Group #18069409 — subgroups

Subgroups — #18069409

Order 4864.

242 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 151 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×#11926297	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
4	#11926297	—	2	2	no	—
5	#11926297	C₄	1	4	yes	—
6	C₂²×C₁₆×C₁₉	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₄×C₁₆×C₁₉	—	2	2	no	—
9	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
11	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	—	4	2	no	—
13	C₂×C₁₆×C₁₉	—	2	2	no	—
14	C₂×C₁₆×C₁₉	—	2	2	no	—
15	C₂×C₁₆×C₁₉	C₈	1	4	yes	complemented
16	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₉	D₄	1	2	yes	—
18	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
19	C₄⋊(C₁₉⋊C₈)	—	4	2	no	—
20	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
25	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₁₉	C₂×C₈	1	2	yes	—
28	C₂×C₈×C₁₉	M₁₆	1	2	yes	—
29	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
30	C₄²×C₁₉	SD₁₆	1	2	yes	—
31	C₂×C₁₉⋊C₈	—	4	4	no	—
32	C₂×C₁₉⋊C₈	—	8	2	no	—
33	C₂×C₁₉⋊C₈	—	8	2	no	—
34	C₁₆×C₁₉	—	2	4	no	—
35	#7154	—	19	1	no	maximal, Sylow
36	C₂³×C₁₉	#107	1	1	yes	characteristic
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
39	C₂×C₄×C₁₉	#102	1	2	yes	—
40	C₂×C₄×C₁₉	#103	1	2	yes	—
41	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
42	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
43	C₂×C₄×C₁₉	#108	1	2	yes	—
44	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
45	C₂×C₄×C₁₉	SD₃₂	1	2	yes	—
46	C₂×C₄×C₁₉	Q₃₂	1	1	yes	characteristic
47	C₈×C₁₉	—	2	2	no	—
48	C₈×C₁₉	C₄×C₈	1	1	yes	characteristic
49	C₈×C₁₉	#97	1	1	yes	characteristic
50	C₈×C₁₉	C₂²⋊C₈	1	2	yes	—
51	C₁₉⋊C₈	—	8	4	no	—
52	C₂×C₄×C₁₆	D₁₉	1	1	yes	characteristic
53	C₂×#335	—	19	2	no	—
54	C₂²×C₁₉	#335	1	2	yes	—
55	C₂²×C₁₉	#340	1	1	yes	characteristic
56	C₂²×C₁₉	#366	1	1	yes	characteristic
57	C₂²×C₁₉	#367	1	1	yes	characteristic
58	C₂²×C₁₉	#368	1	2	yes	—
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	#334	1	2	yes	—
61	C₄×C₁₉	#336	1	1	yes	characteristic
62	C₄×C₁₉	#341	1	1	yes	characteristic
63	C₄×C₁₉	#357	1	2	yes	—
64	C₄×C₁₉	#358	1	2	yes	—
65	C₂²×C₁₆	Dic₁₉	1	2	yes	—
66	C₂×C₄⋊C₈	—	38	2	no	—
67	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
68	C₄×C₁₆	—	2	2	no	—
69	#335	—	19	4	no	—
70	#335	—	38	2	no	—
71	C₂×C₁₉	#1277	1	1	yes	characteristic
72	C₂×C₁₉	#1371	1	2	yes	—
73	C₂×C₁₉	#1372	1	2	yes	—
74	C₂×C₁₉	#1380	1	1	yes	characteristic
75	C₂×C₁₉	#1381	1	1	yes	characteristic
76	C₂²×C₈	—	76	2	no	—
77	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
78	C₂²×C₈	C₂×Dic₁₉	1	1	yes	characteristic
79	C₂×C₄²	D₇₆	1	1	yes	characteristic
80	C₂×C₁₆	—	2	2	no	—
81	C₂×C₁₆	—	2	2	no	—
82	C₂×C₁₆	C₁₉⋊C₈	1	4	yes	complemented
83	C₄⋊C₈	—	38	4	no	—
84	C₄⋊C₈	—	76	2	no	—
85	C₄×C₈	C₄×D₁₉	1	2	yes	—
86	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
87	C₁₉	#7154	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄	D₁₅₂	1	1	yes	characteristic
89	C₂²×C₄	Dic₇₆	1	1	yes	characteristic
90	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	76	4	no	—
93	C₂×C₈	—	152	2	no	—
94	C₂×C₈	—	152	2	no	—
95	C₂×C₈	C₂×C₁₉⋊C₈	1	2	yes	—
96	C₂×C₈	#64520	1	2	yes	—
97	C₂×C₈	C₄×Dic₁₉	1	1	yes	characteristic
98	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
99	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
100	C₄²	#64516	1	2	yes	—
101	C₄²	(C₂×D₁₉)⋊C₄	1	2	yes	—
102	C₁₆	—	2	4	no	—
103	C₂³	#10597275	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	D₃₀₄	1	1	yes	characteristic
106	C₂×C₄	#10597257	1	2	yes	—
107	C₂×C₄	Dic₁₅₂	1	1	yes	characteristic
108	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
109	C₂×C₄	#10597273	1	2	yes	—
110	C₂×C₄	#10597274	1	1	yes	characteristic
111	C₂×C₄	#10597276	1	2	yes	—
112	C₂×C₄	#10597278	1	2	yes	—
113	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	152	4	no	—
116	C₈	C₄×C₁₉⋊C₈	1	1	yes	characteristic
117	C₈	#10597260	1	1	yes	characteristic
118	C₈	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
119	C₂²	#11926297	1	2	yes	—
120	C₂²	#11926307	1	1	yes	characteristic
121	C₂²	#11926370	1	1	yes	characteristic
122	C₂²	#11926372	1	1	yes	characteristic
123	C₂²	#11926374	1	2	yes	—
124	C₄	—	2	2	no	—
125	C₄	#11926295	1	2	yes	—
126	C₄	#11926299	1	1	yes	characteristic
127	C₄	#11926309	1	1	yes	characteristic
128	C₄	#11926346	1	2	yes	—
129	C₄	#11926349	1	2	yes	—
130	C₂	#14561470	1	1	yes	characteristic
131	C₂	#14561707	1	2	yes	—
132	C₂	#14561709	1	2	yes	—
133	C₂	#14561727	1	1	yes	characteristic
134	C₂	#14561729	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926297

C₂

yes

maximal

C₂×C₄×C₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

#11926297

—

#11926297

C₄

yes

—

C₂²×C₁₆×C₁₉

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₈

yes

complemented

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₂×C₈×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

M₁₆

yes

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₂×C₄×C₁₉

#106

yes

characteristic

C₂×C₄×C₁₉

#108

yes

—

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

—

C₂×C₄×C₁₉

Q₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₄×C₈

yes

characteristic

C₈×C₁₉

#97

yes

characteristic

C₈×C₁₉

C₂²⋊C₈

yes

—

C₁₉⋊C₈

—

C₂×C₄×C₁₆

D₁₉

yes

characteristic

C₂×#335

—

C₂²×C₁₉

#335

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

#334

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

#358

yes

—

C₂²×C₁₆

Dic₁₉

yes

—

C₂×C₄⋊C₈

—

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₁₆

—

#335

—

#335

—

C₂×C₁₉

#1277

yes

characteristic

C₂×C₁₉

#1371

yes

—

C₂×C₁₉

#1372

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₁₉⋊C₈

yes

complemented

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

C₂²⋊D₁₉

yes

—

C₁₉

#7154

yes

characteristic, complemented, Sylow

C₂²×C₄

D₁₅₂

yes

characteristic

C₂²×C₄

Dic₇₆

yes

characteristic

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

152

—

C₂×C₈

—

152

—

C₂×C₈

C₂×C₁₉⋊C₈

yes

—

C₂×C₈

#64520

yes

—

C₂×C₈

C₄×Dic₁₉

yes

characteristic

C₂×C₈

Dic₁₉⋊C₄

yes

—

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

100

C₄²

#64516

yes

—

101

C₄²

(C₂×D₁₉)⋊C₄

yes

—

102

C₁₆

—

103

C₂³

#10597275

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

D₃₀₄

yes

characteristic

106

C₂×C₄

#10597257

yes

—

107

C₂×C₄

Dic₁₅₂

yes

characteristic

108

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

—

109

C₂×C₄

#10597273

yes

—

110

C₂×C₄

#10597274

yes

characteristic

111

C₂×C₄

#10597276

yes

—

112

C₂×C₄

#10597278

yes

—

113

C₂×C₄

C₁₉⋊#95

yes

characteristic

114

C₈

—

115

C₈

—

152

—

116

C₈

C₄×C₁₉⋊C₈

yes

characteristic

117

C₈

#10597260

yes

characteristic

118

C₈

C₂²⋊(C₁₉⋊C₈)

yes

—

119

C₂²

#11926297

yes

—

120

C₂²

#11926307

yes

characteristic

121

C₂²

#11926370

yes

characteristic

122

C₂²

#11926372

yes

characteristic

123

C₂²

#11926374

yes

—

124

C₄

—

125

C₄

#11926295

yes

—

126

C₄

#11926299

yes

characteristic

127

C₄

#11926309

yes

characteristic

128

C₄

#11926346

yes

—

129

C₄

#11926349

yes

—

130

C₂

#14561470

yes

characteristic

131

C₂

#14561707

yes

—

132

C₂

#14561709

yes

—

133

C₂

#14561727

yes

characteristic

134

C₂

#14561729

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	D₁₅₂
commutator	C₈×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₄×C₁₆×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	#107
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×C₄×C₁₆	D₁₉
hypocenter	C₁₉	#7154
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

subgroup

G/H

center

C₂²×C₄

D₁₅₂

commutator

C₈×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₂×C₄×C₁₆×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

#107

cosocle

C₂×C₄×C₈×C₁₉

C₂²

hypercenter

C₂×C₄×C₁₆

D₁₉

hypocenter

C₁₉

#7154

LCS

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

N	H ≅ G/N	type
15. C₂×C₁₆×C₁₉	C₈	semidirect
82. C₂×C₁₆	C₁₉⋊C₈	semidirect
87. C₁₉	#7154	semidirect

H ≅ G/N

type

15. C₂×C₁₆×C₁₉

C₈

semidirect

82. C₂×C₁₆

C₁₉⋊C₈

semidirect

87. C₁₉

#7154

semidirect

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

subgroup	index
C₂×#11926297	2
C₂×C₄×C₁₆×C₁₉	2
#7154	19

subgroup

index

C₂×#11926297

C₂×C₄×C₁₆×C₁₉

#7154

Subgroups — #18069409

Conjugacy classes of subgroups

Complements

Maximal subgroups