Group #19136909 — subgroups

Subgroups — #19136909

Order 5504.

112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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	#14583332	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582736	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#14582734	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582732	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×SD₆₄	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063348	—	2	1	no	—
9	D₈×D₄₃	—	2	1	no	—
10	#13063268	—	2	1	no	—
11	D₆₈₈	C₂²	1	1	yes	characteristic
12	D₆₈₈	C₂²	1	1	yes	characteristic, complemented
13	#13063266	—	2	1	no	—
14	C₁₆×D₄₃	C₂²	1	1	yes	characteristic
15	C₄₃⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
16	Q₃₂×C₄₃	C₂²	1	1	yes	characteristic, complemented
17	D₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₃₂×C₄₃	C₂²	1	1	yes	characteristic, complemented
19	#10621902	—	4	1	no	—
20	D₄×D₄₃	—	4	1	no	—
21	Q₁₆×C₄₃	—	2	1	no	—
22	D₈×C₄₃	—	2	1	no	—
23	#10621884	—	4	1	no	—
24	#10621882	—	4	1	no	—
25	D₃₄₄	—	2	1	no	—
26	D₃₄₄	—	2	1	no	—
27	C₈×D₄₃	D₄	1	1	yes	characteristic
28	C₁₆×C₄₃	C₂³	1	1	yes	characteristic
29	C₄₃⋊C₁₆	D₄	1	1	yes	characteristic
30	C₂²×D₄₃	—	8	1	no	—
31	Q₈×C₄₃	—	4	1	no	—
32	D₄×C₄₃	—	4	1	no	—
33	C₂²⋊D₄₃	—	8	1	no	—
34	D₁₇₂	—	4	1	no	—
35	D₁₇₂	—	4	1	no	—
36	D₁₇₂	—	8	1	no	—
37	C₄×D₄₃	—	8	1	no	—
38	C₄×D₄₃	D₈	1	1	yes	characteristic
39	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
40	C₄₃⋊C₈	D₈	1	1	yes	characteristic
41	C₂²×C₄₃	—	8	1	no	—
42	C₂×D₄₃	—	8	1	no	—
43	C₂×D₄₃	—	8	1	no	—
44	C₂×D₄₃	—	16	2	no	—
45	C₂×D₄₃	D₁₆	1	1	yes	characteristic
46	C₄×C₄₃	—	8	1	no	—
47	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
48	Dic₄₃	D₁₆	1	1	yes	characteristic
49	#2263	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	16	1	no	—
51	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
52	D₄₃	—	2	1	no	—
53	D₄₃	—	16	1	no	—
54	D₄₃	—	16	1	no	—
55	#508	—	43	1	no	—
56	C₂×D₁₆	—	43	1	no	—
57	SD₆₄	—	43	1	no	—
58	SD₆₄	D₄₃	1	1	yes	characteristic, complemented
59	D₃₂	—	43	1	no	—
60	D₃₂	—	43	1	no	—
61	M₆₄	—	43	1	no	—
62	C₄₃	#2263	1	1	yes	characteristic, complemented, Sylow
63	#135	—	86	1	no	—
64	C₂×D₈	—	86	1	no	—
65	Q₃₂	C₂×D₄₃	1	1	yes	characteristic, complemented
66	SD₃₂	—	86	1	no	—
67	D₁₆	—	43	1	no	—
68	D₁₆	—	43	1	no	—
69	D₁₆	—	86	1	no	—
70	D₁₆	C₂×D₄₃	1	1	yes	characteristic
71	C₂×C₁₆	—	43	1	no	—
72	C₃₂	—	43	1	no	—
73	C₃₂	C₂×D₄₃	1	1	yes	characteristic, complemented
74	#41	—	172	1	no	—
75	C₂×D₄	—	172	1	no	—
76	Q₁₆	—	2	1	no	—
77	SD₁₆	—	172	1	no	—
78	D₈	—	2	1	no	—
79	D₈	—	86	1	no	—
80	D₈	—	86	1	no	—
81	D₈	—	172	1	no	—
82	C₂×C₈	—	43	1	no	—
83	C₁₆	—	43	1	no	—
84	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
85	C₂³	—	344	1	no	—
86	Q₈	—	4	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	344	1	no	—
89	D₄	—	344	1	no	—
90	D₄	—	172	1	no	—
91	D₄	—	172	1	no	—
92	C₂×C₄	—	43	1	no	—
93	C₂×C₄	—	344	1	no	—
94	C₈	—	43	1	no	—
95	C₈	D₄×D₄₃	1	1	yes	characteristic
96	C₂²	—	8	1	no	—
97	C₂²	—	43	1	no	—
98	C₂²	—	344	1	no	—
99	C₂²	—	344	1	no	—
100	C₂²	—	688	2	no	—
101	C₄	—	8	1	no	—
102	C₄	—	43	1	no	—
103	C₄	D₈×D₄₃	1	1	yes	characteristic
104	C₂	—	16	1	no	—
105	C₂	—	86	1	no	—
106	C₂	—	688	1	no	—
107	C₂	—	688	1	no	—
108	C₂	D₁₆×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583332

C₂

yes

maximal, characteristic, complemented

D₁₆×D₄₃

C₂

yes

maximal, characteristic, complemented

#14582736

C₂

yes

maximal, characteristic, complemented

D₁₃₇₆

C₂

yes

maximal, characteristic, complemented

#14582734

C₂

yes

maximal, characteristic, complemented

#14582732

C₂

yes

maximal, characteristic, complemented

C₄₃×SD₆₄

C₂

yes

maximal, characteristic, complemented

#13063348

—

D₈×D₄₃

—

#13063268

—

D₆₈₈

C₂²

yes

characteristic

D₆₈₈

C₂²

yes

characteristic, complemented

#13063266

—

C₁₆×D₄₃

C₂²

yes

characteristic

C₄₃⋊C₃₂

C₂²

yes

characteristic, complemented

Q₃₂×C₄₃

C₂²

yes

characteristic, complemented

D₁₆×C₄₃

C₂²

yes

characteristic

C₃₂×C₄₃

C₂²

yes

characteristic, complemented

#10621902

—

D₄×D₄₃

—

Q₁₆×C₄₃

—

D₈×C₄₃

—

#10621884

—

#10621882

—

D₃₄₄

—

D₃₄₄

—

C₈×D₄₃

D₄

yes

characteristic

C₁₆×C₄₃

C₂³

yes

characteristic

C₄₃⋊C₁₆

D₄

yes

characteristic

C₂²×D₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

C₂²⋊D₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

D₈

yes

characteristic

C₈×C₄₃

C₂×D₄

yes

characteristic

C₄₃⋊C₈

D₈

yes

characteristic

C₂²×C₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

D₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×D₈

yes

characteristic

Dic₄₃

D₁₆

yes

characteristic

#2263

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×D₁₆

yes

characteristic

D₄₃

—

D₄₃

—

D₄₃

—

#508

—

C₂×D₁₆

—

SD₆₄

—

SD₆₄

D₄₃

yes

characteristic, complemented

D₃₂

—

D₃₂

—

M₆₄

—

C₄₃

#2263

yes

characteristic, complemented, Sylow

#135

—

C₂×D₈

—

Q₃₂

C₂×D₄₃

yes

characteristic, complemented

SD₃₂

—

D₁₆

—

D₁₆

—

D₁₆

—

D₁₆

C₂×D₄₃

yes

characteristic

C₂×C₁₆

—

C₃₂

—

C₃₂

C₂×D₄₃

yes

characteristic, complemented

#41

—

172

—

C₂×D₄

—

172

—

Q₁₆

—

SD₁₆

—

172

—

D₈

—

D₈

—

D₈

—

D₈

—

172

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂²×D₄₃

yes

characteristic

C₂³

—

344

—

Q₈

—

D₄

—

D₄

—

344

—

D₄

—

344

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

344

—

C₈

—

C₈

D₄×D₄₃

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

344

—

C₂²

—

344

—

100

C₂²

—

688

—

101

C₄

—

102

C₄

—

103

C₄

D₈×D₄₃

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

—

688

—

107

C₂

—

688

—

108

C₂

D₁₆×D₄₃

yes

characteristic

	subgroup	G/H
center	C₂	D₁₆×D₄₃
commutator	C₁₆×C₄₃	C₂³
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₄₃×SD₆₄	C₂
socle	C₂×C₄₃	C₂×D₁₆
hypercenter	SD₆₄	D₄₃
hypocenter	C₄₃	#2263
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

subgroup

G/H

center

C₂

D₁₆×D₄₃

commutator

C₁₆×C₄₃

C₂³

Frattini

C₁₆

C₂²×D₄₃

Fitting

C₄₃×SD₆₄

C₂

socle

C₂×C₄₃

C₂×D₁₆

hypercenter

SD₆₄

D₄₃

hypocenter

C₄₃

#2263

LCS

G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

N	H ≅ G/N	type
1. #14583332	C₂	semidirect
2. D₁₆×D₄₃	C₂	semidirect
3. #14582736	C₂	semidirect
4. D₁₃₇₆	C₂	semidirect
5. #14582734	C₂	semidirect
6. #14582732	C₂	semidirect
7. C₄₃×SD₆₄	C₂	semidirect
12. D₆₈₈	C₂²	semidirect
15. C₄₃⋊C₃₂	C₂²	semidirect
16. Q₃₂×C₄₃	C₂²	semidirect
18. C₃₂×C₄₃	C₂²	semidirect
58. SD₆₄	D₄₃	semidirect
62. C₄₃	#2263	semidirect
65. Q₃₂	C₂×D₄₃	semidirect
73. C₃₂	C₂×D₄₃	semidirect

H ≅ G/N

type

1. #14583332

C₂

semidirect

2. D₁₆×D₄₃

C₂

semidirect

3. #14582736

C₂

semidirect

4. D₁₃₇₆

C₂

semidirect

5. #14582734

C₂

semidirect

6. #14582732

C₂

semidirect

7. C₄₃×SD₆₄

C₂

semidirect

12. D₆₈₈

C₂²

semidirect

15. C₄₃⋊C₃₂

C₂²

semidirect

16. Q₃₂×C₄₃

C₂²

semidirect

18. C₃₂×C₄₃

C₂²

semidirect

58. SD₆₄

D₄₃

semidirect

62. C₄₃

#2263

semidirect

65. Q₃₂

C₂×D₄₃

semidirect

73. C₃₂

C₂×D₄₃

semidirect

Subgroups — #19136909

Conjugacy classes of subgroups

Complements