Group #14563468 — subgroups

Subgroups — #14563468

Order 2432.

324 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 129 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	C₂×#10597267	C₂	1	2	yes	maximal
3	C₂×#10597260	C₂	1	1	yes	maximal, characteristic
4	#11926306	C₂	1	2	yes	maximal
5	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₉	—	2	1	no	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₄	—	2	1	no	—
12	C₂×C₄×Dic₁₉	—	2	1	no	—
13	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
14	C₄×Dic₃₈	—	2	2	no	—
15	C₄×Dic₃₈	C₄	1	4	yes	complemented
16	C₁₉×#95	—	2	1	no	—
17	#10597267	C₄	1	8	yes	complemented
18	#10597260	—	2	2	no	—
19	C₂²×C₄×C₁₉	—	2	2	no	—
20	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₉	C₂³	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	2	no	—
27	C₂×Dic₃₈	C₂×C₄	1	4	yes	—
28	C₂×Dic₃₈	C₂×C₄	1	2	yes	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
31	C₄²×C₁₉	—	4	2	no	—
32	C₄²×C₁₉	C₂×C₄	1	2	yes	—
33	C₄²×C₁₉	D₄	1	2	yes	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
36	Dic₁₉⋊C₄	—	2	4	no	—
37	C₄×Dic₁₉	—	2	4	no	—
38	C₂×C₁₉⋊C₈	—	2	2	no	—
39	C₂×C₁₉⋊C₈	—	2	2	no	—
40	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
41	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	4	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
52	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#41	1	2	yes	—
54	C₂×Dic₁₉	—	2	2	no	—
55	C₂×Dic₁₉	—	2	4	no	—
56	C₂×Dic₁₉	—	2	2	no	—
57	C₂×Dic₁₉	—	4	1	no	—
58	C₂×Dic₁₉	—	4	1	no	—
59	Dic₃₈	—	2	2	no	—
60	Dic₃₈	—	2	4	no	—
61	Dic₃₈	C₄²	1	4	yes	complemented
62	C₁₉⋊C₈	—	2	4	no	—
63	#1763	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₁₉	C₄×D₄	1	2	yes	—
66	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
67	C₂²×C₁₉	#137	1	1	yes	characteristic
68	C₂²×C₁₉	#137	1	2	yes	—
69	C₄×C₁₉	—	2	2	no	—
70	C₄×C₁₉	—	2	2	no	—
71	C₄×C₁₉	—	4	4	no	—
72	C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
73	C₄×C₁₉	#117	1	1	yes	characteristic
74	C₄×C₁₉	C₄×D₄	1	2	yes	—
75	Dic₁₉	—	2	4	no	—
76	Dic₁₉	—	4	2	no	—
77	C₂×C₄×Q₈	—	19	1	no	—
78	C₂×#103	—	19	2	no	—
79	C₂×#97	—	19	1	no	—
80	C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
81	#340	—	19	2	no	—
82	C₂×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₁₉	#417	1	1	yes	characteristic
84	C₂×C₁₉	#419	1	1	yes	characteristic
85	C₂×C₁₉	#440	1	2	yes	—
86	C₂×C₁₉	#441	1	2	yes	—
87	C₂²×Q₈	—	19	1	no	—
88	C₂²×C₈	—	19	2	no	—
89	C₄×Q₈	—	19	4	no	—
90	C₄×Q₈	—	38	2	no	—
91	C₂×C₄⋊C₄	—	19	1	no	—
92	C₂×C₄⋊C₄	—	38	1	no	—
93	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
94	C₂×C₄²	—	2	1	no	—
95	C₂×C₄²	—	38	1	no	—
96	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
97	#103	—	19	8	no	—
98	#97	—	38	2	no	—
99	#95	—	2	1	no	—
100	C₁₉	#1763	1	1	yes	characteristic, complemented, Sylow
101	C₂×Q₈	—	19	4	no	—
102	C₂×Q₈	—	19	2	no	—
103	C₂×Q₈	—	38	1	no	—
104	C₂×Q₈	—	38	2	no	—
105	C₂²×C₄	—	2	2	no	—
106	C₂²×C₄	—	38	1	no	—
107	C₂²×C₄	—	38	1	no	—
108	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
109	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
110	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
111	C₂×C₈	—	19	4	no	—
112	C₂×C₈	—	38	2	no	—
113	C₂×C₈	—	38	2	no	—
114	C₄⋊C₄	—	2	2	no	—
115	C₄⋊C₄	—	19	2	no	—
116	C₄⋊C₄	—	38	4	no	—
117	C₄⋊C₄	—	38	1	no	—
118	C₄⋊C₄	C₄×D₁₉	1	4	yes	—
119	C₄²	—	4	2	no	—
120	C₄²	—	38	4	no	—
121	C₄²	C₄×D₁₉	1	2	yes	—
122	C₄²	D₇₆	1	2	yes	—
123	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
124	Q₈	—	19	4	no	—
125	Q₈	—	38	2	no	—
126	Q₈	—	38	4	no	—
127	C₂×C₄	—	2	1	no	—
128	C₂×C₄	—	2	1	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	4	2	no	—
132	C₂×C₄	—	4	2	no	—
133	C₂×C₄	—	38	2	no	—
134	C₂×C₄	—	38	4	no	—
135	C₂×C₄	—	38	2	no	—
136	C₂×C₄	—	76	1	no	—
137	C₂×C₄	—	76	1	no	—
138	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
139	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
140	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
141	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
142	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
143	C₂×C₄	#64541	1	2	yes	—
144	C₈	—	38	4	no	—
145	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
146	C₂²	C₄×C₂²⋊D₁₉	1	2	yes	—
147	C₂²	#10597378	1	1	yes	characteristic
148	C₂²	#10597388	1	1	yes	characteristic
149	C₂²	#10597397	1	2	yes	—
150	C₄	—	2	2	no	—
151	C₄	—	2	2	no	—
152	C₄	—	4	4	no	—
153	C₄	—	38	4	no	—
154	C₄	—	76	2	no	—
155	C₄	C₄²×D₁₉	1	1	yes	characteristic
156	C₄	#10597318	1	1	yes	characteristic
157	C₄	C₄×D₇₆	1	2	yes	—
158	C₂	C₄×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
159	C₂	#11926543	1	1	yes	characteristic
160	C₂	#11926552	1	1	yes	characteristic
161	C₂	#11926644	1	2	yes	—
162	C₂	#11926649	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₃₈

C₂

yes

maximal, characteristic

C₂×#10597267

C₂

yes

maximal

C₂×#10597260

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

C₄×C₄⋊C₄×C₁₉

C₂

yes

maximal, characteristic

C₂²×Dic₃₈

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

C₄×Dic₃₈

—

C₄×Dic₃₈

C₄

yes

complemented

C₁₉×#95

—

#10597267

C₄

yes

complemented

#10597260

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₂×Dic₃₈

C₂×C₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

C₄²

yes

complemented

C₁₉⋊C₈

—

#1763

—

maximal, Sylow

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄²

yes

characteristic

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

—

Dic₁₉

—

Dic₁₉

—

C₂×C₄×Q₈

—

C₂×#103

—

C₂×#97

—

C₄×C₄⋊C₄

D₁₉

yes

characteristic

#340

—

C₂×C₁₉

C₄×C₂²⋊C₄

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×C₁₉

#441

yes

—

C₂²×Q₈

—

C₂²×C₈

—

C₄×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

—

—

—

100

C₁₉

#1763

yes

characteristic, complemented, Sylow

101

C₂×Q₈

—

102

C₂×Q₈

—

103

C₂×Q₈

—

104

C₂×Q₈

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

109

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

110

C₂²×C₄

C₂²×D₁₉

yes

characteristic

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

C₄×D₁₉

yes

—

119

C₄²

—

120

C₄²

—

121

C₄²

C₄×D₁₉

yes

—

122

C₄²

D₇₆

yes

—

123

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

124

Q₈

—

125

Q₈

—

126

Q₈

—

127

C₂×C₄

—

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

—

138

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

139

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

140

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

141

C₂×C₄

C₂×C₄×D₁₉

yes

—

142

C₂×C₄

C₂×D₇₆

yes

characteristic

143

C₂×C₄

#64541

yes

—

144

C₈

—

145

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

146

C₂²

C₄×C₂²⋊D₁₉

yes

—

147

C₂²

#10597378

yes

characteristic

148

C₂²

#10597388

yes

characteristic

149

C₂²

#10597397

yes

—

150

C₄

—

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

C₄²×D₁₉

yes

characteristic

156

C₄

#10597318

yes

characteristic

157

C₄

C₄×D₇₆

yes

—

158

C₂

C₄×(C₂×D₁₉)⋊C₄

yes

characteristic

159

C₂

#11926543

yes

characteristic

160

C₂

#11926552

yes

characteristic

161

C₂

#11926644

yes

—

162

C₂

#11926649

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator	C₄×C₁₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₄×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#1763
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator

C₄×C₁₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₄×C₄⋊C₄×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₄×C₄⋊C₄

D₁₉

hypocenter

C₁₉

#1763

LCS

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

N	H ≅ G/N	type
15. C₄×Dic₃₈	C₄	semidirect
17. #10597267	C₄	semidirect
61. Dic₃₈	C₄²	semidirect
100. C₁₉	#1763	semidirect

H ≅ G/N

type

15. C₄×Dic₃₈

C₄

semidirect

17. #10597267

C₄

semidirect

61. Dic₃₈

C₄²

semidirect

100. C₁₉

#1763

semidirect

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

subgroup	index
C₂×C₄×Dic₃₈	2
C₂×#10597267	2
C₂×#10597260	2
#11926306	2
C₄×C₄⋊C₄×C₁₉	2
#1763	19

subgroup

index

C₂×C₄×Dic₃₈

C₄×C₄⋊C₄×C₁₉

Subgroups — #14563468

Conjugacy classes of subgroups

Complements

Maximal subgroups