Group #14565248 — subgroups

Subgroups — #14565248

Order 2432.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10597347	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597269	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₁₉)⋊C₁₆	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#64541	C₄	1	1	yes	characteristic
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×#64520	C₄	1	1	yes	characteristic
8	#10597347	—	2	2	no	—
9	#10597347	—	2	2	no	—
10	C₂×#64515	C₄	1	2	yes	—
11	C₂×C₈×D₁₉	C₂²	1	2	yes	—
12	C₂×C₁₆×C₁₉	—	2	2	no	—
13	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
14	#10597269	—	2	2	no	—
15	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
16	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₂²⋊D₁₉	C₈	1	2	yes	—
18	#64541	—	2	2	no	—
19	#64541	—	2	2	no	—
20	C₂×D₇₆	C₈	1	1	yes	characteristic
21	C₂×C₄×D₁₉	C₂×C₄	1	2	yes	—
22	C₂×Dic₃₈	C₈	1	1	yes	characteristic
23	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	D₄	1	2	yes	—
25	C₂×C₈×C₁₉	D₄	1	2	yes	—
26	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
27	#64520	—	2	2	no	—
28	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
29	#64515	—	2	4	no	—
30	C₈×D₁₉	—	2	2	no	—
31	C₈×D₁₉	—	2	2	no	—
32	C₁₆×C₁₉	—	2	2	no	—
33	C₁₉⋊C₁₆	—	2	2	no	—
34	C₂³×C₁₉	C₂×C₈	1	1	yes	characteristic
35	C₂²×D₁₉	C₂×C₈	1	2	yes	—
36	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	M₁₆	1	2	yes	—
39	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
40	C₂²⋊D₁₉	—	2	4	no	—
41	C₂×Dic₁₉	C₂×C₈	1	2	yes	—
42	D₇₆	—	2	2	no	—
43	C₄×D₁₉	—	2	2	no	—
44	C₄×D₁₉	—	2	2	no	—
45	Dic₃₈	—	2	2	no	—
46	C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
47	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
48	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
49	C₁₉⋊C₈	—	2	2	no	—
50	#2113	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	—	2	2	no	—
52	C₂²×C₁₉	C₂²⋊C₈	1	2	yes	—
53	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
54	C₂×D₁₉	—	2	2	no	—
55	C₂×D₁₉	—	2	4	no	—
56	C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
57	C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
59	Dic₁₉	—	2	2	no	—
60	C₂×#131	—	19	1	no	—
61	C₂×M₃₂	—	19	1	no	—
62	C₂²×C₁₆	D₁₉	1	1	yes	characteristic, complemented
63	C₂²⋊C₁₆	—	19	4	no	—
64	C₂×C₁₉	—	2	2	no	—
65	C₂×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
66	C₂×C₁₉	#504	1	2	yes	—
67	D₁₉	—	4	2	no	—
68	C₂×#41	—	19	1	no	—
69	#131	—	38	2	no	—
70	#131	—	38	2	no	—
71	C₂×M₁₆	—	19	1	no	—
72	C₂×M₁₆	—	19	2	no	—
73	C₂²×C₈	—	19	2	no	—
74	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
75	M₃₂	—	38	2	no	—
76	C₂×C₁₆	—	2	2	no	—
77	C₂×C₁₆	—	19	2	no	—
78	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
79	C₁₉	#2113	1	1	yes	characteristic, complemented, Sylow
80	#41	—	38	2	no	—
81	#41	—	38	2	no	—
82	C₂×Q₈	—	19	1	no	—
83	C₂×D₄	—	19	2	no	—
84	C₂×D₄	—	19	1	no	—
85	C₂²×C₄	—	19	2	no	—
86	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
87	M₁₆	—	38	2	no	—
88	M₁₆	—	38	4	no	—
89	C₂×C₈	—	19	2	no	—
90	C₂×C₈	—	38	2	no	—
91	C₂×C₈	—	38	2	no	—
92	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
93	C₂×C₈	D₇₆	1	2	yes	—
94	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
95	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
96	C₁₆	—	2	2	no	—
97	C₁₆	—	38	2	no	—
98	C₂³	—	19	2	no	—
99	C₂³	C₈×D₁₉	1	1	yes	characteristic
100	Q₈	—	38	2	no	—
101	D₄	—	38	4	no	—
102	D₄	—	38	2	no	—
103	C₂×C₄	—	19	2	no	—
104	C₂×C₄	—	38	2	no	—
105	C₂×C₄	—	38	2	no	—
106	C₂×C₄	C₈×D₁₉	1	1	yes	characteristic
107	C₂×C₄	#64515	1	2	yes	—
108	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
109	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
110	C₈	—	38	2	no	—
111	C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
112	C₈	C₂×D₇₆	1	1	yes	characteristic
113	C₈	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
114	C₂²	—	2	2	no	—
115	C₂²	—	38	4	no	—
116	C₂²	—	38	2	no	—
117	C₂²	(C₂×D₁₉)⋊C₈	1	2	yes	—
118	C₂²	C₂×C₈×D₁₉	1	1	yes	characteristic
119	C₄	—	38	2	no	—
120	C₄	(C₂×D₁₉)⋊C₈	1	2	yes	—
121	C₄	C₂×#64515	1	1	yes	characteristic
122	C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	76	2	no	—
125	C₂	C₂×(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
126	C₂	#11926960	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597347

C₂

yes

maximal, characteristic

C₂×#10597269

C₂

yes

maximal, characteristic, complemented

(C₂×D₁₉)⋊C₁₆

C₂

yes

maximal, complemented

C₂²×C₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×#64541

C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₄

yes

—

—

C₄

yes

—

C₂×C₈×D₁₉

C₂²

yes

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₂²

yes

—

#10597269

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₁₉

C₈

yes

—

#64541

—

#64541

—

C₂×D₇₆

C₈

yes

characteristic

C₂×C₄×D₁₉

C₂×C₄

yes

—

C₂×Dic₃₈

C₈

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

#64515

—

C₈×D₁₉

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

C₂×C₈

yes

characteristic

C₂²×D₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

C₂×C₈

yes

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

C₂²⋊C₄

yes

—

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

C₁₉⋊C₈

—

#2113

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊C₈

yes

—

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

C₂²⋊C₈

yes

—

C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₉

C₂×M₁₆

yes

characteristic

Dic₁₉

—

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

D₁₉

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₁₉

#504

yes

—

D₁₉

—

C₂×#41

—

#131

—

#131

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

—

C₁₉

#2113

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

D₇₆

yes

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂³

C₈×D₁₉

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₈×D₁₉

yes

characteristic

107

C₂×C₄

#64515

yes

—

108

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

109

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

110

C₈

—

111

C₈

(C₂×D₁₉)⋊C₄

yes

—

112

C₈

C₂×D₇₆

yes

characteristic

113

C₈

C₂×C₂²⋊D₁₉

yes

characteristic

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

(C₂×D₁₉)⋊C₈

yes

—

118

C₂²

C₂×C₈×D₁₉

yes

characteristic

119

C₄

—

120

C₄

(C₂×D₁₉)⋊C₈

yes

—

121

C₄

C₂×#64515

yes

characteristic

122

C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

C₂×(C₂×D₁₉)⋊C₈

yes

characteristic

126

C₂

#11926960

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂²×C₈
Fitting	C₂²×C₁₆×C₁₉	C₂
prime radical	C₂×#64541	C₄
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂²×C₁₆	D₁₉
hypocenter	C₁₉	#2113
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₉

commutator, socle

C₂²×C₁₉

C₂²×C₈

Fitting

C₂²×C₁₆×C₁₉

C₂

prime radical

C₂×#64541

C₄

cosocle

C₂×C₈×C₁₉

C₂³

hypercenter

C₂²×C₁₆

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
2. C₂×#10597269	C₂	semidirect
3. (C₂×D₁₉)⋊C₁₆	C₂	semidirect
4. C₂²×C₁₆×C₁₉	C₂	semidirect
62. C₂²×C₁₆	D₁₉	semidirect
79. C₁₉	#2113	semidirect

H ≅ G/N

type

2. C₂×#10597269

C₂

semidirect

3. (C₂×D₁₉)⋊C₁₆

C₂

semidirect

4. C₂²×C₁₆×C₁₉

C₂

semidirect

62. C₂²×C₁₆

D₁₉

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×#10597347	2
C₂×#10597269	2
(C₂×D₁₉)⋊C₁₆	2
C₂²×C₁₆×C₁₉	2
#2113	19

subgroup

index

C₂×#10597347

C₂×#10597269

(C₂×D₁₉)⋊C₁₆

C₂²×C₁₆×C₁₉

#2113

Subgroups — #14565248

Conjugacy classes of subgroups

Complements

Maximal subgroups