Group #14565517 — subgroups

Subgroups — #14565517

Order 2432.

146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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	#11926976	C₂	1	1	yes	maximal, characteristic
2	#11926662	C₂	1	2	yes	maximal, complemented
3	#11926374	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926352	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597350	C₂²	1	2	yes	—
7	#10597347	—	2	2	no	—
8	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597276	C₂²	1	2	yes	—
12	#10597262	—	2	2	no	—
13	Dic₁₅₂	C₄	1	1	yes	characteristic, complemented
14	#10597257	C₄	1	2	yes	complemented
15	D₃₀₄	C₄	1	1	yes	characteristic, complemented
16	#64541	—	2	2	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	#64520	—	2	2	no	—
21	Dic₇₆	C₂×C₄	1	2	yes	—
22	D₁₅₂	C₂×C₄	1	2	yes	—
23	#64516	—	2	2	no	—
24	#64515	—	4	2	no	—
25	C₈×D₁₉	—	4	2	no	—
26	C₁₆×C₁₉	—	2	1	no	—
27	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₁₉	—	4	2	no	—
32	D₇₆	—	2	2	no	—
33	C₄×D₁₉	—	4	2	no	—
34	Dic₃₈	—	2	2	no	—
35	C₈×C₁₉	D₈	1	1	yes	characteristic
36	C₈×C₁₉	D₈	1	1	yes	characteristic
37	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₁₉	#41	1	1	yes	characteristic
39	C₁₉⋊C₈	—	4	2	no	—
40	#2178	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	#135	1	1	yes	characteristic
42	C₂×D₁₉	—	4	2	no	—
43	C₄×C₁₉	—	2	2	no	—
44	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
45	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
46	Dic₁₉	—	4	2	no	—
47	#508	—	19	1	no	—
48	#443	—	19	2	no	—
49	#368	—	19	1	no	—
50	#359	—	19	2	no	—
51	C₄×C₁₆	D₁₉	1	1	yes	characteristic, complemented
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	C₄×D₈	1	1	yes	characteristic
54	D₁₉	—	8	2	no	—
55	#135	—	19	2	no	—
56	#131	—	38	2	no	—
57	Q₃₂	—	19	1	no	—
58	SD₃₂	—	19	2	no	—
59	D₁₆	—	19	1	no	—
60	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
61	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
62	#108	—	19	2	no	—
63	#104	—	38	2	no	—
64	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
65	C₁₉	#2178	1	1	yes	characteristic, complemented, Sylow
66	#41	—	38	2	no	—
67	Q₁₆	—	19	2	no	—
68	SD₁₆	—	38	2	no	—
69	D₈	—	19	2	no	—
70	M₁₆	—	38	2	no	—
71	M₁₆	—	76	2	no	—
72	C₂×C₈	—	76	2	no	—
73	C₂×C₈	D₇₆	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
75	C₄²	D₇₆	1	1	yes	characteristic
76	C₁₆	—	2	1	no	—
77	C₁₆	C₄×D₁₉	1	1	yes	characteristic
78	C₁₆	C₄×D₁₉	1	1	yes	characteristic
79	Q₈	—	38	2	no	—
80	D₄	—	38	2	no	—
81	D₄	—	76	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	76	2	no	—
84	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
85	C₈	—	76	2	no	—
86	C₈	D₁₅₂	1	1	yes	characteristic
87	C₈	D₁₅₂	1	1	yes	characteristic
88	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
89	C₈	#64541	1	1	yes	characteristic
90	C₂²	—	76	2	no	—
91	C₂²	#10597350	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	76	2	no	—
94	C₄	C₄×D₇₆	1	1	yes	characteristic
95	C₄	C₂×D₁₅₂	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	152	2	no	—
98	C₂	C₄×D₁₅₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926976

C₂

yes

maximal, characteristic

#11926662

C₂

yes

maximal, complemented

#11926374

C₂

yes

maximal, characteristic, complemented

#11926352

C₂

yes

maximal, complemented

C₄×C₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

#10597350

C₂²

yes

—

#10597347

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597276

C₂²

yes

—

#10597262

—

Dic₁₅₂

C₄

yes

characteristic, complemented

#10597257

C₄

yes

complemented

D₃₀₄

C₄

yes

characteristic, complemented

#64541

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

#64520

—

Dic₇₆

C₂×C₄

yes

—

D₁₅₂

C₂×C₄

yes

—

#64516

—

#64515

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

#41

yes

characteristic

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

Dic₁₉

—

—

—

—

—

C₄×C₁₆

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

C₄×D₈

yes

characteristic

D₁₉

—

#135

—

#131

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₆

C₂×D₁₉

yes

characteristic

#108

—

#104

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2178

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

D₇₆

yes

characteristic

C₁₆

—

C₁₆

C₄×D₁₉

yes

characteristic

C₁₆

C₄×D₁₉

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₈

—

C₈

D₁₅₂

yes

characteristic

C₈

D₁₅₂

yes

characteristic

C₈

C₂×C₄×D₁₉

yes

characteristic

C₈

#64541

yes

characteristic

C₂²

—

C₂²

#10597350

yes

characteristic

C₄

—

C₄

—

C₄

C₄×D₇₆

yes

characteristic

C₄

C₂×D₁₅₂

yes

characteristic

C₂

—

C₂

—

152

—

C₂

C₄×D₁₅₂

yes

characteristic

	subgroup	G/H
center	C₈	D₁₅₂
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×C₁₆×C₁₉	C₂
socle	C₂×C₁₉	C₄×D₈
prime radical	#11926976	C₂
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₄×C₁₆	D₁₉
hypocenter	C₁₉	#2178
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₈

D₁₅₂

commutator

C₈×C₁₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₄×C₁₆×C₁₉

C₂

socle

C₂×C₁₉

C₄×D₈

prime radical

#11926976

C₂

cosocle

C₂×C₈×C₁₉

C₂³

hypercenter

C₄×C₁₆

D₁₉

hypocenter

C₁₉

#2178

LCS

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. #11926662	C₂	semidirect
3. #11926374	C₂	semidirect
4. #11926352	C₂	semidirect
5. C₄×C₁₆×C₁₉	C₂	semidirect
13. Dic₁₅₂	C₄	semidirect
14. #10597257	C₄	semidirect
15. D₃₀₄	C₄	semidirect
51. C₄×C₁₆	D₁₉	semidirect
65. C₁₉	#2178	semidirect

H ≅ G/N

type

2. #11926662

C₂

semidirect

3. #11926374

C₂

semidirect

4. #11926352

C₂

semidirect

5. C₄×C₁₆×C₁₉

C₂

semidirect

13. Dic₁₅₂

C₄

semidirect

14. #10597257

C₄

semidirect

15. D₃₀₄

C₄

semidirect

51. C₄×C₁₆

D₁₉

semidirect

65. C₁₉

#2178

semidirect

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

subgroup	index
#11926976	2
#11926662	2
#11926374	2
#11926352	2
C₄×C₁₆×C₁₉	2
#2178	19

subgroup

index

C₄×C₁₆×C₁₉

Subgroups — #14565517

Conjugacy classes of subgroups

Complements

Maximal subgroups