Group #19136766 — subgroups

Subgroups — #19136766

Order 5504.

126 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 49 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	#14583297	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582723	C₂	1	2	yes	maximal, complemented
3	#14582720	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582709	C₂	1	2	yes	maximal
5	C₄₃×#443	C₂	1	1	yes	maximal, characteristic
6	#13063325	—	2	1	no	—
7	#13063265	C₂²	1	2	yes	—
8	#13063257	—	2	1	no	—
9	#13063257	C₂²	1	2	yes	—
10	#135×C₄₃	C₂²	1	1	yes	characteristic
11	#131×C₄₃	—	2	1	no	—
12	#108×C₄₃	C₂²	1	1	yes	characteristic
13	#104×C₄₃	—	2	1	no	—
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	#41×C₄₃	—	2	1	no	—
16	C₂×Dic₈₆	—	4	1	no	—
17	Q₁₆×C₄₃	Q₈	1	1	yes	characteristic, complemented
18	SD₁₆×C₄₃	—	2	1	no	—
19	D₈×C₄₃	Q₈	1	1	yes	characteristic, complemented
20	M₁₆×C₄₃	—	2	1	no	—
21	M₁₆×C₄₃	—	4	1	no	—
22	C₂×C₈×C₄₃	—	4	1	no	—
23	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
25	C₄²×C₄₃	D₄	1	1	yes	characteristic
26	C₄⋊Dic₄₃	—	2	2	no	—
27	C₄⋊Dic₄₃	—	4	1	no	—
28	C₄₃⋊C₁₆	—	2	2	no	—
29	Q₈×C₄₃	—	2	1	no	—
30	D₄×C₄₃	—	2	1	no	—
31	D₄×C₄₃	—	4	1	no	—
32	C₂×C₄×C₄₃	—	2	1	no	—
33	C₂×C₄×C₄₃	—	4	1	no	—
34	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₄₃	—	4	2	no	—
36	Dic₈₆	—	8	2	no	—
37	C₈×C₄₃	—	4	1	no	—
38	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
39	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
40	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
41	C₈×C₄₃	#41	1	1	yes	characteristic
42	C₂²×C₄₃	—	4	1	no	—
43	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
44	C₄×C₄₃	—	2	2	no	—
45	C₄×C₄₃	—	4	1	no	—
46	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
47	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
48	Dic₄₃	—	8	2	no	—
49	#2230	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	1	no	—
51	C₂×C₄₃	—	8	1	no	—
52	C₂×C₄₃	#476	1	1	yes	characteristic
53	#498	—	43	1	no	—
54	#443	D₄₃	1	1	yes	characteristic
55	#365	—	43	2	no	—
56	#364	—	43	1	no	—
57	#360	—	43	2	no	—
58	C₄₃	#2230	1	1	yes	characteristic, complemented, Sylow
59	#135	C₂×D₄₃	1	1	yes	characteristic
60	#131	—	2	1	no	—
61	C₄⋊Q₈	—	86	1	no	—
62	M₃₂	—	43	2	no	—
63	#108	C₂×D₄₃	1	1	yes	characteristic
64	#106	—	43	2	no	—
65	#106	—	86	1	no	—
66	#104	—	2	1	no	—
67	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
68	#41	—	2	1	no	—
69	C₂×Q₈	—	172	1	no	—
70	Q₁₆	Dic₈₆	1	1	yes	characteristic, complemented
71	SD₁₆	—	2	1	no	—
72	D₈	Dic₈₆	1	1	yes	characteristic, complemented
73	M₁₆	—	2	1	no	—
74	M₁₆	—	4	1	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
77	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
78	C₄⋊C₄	—	86	2	no	—
79	C₄⋊C₄	—	172	1	no	—
80	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
81	C₁₆	—	86	2	no	—
82	Q₈	—	2	1	no	—
83	Q₈	—	344	2	no	—
84	D₄	—	2	1	no	—
85	D₄	—	4	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	172	2	no	—
89	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
90	C₈	—	4	1	no	—
91	C₈	#10621883	1	1	yes	characteristic
92	C₈	#10621883	1	1	yes	characteristic
93	C₈	C₂×Dic₈₆	1	1	yes	characteristic
94	C₈	#10621898	1	1	yes	characteristic
95	C₂²	—	4	1	no	—
96	C₂²	#13063350	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	4	1	no	—
99	C₄	—	344	2	no	—
100	C₄	#13063304	1	1	yes	characteristic
101	C₄	C₂×#10621883	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	8	1	no	—
104	C₂	#14583189	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583297

C₂

yes

maximal, characteristic, complemented

#14582723

C₂

yes

maximal, complemented

#14582720

C₂

yes

maximal, characteristic, complemented

#14582709

C₂

yes

maximal

C₄₃×#443

C₂

yes

maximal, characteristic

#13063325

—

#13063265

C₂²

yes

—

#13063257

—

#13063257

C₂²

yes

—

#135×C₄₃

C₂²

yes

characteristic

#131×C₄₃

—

#108×C₄₃

C₂²

yes

characteristic

#104×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

#41×C₄₃

—

C₂×Dic₈₆

—

Q₁₆×C₄₃

Q₈

yes

characteristic, complemented

SD₁₆×C₄₃

—

D₈×C₄₃

Q₈

yes

characteristic, complemented

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄₃⋊C₁₆

—

Q₈×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

SD₁₆

yes

characteristic

C₈×C₄₃

SD₁₆

yes

characteristic

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

#2230

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

D₄₃

yes

—

—

—

C₄₃

#2230

yes

characteristic, complemented, Sylow

#135

C₂×D₄₃

yes

characteristic

#131

—

C₄⋊Q₈

—

M₃₂

—

#108

C₂×D₄₃

yes

—

—

—

C₄×C₈

C₂×D₄₃

yes

characteristic

#41

—

C₂×Q₈

—

172

—

Q₁₆

Dic₈₆

yes

characteristic, complemented

SD₁₆

—

D₈

Dic₈₆

yes

characteristic, complemented

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

344

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

C₈

yes

C₈

yes

C₈

C₂×Dic₈₆

yes

characteristic

C₈

#10621898

yes

characteristic

C₂²

—

C₂²

#13063350

yes

characteristic

C₄

—

C₄

—

C₄

—

344

—

100

C₄

#13063304

yes

characteristic

101

C₄

C₂×#10621883

yes

characteristic

102

C₂

—

103

C₂

—

104

C₂

#14583189

yes

characteristic

	subgroup	G/H
center	C₂	#14583189
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#443	C₂
socle	C₂×C₄₃	#476
hypercenter	#443	D₄₃
hypocenter	C₄₃	#2230
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

subgroup

G/H

center

C₂

#14583189

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#443

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

N	H ≅ G/N	type
1. #14583297	C₂	semidirect
2. #14582723	C₂	semidirect
3. #14582720	C₂	semidirect
17. Q₁₆×C₄₃	Q₈	semidirect
19. D₈×C₄₃	Q₈	semidirect
58. C₄₃	#2230	semidirect
70. Q₁₆	Dic₈₆	semidirect
72. D₈	Dic₈₆	semidirect

H ≅ G/N

type

1. #14583297

C₂

semidirect

2. #14582723

C₂

semidirect

3. #14582720

C₂

semidirect

17. Q₁₆×C₄₃

Q₈

semidirect

19. D₈×C₄₃

Q₈

semidirect

58. C₄₃

#2230

semidirect

70. Q₁₆

Dic₈₆

semidirect

72. D₈

Dic₈₆

semidirect

Subgroups — #19136766

Conjugacy classes of subgroups

Complements