Group #14569597 — subgroups

Subgroups — #14569597

Order 2432.

420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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	#11926472	C₂	1	3	yes	maximal, complemented
2	#11926470	C₂	1	3	yes	maximal, complemented
3	#11926468	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926444	C₂	1	3	yes	maximal
5	#11926439	C₂	1	3	yes	maximal, complemented
6	#11926389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂²⋊D₁₉	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×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	—
13	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	—
14	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
15	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
16	C₂×C₄×Dic₁₉	C₂²	1	3	yes	—
17	C₁₉×#95	C₂²	1	1	yes	characteristic
18	C₁₉⋊#95	C₂²	1	3	yes	—
19	C₁₉⋊#95	C₂²	1	6	yes	—
20	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
21	C₂³×D₁₉	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂×C₂²⋊D₁₉	—	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	C₄⋊C₄×C₁₉	—	4	3	no	—
29	C₂²⋊C₄×C₁₉	—	4	3	no	—
30	C₂²⋊Dic₁₉	—	4	3	no	—
31	(C₂×D₁₉)⋊C₄	—	4	3	no	—
32	(C₂×D₁₉)⋊C₄	—	4	3	no	—
33	Dic₁₉⋊C₄	—	2	6	no	—
34	Dic₁₉⋊C₄	—	4	3	no	—
35	C₄×Dic₁₉	—	2	6	no	—
36	C₂³×C₁₉	—	2	3	no	—
37	C₂³×C₁₉	—	2	3	no	—
38	C₂³×C₁₉	—	2	1	no	—
39	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
40	C₂²×D₁₉	—	2	3	no	—
41	C₂²×D₁₉	—	2	3	no	—
42	C₂²×D₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	3	no	—
44	C₂×C₄×C₁₉	—	2	3	no	—
45	C₂×C₄×C₁₉	—	2	3	no	—
46	C₂×C₄×C₁₉	—	2	3	no	—
47	C₂×C₄×C₁₉	—	2	3	no	—
48	C₂×C₄×C₁₉	—	2	3	no	—
49	C₂²⋊D₁₉	—	4	4	no	—
50	C₂×Dic₁₉	—	2	3	no	—
51	C₂×Dic₁₉	—	2	3	no	—
52	C₂×Dic₁₉	—	2	3	no	—
53	C₂×Dic₁₉	—	2	3	no	—
54	C₂×Dic₁₉	—	2	3	no	—
55	C₂×Dic₁₉	—	2	3	no	—
56	C₂×Dic₁₉	#41	1	6	yes	—
57	#2644	—	19	1	no	maximal, Sylow
58	C₂²×C₁₉	—	4	1	no	—
59	C₂²×C₁₉	—	4	3	no	—
60	C₂²×C₁₉	—	4	3	no	—
61	C₂²×C₁₉	C₂×#41	1	3	yes	—
62	C₂²×C₁₉	H(5,𝔽₂)	1	3	yes	—
63	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
64	C₂×D₁₉	—	4	1	no	—
65	C₂×D₁₉	—	4	3	no	—
66	C₂×D₁₉	—	4	3	no	—
67	C₄×C₁₉	—	4	3	no	—
68	C₄×C₁₉	—	4	3	no	—
69	Dic₁₉	—	4	3	no	—
70	Dic₁₉	—	4	3	no	—
71	Dic₁₉	#126	1	4	yes	—
72	#397	—	19	3	no	—
73	#397	—	19	3	no	—
74	#396	—	19	1	no	—
75	#396	D₁₉	1	1	yes	characteristic, complemented
76	#390	—	19	3	no	—
77	#389	—	19	3	no	—
78	#376	—	19	1	no	—
79	C₂×C₁₉	—	8	1	no	—
80	C₂×C₁₉	C₂×#126	1	1	yes	characteristic
81	C₂×C₁₉	#540	1	3	yes	—
82	C₂×C₁₉	#542	1	3	yes	—
83	D₁₉	—	8	1	no	—
84	C₂²×D₄	—	19	1	no	—
85	C₂×C₄⋊C₄	—	19	3	no	—
86	C₂×C₄⋊C₄	—	19	3	no	—
87	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
88	C₂×C₂²⋊C₄	—	19	3	no	—
89	C₂×C₂²⋊C₄	—	19	3	no	—
90	C₂×C₂²⋊C₄	—	19	3	no	—
91	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
92	C₂×C₄²	—	19	3	no	—
93	#95	—	19	3	no	—
94	#95	—	19	6	no	—
95	#95	C₂×D₁₉	1	1	yes	characteristic
96	C₁₉	#2644	1	1	yes	characteristic, complemented, Sylow
97	C₂⁴	—	19	1	no	—
98	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
99	C₂×D₄	—	38	6	no	—
100	C₂²×C₄	—	19	1	no	—
101	C₂²×C₄	—	19	3	no	—
102	C₂²×C₄	—	19	3	no	—
103	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
104	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
105	C₄⋊C₄	—	4	3	no	—
106	C₄⋊C₄	—	38	6	no	—
107	C₄⋊C₄	—	76	3	no	—
108	C₂²⋊C₄	—	4	3	no	—
109	C₂²⋊C₄	—	76	3	no	—
110	C₂²⋊C₄	—	76	3	no	—
111	C₂²⋊C₄	—	76	3	no	—
112	C₄²	—	38	6	no	—
113	C₂³	—	2	3	no	—
114	C₂³	—	2	1	no	—
115	C₂³	—	2	3	no	—
116	C₂³	—	38	3	no	—
117	C₂³	—	38	1	no	—
118	C₂³	—	38	3	no	—
119	C₂³	C₂³×D₁₉	1	1	yes	characteristic
120	D₄	—	76	4	no	—
121	C₂×C₄	—	2	3	no	—
122	C₂×C₄	—	2	3	no	—
123	C₂×C₄	—	2	3	no	—
124	C₂×C₄	—	2	3	no	—
125	C₂×C₄	—	2	3	no	—
126	C₂×C₄	—	2	3	no	—
127	C₂×C₄	—	19	6	no	—
128	C₂×C₄	—	38	3	no	—
129	C₂×C₄	—	38	3	no	—
130	C₂×C₄	—	38	3	no	—
131	C₂×C₄	—	38	3	no	—
132	C₂×C₄	—	38	3	no	—
133	C₂×C₄	—	38	3	no	—
134	C₂²	—	4	1	no	—
135	C₂²	—	4	3	no	—
136	C₂²	—	4	3	no	—
137	C₂²	—	76	1	no	—
138	C₂²	—	76	3	no	—
139	C₂²	—	76	3	no	—
140	C₂²	#10597430	1	3	yes	—
141	C₂²	#10597433	1	1	yes	characteristic
142	C₂²	#41×D₁₉	1	3	yes	—
143	C₄	—	4	3	no	—
144	C₄	—	4	3	no	—
145	C₄	—	19	4	no	—
146	C₄	—	76	3	no	—
147	C₄	—	76	3	no	—
148	C₂	—	8	1	no	—
149	C₂	—	152	1	no	—
150	C₂	#126×D₁₉	1	1	yes	characteristic
151	C₂	#11927144	1	3	yes	—
152	C₂	#11927164	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926472

C₂

yes

maximal, complemented

#11926470

C₂

yes

maximal, complemented

#11926468

C₂

yes

maximal, characteristic, complemented

#11926444

C₂

yes

maximal

#11926439

C₂

yes

maximal, complemented

#11926389

C₂

yes

maximal, characteristic, complemented

C₁₉×#396

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₁₉×#95

C₂²

yes

characteristic

C₁₉⋊#95

C₂²

yes

—

C₁₉⋊#95

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂³×D₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#41

yes

—

#2644

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

#126

yes

—

—

—

—

D₁₉

yes

characteristic, complemented

#390

—

#389

—

#376

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#126

yes

characteristic

C₂×C₁₉

#540

yes

—

C₂×C₁₉

#542

yes

—

D₁₉

—

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

#95

—

#95

—

#95

C₂×D₁₉

yes

characteristic

C₁₉

#2644

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×D₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

102

C₂²×C₄

—

103

C₂²×C₄

C₂²×D₁₉

yes

—

104

C₂²×C₄

C₂²×D₁₉

yes

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₂²⋊C₄

—

111

C₂²⋊C₄

—

112

C₄²

—

113

C₂³

—

114

C₂³

—

115

C₂³

—

116

C₂³

—

117

C₂³

—

118

C₂³

—

119

C₂³

C₂³×D₁₉

yes

characteristic

120

D₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

#10597430

yes

—

141

C₂²

#10597433

yes

characteristic

142

C₂²

#41×D₁₉

yes

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₂

—

149

C₂

—

152

—

150

C₂

#126×D₁₉

yes

characteristic

151

C₂

#11927144

yes

—

152

C₂

#11927164

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#396	C₂
prime radical	C₂²×C₂²⋊D₁₉	C₂²
hypercenter	#396	D₁₉
hypocenter	C₁₉	#2644
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

C₂²×C₂²⋊D₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #396

N	H ≅ G/N	type
1. #11926472	C₂	semidirect
2. #11926470	C₂	semidirect
3. #11926468	C₂	semidirect
5. #11926439	C₂	semidirect
6. #11926389	C₂	semidirect
7. C₁₉×#396	C₂	semidirect
75. #396	D₁₉	semidirect
96. C₁₉	#2644	semidirect

H ≅ G/N

type

1. #11926472

C₂

semidirect

2. #11926470

C₂

semidirect

3. #11926468

C₂

semidirect

5. #11926439

C₂

semidirect

6. #11926389

C₂

semidirect

7. C₁₉×#396

C₂

semidirect

75. #396

D₁₉

semidirect

96. C₁₉

#2644

semidirect

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

subgroup	index
#11926472	2
#11926470	2
#11926468	2
#11926444	2
#11926439	2
#11926389	2
C₁₉×#396	2
#2644	19

subgroup

index

C₁₉×#396

Subgroups — #14569597

Conjugacy classes of subgroups

Complements

Maximal subgroups