Group #14561534 — subgroups

Subgroups — #14561534

Order 2432.

144 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 61 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	#11926597	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#97	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₉	—	2	1	no	—
5	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×#97	—	2	1	no	—
7	C₁₉×#97	C₄	1	2	yes	—
8	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
9	C₂²⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
10	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
11	C₄⋊(C₁₉⋊C₈)	C₄	1	2	yes	—
12	#10597260	—	2	1	no	—
13	C₄×C₁₉⋊C₈	—	2	1	no	—
14	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₁₉	—	2	4	no	—
18	C₂×C₈×C₁₉	—	2	2	no	—
19	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₁₉	D₄	1	1	yes	characteristic
22	C₄²×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₁₉⋊C₈	—	2	2	no	—
24	C₂×C₁₉⋊C₈	—	2	2	no	—
25	C₂³×C₁₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₉	—	2	2	no	—
27	C₂×C₄×C₁₉	—	2	2	no	—
28	C₂×C₄×C₁₉	—	4	1	no	—
29	C₂×C₄×C₁₉	C₄²	1	1	yes	characteristic
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	C₈×C₁₉	—	2	4	no	—
36	C₁₉⋊C₈	—	4	2	no	—
37	C₁₉⋊C₈	—	4	2	no	—
38	#1302	—	19	1	no	maximal, Sylow
39	C₂²×C₁₉	—	2	1	no	—
40	C₂²×C₁₉	—	2	1	no	—
41	C₂²×C₁₉	#95	1	1	yes	characteristic
42	C₂²×C₁₉	#108	1	2	yes	—
43	C₄×C₁₉	—	2	1	no	—
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	#104	1	2	yes	—
49	#432	—	19	1	no	—
50	#431	—	19	1	no	—
51	C₂×#97	D₁₉	1	1	yes	characteristic
52	C₂×C₁₉	—	2	2	no	—
53	C₂×C₁₉	#339	1	1	yes	characteristic
54	C₂×C₁₉	#341	1	1	yes	characteristic
55	C₂×C₁₉	#344	1	1	yes	characteristic
56	C₂²×C₈	—	2	1	no	—
57	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
58	C₄⋊C₈	—	19	2	no	—
59	C₄⋊C₈	—	38	1	no	—
60	C₂²⋊C₈	—	19	2	no	—
61	C₂²⋊C₈	—	38	1	no	—
62	#97	—	2	1	no	—
63	#97	—	38	1	no	—
64	#97	Dic₁₉	1	2	yes	—
65	C₄×C₈	—	38	1	no	—
66	C₁₉	#1302	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	Dic₃₈	1	1	yes	characteristic
68	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
69	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
70	C₂×C₈	—	2	4	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	38	2	no	—
73	C₂×C₈	—	38	2	no	—
74	C₄²	C₄×D₁₉	1	1	yes	characteristic
75	C₄²	D₇₆	1	1	yes	characteristic
76	C₄²	C₂×Dic₁₉	1	1	yes	characteristic
77	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
78	C₂³	Dic₁₉⋊C₄	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	C₄×Dic₁₉	1	1	yes	characteristic
83	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
84	C₂×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
85	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
86	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
87	C₂×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
88	C₈	—	2	4	no	—
89	C₈	—	76	2	no	—
90	C₈	—	76	2	no	—
91	C₂²	—	2	1	no	—
92	C₂²	—	2	1	no	—
93	C₂²	#10597279	1	2	yes	—
94	C₂²	C₁₉⋊#95	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	2	1	no	—
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	#10597262	1	2	yes	—
101	C₂	—	2	2	no	—
102	C₂	#11926304	1	1	yes	characteristic
103	C₂	#11926308	1	1	yes	characteristic
104	C₂	#11926316	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926601

C₂

yes

maximal, characteristic

#11926597

C₂

yes

maximal, characteristic

C₂×C₁₉×#97

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#97

—

C₁₉×#97

C₄

yes

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

C₄

yes

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

C₄

yes

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

Q₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄²

yes

characteristic

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

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1302

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#95

yes

characteristic

C₂²×C₁₉

#108

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#104

yes

—

#432

—

#431

—

C₂×#97

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

#97

Dic₁₉

yes

—

C₄×C₈

—

C₁₉

#1302

yes

characteristic, complemented, Sylow

C₂²×C₄

Dic₃₈

yes

characteristic

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

C₄×D₁₉

yes

characteristic

C₄²

D₇₆

yes

characteristic

C₄²

C₂×Dic₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

characteristic

C₂³

Dic₁₉⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₁₉

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

#10597279

yes

—

C₂²

C₁₉⋊#95

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

100

C₄

#10597262

yes

—

101

C₂

—

102

C₂

#11926304

yes

characteristic

103

C₂

#11926308

yes

characteristic

104

C₂

#11926316

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₁₉)⋊C₄
commutator	C₂×C₄×C₁₉	C₄²
Frattini	C₂×C₄²	C₂×D₁₉
Fitting	C₂×C₁₉×#97	C₂
socle	C₂²×C₁₉	#95
prime radical	C₂³×C₁₉	C₄⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂²
hypercenter	C₂×#97	D₁₉
hypocenter	C₁₉	#1302
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂×C₄

(C₂×D₁₉)⋊C₄

commutator

C₂×C₄×C₁₉

C₄²

Frattini

C₂×C₄²

C₂×D₁₉

Fitting

C₂×C₁₉×#97

C₂

socle

C₂²×C₁₉

#95

prime radical

C₂³×C₁₉

C₄⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂²

hypercenter

C₂×#97

D₁₉

hypocenter

C₁₉

#1302

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
66. C₁₉	#1302	semidirect

H ≅ G/N

type

66. C₁₉

#1302

semidirect

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

subgroup	index
#11926601	2
#11926597	2
C₂×C₁₉×#97	2
#1302	19

subgroup

index

#11926601

#11926597

C₂×C₁₉×#97

#1302

Subgroups — #14561534

Conjugacy classes of subgroups

Complements

Maximal subgroups