Group #19133402 — subgroups

Subgroups — Q₁₆×C₄₃⋊C₈ #19133402

Order 5504.

164 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 89 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	Q₈×C₄₃⋊C₈	C₂	1	2	yes	maximal
2	#14582652	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal
4	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₄×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
7	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₄×C₄₃⋊C₈	—	2	2	no	—
9	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×Q₁₆×C₄₃	C₄	1	1	yes	characteristic
12	C₄×Q₈×C₄₃	C₂²	1	2	yes	—
13	#107×C₄₃	C₄	1	1	yes	characteristic
14	#103×C₄₃	C₄	1	2	yes	—
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₄₃	C₂×C₄	1	2	yes	—
17	Q₁₆×C₄₃	C₈	1	4	yes	complemented
18	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₄⋊C₄×C₄₃	—	2	2	no	—
21	C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
22	C₄²×C₄₃	—	2	2	no	—
23	C₄²×C₄₃	C₂³	1	1	yes	characteristic
24	C₂×C₄₃⋊C₈	—	2	1	no	—
25	C₂×C₄₃⋊C₈	—	2	2	no	—
26	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
27	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
28	Q₈×C₄₃	—	2	2	no	—
29	Q₈×C₄₃	C₂×C₈	1	4	yes	—
30	C₂×C₄×C₄₃	—	2	2	no	—
31	C₂×C₄×C₄₃	—	2	2	no	—
32	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
35	C₈×C₄₃	—	2	1	no	—
36	C₈×C₄₃	C₂×C₈	1	2	yes	—
37	C₄₃⋊C₈	—	2	2	no	—
38	C₄₃⋊C₈	—	2	1	no	—
39	C₄₃⋊C₈	—	4	2	no	—
40	C₄₃⋊C₈	Q₁₆	1	2	yes	direct product factor
41	C₂²×C₄₃	C₄×D₄	1	1	yes	characteristic
42	C₄×C₄₃	—	2	4	no	—
43	C₄×C₄₃	—	2	1	no	—
44	C₄×C₄₃	—	4	2	no	—
45	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
46	C₄×C₄₃	#131	1	1	yes	characteristic
47	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
48	C₄×C₄₃	#135	1	1	yes	characteristic
49	C₈×Q₁₆	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	C₈×D₄	1	1	yes	characteristic
51	C₂×C₄₃	C₄×Q₁₆	1	1	yes	characteristic
52	C₂×C₄₃	#443	1	1	yes	characteristic
53	C₈×Q₈	—	43	2	no	—
54	C₄×Q₁₆	D₄₃	1	1	yes	characteristic
55	#335	—	43	1	no	—
56	Q₈⋊C₈	—	43	2	no	—
57	C₈²	—	43	1	no	—
58	C₄₃	C₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	Dic₄₃	1	1	yes	characteristic
60	C₄×Q₈	C₂×D₄₃	1	2	yes	—
61	#107	Dic₄₃	1	1	yes	characteristic
62	C₄⋊C₈	—	43	2	no	—
63	C₄⋊C₈	—	86	2	no	—
64	#103	Dic₄₃	1	2	yes	—
65	C₄×C₈	—	43	1	no	—
66	C₄×C₈	—	43	1	no	—
67	C₄×C₈	—	86	2	no	—
68	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
69	C₂×Q₈	C₂×Dic₄₃	1	2	yes	—
70	Q₁₆	C₄₃⋊C₈	1	4	yes	direct product factor
71	C₂×C₈	—	43	1	no	—
72	C₂×C₈	—	43	1	no	—
73	C₂×C₈	—	86	1	no	—
74	C₂×C₈	—	86	2	no	—
75	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
76	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
79	C₄²	—	2	2	no	—
80	C₄²	C₂²×D₄₃	1	1	yes	characteristic
81	Q₈	—	2	2	no	—
82	Q₈	C₂×C₄₃⋊C₈	1	4	yes	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
86	C₂×C₄	#10621900	1	1	yes	characteristic
87	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	43	2	no	—
90	C₈	—	86	2	no	—
91	C₈	—	86	1	no	—
92	C₈	—	172	2	no	—
93	C₈	C₂×C₄₃⋊C₈	1	2	yes	—
94	C₂²	D₄×Dic₄₃	1	1	yes	characteristic
95	C₄	—	2	4	no	—
96	C₄	—	2	1	no	—
97	C₄	—	4	2	no	—
98	C₄	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
99	C₄	#13063332	1	1	yes	characteristic
100	C₄	Q₁₆×D₄₃	1	1	yes	characteristic
101	C₄	#13063348	1	1	yes	characteristic
102	C₂	D₄×C₄₃⋊C₈	1	1	yes	characteristic
103	C₂	Q₁₆×Dic₄₃	1	1	yes	characteristic
104	C₂	#14583016	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×C₄₃⋊C₈

C₂

yes

maximal

#14582652

C₂

yes

maximal, characteristic

Q₈⋊(C₄₃⋊C₈)

C₂

yes

maximal

C₈×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₄₃

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄×C₄₃⋊C₈

—

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₄×C₄₃⋊C₈

C₂²

yes

characteristic

C₂×Q₁₆×C₄₃

C₄

yes

characteristic

C₄×Q₈×C₄₃

C₂²

yes

—

#107×C₄₃

C₄

yes

characteristic

#103×C₄₃

C₄

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

C₂×C₄

yes

—

Q₁₆×C₄₃

C₈

yes

complemented

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₈×C₄₃

—

C₈×C₄₃

C₂×C₈

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

Q₁₆

yes

direct product factor

C₂²×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²×C₈

yes

characteristic

C₄×C₄₃

#131

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₄×C₄₃

#135

yes

characteristic

C₈×Q₁₆

—

maximal, Sylow

C₂×C₄₃

C₈×D₄

yes

characteristic

C₂×C₄₃

C₄×Q₁₆

yes

characteristic

C₂×C₄₃

#443

yes

characteristic

C₈×Q₈

—

C₄×Q₁₆

D₄₃

yes

characteristic

#335

—

Q₈⋊C₈

—

C₈²

—

C₄₃

C₈×Q₁₆

yes

characteristic, complemented, Sylow

C₂×Q₁₆

Dic₄₃

yes

characteristic

C₄×Q₈

C₂×D₄₃

yes

—

#107

Dic₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#103

Dic₄₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

C₂×Dic₄₃

yes

—

Q₁₆

C₄₃⋊C₈

yes

direct product factor

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₂×Dic₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₄₃

yes

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

C₂×C₄₃⋊C₈

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₄₃

yes

characteristic

C₂×C₄

#10621900

yes

characteristic

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

172

—

C₈

C₂×C₄₃⋊C₈

yes

—

C₂²

D₄×Dic₄₃

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₂²×C₄₃⋊C₈

yes

characteristic

C₄

#13063332

yes

characteristic

100

C₄

Q₁₆×D₄₃

yes

characteristic

101

C₄

#13063348

yes

characteristic

102

C₂

D₄×C₄₃⋊C₈

yes

characteristic

103

C₂

Q₁₆×Dic₄₃

yes

characteristic

104

C₂

#14583016

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₈
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₄×D₄
hypercenter	C₄×Q₁₆	D₄₃
hypocenter	C₄₃	C₈×Q₁₆
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

subgroup

G/H

center

C₂×C₄

D₄×D₄₃

commutator

C₄×C₄₃

C₂²×C₈

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄×Q₁₆×C₄₃

C₂

socle

C₂²×C₄₃

C₄×D₄

hypercenter

C₄×Q₁₆

D₄₃

hypocenter

C₄₃

C₈×Q₁₆

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

N	H ≅ G/N	type
17. Q₁₆×C₄₃	C₈	semidirect
40. C₄₃⋊C₈	Q₁₆	direct (N × H)
58. C₄₃	C₈×Q₁₆	semidirect
70. Q₁₆	C₄₃⋊C₈	direct (N × H)

H ≅ G/N

type

17. Q₁₆×C₄₃

C₈

semidirect

40. C₄₃⋊C₈

Q₁₆

direct (N × H)

58. C₄₃

C₈×Q₁₆

semidirect

70. Q₁₆

C₄₃⋊C₈

direct (N × H)

Subgroups — Q₁₆×C₄₃⋊C₈ #19133402

Conjugacy classes of subgroups

Complements

Subgroups — Q16×C43⋊C8 #19133402

Conjugacy classes of subgroups

Complements

Subgroups — Q₁₆×C₄₃⋊C₈ #19133402