Group #22590187 — subgroups

Subgroups — D₁₆×Dic₇₁ #22590187

Order 9088.

174 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 67 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	D₈×Dic₇₁	C₂	1	2	yes	maximal, complemented
2	#17985825	C₂	1	1	yes	maximal, characteristic, complemented
3	#17985800	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
6	D₄×Dic₇₁	—	2	2	no	—
7	C₂×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
8	#14556062	C₂²	1	2	yes	—
9	#14556049	—	2	2	no	—
10	C₈×Dic₇₁	C₂²	1	1	yes	characteristic
11	C₂×D₈×C₇₁	C₂²	1	2	yes	—
12	D₁₆×C₇₁	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
14	C₂²×Dic₇₁	—	4	2	no	—
15	C₂×C₇₁⋊C₈	D₄	1	1	yes	characteristic
16	C₄⋊Dic₇₁	—	2	2	no	—
17	C₂²⋊Dic₇₁	—	4	2	no	—
18	C₄×Dic₇₁	D₄	1	1	yes	characteristic
19	C₇₁⋊C₁₆	—	2	1	no	—
20	C₂×D₄×C₇₁	—	2	2	no	—
21	D₈×C₇₁	—	2	2	no	—
22	D₈×C₇₁	C₂×C₄	1	4	yes	complemented
23	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
24	C₁₆×C₇₁	C₂×C₄	1	2	yes	complemented
25	C₂³×C₇₁	—	4	2	no	—
26	D₄×C₇₁	—	2	4	no	—
27	D₄×C₇₁	—	4	2	no	—
28	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₇₁	—	4	2	no	—
30	C₂×Dic₇₁	—	8	4	no	—
31	C₂×Dic₇₁	D₈	1	1	yes	characteristic
32	C₂×Dic₇₁	D₈	1	1	yes	characteristic
33	C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₇₁	#41	1	1	yes	characteristic
35	C₇₁⋊C₈	—	2	1	no	—
36	C₂²×C₇₁	—	4	4	no	—
37	C₂²×C₇₁	—	8	2	no	—
38	C₂²×C₇₁	—	8	2	no	—
39	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
40	C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
41	C₄×C₇₁	#135	1	1	yes	characteristic
42	Dic₇₁	—	2	1	no	—
43	Dic₇₁	—	8	2	no	—
44	Dic₇₁	D₁₆	1	2	yes	direct product factor
45	C₂×C₇₁	—	8	4	no	—
46	C₂×C₇₁	C₄×D₈	1	1	yes	characteristic
47	C₂×C₇₁	C₂×D₁₆	1	1	yes	characteristic
48	C₂×C₇₁	#508	1	1	yes	characteristic
49	C₄×D₁₆	—	71	1	no	maximal, Sylow
50	C₇₁	C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₁₆	D₇₁	1	1	yes	characteristic
52	C₄×D₈	—	71	2	no	—
53	#366	—	71	1	no	—
54	#357	—	71	2	no	—
55	C₄×C₁₆	—	71	1	no	—
56	C₂×D₈	C₂×D₇₁	1	2	yes	—
57	C₄×D₄	—	142	2	no	—
58	D₁₆	Dic₇₁	1	4	yes	direct product factor
59	C₂×C₁₆	—	71	1	no	—
60	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
61	#107	—	71	2	no	—
62	#102	—	142	2	no	—
63	C₄×C₈	—	71	1	no	—
64	C₂×D₄	—	2	2	no	—
65	C₂²×C₄	—	284	2	no	—
66	D₈	—	2	2	no	—
67	D₈	C₂×Dic₇₁	1	4	yes	complemented
68	C₂×C₈	—	71	1	no	—
69	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
70	C₄⋊C₄	—	142	2	no	—
71	C₂²⋊C₄	—	284	2	no	—
72	C₄²	—	71	1	no	—
73	C₁₆	—	142	1	no	—
74	C₁₆	C₂×Dic₇₁	1	2	yes	complemented
75	C₂³	—	4	2	no	—
76	D₄	—	2	4	no	—
77	D₄	—	4	2	no	—
78	C₂×C₄	—	284	2	no	—
79	C₂×C₄	—	568	4	no	—
80	C₂×C₄	—	71	1	no	—
81	C₂×C₄	—	71	1	no	—
82	C₂×C₄	D₄×D₇₁	1	1	yes	characteristic
83	C₈	—	142	1	no	—
84	C₈	C₂²×Dic₇₁	1	1	yes	characteristic
85	C₈	#11765864	1	1	yes	characteristic
86	C₂²	—	4	4	no	—
87	C₂²	—	8	2	no	—
88	C₂²	—	8	2	no	—
89	C₂²	D₈×D₇₁	1	1	yes	characteristic
90	C₄	—	568	2	no	—
91	C₄	—	71	2	no	—
92	C₄	—	142	1	no	—
93	C₄	D₄×Dic₇₁	1	1	yes	characteristic
94	C₄	#14556147	1	1	yes	characteristic
95	C₂	—	8	4	no	—
96	C₂	D₈×Dic₇₁	1	1	yes	characteristic
97	C₂	D₁₆×D₇₁	1	1	yes	characteristic
98	C₂	#17986428	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₈×Dic₇₁

C₂

yes

maximal, complemented

#17985825

C₂

yes

maximal, characteristic, complemented

#17985800

C₂

yes

maximal, complemented

C₁₆×Dic₇₁

C₂

yes

maximal, characteristic, complemented

C₂×D₁₆×C₇₁

C₂

yes

maximal, characteristic

D₄×Dic₇₁

—

C₂×C₇₁⋊C₁₆

C₂²

yes

characteristic

#14556062

C₂²

yes

—

#14556049

—

C₈×Dic₇₁

C₂²

yes

characteristic

C₂×D₈×C₇₁

C₂²

yes

—

D₁₆×C₇₁

C₄

yes

complemented

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₂²×Dic₇₁

—

C₂×C₇₁⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₁

—

C₂²⋊Dic₇₁

—

C₄×Dic₇₁

D₄

yes

characteristic

C₇₁⋊C₁₆

—

C₂×D₄×C₇₁

—

D₈×C₇₁

—

D₈×C₇₁

C₂×C₄

yes

complemented

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₁₆×C₇₁

C₂×C₄

yes

complemented

C₂³×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

D₈

yes

characteristic

C₂×Dic₇₁

D₈

yes

characteristic

C₈×C₇₁

C₂²×C₄

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×D₈

yes

characteristic

C₄×C₇₁

C₄×D₄

yes

characteristic

C₄×C₇₁

#135

yes

characteristic

Dic₇₁

—

Dic₇₁

—

Dic₇₁

D₁₆

yes

direct product factor

C₂×C₇₁

—

C₂×C₇₁

C₄×D₈

yes

characteristic

C₂×C₇₁

C₂×D₁₆

yes

characteristic

C₂×C₇₁

#508

yes

characteristic

C₄×D₁₆

—

maximal, Sylow

C₇₁

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₁₆

D₇₁

yes

characteristic

C₄×D₈

—

#366

—

#357

—

C₄×C₁₆

—

C₂×D₈

C₂×D₇₁

yes

—

C₄×D₄

—

142

—

D₁₆

Dic₇₁

yes

direct product factor

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₁

yes

characteristic

#107

—

#102

—

142

—

C₄×C₈

—

C₂×D₄

—

C₂²×C₄

—

284

—

D₈

—

D₈

C₂×Dic₇₁

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

284

—

C₄²

—

C₁₆

—

142

—

C₁₆

C₂×Dic₇₁

yes

complemented

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

284

—

C₂×C₄

—

568

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₇₁

yes

characteristic

C₈

—

142

—

C₈

C₂²×Dic₇₁

yes

characteristic

C₈

#11765864

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

D₈×D₇₁

yes

characteristic

C₄

—

568

—

C₄

—

C₄

—

142

—

C₄

D₄×Dic₇₁

yes

characteristic

C₄

#14556147

yes

characteristic

C₂

—

C₂

D₈×Dic₇₁

yes

characteristic

C₂

D₁₆×D₇₁

yes

characteristic

C₂

#17986428

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₁
commutator	C₈×C₇₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₂×D₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	C₂×D₁₆	D₇₁
hypocenter	C₇₁	C₄×D₁₆
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

subgroup

G/H

center

C₂²

D₈×D₇₁

commutator

C₈×C₇₁

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₂×D₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂×D₈

hypercenter

C₂×D₁₆

D₇₁

hypocenter

C₇₁

C₄×D₁₆

LCS

G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

N	H ≅ G/N	type
1. D₈×Dic₇₁	C₂	semidirect
2. #17985825	C₂	semidirect
3. #17985800	C₂	semidirect
4. C₁₆×Dic₇₁	C₂	semidirect
12. D₁₆×C₇₁	C₄	semidirect
22. D₈×C₇₁	C₂×C₄	semidirect
24. C₁₆×C₇₁	C₂×C₄	semidirect
44. Dic₇₁	D₁₆	direct (N × H)
50. C₇₁	C₄×D₁₆	semidirect
58. D₁₆	Dic₇₁	direct (N × H)
67. D₈	C₂×Dic₇₁	semidirect
74. C₁₆	C₂×Dic₇₁	semidirect

H ≅ G/N

type

1. D₈×Dic₇₁

C₂

semidirect

2. #17985825

C₂

semidirect

3. #17985800

C₂

semidirect

4. C₁₆×Dic₇₁

C₂

semidirect

12. D₁₆×C₇₁

C₄

semidirect

22. D₈×C₇₁

C₂×C₄

semidirect

24. C₁₆×C₇₁

C₂×C₄

semidirect

44. Dic₇₁

D₁₆

direct (N × H)

50. C₇₁

C₄×D₁₆

semidirect

58. D₁₆

Dic₇₁

direct (N × H)

67. D₈

C₂×Dic₇₁

semidirect

74. C₁₆

C₂×Dic₇₁

semidirect

Subgroups — D₁₆×Dic₇₁ #22590187

Conjugacy classes of subgroups

Complements

Subgroups — D16×Dic71 #22590187

Conjugacy classes of subgroups

Complements

Subgroups — D₁₆×Dic₇₁ #22590187