Group #14565701 — subgroups

Subgroups — #14565701

Order 2432.

154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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	#11926985	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926980	C₂	1	1	yes	maximal, characteristic
3	#11926662	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926365	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926360	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926357	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×SD₁₆×C₁₉	—	2	1	no	—
10	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#124	—	2	1	no	—
12	#10597350	C₂²	1	1	yes	characteristic
13	#10597347	—	2	1	no	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	#10597286	—	2	1	no	—
16	#10597285	—	2	1	no	—
17	#10597284	—	2	1	no	—
18	#10597283	—	2	1	no	—
19	#10597276	C₂²	1	1	yes	characteristic
20	#10597269	C₂²	1	1	yes	characteristic
21	#10597269	C₂²	1	1	yes	characteristic
22	#10597262	—	2	1	no	—
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	#64541	—	2	1	no	—
26	Q₁₆×C₁₉	—	2	1	no	—
27	Q₁₆×C₁₉	—	2	1	no	—
28	SD₁₆×C₁₉	—	4	1	no	—
29	SD₁₆×C₁₉	—	4	1	no	—
30	D₈×C₁₉	—	2	1	no	—
31	D₈×C₁₉	—	2	1	no	—
32	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
34	C₂²⋊C₄×C₁₉	—	4	2	no	—
35	C₄²×C₁₉	D₄	1	1	yes	characteristic
36	#64520	—	2	1	no	—
37	Dic₇₆	D₄	1	1	yes	characteristic
38	D₁₅₂	D₄	1	1	yes	characteristic
39	#64516	—	2	1	no	—
40	#64515	—	4	1	no	—
41	C₈×D₁₉	—	4	1	no	—
42	C₁₉⋊C₁₆	—	2	1	no	—
43	C₁₉⋊C₁₆	—	2	1	no	—
44	C₂³×C₁₉	—	4	1	no	—
45	Q₈×C₁₉	—	4	1	no	—
46	Q₈×C₁₉	—	4	1	no	—
47	D₄×C₁₉	—	4	1	no	—
48	D₄×C₁₉	—	4	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂²⋊D₁₉	—	4	1	no	—
53	D₇₆	—	2	1	no	—
54	C₄×D₁₉	—	4	1	no	—
55	Dic₃₈	—	2	1	no	—
56	C₈×C₁₉	D₈	1	1	yes	characteristic
57	C₈×C₁₉	D₈	1	1	yes	characteristic
58	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₈×C₁₉	#41	1	1	yes	characteristic
60	C₁₉⋊C₈	—	4	1	no	—
61	#2212	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	8	2	no	—
63	C₂²×C₁₉	—	8	1	no	—
64	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂×D₁₉	—	4	1	no	—
66	C₄×C₁₉	—	4	1	no	—
67	C₄×C₁₉	—	8	1	no	—
68	C₄×C₁₉	#121	1	1	yes	characteristic
69	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
70	Dic₁₉	—	4	1	no	—
71	#510	—	19	1	no	—
72	#509	—	19	1	no	—
73	#495	D₁₉	1	1	yes	characteristic, complemented
74	#443	—	19	1	no	—
75	#364	—	19	1	no	—
76	#362	—	19	1	no	—
77	#361	—	19	1	no	—
78	C₂×C₁₉	—	2	1	no	—
79	C₂×C₁₉	—	16	1	no	—
80	C₂×C₁₉	#459	1	1	yes	characteristic
81	D₁₉	—	8	1	no	—
82	#135	—	19	1	no	—
83	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
84	C₂×SD₁₆	—	2	1	no	—
85	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
86	#131	—	38	1	no	—
87	#124	—	2	1	no	—
88	Q₃₂	—	38	1	no	—
89	SD₃₂	—	38	1	no	—
90	SD₃₂	—	38	1	no	—
91	D₁₆	—	38	1	no	—
92	M₃₂	—	19	1	no	—
93	M₃₂	—	19	1	no	—
94	#108	—	19	1	no	—
95	#104	—	38	1	no	—
96	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
97	C₁₉	#2212	1	1	yes	characteristic, complemented, Sylow
98	#41	—	38	1	no	—
99	C₂×Q₈	—	2	1	no	—
100	C₂×D₄	—	2	1	no	—
101	Q₁₆	—	2	1	no	—
102	Q₁₆	—	2	1	no	—
103	Q₁₆	—	19	1	no	—
104	SD₁₆	—	4	1	no	—
105	SD₁₆	—	4	1	no	—
106	SD₁₆	—	38	1	no	—
107	D₈	—	2	1	no	—
108	D₈	—	2	1	no	—
109	D₈	—	19	1	no	—
110	M₁₆	—	38	1	no	—
111	M₁₆	—	76	1	no	—
112	C₂×C₈	—	76	1	no	—
113	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
114	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
115	C₂²⋊C₄	—	4	2	no	—
116	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
117	C₁₆	—	38	1	no	—
118	C₁₆	—	38	1	no	—
119	C₂³	—	4	1	no	—
120	Q₈	—	4	1	no	—
121	Q₈	—	4	1	no	—
122	Q₈	—	38	1	no	—
123	D₄	—	4	1	no	—
124	D₄	—	4	1	no	—
125	D₄	—	38	1	no	—
126	D₄	—	76	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	4	1	no	—
129	C₂×C₄	—	76	1	no	—
130	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
131	C₈	—	76	1	no	—
132	C₈	#64525	1	1	yes	characteristic
133	C₈	#64525	1	1	yes	characteristic
134	C₈	D₄×D₁₉	1	1	yes	characteristic
135	C₈	#64543	1	1	yes	characteristic
136	C₂²	—	8	2	no	—
137	C₂²	—	8	1	no	—
138	C₂²	—	76	1	no	—
139	C₂²	#10597378	1	1	yes	characteristic
140	C₄	—	4	1	no	—
141	C₄	—	8	1	no	—
142	C₄	—	76	1	no	—
143	C₄	C₂×#64525	1	1	yes	characteristic
144	C₄	#10597384	1	1	yes	characteristic
145	C₂	—	2	1	no	—
146	C₂	—	16	1	no	—
147	C₂	—	152	1	no	—
148	C₂	#11926736	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926985

C₂

yes

maximal, characteristic, complemented

#11926980

C₂

yes

maximal, characteristic

#11926662

C₂

yes

maximal, characteristic, complemented

#11926365

C₂

yes

maximal, characteristic, complemented

#11926360

C₂

yes

maximal, characteristic, complemented

#11926357

C₂

yes

maximal, characteristic, complemented

C₁₉×#495

C₂

yes

maximal, characteristic, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×#124

—

#10597350

C₂²

yes

characteristic

#10597347

—

C₄×C₈×C₁₉

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

#10597269

C₂²

yes

characteristic

#10597269

C₂²

yes

characteristic

#10597262

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

#64541

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

#64520

—

Dic₇₆

D₄

yes

characteristic

D₁₅₂

D₄

yes

characteristic

#64516

—

#64515

—

C₈×D₁₉

—

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

#2212

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

Dic₁₉

—

#510

—

#509

—

#495

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#459

yes

characteristic

D₁₉

—

#135

—

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₁₉

yes

characteristic

#131

—

#124

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

D₁₆

—

M₃₂

—

M₃₂

—

#108

—

#104

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2212

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

—

100

C₂×D₄

—

101

Q₁₆

—

102

Q₁₆

—

103

Q₁₆

—

104

SD₁₆

—

105

SD₁₆

—

106

SD₁₆

—

107

D₈

—

108

D₈

—

109

D₈

—

110

M₁₆

—

111

M₁₆

—

112

C₂×C₈

—

113

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

114

C₂×C₈

C₂²×D₁₉

yes

characteristic

115

C₂²⋊C₄

—

116

C₄²

C₂²⋊D₁₉

yes

characteristic

117

C₁₆

—

118

C₁₆

—

119

C₂³

—

120

Q₈

—

121

Q₈

—

122

Q₈

—

123

D₄

—

124

D₄

—

125

D₄

—

126

D₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

131

C₈

—

132

C₈

#64525

yes

characteristic

133

C₈

#64525

yes

characteristic

134

C₈

D₄×D₁₉

yes

characteristic

135

C₈

#64543

yes

characteristic

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

#10597378

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

C₂×#64525

yes

characteristic

144

C₄

#10597384

yes

characteristic

145

C₂

—

146

C₂

—

147

C₂

—

152

—

148

C₂

#11926736

yes

characteristic

	subgroup	G/H
center	C₂	#11926736
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#495	C₂
socle	C₂×C₁₉	#459
prime radical	#11926980	C₂
hypercenter	#495	D₁₉
hypocenter	C₁₉	#2212
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂

#11926736

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#495

C₂

C₂×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. #11926985	C₂	semidirect
3. #11926662	C₂	semidirect
4. #11926365	C₂	semidirect
5. #11926360	C₂	semidirect
6. #11926357	C₂	semidirect
7. C₁₉×#495	C₂	semidirect
73. #495	D₁₉	semidirect
97. C₁₉	#2212	semidirect

H ≅ G/N

type

1. #11926985

C₂

semidirect

3. #11926662

C₂

semidirect

4. #11926365

C₂

semidirect

5. #11926360

C₂

semidirect

6. #11926357

C₂

semidirect

7. C₁₉×#495

C₂

semidirect

73. #495

D₁₉

semidirect

97. C₁₉

#2212

semidirect

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

subgroup	index
#11926985	2
#11926980	2
#11926662	2
#11926365	2
#11926360	2
#11926357	2
C₁₉×#495	2
#2212	19

subgroup

index

C₁₉×#495

Subgroups — #14565701

Conjugacy classes of subgroups

Complements

Maximal subgroups