Group #14565812 — subgroups

Subgroups — #14565812

Order 2432.

120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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	#11926946	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926662	C₂	1	1	yes	maximal, characteristic
3	#11926367	C₂	1	2	yes	maximal, complemented
4	#11926355	C₂	1	2	yes	maximal
5	C₁₉×#364	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597350	C₂²	1	1	yes	characteristic
7	#10597347	—	2	1	no	—
8	#10597316	—	2	1	no	—
9	C₁₉×M₃₂	C₂²	1	2	yes	—
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597276	C₂²	1	1	yes	characteristic
12	#10597275	—	2	1	no	—
13	#10597274	C₂²	1	2	yes	—
14	#10597262	—	2	1	no	—
15	#64541	—	2	1	no	—
16	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
18	C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₄⋊Dic₁₉	—	2	2	no	—
20	Dic₁₉⋊C₄	—	4	2	no	—
21	#64520	—	2	1	no	—
22	Dic₇₆	Q₈	1	1	yes	characteristic
23	D₁₅₂	Q₈	1	1	yes	characteristic
24	#64516	—	2	1	no	—
25	#64515	—	4	1	no	—
26	C₈×D₁₉	—	4	1	no	—
27	C₁₆×C₁₉	—	2	2	no	—
28	C₂×C₄×C₁₉	—	2	1	no	—
29	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
30	C₂²⋊D₁₉	—	4	1	no	—
31	C₂×Dic₁₉	—	4	2	no	—
32	D₇₆	—	2	1	no	—
33	C₄×D₁₉	—	4	1	no	—
34	Dic₃₈	—	2	1	no	—
35	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
36	C₈×C₁₉	SD₁₆	1	1	yes	characteristic
37	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
38	C₈×C₁₉	#41	1	1	yes	characteristic
39	C₁₉⋊C₈	—	4	1	no	—
40	#2231	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
42	C₂×D₁₉	—	4	1	no	—
43	C₄×C₁₉	—	4	1	no	—
44	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
45	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
46	Dic₁₉	—	4	1	no	—
47	Dic₁₉	—	8	2	no	—
48	#499	—	19	1	no	—
49	#443	—	19	1	no	—
50	#365	—	19	2	no	—
51	#364	D₁₉	1	1	yes	characteristic, complemented
52	#360	—	19	2	no	—
53	C₂×C₁₉	—	2	1	no	—
54	C₂×C₁₉	#476	1	1	yes	characteristic
55	D₁₉	—	8	1	no	—
56	#135	—	19	1	no	—
57	#131	—	38	1	no	—
58	#125	—	38	1	no	—
59	M₃₂	C₂×D₁₉	1	2	yes	—
60	#108	—	19	1	no	—
61	#107	—	38	1	no	—
62	#106	—	19	2	no	—
63	#104	—	38	1	no	—
64	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
65	C₁₉	#2231	1	1	yes	characteristic, complemented, Sylow
66	#41	—	38	1	no	—
67	Q₁₆	—	19	1	no	—
68	SD₁₆	—	38	1	no	—
69	D₈	—	19	1	no	—
70	M₁₆	—	38	1	no	—
71	M₁₆	—	76	1	no	—
72	C₂×C₈	—	76	1	no	—
73	C₂×C₈	D₇₆	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
75	C₄⋊C₄	—	38	2	no	—
76	C₄⋊C₄	—	76	2	no	—
77	C₄²	D₇₆	1	1	yes	characteristic
78	C₁₆	—	2	2	no	—
79	Q₈	—	38	1	no	—
80	D₄	—	38	1	no	—
81	D₄	—	76	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	76	1	no	—
84	C₂×C₄	—	76	2	no	—
85	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
86	C₈	—	76	1	no	—
87	C₈	#64516	1	1	yes	characteristic
88	C₈	#64516	1	1	yes	characteristic
89	C₈	#64543	1	1	yes	characteristic
90	C₈	Q₈×D₁₉	1	1	yes	characteristic
91	C₂²	—	76	1	no	—
92	C₂²	#10597354	1	1	yes	characteristic
93	C₄	—	4	1	no	—
94	C₄	—	76	1	no	—
95	C₄	—	152	2	no	—
96	C₄	#10597343	1	1	yes	characteristic
97	C₄	C₂×#64516	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	152	1	no	—
100	C₂	#11926835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926946

C₂

yes

maximal, characteristic, complemented

#11926662

C₂

yes

maximal, characteristic

#11926367

C₂

yes

maximal, complemented

#11926355

C₂

yes

maximal

C₁₉×#364

C₂

yes

maximal, characteristic, complemented

#10597350

C₂²

yes

characteristic

#10597347

—

#10597316

—

C₁₉×M₃₂

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597276

C₂²

yes

characteristic

#10597275

—

#10597274

C₂²

yes

—

#10597262

—

#64541

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

#64520

—

Dic₇₆

Q₈

yes

characteristic

D₁₅₂

Q₈

yes

characteristic

#64516

—

#64515

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

SD₁₆

yes

characteristic

C₈×C₁₉

SD₁₆

yes

characteristic

C₈×C₁₉

C₂×Q₈

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic, complemented

#360

—

C₂×C₁₉

—

C₂×C₁₉

#476

yes

characteristic

D₁₉

—

#135

—

#131

—

#125

—

M₃₂

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2231

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₇₆

yes

characteristic

C₁₆

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₈

—

C₈

yes

C₈

yes

C₈

yes

C₈

Q₈×D₁₉

yes

characteristic

C₂²

—

C₂²

#10597354

yes

characteristic

C₄

—

C₄

—

C₄

—

152

—

C₄

yes

C₄

yes

C₂

—

C₂

—

152

—

100

C₂

#11926835

yes

characteristic

	subgroup	G/H
center	C₂	#11926835
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#364	C₂
socle	C₂×C₁₉	#476
prime radical	#10597350	C₂²
hypercenter	#364	D₁₉
hypocenter	C₁₉	#2231
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

subgroup

G/H

center

C₂

#11926835

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#364

C₂

C₂×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

N	H ≅ G/N	type
1. #11926946	C₂	semidirect
3. #11926367	C₂	semidirect
5. C₁₉×#364	C₂	semidirect
51. #364	D₁₉	semidirect
65. C₁₉	#2231	semidirect

H ≅ G/N

type

1. #11926946

C₂

semidirect

3. #11926367

C₂

semidirect

5. C₁₉×#364

C₂

semidirect

51. #364

D₁₉

semidirect

65. C₁₉

#2231

semidirect

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

subgroup	index
#11926946	2
#11926662	2
#11926367	2
#11926355	2
C₁₉×#364	2
#2231	19

subgroup

index

C₁₉×#364

Subgroups — #14565812

Conjugacy classes of subgroups

Complements

Maximal subgroups