Group #14565442 — subgroups

Subgroups — #14565442

Order 2432.

138 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₄⋊(C₁₉⋊C₁₆)	C₂	1	2	yes	maximal, complemented
2	C₂²⋊(C₁₉⋊C₁₆)	C₂	1	2	yes	maximal
3	#11926320	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₁₉	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#117	C₄	1	1	yes	characteristic
9	C₁₉×#97	C₄	1	1	yes	characteristic
10	C₁₉×#97	C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
14	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
15	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	M₁₆×C₁₉	—	2	2	no	—
17	C₂×C₈×C₁₉	—	2	2	no	—
18	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	C₈	1	2	yes	—
23	C₂²⋊C₄×C₁₉	C₈	1	2	yes	—
24	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₁₉⋊C₁₆	—	2	2	no	—
27	C₁₉⋊C₁₆	—	2	2	no	—
28	C₂³×C₁₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₉	—	2	1	no	—
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₁₉	—	2	1	no	—
36	C₈×C₁₉	—	2	1	no	—
37	C₈×C₁₉	M₁₆	1	2	yes	—
38	C₈×C₁₉	#41	1	2	yes	—
39	#2164	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	—	2	1	no	—
41	C₂²×C₁₉	—	2	2	no	—
42	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
43	C₄×C₁₉	—	2	1	no	—
44	C₄×C₁₉	—	2	2	no	—
45	C₄×C₁₉	—	2	2	no	—
46	C₄×C₁₉	#117	1	1	yes	characteristic
47	C₄×C₁₉	C₂×M₁₆	1	1	yes	characteristic
48	#405	D₁₉	1	1	yes	characteristic
49	C₄⋊C₁₆	—	19	2	no	—
50	C₂²⋊C₁₆	—	19	2	no	—
51	#346	—	19	1	no	—
52	C₄×C₁₆	—	19	1	no	—
53	C₂×C₁₉	—	4	1	no	—
54	C₂×C₁₉	#431	1	1	yes	characteristic
55	C₂×C₁₉	#504	1	2	yes	—
56	C₂×M₁₆	Dic₁₉	1	1	yes	characteristic
57	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
58	#117	Dic₁₉	1	1	yes	characteristic
59	C₂×C₁₆	—	19	2	no	—
60	C₂×C₁₆	—	19	2	no	—
61	#97	Dic₁₉	1	1	yes	characteristic
62	#97	Dic₁₉	1	1	yes	characteristic
63	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
64	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
65	C₁₉	#2164	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
70	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
71	C₂×C₈	C₂×Dic₁₉	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
73	C₄⋊C₄	C₁₉⋊C₈	1	2	yes	—
74	C₂²⋊C₄	C₁₉⋊C₈	1	2	yes	—
75	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
76	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
77	C₁₆	—	38	2	no	—
78	C₁₆	—	38	2	no	—
79	C₂³	C₂×C₁₉⋊C₈	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
83	C₂×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
84	C₂×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
85	C₂×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	2	1	no	—
88	C₈	#64520	1	2	yes	—
89	C₈	#64541	1	2	yes	—
90	C₂²	—	2	1	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	2	2	no	—
96	C₄	C₂×#64520	1	1	yes	characteristic
97	C₄	#10597372	1	1	yes	characteristic
98	C₂	—	4	1	no	—
99	C₂	#11926597	1	1	yes	characteristic
100	C₂	#11926961	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, complemented

C₂²⋊(C₁₉⋊C₁₆)

C₂

yes

maximal

#11926320

C₂

yes

maximal, characteristic, complemented

C₄×C₁₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×#405

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₄

yes

characteristic

C₁₉×#97

C₄

yes

characteristic

C₁₉×#97

C₄

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

C₈

yes

—

C₂²⋊C₄×C₁₉

C₈

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉⋊C₁₆

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

M₁₆

yes

—

C₈×C₁₉

#41

yes

—

#2164

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₂×M₁₆

yes

characteristic

#405

D₁₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

#431

yes

characteristic

C₂×C₁₉

#504

yes

—

C₂×M₁₆

Dic₁₉

yes

characteristic

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

Dic₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

#97

Dic₁₉

yes

characteristic

#97

Dic₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

characteristic

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#2164

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂×Dic₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

C₁₉⋊C₈

yes

—

C₂²⋊C₄

C₁₉⋊C₈

yes

—

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂×Dic₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

C₂×C₁₉⋊C₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₁₉⋊C₈

yes

—

C₂×C₄

C₂×C₁₉⋊C₈

yes

—

C₂×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂×C₄

C₂²×Dic₁₉

yes

characteristic

C₈

—

C₈

—

C₈

#64520

yes

—

C₈

#64541

yes

—

C₂²

—

C₂²

—

C₂²

C₂²×C₁₉⋊C₈

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

#11926597

yes

characteristic

100

C₂

#11926961

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₉
commutator, socle	C₂²×C₁₉	C₂²×C₈
Fitting	C₁₉×#405	C₂
prime radical	C₂³×C₁₉	C₂×C₈
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	#405	D₁₉
hypocenter	C₁₉	#2164
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₈ ◁ #405

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₉

commutator, socle

C₂²×C₁₉

C₂²×C₈

Fitting

C₁₉×#405

C₂

prime radical

C₂³×C₁₉

C₂×C₈

cosocle

C₂×C₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂×C₈ ◁ #405

N	H ≅ G/N	type
1. C₄⋊(C₁₉⋊C₁₆)	C₂	semidirect
3. #11926320	C₂	semidirect
4. C₄×C₁₉⋊C₁₆	C₂	semidirect
65. C₁₉	#2164	semidirect

H ≅ G/N

type

1. C₄⋊(C₁₉⋊C₁₆)

C₂

semidirect

3. #11926320

C₂

semidirect

4. C₄×C₁₉⋊C₁₆

C₂

semidirect

65. C₁₉

#2164

semidirect

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

subgroup	index
C₄⋊(C₁₉⋊C₁₆)	2
C₂²⋊(C₁₉⋊C₁₆)	2
#11926320	2
C₄×C₁₉⋊C₁₆	2
C₁₉×#405	2
#2164	19

subgroup

index

C₄⋊(C₁₉⋊C₁₆)

C₂²⋊(C₁₉⋊C₁₆)

#11926320

C₄×C₁₉⋊C₁₆

C₁₉×#405

#2164

Subgroups — #14565442

Conjugacy classes of subgroups

Complements

Maximal subgroups