Group #14563003 — subgroups

Subgroups — #14563003

Order 2432.

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

normal subgroups only

This group has 156 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	#11926923	C₂	1	1	yes	maximal, characteristic
2	#11926829	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#11926296	C₂	1	1	yes	maximal, characteristic
5	#11926290	C₂	1	1	yes	maximal, characteristic
6	#11926289	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#475	C₂	1	1	yes	maximal, characteristic
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×#64528	—	2	1	no	—
11	C₂×#64528	—	2	1	no	—
12	#10597315	C₂²	1	1	yes	characteristic
13	C₁₉×#106	—	2	1	no	—
14	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₁₉×#103	—	2	1	no	—
16	#10597292	—	2	1	no	—
17	#10597265	—	2	1	no	—
18	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
19	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₄×C₁₉⋊C₈	—	2	1	no	—
22	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×Dic₃₈	—	2	1	no	—
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₄²×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	#64528	—	4	2	no	—
34	#64528	—	4	2	no	—
35	C₄⋊Dic₁₉	—	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	D₄	1	1	yes	characteristic
40	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
41	Q₈×C₁₉	—	2	1	no	—
42	Q₈×C₁₉	—	4	1	no	—
43	Q₈×C₁₉	—	4	1	no	—
44	Q₈×C₁₉	Q₁₆	1	2	yes	complemented
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	4	1	no	—
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
51	C₂×Dic₁₉	—	4	1	no	—
52	Dic₃₈	—	4	1	no	—
53	Dic₃₈	—	4	1	no	—
54	C₈×C₁₉	—	4	1	no	—
55	C₁₉⋊C₈	—	2	1	no	—
56	C₁₉⋊C₈	—	4	1	no	—
57	C₁₉⋊C₈	—	4	1	no	—
58	C₁₉⋊C₈	SD₁₆	1	2	yes	—
59	#1670	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	#121	1	1	yes	characteristic
61	C₄×C₁₉	—	2	2	no	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	4	1	no	—
64	C₄×C₁₉	—	8	1	no	—
65	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
66	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
67	C₄×C₁₉	#135	1	1	yes	characteristic
68	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
69	Dic₁₉	—	8	1	no	—
70	#494	—	19	1	no	—
71	#475	—	19	1	no	—
72	#475	D₁₉	1	1	yes	characteristic
73	C₈×Q₈	—	19	1	no	—
74	#335	—	19	1	no	—
75	#332	—	19	1	no	—
76	#332	—	19	1	no	—
77	C₂×C₁₉	#460	1	1	yes	characteristic
78	C₂×C₁₉	#467	1	1	yes	characteristic
79	C₂×C₁₉	#473	1	1	yes	characteristic
80	C₂×Q₁₆	—	38	1	no	—
81	C₂×Q₁₆	—	38	1	no	—
82	C₄⋊Q₈	—	19	1	no	—
83	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
84	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
85	#106	—	2	1	no	—
86	#106	—	38	1	no	—
87	C₄⋊C₈	—	19	1	no	—
88	C₄⋊C₈	—	19	1	no	—
89	C₄⋊C₈	—	38	1	no	—
90	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
91	#103	—	2	1	no	—
92	#103	—	38	1	no	—
93	C₄×C₈	—	19	1	no	—
94	C₄×C₈	—	38	1	no	—
95	C₁₉	#1670	1	1	yes	characteristic, complemented, Sylow
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	38	1	no	—
98	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
99	Q₁₆	—	76	2	no	—
100	Q₁₆	—	76	2	no	—
101	C₂×C₈	—	2	1	no	—
102	C₂×C₈	—	19	1	no	—
103	C₂×C₈	—	19	1	no	—
104	C₂×C₈	—	38	1	no	—
105	C₂×C₈	—	38	1	no	—
106	C₄⋊C₄	—	2	1	no	—
107	C₄⋊C₄	—	2	1	no	—
108	C₄⋊C₄	—	2	1	no	—
109	C₄⋊C₄	—	38	1	no	—
110	C₄⋊C₄	—	38	1	no	—
111	C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
112	C₄²	—	2	1	no	—
113	C₄²	C₂²×D₁₉	1	1	yes	characteristic
114	Q₈	—	2	1	no	—
115	Q₈	—	4	1	no	—
116	Q₈	—	4	1	no	—
117	Q₈	—	76	1	no	—
118	Q₈	—	76	1	no	—
119	Q₈	#64528	1	2	yes	complemented
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	2	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	76	1	no	—
124	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
125	C₂×C₄	#64543	1	1	yes	characteristic
126	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
127	C₈	—	4	1	no	—
128	C₈	—	19	2	no	—
129	C₈	—	38	1	no	—
130	C₈	—	76	1	no	—
131	C₈	—	76	1	no	—
132	C₂²	#10597385	1	1	yes	characteristic
133	C₄	—	2	1	no	—
134	C₄	—	2	2	no	—
135	C₄	—	4	1	no	—
136	C₄	—	8	1	no	—
137	C₄	—	152	1	no	—
138	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
139	C₄	#10597360	1	1	yes	characteristic
140	C₄	C₂×#64528	1	1	yes	characteristic
141	C₄	#10597396	1	1	yes	characteristic
142	C₂	#11926742	1	1	yes	characteristic
143	C₂	#11926783	1	1	yes	characteristic
144	C₂	#11926817	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926923

C₂

yes

maximal, characteristic

#11926829

C₂

yes

maximal, characteristic

Q₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic

#11926296

C₂

yes

maximal, characteristic

#11926290

C₂

yes

maximal, characteristic

#11926289

C₂

yes

maximal, characteristic

C₁₉×#475

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₄×Q₈×C₁₉

C₂²

yes

—

—

C₂²

yes

characteristic

C₁₉×#106

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#103

—

#10597292

—

#10597265

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

Q₁₆

yes

complemented

C₂×C₄×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

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

SD₁₆

yes

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#494

—

#475

—

#475

D₁₉

yes

characteristic

C₈×Q₈

—

#335

—

#332

—

#332

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄×Q₈

C₂×D₁₉

yes

characteristic

#106

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

characteristic

#103

—

#103

—

C₄×C₈

—

C₄×C₈

—

C₁₉

#1670

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₁₉

yes

characteristic

Q₁₆

—

100

Q₁₆

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

112

C₄²

—

113

C₄²

C₂²×D₁₉

yes

characteristic

114

Q₈

—

115

Q₈

—

116

Q₈

—

117

Q₈

—

118

Q₈

—

119

Q₈

#64528

yes

complemented

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

D₄×D₁₉

yes

characteristic

125

C₂×C₄

#64543

yes

characteristic

126

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

—

132

C₂²

#10597385

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

152

—

138

C₄

SD₁₆×D₁₉

yes

characteristic

139

C₄

#10597360

yes

characteristic

140

C₄

C₂×#64528

yes

characteristic

141

C₄

#10597396

yes

characteristic

142

C₂

#11926742

yes

characteristic

143

C₂

#11926783

yes

characteristic

144

C₂

#11926817

yes

characteristic

	subgroup	G/H
center	C₂²	#10597385
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#475	C₂
socle, prime radical	C₂²×C₁₉	#121
hypercenter	#475	D₁₉
hypocenter	C₁₉	#1670
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #475

subgroup

G/H

center

C₂²

#10597385

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#475

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #475

N	H ≅ G/N	type
44. Q₈×C₁₉	Q₁₆	semidirect
95. C₁₉	#1670	semidirect
119. Q₈	#64528	semidirect

H ≅ G/N

type

44. Q₈×C₁₉

Q₁₆

semidirect

95. C₁₉

#1670

semidirect

119. Q₈

#64528

semidirect

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

subgroup	index
#11926923	2
#11926829	2
Q₈×C₁₉⋊C₈	2
#11926296	2
#11926290	2
#11926289	2
C₁₉×#475	2
#1670	19

subgroup

index

Q₈×C₁₉⋊C₈

C₁₉×#475

Subgroups — #14563003

Conjugacy classes of subgroups

Complements

Maximal subgroups