Group #14566937 — subgroups

Subgroups — #14566937

Order 2432.

432 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 139 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	C₁₉⋊#401	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926483	C₂	1	3	yes	maximal, complemented
3	#11926469	C₂	1	3	yes	maximal
4	C₄⋊C₄×Dic₁₉	C₂	1	3	yes	maximal, complemented
5	C₂²⋊C₄×Dic₁₉	C₂	1	3	yes	maximal
6	#11926389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#396	C₂	1	1	yes	maximal, characteristic
8	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
10	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
11	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
13	C₂×C₄×Dic₁₉	C₂²	1	3	yes	—
14	C₂×C₄×Dic₁₉	C₂²	1	3	yes	—
15	C₁₉×#95	C₂²	1	1	yes	characteristic
16	C₁₉⋊#95	C₂²	1	3	yes	—
17	C₁₉⋊#95	C₂²	1	3	yes	—
18	C₁₉⋊#95	C₂²	1	3	yes	—
19	C₁₉⋊#95	C₂²	1	3	yes	—
20	C₁₉⋊#95	C₂²	1	3	yes	—
21	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂²×Dic₁₉	—	2	6	no	—
25	C₂²×Dic₁₉	C₂³	1	3	yes	—
26	C₂²×Dic₁₉	C₂³	1	3	yes	—
27	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
28	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
29	C₄⋊C₄×C₁₉	—	2	6	no	—
30	C₂²⋊C₄×C₁₉	—	2	6	no	—
31	C₂²⋊Dic₁₉	—	2	6	no	—
32	C₄⋊Dic₁₉	—	2	6	no	—
33	C₄×Dic₁₉	—	2	6	no	—
34	C₄×Dic₁₉	—	2	6	no	—
35	C₂³×C₁₉	—	2	3	no	—
36	C₂³×C₁₉	—	2	3	no	—
37	C₂³×C₁₉	#41	1	2	yes	—
38	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	2	3	no	—
40	C₂×C₄×C₁₉	—	2	3	no	—
41	C₂×C₄×C₁₉	—	2	3	no	—
42	C₂×C₄×C₁₉	—	2	3	no	—
43	C₂×C₄×C₁₉	—	2	3	no	—
44	C₂×C₄×C₁₉	#41	1	6	yes	—
45	C₂×Dic₁₉	—	2	3	no	—
46	C₂×Dic₁₉	—	2	3	no	—
47	C₂×Dic₁₉	—	2	3	no	—
48	C₂×Dic₁₉	—	2	3	no	—
49	C₂×Dic₁₉	—	2	3	no	—
50	C₂×Dic₁₉	—	2	3	no	—
51	C₂×Dic₁₉	—	2	3	no	—
52	C₂×Dic₁₉	—	4	4	no	—
53	C₂×Dic₁₉	#41	1	6	yes	—
54	#2401	—	19	1	no	maximal, Sylow
55	C₂²×C₁₉	—	2	6	no	—
56	C₂²×C₁₉	—	4	1	no	—
57	C₂²×C₁₉	—	4	3	no	—
58	C₂²×C₁₉	C₂×#41	1	3	yes	—
59	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
60	C₂²×C₁₉	C₂×#41	1	3	yes	—
61	C₄×C₁₉	—	2	6	no	—
62	C₄×C₁₉	—	4	3	no	—
63	Dic₁₉	—	4	1	no	—
64	Dic₁₉	—	4	3	no	—
65	Dic₁₉	—	4	3	no	—
66	Dic₁₉	#126	1	4	yes	—
67	#401	—	19	1	no	—
68	#400	—	19	3	no	—
69	#397	—	19	3	no	—
70	#396	D₁₉	1	1	yes	characteristic
71	C₄×C₄⋊C₄	—	19	3	no	—
72	C₄×C₂²⋊C₄	—	19	3	no	—
73	#376	—	19	1	no	—
74	C₂×C₁₉	—	4	2	no	—
75	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
76	C₂×C₁₉	#529	1	3	yes	—
77	C₂×C₁₉	#529	1	3	yes	—
78	C₂³×C₄	—	19	1	no	—
79	C₂×C₄⋊C₄	—	19	3	no	—
80	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
81	C₂×C₂²⋊C₄	—	19	3	no	—
82	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
83	C₂×C₄²	—	19	3	no	—
84	C₂×C₄²	—	19	3	no	—
85	#95	—	19	3	no	—
86	#95	—	19	3	no	—
87	#95	—	19	3	no	—
88	#95	—	19	3	no	—
89	#95	—	19	3	no	—
90	#95	C₂×D₁₉	1	1	yes	characteristic
91	C₁₉	#2401	1	1	yes	characteristic, complemented, Sylow
92	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
93	C₂²×C₄	—	19	1	no	—
94	C₂²×C₄	—	19	1	no	—
95	C₂²×C₄	—	19	3	no	—
96	C₂²×C₄	—	19	3	no	—
97	C₂²×C₄	—	38	6	no	—
98	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
99	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
100	C₄⋊C₄	—	2	6	no	—
101	C₄⋊C₄	—	38	6	no	—
102	C₂²⋊C₄	—	2	6	no	—
103	C₂²⋊C₄	—	38	6	no	—
104	C₄²	—	38	6	no	—
105	C₄²	—	38	6	no	—
106	C₂³	—	2	3	no	—
107	C₂³	—	2	3	no	—
108	C₂³	#64545	1	2	yes	—
109	C₂³	C₂³×D₁₉	1	1	yes	characteristic
110	C₂×C₄	—	2	3	no	—
111	C₂×C₄	—	2	3	no	—
112	C₂×C₄	—	2	3	no	—
113	C₂×C₄	—	2	3	no	—
114	C₂×C₄	—	2	3	no	—
115	C₂×C₄	—	19	6	no	—
116	C₂×C₄	—	38	3	no	—
117	C₂×C₄	—	38	3	no	—
118	C₂×C₄	—	38	3	no	—
119	C₂×C₄	—	38	3	no	—
120	C₂×C₄	—	38	3	no	—
121	C₂×C₄	—	38	3	no	—
122	C₂×C₄	—	38	3	no	—
123	C₂×C₄	—	76	4	no	—
124	C₂×C₄	#64543	1	6	yes	—
125	C₂²	—	2	6	no	—
126	C₂²	—	4	1	no	—
127	C₂²	—	4	3	no	—
128	C₂²	C₂×#64543	1	3	yes	—
129	C₂²	C₂×#64545	1	1	yes	characteristic
130	C₂²	#41×D₁₉	1	3	yes	—
131	C₄	—	2	6	no	—
132	C₄	—	4	3	no	—
133	C₄	—	19	4	no	—
134	C₄	—	76	1	no	—
135	C₄	—	76	3	no	—
136	C₄	—	76	3	no	—
137	C₂	—	4	2	no	—
138	C₂	#126×D₁₉	1	1	yes	characteristic
139	C₂	#11927075	1	3	yes	—
140	C₂	#11927080	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉⋊#401

C₂

yes

maximal, characteristic, complemented

#11926483

C₂

yes

maximal, complemented

#11926469

C₂

yes

maximal

C₄⋊C₄×Dic₁₉

C₂

yes

maximal, complemented

C₂²⋊C₄×Dic₁₉

C₂

yes

maximal

#11926389

C₂

yes

maximal, characteristic, complemented

C₁₉×#396

C₂

yes

maximal, characteristic

C₂³×Dic₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

characteristic

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#41

yes

—

#2401

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

C₂×#41

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

#126

yes

—

—

—

—

D₁₉

yes

characteristic

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

#376

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#126

yes

characteristic

C₂×C₁₉

#529

yes

—

C₂×C₁₉

#529

yes

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

—

—

—

—

—

C₂×D₁₉

yes

characteristic

C₁₉

#2401

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₄²

—

105

C₄²

—

106

C₂³

—

107

C₂³

—

108

C₂³

#64545

yes

—

109

C₂³

C₂³×D₁₉

yes

characteristic

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

#64543

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

C₂×#64543

yes

—

129

C₂²

C₂×#64545

yes

characteristic

130

C₂²

#41×D₁₉

yes

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₂

—

138

C₂

#126×D₁₉

yes

characteristic

139

C₂

#11927075

yes

—

140

C₂

#11927080

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#396	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	#396	D₁₉
hypocenter	C₁₉	#2401
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #396

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#396

C₂

prime radical

C₂⁴×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #396

N	H ≅ G/N	type
1. C₁₉⋊#401	C₂	semidirect
2. #11926483	C₂	semidirect
4. C₄⋊C₄×Dic₁₉	C₂	semidirect
6. #11926389	C₂	semidirect
91. C₁₉	#2401	semidirect

H ≅ G/N

type

1. C₁₉⋊#401

C₂

semidirect

2. #11926483

C₂

semidirect

4. C₄⋊C₄×Dic₁₉

C₂

semidirect

6. #11926389

C₂

semidirect

91. C₁₉

#2401

semidirect

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

subgroup	index
C₁₉⋊#401	2
#11926483	2
#11926469	2
C₄⋊C₄×Dic₁₉	2
C₂²⋊C₄×Dic₁₉	2
#11926389	2
C₁₉×#396	2
#2401	19

subgroup

index

C₁₉⋊#401

#11926483

#11926469

C₄⋊C₄×Dic₁₉

C₂²⋊C₄×Dic₁₉

#11926389

C₁₉×#396

#2401

Subgroups — #14566937

Conjugacy classes of subgroups

Complements

Maximal subgroups