Group #14561728 — subgroups

Subgroups — #14561728

Order 2432.

128 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₂²×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597276	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#108	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×C₁₉	—	2	1	no	—
5	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×#64520	—	2	1	no	—
7	C₁₉×#108	—	2	1	no	—
8	C₁₉×#108	C₄	1	2	yes	—
9	#10597276	—	2	1	no	—
10	#10597276	C₄	1	2	yes	—
11	C₂×C₁₉⋊C₁₆	—	2	1	no	—
12	C₂×C₁₉⋊C₁₆	—	2	1	no	—
13	C₂×C₁₉⋊C₁₆	C₄	1	2	yes	—
14	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
15	M₁₆×C₁₉	—	2	2	no	—
16	M₁₆×C₁₉	—	4	1	no	—
17	C₂×C₈×C₁₉	—	4	1	no	—
18	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
24	#64520	—	2	2	no	—
25	#64520	—	4	1	no	—
26	C₂×C₁₉⋊C₈	—	4	1	no	—
27	C₁₉⋊C₁₆	—	2	2	no	—
28	C₂³×C₁₉	Q₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
33	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
35	C₈×C₁₉	—	4	2	no	—
36	C₈×C₁₉	C₄²	1	1	yes	characteristic
37	C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
38	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₁₉⋊C₈	—	4	2	no	—
41	#1381	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	2	2	no	—
43	C₂²×C₁₉	#103	1	1	yes	characteristic
44	C₂²×C₁₉	#103	1	1	yes	characteristic
45	C₂²×C₁₉	#107	1	1	yes	characteristic
46	C₄×C₁₉	#95	1	1	yes	characteristic
47	C₄×C₁₉	#102	1	1	yes	characteristic
48	C₄×C₁₉	#102	1	1	yes	characteristic
49	C₄×C₁₉	#106	1	1	yes	characteristic
50	C₂²×C₁₆	—	19	1	no	—
51	C₂×#108	—	19	1	no	—
52	C₂×#108	D₁₉	1	1	yes	characteristic
53	C₂×C₁₉	—	2	1	no	—
54	C₂×C₁₉	—	2	1	no	—
55	C₂×C₁₉	#340	1	1	yes	characteristic
56	C₂×C₁₉	#368	1	2	yes	—
57	C₂×M₁₆	—	2	1	no	—
58	C₂×M₁₆	—	38	1	no	—
59	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
60	C₂×C₁₆	—	19	2	no	—
61	C₂×C₁₆	—	38	1	no	—
62	C₂×C₁₆	—	38	1	no	—
63	#108	—	2	1	no	—
64	#108	—	19	2	no	—
65	#108	—	38	1	no	—
66	#108	Dic₁₉	1	2	yes	—
67	C₁₉	#1381	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	4	1	no	—
71	M₁₆	—	38	2	no	—
72	M₁₆	—	76	1	no	—
73	C₂×C₈	—	4	1	no	—
74	C₂×C₈	—	76	1	no	—
75	C₂×C₈	Dic₃₈	1	1	yes	characteristic
76	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
77	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
78	C₂×C₈	D₇₆	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
81	C₁₆	—	38	2	no	—
82	C₂³	#64528	1	1	yes	characteristic
83	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
84	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
85	C₂×C₄	#64525	1	1	yes	characteristic
86	C₂×C₄	#64526	1	1	yes	characteristic
87	C₂×C₄	#64527	1	1	yes	characteristic
88	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
89	C₈	—	4	2	no	—
90	C₈	—	76	2	no	—
91	C₈	C₄×Dic₁₉	1	1	yes	characteristic
92	C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
93	C₈	C₄⋊Dic₁₉	1	1	yes	characteristic
94	C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
95	C₂²	—	2	2	no	—
96	C₂²	#10597264	1	1	yes	characteristic
97	C₂²	#10597267	1	1	yes	characteristic
98	C₂²	#10597292	1	1	yes	characteristic
99	C₄	#10597265	1	1	yes	characteristic
100	C₄	#10597266	1	1	yes	characteristic
101	C₄	C₁₉⋊#95	1	1	yes	characteristic
102	C₄	#10597289	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	2	1	no	—
105	C₂	#11926306	1	1	yes	characteristic
106	C₂	#11926373	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₉⋊C₁₆

C₂

yes

maximal, characteristic

C₂×#10597276

C₂

yes

maximal, characteristic

C₂×C₁₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×#64520

—

C₁₉×#108

—

C₁₉×#108

C₄

yes

—

#10597276

—

#10597276

C₄

yes

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

—

C₂×C₁₉⋊C₁₆

C₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

Q₁₆

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

D₈

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₄²

yes

characteristic

C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₁₉⋊C₈

—

#1381

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂²×C₁₆

—

C₂×#108

—

C₂×#108

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#340

yes

characteristic

C₂×C₁₉

#368

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

—

—

Dic₁₉

yes

—

C₁₉

#1381

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

#64528

yes

characteristic

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₈

—

C₈

—

C₈

C₄×Dic₁₉

yes

characteristic

C₈

Dic₁₉⋊C₄

yes

characteristic

C₈

C₄⋊Dic₁₉

yes

characteristic

C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

yes

100

C₄

#10597266

yes

characteristic

101

C₄

C₁₉⋊#95

yes

characteristic

102

C₄

#10597289

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

#11926306

yes

characteristic

106

C₂

#11926373

yes

—

	subgroup	G/H
center	C₂×C₄	#64525
commutator	C₈×C₁₉	C₄²
Frattini	C₂²×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#108	C₂
socle	C₂²×C₁₉	#107
prime radical	C₂³×C₁₉	Q₁₆
cosocle	C₂²×C₈×C₁₉	C₂²
hypercenter	C₂×#108	D₁₉
hypocenter	C₁₉	#1381
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

#64525

commutator

C₈×C₁₉

C₄²

Frattini

C₂²×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×#108

C₂

socle

C₂²×C₁₉

#107

prime radical

C₂³×C₁₉

Q₁₆

cosocle

C₂²×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
67. C₁₉	#1381	semidirect

H ≅ G/N

type

67. C₁₉

#1381

semidirect

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

subgroup	index
C₂²×C₁₉⋊C₁₆	2
C₂×#10597276	2
C₂×C₁₉×#108	2
#1381	19

subgroup

index

C₂²×C₁₉⋊C₁₆

C₂×#10597276

C₂×C₁₉×#108

#1381

Subgroups — #14561728

Conjugacy classes of subgroups

Complements

Maximal subgroups