Group #14565870 — subgroups

Subgroups — #14565870

Order 2432.

142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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	#11926948	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926927	C₂	1	1	yes	maximal, characteristic
3	#11926349	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926347	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926345	C₂	1	1	yes	maximal, characteristic
6	#11926319	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#357	C₂	1	1	yes	maximal, characteristic
8	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	#10597382	—	2	1	no	—
10	C₂×#64526	—	2	1	no	—
11	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
12	#10597334	—	2	1	no	—
13	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#107	C₂²	1	1	yes	characteristic
15	#10597275	C₂²	1	1	yes	characteristic
16	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
18	#10597264	—	2	1	no	—
19	C₂×D₄×C₁₉	—	2	1	no	—
20	C₂×Dic₃₈	—	2	1	no	—
21	C₂×Dic₃₈	—	4	1	no	—
22	D₈×C₁₉	—	2	1	no	—
23	D₈×C₁₉	—	2	1	no	—
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₂²⋊Dic₁₉	—	4	1	no	—
27	C₂²⋊Dic₁₉	—	4	1	no	—
28	#64526	—	4	2	no	—
29	C₄⋊Dic₁₉	—	2	1	no	—
30	Dic₁₉⋊C₄	—	4	1	no	—
31	C₄×Dic₁₉	D₄	1	1	yes	characteristic
32	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
33	Dic₇₆	—	2	1	no	—
34	Dic₇₆	—	2	1	no	—
35	C₁₆×C₁₉	—	2	1	no	—
36	C₁₉⋊C₁₆	—	2	1	no	—
37	C₂³×C₁₉	—	4	1	no	—
38	D₄×C₁₉	—	4	1	no	—
39	D₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₁₉	—	4	1	no	—
43	C₂×Dic₁₉	—	4	1	no	—
44	C₂×Dic₁₉	D₈	1	1	yes	characteristic
45	C₂×Dic₁₉	D₈	1	1	yes	characteristic
46	Dic₃₈	—	4	1	no	—
47	Dic₃₈	—	4	1	no	—
48	Dic₃₈	—	8	2	no	—
49	C₈×C₁₉	#41	1	1	yes	characteristic
50	C₈×C₁₉	#41	1	1	yes	characteristic
51	C₁₉⋊C₈	SD₁₆	1	2	yes	—
52	#2243	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	—	8	1	no	—
54	C₂²×C₁₉	—	8	1	no	—
55	C₂²×C₁₉	—	8	1	no	—
56	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
57	C₄×C₁₉	—	8	1	no	—
58	C₄×C₁₉	#124	1	1	yes	characteristic
59	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
60	Dic₁₉	—	2	1	no	—
61	Dic₁₉	—	2	1	no	—
62	Dic₁₉	—	8	1	no	—
63	Dic₁₉	—	8	1	no	—
64	#500	—	19	1	no	—
65	#495	—	19	1	no	—
66	#358	—	19	1	no	—
67	#358	—	19	1	no	—
68	#357	—	19	1	no	—
69	#357	D₁₉	1	1	yes	characteristic
70	#346	—	19	1	no	—
71	C₂×C₁₉	—	16	1	no	—
72	C₂×C₁₉	#486	1	1	yes	characteristic
73	C₂×C₁₉	#509	1	1	yes	characteristic
74	C₂×C₁₉	#510	1	1	yes	characteristic
75	C₂×Q₁₆	—	19	1	no	—
76	C₂×SD₁₆	—	38	1	no	—
77	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
78	C₄⋊Q₈	—	38	1	no	—
79	#124	—	38	1	no	—
80	C₂×C₁₆	—	19	1	no	—
81	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
82	#107	—	19	1	no	—
83	#107	—	38	1	no	—
84	#107	C₂×D₁₉	1	1	yes	characteristic
85	C₄×C₈	—	19	1	no	—
86	C₁₉	#2243	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	38	1	no	—
88	C₂×Q₈	—	76	1	no	—
89	C₂×D₄	—	2	1	no	—
90	Q₁₆	—	38	1	no	—
91	Q₁₆	—	38	1	no	—
92	SD₁₆	—	76	2	no	—
93	D₈	—	2	1	no	—
94	D₈	—	2	1	no	—
95	C₂×C₈	—	19	1	no	—
96	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
97	C₄⋊C₄	—	2	1	no	—
98	C₄⋊C₄	—	38	1	no	—
99	C₄⋊C₄	—	76	1	no	—
100	C₂²⋊C₄	—	76	1	no	—
101	C₂²⋊C₄	—	76	1	no	—
102	C₄²	—	19	1	no	—
103	C₁₆	—	2	1	no	—
104	C₁₆	—	38	1	no	—
105	C₂³	—	4	1	no	—
106	Q₈	—	76	1	no	—
107	Q₈	—	76	1	no	—
108	Q₈	—	152	2	no	—
109	D₄	—	4	1	no	—
110	D₄	—	4	1	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	19	1	no	—
113	C₂×C₄	—	19	1	no	—
114	C₂×C₄	—	76	1	no	—
115	C₂×C₄	—	76	1	no	—
116	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
117	C₈	—	19	2	no	—
118	C₈	#64541	1	1	yes	characteristic
119	C₈	#64543	1	1	yes	characteristic
120	C₂²	—	8	1	no	—
121	C₂²	—	8	1	no	—
122	C₂²	—	8	1	no	—
123	C₂²	D₈×D₁₉	1	1	yes	characteristic
124	C₄	—	8	1	no	—
125	C₄	—	38	1	no	—
126	C₄	—	38	1	no	—
127	C₄	—	152	1	no	—
128	C₄	—	152	1	no	—
129	C₄	#10597331	1	1	yes	characteristic
130	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
131	C₂	—	16	1	no	—
132	C₂	#11926889	1	1	yes	characteristic
133	C₂	#11926978	1	1	yes	characteristic
134	C₂	#11926983	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926948

C₂

yes

maximal, characteristic, complemented

#11926927

C₂

yes

maximal, characteristic

#11926349

C₂

yes

maximal, characteristic, complemented

#11926347

C₂

yes

maximal, characteristic, complemented

#11926345

C₂

yes

maximal, characteristic

#11926319

C₂

yes

maximal, characteristic, complemented

C₁₉×#357

C₂

yes

maximal, characteristic

C₂×D₈×C₁₉

C₂²

yes

characteristic

#10597382

—

C₂×#64526

—

C₂×Dic₇₆

C₂²

yes

characteristic

#10597334

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

characteristic

#10597275

C₂²

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

#10597264

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#64526

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Dic₇₆

—

Dic₇₆

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

D₈

yes

characteristic

C₂×Dic₁₉

D₈

yes

characteristic

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

SD₁₆

yes

—

#2243

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

D₁₉

yes

characteristic

#346

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

C₂×D₁₉

yes

characteristic

C₄⋊Q₈

—

#124

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

—

—

C₂×D₁₉

yes

characteristic

C₄×C₈

—

C₁₉

#2243

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₂²⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₁₆

—

104

C₁₆

—

105

C₂³

—

106

Q₈

—

107

Q₈

—

108

Q₈

—

152

—

109

D₄

—

110

D₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

D₄×D₁₉

yes

characteristic

117

C₈

—

118

C₈

#64541

yes

characteristic

119

C₈

#64543

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

D₈×D₁₉

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

152

—

128

C₄

—

152

—

129

C₄

#10597331

yes

characteristic

130

C₄

SD₁₆×D₁₉

yes

characteristic

131

C₂

—

132

C₂

#11926889

yes

characteristic

133

C₂

#11926978

yes

characteristic

134

C₂

#11926983

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₉
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#357	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×D₈×C₁₉	C₂²
hypercenter	#357	D₁₉
hypocenter	C₁₉	#2243
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₁₉

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#357

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂×D₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. #11926948	C₂	semidirect
3. #11926349	C₂	semidirect
4. #11926347	C₂	semidirect
6. #11926319	C₂	semidirect
86. C₁₉	#2243	semidirect

H ≅ G/N

type

1. #11926948

C₂

semidirect

3. #11926349

C₂

semidirect

4. #11926347

C₂

semidirect

6. #11926319

C₂

semidirect

86. C₁₉

#2243

semidirect

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

subgroup	index
#11926948	2
#11926927	2
#11926349	2
#11926347	2
#11926345	2
#11926319	2
C₁₉×#357	2
#2243	19

subgroup

index

C₁₉×#357

Subgroups — #14565870

Conjugacy classes of subgroups

Complements

Maximal subgroups