Group #14565409 — subgroups

Subgroups — #14565409

Order 2432.

144 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 81 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	C₂×#10597269	C₂	1	1	yes	maximal, characteristic
2	#11926582	C₂	1	1	yes	maximal, characteristic
3	#11926368	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#108	C₂	1	1	yes	maximal, characteristic
5	C₂×M₁₆×C₁₉	—	2	1	no	—
6	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
7	#10597372	—	2	1	no	—
8	C₁₉×#108	—	2	1	no	—
9	C₁₉×#108	C₂²	1	2	yes	—
10	#10597275	—	2	1	no	—
11	#10597274	C₂²	1	2	yes	—
12	#10597269	C₄	1	2	yes	complemented
13	#10597269	C₂²	1	2	yes	—
14	C₂×C₁₉⋊C₁₆	C₄	1	2	yes	complemented
15	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
16	M₁₆×C₁₉	—	2	2	no	—
17	M₁₆×C₁₉	—	4	1	no	—
18	C₂×C₈×C₁₉	—	4	1	no	—
19	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
23	C₂×C₈×C₁₉	Q₈	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²⋊Dic₁₉	—	4	1	no	—
26	C₄⋊Dic₁₉	—	2	2	no	—
27	C₄×Dic₁₉	—	4	1	no	—
28	C₁₉⋊C₁₆	C₂×C₄	1	4	yes	—
29	C₂³×C₁₉	SD₁₆	1	1	yes	characteristic
30	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₁₉	—	4	2	no	—
37	C₈×C₁₉	—	4	2	no	—
38	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
42	#2155	—	19	1	no	maximal, Sylow
43	C₂²×C₁₉	—	4	1	no	—
44	C₂²×C₁₉	#106	1	1	yes	characteristic
45	C₂²×C₁₉	#106	1	1	yes	characteristic
46	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
47	C₄×C₁₉	#106	1	1	yes	characteristic
48	C₄×C₁₉	#106	1	1	yes	characteristic
49	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
51	Dic₁₉	—	8	2	no	—
52	C₂×M₃₂	—	19	1	no	—
53	C₂×#108	D₁₉	1	1	yes	characteristic
54	#427	—	19	1	no	—
55	#365	—	19	4	no	—
56	C₂×C₁₉	—	2	1	no	—
57	C₂×C₁₉	—	2	1	no	—
58	C₂×C₁₉	—	2	1	no	—
59	C₂×C₁₉	C₂×#106	1	1	yes	characteristic
60	C₂×M₁₆	—	2	1	no	—
61	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
62	#117	—	38	1	no	—
63	M₃₂	—	19	2	no	—
64	M₃₂	—	19	2	no	—
65	C₂×C₁₆	—	19	2	no	—
66	#108	—	2	1	no	—
67	#108	C₂×D₁₉	1	2	yes	—
68	#107	—	38	1	no	—
69	#106	—	19	2	no	—
70	C₁₉	#2155	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
72	M₁₆	—	2	2	no	—
73	M₁₆	—	4	1	no	—
74	C₂×C₈	—	4	1	no	—
75	C₂×C₈	Dic₃₈	1	1	yes	characteristic
76	C₂×C₈	Dic₃₈	1	1	yes	characteristic
77	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
78	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
79	C₂×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
80	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
81	C₄⋊C₄	—	38	2	no	—
82	C₂²⋊C₄	—	76	1	no	—
83	C₄²	—	76	1	no	—
84	C₁₆	—	19	4	no	—
85	C₂³	#64527	1	1	yes	characteristic
86	C₂×C₄	—	76	2	no	—
87	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
88	C₂×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
89	C₂×C₄	#64526	1	1	yes	characteristic
90	C₂×C₄	#64526	1	1	yes	characteristic
91	C₂×C₄	#64527	1	1	yes	characteristic
92	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
93	C₈	—	4	2	no	—
94	C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
95	C₈	Dic₁₉⋊C₄	1	1	yes	characteristic
96	C₈	C₂×Dic₃₈	1	1	yes	characteristic
97	C₈	C₂×C₄×D₁₉	1	1	yes	characteristic
98	C₂²	—	4	1	no	—
99	C₂²	#10597265	1	1	yes	characteristic
100	C₂²	#10597265	1	1	yes	characteristic
101	C₂²	C₂×#64527	1	1	yes	characteristic
102	C₄	—	152	2	no	—
103	C₄	#10597265	1	1	yes	characteristic
104	C₄	#10597265	1	1	yes	characteristic
105	C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
106	C₄	C₂×#64526	1	1	yes	characteristic
107	C₂	—	2	1	no	—
108	C₂	—	2	1	no	—
109	C₂	—	2	1	no	—
110	C₂	C₂×#10597265	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597269

C₂

yes

maximal, characteristic

#11926582

C₂

yes

maximal, characteristic

#11926368

C₂

yes

maximal, complemented

C₂×C₁₉×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

#10597372

—

C₁₉×#108

—

C₁₉×#108

C₂²

yes

—

#10597275

—

#10597274

C₂²

yes

—

#10597269

C₄

yes

complemented

#10597269

C₂²

yes

—

C₂×C₁₉⋊C₁₆

C₄

yes

complemented

C₂²×C₄×C₁₉

D₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₁₉⋊C₁₆

C₂×C₄

yes

—

C₂³×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₄⋊C₄

yes

characteristic

C₈×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

C₂×Q₈

yes

characteristic

#2155

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

C₂×SD₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₂×SD₁₆

yes

characteristic

Dic₁₉

—

C₂×M₃₂

—

C₂×#108

D₁₉

yes

characteristic

#427

—

#365

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#106

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

C₂×D₁₉

yes

characteristic

#117

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

C₂×D₁₉

yes

—

#107

—

#106

—

C₁₉

#2155

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

Dic₃₈

yes

characteristic

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₂²⋊D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₂³

#64527

yes

characteristic

C₂×C₄

—

C₂×C₄

Dic₁₉⋊C₄

yes

characteristic

C₂×C₄

Dic₁₉⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

Dic₁₉⋊C₄

yes

characteristic

C₈

Dic₁₉⋊C₄

yes

characteristic

C₈

C₂×Dic₃₈

yes

characteristic

C₈

C₂×C₄×D₁₉

yes

characteristic

C₂²

—

C₂²

#10597265

yes

characteristic

100

C₂²

#10597265

yes

characteristic

101

C₂²

C₂×#64527

yes

characteristic

102

C₄

—

152

—

103

C₄

#10597265

yes

characteristic

104

C₄

#10597265

yes

characteristic

105

C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

106

C₄

C₂×#64526

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

—

110

C₂

C₂×#10597265

yes

characteristic

	subgroup	G/H
center	C₄	#10597265
commutator	C₈×C₁₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₂×C₁₉×#108	C₂
socle	C₂×C₁₉	C₂×#106
prime radical	C₂³×C₁₉	SD₁₆
cosocle	C₂×C₈×C₁₉	C₂³
hypercenter	C₂×#108	D₁₉
hypocenter	C₁₉	#2155
LCS	G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₄

#10597265

commutator

C₈×C₁₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₂×C₁₉×#108

C₂

socle

C₂×C₁₉

C₂×#106

prime radical

C₂³×C₁₉

SD₁₆

cosocle

C₂×C₈×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
3. #11926368	C₂	semidirect
12. #10597269	C₄	semidirect
14. C₂×C₁₉⋊C₁₆	C₄	semidirect
70. C₁₉	#2155	semidirect

H ≅ G/N

type

3. #11926368

C₂

semidirect

12. #10597269

C₄

semidirect

14. C₂×C₁₉⋊C₁₆

C₄

semidirect

70. C₁₉

#2155

semidirect

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

subgroup	index
C₂×#10597269	2
#11926582	2
#11926368	2
C₂×C₁₉×#108	2
#2155	19

subgroup

index

C₂×C₁₉×#108

Subgroups — #14565409

Conjugacy classes of subgroups

Complements

Maximal subgroups