Group #18069986 — subgroups

Subgroups — #18069986

Order 4864.

118 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14561833	C₂	1	1	yes	maximal, characteristic, complemented
2	#14561769	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2170	C₂	1	1	yes	maximal, characteristic
4	#11926378	—	2	1	no	—
5	C₂×C₁₉⋊C₃₂	—	2	1	no	—
6	C₁₉×#504	—	2	1	no	—
7	C₁₉×#443	C₄	1	1	yes	characteristic
8	C₁₉×#364	C₄	1	1	yes	characteristic
9	C₁₉×#350	—	2	1	no	—
10	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×#135	C₈	1	1	yes	characteristic
12	C₁₉×#131	—	2	1	no	—
13	C₁₉×M₃₂	—	2	1	no	—
14	C₁₉×M₃₂	—	4	1	no	—
15	C₂×C₁₆×C₁₉	—	4	1	no	—
16	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
18	C₁₉×#108	C₈	1	1	yes	characteristic
19	C₁₉×#104	—	2	1	no	—
20	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₁₉⋊C₃₂	—	2	2	no	—
22	C₁₉⋊C₃₂	—	4	1	no	—
23	#41×C₁₉	—	2	1	no	—
24	Q₁₆×C₁₉	C₁₆	1	1	yes	characteristic
25	SD₁₆×C₁₉	—	2	1	no	—
26	D₈×C₁₉	C₁₆	1	1	yes	characteristic
27	M₁₆×C₁₉	—	2	1	no	—
28	M₁₆×C₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	—	4	1	no	—
30	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
32	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
33	C₁₆×C₁₉	—	2	1	no	—
34	C₁₆×C₁₉	—	4	1	no	—
35	C₁₆×C₁₉	D₈	1	1	yes	characteristic
36	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
37	#7382	—	19	1	no	maximal, Sylow
38	Q₈×C₁₉	—	2	1	no	—
39	D₄×C₁₉	—	2	1	no	—
40	D₄×C₁₉	—	4	1	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
44	C₈×C₁₉	—	4	1	no	—
45	C₈×C₁₉	#102	1	1	yes	characteristic
46	C₈×C₁₉	#104	1	1	yes	characteristic
47	C₈×C₁₉	C₂×C₁₆	1	1	yes	characteristic
48	C₈×C₁₉	M₃₂	1	1	yes	characteristic
49	#2170	D₁₉	1	1	yes	characteristic
50	#1422	—	19	1	no	—
51	#1397	—	19	1	no	—
52	C₂²×C₁₉	—	4	1	no	—
53	C₂²×C₁₉	#350	1	1	yes	characteristic
54	C₄×C₁₉	—	4	1	no	—
55	C₄×C₁₉	—	4	1	no	—
56	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
57	C₄×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
58	#504	—	2	1	no	—
59	#443	Dic₁₉	1	1	yes	characteristic
60	M₆₄	—	38	1	no	—
61	C₂×C₃₂	—	38	1	no	—
62	#364	Dic₁₉	1	1	yes	characteristic
63	#350	—	2	1	no	—
64	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
65	C₂×C₁₉	—	2	1	no	—
66	C₂×C₁₉	—	8	1	no	—
67	C₂×C₁₉	D₄⋊C₁₆	1	1	yes	characteristic
68	#135	C₁₉⋊C₈	1	1	yes	characteristic
69	#131	—	2	1	no	—
70	M₃₂	—	2	1	no	—
71	M₃₂	—	4	1	no	—
72	C₂×C₁₆	—	4	1	no	—
73	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
74	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
75	#108	C₁₉⋊C₈	1	1	yes	characteristic
76	#104	—	2	1	no	—
77	C₄×C₈	C₂×Dic₁₉	1	1	yes	characteristic
78	C₃₂	—	38	2	no	—
79	C₃₂	—	76	1	no	—
80	C₁₉	#7382	1	1	yes	characteristic, complemented, Sylow
81	#41	—	2	1	no	—
82	Q₁₆	C₁₉⋊C₁₆	1	1	yes	characteristic
83	SD₁₆	—	2	1	no	—
84	D₈	C₁₉⋊C₁₆	1	1	yes	characteristic
85	M₁₆	—	2	1	no	—
86	M₁₆	—	4	1	no	—
87	C₂×C₈	—	4	1	no	—
88	C₂×C₈	C₂×C₁₉⋊C₈	1	1	yes	characteristic
89	C₂×C₈	C₂²⋊Dic₁₉	1	1	yes	characteristic
90	C₄²	#64520	1	1	yes	characteristic
91	C₁₆	—	2	1	no	—
92	C₁₆	—	4	1	no	—
93	C₁₆	#64525	1	1	yes	characteristic
94	C₁₆	#64526	1	1	yes	characteristic
95	Q₈	—	2	1	no	—
96	D₄	—	2	1	no	—
97	D₄	—	4	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	4	1	no	—
100	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
101	C₈	—	4	1	no	—
102	C₈	C₂×C₁₉⋊C₁₆	1	1	yes	characteristic
103	C₈	#10597269	1	1	yes	characteristic
104	C₈	#10597289	1	1	yes	characteristic
105	C₈	#10597294	1	1	yes	characteristic
106	C₂²	—	4	1	no	—
107	C₂²	#11926328	1	1	yes	characteristic
108	C₄	—	4	1	no	—
109	C₄	—	4	1	no	—
110	C₄	D₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
111	C₄	C₂²⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic
112	C₂	—	2	1	no	—
113	C₂	—	8	1	no	—
114	C₂	D₄⋊(C₁₉⋊C₁₆)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561833

C₂

yes

maximal, characteristic, complemented

#14561769

C₂

yes

maximal, characteristic, complemented

C₁₉×#2170

C₂

yes

maximal, characteristic

#11926378

—

C₂×C₁₉⋊C₃₂

—

C₁₉×#504

—

C₁₉×#443

C₄

yes

characteristic

C₁₉×#364

C₄

yes

characteristic

C₁₉×#350

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#135

C₈

yes

characteristic

C₁₉×#131

—

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#108

C₈

yes

characteristic

C₁₉×#104

—

C₄×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉⋊C₃₂

—

C₁₉⋊C₃₂

—

#41×C₁₉

—

Q₁₆×C₁₉

C₁₆

yes

characteristic

SD₁₆×C₁₉

—

D₈×C₁₉

C₁₆

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

characteristic

#7382

—

maximal, Sylow

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₈×C₁₉

C₂×C₁₆

yes

characteristic

C₈×C₁₉

M₃₂

yes

characteristic

#2170

D₁₉

yes

characteristic

#1422

—

#1397

—

C₂²×C₁₉

—

C₂²×C₁₉

#350

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

C₂²⋊C₁₆

yes

characteristic

#504

—

#443

Dic₁₉

yes

characteristic

M₆₄

—

C₂×C₃₂

—

#364

Dic₁₉

yes

characteristic

#350

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

D₄⋊C₁₆

yes

characteristic

#135

C₁₉⋊C₈

yes

characteristic

#131

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

#108

C₁₉⋊C₈

yes

characteristic

#104

—

C₄×C₈

C₂×Dic₁₉

yes

characteristic

C₃₂

—

C₃₂

—

C₁₉

#7382

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

C₁₉⋊C₁₆

yes

characteristic

SD₁₆

—

D₈

C₁₉⋊C₁₆

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂×C₁₉⋊C₈

yes

characteristic

C₂×C₈

C₂²⋊Dic₁₉

yes

characteristic

C₄²

#64520

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

yes

C₁₆

yes

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

101

C₈

—

102

C₈

C₂×C₁₉⋊C₁₆

yes

characteristic

103

C₈

#10597269

yes

characteristic

104

C₈

#10597289

yes

characteristic

105

C₈

#10597294

yes

characteristic

106

C₂²

—

107

C₂²

#11926328

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

D₄⋊(C₁₉⋊C₈)

yes

characteristic

111

C₄

C₂²⋊(C₁₉⋊C₁₆)

yes

characteristic

112

C₂

—

113

C₂

—

114

C₂

D₄⋊(C₁₉⋊C₁₆)

yes

characteristic

	subgroup	G/H
center	C₈	#10597289
commutator	C₈×C₁₉	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#2170	C₂
socle	C₂×C₁₉	D₄⋊C₁₆
prime radical	C₁₉×#135	C₈
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#2170	D₁₉
hypocenter	C₁₉	#7382
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #2170

subgroup

G/H

center

C₈

#10597289

commutator

C₈×C₁₉

C₂×C₁₆

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting

C₁₉×#2170

C₂

socle

C₂×C₁₉

D₄⋊C₁₆

prime radical

C₁₉×#135

C₈

cosocle

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ #2170

N	H ≅ G/N	type
1. #14561833	C₂	semidirect
2. #14561769	C₂	semidirect
80. C₁₉	#7382	semidirect

H ≅ G/N

type

1. #14561833

C₂

semidirect

2. #14561769

C₂

semidirect

80. C₁₉

#7382

semidirect

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

subgroup	index
#14561833	2
#14561769	2
C₁₉×#2170	2
#7382	19

subgroup

index

#14561833

#14561769

C₁₉×#2170

#7382

Subgroups — #18069986

Conjugacy classes of subgroups

Complements

Maximal subgroups