Group #14561545 — subgroups

Subgroups — #14561545

Order 2432.

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

normal subgroups only

This group has 130 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	#11926601	C₂	1	1	yes	maximal, characteristic
2	#11926568	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#432	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×#64520	C₄	1	2	yes	—
6	C₁₉×C₄⋊C₈	—	2	1	no	—
7	C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
8	C₁₉×#97	—	2	1	no	—
9	C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
10	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
12	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
13	#10597260	—	2	1	no	—
14	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₉	—	2	2	no	—
18	C₄²×C₁₉	D₄	1	1	yes	characteristic
19	C₄²×C₁₉	D₄	1	1	yes	characteristic
20	C₄²×C₁₉	D₄	1	1	yes	characteristic
21	C₄²×C₁₉	Q₈	1	1	yes	characteristic
22	#64520	—	4	2	no	—
23	C₂×C₁₉⋊C₈	—	2	2	no	—
24	C₂×C₁₉⋊C₈	—	2	2	no	—
25	C₂³×C₁₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₁₉	—	2	1	no	—
27	C₂×C₄×C₁₉	—	2	1	no	—
28	C₂×C₄×C₁₉	—	4	1	no	—
29	C₂×C₄×C₁₉	—	4	1	no	—
30	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₈×C₁₉	—	4	2	no	—
37	C₁₉⋊C₈	—	4	2	no	—
38	C₁₉⋊C₈	—	4	2	no	—
39	#1307	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	—	2	1	no	—
41	C₂²×C₁₉	—	2	1	no	—
42	C₂²×C₁₉	—	2	1	no	—
43	C₂²×C₁₉	#95	1	1	yes	characteristic
44	C₄×C₁₉	—	2	1	no	—
45	C₄×C₁₉	—	2	1	no	—
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	2	1	no	—
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	#100	1	1	yes	characteristic
50	C₄×C₁₉	#101	1	1	yes	characteristic
51	#432	—	19	1	no	—
52	#432	D₁₉	1	1	yes	characteristic
53	#423	—	19	1	no	—
54	C₂×C₁₉	—	4	1	no	—
55	C₂×C₁₉	#343	1	1	yes	characteristic
56	C₂×C₁₉	#344	1	1	yes	characteristic
57	C₂×C₁₉	#344	1	1	yes	characteristic
58	C₂×M₁₆	—	19	2	no	—
59	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
60	C₄⋊C₈	—	2	1	no	—
61	C₄⋊C₈	—	38	1	no	—
62	C₄⋊C₈	—	38	1	no	—
63	C₄⋊C₈	—	38	1	no	—
64	C₂²⋊C₈	—	19	2	no	—
65	C₂²⋊C₈	Dic₁₉	1	2	yes	—
66	#97	—	2	1	no	—
67	#97	—	38	1	no	—
68	C₁₉	#1307	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
70	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
71	C₂²×C₄	C₂×Dic₁₉	1	1	yes	characteristic
72	M₁₆	—	76	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	38	2	no	—
75	C₂×C₈	—	38	2	no	—
76	C₄²	Dic₃₈	1	1	yes	characteristic
77	C₄²	D₇₆	1	1	yes	characteristic
78	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
79	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
80	C₂³	C₄×Dic₁₉	1	1	yes	characteristic
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	4	1	no	—
84	C₂×C₄	—	4	1	no	—
85	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
86	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
87	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
88	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
89	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
90	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	76	2	no	—
93	C₈	—	76	2	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	2	1	no	—
96	C₂²	—	2	1	no	—
97	C₂²	C₁₉⋊#95	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	2	1	no	—
101	C₄	—	2	1	no	—
102	C₄	—	2	1	no	—
103	C₄	#10597280	1	1	yes	characteristic
104	C₄	#10597281	1	1	yes	characteristic
105	C₂	—	4	1	no	—
106	C₂	#11926312	1	1	yes	characteristic
107	C₂	#11926314	1	1	yes	characteristic
108	C₂	#11926315	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926601

C₂

yes

maximal, characteristic

#11926568

C₂

yes

maximal, characteristic

C₁₉×#432

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

C₄

yes

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

Q₈

yes

characteristic

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₄²

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1307

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#95

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

—

D₁₉

yes

characteristic

#423

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₁₉

yes

—

#97

—

#97

—

C₁₉

#1307

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₂×Dic₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

Dic₃₈

yes

characteristic

C₄²

D₇₆

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

characteristic

C₂³

C₄×Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₁₉⋊#95

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

#10597280

yes

characteristic

104

C₄

#10597281

yes

characteristic

105

C₂

—

106

C₂

#11926312

yes

characteristic

107

C₂

#11926314

yes

characteristic

108

C₂

#11926315

yes

characteristic

	subgroup	G/H
center	C₂²	C₁₉⋊#95
commutator, prime radical	C₂³×C₁₉	C₄²
Frattini	C₂×C₄²	C₂×D₁₉
Fitting	C₁₉×#432	C₂
socle	C₂²×C₁₉	#95
cosocle	C₂×C₄²×C₁₉	C₂²
hypercenter	#432	D₁₉
hypocenter	C₁₉	#1307
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

subgroup

G/H

center

C₂²

C₁₉⋊#95

commutator, prime radical

C₂³×C₁₉

C₄²

Frattini

C₂×C₄²

C₂×D₁₉

Fitting

C₁₉×#432

C₂

socle

C₂²×C₁₉

#95

cosocle

C₂×C₄²×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #432

N	H ≅ G/N	type
68. C₁₉	#1307	semidirect

H ≅ G/N

type

68. C₁₉

#1307

semidirect

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

subgroup	index
#11926601	2
#11926568	2
C₁₉×#432	2
#1307	19

subgroup

index

#11926601

#11926568

C₁₉×#432

#1307

Subgroups — #14561545

Conjugacy classes of subgroups

Complements

Maximal subgroups