Group #22590571 — subgroups

Subgroups — #22590571

Order 9088.

138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 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	#17986401	C₂	1	1	yes	maximal, characteristic, complemented
2	#17985803	C₂	1	2	yes	maximal, complemented
3	#17985800	C₂	1	2	yes	maximal
4	C₄×C₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#495×C₇₁	C₂	1	1	yes	maximal, characteristic
6	#14556120	—	2	1	no	—
7	C₂×C₇₁⋊C₁₆	C₂²	1	2	yes	—
8	#14556062	C₂²	1	2	yes	—
9	#14556060	—	2	1	no	—
10	C₂×Q₁₆×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×SD₁₆×C₇₁	—	2	1	no	—
12	C₂×D₈×C₇₁	C₂²	1	1	yes	characteristic
13	#124×C₇₁	—	2	1	no	—
14	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₇₁	—	2	2	no	—
16	Dic₇₁⋊C₄	—	4	2	no	—
17	C₇₁⋊C₁₆	—	2	2	no	—
18	C₂×Q₈×C₇₁	—	2	1	no	—
19	C₂×D₄×C₇₁	—	2	1	no	—
20	Q₁₆×C₇₁	—	2	2	no	—
21	SD₁₆×C₇₁	—	4	2	no	—
22	D₈×C₇₁	—	2	2	no	—
23	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
24	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
25	C₂²⋊C₄×C₇₁	—	4	2	no	—
26	C₄²×C₇₁	D₄	1	1	yes	characteristic
27	C₂³×C₇₁	—	4	1	no	—
28	Q₈×C₇₁	—	4	1	no	—
29	Q₈×C₇₁	—	4	1	no	—
30	D₄×C₇₁	—	4	1	no	—
31	D₄×C₇₁	—	4	1	no	—
32	C₂×C₄×C₇₁	—	4	1	no	—
33	C₂×C₄×C₇₁	D₈	1	2	yes	—
34	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₁	—	4	2	no	—
36	C₈×C₇₁	SD₁₆	1	2	yes	—
37	C₈×C₇₁	#41	1	2	yes	—
38	C₂²×C₇₁	—	8	1	no	—
39	C₂²×C₇₁	—	8	2	no	—
40	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
41	C₄×C₇₁	—	2	2	no	—
42	C₄×C₇₁	—	8	1	no	—
43	C₄×C₇₁	#124	1	1	yes	characteristic
44	C₄×C₇₁	C₂×SD₁₆	1	1	yes	characteristic
45	Dic₇₁	—	8	2	no	—
46	C₂×C₇₁	—	16	1	no	—
47	C₂×C₇₁	#486	1	1	yes	characteristic
48	C₂×C₇₁	#508	1	2	yes	—
49	#2242	—	71	1	no	maximal, Sylow
50	C₇₁	#2242	1	1	yes	characteristic, complemented, Sylow
51	#499	—	71	1	no	—
52	#495	D₇₁	1	1	yes	characteristic
53	#358	—	71	2	no	—
54	#357	—	71	2	no	—
55	C₄×C₁₆	—	71	1	no	—
56	C₂×Q₁₆	C₂×D₇₁	1	1	yes	characteristic
57	C₂×SD₁₆	—	2	1	no	—
58	C₂×D₈	C₂×D₇₁	1	1	yes	characteristic
59	#125	—	142	1	no	—
60	#124	—	2	1	no	—
61	C₂×C₁₆	—	71	2	no	—
62	#107	—	71	2	no	—
63	#106	—	142	1	no	—
64	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
65	C₂×Q₈	—	2	1	no	—
66	C₂×D₄	—	2	1	no	—
67	Q₁₆	—	2	2	no	—
68	SD₁₆	—	4	2	no	—
69	D₈	—	2	2	no	—
70	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
72	C₄⋊C₄	—	284	2	no	—
73	C₄⋊C₄	—	142	2	no	—
74	C₂²⋊C₄	—	4	2	no	—
75	C₄²	C₂²⋊D₇₁	1	1	yes	characteristic
76	C₁₆	—	142	2	no	—
77	C₂³	—	4	1	no	—
78	Q₈	—	4	1	no	—
79	Q₈	—	4	1	no	—
80	D₄	—	4	1	no	—
81	D₄	—	4	1	no	—
82	C₂×C₄	—	4	1	no	—
83	C₂×C₄	—	284	2	no	—
84	C₂×C₄	#11765850	1	2	yes	—
85	C₂×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
86	C₈	#11765853	1	2	yes	—
87	C₈	#11765864	1	2	yes	—
88	C₂²	—	8	1	no	—
89	C₂²	—	8	2	no	—
90	C₂²	C₂×#11765850	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	8	1	no	—
93	C₄	—	568	2	no	—
94	C₄	#14556115	1	1	yes	characteristic
95	C₄	C₂×#11765853	1	1	yes	characteristic
96	C₂	—	16	1	no	—
97	C₂	#17986345	1	1	yes	characteristic
98	C₂	#17986429	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17986401

C₂

yes

maximal, characteristic, complemented

#17985803

C₂

yes

maximal, complemented

#17985800

C₂

yes

maximal

C₄×C₇₁⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#495×C₇₁

C₂

yes

maximal, characteristic

#14556120

—

C₂×C₇₁⋊C₁₆

C₂²

yes

—

#14556062

C₂²

yes

—

#14556060

—

C₂×Q₁₆×C₇₁

C₂²

yes

characteristic

C₂×SD₁₆×C₇₁

—

C₂×D₈×C₇₁

C₂²

yes

characteristic

#124×C₇₁

—

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

C₇₁⋊C₁₆

—

C₂×Q₈×C₇₁

—

C₂×D₄×C₇₁

—

Q₁₆×C₇₁

—

SD₁₆×C₇₁

—

D₈×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₂²⋊C₄×C₇₁

—

C₄²×C₇₁

D₄

yes

characteristic

C₂³×C₇₁

—

Q₈×C₇₁

—

Q₈×C₇₁

—

D₄×C₇₁

—

D₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

D₈

yes

—

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

C₈×C₇₁

SD₁₆

yes

—

C₈×C₇₁

#41

yes

—

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×D₈

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

—

C₄×C₇₁

#124

yes

characteristic

C₄×C₇₁

C₂×SD₁₆

yes

characteristic

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#486

yes

characteristic

C₂×C₇₁

#508

yes

—

#2242

—

maximal, Sylow

C₇₁

#2242

yes

characteristic, complemented, Sylow

#499

—

#495

D₇₁

yes

characteristic

#358

—

#357

—

C₄×C₁₆

—

C₂×Q₁₆

C₂×D₇₁

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

C₂×D₇₁

yes

characteristic

#125

—

142

—

#124

—

C₂×C₁₆

—

#107

—

#106

—

142

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

D₈

—

C₂×C₈

C₂²⋊D₇₁

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

284

—

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₇₁

yes

characteristic

C₁₆

—

142

—

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

284

—

C₂×C₄

#11765850

yes

—

C₂×C₄

C₂×C₂²⋊D₇₁

yes

characteristic

C₈

#11765853

yes

—

C₈

#11765864

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#11765850

yes

characteristic

C₄

—

C₄

—

C₄

—

568

—

C₄

yes

C₄

yes

C₂

—

C₂

#17986345

yes

characteristic

C₂

#17986429

yes

—

	subgroup	G/H
center	C₂²	C₂×#11765850
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	#495×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	#495	D₇₁
hypocenter	C₇₁	#2242
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

subgroup

G/H

center

C₂²

C₂×#11765850

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

#495×C₇₁

C₂

socle

C₂²×C₇₁

C₂×D₈

D₇₁

C₇₁

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #495

N	H ≅ G/N	type
1. #17986401	C₂	semidirect
2. #17985803	C₂	semidirect
4. C₄×C₇₁⋊C₁₆	C₂	semidirect
50. C₇₁	#2242	semidirect

H ≅ G/N

type

1. #17986401

C₂

semidirect

2. #17985803

C₂

semidirect

4. C₄×C₇₁⋊C₁₆

C₂

semidirect

50. C₇₁

#2242

semidirect

Subgroups — #22590571

Conjugacy classes of subgroups

Complements