Group #14563201 — subgroups

Subgroups — #14563201

Order 2432.

162 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 51 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	#11926890	C₂	1	1	yes	maximal, characteristic
2	#11926754	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926675	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926294	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926291	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926288	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#460	C₂	1	1	yes	maximal, characteristic
8	C₂×SD₁₆×C₁₉	—	2	1	no	—
9	C₁₉×#127	C₂²	1	1	yes	characteristic
10	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×#64528	—	2	1	no	—
12	#10597315	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₁₉×#102	—	2	1	no	—
15	#10597289	—	2	1	no	—
16	#10597289	—	2	1	no	—
17	#10597267	—	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	#10597260	—	2	1	no	—
22	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	2	1	no	—
26	C₂×D₄×C₁₉	—	2	1	no	—
27	C₂×Dic₃₈	—	2	1	no	—
28	SD₁₆×C₁₉	—	4	2	no	—
29	C₂×C₈×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₄²×C₁₉	—	2	1	no	—
33	C₄²×C₁₉	C₂³	1	1	yes	characteristic
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	C₂³×C₁₉	—	4	1	no	—
42	Q₈×C₁₉	—	2	1	no	—
43	Q₈×C₁₉	—	2	1	no	—
44	D₄×C₁₉	—	4	1	no	—
45	D₄×C₁₉	—	4	1	no	—
46	D₄×C₁₉	—	4	1	no	—
47	D₄×C₁₉	—	4	1	no	—
48	D₄×C₁₉	—	8	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	2	1	no	—
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂×Dic₁₉	—	4	1	no	—
55	Dic₃₈	—	4	1	no	—
56	Dic₃₈	—	4	1	no	—
57	C₈×C₁₉	—	4	1	no	—
58	C₁₉⋊C₈	—	2	1	no	—
59	C₁₉⋊C₈	—	2	1	no	—
60	C₁₉⋊C₈	—	4	1	no	—
61	C₁₉⋊C₈	—	4	1	no	—
62	#1702	—	19	1	no	maximal, Sylow
63	C₂²×C₁₉	—	8	1	no	—
64	C₂²×C₁₉	—	8	1	no	—
65	C₂²×C₁₉	—	8	1	no	—
66	C₂²×C₁₉	#121	1	1	yes	characteristic
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	4	1	no	—
69	C₄×C₁₉	—	4	1	no	—
70	C₄×C₁₉	#135	1	1	yes	characteristic
71	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
72	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
73	C₄×C₁₉	#137	1	1	yes	characteristic
74	Dic₁₉	—	8	1	no	—
75	#486	—	19	1	no	—
76	#462	—	19	1	no	—
77	#460	D₁₉	1	1	yes	characteristic
78	#446	—	19	1	no	—
79	#334	—	19	1	no	—
80	#332	—	19	1	no	—
81	#331	—	19	1	no	—
82	C₂×C₁₉	—	16	1	no	—
83	C₂×C₁₉	#464	1	1	yes	characteristic
84	C₂×C₁₉	#469	1	1	yes	characteristic
85	C₂×C₁₉	#471	1	1	yes	characteristic
86	C₂×Q₁₆	—	38	1	no	—
87	C₂×SD₁₆	—	2	1	no	—
88	C₄⋊Q₈	—	19	1	no	—
89	#127	C₂×D₁₉	1	1	yes	characteristic
90	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
91	C₄⋊C₈	—	19	1	no	—
92	C₄⋊C₈	—	19	1	no	—
93	C₄⋊C₈	—	38	1	no	—
94	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
95	#103	—	38	1	no	—
96	#102	—	2	1	no	—
97	#102	—	38	1	no	—
98	#102	—	38	1	no	—
99	#97	—	38	1	no	—
100	C₄×C₈	—	19	1	no	—
101	C₁₉	#1702	1	1	yes	characteristic, complemented, Sylow
102	C₂×Q₈	—	38	1	no	—
103	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
104	C₂×D₄	—	2	1	no	—
105	C₂×D₄	—	2	1	no	—
106	C₂×D₄	—	2	1	no	—
107	Q₁₆	—	76	2	no	—
108	SD₁₆	—	4	2	no	—
109	C₂×C₈	—	2	1	no	—
110	C₂×C₈	—	19	1	no	—
111	C₂×C₈	—	19	1	no	—
112	C₂×C₈	—	38	1	no	—
113	C₂×C₈	—	38	1	no	—
114	C₄⋊C₄	—	2	1	no	—
115	C₄⋊C₄	—	38	1	no	—
116	C₄⋊C₄	—	38	1	no	—
117	C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
118	C₄²	—	2	1	no	—
119	C₄²	C₂²×D₁₉	1	1	yes	characteristic
120	C₂³	—	4	1	no	—
121	Q₈	—	2	1	no	—
122	Q₈	—	2	1	no	—
123	Q₈	—	76	1	no	—
124	Q₈	—	76	1	no	—
125	D₄	—	4	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	4	1	no	—
128	D₄	—	4	1	no	—
129	D₄	—	8	1	no	—
130	C₂×C₄	—	2	1	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	76	1	no	—
133	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
134	C₂×C₄	#64543	1	1	yes	characteristic
135	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
136	C₈	—	4	1	no	—
137	C₈	—	38	1	no	—
138	C₈	—	38	1	no	—
139	C₈	—	76	1	no	—
140	C₈	—	76	1	no	—
141	C₂²	—	8	1	no	—
142	C₂²	—	8	1	no	—
143	C₂²	—	8	1	no	—
144	C₂²	#10597385	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	4	1	no	—
147	C₄	—	4	1	no	—
148	C₄	—	152	1	no	—
149	C₄	#10597361	1	1	yes	characteristic
150	C₄	#10597362	1	1	yes	characteristic
151	C₄	#10597378	1	1	yes	characteristic
152	C₄	#10597395	1	1	yes	characteristic
153	C₂	—	16	1	no	—
154	C₂	#11926764	1	1	yes	characteristic
155	C₂	#11926795	1	1	yes	characteristic
156	C₂	#11926805	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926890

C₂

yes

maximal, characteristic

#11926754

C₂

yes

maximal, characteristic, complemented

#11926675

C₂

yes

maximal, characteristic, complemented

#11926294

C₂

yes

maximal, characteristic, complemented

#11926291

C₂

yes

maximal, characteristic, complemented

#11926288

C₂

yes

maximal, characteristic

C₁₉×#460

C₂

yes

maximal, characteristic

C₂×SD₁₆×C₁₉

—

C₁₉×#127

C₂²

yes

characteristic

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×#64528

—

#10597315

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#102

—

#10597289

—

#10597289

—

#10597267

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#10597260

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×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

—

#1702

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#486

—

#462

—

#460

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

#127

C₂×D₁₉

yes

characteristic

C₄×Q₈

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

—

—

—

—

100

C₄×C₈

—

101

C₁₉

#1702

yes

characteristic, complemented, Sylow

102

C₂×Q₈

—

103

C₂×Q₈

C₂²⋊D₁₉

yes

characteristic

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

107

Q₁₆

—

108

SD₁₆

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

118

C₄²

—

119

C₄²

C₂²×D₁₉

yes

characteristic

120

C₂³

—

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

Q₈

—

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

D₄×D₁₉

yes

characteristic

134

C₂×C₄

#64543

yes

characteristic

135

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

#10597385

yes

characteristic

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

152

—

149

C₄

#10597361

yes

characteristic

150

C₄

#10597362

yes

characteristic

151

C₄

#10597378

yes

characteristic

152

C₄

#10597395

yes

characteristic

153

C₂

—

154

C₂

#11926764

yes

characteristic

155

C₂

#11926795

yes

characteristic

156

C₂

#11926805

yes

characteristic

	subgroup	G/H
center	C₂²	#10597385
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#460	C₂
socle	C₂²×C₁₉	#121
prime radical	C₁₉×#127	C₂²
hypercenter	#460	D₁₉
hypocenter	C₁₉	#1702
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #460

subgroup

G/H

center

C₂²

#10597385

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#460

C₂

socle

C₂²×C₁₉

#121

prime radical

C₁₉×#127

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #460

N	H ≅ G/N	type
2. #11926754	C₂	semidirect
3. #11926675	C₂	semidirect
4. #11926294	C₂	semidirect
5. #11926291	C₂	semidirect
101. C₁₉	#1702	semidirect

H ≅ G/N

type

2. #11926754

C₂

semidirect

3. #11926675

C₂

semidirect

4. #11926294

C₂

semidirect

5. #11926291

C₂

semidirect

101. C₁₉

#1702

semidirect

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

subgroup	index
#11926890	2
#11926754	2
#11926675	2
#11926294	2
#11926291	2
#11926288	2
C₁₉×#460	2
#1702	19

subgroup

index

C₁₉×#460

Subgroups — #14563201

Conjugacy classes of subgroups

Complements

Maximal subgroups