Group #14564368 — subgroups

Subgroups — #14564368

Order 2432.

248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 117 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×#10597275	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597275	C₂	1	1	yes	maximal, characteristic
3	#11926442	C₂	1	2	yes	maximal
4	#11926307	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂×Dic₁₉⋊C₄	—	2	2	no	—
12	C₄×C₈×C₁₉	—	2	2	no	—
13	C₁₉⋊#95	—	2	2	no	—
14	#10597275	—	2	2	no	—
15	#10597275	C₄	1	4	yes	complemented
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂²×Dic₁₉	—	2	2	no	—
20	C₂²×Dic₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₁₉	D₄	1	2	yes	—
25	C₂×C₈×C₁₉	Q₈	1	2	yes	—
26	C₂×C₈×C₁₉	Q₈	1	2	yes	—
27	C₄²×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	—	2	1	no	—
29	C₄⋊Dic₁₉	—	2	2	no	—
30	C₄⋊Dic₁₉	—	2	2	no	—
31	C₄⋊Dic₁₉	—	2	2	no	—
32	C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
33	Dic₁₉⋊C₄	—	4	4	no	—
34	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	2	1	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	D₈	1	2	yes	—
40	C₂×C₄×C₁₉	Q₁₆	1	2	yes	—
41	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₂×Dic₁₉	—	2	4	no	—
48	C₂×Dic₁₉	—	4	2	no	—
49	C₂×Dic₁₉	—	4	2	no	—
50	C₂×Dic₁₉	—	4	2	no	—
51	C₂×Dic₁₉	—	4	2	no	—
52	C₂×Dic₁₉	—	4	2	no	—
53	C₈×C₁₉	—	2	2	no	—
54	C₈×C₁₉	C₄⋊C₄	1	4	yes	complemented
55	#1942	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	C₄×D₄	1	1	yes	characteristic
57	C₂²×C₁₉	#121	1	1	yes	characteristic
58	C₂²×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
59	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
60	C₂²×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
61	C₂²×C₁₉	#135	1	1	yes	characteristic
62	C₂²×C₁₉	#135	1	1	yes	characteristic
63	C₄×C₁₉	—	2	2	no	—
64	C₄×C₁₉	—	2	2	no	—
65	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
67	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
68	C₄×C₁₉	#125	1	1	yes	characteristic
69	Dic₁₉	—	4	4	no	—
70	Dic₁₉	—	8	2	no	—
71	C₂×#107	—	19	1	no	—
72	C₂×#107	—	19	1	no	—
73	C₂×C₄×C₈	D₁₉	1	1	yes	characteristic
74	#389	—	19	2	no	—
75	#340	—	19	2	no	—
76	C₂×C₁₉	#389	1	1	yes	characteristic
77	C₂×C₁₉	C₄×D₈	1	1	yes	characteristic
78	C₂×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
79	C₂×C₁₉	#466	1	1	yes	characteristic
80	C₂×C₁₉	#467	1	1	yes	characteristic
81	C₂×C₁₉	#499	1	1	yes	characteristic
82	C₂×C₁₉	#500	1	1	yes	characteristic
83	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
84	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
85	C₂×C₄⋊C₄	—	19	2	no	—
86	C₂×C₄⋊C₄	—	19	2	no	—
87	C₂×C₄⋊C₄	—	38	2	no	—
88	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
89	#107	—	19	4	no	—
90	#107	—	38	2	no	—
91	C₄×C₈	—	2	2	no	—
92	#95	—	38	2	no	—
93	C₁₉	#1942	1	1	yes	characteristic, complemented, Sylow
94	C₂²×C₄	—	38	2	no	—
95	C₂²×C₄	—	38	2	no	—
96	C₂²×C₄	D₇₆	1	1	yes	characteristic
97	C₂²×C₄	D₇₆	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	Dic₃₈	1	2	yes	—
102	C₂×C₈	Dic₃₈	1	2	yes	—
103	C₂×C₈	C₄×D₁₉	1	2	yes	—
104	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
105	C₄⋊C₄	—	19	4	no	—
106	C₄⋊C₄	—	38	2	no	—
107	C₄⋊C₄	—	38	2	no	—
108	C₄⋊C₄	—	38	2	no	—
109	C₄⋊C₄	—	76	4	no	—
110	C₄²	—	2	1	no	—
111	C₄²	—	2	1	no	—
112	C₂³	C₂×D₇₆	1	1	yes	characteristic
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	1	no	—
117	C₂×C₄	—	38	4	no	—
118	C₂×C₄	—	76	2	no	—
119	C₂×C₄	—	76	2	no	—
120	C₂×C₄	—	76	2	no	—
121	C₂×C₄	—	76	2	no	—
122	C₂×C₄	—	76	2	no	—
123	C₂×C₄	D₁₅₂	1	2	yes	—
124	C₂×C₄	Dic₇₆	1	2	yes	—
125	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
126	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
127	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
128	C₂×C₄	#64541	1	1	yes	characteristic
129	C₂×C₄	#64541	1	1	yes	characteristic
130	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
131	C₈	—	2	2	no	—
132	C₈	Dic₁₉⋊C₄	1	4	yes	complemented
133	C₂²	#10597315	1	1	yes	characteristic
134	C₂²	C₄×D₇₆	1	1	yes	characteristic
135	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
136	C₂²	#10597350	1	1	yes	characteristic
137	C₂²	#10597350	1	1	yes	characteristic
138	C₂²	C₂×Dic₇₆	1	1	yes	characteristic
139	C₂²	#10597376	1	1	yes	characteristic
140	C₄	—	2	2	no	—
141	C₄	—	2	2	no	—
142	C₄	—	76	4	no	—
143	C₄	—	152	2	no	—
144	C₄	C₄×Dic₃₈	1	1	yes	characteristic
145	C₄	#10597316	1	1	yes	characteristic
146	C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
147	C₄	#10597370	1	1	yes	characteristic
148	C₂	#11926442	1	1	yes	characteristic
149	C₂	C₄×D₁₅₂	1	1	yes	characteristic
150	C₂	C₄×Dic₇₆	1	1	yes	characteristic
151	C₂	#11926780	1	1	yes	characteristic
152	C₂	#11926785	1	1	yes	characteristic
153	C₂	#11926946	1	1	yes	characteristic
154	C₂	#11926949	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597275

C₂

yes

maximal, characteristic

C₂×#10597275

C₂

yes

maximal, characteristic

#11926442

C₂

yes

maximal

#11926307

C₂

yes

maximal

C₂×C₄×C₈×C₁₉

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₄×C₈×C₁₉

—

C₁₉⋊#95

—

#10597275

—

#10597275

C₄

yes

complemented

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

Q₈

yes

—

C₂×C₈×C₁₉

Q₈

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

Q₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄⋊C₄

yes

complemented

#1942

—

maximal, Sylow

C₂²×C₁₉

C₄×D₄

yes

characteristic

C₂²×C₁₉

#121

yes

characteristic

C₂²×C₁₉

C₄⋊Q₈

yes

characteristic

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂²×C₁₉

C₂×Q₁₆

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₄×Q₈

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

#125

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×#107

—

C₂×#107

—

C₂×C₄×C₈

D₁₉

yes

characteristic

#389

—

#340

—

C₂×C₁₉

#389

yes

characteristic

C₂×C₁₉

C₄×D₈

yes

characteristic

C₂×C₁₉

C₄×Q₁₆

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#107

—

#107

—

C₄×C₈

—

#95

—

C₁₉

#1942

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

D₇₆

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

Dic₃₈

yes

—

102

C₂×C₈

Dic₃₈

yes

—

103

C₂×C₈

C₄×D₁₉

yes

—

104

C₂×C₈

C₂²⋊D₁₉

yes

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

108

C₄⋊C₄

—

109

C₄⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₂³

C₂×D₇₆

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

D₁₅₂

yes

—

124

C₂×C₄

Dic₇₆

yes

—

125

C₂×C₄

C₂×Dic₃₈

yes

characteristic

126

C₂×C₄

C₂×Dic₃₈

yes

characteristic

127

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

128

C₂×C₄

#64541

yes

characteristic

129

C₂×C₄

#64541

yes

characteristic

130

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

131

C₈

—

132

C₈

Dic₁₉⋊C₄

yes

complemented

133

C₂²

#10597315

yes

characteristic

134

C₂²

C₄×D₇₆

yes

characteristic

135

C₂²

C₂×D₁₅₂

yes

characteristic

136

C₂²

#10597350

yes

characteristic

137

C₂²

#10597350

yes

characteristic

138

C₂²

C₂×Dic₇₆

yes

characteristic

139

C₂²

#10597376

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

152

—

144

C₄

C₄×Dic₃₈

yes

characteristic

145

C₄

#10597316

yes

characteristic

146

C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

147

C₄

#10597370

yes

characteristic

148

C₂

#11926442

yes

characteristic

149

C₂

C₄×D₁₅₂

yes

characteristic

150

C₂

C₄×Dic₇₆

yes

characteristic

151

C₂

#11926780

yes

characteristic

152

C₂

#11926785

yes

characteristic

153

C₂

#11926946

yes

characteristic

154

C₂

#11926949

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₇₆
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₄×C₈×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×C₄×C₈	D₁₉
hypocenter	C₁₉	#1942
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₇₆

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₄×C₈×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₂×C₄×C₈

D₁₉

hypocenter

C₁₉

#1942

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
15. #10597275	C₄	semidirect
54. C₈×C₁₉	C₄⋊C₄	semidirect
93. C₁₉	#1942	semidirect
132. C₈	Dic₁₉⋊C₄	semidirect

H ≅ G/N

type

15. #10597275

C₄

semidirect

54. C₈×C₁₉

C₄⋊C₄

semidirect

93. C₁₉

#1942

semidirect

132. C₈

Dic₁₉⋊C₄

semidirect

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

subgroup	index
C₂×#10597275	2
#11926442	2
#11926307	2
C₂×C₄×C₈×C₁₉	2
#1942	19

subgroup

index

C₂×C₄×C₈×C₁₉

Subgroups — #14564368

Conjugacy classes of subgroups

Complements

Maximal subgroups