Group #14561646 — subgroups

Subgroups — #14561646

Order 2432.

116 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 39 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	#11926785	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₁₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#340	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
6	#10597370	—	2	1	no	—
7	C₂×Dic₇₆	C₄	1	1	yes	characteristic, complemented
8	#10597275	C₄	1	1	yes	characteristic, complemented
9	#10597273	—	2	1	no	—
10	C₂×C₁₉⋊C₁₆	—	2	1	no	—
11	C₂²×C₄×C₁₉	—	4	1	no	—
12	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
13	C₂×Dic₃₈	—	2	1	no	—
14	C₂×C₈×C₁₉	—	4	1	no	—
15	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₁₉	—	2	2	no	—
18	C₄⋊C₄×C₁₉	—	4	1	no	—
19	C₂²⋊Dic₁₉	—	4	1	no	—
20	C₄⋊Dic₁₉	—	2	1	no	—
21	Dic₁₉⋊C₄	—	4	1	no	—
22	Dic₇₆	—	4	1	no	—
23	C₁₉⋊C₁₆	—	4	1	no	—
24	C₂³×C₁₉	D₈	1	1	yes	characteristic
25	C₂×C₄×C₁₉	—	2	1	no	—
26	C₂×C₄×C₁₉	—	2	1	no	—
27	C₂×C₄×C₁₉	—	4	2	no	—
28	C₂×C₄×C₁₉	—	8	1	no	—
29	C₂×C₄×C₁₉	—	8	1	no	—
30	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
32	C₂×Dic₁₉	—	4	1	no	—
33	C₂×Dic₁₉	—	4	1	no	—
34	Dic₃₈	—	4	1	no	—
35	Dic₃₈	—	4	1	no	—
36	C₈×C₁₉	—	2	1	no	—
37	C₈×C₁₉	—	2	1	no	—
38	#1348	—	19	1	no	maximal, Sylow
39	C₂²×C₁₉	—	2	1	no	—
40	C₂²×C₁₉	—	2	1	no	—
41	C₂²×C₁₉	#102	1	1	yes	characteristic
42	C₂²×C₁₉	SD₃₂	1	1	yes	characteristic
43	C₂²×C₁₉	Q₃₂	1	1	yes	characteristic
44	C₄×C₁₉	—	2	1	no	—
45	C₄×C₁₉	—	8	2	no	—
46	C₄×C₁₉	#99	1	1	yes	characteristic
47	C₄×C₁₉	#104	1	1	yes	characteristic
48	Dic₁₉	—	8	1	no	—
49	Dic₁₉	—	8	1	no	—
50	#467	—	19	1	no	—
51	C₂²⋊C₁₆	—	19	1	no	—
52	#340	D₁₉	1	1	yes	characteristic
53	C₂×C₁₉	—	2	1	no	—
54	C₂×C₁₉	—	2	1	no	—
55	C₂×C₁₉	#327	1	1	yes	characteristic
56	C₂×C₁₉	#358	1	1	yes	characteristic
57	C₂×C₁₉	#360	1	1	yes	characteristic
58	C₂×Q₁₆	—	19	1	no	—
59	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
60	C₂²⋊Q₈	—	38	1	no	—
61	C₂×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₆	—	38	1	no	—
63	#107	—	19	1	no	—
64	#103	—	38	1	no	—
65	C₁₉	#1348	1	1	yes	characteristic, complemented, Sylow
66	C₂×Q₈	—	38	1	no	—
67	C₂²×C₄	—	4	1	no	—
68	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
69	Q₁₆	—	76	1	no	—
70	C₂×C₈	—	4	1	no	—
71	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
72	C₂×C₈	D₇₆	1	1	yes	characteristic
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	—	4	1	no	—
75	C₄⋊C₄	—	38	1	no	—
76	C₄⋊C₄	—	76	1	no	—
77	C₂²⋊C₄	—	76	1	no	—
78	C₁₆	—	76	1	no	—
79	C₂³	#64525	1	1	yes	characteristic
80	Q₈	—	76	1	no	—
81	Q₈	—	76	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	4	2	no	—
85	C₂×C₄	—	8	1	no	—
86	C₂×C₄	—	8	1	no	—
87	C₂×C₄	—	76	1	no	—
88	C₂×C₄	—	76	1	no	—
89	C₂×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
90	C₂×C₄	#64527	1	1	yes	characteristic
91	C₈	—	2	1	no	—
92	C₈	—	2	1	no	—
93	C₂²	—	2	1	no	—
94	C₂²	—	2	1	no	—
95	C₂²	#10597266	1	1	yes	characteristic
96	C₂²	#10597284	1	1	yes	characteristic
97	C₂²	#10597286	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	8	2	no	—
100	C₄	—	152	1	no	—
101	C₄	—	152	1	no	—
102	C₄	#10597262	1	1	yes	characteristic
103	C₄	#10597263	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	2	1	no	—
106	C₂	#11926277	1	1	yes	characteristic
107	C₂	#11926347	1	1	yes	characteristic
108	C₂	#11926353	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926785

C₂

yes

maximal, characteristic

C₂²⋊(C₁₉⋊C₁₆)

C₂

yes

maximal, characteristic

C₁₉×#340

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

—

#10597370

—

C₂×Dic₇₆

C₄

yes

characteristic, complemented

#10597275

C₄

yes

characteristic, complemented

#10597273

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

Dic₇₆

—

C₁₉⋊C₁₆

—

C₂³×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

#1348

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#102

yes

characteristic

C₂²×C₁₉

SD₃₂

yes

characteristic

C₂²×C₁₉

Q₃₂

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

#467

—

C₂²⋊C₁₆

—

#340

D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₁₆

—

#107

—

#103

—

C₁₉

#1348

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

Q₁₆

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

D₇₆

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

#64525

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

C₂×C₄

#64527

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

—

C₄

—

100

C₄

—

152

—

101

C₄

—

152

—

102

C₄

#10597262

yes

characteristic

103

C₄

#10597263

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

#11926277

yes

characteristic

107

C₂

#11926347

yes

characteristic

108

C₂

#11926353

yes

characteristic

	subgroup	G/H
center	C₂²	#10597266
commutator	C₂×C₈×C₁₉	C₂×C₄
Frattini	C₂²×C₈	C₂×D₁₉
Fitting	C₁₉×#340	C₂
socle	C₂²×C₁₉	#102
prime radical	C₂³×C₁₉	D₈
cosocle	C₂²×C₈×C₁₉	C₂²
hypercenter	#340	D₁₉
hypocenter	C₁₉	#1348
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #340

subgroup

G/H

center

C₂²

#10597266

commutator

C₂×C₈×C₁₉

C₂×C₄

Frattini

C₂²×C₈

C₂×D₁₉

Fitting

C₁₉×#340

C₂

socle

C₂²×C₁₉

#102

prime radical

C₂³×C₁₉

D₈

cosocle

C₂²×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #340

N	H ≅ G/N	type
7. C₂×Dic₇₆	C₄	semidirect
8. #10597275	C₄	semidirect
65. C₁₉	#1348	semidirect

H ≅ G/N

type

7. C₂×Dic₇₆

C₄

semidirect

8. #10597275

C₄

semidirect

65. C₁₉

#1348

semidirect

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

subgroup	index
#11926785	2
C₂²⋊(C₁₉⋊C₁₆)	2
C₁₉×#340	2
#1348	19

subgroup

index

#11926785

C₂²⋊(C₁₉⋊C₁₆)

C₁₉×#340

#1348

Subgroups — #14561646

Conjugacy classes of subgroups

Complements

Maximal subgroups