Group #14565249 — subgroups

Subgroups — #14565249

Order 2432.

228 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10597269	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊(C₁₉⋊C₁₆)	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#131	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₁₉	C₄	1	1	yes	characteristic
6	C₁₉×#131	—	2	2	no	—
7	C₁₉×#131	—	2	2	no	—
8	C₂×M₁₆×C₁₉	C₄	1	1	yes	characteristic
9	C₂×M₁₆×C₁₉	C₄	1	2	yes	—
10	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597269	—	2	2	no	—
13	C₂×C₁₉⋊C₁₆	—	2	2	no	—
14	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
15	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
16	#41×C₁₉	—	2	2	no	—
17	#41×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	C₈	1	1	yes	characteristic
19	C₂×D₄×C₁₉	C₈	1	2	yes	—
20	C₂×D₄×C₁₉	C₈	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	M₁₆×C₁₉	—	2	2	no	—
24	M₁₆×C₁₉	—	2	4	no	—
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
28	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	D₄	1	2	yes	—
30	C₂×C₈×C₁₉	D₄	1	2	yes	—
31	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
32	C₁₉⋊C₁₆	—	2	2	no	—
33	C₁₉⋊C₁₆	—	2	2	no	—
34	C₂³×C₁₉	C₂×C₈	1	2	yes	—
35	C₂³×C₁₉	C₂×C₈	1	1	yes	characteristic
36	Q₈×C₁₉	—	2	2	no	—
37	D₄×C₁₉	—	2	4	no	—
38	D₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
43	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
44	C₂×C₄×C₁₉	M₁₆	1	2	yes	—
45	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₁₉	—	2	2	no	—
47	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
48	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
50	#2113	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	—	2	2	no	—
52	C₂²×C₁₉	—	2	2	no	—
53	C₂²×C₁₉	—	2	4	no	—
54	C₂²×C₁₉	C₂²⋊C₈	1	2	yes	—
55	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
56	C₄×C₁₉	—	2	2	no	—
57	C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
58	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
60	C₂×#131	D₁₉	1	1	yes	characteristic
61	C₂×M₃₂	—	19	1	no	—
62	C₂²×C₁₆	—	19	1	no	—
63	C₂²⋊C₁₆	—	19	4	no	—
64	C₂×C₁₉	—	2	2	no	—
65	C₂×C₁₉	—	4	2	no	—
66	C₂×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
67	C₂×C₁₉	#504	1	2	yes	—
68	C₂×#41	Dic₁₉	1	1	yes	characteristic
69	#131	—	2	2	no	—
70	#131	—	2	2	no	—
71	C₂×M₁₆	Dic₁₉	1	1	yes	characteristic
72	C₂×M₁₆	Dic₁₉	1	2	yes	—
73	C₂²×C₈	C₂×D₁₉	1	2	yes	—
74	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
75	M₃₂	—	38	2	no	—
76	C₂×C₁₆	—	19	2	no	—
77	C₂×C₁₆	—	19	2	no	—
78	C₂×C₁₆	—	38	2	no	—
79	C₁₉	#2113	1	1	yes	characteristic, complemented, Sylow
80	#41	—	2	2	no	—
81	#41	—	2	2	no	—
82	C₂×Q₈	C₁₉⋊C₈	1	1	yes	characteristic
83	C₂×D₄	C₁₉⋊C₈	1	2	yes	—
84	C₂×D₄	C₁₉⋊C₈	1	1	yes	characteristic
85	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
86	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
87	M₁₆	—	2	2	no	—
88	M₁₆	—	2	4	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	C₂×Dic₁₉	1	2	yes	—
92	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
93	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
94	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
95	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
96	C₁₆	—	38	2	no	—
97	C₁₆	—	38	2	no	—
98	C₂³	C₂×C₁₉⋊C₈	1	2	yes	—
99	C₂³	C₂×C₁₉⋊C₈	1	1	yes	characteristic
100	Q₈	—	2	2	no	—
101	D₄	—	2	4	no	—
102	D₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
106	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
107	C₂×C₄	#64520	1	2	yes	—
108	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
109	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
110	C₈	—	2	2	no	—
111	C₈	C₂²⋊Dic₁₉	1	2	yes	—
112	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
113	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
114	C₂²	—	2	2	no	—
115	C₂²	—	2	4	no	—
116	C₂²	—	2	2	no	—
117	C₂²	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
118	C₂²	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
121	C₄	C₂×#64520	1	1	yes	characteristic
122	C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	4	2	no	—
125	C₂	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
126	C₂	#11926961	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597269

C₂

yes

maximal, characteristic, complemented

C₂²×C₁₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂²⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, complemented

C₂×C₁₉×#131

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₄

yes

characteristic

C₁₉×#131

—

C₁₉×#131

—

C₂×M₁₆×C₁₉

C₄

yes

characteristic

C₂×M₁₆×C₁₉

C₄

yes

—

C₂²×C₈×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₈

yes

characteristic

C₂×D₄×C₁₉

C₈

yes

—

C₂×D₄×C₁₉

C₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

C₂×C₈

yes

—

C₂³×C₁₉

C₂×C₈

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

#2113

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊C₈

yes

—

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊C₈

yes

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₂×M₁₆

yes

characteristic

C₂×#131

D₁₉

yes

characteristic

C₂×M₃₂

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₁₉

#504

yes

—

C₂×#41

Dic₁₉

yes

characteristic

#131

—

#131

—

C₂×M₁₆

Dic₁₉

yes

characteristic

C₂×M₁₆

Dic₁₉

yes

—

C₂²×C₈

C₂×D₁₉

yes

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₁₉

#2113

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

C₁₉⋊C₈

yes

characteristic

C₂×D₄

C₁₉⋊C₈

yes

—

C₂×D₄

C₁₉⋊C₈

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₁₉

yes

—

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

C₂×C₁₉⋊C₈

yes

—

C₂³

C₂×C₁₉⋊C₈

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×C₁₉⋊C₈

yes

—

106

C₂×C₄

C₂×C₁₉⋊C₈

yes

characteristic

107

C₂×C₄

#64520

yes

—

108

C₂×C₄

C₂²⋊Dic₁₉

yes

—

109

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

110

C₈

—

111

C₈

C₂²⋊Dic₁₉

yes

—

112

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

113

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂²⋊(C₁₉⋊C₈)

yes

—

118

C₂²

C₂²×C₁₉⋊C₈

yes

characteristic

119

C₄

—

120

C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

121

C₄

C₂×#64520

yes

characteristic

122

C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

C₂×C₂²⋊(C₁₉⋊C₈)

yes

characteristic

126

C₂

#11926961

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂²×C₈
Fitting	C₂×C₁₉×#131	C₂
prime radical	C₂×#41×C₁₉	C₄
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂×#131	D₁₉
hypocenter	C₁₉	#2113
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#131

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₉

commutator, socle

C₂²×C₁₉

C₂²×C₈

Fitting

C₂×C₁₉×#131

C₂

prime radical

C₂×#41×C₁₉

C₄

cosocle

C₂×C₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₈ ◁ C₂×#131

N	H ≅ G/N	type
1. C₂×#10597269	C₂	semidirect
2. C₂²×C₁₉⋊C₁₆	C₂	semidirect
3. C₂²⋊(C₁₉⋊C₁₆)	C₂	semidirect
79. C₁₉	#2113	semidirect

H ≅ G/N

type

1. C₂×#10597269

C₂

semidirect

2. C₂²×C₁₉⋊C₁₆

C₂

semidirect

3. C₂²⋊(C₁₉⋊C₁₆)

C₂

semidirect

79. C₁₉

#2113

semidirect

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

subgroup	index
C₂×#10597269	2
C₂²×C₁₉⋊C₁₆	2
C₂²⋊(C₁₉⋊C₁₆)	2
C₂×C₁₉×#131	2
#2113	19

subgroup

index

C₂×#10597269

C₂²×C₁₉⋊C₁₆

C₂²⋊(C₁₉⋊C₁₆)

C₂×C₁₉×#131

#2113

Subgroups — #14565249

Conjugacy classes of subgroups

Complements

Maximal subgroups