Group #14565867 — subgroups

Subgroups — #14565867

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	#11926928	C₂	1	1	yes	maximal, characteristic
3	#11926349	C₂	1	2	yes	maximal, complemented
4	#11926346	C₂	1	2	yes	maximal
5	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₇₆	C₂²	1	1	yes	characteristic
7	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
8	C₂×#64516	—	2	1	no	—
9	#10597321	—	2	1	no	—
10	#10597316	—	2	1	no	—
11	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
12	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	#10597275	C₂²	1	2	yes	—
14	#10597274	—	2	1	no	—
15	C₂×D₇₆	—	2	1	no	—
16	C₂×Dic₃₈	—	2	1	no	—
17	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
19	C₄²×C₁₉	D₄	1	1	yes	characteristic
20	(C₂×D₁₉)⋊C₄	—	4	2	no	—
21	C₄⋊Dic₁₉	—	2	2	no	—
22	Dic₁₉⋊C₄	—	4	2	no	—
23	Dic₇₆	—	2	2	no	—
24	D₁₅₂	—	2	2	no	—
25	#64516	—	4	2	no	—
26	C₁₆×C₁₉	—	2	2	no	—
27	C₂²×D₁₉	—	4	1	no	—
28	C₂×C₄×C₁₉	D₈	1	2	yes	—
29	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₁₉	—	4	2	no	—
31	C₂×Dic₁₉	—	4	1	no	—
32	D₇₆	—	4	1	no	—
33	D₇₆	—	4	1	no	—
34	Dic₃₈	—	4	1	no	—
35	Dic₃₈	—	4	1	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	C₂×D₈	1	1	yes	characteristic
40	C₂×D₁₉	—	8	1	no	—
41	C₂×D₁₉	—	8	2	no	—
42	C₄×C₁₉	—	2	2	no	—
43	C₄×C₁₉	#124	1	1	yes	characteristic
44	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
45	Dic₁₉	—	8	1	no	—
46	Dic₁₉	—	8	2	no	—
47	#499	—	19	1	no	—
48	#495	—	19	1	no	—
49	#358	—	19	2	no	—
50	#357	—	19	2	no	—
51	C₄×C₁₆	D₁₉	1	1	yes	characteristic, complemented
52	C₂×C₁₉	#486	1	1	yes	characteristic
53	C₂×C₁₉	#508	1	2	yes	—
54	D₁₉	—	16	1	no	—
55	C₂×Q₁₆	—	19	1	no	—
56	C₂×SD₁₆	—	38	1	no	—
57	C₂×D₈	—	19	1	no	—
58	#125	—	38	1	no	—
59	#124	—	38	1	no	—
60	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
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	—	38	1	no	—
66	C₂×D₄	—	38	1	no	—
67	Q₁₆	—	38	2	no	—
68	SD₁₆	—	76	2	no	—
69	D₈	—	38	2	no	—
70	C₂×C₈	D₇₆	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	—	76	2	no	—
75	C₄²	D₇₆	1	1	yes	characteristic
76	C₁₆	—	2	2	no	—
77	C₂³	—	76	1	no	—
78	Q₈	—	76	1	no	—
79	Q₈	—	76	1	no	—
80	D₄	—	76	1	no	—
81	D₄	—	76	1	no	—
82	C₂×C₄	—	76	1	no	—
83	C₂×C₄	—	76	2	no	—
84	C₂×C₄	D₁₅₂	1	2	yes	—
85	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
86	C₈	#64516	1	2	yes	—
87	C₈	#64541	1	2	yes	—
88	C₂²	—	152	1	no	—
89	C₂²	—	152	2	no	—
90	C₂²	C₂×D₁₅₂	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	152	1	no	—
93	C₄	—	152	2	no	—
94	C₄	#10597321	1	1	yes	characteristic
95	C₄	C₂×#64516	1	1	yes	characteristic
96	C₂	—	304	1	no	—
97	C₂	#11926891	1	1	yes	characteristic
98	C₂	#11926976	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926946

C₂

yes

maximal, characteristic, complemented

#11926928

C₂

yes

maximal, characteristic

#11926349

C₂

yes

maximal, complemented

#11926346

C₂

yes

maximal

C₄×C₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₇₆

C₂²

yes

characteristic

C₂×D₁₅₂

C₂²

yes

—

—

—

C₂×C₁₆×C₁₉

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597275

C₂²

yes

—

#10597274

—

C₂×D₇₆

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₇₆

—

D₁₅₂

—

#64516

—

C₁₆×C₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

SD₁₆

yes

—

C₈×C₁₉

#41

yes

—

#2242

—

maximal, Sylow

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

Dic₁₉

—

—

—

—

—

C₄×C₁₆

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#486

yes

characteristic

C₂×C₁₉

#508

yes

—

D₁₉

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#125

—

#124

—

C₂×C₁₆

C₂×D₁₉

yes

—

#107

—

#106

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2242

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

D₇₆

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₅₂

yes

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₈

#64516

yes

—

C₈

#64541

yes

—

C₂²

—

152

—

C₂²

—

152

—

C₂²

C₂×D₁₅₂

yes

characteristic

C₄

—

C₄

—

152

—

C₄

—

152

—

C₄

yes

C₄

yes

C₂

—

304

—

C₂

#11926891

yes

characteristic

C₂

#11926976

yes

—

	subgroup	G/H
center	C₂²	C₂×D₁₅₂
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×C₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂×D₈
prime radical	C₂×D₁₅₂	C₂²
hypercenter	C₄×C₁₆	D₁₉
hypocenter	C₁₉	#2242
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×D₁₅₂

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₄×C₁₆×C₁₉

C₂

socle

C₂²×C₁₉

C₂×D₈

prime radical

C₂×D₁₅₂

C₂²

hypercenter

C₄×C₁₆

D₁₉

hypocenter

C₁₉

#2242

LCS

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. #11926946	C₂	semidirect
3. #11926349	C₂	semidirect
5. C₄×C₁₆×C₁₉	C₂	semidirect
51. C₄×C₁₆	D₁₉	semidirect
64. C₁₉	#2242	semidirect

H ≅ G/N

type

1. #11926946

C₂

semidirect

3. #11926349

C₂

semidirect

5. C₄×C₁₆×C₁₉

C₂

semidirect

51. C₄×C₁₆

D₁₉

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
#11926928	2
#11926349	2
#11926346	2
C₄×C₁₆×C₁₉	2
#2242	19

subgroup

index

C₄×C₁₆×C₁₉

Subgroups — #14565867

Conjugacy classes of subgroups

Complements

Maximal subgroups