Group #14563757 — subgroups

Subgroups — #14563757

Order 2432.

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

normal subgroups only

This group has 172 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	C₂×#10597279	C₂	1	1	yes	maximal, characteristic
2	#11926580	C₂	1	1	yes	maximal, characteristic
3	#11926500	C₂	1	1	yes	maximal, characteristic
4	#11926316	C₂	1	1	yes	maximal, characteristic
5	#11926314	C₂	1	1	yes	maximal, characteristic
6	#11926300	C₂	1	1	yes	maximal, characteristic
7	C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₁₉×#117	C₂²	1	1	yes	characteristic
11	#10597372	C₂²	1	1	yes	characteristic
12	C₂×#64520	C₂²	1	1	yes	characteristic
13	C₂×#64520	C₂²	1	1	yes	characteristic
14	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	#10597279	—	2	1	no	—
16	#10597279	—	2	1	no	—
17	#10597265	—	2	1	no	—
18	#10597264	—	2	1	no	—
19	#10597260	C₄	1	2	yes	complemented
20	C₄×C₁₉⋊C₈	C₄	1	2	yes	complemented
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₁₉	—	2	1	no	—
23	M₁₆×C₁₉	—	2	1	no	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₄⋊C₄×C₁₉	—	2	1	no	—
27	C₂²⋊C₄×C₁₉	—	2	1	no	—
28	C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	C₂×C₄	1	2	yes	—
31	C₂²⋊Dic₁₉	—	2	1	no	—
32	C₄⋊Dic₁₉	—	2	1	no	—
33	C₄×Dic₁₉	—	2	1	no	—
34	#64520	—	2	1	no	—
35	#64520	—	2	1	no	—
36	#64520	—	2	1	no	—
37	#64520	—	2	1	no	—
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
40	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
43	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
44	C₂×C₁₉⋊C₈	Q₈	1	1	yes	characteristic
45	C₂×C₁₉⋊C₈	Q₈	1	1	yes	characteristic
46	C₂³×C₁₉	#41	1	1	yes	characteristic
47	C₂×C₄×C₁₉	—	2	2	no	—
48	C₂×C₄×C₁₉	—	4	1	no	—
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×Q₈	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
53	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
54	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
55	C₂×Dic₁₉	—	4	1	no	—
56	C₈×C₁₉	—	4	1	no	—
57	C₁₉⋊C₈	—	2	2	no	—
58	C₁₉⋊C₈	—	4	1	no	—
59	C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
60	C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
61	C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
62	C₁₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
63	#1833	—	19	1	no	maximal, Sylow
64	C₂²×C₁₉	—	4	1	no	—
65	C₂²×C₁₉	#117	1	1	yes	characteristic
66	C₂²×C₁₉	#124	1	1	yes	characteristic
67	C₂²×C₁₉	#125	1	1	yes	characteristic
68	C₄×C₁₉	—	4	2	no	—
69	C₄×C₁₉	—	8	1	no	—
70	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₄×C₁₉	#117	1	1	yes	characteristic
72	C₄×C₁₉	#124	1	1	yes	characteristic
73	C₄×C₁₉	#125	1	1	yes	characteristic
74	Dic₁₉	—	8	1	no	—
75	C₂×#108	—	19	1	no	—
76	#427	—	19	1	no	—
77	#405	—	19	1	no	—
78	#344	—	19	1	no	—
79	#344	—	19	1	no	—
80	H(3,ℤ/4)	—	19	1	no	—
81	H(3,ℤ/4)	D₁₉	1	1	yes	characteristic
82	C₂×C₁₉	—	2	1	no	—
83	C₂×C₁₉	—	2	1	no	—
84	C₂×C₁₉	—	2	1	no	—
85	C₂×C₁₉	#382	1	1	yes	characteristic
86	C₂×M₁₆	—	19	1	no	—
87	C₂×M₁₆	—	19	1	no	—
88	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
89	C₂²×C₈	—	19	1	no	—
90	#117	—	19	1	no	—
91	#117	C₂×D₁₉	1	1	yes	characteristic
92	#117	C₂×D₁₉	1	1	yes	characteristic
93	#108	—	38	1	no	—
94	#108	—	38	1	no	—
95	#107	—	38	1	no	—
96	#106	—	38	1	no	—
97	#97	—	19	2	no	—
98	C₄×C₈	—	19	2	no	—
99	C₁₉	#1833	1	1	yes	characteristic, complemented, Sylow
100	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
101	M₁₆	—	2	1	no	—
102	M₁₆	—	2	1	no	—
103	M₁₆	—	38	1	no	—
104	M₁₆	—	38	1	no	—
105	M₁₆	—	38	1	no	—
106	M₁₆	—	38	1	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	19	1	no	—
109	C₂×C₈	—	19	1	no	—
110	C₂×C₈	—	19	1	no	—
111	C₂×C₈	—	19	1	no	—
112	C₂×C₈	—	19	1	no	—
113	C₂×C₈	—	19	1	no	—
114	C₂×C₈	—	19	2	no	—
115	C₂×C₈	—	38	1	no	—
116	C₄⋊C₄	—	2	1	no	—
117	C₄⋊C₄	—	2	1	no	—
118	C₄⋊C₄	—	38	1	no	—
119	C₂²⋊C₄	—	2	1	no	—
120	C₂²⋊C₄	—	2	1	no	—
121	C₂²⋊C₄	—	38	1	no	—
122	C₄²	—	2	1	no	—
123	C₄²	—	38	1	no	—
124	C₄²	C₄×D₁₉	1	2	yes	—
125	C₂³	#64543	1	1	yes	characteristic
126	C₂×C₄	—	2	2	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	76	1	no	—
129	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
130	C₂×C₄	#64541	1	1	yes	characteristic
131	C₂×C₄	#64541	1	1	yes	characteristic
132	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
133	C₂×C₄	#64543	1	1	yes	characteristic
134	C₂×C₄	Q₈×D₁₉	1	1	yes	characteristic
135	C₈	—	4	1	no	—
136	C₈	—	19	1	no	—
137	C₈	—	19	1	no	—
138	C₈	—	19	1	no	—
139	C₈	—	19	1	no	—
140	C₈	—	38	2	no	—
141	C₈	—	76	1	no	—
142	C₂²	—	4	1	no	—
143	C₂²	#10597323	1	1	yes	characteristic
144	C₂²	#10597331	1	1	yes	characteristic
145	C₂²	#10597335	1	1	yes	characteristic
146	C₄	—	4	2	no	—
147	C₄	—	8	1	no	—
148	C₄	—	152	1	no	—
149	C₄	#10597318	1	1	yes	characteristic
150	C₄	#10597331	1	1	yes	characteristic
151	C₄	#10597335	1	1	yes	characteristic
152	C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
153	C₂	—	2	1	no	—
154	C₂	—	2	1	no	—
155	C₂	—	2	1	no	—
156	C₂	#11926408	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597279

C₂

yes

maximal, characteristic

#11926580

C₂

yes

maximal, characteristic

#11926500

C₂

yes

maximal, characteristic

#11926316

C₂

yes

maximal, characteristic

#11926314

C₂

yes

maximal, characteristic

#11926300

C₂

yes

maximal, characteristic

C₁₉×H(3,ℤ/4)

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

—

—

—

C₄

yes

complemented

C₄×C₁₉⋊C₈

C₄

yes

complemented

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

Q₈

yes

characteristic

C₂×C₁₉⋊C₈

Q₈

yes

characteristic

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

C₁₉⋊C₈

C₄⋊C₄

yes

characteristic

#1833

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#382

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

#117

—

#117

C₂×D₁₉

yes

characteristic

#117

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₁₉

#1833

yes

characteristic, complemented, Sylow

100

C₂²×C₄

C₂²×D₁₉

yes

characteristic

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

—

122

C₄²

—

123

C₄²

—

124

C₄²

C₄×D₁₉

yes

—

125

C₂³

#64543

yes

characteristic

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

130

C₂×C₄

#64541

yes

characteristic

131

C₂×C₄

#64541

yes

characteristic

132

C₂×C₄

D₄×D₁₉

yes

characteristic

133

C₂×C₄

#64543

yes

characteristic

134

C₂×C₄

Q₈×D₁₉

yes

characteristic

135

C₈

—

136

C₈

—

137

C₈

—

138

C₈

—

139

C₈

—

140

C₈

—

141

C₈

—

142

C₂²

—

143

C₂²

#10597323

yes

characteristic

144

C₂²

#10597331

yes

characteristic

145

C₂²

#10597335

yes

characteristic

146

C₄

—

147

C₄

—

148

C₄

—

152

—

149

C₄

#10597318

yes

characteristic

150

C₄

#10597331

yes

characteristic

151

C₄

#10597335

yes

characteristic

152

C₄

C₄⋊C₄×D₁₉

yes

characteristic

153

C₂

—

154

C₂

—

155

C₂

—

156

C₂

#11926408

yes

characteristic

	subgroup	G/H
center	C₄	#10597318
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×H(3,ℤ/4)	C₂
socle	C₂×C₁₉	#382
prime radical	C₂³×C₁₉	#41
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	H(3,ℤ/4)	D₁₉
hypocenter	C₁₉	#1833
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ #117 ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#10597318

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×H(3,ℤ/4)

C₂

C₂×C₁₉

C₂³×C₁₉

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ #117 ◁ H(3,ℤ/4)

N	H ≅ G/N	type
19. #10597260	C₄	semidirect
20. C₄×C₁₉⋊C₈	C₄	semidirect
99. C₁₉	#1833	semidirect

H ≅ G/N

type

19. #10597260

C₄

semidirect

20. C₄×C₁₉⋊C₈

C₄

semidirect

99. C₁₉

#1833

semidirect

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

subgroup	index
C₂×#10597279	2
#11926580	2
#11926500	2
#11926316	2
#11926314	2
#11926300	2
C₁₉×H(3,ℤ/4)	2
#1833	19

subgroup

index

C₁₉×H(3,ℤ/4)

Subgroups — #14563757

Conjugacy classes of subgroups

Complements

Maximal subgroups