Group #14561990 — subgroups

Subgroups — #14561990

Order 2432.

204 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 73 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×#10597316	C₂	1	1	yes	maximal, characteristic
2	#11926601	C₂	1	1	yes	maximal, characteristic
3	#11926269	C₂	1	4	yes	maximal
4	C₁₉×#431	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
7	C₂×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
8	C₂×Dic₁₉⋊C₄	C₄	1	2	yes	—
9	C₂×Dic₁₉⋊C₄	C₂²	1	2	yes	—
10	#10597316	—	2	1	no	—
11	#10597316	—	2	1	no	—
12	#10597316	—	2	1	no	—
13	#10597316	—	2	1	no	—
14	C₁₉×C₄⋊C₈	—	2	1	no	—
15	C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₄×C₈×C₁₉	—	2	1	no	—
17	C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
18	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
19	#10597260	—	2	1	no	—
20	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
24	C₂²×Dic₁₉	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₄²×C₁₉	D₄	1	1	yes	characteristic
27	C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₄⋊Dic₁₉	—	2	1	no	—
31	C₄⋊Dic₁₉	—	2	1	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	Dic₁₉⋊C₄	—	2	2	no	—
35	Dic₁₉⋊C₄	—	2	2	no	—
36	Dic₁₉⋊C₄	—	2	2	no	—
37	Dic₁₉⋊C₄	—	2	2	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₁₉	—	2	2	no	—
50	C₂×Dic₁₉	—	2	2	no	—
51	C₂×Dic₁₉	—	2	4	no	—
52	C₂×Dic₁₉	—	4	2	no	—
53	C₈×C₁₉	—	4	2	no	—
54	C₁₉⋊C₈	—	4	2	no	—
55	#1470	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₂²×C₁₉	#131	1	2	yes	—
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	—	2	1	no	—
65	C₄×C₁₉	#101	1	2	yes	—
66	Dic₁₉	—	4	2	no	—
67	Dic₁₉	—	4	2	no	—
68	C₂×#125	—	19	1	no	—
69	#432	—	19	1	no	—
70	#431	D₁₉	1	1	yes	characteristic
71	#324	—	19	4	no	—
72	C₂×C₁₉	—	2	2	no	—
73	C₂×C₁₉	#408	1	1	yes	characteristic
74	C₂×C₁₉	#410	1	1	yes	characteristic
75	C₂×C₁₉	C₂×#101	1	1	yes	characteristic
76	#125	—	38	1	no	—
77	#125	—	38	1	no	—
78	#125	—	38	1	no	—
79	#125	—	38	1	no	—
80	C₂×C₄⋊C₄	—	19	2	no	—
81	C₂×C₄⋊C₄	—	19	1	no	—
82	C₂×C₄⋊C₄	—	19	1	no	—
83	C₂×C₄⋊C₄	—	19	2	no	—
84	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
85	C₄⋊C₈	—	2	1	no	—
86	C₄⋊C₈	—	38	1	no	—
87	C₂²⋊C₈	—	19	2	no	—
88	C₂²⋊C₈	C₂×D₁₉	1	2	yes	—
89	#97	—	38	1	no	—
90	C₄×C₈	—	2	1	no	—
91	C₁₉	#1470	1	1	yes	characteristic, complemented, Sylow
92	C₂²×C₄	—	19	2	no	—
93	C₂²×C₄	—	19	2	no	—
94	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
95	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
96	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
97	C₂×C₈	—	2	2	no	—
98	C₂×C₈	—	38	2	no	—
99	C₄⋊C₄	—	38	2	no	—
100	C₄⋊C₄	—	38	2	no	—
101	C₄⋊C₄	—	38	1	no	—
102	C₄⋊C₄	—	38	1	no	—
103	C₄⋊C₄	—	38	1	no	—
104	C₄⋊C₄	—	38	1	no	—
105	C₄⋊C₄	—	38	2	no	—
106	C₄⋊C₄	—	38	2	no	—
107	C₄²	D₇₆	1	1	yes	characteristic
108	C₄²	D₇₆	1	1	yes	characteristic
109	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
111	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	38	4	no	—
116	C₂×C₄	—	38	2	no	—
117	C₂×C₄	—	38	2	no	—
118	C₂×C₄	—	76	2	no	—
119	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
120	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
121	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
122	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
123	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
124	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
125	C₈	—	4	2	no	—
126	C₈	—	76	2	no	—
127	C₂²	—	2	1	no	—
128	C₂²	—	2	1	no	—
129	C₂²	#10597347	1	2	yes	—
130	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	2	1	no	—
133	C₄	—	2	1	no	—
134	C₄	—	2	1	no	—
135	C₄	—	2	1	no	—
136	C₄	—	76	2	no	—
137	C₄	—	76	2	no	—
138	C₄	#10597281	1	2	yes	—
139	C₂	—	2	2	no	—
140	C₂	#11926510	1	1	yes	characteristic
141	C₂	#11926517	1	1	yes	characteristic
142	C₂	C₂×#10597281	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597316

C₂

yes

maximal, characteristic

#11926601

C₂

yes

maximal, characteristic

#11926269

C₂

yes

maximal

C₁₉×#431

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₄

yes

characteristic

C₂×C₄⋊Dic₁₉

C₄

yes

characteristic

C₂×Dic₁₉⋊C₄

C₄

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

—

—

—

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

C₂²

yes

—

C₄×C₈×C₁₉

—

C₂²⋊(C₁₉⋊C₈)

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1470

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#131

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#101

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×#125

—

#432

—

#431

D₁₉

yes

characteristic

#324

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

—

—

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

C₂×D₁₉

yes

—

#97

—

C₄×C₈

—

C₁₉

#1470

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄²

D₇₆

yes

characteristic

108

C₄²

D₇₆

yes

characteristic

109

C₄²

C₂²⋊D₁₉

yes

characteristic

110

C₄²

C₂²⋊D₁₉

yes

characteristic

111

C₂³

C₂×C₄×D₁₉

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

120

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

121

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

122

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

123

C₂×C₄

C₂×D₇₆

yes

characteristic

124

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

125

C₈

—

126

C₈

—

127

C₂²

—

128

C₂²

—

129

C₂²

#10597347

yes

—

130

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

#10597281

yes

—

139

C₂

—

140

C₂

#11926510

yes

characteristic

141

C₂

#11926517

yes

characteristic

142

C₂

C₂×#10597281

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×(C₂×D₁₉)⋊C₄
commutator, prime radical	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#431	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#431	D₁₉
hypocenter	C₁₉	#1470
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂²

C₂×(C₂×D₁₉)⋊C₄

commutator, prime radical

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#431

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
91. C₁₉	#1470	semidirect

H ≅ G/N

type

91. C₁₉

#1470

semidirect

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

subgroup	index
C₂×#10597316	2
#11926601	2
#11926269	2
C₁₉×#431	2
#1470	19

subgroup

index

C₁₉×#431

Subgroups — #14561990

Conjugacy classes of subgroups

Complements

Maximal subgroups