Group #14564629 — subgroups

Subgroups — #14564629

Order 2432.

228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 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	#11926568	C₂	1	1	yes	maximal, characteristic
2	C₄×#64520	C₂	1	1	yes	maximal, characteristic
3	#11926313	C₂	1	4	yes	maximal
4	C₂×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#125	—	2	1	no	—
6	C₁₉×#125	—	2	1	no	—
7	C₁₉×#125	—	2	2	no	—
8	C₂×C₄⋊C₄×C₁₉	C₄	1	4	yes	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×#64520	C₂²	1	2	yes	—
12	C₂×#64520	C₂²	1	2	yes	—
13	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
14	#10597260	—	2	1	no	—
15	C₄×C₁₉⋊C₈	—	2	1	no	—
16	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₁₉	—	2	4	no	—
20	C₄⋊C₄×C₁₉	—	2	4	no	—
21	C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₄²×C₁₉	D₄	1	1	yes	characteristic
24	C₄²×C₁₉	D₄	1	1	yes	characteristic
25	C₄²×C₁₉	D₄	1	2	yes	—
26	#64520	—	2	2	no	—
27	#64520	—	2	4	no	—
28	#64520	Q₈	1	4	yes	—
29	C₂×C₁₉⋊C₈	—	2	2	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	—	2	4	no	—
33	C₂×C₄×C₁₉	—	4	2	no	—
34	C₂×C₄×C₁₉	—	4	4	no	—
35	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
36	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
40	C₂×C₄×C₁₉	#41	1	2	yes	—
41	C₁₉⋊C₈	—	2	4	no	—
42	C₁₉⋊C₈	—	4	2	no	—
43	#1998	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	—	2	2	no	—
45	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₁₉	C₄×Q₈	1	2	yes	—
47	C₄×C₁₉	—	2	2	no	—
48	C₄×C₁₉	—	2	2	no	—
49	C₄×C₁₉	—	4	4	no	—
50	C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
51	C₄×C₁₉	#124	1	1	yes	characteristic
52	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
53	C₂×#125	D₁₉	1	1	yes	characteristic
54	#423	—	19	1	no	—
55	C₄×M₁₆	—	19	1	no	—
56	#343	—	19	4	no	—
57	C₂×C₁₉	—	2	2	no	—
58	C₂×C₁₉	#391	1	1	yes	characteristic
59	C₂×C₁₉	#413	1	2	yes	—
60	C₂×M₁₆	—	19	2	no	—
61	C₂×M₁₆	—	19	2	no	—
62	#125	—	2	1	no	—
63	#125	—	2	1	no	—
64	#125	—	2	2	no	—
65	C₂×C₄⋊C₄	Dic₁₉	1	4	yes	—
66	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
67	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
68	C₄⋊C₈	—	38	2	no	—
69	#97	—	38	1	no	—
70	C₄×C₈	—	38	1	no	—
71	C₁₉	#1998	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	C₂×Dic₁₉	1	4	yes	—
73	C₂²×C₄	C₂×Dic₁₉	1	2	yes	—
74	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
75	M₁₆	—	19	4	no	—
76	M₁₆	—	38	2	no	—
77	M₁₆	—	38	4	no	—
78	C₂×C₈	—	38	2	no	—
79	C₂×C₈	—	38	2	no	—
80	C₄⋊C₄	—	2	4	no	—
81	C₄⋊C₄	—	2	4	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	2	2	no	—
84	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
85	C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
86	C₄²	C₂²⋊D₁₉	1	2	yes	—
87	C₂³	C₂²×Dic₁₉	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	4	no	—
91	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
92	C₂×C₄	C₂²⋊Dic₁₉	1	2	yes	—
93	C₂×C₄	Q₈×D₁₉	1	2	yes	—
94	C₂×C₄	#64545	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
96	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
97	C₈	—	38	4	no	—
98	C₈	—	76	2	no	—
99	C₂²	—	2	2	no	—
100	C₂²	Q₈×Dic₁₉	1	2	yes	—
101	C₂²	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
102	C₄	—	2	2	no	—
103	C₄	—	2	2	no	—
104	C₄	—	4	4	no	—
105	C₄	#10597390	1	1	yes	characteristic
106	C₄	#10597392	1	2	yes	—
107	C₄	#10597393	1	1	yes	characteristic
108	C₂	—	2	2	no	—
109	C₂	#11926451	1	1	yes	characteristic
110	C₂	#11926528	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926568

C₂

yes

maximal, characteristic

C₄×#64520

C₂

yes

maximal, characteristic

#11926313

C₂

yes

maximal

C₂×C₁₉×#125

C₂

yes

maximal, characteristic

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×#64520

C₂²

yes

—

C₂×#64520

C₂²

yes

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

—

#64520

—

#64520

—

#64520

Q₈

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#1998

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×Q₈

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂²⋊Q₈

yes

—

C₄×C₁₉

#124

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×#125

D₁₉

yes

characteristic

#423

—

C₄×M₁₆

—

#343

—

C₂×C₁₉

—

C₂×C₁₉

#391

yes

characteristic

C₂×C₁₉

#413

yes

—

C₂×M₁₆

—

C₂×M₁₆

—

#125

—

#125

—

#125

—

C₂×C₄⋊C₄

Dic₁₉

yes

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₁₉

#1998

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂×Dic₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

characteristic

C₄²

C₂²⋊D₁₉

yes

—

C₂³

C₂²×Dic₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₁₉

yes

—

C₂×C₄

C₂²⋊Dic₁₉

yes

—

C₂×C₄

Q₈×D₁₉

yes

—

C₂×C₄

#64545

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

—

C₂²

—

100

C₂²

Q₈×Dic₁₉

yes

—

101

C₂²

C₂×C₂²⋊Dic₁₉

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#10597390

yes

characteristic

106

C₄

#10597392

yes

—

107

C₄

#10597393

yes

characteristic

108

C₂

—

109

C₂

#11926451

yes

characteristic

110

C₂

#11926528

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₁₉
commutator, prime radical	C₂³×C₁₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#125	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₂×#125	D₁₉
hypocenter	C₁₉	#1998
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₁₉

commutator, prime radical

C₂³×C₁₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₂×C₁₉×#125

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#125

N	H ≅ G/N	type
71. C₁₉	#1998	semidirect

H ≅ G/N

type

71. C₁₉

#1998

semidirect

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

subgroup	index
#11926568	2
C₄×#64520	2
#11926313	2
C₂×C₁₉×#125	2
#1998	19

subgroup

index

C₂×C₁₉×#125

Subgroups — #14564629

Conjugacy classes of subgroups

Complements

Maximal subgroups