Group #14567916 — subgroups

Subgroups — #14567916

Order 2432.

700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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	C₂²×C₂²⋊Dic₁₉	C₂	1	2	yes	maximal
2	#11926469	C₂	1	4	yes	maximal, complemented
3	#11926419	C₂	1	4	yes	maximal, complemented
4	#11926405	C₂	1	4	yes	maximal, complemented
5	C₁₉×#379	C₂	1	1	yes	maximal, characteristic
6	C₂⁵×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×Dic₁₉	C₂²	1	2	yes	—
8	C₂³×Dic₁₉	C₂²	1	2	yes	—
9	C₂×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
10	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₂×C₂²⋊Dic₁₉	—	2	8	no	—
12	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
13	C₂×C₂²⋊Dic₁₉	C₂²	1	4	yes	—
14	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	complemented
15	C₁₉⋊#95	C₂²	1	4	yes	complemented
16	C₁₉⋊#95	C₂²	1	8	yes	complemented
17	C₂⁴×C₁₉	—	2	8	no	—
18	C₂⁴×C₁₉	—	4	2	no	—
19	C₂⁴×C₁₉	D₄	1	4	yes	—
20	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
21	C₂⁴×C₁₉	C₂³	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
23	C₂²×Dic₁₉	—	2	4	no	—
24	C₂²×Dic₁₉	—	2	4	no	—
25	C₂²×Dic₁₉	—	2	8	no	—
26	C₂²×Dic₁₉	—	4	4	no	—
27	C₂²×Dic₁₉	C₂³	1	4	yes	—
28	C₂²×Dic₁₉	C₂³	1	4	yes	—
29	C₂²⋊C₄×C₁₉	—	2	8	no	—
30	C₂²⋊C₄×C₁₉	—	4	2	no	—
31	C₂²⋊Dic₁₉	—	2	8	no	—
32	C₂²⋊Dic₁₉	—	2	8	no	—
33	C₄⋊Dic₁₉	—	4	4	no	—
34	C₂³×C₁₉	—	2	4	no	—
35	C₂³×C₁₉	—	2	4	no	—
36	C₂³×C₁₉	—	2	16	no	—
37	C₂³×C₁₉	—	2	4	no	—
38	C₂³×C₁₉	—	2	2	no	—
39	C₂³×C₁₉	—	4	4	no	—
40	C₂³×C₁₉	—	4	16	no	—
41	C₂³×C₁₉	C₂×D₄	1	2	yes	—
42	C₂³×C₁₉	C₂×D₄	1	4	yes	—
43	C₂³×C₁₉	#41	1	8	yes	—
44	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
45	C₂×C₄×C₁₉	—	2	8	no	—
46	C₂×C₄×C₁₉	—	2	4	no	—
47	C₂×Dic₁₉	—	2	4	no	—
48	C₂×Dic₁₉	—	2	4	no	—
49	C₂×Dic₁₉	—	2	8	no	—
50	C₂×Dic₁₉	—	2	8	no	—
51	C₂×Dic₁₉	—	4	8	no	—
52	C₂×Dic₁₉	—	4	8	no	—
53	#2483	—	19	1	no	maximal, Sylow
54	C₂²×C₁₉	—	2	4	no	—
55	C₂²×C₁₉	—	2	4	no	—
56	C₂²×C₁₉	—	2	16	no	—
57	C₂²×C₁₉	—	2	4	no	—
58	C₂²×C₁₉	—	2	2	no	—
59	C₂²×C₁₉	—	4	16	no	—
60	C₂²×C₁₉	—	4	4	no	—
61	C₂²×C₁₉	#123	1	8	yes	—
62	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
63	C₂²×C₁₉	C₂×#41	1	4	yes	—
64	C₂²×C₁₉	H(5,𝔽₂)	1	2	yes	—
65	C₄×C₁₉	—	4	4	no	—
66	Dic₁₉	—	4	4	no	—
67	Dic₁₉	—	4	4	no	—
68	C₂²×C₂²⋊C₄	—	19	2	no	—
69	#397	—	19	4	no	—
70	#385	—	19	4	no	—
71	#381	—	19	4	no	—
72	#379	D₁₉	1	1	yes	characteristic
73	C₂×C₁₉	—	2	8	no	—
74	C₂×C₁₉	—	4	2	no	—
75	C₂×C₁₉	C₂×#123	1	2	yes	—
76	C₂×C₁₉	#534	1	1	yes	characteristic
77	C₂×C₁₉	#551	1	4	yes	—
78	C₂⁵	C₂×D₁₉	1	1	yes	characteristic
79	C₂³×C₄	—	19	2	no	—
80	C₂³×C₄	—	19	2	no	—
81	C₂×C₄⋊C₄	—	19	4	no	—
82	C₂×C₂²⋊C₄	—	19	4	no	—
83	C₂×C₂²⋊C₄	—	19	4	no	—
84	C₂×C₂²⋊C₄	—	38	8	no	—
85	C₂×C₂²⋊C₄	C₂×D₁₉	1	4	yes	—
86	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
87	#95	—	19	4	no	—
88	#95	—	19	8	no	—
89	C₁₉	#2483	1	1	yes	characteristic, complemented, Sylow
90	C₂⁴	—	2	8	no	—
91	C₂⁴	—	4	2	no	—
92	C₂⁴	D₇₆	1	4	yes	—
93	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
94	C₂⁴	C₂²×D₁₉	1	2	yes	—
95	C₂²×C₄	—	19	4	no	—
96	C₂²×C₄	—	19	4	no	—
97	C₂²×C₄	—	38	4	no	—
98	C₂²×C₄	—	38	4	no	—
99	C₂²×C₄	—	38	8	no	—
100	C₂²×C₄	—	76	4	no	—
101	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
102	C₄⋊C₄	—	76	4	no	—
103	C₂²⋊C₄	—	2	8	no	—
104	C₂²⋊C₄	—	4	2	no	—
105	C₂²⋊C₄	—	38	8	no	—
106	C₂²⋊C₄	—	38	8	no	—
107	C₂³	—	2	4	no	—
108	C₂³	—	2	4	no	—
109	C₂³	—	2	4	no	—
110	C₂³	—	2	2	no	—
111	C₂³	—	2	16	no	—
112	C₂³	—	4	4	no	—
113	C₂³	—	4	16	no	—
114	C₂³	C₂×D₇₆	1	2	yes	—
115	C₂³	C₂×D₇₆	1	4	yes	—
116	C₂³	#64543	1	8	yes	—
117	C₂³	C₂³×D₁₉	1	1	yes	characteristic
118	C₂×C₄	—	2	8	no	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	38	4	no	—
121	C₂×C₄	—	38	4	no	—
122	C₂×C₄	—	38	8	no	—
123	C₂×C₄	—	38	8	no	—
124	C₂×C₄	—	76	8	no	—
125	C₂×C₄	—	76	8	no	—
126	C₂²	—	2	4	no	—
127	C₂²	—	2	4	no	—
128	C₂²	—	2	16	no	—
129	C₂²	—	2	4	no	—
130	C₂²	—	2	2	no	—
131	C₂²	—	4	16	no	—
132	C₂²	—	4	4	no	—
133	C₂²	#10597332	1	8	yes	—
134	C₂²	C₂²×D₇₆	1	1	yes	characteristic
135	C₂²	C₂×#64543	1	4	yes	—
136	C₂²	#10597430	1	2	yes	—
137	C₄	—	4	4	no	—
138	C₄	—	76	4	no	—
139	C₄	—	76	4	no	—
140	C₂	—	2	8	no	—
141	C₂	—	4	2	no	—
142	C₂	C₂×#10597332	1	2	yes	—
143	C₂	#11927106	1	1	yes	characteristic
144	C₂	#11927225	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₂²⋊Dic₁₉

C₂

yes

maximal

#11926469

C₂

yes

maximal, complemented

#11926419

C₂

yes

maximal, complemented

#11926405

C₂

yes

maximal, complemented

C₁₉×#379

C₂

yes

maximal, characteristic

C₂⁵×C₁₉

C₂²

yes

characteristic

C₂³×Dic₁₉

C₂²

yes

—

C₂³×Dic₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

complemented

C₁₉⋊#95

C₂²

yes

complemented

C₁₉⋊#95

C₂²

yes

complemented

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

D₄

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂⁴×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

—

C₂³×C₁₉

#41

yes

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2483

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#123

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂²×C₂²⋊C₄

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#123

yes

—

C₂×C₁₉

#534

yes

characteristic

C₂×C₁₉

#551

yes

—

C₂⁵

C₂×D₁₉

yes

characteristic

C₂³×C₄

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

#95

—

#95

—

C₁₉

#2483

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

—

C₂⁴

D₇₆

yes

—

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂⁴

C₂²×D₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²×D₁₉

yes

—

102

C₄⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

106

C₂²⋊C₄

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

C₂×D₇₆

yes

—

115

C₂³

C₂×D₇₆

yes

—

116

C₂³

#64543

yes

—

117

C₂³

C₂³×D₁₉

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

#10597332

yes

—

134

C₂²

C₂²×D₇₆

yes

characteristic

135

C₂²

C₂×#64543

yes

—

136

C₂²

#10597430

yes

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₂

—

141

C₂

—

142

C₂

C₂×#10597332

yes

—

143

C₂

#11927106

yes

characteristic

144

C₂

#11927225

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#379	C₂
prime radical	C₂⁵×C₁₉	C₂²
hypercenter	#379	D₁₉
hypocenter	C₁₉	#2483
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #379

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#379

C₂

prime radical

C₂⁵×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #379

N	H ≅ G/N	type
2. #11926469	C₂	semidirect
3. #11926419	C₂	semidirect
4. #11926405	C₂	semidirect
14. C₂×C₄⋊Dic₁₉	C₂²	semidirect
15. C₁₉⋊#95	C₂²	semidirect
16. C₁₉⋊#95	C₂²	semidirect
89. C₁₉	#2483	semidirect

H ≅ G/N

type

2. #11926469

C₂

semidirect

3. #11926419

C₂

semidirect

4. #11926405

C₂

semidirect

14. C₂×C₄⋊Dic₁₉

C₂²

semidirect

15. C₁₉⋊#95

C₂²

semidirect

16. C₁₉⋊#95

C₂²

semidirect

89. C₁₉

#2483

semidirect

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

subgroup	index
C₂²×C₂²⋊Dic₁₉	2
#11926469	2
#11926419	2
#11926405	2
C₁₉×#379	2
#2483	19

subgroup

index

C₂²×C₂²⋊Dic₁₉

C₁₉×#379

Subgroups — #14567916

Conjugacy classes of subgroups

Complements

Maximal subgroups