Group #22590513 — subgroups

Subgroups — #22590513

Order 9088.

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

normal subgroups only

This group has 120 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	#17986117	C₂	1	1	yes	maximal, characteristic
2	#17985821	C₂	1	2	yes	maximal, complemented
3	#17985820	C₂	1	1	yes	maximal, characteristic, complemented
4	#17985808	C₂	1	2	yes	maximal
5	#499×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556150	C₂²	1	1	yes	characteristic
7	#14556134	—	2	1	no	—
8	#14556068	C₂²	1	2	yes	—
9	#14556064	C₂²	1	1	yes	characteristic
10	#14556056	—	2	1	no	—
11	#125×C₇₁	—	2	1	no	—
12	#107×C₇₁	—	2	1	no	—
13	#106×C₇₁	C₂²	1	2	yes	—
14	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
15	#11765865	—	2	1	no	—
16	Dic₂₈₄	Q₈	1	1	yes	characteristic
17	#11765854	—	2	1	no	—
18	D₅₆₈	Q₈	1	1	yes	characteristic
19	#11765849	—	2	1	no	—
20	#11765848	—	4	1	no	—
21	C₈×D₇₁	—	4	1	no	—
22	C₇₁⋊C₁₆	—	2	2	no	—
23	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₇₁	—	2	2	no	—
26	C₄⋊C₄×C₇₁	—	4	2	no	—
27	C₄²×C₇₁	D₄	1	1	yes	characteristic
28	C₂×C₄×C₇₁	—	2	1	no	—
29	C₂×C₄×C₇₁	—	4	2	no	—
30	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
31	C₂²⋊D₇₁	—	4	1	no	—
32	D₂₈₄	—	2	1	no	—
33	C₄×D₇₁	—	4	1	no	—
34	Dic₁₄₂	—	2	1	no	—
35	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
36	C₈×C₇₁	SD₁₆	1	1	yes	characteristic
37	C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
38	C₈×C₇₁	#41	1	1	yes	characteristic
39	C₇₁⋊C₈	—	4	1	no	—
40	C₂²×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
41	C₂×D₇₁	—	4	1	no	—
42	C₄×C₇₁	—	4	1	no	—
43	C₄×C₇₁	—	8	2	no	—
44	C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
45	C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
46	Dic₇₁	—	4	1	no	—
47	C₂×C₇₁	—	2	1	no	—
48	C₂×C₇₁	#476	1	1	yes	characteristic
49	D₇₁	—	8	1	no	—
50	#2231	—	71	1	no	maximal, Sylow
51	C₇₁	#2231	1	1	yes	characteristic, complemented, Sylow
52	#499	D₇₁	1	1	yes	characteristic, complemented
53	#443	—	71	1	no	—
54	#365	—	71	2	no	—
55	#364	—	71	1	no	—
56	#360	—	71	2	no	—
57	#135	—	71	1	no	—
58	#131	—	142	1	no	—
59	#125	—	2	1	no	—
60	M₃₂	—	71	2	no	—
61	#108	—	71	1	no	—
62	#107	—	2	1	no	—
63	#106	C₂×D₇₁	1	2	yes	—
64	#104	—	142	1	no	—
65	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
66	#41	—	142	1	no	—
67	Q₁₆	—	71	1	no	—
68	SD₁₆	—	142	1	no	—
69	D₈	—	71	1	no	—
70	M₁₆	—	284	1	no	—
71	M₁₆	—	142	1	no	—
72	C₂×C₈	—	284	1	no	—
73	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	4	2	no	—
77	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
78	C₁₆	—	142	2	no	—
79	Q₈	—	142	1	no	—
80	D₄	—	284	1	no	—
81	D₄	—	142	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	—	284	1	no	—
85	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
86	C₈	—	284	1	no	—
87	C₈	#11765852	1	1	yes	characteristic
88	C₈	#11765852	1	1	yes	characteristic
89	C₈	Q₈×D₇₁	1	1	yes	characteristic
90	C₈	#11765866	1	1	yes	characteristic
91	C₂²	—	284	1	no	—
92	C₂²	#14556154	1	1	yes	characteristic
93	C₄	—	4	1	no	—
94	C₄	—	8	2	no	—
95	C₄	—	284	1	no	—
96	C₄	#14556104	1	1	yes	characteristic
97	C₄	C₂×#11765852	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	568	1	no	—
100	C₂	#17986286	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986117

C₂

yes

maximal, characteristic

#17985821

C₂

yes

maximal, complemented

#17985820

C₂

yes

maximal, characteristic, complemented

#17985808

C₂

yes

maximal

#499×C₇₁

C₂

yes

maximal, characteristic, complemented

#14556150

C₂²

yes

characteristic

#14556134

—

#14556068

C₂²

yes

—

#14556064

C₂²

yes

characteristic

#14556056

—

#125×C₇₁

—

#107×C₇₁

—

#106×C₇₁

C₂²

yes

—

C₄×C₈×C₇₁

C₂²

yes

characteristic

#11765865

—

Dic₂₈₄

Q₈

yes

characteristic

#11765854

—

D₅₆₈

Q₈

yes

characteristic

#11765849

—

#11765848

—

C₈×D₇₁

—

C₇₁⋊C₁₆

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄⋊C₄×C₇₁

—

C₄⋊C₄×C₇₁

—

C₄²×C₇₁

D₄

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂²⋊D₇₁

—

D₂₈₄

—

C₄×D₇₁

—

Dic₁₄₂

—

C₈×C₇₁

SD₁₆

yes

characteristic

C₈×C₇₁

SD₁₆

yes

characteristic

C₈×C₇₁

C₂×Q₈

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₇₁⋊C₈

—

C₂²×C₇₁

AGL(1,ℤ/8)

yes

characteristic

C₂×D₇₁

—

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

C₂²⋊Q₈

yes

characteristic

C₄×C₇₁

C₂×SD₁₆

yes

characteristic

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#476

yes

characteristic

D₇₁

—

#2231

—

maximal, Sylow

C₇₁

#2231

yes

characteristic, complemented, Sylow

#499

D₇₁

yes

characteristic, complemented

—

—

—

—

—

—

142

—

#125

—

M₃₂

—

#108

—

#107

—

#106

C₂×D₇₁

yes

—

#104

—

142

—

C₄×C₈

C₂×D₇₁

yes

characteristic

#41

—

142

—

Q₁₆

—

SD₁₆

—

142

—

D₈

—

M₁₆

—

284

—

M₁₆

—

142

—

C₂×C₈

—

284

—

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₇₁

yes

characteristic

C₁₆

—

142

—

Q₈

—

142

—

D₄

—

284

—

D₄

—

142

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

284

—

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

C₈

—

284

—

C₈

yes

C₈

yes

C₈

Q₈×D₇₁

yes

characteristic

C₈

#11765866

yes

characteristic

C₂²

—

284

—

C₂²

#14556154

yes

characteristic

C₄

—

C₄

—

C₄

—

284

—

C₄

yes

C₄

yes

C₂

—

C₂

—

568

—

100

C₂

#17986286

yes

characteristic

	subgroup	G/H
center	C₂	#17986286
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#499×C₇₁	C₂
socle	C₂×C₇₁	#476
hypercenter	#499	D₇₁
hypocenter	C₇₁	#2231
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #499

subgroup

G/H

center

C₂

#17986286

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#499×C₇₁

C₂

C₂×C₇₁

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #499

N	H ≅ G/N	type
2. #17985821	C₂	semidirect
3. #17985820	C₂	semidirect
5. #499×C₇₁	C₂	semidirect
51. C₇₁	#2231	semidirect
52. #499	D₇₁	semidirect

H ≅ G/N

type

2. #17985821

C₂

semidirect

3. #17985820

C₂

semidirect

5. #499×C₇₁

C₂

semidirect

51. C₇₁

#2231

semidirect

52. #499

D₇₁

semidirect

Subgroups — #22590513

Conjugacy classes of subgroups

Complements