Group #14564374 — subgroups

Subgroups — #14564374

Order 2432.

240 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 113 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×#10597274	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597272	C₂	1	1	yes	maximal, characteristic
3	#11926443	C₂	1	2	yes	maximal
4	#11926306	C₂	1	2	yes	maximal
5	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₁₉	—	2	2	no	—
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₁₉×#107	C₄	1	4	yes	complemented
13	C₁₉⋊#95	—	2	2	no	—
14	#10597274	—	2	2	no	—
15	#10597272	—	2	2	no	—
16	C₂²×C₄×C₁₉	—	2	2	no	—
17	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₉	—	2	2	no	—
19	C₂²×Dic₁₉	D₄	1	2	yes	—
20	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₁₉	D₄	1	2	yes	—
22	C₂×C₈×C₁₉	Q₈	1	2	yes	—
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
25	C₄⋊Dic₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	C₄⋊Dic₁₉	—	4	4	no	—
28	C₄×Dic₁₉	—	2	1	no	—
29	C₄×Dic₁₉	—	2	1	no	—
30	C₂×C₁₉⋊C₈	—	2	1	no	—
31	C₂×C₁₉⋊C₈	—	2	1	no	—
32	C₂×C₁₉⋊C₈	Q₈	1	2	yes	—
33	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	—	4	2	no	—
36	C₂×C₄×C₁₉	—	4	2	no	—
37	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
42	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
43	C₂×Dic₁₉	—	2	2	no	—
44	C₂×Dic₁₉	—	2	2	no	—
45	C₂×Dic₁₉	—	2	2	no	—
46	C₂×Dic₁₉	—	4	2	no	—
47	C₂×Dic₁₉	—	4	2	no	—
48	C₂×Dic₁₉	—	4	2	no	—
49	C₈×C₁₉	C₄⋊C₄	1	4	yes	complemented
50	C₁₉⋊C₈	—	2	2	no	—
51	#1943	—	19	1	no	maximal, Sylow
52	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
53	C₂²×C₁₉	#121	1	1	yes	characteristic
54	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
55	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
56	C₂²×C₁₉	#137	1	2	yes	—
57	C₄×C₁₉	—	4	4	no	—
58	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
60	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
61	C₄×C₁₉	#125	1	1	yes	characteristic
62	Dic₁₉	—	4	2	no	—
63	Dic₁₉	—	8	2	no	—
64	C₂×#107	D₁₉	1	1	yes	characteristic
65	C₂×#106	—	19	1	no	—
66	C₂×#97	—	19	1	no	—
67	#389	—	19	2	no	—
68	#340	—	19	2	no	—
69	C₂×C₁₉	#389	1	1	yes	characteristic
70	C₂×C₁₉	#441	1	1	yes	characteristic
71	C₂×C₁₉	#442	1	1	yes	characteristic
72	C₂×C₁₉	#468	1	2	yes	—
73	C₂×C₁₉	#501	1	2	yes	—
74	C₂²×C₈	—	19	1	no	—
75	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
76	C₂×C₄⋊C₄	—	19	2	no	—
77	C₂×C₄⋊C₄	—	38	2	no	—
78	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
79	C₂×C₄²	—	19	1	no	—
80	#107	Dic₁₉	1	4	yes	complemented
81	#106	—	38	2	no	—
82	#97	—	38	2	no	—
83	#95	—	38	2	no	—
84	C₁₉	#1943	1	1	yes	characteristic, complemented, Sylow
85	C₂²×C₄	—	2	2	no	—
86	C₂²×C₄	—	19	2	no	—
87	C₂²×C₄	—	38	2	no	—
88	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
89	C₂×C₈	—	19	2	no	—
90	C₂×C₈	—	38	1	no	—
91	C₂×C₈	—	38	1	no	—
92	C₂×C₈	Dic₃₈	1	2	yes	—
93	C₂×C₈	D₇₆	1	2	yes	—
94	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
95	C₄⋊C₄	—	2	2	no	—
96	C₄⋊C₄	—	38	2	no	—
97	C₄⋊C₄	—	38	2	no	—
98	C₄⋊C₄	—	76	4	no	—
99	C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
100	C₄²	—	38	1	no	—
101	C₄²	—	38	1	no	—
102	C₂³	D₄×D₁₉	1	1	yes	characteristic
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	38	2	no	—
107	C₂×C₄	—	38	2	no	—
108	C₂×C₄	—	38	2	no	—
109	C₂×C₄	—	76	2	no	—
110	C₂×C₄	—	76	2	no	—
111	C₂×C₄	—	76	2	no	—
112	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
113	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
114	C₂×C₄	#64543	1	1	yes	characteristic
115	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
116	C₂×C₄	#64545	1	1	yes	characteristic
117	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
118	C₈	—	38	2	no	—
119	C₈	C₄⋊Dic₁₉	1	4	yes	complemented
120	C₂²	#10597334	1	1	yes	characteristic
121	C₂²	#10597341	1	1	yes	characteristic
122	C₂²	#10597357	1	2	yes	—
123	C₂²	#10597364	1	2	yes	—
124	C₂²	D₄×Dic₁₉	1	1	yes	characteristic
125	C₄	—	4	4	no	—
126	C₄	—	76	2	no	—
127	C₄	—	152	2	no	—
128	C₄	#10597336	1	1	yes	characteristic
129	C₄	#10597343	1	1	yes	characteristic
130	C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
131	C₄	Q₈×Dic₁₉	1	1	yes	characteristic
132	C₂	#11926443	1	1	yes	characteristic
133	C₂	#11926651	1	1	yes	characteristic
134	C₂	#11926656	1	1	yes	characteristic
135	C₂	#11926791	1	2	yes	—
136	C₂	#11926952	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597274

C₂

yes

maximal, characteristic

C₂×#10597272

C₂

yes

maximal, characteristic

#11926443

C₂

yes

maximal

#11926306

C₂

yes

maximal

C₂×C₁₉×#107

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#107

C₄

yes

complemented

C₁₉⋊#95

—

#10597274

—

#10597272

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

D₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

Q₈

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

Q₈

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

C₄⋊C₄

yes

complemented

C₁₉⋊C₈

—

#1943

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

characteristic

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₂²×C₁₉

#137

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₄×Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#125

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×#107

D₁₉

yes

characteristic

C₂×#106

—

C₂×#97

—

#389

—

#340

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#501

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

#107

Dic₁₉

yes

—

—

—

C₁₉

#1943

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

—

C₂×C₈

D₇₆

yes

—

C₂×C₈

C₂×Dic₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₁₉

yes

—

100

C₄²

—

101

C₄²

—

102

C₂³

D₄×D₁₉

yes

characteristic

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

—

112

C₂×C₄

C₂×Dic₃₈

yes

characteristic

113

C₂×C₄

C₂×D₇₆

yes

characteristic

114

C₂×C₄

#64543

yes

characteristic

115

C₂×C₄

Q₈×D₁₉

yes

characteristic

116

C₂×C₄

#64545

yes

characteristic

117

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

118

C₈

—

119

C₈

C₄⋊Dic₁₉

yes

complemented

120

C₂²

#10597334

yes

characteristic

121

C₂²

#10597341

yes

characteristic

122

C₂²

#10597357

yes

—

123

C₂²

#10597364

yes

—

124

C₂²

D₄×Dic₁₉

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

152

—

128

C₄

#10597336

yes

characteristic

129

C₄

#10597343

yes

characteristic

130

C₄

C₂×C₄⋊Dic₁₉

yes

characteristic

131

C₄

Q₈×Dic₁₉

yes

characteristic

132

C₂

#11926443

yes

characteristic

133

C₂

#11926651

yes

characteristic

134

C₂

#11926656

yes

characteristic

135

C₂

#11926791

yes

—

136

C₂

#11926952

yes

—

	subgroup	G/H
center	C₂³	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#107	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#107	D₁₉
hypocenter	C₁₉	#1943
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂³

D₄×D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#107

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
12. C₁₉×#107	C₄	semidirect
49. C₈×C₁₉	C₄⋊C₄	semidirect
80. #107	Dic₁₉	semidirect
84. C₁₉	#1943	semidirect
119. C₈	C₄⋊Dic₁₉	semidirect

H ≅ G/N

type

12. C₁₉×#107

C₄

semidirect

49. C₈×C₁₉

C₄⋊C₄

semidirect

80. #107

Dic₁₉

semidirect

84. C₁₉

#1943

semidirect

119. C₈

C₄⋊Dic₁₉

semidirect

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

subgroup	index
C₂×#10597274	2
C₂×#10597272	2
#11926443	2
#11926306	2
C₂×C₁₉×#107	2
#1943	19

subgroup

index

C₂×C₁₉×#107

Subgroups — #14564374

Conjugacy classes of subgroups

Complements

Maximal subgroups