Group #19148169 — subgroups

Subgroups — Q₈²×D₄₃ #19148169

Order 5504.

1112 conjugacy classes of subgroups; only the 575 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 575 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×Dic₈₆	C₂	1	6	yes	maximal, complemented
2	#14583629	C₂	1	9	yes	maximal, complemented
3	C₄⋊Q₈×D₄₃	C₂	1	9	yes	maximal
4	C₄×Q₈×D₄₃	C₂	1	6	yes	maximal
5	Q₈²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×D₄₃	C₂²	1	6	yes	—
7	C₂×Q₈×D₄₃	C₂²	1	2	yes	—
8	#13063325	C₂²	1	9	yes	—
9	#13063324	C₂²	1	36	yes	—
10	#13063323	C₂²	1	18	yes	—
11	Q₈×Dic₄₃	C₂²	1	6	yes	—
12	C₄×Dic₈₆	C₂²	1	18	yes	—
13	#13063290	C₂²	1	18	yes	—
14	C₄⋊C₄×D₄₃	C₂²	1	18	yes	—
15	C₄²×D₄₃	C₂²	1	9	yes	—
16	C₄⋊Q₈×C₄₃	C₂²	1	9	yes	—
17	C₄×Q₈×C₄₃	C₂²	1	6	yes	—
18	C₂×Q₈×C₄₃	C₂³	1	6	yes	—
19	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
20	Q₈×D₄₃	—	4	12	no	—
21	Q₈×D₄₃	Q₈	1	16	yes	direct product factor
22	C₂×C₄×D₄₃	C₂³	1	9	yes	—
23	C₂×C₄×D₄₃	C₂³	1	6	yes	—
24	C₂×Dic₈₆	C₂³	1	18	yes	—
25	C₂×Dic₈₆	C₂³	1	6	yes	—
26	C₄⋊C₄×C₄₃	C₂³	1	18	yes	—
27	C₄²×C₄₃	C₂³	1	9	yes	—
28	C₄⋊Dic₄₃	C₂³	1	18	yes	—
29	Dic₄₃⋊C₄	C₂³	1	36	yes	—
30	C₄×Dic₄₃	C₂³	1	9	yes	—
31	C₄×Dic₄₃	C₂³	1	18	yes	—
32	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
33	Q₈×C₄₃	—	4	6	no	—
34	Q₈×C₄₃	C₂×Q₈	1	8	yes	complemented
35	C₂×C₄×C₄₃	C₂⁴	1	9	yes	—
36	C₂×C₄×C₄₃	C₂⁴	1	6	yes	—
37	C₂×Dic₄₃	C₂⁴	1	9	yes	—
38	C₂×Dic₄₃	C₂⁴	1	6	yes	—
39	C₄×D₄₃	—	2	18	no	—
40	C₄×D₄₃	C₂×Q₈	1	24	yes	—
41	Dic₈₆	—	4	18	no	—
42	Dic₈₆	C₂×Q₈	1	24	yes	complemented
43	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
44	C₂×D₄₃	C₂²×Q₈	1	4	yes	—
45	C₂×D₄₃	H(5,𝔽₂)	1	2	yes	—
46	C₄×C₄₃	—	2	9	no	—
47	C₄×C₄₃	C₂²×Q₈	1	12	yes	—
48	Dic₄₃	—	2	9	no	—
49	Dic₄₃	C₂²×Q₈	1	12	yes	—
50	C₂×Q₈²	—	43	1	no	maximal, Sylow
51	C₂×C₄₃	C₂³×Q₈	1	2	yes	—
52	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
53	D₄₃	Q₈²	1	4	yes	direct product factor
54	Q₈²	—	43	9	no	—
55	Q₈²	—	43	6	no	—
56	Q₈²	D₄₃	1	1	yes	characteristic, direct product factor
57	C₂×C₄⋊Q₈	—	43	9	no	—
58	C₂×C₄×Q₈	—	43	6	no	—
59	C₄₃	C₂×Q₈²	1	1	yes	characteristic, complemented, Sylow
60	C₂²×Q₈	—	43	2	no	—
61	C₂²×Q₈	—	43	6	no	—
62	C₄⋊Q₈	—	43	18	no	—
63	C₄⋊Q₈	—	43	36	no	—
64	C₄⋊Q₈	—	43	9	no	—
65	C₄⋊Q₈	C₂×D₄₃	1	9	yes	—
66	C₄×Q₈	—	43	6	no	—
67	C₄×Q₈	—	43	18	no	—
68	C₄×Q₈	—	43	18	no	—
69	C₄×Q₈	C₂×D₄₃	1	6	yes	—
70	C₂×C₄⋊C₄	—	43	18	no	—
71	C₂×C₄²	—	43	9	no	—
72	C₂×Q₈	—	43	16	no	—
73	C₂×Q₈	—	43	6	no	—
74	C₂×Q₈	—	43	18	no	—
75	C₂×Q₈	—	172	12	no	—
76	C₂×Q₈	C₂²×D₄₃	1	6	yes	—
77	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
78	C₂²×C₄	—	43	6	no	—
79	C₂²×C₄	—	43	9	no	—
80	C₄⋊C₄	—	43	36	no	—
81	C₄⋊C₄	—	43	18	no	—
82	C₄⋊C₄	C₂²×D₄₃	1	18	yes	—
83	C₄²	—	43	9	no	—
84	C₄²	—	43	18	no	—
85	C₄²	C₂²×D₄₃	1	9	yes	—
86	C₂³	—	43	1	no	—
87	Q₈	—	4	6	no	—
88	Q₈	—	43	24	no	—
89	Q₈	—	172	18	no	—
90	Q₈	Q₈×D₄₃	1	8	yes	direct product factor
91	C₂×C₄	—	43	6	no	—
92	C₂×C₄	—	43	24	no	—
93	C₂×C₄	—	43	9	no	—
94	C₂×C₄	—	86	18	no	—
95	C₂×C₄	C₂³×D₄₃	1	9	yes	—
96	C₂×C₄	C₂³×D₄₃	1	6	yes	—
97	C₂²	—	43	4	no	—
98	C₂²	—	43	2	no	—
99	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
100	C₄	—	2	9	no	—
101	C₄	—	43	12	no	—
102	C₄	—	86	9	no	—
103	C₄	C₂×Q₈×D₄₃	1	12	yes	—
104	C₂	—	43	4	no	—
105	C₂	C₂²×Q₈×D₄₃	1	2	yes	—
106	C₂	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₈₆

C₂

yes

maximal, complemented

#14583629

C₂

yes

maximal, complemented

C₄⋊Q₈×D₄₃

C₂

yes

maximal

C₄×Q₈×D₄₃

C₂

yes

maximal

Q₈²×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₄₃

C₂²

yes

—

C₂×Q₈×D₄₃

C₂²

yes

—

#13063325

C₂²

yes

—

#13063324

C₂²

yes

—

#13063323

C₂²

yes

—

Q₈×Dic₄₃

C₂²

yes

—

C₄×Dic₈₆

C₂²

yes

—

#13063290

C₂²

yes

—

C₄⋊C₄×D₄₃

C₂²

yes

—

C₄²×D₄₃

C₂²

yes

—

C₄⋊Q₈×C₄₃

C₂²

yes

—

C₄×Q₈×C₄₃

C₂²

yes

—

C₂×Q₈×C₄₃

C₂³

yes

—

C₂×Q₈×C₄₃

C₂³

yes

—

Q₈×D₄₃

—

Q₈×D₄₃

Q₈

yes

direct product factor

C₂×C₄×D₄₃

C₂³

yes

—

C₂×C₄×D₄₃

C₂³

yes

—

C₂×Dic₈₆

C₂³

yes

—

C₂×Dic₈₆

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄²×C₄₃

C₂³

yes

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

C₂³

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₂²×D₄₃

C₂⁴

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

C₂×Q₈

yes

complemented

C₂×C₄×C₄₃

C₂⁴

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

—

C₂×Dic₄₃

C₂⁴

yes

—

C₂×Dic₄₃

C₂⁴

yes

—

C₄×D₄₃

—

C₄×D₄₃

C₂×Q₈

yes

—

Dic₈₆

—

Dic₈₆

C₂×Q₈

yes

complemented

C₂²×C₄₃

C₂⁵

yes

characteristic

C₂×D₄₃

C₂²×Q₈

yes

—

C₂×D₄₃

H(5,𝔽₂)

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂²×Q₈

yes

—

Dic₄₃

—

Dic₄₃

C₂²×Q₈

yes

—

C₂×Q₈²

—

maximal, Sylow

C₂×C₄₃

C₂³×Q₈

yes

—

C₂×C₄₃

C₂×H(5,𝔽₂)

yes

characteristic

D₄₃

Q₈²

yes

direct product factor

Q₈²

—

Q₈²

—

Q₈²

D₄₃

yes

characteristic, direct product factor

C₂×C₄⋊Q₈

—

C₂×C₄×Q₈

—

C₄₃

C₂×Q₈²

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

172

—

C₂×Q₈

C₂²×D₄₃

yes

—

C₂×Q₈

C₂²×D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₃

yes

—

C₂³

—

Q₈

—

Q₈

—

Q₈

—

172

—

Q₈

Q₈×D₄₃

yes

direct product factor

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂³×D₄₃

yes

—

C₂×C₄

C₂³×D₄₃

yes

—

C₂²

—

C₂²

—

C₂²

C₂⁴×D₄₃

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

C₂×Q₈×D₄₃

yes

—

104

C₂

—

105

C₂

C₂²×Q₈×D₄₃

yes

—

106

C₂

H(5,𝔽₂)×D₄₃

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	Q₈²×C₄₃	C₂
hypercenter	Q₈²	D₄₃
hypocenter	C₄₃	C₂×Q₈²
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ Q₈²

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₄₃

commutator, socle

C₂²×C₄₃

C₂⁵

Fitting

Q₈²×C₄₃

C₂

hypercenter

Q₈²

D₄₃

hypocenter

C₄₃

C₂×Q₈²

LCS

G ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ Q₈²

N	H ≅ G/N	type
1. Q₈×Dic₈₆	C₂	semidirect
2. #14583629	C₂	semidirect
5. Q₈²×C₄₃	C₂	semidirect
21. Q₈×D₄₃	Q₈	direct (N × H)
34. Q₈×C₄₃	C₂×Q₈	semidirect
42. Dic₈₆	C₂×Q₈	semidirect
53. D₄₃	Q₈²	direct (N × H)
56. Q₈²	D₄₃	direct (N × H)
59. C₄₃	C₂×Q₈²	semidirect
90. Q₈	Q₈×D₄₃	direct (N × H)

H ≅ G/N

type

1. Q₈×Dic₈₆

C₂

semidirect

2. #14583629

C₂

semidirect

5. Q₈²×C₄₃

C₂

semidirect

21. Q₈×D₄₃

Q₈

direct (N × H)

34. Q₈×C₄₃

C₂×Q₈

semidirect

42. Dic₈₆

C₂×Q₈

semidirect

53. D₄₃

Q₈²

direct (N × H)

56. Q₈²

D₄₃

direct (N × H)

59. C₄₃

C₂×Q₈²

semidirect

90. Q₈

Q₈×D₄₃

direct (N × H)

Subgroups — Q₈²×D₄₃ #19148169

Conjugacy classes of subgroups

Complements

Subgroups — Q82×D43 #19148169

Conjugacy classes of subgroups

Complements

Subgroups — Q₈²×D₄₃ #19148169