Group #18070263 — subgroups

Subgroups — #18070263

Order 4864.

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

normal subgroups only

This group has 166 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×#11926374	C₂	1	1	yes	maximal, characteristic
2	#14565419	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597276	—	2	1	no	—
5	#11926582	—	2	1	no	—
6	#11926374	—	2	1	no	—
7	#11926374	C₄	1	2	yes	complemented
8	#11926372	C₄	1	2	yes	—
9	#11926370	—	2	1	no	—
10	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×M₆₄	—	2	1	no	—
12	C₁₉×M₆₄	C₄	1	2	yes	complemented
13	C₂×C₁₉×C₃₂	—	2	1	no	—
14	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
15	#10597372	—	4	1	no	—
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	#10597276	—	2	2	no	—
24	#10597276	—	4	1	no	—
25	#10597275	—	2	2	no	—
26	#10597274	—	4	1	no	—
27	C₁₉×C₃₂	—	2	2	no	—
28	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
29	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
34	C₂×C₈×C₁₉	Q₁₆	1	1	yes	characteristic
35	C₂²⋊Dic₁₉	—	8	1	no	—
36	C₄⋊Dic₁₉	—	4	2	no	—
37	C₄×Dic₁₉	—	8	1	no	—
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	#7480	—	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	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	D₁₉	1	1	yes	characteristic
60	C₂×#368	—	19	1	no	—
61	#2158	—	19	1	no	—
62	C₂²×C₁₉	—	4	1	no	—
63	C₂²×C₁₉	#357	1	1	yes	characteristic
64	C₂²×C₁₉	#358	1	1	yes	characteristic
65	C₂²×C₁₉	#367	1	1	yes	characteristic
66	C₄×C₁₉	#340	1	1	yes	characteristic
67	C₄×C₁₉	#357	1	1	yes	characteristic
68	C₄×C₁₉	#358	1	1	yes	characteristic
69	C₄×C₁₉	#366	1	1	yes	characteristic
70	Dic₁₉	—	16	2	no	—
71	C₂²×C₁₆	C₂×D₁₉	1	1	yes	characteristic
72	C₂×#108	—	38	1	no	—
73	#427	—	38	1	no	—
74	M₆₄	—	2	1	no	—
75	M₆₄	Dic₁₉	1	2	yes	complemented
76	C₂×C₃₂	—	2	1	no	—
77	#368	—	19	2	no	—
78	#368	—	38	1	no	—
79	#367	—	19	2	no	—
80	#366	—	38	1	no	—
81	C₂×C₁₉	—	2	1	no	—
82	C₂×C₁₉	—	2	1	no	—
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	#1380	1	1	yes	characteristic
85	C₂×M₁₆	—	76	1	no	—
86	C₂²×C₈	D₇₆	1	1	yes	characteristic
87	#117	—	76	1	no	—
88	C₂×C₁₆	Dic₃₈	1	1	yes	characteristic
89	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
90	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
91	C₂×C₁₆	C₂×Dic₁₉	1	1	yes	characteristic
92	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
93	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
94	#108	—	38	2	no	—
95	#108	—	76	1	no	—
96	#107	—	38	2	no	—
97	#106	—	76	1	no	—
98	C₃₂	—	2	2	no	—
99	C₁₉	#7480	1	1	yes	characteristic, complemented, Sylow
100	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
101	M₁₆	—	76	2	no	—
102	M₁₆	—	152	1	no	—
103	C₂×C₈	—	152	1	no	—
104	C₂×C₈	#64516	1	1	yes	characteristic
105	C₂×C₈	#64516	1	1	yes	characteristic
106	C₂×C₈	Dic₇₆	1	1	yes	characteristic
107	C₂×C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
108	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
109	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
110	C₄⋊C₄	—	76	2	no	—
111	C₂²⋊C₄	—	152	1	no	—
112	C₄²	—	152	1	no	—
113	C₁₆	C₄×Dic₁₉	1	1	yes	characteristic
114	C₁₆	Dic₁₉⋊C₄	1	1	yes	characteristic
115	C₁₆	Dic₁₉⋊C₄	1	1	yes	characteristic
116	C₁₆	C₂²⋊Dic₁₉	1	1	yes	characteristic
117	C₂³	#10597257	1	1	yes	characteristic
118	C₂×C₄	—	152	2	no	—
119	C₂×C₄	D₃₀₄	1	1	yes	characteristic
120	C₂×C₄	#10597257	1	1	yes	characteristic
121	C₂×C₄	Dic₁₅₂	1	1	yes	characteristic
122	C₂×C₄	#10597275	1	1	yes	characteristic
123	C₂×C₄	#10597278	1	1	yes	characteristic
124	C₂×C₄	#10597278	1	1	yes	characteristic
125	C₈	—	152	2	no	—
126	C₈	#10597273	1	1	yes	characteristic
127	C₈	#10597273	1	1	yes	characteristic
128	C₈	#10597274	1	1	yes	characteristic
129	C₈	C₁₉⋊#95	1	1	yes	characteristic
130	C₂²	—	4	1	no	—
131	C₂²	#11926346	1	1	yes	characteristic
132	C₂²	#11926349	1	1	yes	characteristic
133	C₂²	#11926372	1	1	yes	characteristic
134	C₄	—	304	2	no	—
135	C₄	#11926307	1	1	yes	characteristic
136	C₄	#11926346	1	1	yes	characteristic
137	C₄	#11926349	1	1	yes	characteristic
138	C₄	#11926370	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	2	1	no	—
141	C₂	—	2	1	no	—
142	C₂	#14561727	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926374

C₂

yes

maximal, characteristic

#14565419

C₂

yes

maximal, characteristic

C₂×C₁₉×M₆₄

C₂

yes

maximal, characteristic

—

—

—

C₄

yes

complemented

#11926372

C₄

yes

—

#11926370

—

C₂²×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×M₆₄

—

C₁₉×M₆₄

C₄

yes

complemented

C₂×C₁₉×C₃₂

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

#10597372

—

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

—

—

—

—

C₁₉×C₃₂

—

C₂²×C₄×C₁₉

D₈

yes

characteristic

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

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#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

#7480

—

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

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

C₂×M₆₄

D₁₉

yes

characteristic

C₂×#368

—

#2158

—

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

—

#427

—

M₆₄

—

M₆₄

Dic₁₉

yes

complemented

C₂×C₃₂

—

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1380

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

D₇₆

yes

characteristic

#117

—

C₂×C₁₆

Dic₃₈

yes

characteristic

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

—

—

—

—

C₃₂

—

C₁₉

#7480

yes

characteristic, complemented, Sylow

100

C₂²×C₄

D₁₅₂

yes

characteristic

101

M₁₆

—

102

M₁₆

—

152

—

103

C₂×C₈

—

152

—

104

C₂×C₈

#64516

yes

characteristic

105

C₂×C₈

#64516

yes

characteristic

106

C₂×C₈

Dic₇₆

yes

characteristic

107

C₂×C₈

C₄⋊Dic₁₉

yes

characteristic

108

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

109

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

152

—

112

C₄²

—

152

—

113

C₁₆

C₄×Dic₁₉

yes

characteristic

114

C₁₆

Dic₁₉⋊C₄

yes

characteristic

115

C₁₆

Dic₁₉⋊C₄

yes

characteristic

116

C₁₆

C₂²⋊Dic₁₉

yes

characteristic

117

C₂³

#10597257

yes

characteristic

118

C₂×C₄

—

152

—

119

C₂×C₄

D₃₀₄

yes

characteristic

120

C₂×C₄

#10597257

yes

characteristic

121

C₂×C₄

Dic₁₅₂

yes

characteristic

122

C₂×C₄

#10597275

yes

characteristic

123

C₂×C₄

#10597278

yes

characteristic

124

C₂×C₄

#10597278

yes

characteristic

125

C₈

—

152

—

126

C₈

#10597273

yes

characteristic

127

C₈

#10597273

yes

characteristic

128

C₈

#10597274

yes

characteristic

129

C₈

C₁₉⋊#95

yes

characteristic

130

C₂²

—

131

C₂²

#11926346

yes

characteristic

132

C₂²

#11926349

yes

characteristic

133

C₂²

#11926372

yes

characteristic

134

C₄

—

304

—

135

C₄

#11926307

yes

characteristic

136

C₄

#11926346

yes

characteristic

137

C₄

#11926349

yes

characteristic

138

C₄

#11926370

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

142

C₂

#14561727

yes

characteristic

	subgroup	G/H
center	C₄	#11926346
commutator	C₁₆×C₁₉	C₄²
Frattini	C₂²×C₁₆	C₂×D₁₉
Fitting	C₂×C₁₉×M₆₄	C₂
socle	C₂×C₁₉	#1380
prime radical	C₂³×C₁₉	SD₃₂
cosocle	C₂²×C₁₆×C₁₉	C₂²
hypercenter	C₂×M₆₄	D₁₉
hypocenter	C₁₉	#7480
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

subgroup

G/H

center

C₄

#11926346

commutator

C₁₆×C₁₉

C₄²

Frattini

C₂²×C₁₆

C₂×D₁₉

Fitting

C₂×C₁₉×M₆₄

C₂

socle

C₂×C₁₉

#1380

prime radical

C₂³×C₁₉

SD₃₂

cosocle

C₂²×C₁₆×C₁₉

C₂²

hypercenter

C₂×M₆₄

D₁₉

hypocenter

C₁₉

#7480

LCS

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

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

N	H ≅ G/N	type
7. #11926374	C₄	semidirect
12. C₁₉×M₆₄	C₄	semidirect
75. M₆₄	Dic₁₉	semidirect
99. C₁₉	#7480	semidirect

H ≅ G/N

type

7. #11926374

C₄

semidirect

12. C₁₉×M₆₄

C₄

semidirect

75. M₆₄

Dic₁₉

semidirect

99. C₁₉

#7480

semidirect

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

subgroup	index
C₂×#11926374	2
#14565419	2
C₂×C₁₉×M₆₄	2
#7480	19

subgroup

index

C₂×#11926374

#14565419

C₂×C₁₉×M₆₄

#7480

Subgroups — #18070263

Conjugacy classes of subgroups

Complements

Maximal subgroups