Group #14563026 — subgroups

Subgroups — #14563026

Order 2432.

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

normal subgroups only

This group has 156 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	#11926751	C₂	1	2	yes	maximal
2	C₈×Dic₃₈	C₂	1	1	yes	maximal, characteristic
3	#11926297	C₂	1	1	yes	maximal, characteristic
4	#11926290	C₂	1	2	yes	maximal
5	C₁₉×#500	C₂	1	1	yes	maximal, characteristic
6	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×#64528	—	2	2	no	—
8	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
9	C₁₉×#107	—	2	1	no	—
10	C₁₉×#107	—	2	1	no	—
11	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	#10597292	—	2	2	no	—
13	Dic₁₉⋊C₈	—	2	1	no	—
14	C₈×Dic₁₉	—	2	1	no	—
15	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Dic₃₈	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	#64528	—	4	4	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	2	no	—
29	C₂×C₁₉⋊C₈	—	2	1	no	—
30	Q₈×C₁₉	—	4	2	no	—
31	Q₈×C₁₉	—	4	2	no	—
32	C₂×C₄×C₁₉	—	4	2	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	—	2	1	no	—
37	C₂×Dic₁₉	—	2	1	no	—
38	Dic₃₈	—	2	1	no	—
39	Dic₃₈	D₈	1	2	yes	—
40	C₈×C₁₉	—	2	1	no	—
41	C₈×C₁₉	Q₁₆	1	2	yes	complemented
42	C₁₉⋊C₈	—	4	2	no	—
43	C₁₉⋊C₈	—	4	1	no	—
44	#1674	—	19	1	no	maximal, Sylow
45	C₂²×C₁₉	#121	1	1	yes	characteristic
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	8	2	no	—
48	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
49	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
50	C₄×C₁₉	#135	1	1	yes	characteristic
51	C₄×C₁₉	#137	1	1	yes	characteristic
52	Dic₁₉	—	2	2	no	—
53	Dic₁₉	—	4	1	no	—
54	#500	D₁₉	1	1	yes	characteristic
55	#462	—	19	2	no	—
56	C₈×Q₈	—	19	1	no	—
57	#335	—	19	1	no	—
58	#332	—	19	2	no	—
59	C₂×C₁₉	#462	1	1	yes	characteristic
60	C₂×C₁₉	#466	1	1	yes	characteristic
61	C₂×C₁₉	#473	1	1	yes	characteristic
62	C₂×Q₁₆	—	38	2	no	—
63	C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
64	C₄×Q₈	—	19	1	no	—
65	#107	—	2	1	no	—
66	#107	—	2	1	no	—
67	C₄⋊C₈	—	19	1	no	—
68	C₄⋊C₈	—	19	2	no	—
69	C₄⋊C₈	—	38	1	no	—
70	#103	—	38	2	no	—
71	C₄×C₈	—	38	1	no	—
72	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
73	C₁₉	#1674	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	2	2	no	—
75	C₂×Q₈	—	19	1	no	—
76	Q₁₆	—	76	4	no	—
77	C₂×C₈	—	38	2	no	—
78	C₂×C₈	—	38	1	no	—
79	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	19	1	no	—
84	C₄⋊C₄	—	38	1	no	—
85	C₄²	—	38	1	no	—
86	C₄²	C₂²×D₁₉	1	1	yes	characteristic
87	Q₈	—	4	2	no	—
88	Q₈	—	4	2	no	—
89	Q₈	—	19	2	no	—
90	Q₈	—	38	1	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	—	38	1	no	—
93	C₂×C₄	—	38	1	no	—
94	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
95	C₂×C₄	#64543	1	1	yes	characteristic
96	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
97	C₈	—	2	1	no	—
98	C₈	—	76	1	no	—
99	C₈	—	76	2	no	—
100	C₈	#64528	1	2	yes	complemented
101	C₂²	#10597384	1	1	yes	characteristic
102	C₄	—	2	1	no	—
103	C₄	—	8	2	no	—
104	C₄	—	38	2	no	—
105	C₄	—	76	1	no	—
106	C₄	D₈×D₁₉	1	1	yes	characteristic
107	C₄	#10597358	1	1	yes	characteristic
108	C₄	#10597388	1	1	yes	characteristic
109	C₄	C₂×#64528	1	1	yes	characteristic
110	C₂	#11926751	1	1	yes	characteristic
111	C₂	#11926777	1	1	yes	characteristic
112	C₂	#11926816	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926751

C₂

yes

maximal

C₈×Dic₃₈

C₂

yes

maximal, characteristic

#11926297

C₂

yes

maximal, characteristic

#11926290

C₂

yes

maximal

C₁₉×#500

C₂

yes

maximal, characteristic

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₂×#64528

—

C₄×Dic₃₈

C₂²

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597292

—

Dic₁₉⋊C₈

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Dic₃₈

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64528

—

C₄⋊Dic₁₉

D₄

yes

characteristic

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

Q₈×C₁₉

—

Q₈×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

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

D₈

yes

—

C₈×C₁₉

—

C₈×C₁₉

Q₁₆

yes

complemented

C₁₉⋊C₈

—

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

#500

D₁₉

yes

characteristic

#462

—

C₈×Q₈

—

#335

—

#332

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

C₂×D₁₉

yes

—

C₄×Q₈

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1674

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

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

—

C₄²

—

C₄²

C₂²×D₁₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₉

yes

characteristic

C₂×C₄

#64543

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

100

C₈

#64528

yes

complemented

101

C₂²

#10597384

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

D₈×D₁₉

yes

characteristic

107

C₄

#10597358

yes

characteristic

108

C₄

#10597388

yes

characteristic

109

C₄

C₂×#64528

yes

characteristic

110

C₂

#11926751

yes

characteristic

111

C₂

#11926777

yes

characteristic

112

C₂

#11926816

yes

characteristic

	subgroup	G/H
center	C₂²	#10597384
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#500	C₂
socle, prime radical	C₂²×C₁₉	#121
hypercenter	#500	D₁₉
hypocenter	C₁₉	#1674
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#10597384

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#500

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
41. C₈×C₁₉	Q₁₆	semidirect
73. C₁₉	#1674	semidirect
100. C₈	#64528	semidirect

H ≅ G/N

type

41. C₈×C₁₉

Q₁₆

semidirect

73. C₁₉

#1674

semidirect

100. C₈

#64528

semidirect

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

subgroup	index
#11926751	2
C₈×Dic₃₈	2
#11926297	2
#11926290	2
C₁₉×#500	2
#1674	19

subgroup

index

C₈×Dic₃₈

C₁₉×#500

Subgroups — #14563026

Conjugacy classes of subgroups

Complements

Maximal subgroups