Group #14563153 — subgroups

Subgroups — #14563153

Order 2432.

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

normal subgroups only

This group has 152 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	#11926949	C₂	1	1	yes	maximal, characteristic
2	#11926754	C₂	1	2	yes	maximal
3	#11926295	C₂	1	1	yes	maximal, characteristic
4	#11926289	C₂	1	2	yes	maximal
5	C₁₉×#446	C₂	1	1	yes	maximal, characteristic
6	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×#64528	—	2	2	no	—
8	#10597315	C₂²	1	2	yes	—
9	C₁₉×C₄⋊C₈	—	2	1	no	—
10	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₉×#97	—	2	1	no	—
12	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	#10597275	—	2	1	no	—
14	#10597275	—	2	1	no	—
15	#10597267	—	2	2	no	—
16	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
18	C₂×Dic₃₈	—	2	2	no	—
19	C₂×C₈×C₁₉	—	2	1	no	—
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	—	2	1	no	—
23	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
24	C₄²×C₁₉	—	2	1	no	—
25	C₄²×C₁₉	C₂³	1	1	yes	characteristic
26	#64528	—	4	4	no	—
27	C₄⋊Dic₁₉	—	2	2	no	—
28	C₄⋊Dic₁₉	—	2	2	no	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	Q₈×C₁₉	—	2	2	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
36	C₂×Dic₁₉	—	4	2	no	—
37	Dic₃₈	—	4	2	no	—
38	Dic₃₈	—	4	2	no	—
39	C₈×C₁₉	—	2	1	no	—
40	C₈×C₁₉	—	4	1	no	—
41	C₈×C₁₉	Q₁₆	1	2	yes	complemented
42	C₁₉⋊C₈	—	4	2	no	—
43	#1694	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	#121	1	1	yes	characteristic
45	C₄×C₁₉	—	2	1	no	—
46	C₄×C₁₉	—	4	1	no	—
47	C₄×C₁₉	—	4	1	no	—
48	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
49	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
50	C₄×C₁₉	#137	1	1	yes	characteristic
51	Dic₁₉	—	8	2	no	—
52	#500	—	19	1	no	—
53	#462	—	19	2	no	—
54	#446	D₁₉	1	1	yes	characteristic
55	#334	—	19	1	no	—
56	#332	—	19	2	no	—
57	C₂×C₁₉	#462	1	1	yes	characteristic
58	C₂×C₁₉	#469	1	1	yes	characteristic
59	C₂×C₁₉	#473	1	1	yes	characteristic
60	C₂×Q₁₆	—	38	2	no	—
61	C₄⋊Q₈	—	19	2	no	—
62	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
63	#107	—	38	1	no	—
64	#107	—	38	1	no	—
65	C₄⋊C₈	—	2	1	no	—
66	C₄⋊C₈	—	19	2	no	—
67	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
68	#103	—	38	2	no	—
69	#97	—	2	1	no	—
70	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
71	C₁₉	#1694	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₈	—	38	2	no	—
73	C₂×Q₈	D₇₆	1	1	yes	characteristic
74	Q₁₆	—	76	4	no	—
75	C₂×C₈	—	2	1	no	—
76	C₂×C₈	—	38	2	no	—
77	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
79	C₄⋊C₄	—	2	1	no	—
80	C₄⋊C₄	—	38	2	no	—
81	C₄⋊C₄	—	38	2	no	—
82	C₄⋊C₄	D₇₆	1	1	yes	characteristic
83	C₄²	—	2	1	no	—
84	C₄²	C₂²×D₁₉	1	1	yes	characteristic
85	Q₈	—	2	2	no	—
86	Q₈	—	76	2	no	—
87	Q₈	—	76	2	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	76	2	no	—
91	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
92	C₂×C₄	#64541	1	1	yes	characteristic
93	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	4	1	no	—
96	C₈	—	76	2	no	—
97	C₈	#64528	1	2	yes	complemented
98	C₂²	#10597376	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	4	1	no	—
101	C₄	—	4	1	no	—
102	C₄	—	152	2	no	—
103	C₄	#10597354	1	2	yes	—
104	C₄	C₂×#64528	1	1	yes	characteristic
105	C₄	#10597397	1	1	yes	characteristic
106	C₂	#11926754	1	1	yes	characteristic
107	C₂	#11926797	1	1	yes	characteristic
108	C₂	#11926819	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926949

C₂

yes

maximal, characteristic

#11926754

C₂

yes

maximal

#11926295

C₂

yes

maximal, characteristic

#11926289

C₂

yes

maximal

C₁₉×#446

C₂

yes

maximal, characteristic

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₂×#64528

—

#10597315

C₂²

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×#97

—

C₄×C₈×C₁₉

C₂²

yes

—

—

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

Q₁₆

yes

complemented

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

#137

yes

characteristic

Dic₁₉

—

#500

—

#462

—

#446

D₁₉

yes

characteristic

#334

—

#332

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₁₉

yes

characteristic

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

characteristic

#103

—

#97

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1694

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

D₇₆

yes

characteristic

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₇₆

yes

characteristic

C₄²

—

C₄²

C₂²×D₁₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

#64541

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

yes

C₂²

yes

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

152

—

103

C₄

#10597354

yes

—

104

C₄

C₂×#64528

yes

characteristic

105

C₄

#10597397

yes

characteristic

106

C₂

#11926754

yes

characteristic

107

C₂

#11926797

yes

characteristic

108

C₂

#11926819

yes

characteristic

	subgroup	G/H
center	C₂²	#10597376
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#446	C₂
socle, prime radical	C₂²×C₁₉	#121
hypercenter	#446	D₁₉
hypocenter	C₁₉	#1694
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#10597376

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#446

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
41. C₈×C₁₉	Q₁₆	semidirect
71. C₁₉	#1694	semidirect
97. C₈	#64528	semidirect

H ≅ G/N

type

41. C₈×C₁₉

Q₁₆

semidirect

71. C₁₉

#1694

semidirect

97. C₈

#64528

semidirect

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

subgroup	index
#11926949	2
#11926754	2
#11926295	2
#11926289	2
C₁₉×#446	2
#1694	19

subgroup

index

C₁₉×#446

Subgroups — #14563153

Conjugacy classes of subgroups

Complements

Maximal subgroups