Group #14565048 — subgroups

Subgroups — #14565048

Order 2432.

258 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 81 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×#10597289	C₂	1	2	yes	maximal
2	#11926410	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926306	C₂	1	2	yes	maximal, complemented
4	#11926299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#390	C₂	1	1	yes	maximal, characteristic
6	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
11	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
12	#10597289	—	2	4	no	—
13	C₁₉⋊#95	—	2	2	no	—
14	C₂⁴×C₁₉	—	2	1	no	—
15	C₂×D₄×C₁₉	—	2	2	no	—
16	C₂×D₄×C₁₉	—	2	2	no	—
17	C₂×D₄×C₁₉	—	2	1	no	—
18	C₂×D₄×C₁₉	D₄	1	2	yes	—
19	C₂²×C₄×C₁₉	—	2	1	no	—
20	C₂²×C₄×C₁₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₁₉	—	2	2	no	—
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₂²⋊C₄×C₁₉	—	4	4	no	—
25	C₄²×C₁₉	—	2	2	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	C₄⋊Dic₁₉	—	2	2	no	—
28	C₂×C₁₉⋊C₈	—	2	2	no	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂³×C₁₉	—	2	2	no	—
32	C₂³×C₁₉	—	4	1	no	—
33	C₂³×C₁₉	—	4	1	no	—
34	C₂³×C₁₉	—	4	2	no	—
35	C₂³×C₁₉	—	4	2	no	—
36	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
37	D₄×C₁₉	—	2	4	no	—
38	D₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	2	yes	—
47	C₂×C₄×C₁₉	#41	1	2	yes	—
48	C₂×Dic₁₉	—	4	2	no	—
49	C₂×Dic₁₉	—	4	2	no	—
50	C₂×Dic₁₉	—	4	2	no	—
51	C₁₉⋊C₈	—	4	2	no	—
52	#2073	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	—	4	2	no	—
54	C₂²×C₁₉	—	4	4	no	—
55	C₂²×C₁₉	—	8	2	no	—
56	C₂²×C₁₉	—	8	1	no	—
57	C₂²×C₁₉	—	8	1	no	—
58	C₂²×C₁₉	#121	1	1	yes	characteristic
59	C₂²×C₁₉	#123	1	1	yes	characteristic
60	C₂²×C₁₉	#124	1	1	yes	characteristic
61	C₂²×C₁₉	#135	1	2	yes	—
62	C₂²×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
63	C₄×C₁₉	—	4	2	no	—
64	C₄×C₁₉	—	8	1	no	—
65	C₄×C₁₉	#123	1	2	yes	—
66	C₄×C₁₉	#126	1	2	yes	—
67	Dic₁₉	—	8	2	no	—
68	C₂×#102	—	19	2	no	—
69	#390	D₁₉	1	1	yes	characteristic
70	#382	—	19	1	no	—
71	#340	—	19	2	no	—
72	#336	—	19	1	no	—
73	C₂×C₁₉	—	8	2	no	—
74	C₂×C₁₉	#397	1	1	yes	characteristic
75	C₂×C₁₉	#463	1	2	yes	—
76	C₂×C₁₉	#482	1	2	yes	—
77	C₂×C₁₉	#488	1	1	yes	characteristic
78	C₂×C₁₉	#490	1	1	yes	characteristic
79	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
80	C₂²×C₈	—	19	2	no	—
81	C₂×C₄⋊C₄	—	19	2	no	—
82	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
83	C₂×C₂²⋊C₄	—	2	2	no	—
84	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
85	#102	—	38	4	no	—
86	#95	—	38	2	no	—
87	C₁₉	#2073	1	1	yes	characteristic, complemented, Sylow
88	C₂⁴	—	2	1	no	—
89	C₂×D₄	—	2	1	no	—
90	C₂×D₄	—	2	2	no	—
91	C₂×D₄	—	2	2	no	—
92	C₂×D₄	D₇₆	1	2	yes	—
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	38	2	no	—
95	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
96	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
97	C₂×C₈	—	38	2	no	—
98	C₂×C₈	—	38	2	no	—
99	C₂×C₈	—	38	2	no	—
100	C₄⋊C₄	—	2	2	no	—
101	C₄⋊C₄	—	38	2	no	—
102	C₄⋊C₄	—	38	2	no	—
103	C₂²⋊C₄	—	4	4	no	—
104	C₄²	—	2	2	no	—
105	C₂³	—	2	2	no	—
106	C₂³	—	4	2	no	—
107	C₂³	—	4	1	no	—
108	C₂³	—	4	1	no	—
109	C₂³	—	4	2	no	—
110	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
111	D₄	—	2	4	no	—
112	D₄	—	4	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	4	2	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	76	2	no	—
119	C₂×C₄	—	76	2	no	—
120	C₂×C₄	—	76	2	no	—
121	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
122	C₂×C₄	#64541	1	1	yes	characteristic
123	C₂×C₄	#64543	1	2	yes	—
124	C₂×C₄	#64543	1	2	yes	—
125	C₈	—	76	2	no	—
126	C₂²	—	4	2	no	—
127	C₂²	—	4	4	no	—
128	C₂²	—	8	2	no	—
129	C₂²	—	8	1	no	—
130	C₂²	—	8	1	no	—
131	C₂²	#10597376	1	1	yes	characteristic
132	C₂²	#10597378	1	2	yes	—
133	C₂²	#10597381	1	1	yes	characteristic
134	C₂²	#10597382	1	1	yes	characteristic
135	C₂²	#10597396	1	2	yes	—
136	C₄	—	4	2	no	—
137	C₄	—	8	1	no	—
138	C₄	—	152	2	no	—
139	C₄	#10597325	1	2	yes	—
140	C₄	#10597332	1	2	yes	—
141	C₂	—	8	2	no	—
142	C₂	#11926469	1	1	yes	characteristic
143	C₂	#11926759	1	2	yes	—
144	C₂	#11926865	1	2	yes	—
145	C₂	#11926898	1	1	yes	characteristic
146	C₂	#11926908	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597289

C₂

yes

maximal

#11926410

C₂

yes

maximal, characteristic, complemented

#11926306

C₂

yes

maximal, complemented

#11926299

C₂

yes

maximal, characteristic, complemented

C₁₉×#390

C₂

yes

maximal, characteristic

C₂²×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597289

—

C₁₉⋊#95

—

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

#2073

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#123

yes

—

C₄×C₁₉

#126

yes

—

Dic₁₉

—

C₂×#102

—

#390

D₁₉

yes

—

—

—

C₂×C₁₉

—

C₂×C₁₉

#397

yes

characteristic

C₂×C₁₉

#463

yes

—

C₂×C₁₉

#482

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×D₄

C₂×D₁₉

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#102

—

#95

—

C₁₉

#2073

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

D₇₆

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₂²⋊C₄

—

104

C₄²

—

105

C₂³

—

106

C₂³

—

107

C₂³

—

108

C₂³

—

109

C₂³

—

110

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

111

D₄

—

112

D₄

—

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

C₂×D₇₆

yes

characteristic

122

C₂×C₄

#64541

yes

characteristic

123

C₂×C₄

#64543

yes

—

124

C₂×C₄

#64543

yes

—

125

C₈

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

#10597376

yes

characteristic

132

C₂²

#10597378

yes

—

133

C₂²

#10597381

yes

characteristic

134

C₂²

#10597382

yes

characteristic

135

C₂²

#10597396

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

152

—

139

C₄

#10597325

yes

—

140

C₄

#10597332

yes

—

141

C₂

—

142

C₂

#11926469

yes

characteristic

143

C₂

#11926759

yes

—

144

C₂

#11926865

yes

—

145

C₂

#11926898

yes

characteristic

146

C₂

#11926908

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂²×C₄×C₁₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#390	C₂
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	#390	D₁₉
hypocenter	C₁₉	#2073
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂²×C₄×C₁₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#390

C₂

socle

C₂³×C₁₉

C₂×D₄

prime radical

C₂²×D₄×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

N	H ≅ G/N	type
2. #11926410	C₂	semidirect
3. #11926306	C₂	semidirect
4. #11926299	C₂	semidirect
87. C₁₉	#2073	semidirect

H ≅ G/N

type

2. #11926410

C₂

semidirect

3. #11926306

C₂

semidirect

4. #11926299

C₂

semidirect

87. C₁₉

#2073

semidirect

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

subgroup	index
C₂×#10597289	2
#11926410	2
#11926306	2
#11926299	2
C₁₉×#390	2
#2073	19

subgroup

index

C₁₉×#390

Subgroups — #14565048

Conjugacy classes of subgroups

Complements

Maximal subgroups