Group #18076319 — subgroups

Subgroups — #18076319

Order 4864.

486 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 235 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	#14563795	C₂	1	1	yes	maximal, characteristic
2	#14563794	C₂	1	4	yes	maximal
3	C₂×C₈×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1845	C₂	1	1	yes	maximal, characteristic
5	C₂×#10597275	—	2	2	no	—
6	C₂×#10597264	—	2	8	no	—
7	C₂×C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
8	#11926414	C₂²	1	2	yes	—
9	C₈×C₁₉⋊C₈	C₄	1	4	yes	complemented
10	C₂×C₁₉×#107	—	2	2	no	—
11	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#384	C₂²	1	2	yes	—
13	C₂²×C₈×C₁₉	D₄	1	2	yes	—
14	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
16	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₉	—	2	4	no	—
18	C₂×C₄⋊Dic₁₉	—	2	2	no	—
19	C₂²×C₁₉⋊C₈	D₄	1	4	yes	—
20	C₁₉×#107	—	4	4	no	—
21	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₉	Q₈	1	2	yes	—
23	#10597275	—	4	4	no	—
24	#10597264	—	4	16	no	—
25	C₄×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
26	C₄×C₁₉⋊C₈	Q₈	1	4	yes	—
27	C₂²×C₄×C₁₉	—	4	2	no	—
28	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
29	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
30	C₂²×Dic₁₉	—	4	2	no	—
31	C₂×C₈×C₁₉	C₄⋊C₄	1	4	yes	—
32	C₂×C₈×C₁₉	D₈	1	4	yes	—
33	C₂×C₈×C₁₉	Q₁₆	1	4	yes	—
34	C₄⋊C₄×C₁₉	—	4	8	no	—
35	C₄⋊C₄×C₁₉	—	4	4	no	—
36	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₄²×C₁₉	C₂×Q₈	1	2	yes	—
39	C₄⋊Dic₁₉	—	4	8	no	—
40	C₄⋊Dic₁₉	—	4	4	no	—
41	C₂×C₁₉⋊C₈	C₄⋊C₄	1	8	yes	—
42	C₂×C₁₉⋊C₈	D₈	1	8	yes	—
43	C₂×C₁₉⋊C₈	Q₁₆	1	8	yes	—
44	#8818	—	19	1	no	maximal, Sylow
45	C₂³×C₁₉	#127	1	1	yes	characteristic
46	C₂×C₄×C₁₉	—	8	4	no	—
47	C₂×C₄×C₁₉	—	8	2	no	—
48	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₄⋊Q₈	1	2	yes	—
52	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
53	C₂×C₄×C₁₉	C₂×D₈	1	4	yes	—
54	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
55	C₂×C₄×C₁₉	C₂×Q₁₆	1	4	yes	—
56	C₂×Dic₁₉	—	8	4	no	—
57	C₂×Dic₁₉	—	8	2	no	—
58	C₈×C₁₉	#107	1	8	yes	complemented
59	C₁₉⋊C₈	#107	1	16	yes	complemented
60	#1845	—	19	1	no	—
61	#1845	—	19	4	no	—
62	#1845	D₁₉	1	1	yes	characteristic
63	C₂×C₈²	—	19	1	no	—
64	C₂²×C₁₉	#384	1	1	yes	characteristic
65	C₂²×C₁₉	#493	1	2	yes	—
66	C₂²×C₁₉	#493	1	1	yes	characteristic
67	C₂²×C₁₉	#494	1	2	yes	—
68	C₂²×C₁₉	#494	1	1	yes	characteristic
69	C₄×C₁₉	—	16	2	no	—
70	C₄×C₁₉	C₂×#107	1	4	yes	—
71	C₄×C₁₉	C₂×#107	1	2	yes	—
72	C₄×C₁₉	#500	1	2	yes	—
73	C₄×C₁₉	#500	1	4	yes	—
74	Dic₁₉	—	16	2	no	—
75	C₂×#107	—	2	2	no	—
76	C₂×#107	—	38	8	no	—
77	C₂×#107	—	38	2	no	—
78	C₂×C₄×C₈	—	19	2	no	—
79	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
80	#384	—	19	2	no	—
81	#384	C₂×D₁₉	1	2	yes	—
82	C₈²	—	19	4	no	—
83	C₂×C₁₉	#1712	1	1	yes	characteristic
84	C₂×C₁₉	#1713	1	1	yes	characteristic
85	C₂×C₁₉	#1713	1	2	yes	—
86	C₂×C₁₉	#1845	1	2	yes	—
87	C₂×C₁₉	#1845	1	1	yes	characteristic
88	C₂²×C₈	—	19	4	no	—
89	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
90	C₂×C₄⋊C₄	—	2	4	no	—
91	C₂×C₄⋊C₄	—	2	2	no	—
92	C₂×C₄⋊C₄	—	38	4	no	—
93	C₂×C₄⋊C₄	—	38	2	no	—
94	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
95	#107	—	4	4	no	—
96	#107	—	76	16	no	—
97	#107	—	76	4	no	—
98	C₄×C₈	—	19	4	no	—
99	C₄×C₈	—	19	4	no	—
100	C₄×C₈	Dic₃₈	1	2	yes	—
101	C₄×C₈	C₄×D₁₉	1	2	yes	—
102	C₁₉	#8818	1	1	yes	characteristic, complemented, Sylow
103	C₂²×C₄	—	4	2	no	—
104	C₂²×C₄	—	76	2	no	—
105	C₂²×C₄	D₄×D₁₉	1	2	yes	—
106	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
107	C₂×C₈	—	19	8	no	—
108	C₂×C₈	—	19	8	no	—
109	C₂×C₈	—	19	8	no	—
110	C₂×C₈	Dic₁₉⋊C₄	1	4	yes	—
111	C₂×C₈	#64525	1	4	yes	—
112	C₂×C₈	#64528	1	4	yes	—
113	C₄⋊C₄	—	4	4	no	—
114	C₄⋊C₄	—	4	8	no	—
115	C₄⋊C₄	—	76	4	no	—
116	C₄⋊C₄	—	76	8	no	—
117	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
118	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
119	C₄²	Q₈×D₁₉	1	2	yes	—
120	C₂³	#10597386	1	1	yes	characteristic
121	C₂×C₄	—	8	4	no	—
122	C₂×C₄	—	8	2	no	—
123	C₂×C₄	—	152	4	no	—
124	C₂×C₄	—	152	2	no	—
125	C₂×C₄	#10597334	1	2	yes	—
126	C₂×C₄	C₄⋊C₄×D₁₉	1	2	yes	—
127	C₂×C₄	D₈×D₁₉	1	4	yes	—
128	C₂×C₄	Q₁₆×D₁₉	1	4	yes	—
129	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
130	C₂×C₄	C₂×#64525	1	2	yes	—
131	C₂×C₄	C₂×#64528	1	2	yes	—
132	C₂×C₄	#10597390	1	1	yes	characteristic
133	C₈	—	19	16	no	—
134	C₈	#10597264	1	8	yes	complemented
135	C₂²	#11926413	1	1	yes	characteristic
136	C₂²	#11926919	1	2	yes	—
137	C₂²	#11926920	1	1	yes	characteristic
138	C₂²	#11926922	1	2	yes	—
139	C₂²	#11926923	1	1	yes	characteristic
140	C₄	—	16	2	no	—
141	C₄	—	304	2	no	—
142	C₄	#107×D₁₉	1	4	yes	—
143	C₄	C₂×#10597264	1	2	yes	—
144	C₄	#11926947	1	2	yes	—
145	C₄	#11926948	1	4	yes	—
146	C₂	#14563249	1	1	yes	characteristic
147	C₂	#14563251	1	1	yes	characteristic
148	C₂	#14563252	1	2	yes	—
149	C₂	#14563793	1	2	yes	—
150	C₂	#14563794	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563795

C₂

yes

maximal, characteristic

#14563794

C₂

yes

maximal

C₂×C₈×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₁₉×#1845

C₂

yes

maximal, characteristic

C₂×#10597275

—

C₂×#10597264

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

#11926414

C₂²

yes

—

C₈×C₁₉⋊C₈

C₄

yes

complemented

C₂×C₁₉×#107

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#384

C₂²

yes

—

C₂²×C₈×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂²×C₁₉⋊C₈

D₄

yes

—

C₁₉×#107

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

Q₈

yes

—

#10597275

—

#10597264

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

—

C₄×C₁₉⋊C₈

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

D₈

yes

—

C₂×C₈×C₁₉

Q₁₆

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

C₄⋊C₄

yes

—

C₂×C₁₉⋊C₈

D₈

yes

—

C₂×C₁₉⋊C₈

Q₁₆

yes

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊Q₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

yes

C₁₉⋊C₈

yes

—

—

D₁₉

yes

characteristic

C₂×C₈²

—

C₂²×C₁₉

#384

yes

characteristic

C₂²×C₁₉

#493

yes

—

C₂²×C₁₉

#493

yes

characteristic

C₂²×C₁₉

#494

yes

—

C₂²×C₁₉

#494

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₂×#107

yes

—

C₄×C₁₉

C₂×#107

yes

—

C₄×C₁₉

#500

yes

—

C₄×C₁₉

#500

yes

—

Dic₁₉

—

C₂×#107

—

C₂×#107

—

C₂×#107

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

#384

—

#384

C₂×D₁₉

yes

—

C₈²

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#1845

yes

—

C₂×C₁₉

#1845

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₉

yes

—

—

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

Dic₃₈

yes

—

101

C₄×C₈

C₄×D₁₉

yes

—

102

C₁₉

#8818

yes

characteristic, complemented, Sylow

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

D₄×D₁₉

yes

—

106

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

Dic₁₉⋊C₄

yes

—

111

C₂×C₈

#64525

yes

—

112

C₂×C₈

#64528

yes

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄²

C₂×Dic₃₈

yes

characteristic

118

C₄²

C₂×C₄×D₁₉

yes

characteristic

119

C₄²

Q₈×D₁₉

yes

—

120

C₂³

#10597386

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

152

—

124

C₂×C₄

—

152

—

125

C₂×C₄

#10597334

yes

—

126

C₂×C₄

C₄⋊C₄×D₁₉

yes

—

127

C₂×C₄

D₈×D₁₉

yes

—

128

C₂×C₄

Q₁₆×D₁₉

yes

—

129

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

130

C₂×C₄

C₂×#64525

yes

—

131

C₂×C₄

C₂×#64528

yes

—

132

C₂×C₄

#10597390

yes

characteristic

133

C₈

—

134

C₈

#10597264

yes

complemented

135

C₂²

#11926413

yes

characteristic

136

C₂²

#11926919

yes

—

137

C₂²

#11926920

yes

characteristic

138

C₂²

#11926922

yes

—

139

C₂²

#11926923

yes

characteristic

140

C₄

—

141

C₄

—

304

—

142

C₄

#107×D₁₉

yes

—

143

C₄

C₂×#10597264

yes

—

144

C₄

#11926947

yes

—

145

C₄

#11926948

yes

—

146

C₂

#14563249

yes

characteristic

147

C₂

#14563251

yes

characteristic

148

C₂

#14563252

yes

—

149

C₂

#14563793

yes

—

150

C₂

#14563794

yes

characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1845	C₂
socle, prime radical	C₂³×C₁₉	#127
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1845	D₁₉
hypocenter	C₁₉	#8818
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

subgroup

G/H

center

C₂³

#10597386

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1845

C₂

socle, prime radical

C₂³×C₁₉

#127

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

N	H ≅ G/N	type
9. C₈×C₁₉⋊C₈	C₄	semidirect
58. C₈×C₁₉	#107	semidirect
59. C₁₉⋊C₈	#107	semidirect
102. C₁₉	#8818	semidirect
134. C₈	#10597264	semidirect

H ≅ G/N

type

9. C₈×C₁₉⋊C₈

C₄

semidirect

58. C₈×C₁₉

#107

semidirect

59. C₁₉⋊C₈

#107

semidirect

102. C₁₉

#8818

semidirect

134. C₈

#10597264

semidirect

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

subgroup	index
#14563795	2
#14563794	2
C₂×C₈×C₁₉⋊C₈	2
C₁₉×#1845	2
#8818	19

subgroup

index

#14563795

#14563794

C₂×C₈×C₁₉⋊C₈

C₁₉×#1845

#8818

Subgroups — #18076319

Conjugacy classes of subgroups

Complements

Maximal subgroups