Group #18070258 — subgroups

Subgroups — #18070258

Order 4864.

174 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 95 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	C₂×#11926378	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926370	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#368	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597275	—	2	1	no	—
5	#11926378	—	2	1	no	—
6	#11926378	C₄	1	2	yes	complemented
7	C₂×C₁₉⋊C₃₂	—	2	1	no	—
8	#11926370	—	2	1	no	—
9	#11926370	C₄	1	2	yes	—
10	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#108	—	2	1	no	—
12	C₁₉×#368	—	2	1	no	—
13	C₁₉×#368	C₄	1	2	yes	complemented
14	C₂×M₁₆×C₁₉	—	4	1	no	—
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₉	—	4	1	no	—
17	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₁₆×C₁₉	Q₈	1	1	yes	characteristic
23	C₁₉×#108	—	2	2	no	—
24	C₁₉×#108	—	4	1	no	—
25	#10597275	—	2	2	no	—
26	#10597275	—	4	1	no	—
27	C₁₉⋊C₃₂	—	2	2	no	—
28	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
29	C₂²×Dic₁₉	—	8	1	no	—
30	M₁₆×C₁₉	—	4	2	no	—
31	M₁₆×C₁₉	—	8	1	no	—
32	C₂×C₈×C₁₉	—	8	1	no	—
33	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
37	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
38	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
39	C₄⋊Dic₁₉	—	4	2	no	—
40	C₄⋊Dic₁₉	—	8	1	no	—
41	C₁₆×C₁₉	C₄²	1	1	yes	characteristic
42	C₁₆×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
43	C₁₆×C₁₉	C₄⋊C₄	1	1	yes	characteristic
44	C₁₆×C₁₉	C₄⋊C₄	1	1	yes	characteristic
45	#7478	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	SD₃₂	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
50	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
51	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
52	C₂×C₄×C₁₉	Q₃₂	1	1	yes	characteristic
53	C₂×Dic₁₉	—	8	2	no	—
54	C₂×Dic₁₉	—	16	2	no	—
55	C₈×C₁₉	—	8	2	no	—
56	C₈×C₁₉	#95	1	1	yes	characteristic
57	C₈×C₁₉	#103	1	1	yes	characteristic
58	C₈×C₁₉	#103	1	1	yes	characteristic
59	C₈×C₁₉	#106	1	1	yes	characteristic
60	C₂×M₆₄	—	19	1	no	—
61	C₂×#368	D₁₉	1	1	yes	characteristic
62	C₂×#366	—	19	1	no	—
63	C₂²×C₁₉	—	2	1	no	—
64	C₂²×C₁₉	—	2	1	no	—
65	C₂²×C₁₉	#357	1	1	yes	characteristic
66	C₂²×C₁₉	#358	1	1	yes	characteristic
67	C₂²×C₁₉	#367	1	1	yes	characteristic
68	C₄×C₁₉	#340	1	1	yes	characteristic
69	C₄×C₁₉	#357	1	1	yes	characteristic
70	C₄×C₁₉	#358	1	1	yes	characteristic
71	C₄×C₁₉	#366	1	1	yes	characteristic
72	Dic₁₉	—	16	2	no	—
73	C₂²×C₁₆	C₂×D₁₉	1	1	yes	characteristic
74	C₂×#108	—	2	1	no	—
75	C₂×#107	—	38	1	no	—
76	M₆₄	—	19	2	no	—
77	M₆₄	—	38	1	no	—
78	C₂×C₃₂	—	38	1	no	—
79	#368	—	2	1	no	—
80	#368	Dic₁₉	1	2	yes	complemented
81	#366	—	19	2	no	—
82	#366	—	38	1	no	—
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	—	2	1	no	—
85	C₂×C₁₉	#1380	1	1	yes	characteristic
86	C₂×C₁₉	#1419	1	1	yes	characteristic
87	C₂×C₁₉	#1420	1	1	yes	characteristic
88	C₂×M₁₆	—	4	1	no	—
89	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
90	C₂×C₄⋊C₄	—	76	1	no	—
91	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
92	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
93	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
94	C₂×C₁₆	D₇₆	1	1	yes	characteristic
95	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
96	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
97	#108	—	2	2	no	—
98	#108	—	4	1	no	—
99	#107	—	38	2	no	—
100	#107	—	76	1	no	—
101	C₃₂	—	38	2	no	—
102	C₁₉	#7478	1	1	yes	characteristic, complemented, Sylow
103	C₂²×C₄	—	152	1	no	—
104	C₂²×C₄	#64525	1	1	yes	characteristic
105	M₁₆	—	4	2	no	—
106	M₁₆	—	8	1	no	—
107	C₂×C₈	—	8	1	no	—
108	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
109	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
110	C₂×C₈	#64526	1	1	yes	characteristic
111	C₂×C₈	#64527	1	1	yes	characteristic
112	C₂×C₈	#64528	1	1	yes	characteristic
113	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
114	C₄⋊C₄	—	76	2	no	—
115	C₄⋊C₄	—	152	1	no	—
116	C₁₆	C₄×Dic₁₉	1	1	yes	characteristic
117	C₁₆	Dic₁₉⋊C₄	1	1	yes	characteristic
118	C₁₆	C₄⋊Dic₁₉	1	1	yes	characteristic
119	C₁₆	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
120	C₂³	#10597285	1	1	yes	characteristic
121	C₂×C₄	—	304	2	no	—
122	C₂×C₄	—	152	2	no	—
123	C₂×C₄	#10597264	1	1	yes	characteristic
124	C₂×C₄	#10597266	1	1	yes	characteristic
125	C₂×C₄	#10597283	1	1	yes	characteristic
126	C₂×C₄	#10597284	1	1	yes	characteristic
127	C₂×C₄	#10597286	1	1	yes	characteristic
128	C₂×C₄	#10597289	1	1	yes	characteristic
129	C₈	—	8	2	no	—
130	C₈	#10597265	1	1	yes	characteristic
131	C₈	#10597267	1	1	yes	characteristic
132	C₈	C₁₉⋊#95	1	1	yes	characteristic
133	C₈	#10597292	1	1	yes	characteristic
134	C₂²	—	2	1	no	—
135	C₂²	—	2	1	no	—
136	C₂²	#11926344	1	1	yes	characteristic
137	C₂²	#11926348	1	1	yes	characteristic
138	C₂²	#11926371	1	1	yes	characteristic
139	C₄	—	304	2	no	—
140	C₄	#11926306	1	1	yes	characteristic
141	C₄	#11926345	1	1	yes	characteristic
142	C₄	#11926347	1	1	yes	characteristic
143	C₄	#11926369	1	1	yes	characteristic
144	C₂	—	2	1	no	—
145	C₂	—	2	1	no	—
146	C₂	#14561726	1	1	yes	characteristic
147	C₂	#14561824	1	1	yes	characteristic
148	C₂	#14561827	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926378

C₂

yes

maximal, characteristic

C₂×#11926370

C₂

yes

maximal, characteristic

C₂×C₁₉×#368

C₂

yes

maximal, characteristic

C₂×#10597275

—

#11926378

—

#11926378

C₄

yes

complemented

C₂×C₁₉⋊C₃₂

—

#11926370

—

#11926370

C₄

yes

—

C₂²×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#108

—

C₁₉×#368

—

C₁₉×#368

C₄

yes

complemented

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

Q₈

yes

characteristic

C₁₉×#108

—

C₁₉×#108

—

#10597275

—

#10597275

—

C₁₉⋊C₃₂

—

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×Dic₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂×C₈×C₁₉

Q₁₆

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₁₆×C₁₉

C₄²

yes

characteristic

C₁₆×C₁₉

C₂²⋊C₄

yes

characteristic

C₁₆×C₁₉

C₄⋊C₄

yes

characteristic

C₁₆×C₁₉

C₄⋊C₄

yes

characteristic

#7478

—

maximal, Sylow

C₂³×C₁₉

SD₃₂

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₂×C₄×C₁₉

Q₃₂

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×M₆₄

—

C₂×#368

D₁₉

yes

characteristic

C₂×#366

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

C₂²×C₁₆

C₂×D₁₉

yes

characteristic

C₂×#108

—

C₂×#107

—

M₆₄

—

M₆₄

—

C₂×C₃₂

—

#368

—

#368

Dic₁₉

yes

complemented

#366

—

#366

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₁₆

Dic₃₈

yes

characteristic

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

D₇₆

yes

characteristic

C₂×C₁₆

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

—

—

—

100

#107

—

101

C₃₂

—

102

C₁₉

#7478

yes

characteristic, complemented, Sylow

103

C₂²×C₄

—

152

—

104

C₂²×C₄

#64525

yes

characteristic

105

M₁₆

—

106

M₁₆

—

107

C₂×C₈

—

108

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

109

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

110

C₂×C₈

#64526

yes

characteristic

111

C₂×C₈

#64527

yes

characteristic

112

C₂×C₈

#64528

yes

characteristic

113

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

114

C₄⋊C₄

—

115

C₄⋊C₄

—

152

—

116

C₁₆

C₄×Dic₁₉

yes

characteristic

117

C₁₆

Dic₁₉⋊C₄

yes

characteristic

118

C₁₆

C₄⋊Dic₁₉

yes

characteristic

119

C₁₆

(C₂×D₁₉)⋊C₄

yes

characteristic

120

C₂³

#10597285

yes

characteristic

121

C₂×C₄

—

304

—

122

C₂×C₄

—

152

—

123

C₂×C₄

#10597264

yes

characteristic

124

C₂×C₄

#10597266

yes

characteristic

125

C₂×C₄

#10597283

yes

characteristic

126

C₂×C₄

#10597284

yes

characteristic

127

C₂×C₄

#10597286

yes

characteristic

128

C₂×C₄

#10597289

yes

characteristic

129

C₈

—

130

C₈

#10597265

yes

characteristic

131

C₈

#10597267

yes

characteristic

132

C₈

C₁₉⋊#95

yes

characteristic

133

C₈

#10597292

yes

characteristic

134

C₂²

—

135

C₂²

—

136

C₂²

#11926344

yes

characteristic

137

C₂²

#11926348

yes

characteristic

138

C₂²

#11926371

yes

characteristic

139

C₄

—

304

—

140

C₄

#11926306

yes

characteristic

141

C₄

#11926345

yes

characteristic

142

C₄

#11926347

yes

characteristic

143

C₄

#11926369

yes

characteristic

144

C₂

—

145

C₂

—

146

C₂

#14561726

yes

characteristic

147

C₂

#14561824

yes

characteristic

148

C₂

#14561827

yes

characteristic

	subgroup	G/H
center	C₂²	#11926344
commutator	C₁₆×C₁₉	C₄²
Frattini	C₂²×C₁₆	C₂×D₁₉
Fitting	C₂×C₁₉×#368	C₂
socle	C₂²×C₁₉	#357
prime radical	C₂³×C₁₉	SD₃₂
cosocle	C₂²×C₁₆×C₁₉	C₂²
hypercenter	C₂×#368	D₁₉
hypocenter	C₁₉	#7478
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×#368

subgroup

G/H

center

C₂²

#11926344

commutator

C₁₆×C₁₉

C₄²

Frattini

C₂²×C₁₆

C₂×D₁₉

Fitting

C₂×C₁₉×#368

C₂

socle

C₂²×C₁₉

#357

prime radical

C₂³×C₁₉

SD₃₂

cosocle

C₂²×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×#368

N	H ≅ G/N	type
6. #11926378	C₄	semidirect
13. C₁₉×#368	C₄	semidirect
80. #368	Dic₁₉	semidirect
102. C₁₉	#7478	semidirect

H ≅ G/N

type

6. #11926378

C₄

semidirect

13. C₁₉×#368

C₄

semidirect

80. #368

Dic₁₉

semidirect

102. C₁₉

#7478

semidirect

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

subgroup	index
C₂×#11926378	2
C₂×#11926370	2
C₂×C₁₉×#368	2
#7478	19

subgroup

index

C₂×#11926378

C₂×#11926370

C₂×C₁₉×#368

#7478

Subgroups — #18070258

Conjugacy classes of subgroups

Complements

Maximal subgroups