Group #14563161 — subgroups

Subgroups — #14563161

Order 2432.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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	#11926947	C₂	1	1	yes	maximal, characteristic
2	#11926839	C₂	1	1	yes	maximal, characteristic
3	#11926675	C₂	1	1	yes	maximal, characteristic
4	#11926294	C₂	1	1	yes	maximal, characteristic
5	#11926293	C₂	1	1	yes	maximal, characteristic
6	#11926292	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#477	C₂	1	1	yes	maximal, characteristic
8	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	#10597315	C₂²	1	1	yes	characteristic
11	C₁₉×#107	—	2	1	no	—
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×#103	—	2	1	no	—
14	#10597292	—	2	1	no	—
15	#10597264	—	2	1	no	—
16	#10597264	—	2	1	no	—
17	#10597264	—	2	1	no	—
18	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
19	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
21	#10597260	—	2	1	no	—
22	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Q₈×C₁₉	—	2	1	no	—
24	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
25	C₂×Dic₃₈	—	2	1	no	—
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₄⋊C₄×C₁₉	—	2	1	no	—
29	C₄⋊C₄×C₁₉	—	2	1	no	—
30	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
31	C₄²×C₁₉	—	2	1	no	—
32	C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₄⋊Dic₁₉	—	2	1	no	—
34	C₄⋊Dic₁₉	—	2	1	no	—
35	C₂×C₁₉⋊C₈	—	2	1	no	—
36	C₂×C₁₉⋊C₈	—	2	1	no	—
37	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
38	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
39	Q₈×C₁₉	—	2	1	no	—
40	Q₈×C₁₉	—	2	1	no	—
41	Q₈×C₁₉	—	8	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	4	1	no	—
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
48	C₂×Dic₁₉	—	4	1	no	—
49	Dic₃₈	—	8	1	no	—
50	C₈×C₁₉	—	4	1	no	—
51	C₁₉⋊C₈	—	2	1	no	—
52	C₁₉⋊C₈	—	4	1	no	—
53	C₁₉⋊C₈	—	4	1	no	—
54	C₁₉⋊C₈	Q₁₆	1	2	yes	—
55	#1696	—	19	1	no	maximal, Sylow
56	C₂²×C₁₉	#121	1	1	yes	characteristic
57	C₄×C₁₉	—	2	1	no	—
58	C₄×C₁₉	—	4	1	no	—
59	C₄×C₁₉	—	4	1	no	—
60	C₄×C₁₉	—	8	1	no	—
61	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
62	C₄×C₁₉	#137	1	1	yes	characteristic
63	C₄×C₁₉	#137	1	1	yes	characteristic
64	C₄×C₁₉	#137	1	1	yes	characteristic
65	Dic₁₉	—	8	1	no	—
66	#500	—	19	1	no	—
67	#477	—	19	1	no	—
68	#477	D₁₉	1	1	yes	characteristic
69	#446	—	19	1	no	—
70	#334	—	19	1	no	—
71	#333	—	19	1	no	—
72	#333	—	19	1	no	—
73	C₂×C₁₉	#462	1	1	yes	characteristic
74	C₂×C₁₉	#470	1	1	yes	characteristic
75	C₂×C₁₉	#472	1	1	yes	characteristic
76	C₄⋊Q₈	—	19	1	no	—
77	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
78	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
79	#107	—	2	1	no	—
80	#107	—	38	1	no	—
81	#107	—	38	1	no	—
82	#107	—	38	1	no	—
83	C₄⋊C₈	—	19	1	no	—
84	C₄⋊C₈	—	19	1	no	—
85	C₄⋊C₈	—	38	1	no	—
86	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
87	#103	—	2	1	no	—
88	#103	—	38	1	no	—
89	#97	—	38	1	no	—
90	C₄×C₈	—	19	1	no	—
91	C₁₉	#1696	1	1	yes	characteristic, complemented, Sylow
92	C₂×Q₈	—	2	1	no	—
93	C₂×Q₈	—	38	1	no	—
94	C₂×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	19	1	no	—
97	C₂×C₈	—	19	1	no	—
98	C₂×C₈	—	38	1	no	—
99	C₂×C₈	—	38	1	no	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	2	1	no	—
103	C₄⋊C₄	—	38	1	no	—
104	C₄⋊C₄	—	38	1	no	—
105	C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
106	C₄²	—	2	1	no	—
107	C₄²	C₂²×D₁₉	1	1	yes	characteristic
108	Q₈	—	2	1	no	—
109	Q₈	—	2	1	no	—
110	Q₈	—	8	1	no	—
111	Q₈	—	152	1	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	76	1	no	—
116	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
117	C₂×C₄	#64543	1	1	yes	characteristic
118	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
119	C₈	—	4	1	no	—
120	C₈	—	19	2	no	—
121	C₈	—	38	1	no	—
122	C₈	—	76	1	no	—
123	C₈	—	76	1	no	—
124	C₂²	#10597385	1	1	yes	characteristic
125	C₄	—	2	1	no	—
126	C₄	—	4	1	no	—
127	C₄	—	4	1	no	—
128	C₄	—	8	1	no	—
129	C₄	—	152	1	no	—
130	C₄	Q₁₆×D₁₉	1	1	yes	characteristic
131	C₄	#10597364	1	1	yes	characteristic
132	C₄	#10597388	1	1	yes	characteristic
133	C₄	#10597397	1	1	yes	characteristic
134	C₂	#11926752	1	1	yes	characteristic
135	C₂	#11926800	1	1	yes	characteristic
136	C₂	#11926812	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926947

C₂

yes

maximal, characteristic

#11926839

C₂

yes

maximal, characteristic

#11926675

C₂

yes

maximal, characteristic

#11926294

C₂

yes

maximal, characteristic

#11926293

C₂

yes

maximal, characteristic

#11926292

C₂

yes

maximal, characteristic

C₁₉×#477

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₄×Q₈×C₁₉

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₁₉×#107

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#103

—

—

—

—

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

#10597260

—

C₄×C₁₉⋊C₈

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₂×C₁₉⋊C₈

D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

Q₁₆

yes

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#500

—

#477

—

#477

D₁₉

yes

—

—

—

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

C₄×Q₈

C₂×D₁₉

yes

—

—

—

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

—

—

C₄×C₈

—

C₁₉

#1696

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

C₂²⋊D₁₉

yes

characteristic

106

C₄²

—

107

C₄²

C₂²×D₁₉

yes

characteristic

108

Q₈

—

109

Q₈

—

110

Q₈

—

111

Q₈

—

152

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

D₄×D₁₉

yes

characteristic

117

C₂×C₄

#64543

yes

characteristic

118

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

119

C₈

—

120

C₈

—

121

C₈

—

122

C₈

—

123

C₈

—

124

C₂²

#10597385

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

152

—

130

C₄

Q₁₆×D₁₉

yes

characteristic

131

C₄

#10597364

yes

characteristic

132

C₄

#10597388

yes

characteristic

133

C₄

#10597397

yes

characteristic

134

C₂

#11926752

yes

characteristic

135

C₂

#11926800

yes

characteristic

136

C₂

#11926812

yes

characteristic

	subgroup	G/H
center	C₂²	#10597385
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#477	C₂
socle, prime radical	C₂²×C₁₉	#121
hypercenter	#477	D₁₉
hypocenter	C₁₉	#1696
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #477

subgroup

G/H

center

C₂²

#10597385

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#477

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #477

N	H ≅ G/N	type
91. C₁₉	#1696	semidirect

H ≅ G/N

type

91. C₁₉

#1696

semidirect

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

subgroup	index
#11926947	2
#11926839	2
#11926675	2
#11926294	2
#11926293	2
#11926292	2
C₁₉×#477	2
#1696	19

subgroup

index

C₁₉×#477

Subgroups — #14563161

Conjugacy classes of subgroups

Complements

Maximal subgroups