Group #14564942 — subgroups

Subgroups — #14564942

Order 2432.

264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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	#11927344	C₂	1	1	yes	maximal, characteristic
2	#11926572	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926538	C₂	1	2	yes	maximal, complemented
4	#11926517	C₂	1	2	yes	maximal, complemented
5	C₁₉×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#64541	C₂²	1	2	yes	—
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#117	C₂²	1	2	yes	—
9	#10597372	C₂²	1	1	yes	characteristic
10	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
11	#10597355	—	2	2	no	—
12	#10597354	—	2	2	no	—
13	#10597350	—	2	2	no	—
14	Dic₁₉⋊C₈	—	2	2	no	—
15	#10597267	—	2	2	no	—
16	#10597266	—	2	2	no	—
17	#10597263	—	2	4	no	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₂×C₂²⋊D₁₉	—	2	2	no	—
20	#64541	—	2	2	no	—
21	#64541	—	2	2	no	—
22	#64541	—	2	2	no	—
23	#64541	—	2	2	no	—
24	C₂×D₇₆	D₄	1	2	yes	—
25	C₂×C₄×D₁₉	—	2	2	no	—
26	C₂×Dic₃₈	D₄	1	2	yes	—
27	M₁₆×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	D₄	1	2	yes	—
29	C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂²⋊C₄×C₁₉	—	2	2	no	—
31	C₄²×C₁₉	—	2	2	no	—
32	C₂²⋊Dic₁₉	D₄	1	2	yes	—
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄×Dic₁₉	—	2	1	no	—
35	C₂×C₁₉⋊C₈	—	2	2	no	—
36	C₂×C₁₉⋊C₈	—	2	1	no	—
37	Dic₇₆	—	2	2	no	—
38	D₁₅₂	—	2	2	no	—
39	#64516	—	2	4	no	—
40	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×D₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	4	2	no	—
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₉	#41	1	2	yes	—
46	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₂²⋊D₁₉	—	4	2	no	—
48	C₂²⋊D₁₉	—	4	2	no	—
49	C₂×Dic₁₉	—	2	2	no	—
50	C₂×Dic₁₉	—	2	2	no	—
51	D₇₆	—	2	2	no	—
52	D₇₆	—	2	2	no	—
53	C₄×D₁₉	—	4	2	no	—
54	C₄×D₁₉	—	4	2	no	—
55	Dic₃₈	—	2	2	no	—
56	Dic₃₈	—	2	2	no	—
57	C₈×C₁₉	—	2	2	no	—
58	C₁₉⋊C₈	—	4	1	no	—
59	#2053	—	19	1	no	maximal, Sylow
60	C₂²×C₁₉	—	4	1	no	—
61	C₂²×C₁₉	#121	1	2	yes	—
62	C₂²×C₁₉	#121	1	1	yes	characteristic
63	C₂×D₁₉	—	4	2	no	—
64	C₂×D₁₉	—	8	2	no	—
65	C₄×C₁₉	—	8	2	no	—
66	C₄×C₁₉	#120	1	1	yes	characteristic
67	C₄×C₁₉	#123	1	2	yes	—
68	C₄×C₁₉	#124	1	1	yes	characteristic
69	Dic₁₉	—	4	2	no	—
70	Dic₁₉	—	4	2	no	—
71	#575	—	19	1	no	—
72	#424	—	19	1	no	—
73	#416	—	19	2	no	—
74	#410	—	19	2	no	—
75	H(3,ℤ/4)	D₁₉	1	1	yes	characteristic, complemented
76	C₂×C₁₉	—	2	1	no	—
77	C₂×C₁₉	—	2	2	no	—
78	C₂×C₁₉	#394	1	1	yes	characteristic
79	D₁₉	—	8	2	no	—
80	C₂×#41	—	19	2	no	—
81	#137	—	38	2	no	—
82	AGL(1,ℤ/8)	—	38	2	no	—
83	#135	—	38	2	no	—
84	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
85	C₂²×C₈	—	19	1	no	—
86	#117	—	19	1	no	—
87	#117	C₂×D₁₉	1	2	yes	—
88	C₄⋊C₈	—	38	2	no	—
89	#103	—	38	2	no	—
90	#102	—	38	2	no	—
91	#99	—	38	4	no	—
92	C₁₉	#2053	1	1	yes	characteristic, complemented, Sylow
93	#41	—	38	2	no	—
94	#41	—	38	2	no	—
95	#41	—	38	2	no	—
96	#41	—	38	2	no	—
97	C₂×Q₈	—	19	2	no	—
98	C₂×D₄	—	19	2	no	—
99	C₂×D₄	—	38	2	no	—
100	C₂²×C₄	—	38	2	no	—
101	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
102	Q₁₆	—	38	2	no	—
103	SD₁₆	—	38	4	no	—
104	D₈	—	38	2	no	—
105	M₁₆	—	2	2	no	—
106	C₂×C₈	—	38	1	no	—
107	C₂×C₈	—	38	2	no	—
108	C₂×C₈	D₇₆	1	2	yes	—
109	C₄⋊C₄	—	2	2	no	—
110	C₄⋊C₄	—	38	1	no	—
111	C₂²⋊C₄	—	2	2	no	—
112	C₂²⋊C₄	—	19	2	no	—
113	C₄²	—	2	2	no	—
114	C₄²	—	38	1	no	—
115	C₂³	—	38	2	no	—
116	C₂³	D₄×D₁₉	1	1	yes	characteristic
117	Q₈	—	38	2	no	—
118	Q₈	—	38	2	no	—
119	D₄	—	38	2	no	—
120	D₄	—	38	2	no	—
121	D₄	—	76	2	no	—
122	D₄	—	76	2	no	—
123	C₂×C₄	—	4	2	no	—
124	C₂×C₄	—	38	2	no	—
125	C₂×C₄	—	38	2	no	—
126	C₂×C₄	—	76	2	no	—
127	C₂×C₄	—	76	2	no	—
128	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
129	C₂×C₄	#64541	1	2	yes	—
130	C₂×C₄	D₄×D₁₉	1	2	yes	—
131	C₂×C₄	#64545	1	1	yes	characteristic
132	C₈	—	2	2	no	—
133	C₈	—	76	1	no	—
134	C₂²	—	4	1	no	—
135	C₂²	—	76	2	no	—
136	C₂²	—	152	2	no	—
137	C₂²	#10597330	1	2	yes	—
138	C₂²	#10597341	1	1	yes	characteristic
139	C₄	—	8	2	no	—
140	C₄	—	76	2	no	—
141	C₄	—	76	2	no	—
142	C₄	#10597321	1	1	yes	characteristic
143	C₄	#10597328	1	1	yes	characteristic
144	C₄	#10597340	1	2	yes	—
145	C₂	—	2	2	no	—
146	C₂	—	2	1	no	—
147	C₂	—	152	2	no	—
148	C₂	#11926462	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927344

C₂

yes

maximal, characteristic

#11926572

C₂

yes

maximal, characteristic, complemented

#11926538

C₂

yes

maximal, complemented

#11926517

C₂

yes

maximal, complemented

C₁₉×H(3,ℤ/4)

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

—

#10597372

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

—

—

—

Dic₁₉⋊C₈

—

#10597267

—

#10597266

—

#10597263

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

—

—

—

—

C₂×D₇₆

D₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

D₄

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂²⋊Dic₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

D₁₅₂

—

#64516

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

#41

yes

characteristic

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2053

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

#121

yes

—

C₂²×C₁₉

#121

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#120

yes

characteristic

C₄×C₁₉

#123

yes

—

C₄×C₁₉

#124

yes

characteristic

Dic₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#394

yes

characteristic

D₁₉

—

C₂×#41

—

#137

—

AGL(1,ℤ/8)

—

#135

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

#117

—

#117

C₂×D₁₉

yes

—

C₄⋊C₈

—

#103

—

#102

—

#99

—

C₁₉

#2053

yes

characteristic, complemented, Sylow

—

—

—

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

100

C₂²×C₄

—

101

C₂²×C₄

C₂²×D₁₉

yes

characteristic

102

Q₁₆

—

103

SD₁₆

—

104

D₈

—

105

M₁₆

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

D₇₆

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₂²⋊C₄

—

112

C₂²⋊C₄

—

113

C₄²

—

114

C₄²

—

115

C₂³

—

116

C₂³

D₄×D₁₉

yes

characteristic

117

Q₈

—

118

Q₈

—

119

D₄

—

120

D₄

—

121

D₄

—

122

D₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₂×D₇₆

yes

characteristic

129

C₂×C₄

#64541

yes

—

130

C₂×C₄

D₄×D₁₉

yes

—

131

C₂×C₄

#64545

yes

characteristic

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

152

—

137

C₂²

#10597330

yes

—

138

C₂²

#10597341

yes

characteristic

139

C₄

—

140

C₄

—

141

C₄

—

142

C₄

#10597321

yes

characteristic

143

C₄

#10597328

yes

characteristic

144

C₄

#10597340

yes

—

145

C₂

—

146

C₂

—

147

C₂

—

152

—

148

C₂

#11926462

yes

characteristic

	subgroup	G/H
center	C₄	#10597321
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×H(3,ℤ/4)	C₂
socle	C₂×C₁₉	#394
prime radical	#11927344	C₂
hypercenter	H(3,ℤ/4)	D₁₉
hypocenter	C₁₉	#2053
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#10597321

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×H(3,ℤ/4)

C₂

C₂×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
2. #11926572	C₂	semidirect
3. #11926538	C₂	semidirect
4. #11926517	C₂	semidirect
5. C₁₉×H(3,ℤ/4)	C₂	semidirect
75. H(3,ℤ/4)	D₁₉	semidirect
92. C₁₉	#2053	semidirect

H ≅ G/N

type

2. #11926572

C₂

semidirect

3. #11926538

C₂

semidirect

4. #11926517

C₂

semidirect

5. C₁₉×H(3,ℤ/4)

C₂

semidirect

75. H(3,ℤ/4)

D₁₉

semidirect

92. C₁₉

#2053

semidirect

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

subgroup	index
#11927344	2
#11926572	2
#11926538	2
#11926517	2
C₁₉×H(3,ℤ/4)	2
#2053	19

subgroup

index

C₁₉×H(3,ℤ/4)

Subgroups — #14564942

Conjugacy classes of subgroups

Complements

Maximal subgroups