Group #14562063 — subgroups

Subgroups — #14562063

Order 2432.

248 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 93 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×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic
2	#11926597	C₂	1	1	yes	maximal, characteristic
3	#11926274	C₂	1	4	yes	maximal, complemented
4	C₁₉×#423	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₃₈	C₄	1	1	yes	characteristic
6	C₂×M₁₆×C₁₉	—	2	1	no	—
7	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₁₉	C₄	1	1	yes	characteristic
9	C₂×Dic₁₉⋊C₄	—	2	1	no	—
10	C₂×C₄×Dic₁₉	—	2	1	no	—
11	C₄×Dic₃₈	—	2	1	no	—
12	C₄×Dic₃₈	—	2	1	no	—
13	C₄×Dic₃₈	C₄	1	2	yes	—
14	C₄×Dic₃₈	C₂²	1	2	yes	—
15	C₁₉×C₄⋊C₈	—	2	1	no	—
16	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
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	C₂²×Dic₁₉	—	2	1	no	—
24	C₂²×Dic₁₉	—	2	1	no	—
25	C₂×Dic₃₈	—	2	1	no	—
26	C₂×Dic₃₈	—	2	4	no	—
27	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
28	M₁₆×C₁₉	—	4	2	no	—
29	C₂×C₈×C₁₉	—	2	2	no	—
30	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
36	Dic₁₉⋊C₄	—	2	2	no	—
37	Dic₁₉⋊C₄	—	2	2	no	—
38	C₄×Dic₁₉	—	2	2	no	—
39	C₄×Dic₁₉	—	2	2	no	—
40	C₂×C₁₉⋊C₈	—	2	2	no	—
41	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
48	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
49	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₁₉	—	2	4	no	—
53	C₂×Dic₁₉	—	2	2	no	—
54	C₂×Dic₁₉	—	2	2	no	—
55	C₂×Dic₁₉	—	4	2	no	—
56	Dic₃₈	—	2	4	no	—
57	Dic₃₈	—	2	2	no	—
58	Dic₃₈	M₁₆	1	4	yes	complemented
59	C₈×C₁₉	—	4	2	no	—
60	C₁₉⋊C₈	—	4	2	no	—
61	#1487	—	19	1	no	maximal, Sylow
62	C₂²×C₁₉	—	2	1	no	—
63	C₂²×C₁₉	—	2	1	no	—
64	C₂²×C₁₉	#103	1	2	yes	—
65	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₄×C₁₉	—	2	1	no	—
67	C₄×C₁₉	—	2	1	no	—
68	C₄×C₁₉	—	2	1	no	—
69	C₄×C₁₉	#103	1	2	yes	—
70	C₄×C₁₉	C₂×M₁₆	1	2	yes	—
71	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
72	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
73	Dic₁₉	—	2	4	no	—
74	Dic₁₉	—	4	2	no	—
75	C₂×C₄×Q₈	—	19	1	no	—
76	#431	—	19	1	no	—
77	#423	D₁₉	1	1	yes	characteristic
78	Q₈⋊C₈	—	19	4	no	—
79	C₂×C₁₉	—	2	2	no	—
80	C₂×C₁₉	#407	1	1	yes	characteristic
81	C₂×C₁₉	C₂×#103	1	1	yes	characteristic
82	C₂×C₁₉	#421	1	1	yes	characteristic
83	C₂²×Q₈	—	19	1	no	—
84	C₂×M₁₆	—	2	1	no	—
85	C₄×Q₈	—	19	2	no	—
86	C₄×Q₈	—	19	2	no	—
87	C₄×Q₈	—	38	1	no	—
88	C₄×Q₈	—	38	1	no	—
89	C₂×C₄⋊C₄	—	19	1	no	—
90	C₂×C₄⋊C₄	—	38	1	no	—
91	C₂×C₄²	—	38	1	no	—
92	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
93	C₄⋊C₈	—	2	1	no	—
94	C₄⋊C₈	—	38	1	no	—
95	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
96	C₂²⋊C₈	—	38	1	no	—
97	C₄×C₈	—	19	2	no	—
98	C₁₉	#1487	1	1	yes	characteristic, complemented, Sylow
99	C₂×Q₈	—	19	2	no	—
100	C₂×Q₈	—	38	4	no	—
101	C₂×Q₈	—	38	1	no	—
102	C₂²×C₄	—	38	1	no	—
103	C₂²×C₄	—	38	1	no	—
104	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
105	C₂²×C₄	D₇₆	1	1	yes	characteristic
106	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
107	M₁₆	—	4	2	no	—
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	—	38	2	no	—
110	C₄⋊C₄	—	19	2	no	—
111	C₄⋊C₄	—	38	2	no	—
112	C₄⋊C₄	—	38	1	no	—
113	C₄⋊C₄	—	38	2	no	—
114	C₄²	—	38	2	no	—
115	C₄²	—	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	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
121	Q₈	—	19	4	no	—
122	Q₈	—	38	4	no	—
123	Q₈	—	38	2	no	—
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	38	4	no	—
127	C₂×C₄	—	38	2	no	—
128	C₂×C₄	—	38	2	no	—
129	C₂×C₄	—	76	2	no	—
130	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
131	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
132	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
133	C₂×C₄	#64526	1	2	yes	—
134	C₂×C₄	#64528	1	2	yes	—
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	#10597267	1	2	yes	—
143	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
144	C₄	—	2	1	no	—
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	—	38	4	no	—
148	C₄	—	76	2	no	—
149	C₄	#10597267	1	2	yes	—
150	C₄	M₁₆×D₁₉	1	2	yes	—
151	C₄	C₂×#64526	1	1	yes	characteristic
152	C₄	C₂×#64528	1	1	yes	characteristic
153	C₂	—	2	2	no	—
154	C₂	#11926507	1	1	yes	characteristic
155	C₂	C₂×#10597267	1	1	yes	characteristic
156	C₂	#11926560	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₃₈

C₂

yes

maximal, characteristic

#11926597

C₂

yes

maximal, characteristic

#11926274

C₂

yes

maximal, complemented

C₁₉×#423

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₄

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

C₄

yes

—

C₄×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₂²

yes

—

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

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

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

SD₁₆

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

M₁₆

yes

complemented

C₈×C₁₉

—

C₁₉⋊C₈

—

#1487

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#103

yes

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#103

yes

—

C₄×C₁₉

C₂×M₁₆

yes

—

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

C₂×Q₁₆

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×C₄×Q₈

—

#431

—

#423

D₁₉

yes

characteristic

Q₈⋊C₈

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×Q₈

—

C₂×M₁₆

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

C₂²⋊C₈

—

C₄×C₈

—

C₁₉

#1487

yes

characteristic, complemented, Sylow

C₂×Q₈

—

100

C₂×Q₈

—

101

C₂×Q₈

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₄×D₁₉

yes

characteristic

105

C₂²×C₄

D₇₆

yes

characteristic

106

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

107

M₁₆

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄²

—

115

C₄²

—

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

(C₂×D₁₉)⋊C₄

yes

characteristic

121

Q₈

—

122

Q₈

—

123

Q₈

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

131

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

132

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

133

C₂×C₄

#64526

yes

—

134

C₂×C₄

#64528

yes

—

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

#10597267

yes

—

143

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

144

C₄

—

145

C₄

—

146

C₄

—

147

C₄

—

148

C₄

—

149

C₄

#10597267

yes

—

150

C₄

M₁₆×D₁₉

yes

—

151

C₄

C₂×#64526

yes

characteristic

152

C₄

C₂×#64528

yes

characteristic

153

C₂

—

154

C₂

#11926507

yes

characteristic

155

C₂

C₂×#10597267

yes

characteristic

156

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×#423	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₉	C₂²⋊C₄
cosocle	C₄²×C₁₉	C₂³
hypercenter	#423	D₁₉
hypocenter	C₁₉	#1487
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₁₉

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#423

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₉

C₂²⋊C₄

cosocle

C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

N	H ≅ G/N	type
3. #11926274	C₂	semidirect
58. Dic₃₈	M₁₆	semidirect
98. C₁₉	#1487	semidirect

H ≅ G/N

type

3. #11926274

C₂

semidirect

58. Dic₃₈

M₁₆

semidirect

98. C₁₉

#1487

semidirect

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

subgroup	index
C₂×C₄×Dic₃₈	2
#11926597	2
#11926274	2
C₁₉×#423	2
#1487	19

subgroup

index

C₂×C₄×Dic₃₈

#11926597

#11926274

C₁₉×#423

#1487

Subgroups — #14562063

Conjugacy classes of subgroups

Complements

Maximal subgroups