Group #14564923 — subgroups

Subgroups — #14564923

Order 2432.

266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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	#11927344	C₂	1	1	yes	maximal, characteristic
2	#11926567	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597282	C₂	1	2	yes	maximal, complemented
4	#11926526	C₂	1	2	yes	maximal, complemented
5	C₁₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	C₂²	1	2	yes	—
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
10	C₂×#64520	C₂²	1	1	yes	characteristic
11	#10597355	—	2	2	no	—
12	#10597354	—	2	2	no	—
13	#10597350	—	2	2	no	—
14	#10597282	—	2	2	no	—
15	#10597282	—	2	2	no	—
16	#10597281	—	2	2	no	—
17	#10597280	—	2	2	no	—
18	Dic₁₉⋊C₈	—	2	2	no	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂×C₂²⋊D₁₉	—	2	2	no	—
21	C₂²×Dic₁₉	—	2	1	no	—
22	#64541	—	2	2	no	—
23	#64541	—	2	2	no	—
24	#64541	—	2	2	no	—
25	#64541	—	2	2	no	—
26	C₂×D₇₆	D₄	1	2	yes	—
27	C₂×C₄×D₁₉	—	2	2	no	—
28	C₂×Dic₃₈	D₄	1	2	yes	—
29	M₁₆×C₁₉	—	2	2	no	—
30	M₁₆×C₁₉	—	2	2	no	—
31	M₁₆×C₁₉	—	2	2	no	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	D₄	1	2	yes	—
34	C₄×Dic₁₉	—	2	1	no	—
35	C₄×Dic₁₉	D₄	1	1	yes	characteristic
36	C₄×Dic₁₉	D₄	1	1	yes	characteristic
37	#64520	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	Dic₇₆	—	2	2	no	—
40	D₁₅₂	—	2	2	no	—
41	#64516	—	2	4	no	—
42	C₂³×C₁₉	#41	1	1	yes	characteristic
43	C₂²×D₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#41	1	2	yes	—
48	C₂²⋊D₁₉	—	4	2	no	—
49	C₂²⋊D₁₉	—	4	2	no	—
50	C₂×Dic₁₉	—	2	1	no	—
51	C₂×Dic₁₉	—	2	1	no	—
52	C₂×Dic₁₉	—	2	2	no	—
53	C₂×Dic₁₉	—	4	2	no	—
54	D₇₆	—	2	2	no	—
55	D₇₆	—	2	2	no	—
56	C₄×D₁₉	—	4	2	no	—
57	C₄×D₁₉	—	4	2	no	—
58	Dic₃₈	—	2	2	no	—
59	Dic₃₈	—	2	2	no	—
60	C₈×C₁₉	—	2	2	no	—
61	C₈×C₁₉	—	4	2	no	—
62	C₁₉⋊C₈	—	4	1	no	—
63	#2050	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	4	1	no	—
65	C₂²×C₁₉	#121	1	1	yes	characteristic
66	C₂²×C₁₉	#123	1	2	yes	—
67	C₂×D₁₉	—	4	2	no	—
68	C₂×D₁₉	—	8	2	no	—
69	C₄×C₁₉	#120	1	1	yes	characteristic
70	C₄×C₁₉	#121	1	2	yes	—
71	C₄×C₁₉	#124	1	1	yes	characteristic
72	Dic₁₉	—	2	2	no	—
73	Dic₁₉	—	4	1	no	—
74	Dic₁₉	—	4	2	no	—
75	#575	—	19	1	no	—
76	#423	—	19	1	no	—
77	C₂×#104	—	19	2	no	—
78	#413	—	19	2	no	—
79	#338	D₁₉	1	1	yes	characteristic, complemented
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	—	2	2	no	—
82	C₂×C₁₉	#394	1	1	yes	characteristic
83	D₁₉	—	8	2	no	—
84	C₂×#41	—	19	2	no	—
85	#137	—	38	2	no	—
86	AGL(1,ℤ/8)	—	38	2	no	—
87	#135	—	38	2	no	—
88	C₂×M₁₆	—	19	1	no	—
89	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
90	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
91	C₂×C₄²	—	19	1	no	—
92	C₄⋊C₈	—	38	2	no	—
93	#104	—	38	2	no	—
94	#104	—	38	2	no	—
95	#101	—	38	2	no	—
96	#100	—	38	2	no	—
97	C₁₉	#2050	1	1	yes	characteristic, complemented, Sylow
98	#41	—	38	2	no	—
99	#41	—	38	2	no	—
100	#41	—	38	2	no	—
101	#41	—	38	2	no	—
102	C₂×Q₈	—	19	2	no	—
103	C₂×D₄	—	19	2	no	—
104	C₂×D₄	—	38	2	no	—
105	C₂²×C₄	—	38	1	no	—
106	C₂²×C₄	—	38	2	no	—
107	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
108	Q₁₆	—	38	2	no	—
109	SD₁₆	—	38	4	no	—
110	D₈	—	38	2	no	—
111	M₁₆	—	2	2	no	—
112	M₁₆	—	2	2	no	—
113	M₁₆	—	2	2	no	—
114	M₁₆	—	38	2	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	38	1	no	—
117	C₂×C₈	D₇₆	1	2	yes	—
118	C₄²	—	19	1	no	—
119	C₄²	—	19	1	no	—
120	C₄²	—	38	1	no	—
121	C₂³	—	38	2	no	—
122	C₂³	#64545	1	1	yes	characteristic
123	Q₈	—	38	2	no	—
124	Q₈	—	38	2	no	—
125	D₄	—	38	2	no	—
126	D₄	—	38	2	no	—
127	D₄	—	76	2	no	—
128	D₄	—	76	2	no	—
129	C₂×C₄	—	38	1	no	—
130	C₂×C₄	—	38	2	no	—
131	C₂×C₄	—	38	1	no	—
132	C₂×C₄	—	76	2	no	—
133	C₂×C₄	—	76	2	no	—
134	C₂×C₄	—	76	2	no	—
135	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
136	C₂×C₄	#64541	1	2	yes	—
137	C₂×C₄	D₄×D₁₉	1	2	yes	—
138	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
139	C₈	—	2	2	no	—
140	C₈	—	4	2	no	—
141	C₈	—	76	1	no	—
142	C₂²	—	4	1	no	—
143	C₂²	—	76	2	no	—
144	C₂²	—	152	2	no	—
145	C₂²	#10597340	1	2	yes	—
146	C₂²	#10597341	1	1	yes	characteristic
147	C₄	—	38	2	no	—
148	C₄	—	76	1	no	—
149	C₄	—	76	2	no	—
150	C₄	#10597321	1	1	yes	characteristic
151	C₄	#10597328	1	1	yes	characteristic
152	C₄	#10597330	1	2	yes	—
153	C₂	—	2	1	no	—
154	C₂	—	2	2	no	—
155	C₂	—	152	2	no	—
156	C₂	#11926462	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927344

C₂

yes

maximal, characteristic

#11926567

C₂

yes

maximal, characteristic, complemented

C₂×#10597282

C₂

yes

maximal, complemented

#11926526

C₂

yes

maximal, complemented

C₁₉×#338

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

—

—

—

—

—

—

Dic₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

—

—

—

—

C₂×D₇₆

D₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

D₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

D₁₅₂

—

#64516

—

C₂³×C₁₉

#41

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2050

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

#123

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#121

yes

—

C₄×C₁₉

#124

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#394

yes

characteristic

D₁₉

—

C₂×#41

—

#137

—

AGL(1,ℤ/8)

—

#135

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

—

—

—

—

C₁₉

#2050

yes

characteristic, complemented, Sylow

#41

—

#41

—

100

#41

—

101

#41

—

102

C₂×Q₈

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

C₂²×D₁₉

yes

characteristic

108

Q₁₆

—

109

SD₁₆

—

110

D₈

—

111

M₁₆

—

112

M₁₆

—

113

M₁₆

—

114

M₁₆

—

115

C₂×C₈

—

116

C₂×C₈

—

117

C₂×C₈

D₇₆

yes

—

118

C₄²

—

119

C₄²

—

120

C₄²

—

121

C₂³

—

122

C₂³

#64545

yes

characteristic

123

Q₈

—

124

Q₈

—

125

D₄

—

126

D₄

—

127

D₄

—

128

D₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

C₂×D₇₆

yes

characteristic

136

C₂×C₄

#64541

yes

—

137

C₂×C₄

D₄×D₁₉

yes

—

138

C₂×C₄

D₄×D₁₉

yes

characteristic

139

C₈

—

140

C₈

—

141

C₈

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

152

—

145

C₂²

#10597340

yes

—

146

C₂²

#10597341

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

#10597321

yes

characteristic

151

C₄

#10597328

yes

characteristic

152

C₄

#10597330

yes

—

153

C₂

—

154

C₂

—

155

C₂

—

152

—

156

C₂

#11926462

yes

characteristic

	subgroup	G/H
center	C₄	#10597321
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#338	C₂
socle	C₂×C₁₉	#394
prime radical	#11927344	C₂
hypercenter	#338	D₁₉
hypocenter	C₁₉	#2050
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

subgroup

G/H

center

C₄

#10597321

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#338

C₂

C₂×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

N	H ≅ G/N	type
2. #11926567	C₂	semidirect
3. C₂×#10597282	C₂	semidirect
4. #11926526	C₂	semidirect
5. C₁₉×#338	C₂	semidirect
79. #338	D₁₉	semidirect
97. C₁₉	#2050	semidirect

H ≅ G/N

type

2. #11926567

C₂

semidirect

3. C₂×#10597282

C₂

semidirect

4. #11926526

C₂

semidirect

5. C₁₉×#338

C₂

semidirect

79. #338

D₁₉

semidirect

97. C₁₉

#2050

semidirect

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

subgroup	index
#11927344	2
#11926567	2
C₂×#10597282	2
#11926526	2
C₁₉×#338	2
#2050	19

subgroup

index

C₁₉×#338

Subgroups — #14564923

Conjugacy classes of subgroups

Complements

Maximal subgroups