Group #14561658 — subgroups

Subgroups — #14561658

Order 2432.

154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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	#11926480	C₂	1	1	yes	maximal, characteristic
2	#11926268	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#342	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
5	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
7	C₂×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic, complemented
8	C₂×Dic₁₉⋊C₄	—	2	1	no	—
9	C₁₉⋊#95	C₄	1	1	yes	characteristic, complemented
10	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₂⁴×C₁₉	D₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₉	—	4	1	no	—
13	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂²×Dic₁₉	—	2	1	no	—
16	C₂²×Dic₁₉	—	2	1	no	—
17	C₂²⋊C₄×C₁₉	—	2	2	no	—
18	C₂²⋊C₄×C₁₉	—	4	1	no	—
19	C₂²⋊C₄×C₁₉	—	4	1	no	—
20	C₂²⋊Dic₁₉	—	4	2	no	—
21	C₄⋊Dic₁₉	—	4	1	no	—
22	Dic₁₉⋊C₄	—	4	2	no	—
23	C₂×C₁₉⋊C₈	—	4	1	no	—
24	C₂³×C₁₉	—	2	1	no	—
25	C₂³×C₁₉	—	2	1	no	—
26	C₂³×C₁₉	—	4	1	no	—
27	C₂³×C₁₉	—	4	1	no	—
28	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂³×C₁₉	SD₁₆	1	1	yes	characteristic
30	C₂³×C₁₉	Q₁₆	1	1	yes	characteristic
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	4	1	no	—
34	C₂×C₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	—	4	2	no	—
36	C₂×C₄×C₁₉	—	8	1	no	—
37	C₂×C₄×C₁₉	—	8	1	no	—
38	C₂×Dic₁₉	—	2	2	no	—
39	C₂×Dic₁₉	—	4	1	no	—
40	C₂×Dic₁₉	—	4	1	no	—
41	C₂×Dic₁₉	—	4	1	no	—
42	C₂×Dic₁₉	—	4	1	no	—
43	C₂×Dic₁₉	—	4	1	no	—
44	C₁₉⋊C₈	—	8	1	no	—
45	#1352	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	—	2	1	no	—
47	C₂²×C₁₉	—	2	1	no	—
48	C₂²×C₁₉	—	2	1	no	—
49	C₂²×C₁₉	—	2	1	no	—
50	C₂²×C₁₉	—	4	1	no	—
51	C₂²×C₁₉	—	4	1	no	—
52	C₂²×C₁₉	—	4	1	no	—
53	C₂²×C₁₉	—	4	1	no	—
54	C₂²×C₁₉	—	8	1	no	—
55	C₂²×C₁₉	#99	1	1	yes	characteristic
56	C₂²×C₁₉	#103	1	1	yes	characteristic
57	C₂²×C₁₉	#104	1	1	yes	characteristic
58	C₄×C₁₉	—	4	1	no	—
59	C₄×C₁₉	—	4	1	no	—
60	C₄×C₁₉	—	8	2	no	—
61	Dic₁₉	—	4	2	no	—
62	Dic₁₉	—	8	1	no	—
63	#399	—	19	1	no	—
64	#342	D₁₉	1	1	yes	characteristic
65	#323	—	19	1	no	—
66	C₂×C₁₉	—	2	1	no	—
67	C₂×C₁₉	—	2	1	no	—
68	C₂×C₁₉	—	4	1	no	—
69	C₂×C₁₉	—	4	1	no	—
70	C₂×C₁₉	#328	1	1	yes	characteristic
71	C₂×C₁₉	#352	1	1	yes	characteristic
72	C₂×C₁₉	#353	1	1	yes	characteristic
73	C₂×C₄⋊C₄	—	19	1	no	—
74	C₂×C₄⋊C₄	—	38	1	no	—
75	C₂×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₂²⋊C₄	—	38	1	no	—
77	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
78	C₂²⋊C₈	—	38	1	no	—
79	#95	—	19	1	no	—
80	C₁₉	#1352	1	1	yes	characteristic, complemented, Sylow
81	C₂⁴	C₂²⋊D₁₉	1	1	yes	characteristic
82	C₂²×C₄	—	4	1	no	—
83	C₂²×C₄	—	38	1	no	—
84	C₂²×C₄	—	38	1	no	—
85	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
86	C₂²×C₄	D₇₆	1	1	yes	characteristic
87	C₂×C₈	—	76	1	no	—
88	C₄⋊C₄	—	76	1	no	—
89	C₄⋊C₄	—	76	2	no	—
90	C₂²⋊C₄	—	2	2	no	—
91	C₂²⋊C₄	—	4	1	no	—
92	C₂²⋊C₄	—	4	1	no	—
93	C₂²⋊C₄	—	76	2	no	—
94	C₂³	—	2	1	no	—
95	C₂³	—	2	1	no	—
96	C₂³	—	4	1	no	—
97	C₂³	—	4	1	no	—
98	C₂³	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
99	C₂³	#64526	1	1	yes	characteristic
100	C₂³	#64528	1	1	yes	characteristic
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	4	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	8	1	no	—
107	C₂×C₄	—	8	1	no	—
108	C₂×C₄	—	38	2	no	—
109	C₂×C₄	—	76	1	no	—
110	C₂×C₄	—	76	1	no	—
111	C₂×C₄	—	76	1	no	—
112	C₂×C₄	—	76	1	no	—
113	C₂×C₄	—	76	1	no	—
114	C₈	—	152	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	—	4	1	no	—
120	C₂²	—	4	1	no	—
121	C₂²	—	4	1	no	—
122	C₂²	—	4	1	no	—
123	C₂²	—	8	1	no	—
124	C₂²	#10597262	1	1	yes	characteristic
125	C₂²	#10597263	1	1	yes	characteristic
126	C₂²	#10597267	1	1	yes	characteristic
127	C₄	—	4	1	no	—
128	C₄	—	4	1	no	—
129	C₄	—	8	2	no	—
130	C₄	—	76	2	no	—
131	C₄	—	152	1	no	—
132	C₂	—	2	1	no	—
133	C₂	—	2	1	no	—
134	C₂	—	4	1	no	—
135	C₂	—	4	1	no	—
136	C₂	#11926280	1	1	yes	characteristic
137	C₂	#11926333	1	1	yes	characteristic
138	C₂	#11926336	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926480

C₂

yes

maximal, characteristic

#11926268

C₂

yes

maximal, characteristic

C₁₉×#342

C₂

yes

maximal, characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₄

yes

characteristic, complemented

C₂×Dic₁₉⋊C₄

—

C₁₉⋊#95

C₄

yes

characteristic, complemented

C₂²⋊(C₁₉⋊C₈)

—

C₂⁴×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

SD₁₆

yes

characteristic

C₂³×C₁₉

Q₁₆

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#1352

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#399

—

#342

D₁₉

yes

characteristic

#323

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

characteristic

C₂²⋊C₈

—

#95

—

C₁₉

#1352

yes

characteristic, complemented, Sylow

C₂⁴

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂³

#64526

yes

characteristic

100

C₂³

#64528

yes

characteristic

101

C₂×C₄

—

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

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₈

—

152

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

#10597262

yes

characteristic

125

C₂²

#10597263

yes

characteristic

126

C₂²

#10597267

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

152

—

132

C₂

—

133

C₂

—

134

C₂

—

135

C₂

—

136

C₂

#11926280

yes

characteristic

137

C₂

#11926333

yes

characteristic

138

C₂

#11926336

yes

characteristic

	subgroup	G/H
center	C₂²	#10597263
commutator	C₂²×C₄×C₁₉	C₂×C₄
Frattini	C₂×C₂²⋊C₄	C₂×D₁₉
Fitting	C₁₉×#342	C₂
socle	C₂²×C₁₉	#99
prime radical	C₂⁴×C₁₉	D₄
cosocle	C₂×C₂²⋊C₄×C₁₉	C₂²
hypercenter	#342	D₁₉
hypocenter	C₁₉	#1352
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₂²⋊C₄ ◁ #342

subgroup

G/H

center

C₂²

#10597263

commutator

C₂²×C₄×C₁₉

C₂×C₄

Frattini

C₂×C₂²⋊C₄

C₂×D₁₉

Fitting

C₁₉×#342

C₂

socle

C₂²×C₁₉

#99

prime radical

C₂⁴×C₁₉

D₄

cosocle

C₂×C₂²⋊C₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₂²⋊C₄ ◁ #342

N	H ≅ G/N	type
7. C₂×C₄⋊Dic₁₉	C₄	semidirect
9. C₁₉⋊#95	C₄	semidirect
80. C₁₉	#1352	semidirect

H ≅ G/N

type

7. C₂×C₄⋊Dic₁₉

C₄

semidirect

9. C₁₉⋊#95

C₄

semidirect

80. C₁₉

#1352

semidirect

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

subgroup	index
#11926480	2
#11926268	2
C₁₉×#342	2
#1352	19

subgroup

index

#11926480

#11926268

C₁₉×#342

#1352

Subgroups — #14561658

Conjugacy classes of subgroups

Complements

Maximal subgroups