Group #22590161 — subgroups

Subgroups — C₁₆×D₂₈₄ #22590161

Order 9088.

174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 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	C₂×C₁₆×D₇₁	C₂	1	2	yes	maximal, complemented
2	C₈×D₂₈₄	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₇₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₇₁)⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇₁	C₂²	1	2	yes	—
7	C₄×D₂₈₄	C₄	1	1	yes	characteristic
8	C₂×C₇₁⋊C₁₆	C₂²	1	2	yes	—
9	C₁₆×D₇₁	—	2	4	no	—
10	C₄⋊(C₇₁⋊C₈)	C₄	1	1	yes	characteristic
11	(C₂×D₇₁)⋊C₈	C₄	1	2	yes	—
12	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×D₂₈₄	C₈	1	1	yes	characteristic
16	C₂×C₄×D₇₁	C₂×C₄	1	2	yes	—
17	C₂×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
18	C₈×D₇₁	—	2	2	no	—
19	C₈×D₇₁	—	2	2	no	—
20	C₄⋊Dic₇₁	C₈	1	1	yes	characteristic
21	(C₂×D₇₁)⋊C₄	C₈	1	2	yes	—
22	C₇₁⋊C₁₆	—	2	2	no	—
23	C₂×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
25	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
26	C₁₆×C₇₁	—	2	1	no	—
27	C₁₆×C₇₁	D₄	1	2	yes	complemented
28	C₂²×D₇₁	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₇₁	C₂×C₈	1	2	yes	—
33	D₂₈₄	C₁₆	1	4	yes	direct product factor
34	C₄×D₇₁	—	2	2	no	—
35	C₄×D₇₁	—	2	2	no	—
36	C₈×C₇₁	—	2	1	no	—
37	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
38	C₈×C₇₁	#41	1	1	yes	characteristic
39	C₇₁⋊C₈	—	2	2	no	—
40	C₂²×C₇₁	C₂²×C₈	1	1	yes	characteristic
41	C₂×D₇₁	—	2	2	no	—
42	C₂×D₇₁	—	2	2	no	—
43	C₂×D₇₁	C₂×C₁₆	1	4	yes	complemented
44	C₄×C₇₁	—	2	1	no	—
45	C₄×C₇₁	C₂×C₁₆	1	2	yes	complemented
46	C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
47	C₄×C₇₁	#131	1	1	yes	characteristic
48	Dic₇₁	—	2	2	no	—
49	C₂×C₇₁	C₈×D₄	1	1	yes	characteristic
50	C₂×C₇₁	C₂²×C₁₆	1	1	yes	characteristic
51	C₂×C₇₁	#504	1	1	yes	characteristic
52	D₇₁	—	2	4	no	—
53	D₄×C₁₆	—	71	1	no	maximal, Sylow
54	C₇₁	D₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₁₆	—	71	2	no	—
56	C₈×D₄	—	71	1	no	—
57	C₄⋊C₁₆	—	71	1	no	—
58	C₂²⋊C₁₆	—	71	2	no	—
59	C₄×C₁₆	D₇₁	1	1	yes	characteristic, complemented
60	C₂²×C₈	—	71	2	no	—
61	C₄×D₄	—	71	1	no	—
62	C₂×C₁₆	—	71	2	no	—
63	C₂×C₁₆	—	142	4	no	—
64	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
65	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
66	C₄⋊C₈	—	71	1	no	—
67	C₂²⋊C₈	—	71	2	no	—
68	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
69	C₂×D₄	—	71	1	no	—
70	C₂²×C₄	—	71	2	no	—
71	C₂×C₈	—	71	2	no	—
72	C₂×C₈	—	142	2	no	—
73	C₂×C₈	—	142	2	no	—
74	C₂×C₈	C₄×D₇₁	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
76	C₄⋊C₄	—	71	1	no	—
77	C₂²⋊C₄	—	71	2	no	—
78	C₄²	C₄×D₇₁	1	1	yes	characteristic
79	C₁₆	—	2	1	no	—
80	C₁₆	—	142	2	no	—
81	C₁₆	D₂₈₄	1	2	yes	direct product factor
82	C₂³	—	71	2	no	—
83	D₄	—	71	4	no	—
84	C₂×C₄	—	71	2	no	—
85	C₂×C₄	—	142	2	no	—
86	C₂×C₄	—	142	2	no	—
87	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
88	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
89	C₂×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
90	C₈	—	2	1	no	—
91	C₈	—	142	2	no	—
92	C₈	C₂×D₂₈₄	1	1	yes	characteristic
93	C₈	#11765865	1	1	yes	characteristic
94	C₂²	—	71	4	no	—
95	C₂²	—	142	2	no	—
96	C₂²	—	142	2	no	—
97	C₂²	C₂×C₈×D₇₁	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	142	2	no	—
100	C₄	C₁₆×D₇₁	1	2	yes	complemented
101	C₄	C₄×D₂₈₄	1	1	yes	characteristic
102	C₄	#14556134	1	1	yes	characteristic
103	C₂	—	142	4	no	—
104	C₂	C₈×D₂₈₄	1	1	yes	characteristic
105	C₂	C₂×C₁₆×D₇₁	1	1	yes	characteristic
106	C₂	#17986415	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₇₁

C₂

yes

maximal, complemented

C₈×D₂₈₄

C₂

yes

maximal, characteristic

C₄⋊(C₇₁⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

(C₂×D₇₁)⋊C₁₆

C₂

yes

maximal, complemented

C₄×C₁₆×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₁

C₂²

yes

—

C₄×D₂₈₄

C₄

yes

characteristic

C₂×C₇₁⋊C₁₆

C₂²

yes

—

C₁₆×D₇₁

—

C₄⋊(C₇₁⋊C₈)

C₄

yes

characteristic

(C₂×D₇₁)⋊C₈

C₄

yes

—

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×D₂₈₄

C₈

yes

characteristic

C₂×C₄×D₇₁

C₂×C₄

yes

—

C₂×C₇₁⋊C₈

C₂×C₄

yes

—

C₈×D₇₁

—

C₈×D₇₁

—

C₄⋊Dic₇₁

C₈

yes

characteristic

(C₂×D₇₁)⋊C₄

C₈

yes

—

C₇₁⋊C₁₆

—

C₂×C₈×C₇₁

C₂×C₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄²×C₇₁

C₂×C₄

yes

characteristic

C₁₆×C₇₁

—

C₁₆×C₇₁

D₄

yes

complemented

C₂²×D₇₁

C₂×C₈

yes

—

C₂×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

C₂²×C₄

yes

characteristic

C₂×Dic₇₁

C₂×C₈

yes

—

D₂₈₄

C₁₆

yes

direct product factor

C₄×D₇₁

—

C₄×D₇₁

—

C₈×C₇₁

—

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

C₂²×C₈

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

C₂×C₁₆

yes

complemented

C₄×C₇₁

—

C₄×C₇₁

C₂×C₁₆

yes

complemented

C₄×C₇₁

C₄×D₄

yes

characteristic

C₄×C₇₁

#131

yes

characteristic

Dic₇₁

—

C₂×C₇₁

C₈×D₄

yes

characteristic

C₂×C₇₁

C₂²×C₁₆

yes

characteristic

C₂×C₇₁

#504

yes

characteristic

D₇₁

—

D₄×C₁₆

—

maximal, Sylow

C₇₁

D₄×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₈×D₄

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

D₇₁

yes

characteristic, complemented

C₂²×C₈

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

—

142

—

C₂×C₁₆

C₂×D₇₁

yes

characteristic

C₂×C₁₆

C₂×D₇₁

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

142

—

C₂×C₈

—

142

—

C₂×C₈

C₄×D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₄×D₇₁

yes

characteristic

C₁₆

—

C₁₆

—

142

—

C₁₆

D₂₈₄

yes

direct product factor

C₂³

—

D₄

—

C₂×C₄

—

C₂×C₄

—

142

—

C₂×C₄

—

142

—

C₂×C₄

C₈×D₇₁

yes

characteristic

C₂×C₄

C₈×D₇₁

yes

characteristic

C₂×C₄

C₂×C₄×D₇₁

yes

characteristic

C₈

—

C₈

—

142

—

C₈

C₂×D₂₈₄

yes

characteristic

C₈

#11765865

yes

characteristic

C₂²

—

C₂²

—

142

—

C₂²

—

142

—

C₂²

C₂×C₈×D₇₁

yes

characteristic

C₄

—

C₄

—

142

—

100

C₄

C₁₆×D₇₁

yes

complemented

101

C₄

C₄×D₂₈₄

yes

characteristic

102

C₄

#14556134

yes

characteristic

103

C₂

—

142

—

104

C₂

C₈×D₂₈₄

yes

characteristic

105

C₂

C₂×C₁₆×D₇₁

yes

characteristic

106

C₂

#17986415

yes

characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₇₁
commutator	C₂×C₇₁	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂²×C₈
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	D₄×C₁₆
LCS	G ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₁₆

C₂×D₇₁

commutator

C₂×C₇₁

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₄×C₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂²×C₈

hypercenter

C₄×C₁₆

D₇₁

hypocenter

C₇₁

D₄×C₁₆

LCS

G ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. C₂×C₁₆×D₇₁	C₂	semidirect
3. C₄⋊(C₇₁⋊C₁₆)	C₂	semidirect
4. (C₂×D₇₁)⋊C₁₆	C₂	semidirect
5. C₄×C₁₆×C₇₁	C₂	semidirect
27. C₁₆×C₇₁	D₄	semidirect
33. D₂₈₄	C₁₆	direct (N × H)
43. C₂×D₇₁	C₂×C₁₆	semidirect
45. C₄×C₇₁	C₂×C₁₆	semidirect
54. C₇₁	D₄×C₁₆	semidirect
59. C₄×C₁₆	D₇₁	semidirect
81. C₁₆	D₂₈₄	direct (N × H)
100. C₄	C₁₆×D₇₁	semidirect

H ≅ G/N

type

1. C₂×C₁₆×D₇₁

C₂

semidirect

3. C₄⋊(C₇₁⋊C₁₆)

C₂

semidirect

4. (C₂×D₇₁)⋊C₁₆

C₂

semidirect

5. C₄×C₁₆×C₇₁

C₂

semidirect

27. C₁₆×C₇₁

D₄

semidirect

33. D₂₈₄

C₁₆

direct (N × H)

43. C₂×D₇₁

C₂×C₁₆

semidirect

45. C₄×C₇₁

C₂×C₁₆

semidirect

54. C₇₁

D₄×C₁₆

semidirect

59. C₄×C₁₆

D₇₁

semidirect

81. C₁₆

D₂₈₄

direct (N × H)

100. C₄

C₁₆×D₇₁

semidirect

Subgroups — C₁₆×D₂₈₄ #22590161

Conjugacy classes of subgroups

Complements

Subgroups — C16×D284 #22590161

Conjugacy classes of subgroups

Complements

Subgroups — C₁₆×D₂₈₄ #22590161