Group #22586296 — subgroups

Subgroups — #22586296

Order 9088.

110 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 47 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	C₈×D₂₈₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₇₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₇₁	—	2	1	no	—
5	C₄×D₂₈₄	C₄	1	1	yes	characteristic
6	C₂×C₇₁⋊C₁₆	—	2	1	no	—
7	C₄⋊(C₇₁⋊C₈)	C₄	1	1	yes	characteristic
8	(C₂×D₇₁)⋊C₈	—	2	1	no	—
9	C₂×C₁₆×C₇₁	—	2	1	no	—
10	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×D₂₈₄	C₈	1	1	yes	characteristic
12	C₂×C₄×D₇₁	—	2	1	no	—
13	C₂×C₇₁⋊C₈	—	2	1	no	—
14	C₈×D₇₁	—	4	1	no	—
15	C₈×D₇₁	—	4	1	no	—
16	C₄⋊Dic₇₁	C₈	1	1	yes	characteristic
17	(C₂×D₇₁)⋊C₄	—	2	1	no	—
18	C₇₁⋊C₁₆	—	4	1	no	—
19	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
21	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
22	C₁₆×C₇₁	—	2	2	no	—
23	C₂²×D₇₁	—	2	1	no	—
24	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₁	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₇₁	M₁₆	1	1	yes	characteristic
27	C₂×Dic₇₁	—	2	1	no	—
28	D₂₈₄	—	2	1	no	—
29	D₂₈₄	C₁₆	1	2	yes	complemented
30	C₄×D₇₁	—	4	1	no	—
31	C₄×D₇₁	—	4	1	no	—
32	C₈×C₇₁	—	2	1	no	—
33	C₈×C₇₁	D₈	1	1	yes	characteristic
34	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
35	C₇₁⋊C₈	—	4	1	no	—
36	C₂²×C₇₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₇₁	—	2	2	no	—
38	C₂×D₇₁	—	4	1	no	—
39	C₂×D₇₁	—	4	1	no	—
40	C₄×C₇₁	—	2	1	no	—
41	C₄×C₇₁	#102	1	1	yes	characteristic
42	C₄×C₇₁	#104	1	1	yes	characteristic
43	C₄×C₇₁	C₂×C₁₆	1	1	yes	characteristic
44	C₄×C₇₁	M₃₂	1	1	yes	characteristic
45	Dic₇₁	—	4	1	no	—
46	C₂×C₇₁	D₄⋊C₈	1	1	yes	characteristic
47	C₂×C₇₁	C₂²⋊C₁₆	1	1	yes	characteristic
48	C₂×C₇₁	#350	1	1	yes	characteristic
49	D₇₁	—	4	2	no	—
50	D₄⋊C₁₆	—	71	1	no	maximal, Sylow
51	C₇₁	D₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
52	C₈×D₄	—	71	1	no	—
53	C₄⋊C₁₆	—	71	1	no	—
54	C₄×C₁₆	D₇₁	1	1	yes	characteristic, complemented
55	C₂²×C₈	—	142	1	no	—
56	C₄×D₄	—	71	1	no	—
57	C₂×C₁₆	—	2	1	no	—
58	C₂×C₁₆	—	142	1	no	—
59	C₄⋊C₈	—	71	1	no	—
60	C₂²⋊C₈	—	142	1	no	—
61	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
62	C₂×D₄	—	71	1	no	—
63	C₂²×C₄	—	142	1	no	—
64	C₂×C₈	—	284	1	no	—
65	C₂×C₈	—	284	1	no	—
66	C₂×C₈	—	142	1	no	—
67	C₂×C₈	D₂₈₄	1	1	yes	characteristic
68	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
69	C₄⋊C₄	—	71	1	no	—
70	C₂²⋊C₄	—	142	1	no	—
71	C₄²	C₄×D₇₁	1	1	yes	characteristic
72	C₁₆	—	2	2	no	—
73	C₁₆	—	284	1	no	—
74	C₂³	—	142	1	no	—
75	D₄	—	71	2	no	—
76	D₄	—	142	1	no	—
77	C₂×C₄	—	284	1	no	—
78	C₂×C₄	—	284	1	no	—
79	C₂×C₄	—	142	1	no	—
80	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
81	C₂×C₄	C₈×D₇₁	1	1	yes	characteristic
82	C₂×C₄	#11765848	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	284	1	no	—
85	C₈	D₅₆₈	1	1	yes	characteristic
86	C₈	#11765854	1	1	yes	characteristic
87	C₂²	—	284	1	no	—
88	C₂²	—	284	1	no	—
89	C₂²	—	142	2	no	—
90	C₂²	(C₂×D₇₁)⋊C₈	1	1	yes	characteristic
91	C₄	—	2	1	no	—
92	C₄	—	284	1	no	—
93	C₄	#14556050	1	1	yes	characteristic
94	C₄	#14556056	1	1	yes	characteristic
95	C₄	C₁₆×D₇₁	1	1	yes	characteristic
96	C₄	#14556067	1	1	yes	characteristic
97	C₂	—	284	2	no	—
98	C₂	#17985728	1	1	yes	characteristic
99	C₂	(C₂×D₇₁)⋊C₁₆	1	1	yes	characteristic
100	C₂	#17985782	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×D₂₈₄

C₂

yes

maximal, characteristic

C₄⋊(C₇₁⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₇₁

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₁

—

C₄×D₂₈₄

C₄

yes

characteristic

C₂×C₇₁⋊C₁₆

—

C₄⋊(C₇₁⋊C₈)

C₄

yes

characteristic

(C₂×D₇₁)⋊C₈

—

C₂×C₁₆×C₇₁

—

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×D₂₈₄

C₈

yes

characteristic

C₂×C₄×D₇₁

—

C₂×C₇₁⋊C₈

—

C₈×D₇₁

—

C₈×D₇₁

—

C₄⋊Dic₇₁

C₈

yes

characteristic

(C₂×D₇₁)⋊C₄

—

C₇₁⋊C₁₆

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

D₄

yes

characteristic

C₄²×C₇₁

C₂×C₄

yes

characteristic

C₁₆×C₇₁

—

C₂²×D₇₁

—

C₂×C₄×C₇₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₁

C₂×C₈

yes

characteristic

C₂×C₄×C₇₁

M₁₆

yes

characteristic

C₂×Dic₇₁

—

D₂₈₄

—

D₂₈₄

C₁₆

yes

complemented

C₄×D₇₁

—

C₄×D₇₁

—

C₈×C₇₁

—

C₈×C₇₁

D₈

yes

characteristic

C₈×C₇₁

SD₁₆

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

C₂²⋊C₈

yes

characteristic

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

C₄×C₇₁

C₂×C₁₆

yes

characteristic

C₄×C₇₁

M₃₂

yes

characteristic

Dic₇₁

—

C₂×C₇₁

D₄⋊C₈

yes

characteristic

C₂×C₇₁

C₂²⋊C₁₆

yes

characteristic

C₂×C₇₁

#350

yes

characteristic

D₇₁

—

D₄⋊C₁₆

—

maximal, Sylow

C₇₁

D₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₈×D₄

—

C₄⋊C₁₆

—

C₄×C₁₆

D₇₁

yes

characteristic, complemented

C₂²×C₈

—

142

—

C₄×D₄

—

C₂×C₁₆

—

C₂×C₁₆

—

142

—

C₄⋊C₈

—

C₂²⋊C₈

—

142

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

142

—

C₂×C₈

—

284

—

C₂×C₈

—

284

—

C₂×C₈

—

142

—

C₂×C₈

D₂₈₄

yes

characteristic

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

142

—

C₄²

C₄×D₇₁

yes

characteristic

C₁₆

—

C₁₆

—

284

—

C₂³

—

142

—

D₄

—

D₄

—

142

—

C₂×C₄

—

284

—

C₂×C₄

—

284

—

C₂×C₄

—

142

—

C₂×C₄

(C₂×D₇₁)⋊C₄

yes

characteristic

C₂×C₄

C₈×D₇₁

yes

characteristic

C₂×C₄

#11765848

yes

characteristic

C₈

—

C₈

—

284

—

C₈

D₅₆₈

yes

characteristic

C₈

#11765854

yes

characteristic

C₂²

—

284

—

C₂²

—

284

—

C₂²

—

142

—

C₂²

(C₂×D₇₁)⋊C₈

yes

characteristic

C₄

—

C₄

—

284

—

C₄

yes

C₄

yes

C₄

C₁₆×D₇₁

yes

characteristic

C₄

#14556067

yes

characteristic

C₂

—

284

—

C₂

#17985728

yes

characteristic

C₂

(C₂×D₇₁)⋊C₁₆

yes

characteristic

100

C₂

#17985782

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₂₈₄
commutator	C₄×C₇₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₇₁
Fitting	C₄×C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂²⋊C₈
hypercenter	C₄×C₁₆	D₇₁
hypocenter	C₇₁	D₄⋊C₁₆
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₈

D₂₈₄

commutator

C₄×C₇₁

C₂×C₁₆

Frattini

C₄×C₈

C₂×D₇₁

Fitting

C₄×C₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂²⋊C₈

hypercenter

C₄×C₁₆

D₇₁

hypocenter

C₇₁

D₄⋊C₁₆

LCS

G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. C₄⋊(C₇₁⋊C₁₆)	C₂	semidirect
3. C₄×C₁₆×C₇₁	C₂	semidirect
29. D₂₈₄	C₁₆	semidirect
51. C₇₁	D₄⋊C₁₆	semidirect
54. C₄×C₁₆	D₇₁	semidirect

H ≅ G/N

type

2. C₄⋊(C₇₁⋊C₁₆)

C₂

semidirect

3. C₄×C₁₆×C₇₁

C₂

semidirect

29. D₂₈₄

C₁₆

semidirect

51. C₇₁

D₄⋊C₁₆

semidirect

54. C₄×C₁₆

D₇₁

semidirect

Subgroups — #22586296

Conjugacy classes of subgroups

Complements