Group #14563173 — subgroups

Subgroups — #14563173

Order 2432.

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

normal subgroups only

This group has 156 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	#11926839	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926675	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926296	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926292	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	#10597315	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×#102	—	2	1	no	—
14	#10597292	—	2	1	no	—
15	#10597289	—	2	1	no	—
16	#10597289	—	2	1	no	—
17	#10597264	—	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	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	1	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
39	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
40	C₂³×C₁₉	—	4	1	no	—
41	Q₈×C₁₉	—	2	1	no	—
42	Q₈×C₁₉	—	2	1	no	—
43	D₄×C₁₉	—	4	1	no	—
44	D₄×C₁₉	—	4	1	no	—
45	D₄×C₁₉	—	4	1	no	—
46	D₄×C₁₉	—	4	1	no	—
47	D₄×C₁₉	—	8	1	no	—
48	C₂×C₄×C₁₉	—	2	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂×Dic₁₉	—	4	1	no	—
54	Dic₃₈	—	8	1	no	—
55	C₈×C₁₉	—	4	1	no	—
56	C₁₉⋊C₈	—	2	1	no	—
57	C₁₉⋊C₈	—	2	1	no	—
58	C₁₉⋊C₈	—	4	1	no	—
59	C₁₉⋊C₈	—	4	1	no	—
60	#1698	—	19	1	no	maximal, Sylow
61	C₂²×C₁₉	—	8	1	no	—
62	C₂²×C₁₉	—	8	1	no	—
63	C₂²×C₁₉	—	8	1	no	—
64	C₂²×C₁₉	#121	1	1	yes	characteristic
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	4	1	no	—
67	C₄×C₁₉	—	4	1	no	—
68	C₄×C₁₉	#135	1	1	yes	characteristic
69	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
70	C₄×C₁₉	#137	1	1	yes	characteristic
71	C₄×C₁₉	#137	1	1	yes	characteristic
72	Dic₁₉	—	8	1	no	—
73	#486	—	19	1	no	—
74	#477	—	19	1	no	—
75	#460	D₁₉	1	1	yes	characteristic
76	#446	—	19	1	no	—
77	#335	—	19	1	no	—
78	#333	—	19	1	no	—
79	#331	—	19	1	no	—
80	C₂×C₁₉	—	16	1	no	—
81	C₂×C₁₉	#464	1	1	yes	characteristic
82	C₂×C₁₉	#468	1	1	yes	characteristic
83	C₂×C₁₉	#472	1	1	yes	characteristic
84	C₂×SD₁₆	—	2	1	no	—
85	C₄⋊Q₈	—	19	1	no	—
86	#127	C₂×D₁₉	1	1	yes	characteristic
87	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
88	#107	—	38	1	no	—
89	C₄⋊C₈	—	19	1	no	—
90	C₄⋊C₈	—	19	1	no	—
91	C₄⋊C₈	—	38	1	no	—
92	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
93	#103	—	38	1	no	—
94	#102	—	2	1	no	—
95	#102	—	38	1	no	—
96	#102	—	38	1	no	—
97	#97	—	38	1	no	—
98	C₄×C₈	—	19	1	no	—
99	C₁₉	#1698	1	1	yes	characteristic, complemented, Sylow
100	C₂×Q₈	—	38	1	no	—
101	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
102	C₂×D₄	—	2	1	no	—
103	C₂×D₄	—	2	1	no	—
104	C₂×D₄	—	2	1	no	—
105	SD₁₆	—	4	2	no	—
106	C₂×C₈	—	2	1	no	—
107	C₂×C₈	—	19	1	no	—
108	C₂×C₈	—	19	1	no	—
109	C₂×C₈	—	38	1	no	—
110	C₂×C₈	—	38	1	no	—
111	C₄⋊C₄	—	2	1	no	—
112	C₄⋊C₄	—	38	1	no	—
113	C₄⋊C₄	—	38	1	no	—
114	C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
115	C₄²	—	2	1	no	—
116	C₄²	C₂²×D₁₉	1	1	yes	characteristic
117	C₂³	—	4	1	no	—
118	Q₈	—	2	1	no	—
119	Q₈	—	2	1	no	—
120	Q₈	—	152	1	no	—
121	D₄	—	4	1	no	—
122	D₄	—	4	1	no	—
123	D₄	—	4	1	no	—
124	D₄	—	4	1	no	—
125	D₄	—	8	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	76	1	no	—
129	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
130	C₂×C₄	#64543	1	1	yes	characteristic
131	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
132	C₈	—	4	1	no	—
133	C₈	—	38	1	no	—
134	C₈	—	38	1	no	—
135	C₈	—	76	1	no	—
136	C₈	—	76	1	no	—
137	C₂²	—	8	1	no	—
138	C₂²	—	8	1	no	—
139	C₂²	—	8	1	no	—
140	C₂²	#10597385	1	1	yes	characteristic
141	C₄	—	2	1	no	—
142	C₄	—	4	1	no	—
143	C₄	—	4	1	no	—
144	C₄	—	152	1	no	—
145	C₄	#10597361	1	1	yes	characteristic
146	C₄	#10597362	1	1	yes	characteristic
147	C₄	#10597378	1	1	yes	characteristic
148	C₄	#10597397	1	1	yes	characteristic
149	C₂	—	16	1	no	—
150	C₂	#11926764	1	1	yes	characteristic
151	C₂	#11926788	1	1	yes	characteristic
152	C₂	#11926812	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926890

C₂

yes

maximal, characteristic

#11926839

C₂

yes

maximal, characteristic, complemented

#11926675

C₂

yes

maximal, characteristic, complemented

#11926296

C₂

yes

maximal, characteristic, complemented

#11926292

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

#10597315

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#102

—

—

—

—

—

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

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

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1698

—

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

—

#477

—

#460

D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×SD₁₆

—

C₄⋊Q₈

—

#127

C₂×D₁₉

yes

characteristic

C₄×Q₈

C₂×D₁₉

yes

characteristic

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₁₉

#1698

yes

characteristic, complemented, Sylow

100

C₂×Q₈

—

101

C₂×Q₈

C₂²⋊D₁₉

yes

characteristic

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

SD₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

115

C₄²

—

116

C₄²

C₂²×D₁₉

yes

characteristic

117

C₂³

—

118

Q₈

—

119

Q₈

—

120

Q₈

—

152

—

121

D₄

—

122

D₄

—

123

D₄

—

124

D₄

—

125

D₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

D₄×D₁₉

yes

characteristic

130

C₂×C₄

#64543

yes

characteristic

131

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

#10597385

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

152

—

145

C₄

#10597361

yes

characteristic

146

C₄

#10597362

yes

characteristic

147

C₄

#10597378

yes

characteristic

148

C₄

#10597397

yes

characteristic

149

C₂

—

150

C₂

#11926764

yes

characteristic

151

C₂

#11926788

yes

characteristic

152

C₂

#11926812

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	#1698
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. #11926839	C₂	semidirect
3. #11926675	C₂	semidirect
4. #11926296	C₂	semidirect
5. #11926292	C₂	semidirect
99. C₁₉	#1698	semidirect

H ≅ G/N

type

2. #11926839

C₂

semidirect

3. #11926675

C₂

semidirect

4. #11926296

C₂

semidirect

5. #11926292

C₂

semidirect

99. C₁₉

#1698

semidirect

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

subgroup	index
#11926890	2
#11926839	2
#11926675	2
#11926296	2
#11926292	2
#11926288	2
C₁₉×#460	2
#1698	19

subgroup

index

C₁₉×#460

Subgroups — #14563173

Conjugacy classes of subgroups

Complements

Maximal subgroups