Group #14565213 — subgroups

Subgroups — #14565213

Order 2432.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#11926592	C₂	1	1	yes	maximal, characteristic
2	#11926568	C₂	1	1	yes	maximal, characteristic
3	#11926315	C₂	1	1	yes	maximal, characteristic
4	#11926314	C₂	1	1	yes	maximal, characteristic
5	#11926304	C₂	1	1	yes	maximal, characteristic
6	#11926300	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₉	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	C₂×#64520	C₂²	1	1	yes	characteristic
15	#10597279	—	2	2	no	—
16	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
17	C₂²×C₄×C₁₉	—	2	1	no	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	M₁₆×C₁₉	—	2	1	no	—
20	M₁₆×C₁₉	—	2	1	no	—
21	C₂×C₈×C₁₉	—	2	1	no	—
22	C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₂²⋊C₄×C₁₉	—	2	1	no	—
24	C₄²×C₁₉	—	2	1	no	—
25	C₄²×C₁₉	—	2	1	no	—
26	C₄²×C₁₉	Q₈	1	1	yes	characteristic
27	C₄²×C₁₉	Q₈	1	1	yes	characteristic
28	C₂²⋊Dic₁₉	—	2	1	no	—
29	C₄⋊Dic₁₉	—	2	1	no	—
30	C₄×Dic₁₉	—	2	1	no	—
31	#64520	—	2	1	no	—
32	#64520	—	2	1	no	—
33	#64520	—	2	1	no	—
34	#64520	—	2	1	no	—
35	#64520	—	2	1	no	—
36	#64520	—	2	1	no	—
37	C₂×C₁₉⋊C₈	—	2	1	no	—
38	C₂×C₁₉⋊C₈	—	2	1	no	—
39	C₂×C₁₉⋊C₈	D₄	1	2	yes	—
40	C₂³×C₁₉	#41	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
48	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
51	C₂×Dic₁₉	—	4	1	no	—
52	C₈×C₁₉	—	4	1	no	—
53	C₁₉⋊C₈	—	2	2	no	—
54	C₁₉⋊C₈	—	4	1	no	—
55	C₁₉⋊C₈	—	4	1	no	—
56	#2102	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	4	1	no	—
58	C₂²×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
59	C₂²×C₁₉	#126	1	1	yes	characteristic
60	C₂²×C₁₉	#126	1	1	yes	characteristic
61	C₄×C₁₉	—	2	2	no	—
62	C₄×C₁₉	—	4	1	no	—
63	C₄×C₁₉	—	8	1	no	—
64	C₄×C₁₉	#123	1	1	yes	characteristic
65	C₄×C₁₉	#124	1	1	yes	characteristic
66	C₄×C₁₉	#125	1	1	yes	characteristic
67	C₄×C₁₉	#125	1	1	yes	characteristic
68	Dic₁₉	—	8	1	no	—
69	#430	—	19	1	no	—
70	#423	—	19	1	no	—
71	#344	—	19	1	no	—
72	#344	—	19	1	no	—
73	#339	—	19	1	no	—
74	#339	D₁₉	1	1	yes	characteristic
75	H(3,ℤ/4)	—	19	1	no	—
76	C₂×C₁₉	—	2	1	no	—
77	C₂×C₁₉	—	2	1	no	—
78	C₂×C₁₉	—	2	1	no	—
79	C₂×C₁₉	#400	1	1	yes	characteristic
80	C₂×M₁₆	—	19	1	no	—
81	C₂×M₁₆	—	19	1	no	—
82	C₂×M₁₆	—	19	1	no	—
83	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
84	#117	—	19	1	no	—
85	#117	C₂×D₁₉	1	1	yes	characteristic
86	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
87	#108	—	38	2	no	—
88	C₄⋊C₈	—	38	2	no	—
89	C₁₉	#2102	1	1	yes	characteristic, complemented, Sylow
90	C₂²×C₄	—	2	1	no	—
91	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
92	M₁₆	—	2	1	no	—
93	M₁₆	—	2	1	no	—
94	M₁₆	—	38	1	no	—
95	M₁₆	—	38	1	no	—
96	M₁₆	—	38	1	no	—
97	M₁₆	—	38	1	no	—
98	M₁₆	—	38	1	no	—
99	M₁₆	—	38	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	—	19	2	no	—
102	C₂×C₈	—	38	1	no	—
103	C₂×C₈	—	38	1	no	—
104	C₄⋊C₄	—	2	1	no	—
105	C₄⋊C₄	—	38	1	no	—
106	C₂²⋊C₄	—	2	1	no	—
107	C₂²⋊C₄	—	38	1	no	—
108	C₄²	—	2	1	no	—
109	C₄²	—	2	1	no	—
110	C₄²	—	38	1	no	—
111	C₄²	Dic₃₈	1	1	yes	characteristic
112	C₄²	Dic₃₈	1	1	yes	characteristic
113	C₂³	#64543	1	1	yes	characteristic
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	76	1	no	—
119	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
120	C₂×C₄	#64541	1	1	yes	characteristic
121	C₂×C₄	#64541	1	1	yes	characteristic
122	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
123	C₂×C₄	#64543	1	1	yes	characteristic
124	C₂×C₄	#64545	1	1	yes	characteristic
125	C₈	—	4	1	no	—
126	C₈	—	38	2	no	—
127	C₈	—	76	1	no	—
128	C₈	—	76	1	no	—
129	C₂²	—	4	1	no	—
130	C₂²	#10597324	1	1	yes	characteristic
131	C₂²	#10597325	1	1	yes	characteristic
132	C₂²	#10597344	1	1	yes	characteristic
133	C₄	—	2	2	no	—
134	C₄	—	4	1	no	—
135	C₄	—	8	1	no	—
136	C₄	—	152	1	no	—
137	C₄	#10597316	1	1	yes	characteristic
138	C₄	#10597331	1	1	yes	characteristic
139	C₄	#10597336	1	1	yes	characteristic
140	C₄	#10597340	1	1	yes	characteristic
141	C₂	—	2	1	no	—
142	C₂	—	2	1	no	—
143	C₂	—	2	1	no	—
144	C₂	#11926486	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926592

C₂

yes

maximal, characteristic

#11926568

C₂

yes

maximal, characteristic

#11926315

C₂

yes

maximal, characteristic

#11926314

C₂

yes

maximal, characteristic

#11926304

C₂

yes

maximal, characteristic

#11926300

C₂

yes

maximal, characteristic

C₁₉×#339

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597372

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

characteristic

#10597279

—

C₄⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

Q₈

yes

characteristic

C₄²×C₁₉

Q₈

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

—

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

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×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2102

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

H(3,ℤ/4)

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#400

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

#117

—

#117

C₂×D₁₉

yes

characteristic

C₂×C₄²

C₂×D₁₉

yes

characteristic

#108

—

C₄⋊C₈

—

C₁₉

#2102

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

Dic₃₈

yes

characteristic

112

C₄²

Dic₃₈

yes

characteristic

113

C₂³

#64543

yes

characteristic

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂×Dic₃₈

yes

characteristic

120

C₂×C₄

#64541

yes

characteristic

121

C₂×C₄

#64541

yes

characteristic

122

C₂×C₄

D₄×D₁₉

yes

characteristic

123

C₂×C₄

#64543

yes

characteristic

124

C₂×C₄

#64545

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₂²

—

130

C₂²

#10597324

yes

characteristic

131

C₂²

#10597325

yes

characteristic

132

C₂²

#10597344

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

152

—

137

C₄

#10597316

yes

characteristic

138

C₄

#10597331

yes

characteristic

139

C₄

#10597336

yes

characteristic

140

C₄

#10597340

yes

characteristic

141

C₂

—

142

C₂

—

143

C₂

—

144

C₂

#11926486

yes

characteristic

	subgroup	G/H
center	C₄	#10597331
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#339	C₂
socle	C₂×C₁₉	#400
prime radical	C₂³×C₁₉	#41
hypercenter	#339	D₁₉
hypocenter	C₁₉	#2102
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #339

subgroup

G/H

center

C₄

#10597331

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#339

C₂

C₂×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #339

N	H ≅ G/N	type
89. C₁₉	#2102	semidirect

H ≅ G/N

type

89. C₁₉

#2102

semidirect

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

subgroup	index
#11926592	2
#11926568	2
#11926315	2
#11926314	2
#11926304	2
#11926300	2
C₁₉×#339	2
#2102	19

subgroup

index

C₁₉×#339

Subgroups — #14565213

Conjugacy classes of subgroups

Complements

Maximal subgroups