Group #18070261 — subgroups

Subgroups — #18070261

Order 4864.

162 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 91 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×#11926374	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#368	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597276	—	2	1	no	—
5	#11926378	—	2	1	no	—
6	#11926378	C₄	1	2	yes	—
7	C₂×C₁₉⋊C₃₂	—	2	1	no	—
8	#11926374	—	2	1	no	—
9	#11926374	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	—
14	C₂×M₁₆×C₁₉	—	4	1	no	—
15	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
16	C₂×#64520	—	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	#10597276	—	2	2	no	—
26	#10597276	—	4	1	no	—
27	C₁₉⋊C₃₂	—	2	2	no	—
28	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
29	M₁₆×C₁₉	—	4	2	no	—
30	M₁₆×C₁₉	—	8	1	no	—
31	C₂×C₈×C₁₉	—	8	1	no	—
32	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
36	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
37	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
38	#64520	—	4	2	no	—
39	#64520	—	8	1	no	—
40	C₂×C₁₉⋊C₈	—	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	#7479	—	19	1	no	maximal, Sylow
46	C₂³×C₁₉	Q₃₂	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	SD₃₂	1	1	yes	characteristic
53	C₈×C₁₉	—	8	2	no	—
54	C₈×C₁₉	#95	1	1	yes	characteristic
55	C₈×C₁₉	#103	1	1	yes	characteristic
56	C₈×C₁₉	#103	1	1	yes	characteristic
57	C₈×C₁₉	#106	1	1	yes	characteristic
58	C₁₉⋊C₈	—	8	2	no	—
59	C₂×M₆₄	—	19	1	no	—
60	C₂×#368	—	19	1	no	—
61	C₂×#368	D₁₉	1	1	yes	characteristic
62	C₂²×C₁₉	—	4	1	no	—
63	C₂²×C₁₉	#358	1	1	yes	characteristic
64	C₂²×C₁₉	#358	1	1	yes	characteristic
65	C₂²×C₁₉	#366	1	1	yes	characteristic
66	C₄×C₁₉	#340	1	1	yes	characteristic
67	C₄×C₁₉	#357	1	1	yes	characteristic
68	C₄×C₁₉	#357	1	1	yes	characteristic
69	C₄×C₁₉	#367	1	1	yes	characteristic
70	C₂²×C₁₆	C₂×D₁₉	1	1	yes	characteristic
71	C₂×#108	—	2	1	no	—
72	C₂×#108	—	38	1	no	—
73	M₆₄	—	19	2	no	—
74	M₆₄	—	38	1	no	—
75	C₂×C₃₂	—	38	1	no	—
76	#368	—	2	1	no	—
77	#368	—	19	2	no	—
78	#368	—	38	1	no	—
79	#368	Dic₁₉	1	2	yes	—
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	—	2	1	no	—
82	C₂×C₁₉	—	2	1	no	—
83	C₂×C₁₉	#1380	1	1	yes	characteristic
84	C₂×M₁₆	—	4	1	no	—
85	C₂×M₁₆	—	76	1	no	—
86	C₂²×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
87	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
88	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
89	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
90	C₂×C₁₆	D₇₆	1	1	yes	characteristic
91	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
92	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
93	#108	—	2	2	no	—
94	#108	—	4	1	no	—
95	#108	—	38	2	no	—
96	#108	—	76	1	no	—
97	C₃₂	—	38	2	no	—
98	C₁₉	#7479	1	1	yes	characteristic, complemented, Sylow
99	C₂²×C₄	#64525	1	1	yes	characteristic
100	M₁₆	—	4	2	no	—
101	M₁₆	—	8	1	no	—
102	M₁₆	—	76	2	no	—
103	M₁₆	—	152	1	no	—
104	C₂×C₈	—	8	1	no	—
105	C₂×C₈	—	152	1	no	—
106	C₂×C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
107	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
108	C₂×C₈	#64526	1	1	yes	characteristic
109	C₂×C₈	#64527	1	1	yes	characteristic
110	C₂×C₈	#64528	1	1	yes	characteristic
111	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
112	C₁₆	C₄×Dic₁₉	1	1	yes	characteristic
113	C₁₆	Dic₁₉⋊C₄	1	1	yes	characteristic
114	C₁₆	C₄⋊Dic₁₉	1	1	yes	characteristic
115	C₁₆	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
116	C₂³	#10597286	1	1	yes	characteristic
117	C₂×C₄	#10597264	1	1	yes	characteristic
118	C₂×C₄	#10597266	1	1	yes	characteristic
119	C₂×C₄	#10597283	1	1	yes	characteristic
120	C₂×C₄	#10597284	1	1	yes	characteristic
121	C₂×C₄	#10597285	1	1	yes	characteristic
122	C₂×C₄	#10597289	1	1	yes	characteristic
123	C₈	—	8	2	no	—
124	C₈	—	152	2	no	—
125	C₈	#10597265	1	1	yes	characteristic
126	C₈	#10597267	1	1	yes	characteristic
127	C₈	C₁₉⋊#95	1	1	yes	characteristic
128	C₈	#10597292	1	1	yes	characteristic
129	C₂²	—	4	1	no	—
130	C₂²	#11926347	1	1	yes	characteristic
131	C₂²	#11926348	1	1	yes	characteristic
132	C₂²	#11926369	1	1	yes	characteristic
133	C₄	#11926306	1	1	yes	characteristic
134	C₄	#11926344	1	1	yes	characteristic
135	C₄	#11926345	1	1	yes	characteristic
136	C₄	#11926371	1	1	yes	characteristic
137	C₂	—	2	1	no	—
138	C₂	—	2	1	no	—
139	C₂	—	2	1	no	—
140	C₂	#14561726	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926378

C₂

yes

maximal, characteristic

C₂×#11926374

C₂

yes

maximal, characteristic

C₂×C₁₉×#368

C₂

yes

maximal, characteristic

C₂×#10597276

—

#11926378

—

#11926378

C₄

yes

—

C₂×C₁₉⋊C₃₂

—

#11926374

—

#11926374

C₄

yes

—

C₂²×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#108

—

C₁₉×#368

—

C₁₉×#368

C₄

yes

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×#64520

—

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

—

#10597276

—

#10597276

—

C₁₉⋊C₃₂

—

C₂²×C₄×C₁₉

D₈

yes

characteristic

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

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

C₄²

yes

characteristic

C₁₆×C₁₉

C₂²⋊C₄

yes

characteristic

C₁₆×C₁₉

C₄⋊C₄

yes

characteristic

C₁₆×C₁₉

C₄⋊C₄

yes

characteristic

#7479

—

maximal, Sylow

C₂³×C₁₉

Q₃₂

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

SD₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

C₂×M₆₄

—

C₂×#368

—

C₂×#368

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂²×C₁₆

C₂×D₁₉

yes

characteristic

C₂×#108

—

C₂×#108

—

M₆₄

—

M₆₄

—

C₂×C₃₂

—

—

—

—

Dic₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1380

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₉

yes

characteristic

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

—

—

—

—

C₃₂

—

C₁₉

#7479

yes

characteristic, complemented, Sylow

C₂²×C₄

#64525

yes

characteristic

100

M₁₆

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

152

—

104

C₂×C₈

—

105

C₂×C₈

—

152

—

106

C₂×C₈

Dic₁₉⋊C₄

yes

characteristic

107

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

108

C₂×C₈

#64526

yes

characteristic

109

C₂×C₈

#64527

yes

characteristic

110

C₂×C₈

#64528

yes

characteristic

111

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

112

C₁₆

C₄×Dic₁₉

yes

characteristic

113

C₁₆

Dic₁₉⋊C₄

yes

characteristic

114

C₁₆

C₄⋊Dic₁₉

yes

characteristic

115

C₁₆

(C₂×D₁₉)⋊C₄

yes

characteristic

116

C₂³

#10597286

yes

characteristic

117

C₂×C₄

#10597264

yes

characteristic

118

C₂×C₄

#10597266

yes

characteristic

119

C₂×C₄

#10597283

yes

characteristic

120

C₂×C₄

#10597284

yes

characteristic

121

C₂×C₄

#10597285

yes

characteristic

122

C₂×C₄

#10597289

yes

characteristic

123

C₈

—

124

C₈

—

152

—

125

C₈

#10597265

yes

characteristic

126

C₈

#10597267

yes

characteristic

127

C₈

C₁₉⋊#95

yes

characteristic

128

C₈

#10597292

yes

characteristic

129

C₂²

—

130

C₂²

#11926347

yes

characteristic

131

C₂²

#11926348

yes

characteristic

132

C₂²

#11926369

yes

characteristic

133

C₄

#11926306

yes

characteristic

134

C₄

#11926344

yes

characteristic

135

C₄

#11926345

yes

characteristic

136

C₄

#11926371

yes

characteristic

137

C₂

—

138

C₂

—

139

C₂

—

140

C₂

#14561726

yes

characteristic

	subgroup	G/H
center	C₄	#11926344
commutator	C₁₆×C₁₉	C₄²
Frattini	C₂²×C₁₆	C₂×D₁₉
Fitting	C₂×C₁₉×#368	C₂
socle	C₂×C₁₉	#1380
prime radical	C₂³×C₁₉	Q₃₂
cosocle	C₂²×C₁₆×C₁₉	C₂²
hypercenter	C₂×#368	D₁₉
hypocenter	C₁₉	#7479
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×#368

subgroup

G/H

center

C₄

#11926344

commutator

C₁₆×C₁₉

C₄²

Frattini

C₂²×C₁₆

C₂×D₁₉

Fitting

C₂×C₁₉×#368

C₂

socle

C₂×C₁₉

#1380

prime radical

C₂³×C₁₉

Q₃₂

cosocle

C₂²×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

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

UCS

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

N	H ≅ G/N	type
98. C₁₉	#7479	semidirect

H ≅ G/N

type

98. C₁₉

#7479

semidirect

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

subgroup	index
C₂×#11926378	2
C₂×#11926374	2
C₂×C₁₉×#368	2
#7479	19

subgroup

index

C₂×#11926378

C₂×#11926374

C₂×C₁₉×#368

#7479

Subgroups — #18070261

Conjugacy classes of subgroups

Complements

Maximal subgroups