Group #14563154 — subgroups

Subgroups — #14563154

Order 2432.

152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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	#11926755	C₂	1	2	yes	maximal
3	#11926674	C₂	1	1	yes	maximal, characteristic
4	#11926291	C₂	1	2	yes	maximal
5	C₁₉×#334	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₆	—	2	2	no	—
7	#10597315	C₂²	1	2	yes	—
8	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	#10597275	—	2	1	no	—
12	#10597275	—	2	1	no	—
13	#10597273	—	2	2	no	—
14	#10597272	—	2	1	no	—
15	Dic₁₉⋊C₈	—	2	1	no	—
16	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₃₈	—	2	2	no	—
18	C₂×Dic₃₈	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	—	2	2	no	—
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₁₉	—	2	2	no	—
24	C₄⋊Dic₁₉	—	2	2	no	—
25	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
26	Dic₁₉⋊C₄	—	2	1	no	—
27	C₄×Dic₁₉	—	2	1	no	—
28	C₂×C₁₉⋊C₈	—	2	1	no	—
29	Dic₇₆	—	4	4	no	—
30	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
33	C₂×Dic₁₉	—	2	1	no	—
34	C₂×Dic₁₉	—	2	1	no	—
35	C₂×Dic₁₉	—	4	2	no	—
36	Dic₃₈	—	2	2	no	—
37	Dic₃₈	—	4	2	no	—
38	Dic₃₈	—	4	2	no	—
39	C₈×C₁₉	—	2	1	no	—
40	C₈×C₁₉	—	4	2	no	—
41	C₈×C₁₉	Q₁₆	1	2	yes	complemented
42	C₁₉⋊C₈	—	4	1	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	C₂×Q₁₆	1	1	yes	characteristic
47	C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
48	C₄×C₁₉	#137	1	1	yes	characteristic
49	Dic₁₉	—	4	1	no	—
50	Dic₁₉	—	4	1	no	—
51	Dic₁₉	—	8	2	no	—
52	#500	—	19	1	no	—
53	#462	—	19	2	no	—
54	#446	—	19	1	no	—
55	#334	D₁₉	1	1	yes	characteristic
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	—	19	1	no	—
63	#107	—	38	1	no	—
64	#107	—	38	1	no	—
65	C₄⋊C₈	—	19	1	no	—
66	C₄⋊C₈	—	38	1	no	—
67	C₄⋊C₈	C₂×D₁₉	1	2	yes	—
68	#103	—	38	2	no	—
69	#97	—	38	1	no	—
70	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
71	C₁₉	#1694	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₈	—	19	1	no	—
73	C₂×Q₈	—	38	2	no	—
74	Q₁₆	—	76	4	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	38	1	no	—
77	C₂×C₈	D₇₆	1	1	yes	characteristic
78	C₂×C₈	D₇₆	1	1	yes	characteristic
79	C₄⋊C₄	—	19	1	no	—
80	C₄⋊C₄	—	38	1	no	—
81	C₄⋊C₄	—	38	2	no	—
82	C₄⋊C₄	—	38	2	no	—
83	C₄²	—	38	1	no	—
84	C₄²	C₂²×D₁₉	1	1	yes	characteristic
85	Q₈	—	38	2	no	—
86	Q₈	—	76	2	no	—
87	Q₈	—	76	2	no	—
88	C₂×C₄	—	38	1	no	—
89	C₂×C₄	—	38	1	no	—
90	C₂×C₄	—	76	2	no	—
91	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
92	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
93	C₂×C₄	#64545	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	4	2	no	—
96	C₈	—	76	1	no	—
97	C₈	Dic₇₆	1	2	yes	complemented
98	C₂²	#10597341	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	76	1	no	—
101	C₄	—	76	1	no	—
102	C₄	—	152	2	no	—
103	C₄	C₂×Dic₇₆	1	1	yes	characteristic
104	C₄	#10597355	1	1	yes	characteristic
105	C₄	#10597360	1	2	yes	—
106	C₂	#11926755	1	1	yes	characteristic
107	C₂	#11926798	1	1	yes	characteristic
108	C₂	#11926820	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926949

C₂

yes

maximal, characteristic

#11926755

C₂

yes

maximal

#11926674

C₂

yes

maximal, characteristic

#11926291

C₂

yes

maximal

C₁₉×#334

C₂

yes

maximal, characteristic

C₂×Dic₇₆

—

#10597315

C₂²

yes

—

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

—

—

—

—

Dic₁₉⋊C₈

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

Q₁₆

yes

complemented

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₄×C₁₉

#137

yes

characteristic

Dic₁₉

—

Dic₁₉

—

Dic₁₉

—

—

—

—

D₁₉

yes

characteristic

#332

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₉

yes

—

#103

—

#97

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1694

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₁₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₇₆

yes

characteristic

C₂×C₄

D₄×D₁₉

yes

characteristic

C₂×C₄

#64545

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

Dic₇₆

yes

complemented

C₂²

#10597341

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

152

—

103

C₄

C₂×Dic₇₆

yes

characteristic

104

C₄

#10597355

yes

characteristic

105

C₄

#10597360

yes

—

106

C₂

#11926755

yes

characteristic

107

C₂

#11926798

yes

characteristic

108

C₂

#11926820

yes

characteristic

	subgroup	G/H
center	C₂²	#10597341
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#334	C₂
socle, prime radical	C₂²×C₁₉	#121
hypercenter	#334	D₁₉
hypocenter	C₁₉	#1694
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#10597341

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#334

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
41. C₈×C₁₉	Q₁₆	semidirect
71. C₁₉	#1694	semidirect
97. C₈	Dic₇₆	semidirect

H ≅ G/N

type

41. C₈×C₁₉

Q₁₆

semidirect

71. C₁₉

#1694

semidirect

97. C₈

Dic₇₆

semidirect

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

subgroup	index
#11926949	2
#11926755	2
#11926674	2
#11926291	2
C₁₉×#334	2
#1694	19

subgroup

index

C₁₉×#334

Subgroups — #14563154

Conjugacy classes of subgroups

Complements

Maximal subgroups