Group #18069172 — subgroups

Subgroups — #18069172

Order 4864.

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

normal subgroups only

This group has 188 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	#14561575	C₂	1	2	yes	maximal
2	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₂×C₄×Q₈×C₁₉	C₄	1	1	yes	characteristic
5	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
6	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
7	C₁₉×#336	—	2	2	no	—
8	C₂²×Q₈×C₁₉	C₈	1	1	yes	characteristic
9	C₂²×C₈×C₁₉	—	2	1	no	—
10	C₂²×C₈×C₁₉	D₄	1	2	yes	—
11	C₄×Q₈×C₁₉	—	4	1	no	—
12	C₄×Q₈×C₁₉	—	4	1	no	—
13	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
14	C₂×C₄⋊C₄×C₁₉	C₈	1	1	yes	characteristic
15	C₂×C₄²×C₁₉	—	2	1	no	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	C₁₉×#97	—	4	1	no	—
19	C₂×C₁₉⋊C₁₆	—	4	2	no	—
20	C₂×Q₈×C₁₉	—	4	2	no	—
21	C₂×Q₈×C₁₉	—	4	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	—	2	1	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₂×C₈×C₁₉	—	4	1	no	—
30	C₂×C₈×C₁₉	—	4	1	no	—
31	C₂×C₈×C₁₉	—	4	2	no	—
32	C₄⋊C₄×C₁₉	—	4	1	no	—
33	C₄⋊C₄×C₁₉	—	4	2	no	—
34	C₄²×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	C₄²×C₁₉	—	4	1	no	—
37	C₄²×C₁₉	—	4	1	no	—
38	C₁₉⋊C₁₆	—	8	2	no	—
39	#7061	—	19	1	no	maximal, Sylow
40	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
41	Q₈×C₁₉	—	4	2	no	—
42	Q₈×C₁₉	—	4	2	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	1	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	—	2	1	no	—
47	C₂×C₄×C₁₉	—	2	1	no	—
48	C₂×C₄×C₁₉	—	2	2	no	—
49	C₂×C₄×C₁₉	—	4	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	—	4	1	no	—
52	C₂×C₄×C₁₉	—	4	1	no	—
53	C₂×C₄×C₁₉	—	4	2	no	—
54	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
55	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
56	C₈×C₁₉	—	4	2	no	—
57	C₈×C₁₉	—	4	2	no	—
58	#1985	D₁₉	1	1	yes	characteristic
59	#1322	—	19	2	no	—
60	C₂²×C₁₉	—	2	1	no	—
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	#323	1	1	yes	characteristic
63	C₂²×C₁₉	#350	1	2	yes	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	—	4	1	no	—
66	C₄×C₁₉	—	4	2	no	—
67	C₄×C₁₉	—	4	1	no	—
68	C₄×C₁₉	—	8	1	no	—
69	C₄×C₁₉	#354	1	1	yes	characteristic
70	C₄×C₁₉	#356	1	1	yes	characteristic
71	C₂×C₄×Q₈	Dic₁₉	1	1	yes	characteristic
72	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
73	C₂×#97	Dic₁₉	1	1	yes	characteristic
74	C₂²⋊C₁₆	—	38	2	no	—
75	#336	—	2	2	no	—
76	C₂×C₁₉	—	2	2	no	—
77	C₂×C₁₉	#1315	1	1	yes	characteristic
78	C₂×C₁₉	#1319	1	1	yes	characteristic
79	C₂×C₁₉	#1320	1	1	yes	characteristic
80	C₂²×Q₈	C₁₉⋊C₈	1	1	yes	characteristic
81	C₂²×C₈	—	2	1	no	—
82	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
83	C₄×Q₈	—	4	1	no	—
84	C₄×Q₈	—	4	1	no	—
85	C₂×C₄⋊C₄	—	2	1	no	—
86	C₂×C₄⋊C₄	C₁₉⋊C₈	1	1	yes	characteristic
87	C₂×C₄²	—	2	1	no	—
88	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
89	C₂×C₁₆	—	76	2	no	—
90	C₄⋊C₈	—	4	1	no	—
91	#97	—	4	1	no	—
92	C₁₉	#7061	1	1	yes	characteristic, complemented, Sylow
93	C₂×Q₈	—	4	2	no	—
94	C₂×Q₈	—	4	1	no	—
95	C₂²×C₄	—	2	1	no	—
96	C₂²×C₄	—	2	1	no	—
97	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
98	C₂²×C₄	#64520	1	1	yes	characteristic
99	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	2	2	no	—
102	C₂×C₈	—	4	1	no	—
103	C₂×C₈	—	4	1	no	—
104	C₂×C₈	—	4	2	no	—
105	C₄⋊C₄	—	4	1	no	—
106	C₄⋊C₄	—	4	2	no	—
107	C₄²	—	2	1	no	—
108	C₄²	—	2	1	no	—
109	C₄²	—	4	1	no	—
110	C₄²	—	4	1	no	—
111	C₁₆	—	152	2	no	—
112	C₂³	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
113	Q₈	—	4	2	no	—
114	Q₈	—	4	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	2	2	no	—
118	C₂×C₄	—	2	2	no	—
119	C₂×C₄	—	2	1	no	—
120	C₂×C₄	—	2	1	no	—
121	C₂×C₄	—	4	1	no	—
122	C₂×C₄	—	4	1	no	—
123	C₂×C₄	—	4	1	no	—
124	C₂×C₄	—	4	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	#10597290	1	1	yes	characteristic
127	C₂×C₄	#10597291	1	1	yes	characteristic
128	C₈	—	4	2	no	—
129	C₈	—	4	2	no	—
130	C₂²	—	2	1	no	—
131	C₂²	—	2	1	no	—
132	C₂²	#11926268	1	1	yes	characteristic
133	C₂²	#11926328	1	2	yes	—
134	C₄	—	2	1	no	—
135	C₄	—	4	1	no	—
136	C₄	—	4	2	no	—
137	C₄	—	4	1	no	—
138	C₄	—	8	1	no	—
139	C₄	#11926339	1	1	yes	characteristic
140	C₄	#11926343	1	1	yes	characteristic
141	C₂	—	2	2	no	—
142	C₂	#14561561	1	1	yes	characteristic
143	C₂	#14561569	1	1	yes	characteristic
144	C₂	#14561571	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561575

C₂

yes

maximal

C₁₉×#1985

C₂

yes

maximal, characteristic

C₂²⋊(C₁₉⋊C₁₆)

—

C₂×C₄×Q₈×C₁₉

C₄

yes

characteristic

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₁₉×#97

C₄

yes

characteristic

C₁₉×#336

—

C₂²×Q₈×C₁₉

C₈

yes

characteristic

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₈

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×#97

—

C₂×C₁₉⋊C₁₆

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₁₉⋊C₁₆

—

#7061

—

maximal, Sylow

C₂³×C₁₉

C₂²⋊C₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

#1985

D₁₉

yes

characteristic

#1322

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₂²×C₁₉

#350

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₄×Q₈

Dic₁₉

yes

characteristic

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

C₂×#97

Dic₁₉

yes

characteristic

C₂²⋊C₁₆

—

#336

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₁₉⋊C₈

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂²⋊D₁₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₁₉⋊C₈

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

—

C₄⋊C₈

—

#97

—

C₁₉

#7061

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂²×C₄

#64520

yes

characteristic

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄²

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₁₆

—

152

—

112

C₂³

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

113

Q₈

—

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

#10597290

yes

characteristic

127

C₂×C₄

#10597291

yes

characteristic

128

C₈

—

129

C₈

—

130

C₂²

—

131

C₂²

—

132

C₂²

#11926268

yes

characteristic

133

C₂²

#11926328

yes

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

#11926339

yes

characteristic

140

C₄

#11926343

yes

characteristic

141

C₂

—

142

C₂

#14561561

yes

characteristic

143

C₂

#14561569

yes

characteristic

144

C₂

#14561571

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597291
commutator	C₂²×C₄×C₁₉	C₂×C₈
Frattini	C₂×C₄⋊C₈	C₂×D₁₉
Fitting	C₁₉×#1985	C₂
socle	C₂²×C₁₉	#323
prime radical	C₂³×C₁₉	C₂²⋊C₈
cosocle	C₂×C₁₉×C₄⋊C₈	C₂²
hypercenter	#1985	D₁₉
hypocenter	C₁₉	#7061
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1985

subgroup

G/H

center

C₂×C₄

#10597291

commutator

C₂²×C₄×C₁₉

C₂×C₈

Frattini

C₂×C₄⋊C₈

C₂×D₁₉

Fitting

C₁₉×#1985

C₂

socle

C₂²×C₁₉

#323

prime radical

C₂³×C₁₉

C₂²⋊C₈

cosocle

C₂×C₁₉×C₄⋊C₈

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈ ◁ #1985

N	H ≅ G/N	type
92. C₁₉	#7061	semidirect

H ≅ G/N

type

92. C₁₉

#7061

semidirect

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

subgroup	index
#14561575	2
C₁₉×#1985	2
#7061	19

subgroup

index

#14561575

C₁₉×#1985

#7061

Subgroups — #18069172

Conjugacy classes of subgroups

Complements

Maximal subgroups