Group #14565866 — subgroups

Subgroups — #14565866

Order 2432.

138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 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	#11926348	C₂	1	2	yes	maximal, complemented
3	#11926345	C₂	1	2	yes	maximal
4	C₄×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#495	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×SD₁₆×C₁₉	—	2	1	no	—
8	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#124	—	2	1	no	—
10	#10597316	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597275	C₂²	1	2	yes	—
13	#10597274	—	2	1	no	—
14	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂×D₄×C₁₉	—	2	1	no	—
17	Q₁₆×C₁₉	—	2	2	no	—
18	SD₁₆×C₁₉	—	4	2	no	—
19	D₈×C₁₉	—	2	2	no	—
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²⋊C₄×C₁₉	—	4	2	no	—
23	C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₄⋊Dic₁₉	—	2	2	no	—
25	Dic₁₉⋊C₄	—	4	2	no	—
26	C₁₉⋊C₁₆	—	2	2	no	—
27	C₂³×C₁₉	—	4	1	no	—
28	Q₈×C₁₉	—	4	1	no	—
29	Q₈×C₁₉	—	4	1	no	—
30	D₄×C₁₉	—	4	1	no	—
31	D₄×C₁₉	—	4	1	no	—
32	C₂×C₄×C₁₉	—	4	1	no	—
33	C₂×C₄×C₁₉	D₈	1	2	yes	—
34	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₁₉	—	4	2	no	—
36	C₈×C₁₉	SD₁₆	1	2	yes	—
37	C₈×C₁₉	#41	1	2	yes	—
38	#2242	—	19	1	no	maximal, Sylow
39	C₂²×C₁₉	—	8	1	no	—
40	C₂²×C₁₉	—	8	2	no	—
41	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₉	—	2	2	no	—
43	C₄×C₁₉	—	8	1	no	—
44	C₄×C₁₉	#124	1	1	yes	characteristic
45	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
46	Dic₁₉	—	8	2	no	—
47	#499	—	19	1	no	—
48	#495	D₁₉	1	1	yes	characteristic
49	#358	—	19	2	no	—
50	#357	—	19	2	no	—
51	C₄×C₁₆	—	19	1	no	—
52	C₂×C₁₉	—	16	1	no	—
53	C₂×C₁₉	#486	1	1	yes	characteristic
54	C₂×C₁₉	#508	1	2	yes	—
55	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic
56	C₂×SD₁₆	—	2	1	no	—
57	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
58	#125	—	38	1	no	—
59	#124	—	2	1	no	—
60	C₂×C₁₆	—	19	2	no	—
61	#107	—	19	2	no	—
62	#106	—	38	1	no	—
63	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
64	C₁₉	#2242	1	1	yes	characteristic, complemented, Sylow
65	C₂×Q₈	—	2	1	no	—
66	C₂×D₄	—	2	1	no	—
67	Q₁₆	—	2	2	no	—
68	SD₁₆	—	4	2	no	—
69	D₈	—	2	2	no	—
70	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
72	C₄⋊C₄	—	38	2	no	—
73	C₄⋊C₄	—	76	2	no	—
74	C₂²⋊C₄	—	4	2	no	—
75	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
76	C₁₆	—	38	2	no	—
77	C₂³	—	4	1	no	—
78	Q₈	—	4	1	no	—
79	Q₈	—	4	1	no	—
80	D₄	—	4	1	no	—
81	D₄	—	4	1	no	—
82	C₂×C₄	—	4	1	no	—
83	C₂×C₄	—	76	2	no	—
84	C₂×C₄	#64525	1	2	yes	—
85	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
86	C₈	#64526	1	2	yes	—
87	C₈	#64543	1	2	yes	—
88	C₂²	—	8	1	no	—
89	C₂²	—	8	2	no	—
90	C₂²	C₂×#64525	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	8	1	no	—
93	C₄	—	152	2	no	—
94	C₄	C₂×#64526	1	1	yes	characteristic
95	C₄	#10597382	1	1	yes	characteristic
96	C₂	—	16	1	no	—
97	C₂	#11926890	1	1	yes	characteristic
98	C₂	#11926974	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926946

C₂

yes

maximal, characteristic, complemented

#11926348

C₂

yes

maximal, complemented

#11926345

C₂

yes

maximal

C₄×C₁₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×#495

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

C₂²

yes

characteristic

C₁₉×#124

—

#10597316

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597275

C₂²

yes

—

#10597274

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

SD₁₆

yes

—

C₈×C₁₉

#41

yes

—

#2242

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

#499

—

#495

D₁₉

yes

characteristic

#358

—

#357

—

C₄×C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

#486

yes

characteristic

C₂×C₁₉

#508

yes

—

C₂×Q₁₆

C₂×D₁₉

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₁₉

yes

characteristic

#125

—

#124

—

C₂×C₁₆

—

#107

—

#106

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2242

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64525

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

#64526

yes

—

C₈

#64543

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#64525

yes

characteristic

C₄

—

C₄

—

C₄

—

152

—

C₄

yes

C₄

yes

C₂

—

C₂

#11926890

yes

characteristic

C₂

#11926974

yes

—

	subgroup	G/H
center	C₂²	C₂×#64525
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#495	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×D₈×C₁₉	C₂²
hypercenter	#495	D₁₉
hypocenter	C₁₉	#2242
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

C₂×#64525

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#495

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂×D₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. #11926946	C₂	semidirect
2. #11926348	C₂	semidirect
4. C₄×C₁₉⋊C₁₆	C₂	semidirect
64. C₁₉	#2242	semidirect

H ≅ G/N

type

1. #11926946

C₂

semidirect

2. #11926348

C₂

semidirect

4. C₄×C₁₉⋊C₁₆

C₂

semidirect

64. C₁₉

#2242

semidirect

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

subgroup	index
#11926946	2
#11926348	2
#11926345	2
C₄×C₁₉⋊C₁₆	2
C₁₉×#495	2
#2242	19

subgroup

index

#11926946

#11926348

#11926345

C₄×C₁₉⋊C₁₆

C₁₉×#495

#2242

Subgroups — #14565866

Conjugacy classes of subgroups

Complements

Maximal subgroups