Group #14565804 — subgroups

Subgroups — #14565804

Order 2432.

126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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	#11926941	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926661	C₂	1	1	yes	maximal, characteristic
3	#11926367	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926366	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926364	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926354	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#360	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#135	C₂²	1	1	yes	characteristic
9	#10597394	—	2	1	no	—
10	#10597334	—	2	1	no	—
11	C₁₉×M₃₂	C₂²	1	1	yes	characteristic
12	C₁₉×#106	C₂²	1	1	yes	characteristic
13	#10597294	—	2	1	no	—
14	#10597276	C₂²	1	1	yes	characteristic
15	#10597274	C₂²	1	1	yes	characteristic
16	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
17	#10597269	C₂²	1	1	yes	characteristic
18	#10597265	—	2	1	no	—
19	#41×C₁₉	—	2	1	no	—
20	C₂×Dic₃₈	—	4	1	no	—
21	Q₁₆×C₁₉	Q₈	1	1	yes	characteristic, complemented
22	SD₁₆×C₁₉	—	2	1	no	—
23	D₈×C₁₉	Q₈	1	1	yes	characteristic, complemented
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₁₉	—	2	1	no	—
26	C₄⋊Dic₁₉	—	2	1	no	—
27	Dic₁₉⋊C₄	—	4	1	no	—
28	C₄×Dic₁₉	D₄	1	1	yes	characteristic
29	#64520	—	2	1	no	—
30	#64520	—	4	1	no	—
31	C₂×C₁₉⋊C₈	—	4	1	no	—
32	C₂×C₁₉⋊C₈	D₄	1	1	yes	characteristic
33	C₁₆×C₁₉	—	2	1	no	—
34	C₁₉⋊C₁₆	—	2	1	no	—
35	Q₈×C₁₉	—	2	1	no	—
36	D₄×C₁₉	—	2	1	no	—
37	D₄×C₁₉	—	4	1	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	—	4	1	no	—
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₁₉	—	2	1	no	—
42	C₂×Dic₁₉	—	4	1	no	—
43	Dic₃₈	—	8	2	no	—
44	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₁₉	#41	1	1	yes	characteristic
46	C₁₉⋊C₈	—	4	1	no	—
47	C₁₉⋊C₈	SD₁₆	1	1	yes	characteristic
48	C₁₉⋊C₈	SD₁₆	1	1	yes	characteristic
49	#2230	—	19	1	no	maximal, Sylow
50	C₂²×C₁₉	—	4	1	no	—
51	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
52	C₄×C₁₉	—	4	1	no	—
53	C₄×C₁₉	—	8	1	no	—
54	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
55	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
56	Dic₁₉	—	2	2	no	—
57	Dic₁₉	—	8	1	no	—
58	#498	—	19	1	no	—
59	#443	—	19	1	no	—
60	#365	—	19	1	no	—
61	#365	—	19	1	no	—
62	#364	—	19	1	no	—
63	#360	—	19	1	no	—
64	#360	D₁₉	1	1	yes	characteristic
65	C₂×C₁₉	—	2	1	no	—
66	C₂×C₁₉	—	8	1	no	—
67	C₂×C₁₉	#476	1	1	yes	characteristic
68	#135	C₂×D₁₉	1	1	yes	characteristic
69	#131	—	38	1	no	—
70	C₄⋊Q₈	—	38	1	no	—
71	M₃₂	—	19	1	no	—
72	M₃₂	C₂×D₁₉	1	1	yes	characteristic
73	#108	—	19	1	no	—
74	#106	—	19	1	no	—
75	#106	—	38	1	no	—
76	#106	C₂×D₁₉	1	1	yes	characteristic
77	#104	—	38	1	no	—
78	C₄×C₈	—	19	1	no	—
79	C₁₉	#2230	1	1	yes	characteristic, complemented, Sylow
80	#41	—	2	1	no	—
81	C₂×Q₈	—	76	1	no	—
82	Q₁₆	Dic₃₈	1	1	yes	characteristic, complemented
83	SD₁₆	—	2	1	no	—
84	D₈	Dic₃₈	1	1	yes	characteristic, complemented
85	M₁₆	—	38	1	no	—
86	M₁₆	—	76	1	no	—
87	C₂×C₈	—	19	1	no	—
88	C₂×C₈	—	76	1	no	—
89	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
90	C₄⋊C₄	—	2	1	no	—
91	C₄⋊C₄	—	38	1	no	—
92	C₄⋊C₄	—	76	1	no	—
93	C₄²	—	19	1	no	—
94	C₁₆	—	2	1	no	—
95	C₁₆	—	38	1	no	—
96	Q₈	—	2	1	no	—
97	Q₈	—	152	2	no	—
98	D₄	—	2	1	no	—
99	D₄	—	4	1	no	—
100	C₂×C₄	—	4	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	38	1	no	—
103	C₂×C₄	—	76	1	no	—
104	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
105	C₈	—	19	1	no	—
106	C₈	—	19	1	no	—
107	C₈	—	76	1	no	—
108	C₈	C₂×Dic₃₈	1	1	yes	characteristic
109	C₈	#64543	1	1	yes	characteristic
110	C₂²	—	4	1	no	—
111	C₂²	#10597357	1	1	yes	characteristic
112	C₄	—	4	1	no	—
113	C₄	—	8	1	no	—
114	C₄	—	38	2	no	—
115	C₄	—	152	1	no	—
116	C₄	#10597324	1	1	yes	characteristic
117	C₄	SD₁₆×D₁₉	1	1	yes	characteristic
118	C₂	—	2	1	no	—
119	C₂	—	8	1	no	—
120	C₂	#11926832	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926941

C₂

yes

maximal, characteristic, complemented

#11926661

C₂

yes

maximal, characteristic

#11926367

C₂

yes

maximal, characteristic, complemented

#11926366

C₂

yes

maximal, characteristic, complemented

#11926364

C₂

yes

maximal, characteristic, complemented

#11926354

C₂

yes

maximal, characteristic

C₁₉×#360

C₂

yes

maximal, characteristic

C₁₉×#135

C₂²

yes

characteristic

#10597394

—

#10597334

—

C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×#106

C₂²

yes

characteristic

#10597294

—

#10597276

C₂²

yes

characteristic

#10597274

C₂²

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

#10597269

C₂²

yes

characteristic

#10597265

—

#41×C₁₉

—

C₂×Dic₃₈

—

Q₁₆×C₁₉

Q₈

yes

characteristic, complemented

SD₁₆×C₁₉

—

D₈×C₁₉

Q₈

yes

characteristic, complemented

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

characteristic

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

C₂×Q₈

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

C₁₉⋊C₈

SD₁₆

yes

characteristic

C₁₉⋊C₈

SD₁₆

yes

characteristic

#2230

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

AGL(1,ℤ/8)

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

Dic₁₉

—

—

—

—

—

—

—

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#476

yes

characteristic

#135

C₂×D₁₉

yes

characteristic

#131

—

C₄⋊Q₈

—

M₃₂

—

M₃₂

C₂×D₁₉

yes

—

—

—

C₂×D₁₉

yes

characteristic

#104

—

C₄×C₈

—

C₁₉

#2230

yes

characteristic, complemented, Sylow

#41

—

C₂×Q₈

—

Q₁₆

Dic₃₈

yes

characteristic, complemented

SD₁₆

—

D₈

Dic₃₈

yes

characteristic, complemented

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

152

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

D₄×D₁₉

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

C₂×Dic₃₈

yes

characteristic

109

C₈

#64543

yes

characteristic

110

C₂²

—

111

C₂²

#10597357

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

152

—

116

C₄

#10597324

yes

characteristic

117

C₄

SD₁₆×D₁₉

yes

characteristic

118

C₂

—

119

C₂

—

120

C₂

#11926832

yes

characteristic

	subgroup	G/H
center	C₂	#11926832
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#360	C₂
socle	C₂×C₁₉	#476
prime radical	C₁₉×#135	C₂²
hypercenter	#360	D₁₉
hypocenter	C₁₉	#2230
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

subgroup

G/H

center

C₂

#11926832

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#360

C₂

socle

C₂×C₁₉

#476

prime radical

C₁₉×#135

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

N	H ≅ G/N	type
1. #11926941	C₂	semidirect
3. #11926367	C₂	semidirect
4. #11926366	C₂	semidirect
5. #11926364	C₂	semidirect
21. Q₁₆×C₁₉	Q₈	semidirect
23. D₈×C₁₉	Q₈	semidirect
79. C₁₉	#2230	semidirect
82. Q₁₆	Dic₃₈	semidirect
84. D₈	Dic₃₈	semidirect

H ≅ G/N

type

1. #11926941

C₂

semidirect

3. #11926367

C₂

semidirect

4. #11926366

C₂

semidirect

5. #11926364

C₂

semidirect

21. Q₁₆×C₁₉

Q₈

semidirect

23. D₈×C₁₉

Q₈

semidirect

79. C₁₉

#2230

semidirect

82. Q₁₆

Dic₃₈

semidirect

84. D₈

Dic₃₈

semidirect

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

subgroup	index
#11926941	2
#11926661	2
#11926367	2
#11926366	2
#11926364	2
#11926354	2
C₁₉×#360	2
#2230	19

subgroup

index

C₁₉×#360

Subgroups — #14565804

Conjugacy classes of subgroups

Complements

Maximal subgroups