926290	C₂	1	1	yes	maximal, characteristic
6	#11926290	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#487	C₂	1	1	yes	maximal, characteristic
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×#64528	—	2	1	no	—
11	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
12	C₁₉×#103	—	2	1	no	—
13	C₁₉×#103	—	2	1	no	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	#10597292	—	2	1	no	—
16	Dic₁₉⋊C₈	—	2	1	no	—
17	C₈×Dic₁₉	—	2	1	no	—
18	#10597267	—	2	1	no	—
19	#10597265	—	2	1	no	—
20	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	—	2	1	no	—
25	C₂×Dic₃₈	D₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	#64528	—	4	2	no	—
34	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
35	Dic₁₉⋊C₄	—	2	1	no	—
36	C₄×Dic₁₉	—	2	1	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	C₂×C₁₉⋊C₈	—	2	1	no	—
40	Q₈×C₁₉	—	4	1	no	—
41	Q₈×C₁₉	—	4	1	no	—
42	Q₈×C₁₉	—	4	1	no	—
43	Q₈×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
49	C₂×Dic₁₉	—	2	1	no	—
50	C₂×Dic₁₉	—	2	1	no	—
51	Dic₃₈	—	2	1	no	—
52	Dic₃₈	SD₁₆	1	2	yes	—
53	C₈×C₁₉	—	2	1	no	—
54	C₈×C₁₉	—	2	1	no	—
55	C₁₉⋊C₈	—	4	1	no	—
56	C₁₉⋊C₈	—	4	1	no	—
57	C₁₉⋊C₈	—	4	1	no	—
58	#1680	—	19	1	no	maximal, Sylow
59	C₂²×C₁₉	#121	1	1	yes	characteristic
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	—	8	1	no	—
62	C₄×C₁₉	—	8	1	no	—
63	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
64	C₄×C₁₉	#135	1	1	yes	characteristic
65	C₄×C₁₉	#135	1	1	yes	characteristic
66	C₄×C₁₉	#137	1	1	yes	characteristic
67	Dic₁₉	—	2	2	no	—
68	Dic₁₉	—	4	1	no	—
69	#487	D₁₉	1	1	yes	characteristic
70	#475	—	19	1	no	—
71	#462	—	19	1	no	—
72	C₈×Q₈	—	19	1	no	—
73	#334	—	19	1	no	—
74	#332	—	19	1	no	—
75	#332	—	19	1	no	—
76	C₂×C₁₉	#464	1	1	yes	characteristic
77	C₂×C₁₉	#465	1	1	yes	characteristic
78	C₂×C₁₉	#473	1	1	yes	characteristic
79	C₂×Q₁₆	—	38	1	no	—
80	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
81	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
82	C₄×Q₈	—	19	1	no	—
83	#106	—	38	1	no	—
84	C₄⋊C₈	—	19	1	no	—
85	C₄⋊C₈	—	19	1	no	—
86	C₄⋊C₈	—	19	1	no	—
87	C₄⋊C₈	—	38	1	no	—
88	#103	—	2	1	no	—
89	#103	—	2	1	no	—
90	#103	—	38	1	no	—
91	#103	—	38	1	no	—
92	C₄×C₈	—	38	1	no	—
93	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
94	C₁₉	#1680	1	1	yes	characteristic, complemented, Sylow
95	C₂×Q₈	—	2	1	no	—
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	19	1	no	—
98	Q₁₆	—	76	2	no	—
99	C₂×C₈	—	38	1	no	—
100	C₂×C₈	—	38	1	no	—
101	C₂×C₈	—	38	1	no	—
102	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
103	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	2	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	2	1	no	—
108	C₄⋊C₄	—	19	1	no	—
109	C₄⋊C₄	—	38	1	no	—
110	C₄²	—	38	1	no	—
111	C₄²	C₂²×D₁₉	1	1	yes	characteristic
112	Q₈	—	4	1	no	—
113	Q₈	—	4	1	no	—
114	Q₈	—	4	1	no	—
115	Q₈	—	4	1	no	—
116	Q₈	—	19	2	no	—
117	Q₈	—	38	1	no	—
118	C₂×C₄	—	4	1	no	—
119	C₂×C₄	—	4	1	no	—
120	C₂×C₄	—	38	1	no	—
121	C₂×C₄	—	38	1	no	—
122	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
123	C₂×C₄	#64543	1	1	yes	characteristic
124	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
125	C₈	—	2	1	no	—
126	C₈	—	2	1	no	—
127	C₈	—	76	1	no	—
128	C₈	—	76	1	no	—
129	C₈	—	76	1	no	—
130	C₂²	#10597384	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	8	1	no	—
133	C₄	—	8	1	no	—
134	C₄	—	38	2	no	—
135	C₄	—	76	1	no	—
136	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
137	C₄	#10597362	1	1	yes	characteristic
138	C₄	#10597396	1	1	yes	characteristic
139	C₄	#10597397	1	1	yes	characteristic
140	C₂	#11926763	1	1	yes	characteristic
141	C₂	#11926770	1	1	yes	characteristic
142	C₂	#11926816	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926826

C₂

yes

maximal, characteristic

#11926751

C₂

yes

maximal, characteristic

C₈×Dic₃₈

C₂

yes

maximal, characteristic

#11926295

C₂

yes

maximal, characteristic

#11926290

C₂

yes

maximal, characteristic

#11926290

C₂

yes

maximal, characteristic

C₁₉×#487

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×#64528

—

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×#103

—

C₁₉×#103

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597292

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

#10597267

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

SD₁₆

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

#487

D₁₉

yes

characteristic

#475

—

#462

—

C₈×Q₈

—

#334

—

#332

—

#332

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄×Q₈

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

—

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1680

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

103

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄²

—

111

C₄²

C₂²×D₁₉

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

D₄×D₁₉

yes

characteristic

123

C₂×C₄

#64543

yes

characteristic

124

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₂²

#10597384

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

SD₁₆×D₁₉

yes

characteristic

137

C₄

#10597362

yes

characteristic

138

C₄

#10597396

yes

characteristic

139

C₄

#10597397

yes

characteristic

140

C₂

#11926763

yes

characteristic

141

C₂

#11926770

yes

characteristic

142

C₂

#11926816

yes

characteristic

	subgroup	G/H
center	C₂²	#10597384
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#487	C₂
socle, prime radical	C₂²×C₁₉	#121
hypercenter	#487	D₁₉
hypocenter	C₁₉	#1680
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

#10597384

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#487

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
94. C₁₉	#1680	semidirect

H ≅ G/N

type

94. C₁₉

#1680

semidirect

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

subgroup	index
#11926826	2
#11926751	2
C₈×Dic₃₈	2
#11926295	2
#11926290	2
C₁₉×#487	2
#1680	19

subgroup

index

C₈×Dic₃₈

C₁₉×#487

Subgroups — #14563062

Conjugacy classes of subgroups

Complements

Maximal subgroups