Group #14565476 — subgroups

Subgroups — #14565476

Order 2432.

144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 63 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	#11926962	C₂	1	2	yes	maximal, complemented
2	#11926662	C₂	1	1	yes	maximal, characteristic
3	#11926329	C₂	1	2	yes	maximal, complemented
4	#11926320	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597350	C₄	1	1	yes	characteristic
7	#10597347	C₂²	1	2	yes	—
8	C₁₉×M₃₂	C₂²	1	2	yes	—
9	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
10	#10597276	C₄	1	1	yes	characteristic
11	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₉⋊C₁₆	C₂²	1	1	yes	characteristic
13	#10597262	C₄	1	2	yes	—
14	#10597255	—	2	2	no	—
15	C₁₆×D₁₉	—	2	2	no	—
16	#64541	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
19	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	#64520	C₂×C₄	1	2	yes	—
21	Dic₇₆	C₈	1	1	yes	characteristic
22	D₁₅₂	C₈	1	1	yes	characteristic
23	#64516	C₈	1	2	yes	—
24	#64515	—	2	2	no	—
25	C₈×D₁₉	—	2	2	no	—
26	C₁₆×C₁₉	—	2	2	no	—
27	C₁₉⋊C₁₆	—	2	1	no	—
28	C₁₉⋊C₁₆	D₄	1	2	yes	—
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
31	C₂²⋊D₁₉	—	2	2	no	—
32	D₇₆	C₂×C₈	1	2	yes	—
33	C₄×D₁₉	—	2	2	no	—
34	Dic₃₈	C₂×C₈	1	2	yes	—
35	C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
36	C₈×C₁₉	C₂×C₈	1	1	yes	characteristic
37	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₁₉	#41	1	1	yes	characteristic
39	C₁₉⋊C₈	—	2	2	no	—
40	#2171	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	#131	1	1	yes	characteristic
42	C₂×D₁₉	—	2	2	no	—
43	C₄×C₁₉	—	4	1	no	—
44	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
45	C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
46	Dic₁₉	—	2	2	no	—
47	#504	—	19	2	no	—
48	#443	—	19	1	no	—
49	#364	D₁₉	1	1	yes	characteristic, complemented
50	#350	—	19	2	no	—
51	#346	—	19	1	no	—
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	C₈×D₄	1	1	yes	characteristic
54	D₁₉	—	4	2	no	—
55	#135	—	19	1	no	—
56	#131	—	19	2	no	—
57	M₃₂	—	38	2	no	—
58	M₃₂	C₂×D₁₉	1	2	yes	—
59	C₂×C₁₆	—	19	1	no	—
60	C₂×C₁₆	—	19	1	no	—
61	C₂×C₁₆	—	38	2	no	—
62	#108	—	19	1	no	—
63	#104	—	19	2	no	—
64	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
65	C₁₉	#2171	1	1	yes	characteristic, complemented, Sylow
66	#41	—	19	2	no	—
67	Q₁₆	—	19	1	no	—
68	SD₁₆	—	19	2	no	—
69	D₈	—	19	1	no	—
70	M₁₆	—	19	2	no	—
71	M₁₆	—	38	2	no	—
72	C₂×C₈	—	38	2	no	—
73	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
75	C₄²	C₄×D₁₉	1	1	yes	characteristic
76	C₁₆	—	2	2	no	—
77	C₁₆	—	19	2	no	—
78	C₁₆	—	38	1	no	—
79	Q₈	—	19	2	no	—
80	D₄	—	19	2	no	—
81	D₄	—	38	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	38	2	no	—
84	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
85	C₈	—	38	2	no	—
86	C₈	C₈×D₁₉	1	1	yes	characteristic
87	C₈	C₈×D₁₉	1	1	yes	characteristic
88	C₈	D₄×D₁₉	1	1	yes	characteristic
89	C₈	#64545	1	1	yes	characteristic
90	C₂²	—	38	2	no	—
91	C₂²	#10597353	1	1	yes	characteristic
92	C₄	—	4	1	no	—
93	C₄	—	38	2	no	—
94	C₄	#10597339	1	1	yes	characteristic
95	C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	76	2	no	—
98	C₂	#11926609	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926962

C₂

yes

maximal, complemented

#11926662

C₂

yes

maximal, characteristic

#11926329

C₂

yes

maximal, complemented

#11926320

C₂

yes

maximal, characteristic, complemented

C₁₉×#364

C₂

yes

maximal, characteristic, complemented

#10597350

C₄

yes

characteristic

#10597347

C₂²

yes

—

C₁₉×M₃₂

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597276

C₄

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

characteristic

#10597262

C₄

yes

—

#10597255

—

C₁₆×D₁₉

—

#64541

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

#64520

C₂×C₄

yes

—

Dic₇₆

C₈

yes

characteristic

D₁₅₂

C₈

yes

characteristic

#64516

C₈

yes

—

#64515

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

D₄

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²⋊D₁₉

—

D₇₆

C₂×C₈

yes

—

C₄×D₁₉

—

Dic₃₈

C₂×C₈

yes

—

C₈×C₁₉

C₂×C₈

yes

characteristic

C₈×C₁₉

C₂×C₈

yes

characteristic

C₈×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₂²×C₈

yes

characteristic

Dic₁₉

—

#504

—

#443

—

#364

D₁₉

yes

characteristic, complemented

#350

—

#346

—

C₂×C₁₉

—

C₂×C₁₉

C₈×D₄

yes

characteristic

D₁₉

—

#135

—

#131

—

M₃₂

—

M₃₂

C₂×D₁₉

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#104

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2171

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

C₄×D₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

C₈

—

C₈

C₈×D₁₉

yes

characteristic

C₈

C₈×D₁₉

yes

characteristic

C₈

D₄×D₁₉

yes

characteristic

C₈

#64545

yes

characteristic

C₂²

—

C₂²

#10597353

yes

characteristic

C₄

—

C₄

—

C₄

#10597339

yes

characteristic

C₄

C₂×C₈×D₁₉

yes

characteristic

C₂

—

C₂

—

C₂

#11926609

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₁₉
commutator	C₄×C₁₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#364	C₂
socle	C₂×C₁₉	C₈×D₄
prime radical	#10597350	C₄
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	#364	D₁₉
hypocenter	C₁₉	#2171
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×D₁₉

commutator

C₄×C₁₉

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#364

C₂

socle

C₂×C₁₉

C₈×D₄

prime radical

#10597350

C₄

cosocle

C₂×C₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
1. #11926962	C₂	semidirect
3. #11926329	C₂	semidirect
4. #11926320	C₂	semidirect
5. C₁₉×#364	C₂	semidirect
49. #364	D₁₉	semidirect
65. C₁₉	#2171	semidirect

H ≅ G/N

type

1. #11926962

C₂

semidirect

3. #11926329

C₂

semidirect

4. #11926320

C₂

semidirect

5. C₁₉×#364

C₂

semidirect

49. #364

D₁₉

semidirect

65. C₁₉

#2171

semidirect

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

subgroup	index
#11926962	2
#11926662	2
#11926329	2
#11926320	2
C₁₉×#364	2
#2171	19

subgroup

index

C₁₉×#364

Subgroups — #14565476

Conjugacy classes of subgroups

Complements

Maximal subgroups