Group #14569744 — subgroups

Subgroups — #14569744

Order 2432.

612 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 153 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×#10597334	C₂	1	3	yes	maximal, complemented
2	C₂×#10597331	C₂	1	3	yes	maximal
3	#11926481	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926480	C₂	1	3	yes	maximal, complemented
5	#11926479	C₂	1	3	yes	maximal, complemented
6	#11926389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#399	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₈	C₂²	1	3	yes	—
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
11	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
12	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
13	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	—
14	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	—
15	C₂×C₄⋊Dic₁₉	C₂²	1	3	yes	—
16	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	—
17	C₂×C₄×Dic₁₉	C₂²	1	3	yes	—
18	#10597334	—	2	12	no	—
19	#10597331	—	2	12	no	—
20	C₁₉×#95	C₂²	1	1	yes	characteristic
21	C₁₉⋊#95	C₂²	1	3	yes	—
22	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
23	C₂³×D₁₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
26	C₂×C₂²⋊D₁₉	—	2	6	no	—
27	C₂²×Dic₁₉	C₂³	1	3	yes	—
28	C₂²×Dic₁₉	C₂³	1	3	yes	—
29	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
30	C₂×Dic₃₈	—	2	6	no	—
31	C₂×Dic₃₈	—	2	12	no	—
32	C₄⋊C₄×C₁₉	—	2	6	no	—
33	C₂²⋊C₄×C₁₉	—	2	6	no	—
34	C₂²⋊Dic₁₉	—	2	6	no	—
35	(C₂×D₁₉)⋊C₄	—	2	6	no	—
36	(C₂×D₁₉)⋊C₄	—	2	6	no	—
37	C₄⋊Dic₁₉	—	2	6	no	—
38	Dic₁₉⋊C₄	—	2	12	no	—
39	C₄×Dic₁₉	D₄	1	12	yes	—
40	C₂³×C₁₉	—	2	3	no	—
41	C₂³×C₁₉	—	2	1	no	—
42	C₂³×C₁₉	—	2	3	no	—
43	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
44	C₂²×D₁₉	—	2	3	no	—
45	C₂²×D₁₉	—	2	1	no	—
46	C₂²×D₁₉	—	2	3	no	—
47	C₂×C₄×C₁₉	—	2	6	no	—
48	C₂×C₄×C₁₉	—	2	6	no	—
49	C₂×C₄×C₁₉	—	2	3	no	—
50	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
51	C₂²⋊D₁₉	—	4	4	no	—
52	C₂×Dic₁₉	—	2	3	no	—
53	C₂×Dic₁₉	—	2	3	no	—
54	C₂×Dic₁₉	—	2	6	no	—
55	C₂×Dic₁₉	—	2	3	no	—
56	C₂×Dic₁₉	C₂×D₄	1	6	yes	—
57	C₂×Dic₁₉	C₂×D₄	1	6	yes	—
58	Dic₃₈	—	4	12	no	—
59	#2658	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	4	1	no	—
61	C₂²×C₁₉	—	4	3	no	—
62	C₂²×C₁₉	—	4	3	no	—
63	C₂²×C₁₉	C₂²×D₄	1	3	yes	—
64	C₂²×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
65	C₂²×C₁₉	2₋¹⁺⁴	1	3	yes	—
66	C₂×D₁₉	—	4	1	no	—
67	C₂×D₁₉	—	4	3	no	—
68	C₂×D₁₉	—	4	3	no	—
69	C₄×C₁₉	—	2	6	no	—
70	C₄×C₁₉	—	4	3	no	—
71	Dic₁₉	—	2	6	no	—
72	Dic₁₉	—	4	3	no	—
73	Dic₁₉	#127	1	4	yes	—
74	C₂×C₄⋊Q₈	—	19	3	no	—
75	C₂×#124	—	19	3	no	—
76	#399	—	19	3	no	—
77	#399	—	19	3	no	—
78	#399	—	19	1	no	—
79	#399	D₁₉	1	1	yes	characteristic, complemented
80	#376	—	19	1	no	—
81	C₂×C₁₉	—	8	1	no	—
82	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
83	C₂×C₁₉	#536	1	3	yes	—
84	C₂×C₁₉	#536	1	3	yes	—
85	D₁₉	—	8	1	no	—
86	C₂²×Q₈	—	19	3	no	—
87	C₂²×D₄	—	19	1	no	—
88	C₄⋊Q₈	—	38	12	no	—
89	#124	—	38	12	no	—
90	C₂×C₄⋊C₄	—	19	6	no	—
91	C₂×C₄⋊C₄	—	19	3	no	—
92	C₂×C₄⋊C₄	C₂×D₁₉	1	3	yes	—
93	C₂×C₂²⋊C₄	—	19	3	no	—
94	C₂×C₂²⋊C₄	—	19	3	no	—
95	C₂×C₂²⋊C₄	—	19	3	no	—
96	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
97	C₂×C₄²	—	19	3	no	—
98	#95	—	19	3	no	—
99	#95	C₂×D₁₉	1	1	yes	characteristic
100	C₁₉	#2658	1	1	yes	characteristic, complemented, Sylow
101	C₂⁴	—	19	1	no	—
102	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
103	C₂×Q₈	—	38	6	no	—
104	C₂×Q₈	—	38	12	no	—
105	C₂×D₄	—	38	6	no	—
106	C₂²×C₄	—	19	1	no	—
107	C₂²×C₄	—	19	3	no	—
108	C₂²×C₄	—	19	3	no	—
109	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
110	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
111	C₄⋊C₄	—	2	6	no	—
112	C₄⋊C₄	—	38	12	no	—
113	C₄⋊C₄	—	38	6	no	—
114	C₂²⋊C₄	—	2	6	no	—
115	C₂²⋊C₄	—	38	6	no	—
116	C₂²⋊C₄	—	38	6	no	—
117	C₂²⋊C₄	—	38	6	no	—
118	C₄²	—	19	12	no	—
119	C₂³	—	2	3	no	—
120	C₂³	—	2	1	no	—
121	C₂³	—	2	3	no	—
122	C₂³	—	38	3	no	—
123	C₂³	—	38	1	no	—
124	C₂³	—	38	3	no	—
125	C₂³	C₂³×D₁₉	1	1	yes	characteristic
126	Q₈	—	76	12	no	—
127	D₄	—	76	4	no	—
128	C₂×C₄	—	2	6	no	—
129	C₂×C₄	—	2	3	no	—
130	C₂×C₄	—	2	6	no	—
131	C₂×C₄	—	19	6	no	—
132	C₂×C₄	—	19	6	no	—
133	C₂×C₄	—	38	3	no	—
134	C₂×C₄	—	38	3	no	—
135	C₂×C₄	—	38	3	no	—
136	C₂×C₄	—	38	6	no	—
137	C₂×C₄	D₄×D₁₉	1	6	yes	—
138	C₂²	—	4	1	no	—
139	C₂²	—	4	3	no	—
140	C₂²	—	4	3	no	—
141	C₂²	—	76	1	no	—
142	C₂²	—	76	3	no	—
143	C₂²	—	76	3	no	—
144	C₂²	C₂×D₄×D₁₉	1	3	yes	—
145	C₂²	#10597433	1	1	yes	characteristic
146	C₂²	#10597436	1	3	yes	—
147	C₄	—	2	6	no	—
148	C₄	—	4	3	no	—
149	C₄	—	19	4	no	—
150	C₄	—	38	6	no	—
151	C₄	—	76	3	no	—
152	C₂	—	8	1	no	—
153	C₂	—	152	1	no	—
154	C₂	#127×D₁₉	1	1	yes	characteristic
155	C₂	#11927116	1	3	yes	—
156	C₂	#11927117	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597334

C₂

yes

maximal, complemented

C₂×#10597331

C₂

yes

maximal

#11926481

C₂

yes

maximal, characteristic, complemented

#11926480

C₂

yes

maximal, complemented

#11926479

C₂

yes

maximal, complemented

#11926389

C₂

yes

maximal, characteristic, complemented

C₁₉×#399

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

C₂²

yes

—

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×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597334

—

#10597331

—

C₁₉×#95

C₂²

yes

characteristic

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

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

—

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×D₄

yes

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×D₄

yes

—

Dic₃₈

—

#2658

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

2₋¹⁺⁴

yes

characteristic

C₂²×C₁₉

2₋¹⁺⁴

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

#127

yes

—

C₂×C₄⋊Q₈

—

—

—

—

—

D₁₉

yes

characteristic, complemented

#376

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#127

yes

characteristic

C₂×C₁₉

#536

yes

—

C₂×C₁₉

#536

yes

—

D₁₉

—

C₂²×Q₈

—

C₂²×D₄

—

C₄⋊Q₈

—

#124

—

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

C₂×D₁₉

yes

characteristic

100

C₁₉

#2658

yes

characteristic, complemented, Sylow

101

C₂⁴

—

102

C₂⁴

C₂²×D₁₉

yes

characteristic

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂×D₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

C₂²×D₁₉

yes

—

110

C₂²×C₄

C₂²×D₁₉

yes

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

116

C₂²⋊C₄

—

117

C₂²⋊C₄

—

118

C₄²

—

119

C₂³

—

120

C₂³

—

121

C₂³

—

122

C₂³

—

123

C₂³

—

124

C₂³

—

125

C₂³

C₂³×D₁₉

yes

characteristic

126

Q₈

—

127

D₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

D₄×D₁₉

yes

—

138

C₂²

—

139

C₂²

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

C₂×D₄×D₁₉

yes

—

145

C₂²

#10597433

yes

characteristic

146

C₂²

#10597436

yes

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₂

—

153

C₂

—

152

—

154

C₂

#127×D₁₉

yes

characteristic

155

C₂

#11927116

yes

—

156

C₂

#11927117

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#399	C₂
prime radical	C₂²×C₂²⋊D₁₉	C₂²
hypercenter	#399	D₁₉
hypocenter	C₁₉	#2658
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #399

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#399

C₂

prime radical

C₂²×C₂²⋊D₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #399

N	H ≅ G/N	type
1. C₂×#10597334	C₂	semidirect
3. #11926481	C₂	semidirect
4. #11926480	C₂	semidirect
5. #11926479	C₂	semidirect
6. #11926389	C₂	semidirect
7. C₁₉×#399	C₂	semidirect
79. #399	D₁₉	semidirect
100. C₁₉	#2658	semidirect

H ≅ G/N

type

1. C₂×#10597334

C₂

semidirect

3. #11926481

C₂

semidirect

4. #11926480

C₂

semidirect

5. #11926479

C₂

semidirect

6. #11926389

C₂

semidirect

7. C₁₉×#399

C₂

semidirect

79. #399

D₁₉

semidirect

100. C₁₉

#2658

semidirect

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

subgroup	index
C₂×#10597334	2
C₂×#10597331	2
#11926481	2
#11926480	2
#11926479	2
#11926389	2
C₁₉×#399	2
#2658	19

subgroup

index

C₁₉×#399

Subgroups — #14569744

Conjugacy classes of subgroups

Complements

Maximal subgroups