Group #14565173 — subgroups

Subgroups — #14565173

Order 2432.

254 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10597264	C₂	1	2	yes	maximal
2	C₂×#10597292	C₂	1	2	yes	maximal
3	#11926414	C₂	1	1	yes	maximal, characteristic
4	#11926299	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	—	2	2	no	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
12	C₁₉×#95	—	2	2	no	—
13	#10597292	—	2	4	no	—
14	#10597264	—	2	4	no	—
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂×Q₈×C₁₉	—	2	2	no	—
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	Q₈	1	2	yes	—
19	C₂²×C₄×C₁₉	—	2	1	no	—
20	C₂²×C₄×C₁₉	—	2	1	no	—
21	C₂²×C₄×C₁₉	D₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₄²×C₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	C₄⋊Dic₁₉	—	2	2	no	—
28	C₄⋊Dic₁₉	—	4	4	no	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
32	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
33	Q₈×C₁₉	—	2	4	no	—
34	Q₈×C₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	—	2	2	no	—
36	C₂×C₄×C₁₉	—	2	2	no	—
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	—	4	2	no	—
42	C₂×C₄×C₁₉	Q₁₆	1	4	yes	—
43	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	2	yes	—
47	C₂×Dic₁₉	—	4	2	no	—
48	C₂×Dic₁₉	—	4	4	no	—
49	C₁₉⋊C₈	—	2	4	no	—
50	#2095	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
52	C₂²×C₁₉	#123	1	1	yes	characteristic
53	C₂²×C₁₉	#127	1	1	yes	characteristic
54	C₂²×C₁₉	C₂×Q₁₆	1	2	yes	—
55	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
56	C₄×C₁₉	—	2	4	no	—
57	C₄×C₁₉	—	4	2	no	—
58	C₄×C₁₉	—	8	1	no	—
59	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
60	C₄×C₁₉	#123	1	2	yes	—
61	Dic₁₉	—	8	2	no	—
62	C₂×#107	—	19	2	no	—
63	C₂×#103	—	19	2	no	—
64	#391	D₁₉	1	1	yes	characteristic
65	#384	—	19	1	no	—
66	#336	—	19	1	no	—
67	C₂×C₁₉	#399	1	1	yes	characteristic
68	C₂×C₁₉	#477	1	2	yes	—
69	C₂×C₁₉	#484	1	2	yes	—
70	C₂×C₁₉	#494	1	1	yes	characteristic
71	C₂×C₁₉	#496	1	1	yes	characteristic
72	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
73	C₂²×C₈	—	19	2	no	—
74	C₂×C₄⋊C₄	—	19	2	no	—
75	C₂×C₄⋊C₄	—	38	2	no	—
76	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
77	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
78	#107	—	38	4	no	—
79	#103	—	38	4	no	—
80	#95	—	2	2	no	—
81	C₁₉	#2095	1	1	yes	characteristic, complemented, Sylow
82	C₂×Q₈	—	2	1	no	—
83	C₂×Q₈	—	2	2	no	—
84	C₂×Q₈	—	2	2	no	—
85	C₂×Q₈	Dic₃₈	1	2	yes	—
86	C₂²×C₄	—	2	1	no	—
87	C₂²×C₄	—	2	1	no	—
88	C₂²×C₄	—	38	2	no	—
89	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
91	C₂×C₈	—	19	4	no	—
92	C₂×C₈	—	38	2	no	—
93	C₂×C₈	—	38	2	no	—
94	C₄⋊C₄	—	2	2	no	—
95	C₄⋊C₄	—	38	2	no	—
96	C₄⋊C₄	—	38	2	no	—
97	C₄⋊C₄	—	76	4	no	—
98	C₄²	—	2	2	no	—
99	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
100	Q₈	—	2	4	no	—
101	Q₈	—	4	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	1	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	76	2	no	—
110	C₂×C₄	—	76	4	no	—
111	C₂×C₄	#64528	1	4	yes	—
112	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
113	C₂×C₄	#64541	1	1	yes	characteristic
114	C₂×C₄	D₄×D₁₉	1	2	yes	—
115	C₂×C₄	#64543	1	2	yes	—
116	C₈	—	38	4	no	—
117	C₂²	#10597370	1	1	yes	characteristic
118	C₂²	#10597381	1	1	yes	characteristic
119	C₂²	#10597386	1	1	yes	characteristic
120	C₂²	C₂×#64528	1	2	yes	—
121	C₂²	#10597395	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	—	4	2	no	—
124	C₄	—	8	1	no	—
125	C₄	—	152	2	no	—
126	C₄	#10597324	1	2	yes	—
127	C₄	#10597329	1	2	yes	—
128	C₂	#11926480	1	1	yes	characteristic
129	C₂	#11926839	1	2	yes	—
130	C₂	#11926877	1	2	yes	—
131	C₂	#11926923	1	1	yes	characteristic
132	C₂	#11926934	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597264

C₂

yes

maximal

C₂×#10597292

C₂

yes

maximal

#11926414

C₂

yes

maximal, characteristic

#11926299

C₂

yes

maximal, characteristic

C₁₉×#391

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₁₉×#95

—

#10597292

—

#10597264

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

C₂×D₄

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

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#2095

—

maximal, Sylow

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×Q₁₆

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#123

yes

—

Dic₁₉

—

C₂×#107

—

C₂×#103

—

#391

D₁₉

yes

characteristic

#384

—

#336

—

C₂×C₁₉

#399

yes

characteristic

C₂×C₁₉

#477

yes

—

C₂×C₁₉

#484

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

—

—

—

C₁₉

#2095

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₃₈

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

#64528

yes

—

112

C₂×C₄

C₂×Dic₃₈

yes

characteristic

113

C₂×C₄

#64541

yes

characteristic

114

C₂×C₄

D₄×D₁₉

yes

—

115

C₂×C₄

#64543

yes

—

116

C₈

—

117

C₂²

#10597370

yes

characteristic

118

C₂²

#10597381

yes

characteristic

119

C₂²

#10597386

yes

characteristic

120

C₂²

C₂×#64528

yes

—

121

C₂²

#10597395

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

152

—

126

C₄

#10597324

yes

—

127

C₄

#10597329

yes

—

128

C₂

#11926480

yes

characteristic

129

C₂

#11926839

yes

—

130

C₂

#11926877

yes

—

131

C₂

#11926923

yes

characteristic

132

C₂

#11926934

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#391	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	#391	D₁₉
hypocenter	C₁₉	#2095
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#391

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
81. C₁₉	#2095	semidirect

H ≅ G/N

type

81. C₁₉

#2095

semidirect

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

subgroup	index
C₂×#10597264	2
C₂×#10597292	2
#11926414	2
#11926299	2
C₁₉×#391	2
#2095	19

subgroup

index

C₁₉×#391

Subgroups — #14565173

Conjugacy classes of subgroups

Complements

Maximal subgroups