Group #14561538 — subgroups

Subgroups — #14561538

Order 2432.

176 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 77 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	#11926597	C₂	1	1	yes	maximal, characteristic
2	#11926568	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
5	C₂×C₄²×C₁₉	—	2	1	no	—
6	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×#64520	—	2	1	no	—
8	C₁₉×#95	C₄	1	2	yes	—
9	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
10	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	complemented
12	C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	complemented
13	C₄×C₁₉⋊C₈	—	2	1	no	—
14	C₂²×C₄×C₁₉	—	2	2	no	—
15	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₄⋊C₄×C₁₉	—	2	4	no	—
19	C₄²×C₁₉	—	4	1	no	—
20	C₄²×C₁₉	—	4	1	no	—
21	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₄²×C₁₉	Q₈	1	1	yes	characteristic
25	#64520	—	4	1	no	—
26	#64520	—	4	1	no	—
27	C₂×C₁₉⋊C₈	—	2	2	no	—
28	C₂×C₁₉⋊C₈	—	2	2	no	—
29	C₂³×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₉	—	2	2	no	—
31	C₂×C₄×C₁₉	—	2	4	no	—
32	C₂×C₄×C₁₉	—	4	1	no	—
33	C₂×C₄×C₁₉	—	4	2	no	—
34	C₂×C₄×C₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
44	C₂×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
45	C₁₉⋊C₈	—	4	2	no	—
46	C₁₉⋊C₈	—	4	2	no	—
47	#1303	—	19	1	no	maximal, Sylow
48	C₂²×C₁₉	—	2	1	no	—
49	C₂²×C₁₉	—	2	1	no	—
50	C₂²×C₁₉	#95	1	1	yes	characteristic
51	C₂²×C₁₉	#102	1	1	yes	characteristic
52	C₂²×C₁₉	#103	1	1	yes	characteristic
53	C₄×C₁₉	—	2	1	no	—
54	C₄×C₁₉	—	2	1	no	—
55	C₄×C₁₉	—	2	1	no	—
56	C₄×C₁₉	—	4	4	no	—
57	C₄×C₁₉	#102	1	1	yes	characteristic
58	C₄×C₁₉	#103	1	1	yes	characteristic
59	C₄×C₁₉	#104	1	2	yes	—
60	C₄×C₁₉	#106	1	1	yes	characteristic
61	C₄×C₁₉	#107	1	1	yes	characteristic
62	#431	—	19	1	no	—
63	#423	—	19	1	no	—
64	C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
65	C₂×C₁₉	—	2	1	no	—
66	C₂×C₁₉	—	2	1	no	—
67	C₂×C₁₉	#339	1	1	yes	characteristic
68	C₂×C₁₉	#340	1	1	yes	characteristic
69	C₂×C₁₉	#344	1	1	yes	characteristic
70	C₂×M₁₆	—	38	1	no	—
71	C₂×C₄⋊C₄	—	2	1	no	—
72	C₂×C₄²	—	2	1	no	—
73	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
74	C₄⋊C₈	—	19	2	no	—
75	C₄⋊C₈	—	19	2	no	—
76	C₄⋊C₈	—	38	1	no	—
77	C₂²⋊C₈	—	38	1	no	—
78	C₄×C₈	—	38	1	no	—
79	#95	Dic₁₉	1	2	yes	—
80	C₁₉	#1303	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	—	2	2	no	—
82	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
83	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
84	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
85	M₁₆	—	76	1	no	—
86	M₁₆	—	76	1	no	—
87	C₂×C₈	—	38	2	no	—
88	C₂×C₈	—	38	2	no	—
89	C₄⋊C₄	—	2	4	no	—
90	C₄²	—	4	1	no	—
91	C₄²	—	4	1	no	—
92	C₄²	Dic₃₈	1	1	yes	characteristic
93	C₄²	C₄×D₁₉	1	1	yes	characteristic
94	C₄²	C₄×D₁₉	1	1	yes	characteristic
95	C₄²	D₇₆	1	1	yes	characteristic
96	C₂³	C₂²⋊Dic₁₉	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	2	4	no	—
99	C₂×C₄	—	4	1	no	—
100	C₂×C₄	—	4	2	no	—
101	C₂×C₄	—	4	2	no	—
102	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
103	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
104	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
105	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
106	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
107	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
108	C₂×C₄	#64525	1	1	yes	characteristic
109	C₂×C₄	#64526	1	1	yes	characteristic
110	C₂×C₄	#64527	1	1	yes	characteristic
111	C₂×C₄	#64528	1	1	yes	characteristic
112	C₈	—	76	2	no	—
113	C₈	—	76	2	no	—
114	C₂²	—	2	1	no	—
115	C₂²	—	2	1	no	—
116	C₂²	C₁₉⋊#95	1	1	yes	characteristic
117	C₂²	#10597289	1	1	yes	characteristic
118	C₂²	#10597292	1	1	yes	characteristic
119	C₄	—	2	1	no	—
120	C₄	—	2	1	no	—
121	C₄	—	2	1	no	—
122	C₄	—	4	4	no	—
123	C₄	#10597262	1	2	yes	—
124	C₄	#10597264	1	1	yes	characteristic
125	C₄	#10597265	1	1	yes	characteristic
126	C₄	#10597266	1	1	yes	characteristic
127	C₄	#10597267	1	1	yes	characteristic
128	C₂	—	2	1	no	—
129	C₂	—	2	1	no	—
130	C₂	#11926304	1	1	yes	characteristic
131	C₂	#11926306	1	1	yes	characteristic
132	C₂	#11926314	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926597

C₂

yes

maximal, characteristic

#11926568

C₂

yes

maximal, characteristic

C₄×C₄⋊C₄×C₁₉

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

—

C₁₉×#95

C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₄

yes

complemented

C₄⋊(C₁₉⋊C₈)

C₄

yes

complemented

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

Q₈

yes

characteristic

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

Q₁₆

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1303

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

—

C₄×C₄⋊C₄

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

#95

Dic₁₉

yes

—

C₁₉

#1303

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

Dic₃₈

yes

characteristic

C₄²

C₄×D₁₉

yes

characteristic

C₄²

C₄×D₁₉

yes

characteristic

C₄²

D₇₆

yes

characteristic

C₂³

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₄×Dic₁₉

yes

characteristic

103

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

104

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

105

C₂×C₄

C₄⋊Dic₁₉

yes

characteristic

106

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

107

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

108

C₂×C₄

#64525

yes

characteristic

109

C₂×C₄

#64526

yes

characteristic

110

C₂×C₄

#64527

yes

characteristic

111

C₂×C₄

#64528

yes

characteristic

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

—

116

C₂²

C₁₉⋊#95

yes

characteristic

117

C₂²

#10597289

yes

characteristic

118

C₂²

#10597292

yes

characteristic

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

#10597262

yes

—

124

C₄

#10597264

yes

characteristic

125

C₄

#10597265

yes

characteristic

126

C₄

#10597266

yes

characteristic

127

C₄

#10597267

yes

characteristic

128

C₂

—

129

C₂

—

130

C₂

#11926304

yes

characteristic

131

C₂

#11926306

yes

characteristic

132

C₂

#11926314

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₄²
Frattini	C₂×C₄²	C₂×D₁₉
Fitting	C₄×C₄⋊C₄×C₁₉	C₂
socle	C₂²×C₁₉	#95
prime radical	C₂³×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂²
hypercenter	C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	#1303
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

subgroup

G/H

center

C₂×C₄

(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₄²

Frattini

C₂×C₄²

C₂×D₁₉

Fitting

C₄×C₄⋊C₄×C₁₉

C₂

socle

C₂²×C₁₉

#95

prime radical

C₂³×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂²

hypercenter

C₄×C₄⋊C₄

D₁₉

hypocenter

C₁₉

#1303

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

N	H ≅ G/N	type
11. C₄⋊(C₁₉⋊C₈)	C₄	semidirect
12. C₄⋊(C₁₉⋊C₈)	C₄	semidirect
80. C₁₉	#1303	semidirect

H ≅ G/N

type

11. C₄⋊(C₁₉⋊C₈)

C₄

semidirect

12. C₄⋊(C₁₉⋊C₈)

C₄

semidirect

80. C₁₉

#1303

semidirect

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

subgroup	index
#11926597	2
#11926568	2
C₄×C₄⋊C₄×C₁₉	2
#1303	19

subgroup

index

#11926597

#11926568

C₄×C₄⋊C₄×C₁₉

#1303

Subgroups — #14561538

Conjugacy classes of subgroups

Complements

Maximal subgroups