Group #14563683 — subgroups

Subgroups — #14563683

Order 2432.

252 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 89 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×#10597394	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597279	C₂	1	2	yes	maximal, complemented
3	#11926528	C₂	1	1	yes	maximal, characteristic
4	C₁₉⋊#338	C₂	1	2	yes	maximal, complemented
5	C₁₉×#413	C₂	1	1	yes	maximal, characteristic
6	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	#10597394	—	2	4	no	—
9	C₂×#64520	C₄	1	2	yes	—
10	C₂×#64520	C₂²	1	2	yes	—
11	C₂×#64520	C₂²	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	C₄	1	2	yes	—
13	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₁₉×#101	—	2	1	no	—
15	C₁₉×#100	—	2	1	no	—
16	#10597293	—	2	1	no	—
17	#10597290	—	2	1	no	—
18	#10597279	—	2	4	no	—
19	#41×C₁₉	—	2	2	no	—
20	#41×C₁₉	—	2	2	no	—
21	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
23	C₂×D₄×C₁₉	Q₈	1	2	yes	—
24	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	M₁₆×C₁₉	—	2	2	no	—
27	M₁₆×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	#64520	—	2	2	no	—
30	#64520	—	2	4	no	—
31	#64520	—	2	2	no	—
32	#64520	—	2	2	no	—
33	C₂×C₁₉⋊C₈	—	2	4	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
36	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
38	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
39	C₂³×C₁₉	C₄⋊C₄	1	2	yes	—
40	C₂³×C₁₉	C₂×Q₈	1	1	yes	characteristic
41	Q₈×C₁₉	—	2	2	no	—
42	D₄×C₁₉	—	2	4	no	—
43	D₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	2	no	—
46	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
47	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#41	1	2	yes	—
51	C₈×C₁₉	—	4	2	no	—
52	C₁₉⋊C₈	—	2	2	no	—
53	C₁₉⋊C₈	—	4	2	no	—
54	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
55	C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
56	#1813	—	19	1	no	maximal, Sylow
57	C₂²×C₁₉	—	2	2	no	—
58	C₂²×C₁₉	—	4	1	no	—
59	C₂²×C₁₉	—	4	2	no	—
60	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₁₉	C₂²⋊Q₈	1	2	yes	—
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₄×C₁₉	#117	1	1	yes	characteristic
65	C₄×C₁₉	#121	1	2	yes	—
66	C₂×#131	—	19	1	no	—
67	C₂×#108	—	19	2	no	—
68	#413	—	19	1	no	—
69	#413	D₁₉	1	1	yes	characteristic
70	#338	—	19	2	no	—
71	C₂×C₁₉	—	2	1	no	—
72	C₂×C₁₉	—	2	2	no	—
73	C₂×C₁₉	—	4	2	no	—
74	C₂×C₁₉	#380	1	1	yes	characteristic
75	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
76	#131	—	38	4	no	—
77	C₂×M₁₆	—	19	2	no	—
78	C₂×M₁₆	—	19	1	no	—
79	C₂×M₁₆	—	19	2	no	—
80	C₂×M₁₆	C₂×D₁₉	1	2	yes	—
81	C₂²×C₈	—	19	1	no	—
82	C₂²×C₈	—	19	2	no	—
83	#108	—	38	4	no	—
84	#101	—	2	1	no	—
85	#101	—	38	1	no	—
86	#100	—	2	1	no	—
87	#100	—	38	1	no	—
88	C₁₉	#1813	1	1	yes	characteristic, complemented, Sylow
89	#41	—	2	2	no	—
90	#41	—	2	2	no	—
91	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
92	C₂×D₄	Dic₃₈	1	2	yes	—
93	C₂×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
94	C₂²×C₄	C₄×D₁₉	1	2	yes	—
95	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
96	M₁₆	—	2	2	no	—
97	M₁₆	—	2	2	no	—
98	M₁₆	—	38	4	no	—
99	M₁₆	—	38	2	no	—
100	M₁₆	—	38	2	no	—
101	M₁₆	—	38	2	no	—
102	C₂×C₈	—	2	2	no	—
103	C₂×C₈	—	19	1	no	—
104	C₂×C₈	—	19	1	no	—
105	C₂×C₈	—	19	4	no	—
106	C₂×C₈	—	19	2	no	—
107	C₂×C₈	—	38	4	no	—
108	C₂×C₈	—	38	2	no	—
109	C₂³	Dic₁₉⋊C₄	1	2	yes	—
110	C₂³	C₂×Dic₃₈	1	1	yes	characteristic
111	Q₈	—	2	2	no	—
112	D₄	—	2	4	no	—
113	D₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
117	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
118	C₂×C₄	D₄×D₁₉	1	2	yes	—
119	C₂×C₄	#64543	1	2	yes	—
120	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
121	C₈	—	4	2	no	—
122	C₈	—	19	2	no	—
123	C₈	—	19	2	no	—
124	C₈	—	38	2	no	—
125	C₈	—	76	2	no	—
126	C₂²	—	2	2	no	—
127	C₂²	—	4	1	no	—
128	C₂²	—	4	2	no	—
129	C₂²	#10597324	1	2	yes	—
130	C₂²	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
131	C₄	—	2	2	no	—
132	C₄	#10597323	1	1	yes	characteristic
133	C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
134	C₄	#10597385	1	2	yes	—
135	C₂	—	2	1	no	—
136	C₂	—	2	2	no	—
137	C₂	—	4	2	no	—
138	C₂	#11926402	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597394

C₂

yes

maximal, characteristic

C₂×#10597279

C₂

yes

maximal, complemented

#11926528

C₂

yes

maximal, characteristic

C₁₉⋊#338

C₂

yes

maximal, complemented

C₁₉×#413

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₂²

yes

—

#10597394

—

C₂×#64520

C₄

yes

—

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₄

yes

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#101

—

C₁₉×#100

—

#10597293

—

#10597290

—

#10597279

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂×D₄×C₁₉

Q₈

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

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

—

C₂³×C₁₉

C₄⋊C₄

yes

—

C₂³×C₁₉

C₂×Q₈

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₁₉⋊C₈

C₂²⋊C₄

yes

—

#1813

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

—

—

D₁₉

yes

characteristic

#338

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#380

yes

characteristic

C₂×#41

C₂×D₁₉

yes

characteristic

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

—

C₂²×C₈

—

C₂²×C₈

—

—

—

—

—

—

C₁₉

#1813

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

C₂²⋊D₁₉

yes

characteristic

C₂×D₄

Dic₃₈

yes

—

C₂×D₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₄×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

100

M₁₆

—

101

M₁₆

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂³

Dic₁₉⋊C₄

yes

—

110

C₂³

C₂×Dic₃₈

yes

characteristic

111

Q₈

—

112

D₄

—

113

D₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

Dic₁₉⋊C₄

yes

—

117

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

118

C₂×C₄

D₄×D₁₉

yes

—

119

C₂×C₄

#64543

yes

—

120

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

121

C₈

—

122

C₈

—

123

C₈

—

124

C₈

—

125

C₈

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

#10597324

yes

—

130

C₂²

C₂×Dic₁₉⋊C₄

yes

characteristic

131

C₄

—

132

C₄

#10597323

yes

characteristic

133

C₄

C₂²⋊C₄×D₁₉

yes

characteristic

134

C₄

#10597385

yes

—

135

C₂

—

136

C₂

—

137

C₂

—

138

C₂

#11926402

yes

characteristic

	subgroup	G/H
center	C₄	#10597323
commutator	C₂×C₄×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₁₉×#413	C₂
socle	C₂×C₁₉	#380
prime radical	C₂×#41×C₁₉	C₂²
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	#413	D₁₉
hypocenter	C₁₉	#1813
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #413

subgroup

G/H

center

C₄

#10597323

commutator

C₂×C₄×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₁₉×#413

C₂

socle

C₂×C₁₉

#380

prime radical

C₂×#41×C₁₉

C₂²

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #413

N	H ≅ G/N	type
2. C₂×#10597279	C₂	semidirect
4. C₁₉⋊#338	C₂	semidirect
88. C₁₉	#1813	semidirect

H ≅ G/N

type

2. C₂×#10597279

C₂

semidirect

4. C₁₉⋊#338

C₂

semidirect

88. C₁₉

#1813

semidirect

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

subgroup	index
C₂×#10597394	2
C₂×#10597279	2
#11926528	2
C₁₉⋊#338	2
C₁₉×#413	2
#1813	19

subgroup

index

C₂×#10597394

C₂×#10597279

#11926528

C₁₉⋊#338

C₁₉×#413

#1813

Subgroups — #14563683

Conjugacy classes of subgroups

Complements

Maximal subgroups