Group #14562103 — subgroups

Subgroups — #14562103

Order 2432.

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

normal subgroups only

This group has 246 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	#11927094	C₂	1	1	yes	maximal, characteristic
2	#11926597	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926271	C₂	1	4	yes	maximal, complemented
4	C₁₉×#432	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#64541	—	2	1	no	—
6	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	#10597376	—	2	1	no	—
8	#10597376	C₄	1	2	yes	—
9	#10597321	—	2	1	no	—
10	#10597320	C₄	1	1	yes	characteristic
11	C₄×D₇₆	—	2	1	no	—
12	C₄×D₇₆	C₂²	1	2	yes	—
13	#10597315	C₄	1	1	yes	characteristic
14	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₁₉×C₂²⋊C₈	—	2	1	no	—
16	C₁₉×#97	—	2	1	no	—
17	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
18	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
19	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
20	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₂²⋊D₁₉	—	2	2	no	—
24	#64541	—	4	4	no	—
25	C₂×D₇₆	—	2	1	no	—
26	C₂×D₇₆	—	2	1	no	—
27	C₂×D₇₆	C₂×C₄	1	2	yes	—
28	C₂×C₄×D₁₉	—	2	2	no	—
29	C₂×Dic₃₈	—	2	1	no	—
30	C₂×C₈×C₁₉	—	2	2	no	—
31	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₄²×C₁₉	D₄	1	1	yes	characteristic
34	C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	(C₂×D₁₉)⋊C₄	—	2	2	no	—
36	(C₂×D₁₉)⋊C₄	—	2	2	no	—
37	C₄⋊Dic₁₉	—	2	1	no	—
38	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×D₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂²⋊D₁₉	—	4	4	no	—
52	C₂×Dic₁₉	—	2	2	no	—
53	D₇₆	—	2	4	no	—
54	D₇₆	—	4	2	no	—
55	D₇₆	—	4	2	no	—
56	C₄×D₁₉	—	4	4	no	—
57	Dic₃₈	—	4	2	no	—
58	C₈×C₁₉	—	4	2	no	—
59	C₁₉⋊C₈	—	4	2	no	—
60	#1496	—	19	1	no	maximal, Sylow
61	C₂²×C₁₉	—	2	1	no	—
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	—	2	1	no	—
64	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×D₁₉	—	4	2	no	—
66	C₂×D₁₉	—	4	2	no	—
67	C₂×D₁₉	—	4	2	no	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	2	1	no	—
71	C₄×C₁₉	—	2	1	no	—
72	C₄×C₁₉	#131	1	2	yes	—
73	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
74	Dic₁₉	—	4	2	no	—
75	#532	—	19	1	no	—
76	#432	D₁₉	1	1	yes	characteristic, complemented
77	#431	—	19	1	no	—
78	D₄⋊C₈	—	19	4	no	—
79	C₂×C₁₉	—	4	1	no	—
80	C₂×C₁₉	#408	1	1	yes	characteristic
81	C₂×C₁₉	#418	1	1	yes	characteristic
82	C₂×C₁₉	#421	1	1	yes	characteristic
83	D₁₉	—	8	2	no	—
84	C₂×#41	—	38	1	no	—
85	C₄⋊Q₈	—	19	1	no	—
86	#127	—	19	1	no	—
87	#124	—	38	1	no	—
88	#121	—	19	2	no	—
89	#121	—	38	1	no	—
90	C₄×D₄	—	19	2	no	—
91	C₄×D₄	—	38	1	no	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	C₄⋊C₈	—	38	1	no	—
94	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
95	C₂²⋊C₈	—	2	1	no	—
96	C₂²⋊C₈	—	38	1	no	—
97	#97	—	2	1	no	—
98	C₄×C₈	—	19	2	no	—
99	C₁₉	#1496	1	1	yes	characteristic, complemented, Sylow
100	#41	—	76	4	no	—
101	C₂×Q₈	—	38	1	no	—
102	C₂×D₄	—	19	2	no	—
103	C₂×D₄	—	38	2	no	—
104	C₂×D₄	—	38	1	no	—
105	C₂×D₄	—	38	1	no	—
106	C₂²×C₄	—	38	2	no	—
107	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
108	C₂²×C₄	D₇₆	1	1	yes	characteristic
109	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂×C₈	—	2	2	no	—
111	C₂×C₈	—	38	2	no	—
112	C₄⋊C₄	—	19	2	no	—
113	C₄⋊C₄	—	38	1	no	—
114	C₂²⋊C₄	—	38	2	no	—
115	C₂²⋊C₄	—	38	2	no	—
116	C₄²	C₄×D₁₉	1	1	yes	characteristic
117	C₄²	D₇₆	1	1	yes	characteristic
118	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
119	C₄²	C₂²×D₁₉	1	1	yes	characteristic
120	C₂³	—	38	2	no	—
121	C₂³	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
122	Q₈	—	76	2	no	—
123	D₄	—	38	4	no	—
124	D₄	—	76	2	no	—
125	D₄	—	76	2	no	—
126	D₄	—	76	4	no	—
127	C₂×C₄	—	2	2	no	—
128	C₂×C₄	—	2	2	no	—
129	C₂×C₄	—	4	1	no	—
130	C₂×C₄	—	38	2	no	—
131	C₂×C₄	—	76	4	no	—
132	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
133	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
134	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
135	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
136	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
137	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
138	C₈	—	4	2	no	—
139	C₈	—	76	2	no	—
140	C₂²	—	2	1	no	—
141	C₂²	—	2	1	no	—
142	C₂²	—	2	1	no	—
143	C₂²	—	76	2	no	—
144	C₂²	—	76	2	no	—
145	C₂²	—	76	2	no	—
146	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
147	C₄	—	2	1	no	—
148	C₄	—	2	1	no	—
149	C₄	—	2	1	no	—
150	C₄	—	2	1	no	—
151	C₄	—	76	2	no	—
152	C₄	#10597353	1	2	yes	—
153	C₄	#10597395	1	2	yes	—
154	C₂	—	4	1	no	—
155	C₂	—	152	2	no	—
156	C₂	#11926512	1	1	yes	characteristic
157	C₂	#11926548	1	1	yes	characteristic
158	C₂	#11926560	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927094

C₂

yes

maximal, characteristic

#11926597

C₂

yes

maximal, characteristic, complemented

#11926271

C₂

yes

maximal, complemented

C₁₉×#432

C₂

yes

maximal, characteristic, complemented

C₂×#64541

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597376

—

#10597376

C₄

yes

—

#10597321

—

#10597320

C₄

yes

characteristic

C₄×D₇₆

—

C₄×D₇₆

C₂²

yes

—

#10597315

C₄

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

C₂×C₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×D₁₉

—

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

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1496

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#131

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

Dic₁₉

—

#532

—

#432

D₁₉

yes

characteristic, complemented

#431

—

D₄⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

D₁₉

—

C₂×#41

—

C₄⋊Q₈

—

—

—

—

—

C₄×D₄

—

C₄×D₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₁₉

#1496

yes

characteristic, complemented, Sylow

100

#41

—

101

C₂×Q₈

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂²×C₄

—

107

C₂²×C₄

C₄×D₁₉

yes

characteristic

108

C₂²×C₄

D₇₆

yes

characteristic

109

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

116

C₄²

C₄×D₁₉

yes

characteristic

117

C₄²

D₇₆

yes

characteristic

118

C₄²

C₂²⋊D₁₉

yes

characteristic

119

C₄²

C₂²×D₁₉

yes

characteristic

120

C₂³

—

121

C₂³

(C₂×D₁₉)⋊C₄

yes

characteristic

122

Q₈

—

123

D₄

—

124

D₄

—

125

D₄

—

126

D₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

133

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

134

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

135

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

136

C₂×C₄

C₂×D₇₆

yes

characteristic

137

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

138

C₈

—

139

C₈

—

140

C₂²

—

141

C₂²

—

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

146

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

—

151

C₄

—

152

C₄

#10597353

yes

—

153

C₄

#10597395

yes

—

154

C₂

—

155

C₂

—

152

—

156

C₂

#11926512

yes

characteristic

157

C₂

#11926548

yes

characteristic

158

C₂

#11926560

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₁₉
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#432	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	#11927094	C₂
cosocle	C₄²×C₁₉	C₂³
hypercenter	#432	D₁₉
hypocenter	C₁₉	#1496
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #432

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#432

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

#11927094

C₂

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #432

N	H ≅ G/N	type
2. #11926597	C₂	semidirect
3. #11926271	C₂	semidirect
4. C₁₉×#432	C₂	semidirect
76. #432	D₁₉	semidirect
99. C₁₉	#1496	semidirect

H ≅ G/N

type

2. #11926597

C₂

semidirect

3. #11926271

C₂

semidirect

4. C₁₉×#432

C₂

semidirect

76. #432

D₁₉

semidirect

99. C₁₉

#1496

semidirect

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

subgroup	index
#11927094	2
#11926597	2
#11926271	2
C₁₉×#432	2
#1496	19

subgroup

index

C₁₉×#432

Subgroups — #14562103

Conjugacy classes of subgroups

Complements

Maximal subgroups