Group #19134744 — subgroups

Subgroups — #19134744

Order 5504.

162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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	#14582670	C₂	1	2	yes	maximal
2	#14582659	C₂	1	2	yes	maximal
3	C₄₃⋊#338	C₂	1	1	yes	maximal, characteristic
4	#14582656	C₂	1	1	yes	maximal, characteristic
5	C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	#13063284	C₂²	1	2	yes	—
8	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	#97×C₄₃	C₄	1	2	yes	complemented
12	C₄×C₈×C₄₃	C₄	1	2	yes	complemented
13	C₂²×C₄×C₄₃	—	2	1	no	—
14	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
15	M₁₆×C₄₃	—	2	2	no	—
16	M₁₆×C₄₃	—	2	2	no	—
17	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
19	C₄²×C₄₃	—	2	1	no	—
20	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂²⋊Dic₄₃	—	2	2	no	—
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄×Dic₄₃	—	2	2	no	—
25	#10621877	—	2	2	no	—
26	#10621877	—	2	2	no	—
27	C₂×C₄₃⋊C₈	—	2	2	no	—
28	C₂³×C₄₃	#41	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	—	4	2	no	—
32	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	#41	1	2	yes	—
34	C₂×C₄×C₄₃	#41	1	2	yes	—
35	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
36	C₂×Dic₄₃	—	4	2	no	—
37	C₈×C₄₃	—	2	2	no	—
38	C₈×C₄₃	—	2	2	no	—
39	C₄₃⋊C₈	—	4	2	no	—
40	C₂²×C₄₃	—	4	1	no	—
41	C₂²×C₄₃	#117	1	1	yes	characteristic
42	C₂²×C₄₃	#126	1	2	yes	—
43	C₄×C₄₃	—	2	2	no	—
44	C₄×C₄₃	—	4	1	no	—
45	C₄×C₄₃	#117	1	1	yes	characteristic
46	C₄×C₄₃	#117	1	1	yes	characteristic
47	C₄×C₄₃	#126	1	2	yes	—
48	Dic₄₃	—	8	2	no	—
49	#1841	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	2	no	—
51	C₂×C₄₃	—	2	1	no	—
52	C₂×C₄₃	#383	1	1	yes	characteristic
53	C₄×M₁₆	D₄₃	1	1	yes	characteristic
54	#344	—	43	2	no	—
55	#339	—	43	2	no	—
56	#338	—	43	1	no	—
57	H(3,ℤ/4)	—	43	1	no	—
58	C₄₃	#1841	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	43	2	no	—
60	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
61	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
62	#117	—	43	2	no	—
63	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
64	#97	Dic₄₃	1	2	yes	complemented
65	C₄×C₈	Dic₄₃	1	2	yes	complemented
66	C₂²×C₄	—	2	1	no	—
67	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	86	2	no	—
71	M₁₆	—	86	2	no	—
72	C₂×C₈	—	86	2	no	—
73	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
74	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
75	C₄⋊C₄	—	86	2	no	—
76	C₂²⋊C₄	—	86	2	no	—
77	C₄²	—	2	1	no	—
78	C₄²	—	86	2	no	—
79	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
80	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
81	C₂³	#10621898	1	1	yes	characteristic
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	4	2	no	—
85	C₂×C₄	—	172	2	no	—
86	C₂×C₄	#10621898	1	2	yes	—
87	C₂×C₄	#10621898	1	2	yes	—
88	C₂×C₄	#10621898	1	1	yes	characteristic
89	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	2	2	no	—
92	C₈	—	172	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#13063284	1	1	yes	characteristic
95	C₂²	#13063319	1	2	yes	—
96	C₄	—	2	2	no	—
97	C₄	—	4	1	no	—
98	C₄	—	344	2	no	—
99	C₄	#13063284	1	1	yes	characteristic
100	C₄	#13063284	1	1	yes	characteristic
101	C₄	#13063319	1	2	yes	—
102	C₂	—	2	1	no	—
103	C₂	—	2	2	no	—
104	C₂	#14582767	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582670

C₂

yes

maximal

#14582659

C₂

yes

maximal

C₄₃⋊#338

C₂

yes

maximal, characteristic

#14582656

C₂

yes

maximal, characteristic

C₄×M₁₆×C₄₃

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

#13063284

C₂²

yes

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#97×C₄₃

C₄

yes

complemented

C₄×C₈×C₄₃

C₄

yes

complemented

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄×Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#41

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

#117

yes

characteristic

C₂²×C₄₃

#126

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

Dic₄₃

—

#1841

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#383

yes

characteristic

C₄×M₁₆

D₄₃

yes

—

—

—

—

C₄₃

#1841

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂×M₁₆

C₂×D₄₃

yes

characteristic

#117

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#97

Dic₄₃

yes

complemented

C₄×C₈

Dic₄₃

yes

complemented

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂×Dic₄₃

yes

characteristic

C₂³

#10621898

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

#10621898

yes

—

C₂×C₄

#10621898

yes

—

C₂×C₄

#10621898

yes

characteristic

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₈

—

C₈

—

C₈

—

172

—

C₂²

—

C₂²

#13063284

yes

characteristic

C₂²

#13063319

yes

—

C₄

—

C₄

—

C₄

—

344

—

C₄

#13063284

yes

characteristic

100

C₄

#13063284

yes

characteristic

101

C₄

#13063319

yes

—

102

C₂

—

103

C₂

—

104

C₂

#14582767

yes

characteristic

	subgroup	G/H
center	C₄	#13063284
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄×M₁₆×C₄₃	C₂
socle	C₂×C₄₃	#383
hypercenter	C₄×M₁₆	D₄₃
hypocenter	C₄₃	#1841
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ C₄×M₁₆

subgroup

G/H

center

C₄

#13063284

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄×M₁₆×C₄₃

C₂

socle

C₂×C₄₃

#383

hypercenter

C₄×M₁₆

D₄₃

hypocenter

C₄₃

#1841

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ C₄×M₁₆

N	H ≅ G/N	type
11. #97×C₄₃	C₄	semidirect
12. C₄×C₈×C₄₃	C₄	semidirect
58. C₄₃	#1841	semidirect
64. #97	Dic₄₃	semidirect
65. C₄×C₈	Dic₄₃	semidirect

H ≅ G/N

type

11. #97×C₄₃

C₄

semidirect

12. C₄×C₈×C₄₃

C₄

semidirect

58. C₄₃

#1841

semidirect

64. #97

Dic₄₃

semidirect

65. C₄×C₈

Dic₄₃

semidirect

Subgroups — #19134744

Conjugacy classes of subgroups

Complements