Group #19136763 — subgroups

Subgroups — #19136763

Order 5504.

126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14583017	C₂	1	1	yes	maximal, characteristic
2	#14582721	C₂	1	2	yes	maximal, complemented
3	#14582720	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582708	C₂	1	2	yes	maximal
5	C₄₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063347	C₂²	1	1	yes	characteristic
7	#13063331	—	2	1	no	—
8	#13063265	C₂²	1	2	yes	—
9	#13063261	C₂²	1	1	yes	characteristic
10	#13063253	—	2	1	no	—
11	C₄⋊Q₈×C₄₃	—	2	1	no	—
12	#106×C₄₃	—	2	1	no	—
13	#106×C₄₃	C₂²	1	2	yes	—
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₃	—	4	1	no	—
16	#10621898	—	2	1	no	—
17	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₄₃	—	2	2	no	—
20	C₄⋊C₄×C₄₃	—	4	1	no	—
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	#10621877	—	2	1	no	—
23	Dic₁₇₂	Q₈	1	1	yes	characteristic, complemented
24	D₃₄₄	Q₈	1	1	yes	characteristic, complemented
25	#10621873	—	2	1	no	—
26	#10621872	—	4	1	no	—
27	C₈×D₄₃	—	4	1	no	—
28	C₄₃⋊C₁₆	—	2	2	no	—
29	Q₈×C₄₃	—	8	2	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	—	4	2	no	—
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂²⋊D₄₃	—	4	1	no	—
34	D₁₇₂	—	2	1	no	—
35	C₄×D₄₃	—	4	1	no	—
36	Dic₈₆	—	2	1	no	—
37	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
38	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
39	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
40	C₈×C₄₃	#41	1	1	yes	characteristic
41	C₄₃⋊C₈	—	4	1	no	—
42	C₂²×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
43	C₂×D₄₃	—	4	1	no	—
44	C₄×C₄₃	—	2	2	no	—
45	C₄×C₄₃	—	8	2	no	—
46	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
47	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
48	Dic₄₃	—	4	1	no	—
49	#2230	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	1	no	—
51	C₂×C₄₃	#476	1	1	yes	characteristic
52	D₄₃	—	8	1	no	—
53	#498	D₄₃	1	1	yes	characteristic, complemented
54	#443	—	43	1	no	—
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	—	43	1	no	—
60	#131	—	86	1	no	—
61	C₄⋊Q₈	—	2	1	no	—
62	M₃₂	—	43	2	no	—
63	#108	—	43	1	no	—
64	#106	—	2	1	no	—
65	#106	C₂×D₄₃	1	2	yes	—
66	#104	—	86	1	no	—
67	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
68	#41	—	86	1	no	—
69	C₂×Q₈	—	4	1	no	—
70	Q₁₆	—	43	1	no	—
71	SD₁₆	—	86	1	no	—
72	D₈	—	43	1	no	—
73	M₁₆	—	86	1	no	—
74	M₁₆	—	172	1	no	—
75	C₂×C₈	—	172	1	no	—
76	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
77	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
78	C₄⋊C₄	—	2	2	no	—
79	C₄⋊C₄	—	4	1	no	—
80	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
81	C₁₆	—	86	2	no	—
82	Q₈	—	8	2	no	—
83	Q₈	—	86	1	no	—
84	D₄	—	86	1	no	—
85	D₄	—	172	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	4	2	no	—
88	C₂×C₄	—	172	1	no	—
89	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
90	C₈	—	172	1	no	—
91	C₈	#10621884	1	1	yes	characteristic
92	C₈	#10621884	1	1	yes	characteristic
93	C₈	Q₈×D₄₃	1	1	yes	characteristic
94	C₈	#10621902	1	1	yes	characteristic
95	C₂²	—	172	1	no	—
96	C₂²	#13063351	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	8	2	no	—
99	C₄	—	172	1	no	—
100	C₄	#13063301	1	1	yes	characteristic
101	C₄	C₂×#10621884	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	344	1	no	—
104	C₂	#14583186	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583017

C₂

yes

maximal, characteristic

#14582721

C₂

yes

maximal, complemented

#14582720

C₂

yes

maximal, characteristic, complemented

#14582708

C₂

yes

maximal

C₄₃×#498

C₂

yes

maximal, characteristic, complemented

#13063347

C₂²

yes

characteristic

#13063331

—

#13063265

C₂²

yes

—

#13063261

C₂²

yes

characteristic

#13063253

—

C₄⋊Q₈×C₄₃

—

#106×C₄₃

—

#106×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

#10621898

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

#10621877

—

Dic₁₇₂

Q₈

yes

characteristic, complemented

D₃₄₄

Q₈

yes

characteristic, complemented

#10621873

—

#10621872

—

C₈×D₄₃

—

C₄₃⋊C₁₆

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

SD₁₆

yes

characteristic

C₈×C₄₃

SD₁₆

yes

characteristic

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

Dic₄₃

—

#2230

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#476

yes

characteristic

D₄₃

—

#498

D₄₃

yes

characteristic, complemented

—

—

—

—

C₄₃

#2230

yes

characteristic, complemented, Sylow

#135

—

#131

—

C₄⋊Q₈

—

M₃₂

—

#108

—

#106

—

#106

C₂×D₄₃

yes

—

#104

—

C₄×C₈

C₂×D₄₃

yes

characteristic

#41

—

C₂×Q₈

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

D₄

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

172

—

C₈

yes

C₈

yes

C₈

Q₈×D₄₃

yes

characteristic

C₈

#10621902

yes

characteristic

C₂²

—

172

—

C₂²

#13063351

yes

characteristic

C₄

—

C₄

—

C₄

—

172

—

100

C₄

#13063301

yes

characteristic

101

C₄

C₂×#10621884

yes

characteristic

102

C₂

—

103

C₂

—

344

—

104

C₂

#14583186

yes

characteristic

	subgroup	G/H
center	C₂	#14583186
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#498	C₂
socle	C₂×C₄₃	#476
hypercenter	#498	D₄₃
hypocenter	C₄₃	#2230
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #498

subgroup

G/H

center

C₂

#14583186

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#498

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #498

N	H ≅ G/N	type
2. #14582721	C₂	semidirect
3. #14582720	C₂	semidirect
5. C₄₃×#498	C₂	semidirect
23. Dic₁₇₂	Q₈	semidirect
24. D₃₄₄	Q₈	semidirect
53. #498	D₄₃	semidirect
58. C₄₃	#2230	semidirect

H ≅ G/N

type

2. #14582721

C₂

semidirect

3. #14582720

C₂

semidirect

5. C₄₃×#498

C₂

semidirect

23. Dic₁₇₂

Q₈

semidirect

24. D₃₄₄

Q₈

semidirect

53. #498

D₄₃

semidirect

58. C₄₃

#2230

semidirect

Subgroups — #19136763

Conjugacy classes of subgroups

Complements