Group #22590448 — subgroups

Subgroups — #22590448

Order 9088.

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

normal subgroups only

This group has 150 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	C₂×Dic₅₆₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#17986240	C₂	1	2	yes	maximal
3	#17985827	C₂	1	1	yes	maximal, characteristic, complemented
4	#17985804	C₂	1	2	yes	maximal, complemented
5	C₂×M₃₂×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₈₄	C₂²	1	2	yes	—
7	#14556107	—	2	2	no	—
8	Dic₅₆₈	—	2	2	no	—
9	#14556062	C₂²	1	2	yes	—
10	#14556053	—	2	2	no	—
11	C₂²×C₈×C₇₁	C₂²	1	1	yes	characteristic
12	M₃₂×C₇₁	—	2	2	no	—
13	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₁	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₄₂	—	2	2	no	—
16	Dic₂₈₄	—	2	2	no	—
17	Dic₂₈₄	—	2	2	no	—
18	C₄⋊Dic₇₁	—	2	2	no	—
19	Dic₇₁⋊C₄	—	4	2	no	—
20	C₂²⋊Dic₇₁	—	4	2	no	—
21	C₂²×C₄×C₇₁	D₄	1	1	yes	characteristic
22	C₂×C₈×C₇₁	—	2	1	no	—
23	C₂×C₈×C₇₁	—	2	1	no	—
24	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
25	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
26	C₁₆×C₇₁	—	2	1	no	—
27	C₁₆×C₇₁	D₄	1	2	yes	—
28	C₂³×C₇₁	D₈	1	1	yes	characteristic
29	C₂×C₄×C₇₁	—	2	1	no	—
30	C₂×C₄×C₇₁	—	2	1	no	—
31	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
32	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₇₁	—	4	2	no	—
34	C₂×Dic₇₁	—	4	2	no	—
35	Dic₁₄₂	—	4	2	no	—
36	Dic₁₄₂	—	4	2	no	—
37	C₈×C₇₁	—	2	1	no	—
38	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₁	#41	1	1	yes	characteristic
40	C₂²×C₇₁	—	2	1	no	—
41	C₂²×C₇₁	—	2	2	no	—
42	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
43	C₄×C₇₁	—	2	1	no	—
44	C₄×C₇₁	#121	1	1	yes	characteristic
45	C₄×C₇₁	#135	1	1	yes	characteristic
46	Dic₇₁	—	8	2	no	—
47	Dic₇₁	—	8	2	no	—
48	C₂×C₇₁	—	4	1	no	—
49	C₂×C₇₁	#466	1	1	yes	characteristic
50	C₂×C₇₁	#510	1	2	yes	—
51	#2219	—	71	1	no	maximal, Sylow
52	C₇₁	#2219	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₃₂	—	71	1	no	—
54	C₂×M₃₂	D₇₁	1	1	yes	characteristic
55	#467	—	71	2	no	—
56	#367	—	71	1	no	—
57	#358	—	71	2	no	—
58	C₂×Q₁₆	—	71	2	no	—
59	C₂²×C₈	C₂×D₇₁	1	1	yes	characteristic
60	C₂²⋊Q₈	—	142	2	no	—
61	Q₃₂	—	142	2	no	—
62	M₃₂	—	2	2	no	—
63	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
64	C₂×C₁₆	C₂×D₇₁	1	1	yes	characteristic
65	#107	—	71	2	no	—
66	#103	—	142	2	no	—
67	C₂×Q₈	—	142	2	no	—
68	C₂²×C₄	D₂₈₄	1	1	yes	characteristic
69	Q₁₆	—	142	2	no	—
70	Q₁₆	—	142	2	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	D₂₈₄	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
75	C₄⋊C₄	—	284	2	no	—
76	C₄⋊C₄	—	142	2	no	—
77	C₂²⋊C₄	—	284	2	no	—
78	C₁₆	—	2	1	no	—
79	C₁₆	C₂²⋊D₇₁	1	2	yes	—
80	C₂³	D₅₆₈	1	1	yes	characteristic
81	Q₈	—	284	2	no	—
82	Q₈	—	284	2	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	284	2	no	—
86	C₂×C₄	—	284	2	no	—
87	C₂×C₄	D₅₆₈	1	1	yes	characteristic
88	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
91	C₈	#11765865	1	1	yes	characteristic
92	C₂²	—	2	2	no	—
93	C₂²	—	2	1	no	—
94	C₂²	C₂×D₅₆₈	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	568	2	no	—
97	C₄	—	568	2	no	—
98	C₄	#14556102	1	1	yes	characteristic
99	C₄	#14556150	1	1	yes	characteristic
100	C₂	—	4	1	no	—
101	C₂	#17986235	1	1	yes	characteristic
102	C₂	#17986442	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₆₈

C₂

yes

maximal, characteristic, complemented

#17986240

C₂

yes

maximal

#17985827

C₂

yes

maximal, characteristic, complemented

#17985804

C₂

yes

maximal, complemented

C₂×M₃₂×C₇₁

C₂

yes

maximal, characteristic

C₂×Dic₂₈₄

C₂²

yes

—

#14556107

—

Dic₅₆₈

—

#14556062

C₂²

yes

—

#14556053

—

C₂²×C₈×C₇₁

C₂²

yes

characteristic

M₃₂×C₇₁

—

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₂×C₁₆×C₇₁

C₂²

yes

characteristic

C₂×Dic₁₄₂

—

Dic₂₈₄

—

Dic₂₈₄

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

C₂²⋊Dic₇₁

—

C₂²×C₄×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₁₆×C₇₁

—

C₁₆×C₇₁

D₄

yes

—

C₂³×C₇₁

D₈

yes

characteristic

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

—

C₂×C₄×C₇₁

D₈

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₂²×C₇₁

—

C₂²×C₇₁

—

C₂²×C₇₁

C₂×D₈

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

yes

C₄×C₇₁

yes

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

—

C₂×C₇₁

#466

yes

characteristic

C₂×C₇₁

#510

yes

—

#2219

—

maximal, Sylow

C₇₁

#2219

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×M₃₂

D₇₁

yes

—

—

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₇₁

yes

characteristic

C₂²⋊Q₈

—

142

—

Q₃₂

—

142

—

M₃₂

—

C₂×C₁₆

C₂×D₇₁

yes

characteristic

C₂×C₁₆

C₂×D₇₁

yes

characteristic

#107

—

#103

—

142

—

C₂×Q₈

—

142

—

C₂²×C₄

D₂₈₄

yes

characteristic

Q₁₆

—

142

—

Q₁₆

—

142

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₂₈₄

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

284

—

C₄⋊C₄

—

142

—

C₂²⋊C₄

—

284

—

C₁₆

—

C₁₆

C₂²⋊D₇₁

yes

—

C₂³

D₅₆₈

yes

characteristic

Q₈

—

284

—

Q₈

—

284

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

284

—

C₂×C₄

—

284

—

C₂×C₄

D₅₆₈

yes

characteristic

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₈

—

C₈

C₂×C₂²⋊D₇₁

yes

characteristic

C₈

#11765865

yes

characteristic

C₂²

—

C₂²

—

C₂²

C₂×D₅₆₈

yes

characteristic

C₄

—

C₄

—

568

—

C₄

—

568

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#17986235

yes

characteristic

102

C₂

#17986442

yes

—

	subgroup	G/H
center	C₂²	C₂×D₅₆₈
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₂×M₃₂×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	C₂×M₃₂	D₇₁
hypocenter	C₇₁	#2219
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

C₂×D₅₆₈

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₂×M₃₂×C₇₁

C₂

socle

C₂²×C₇₁

C₂×D₈

hypercenter

C₂×M₃₂

D₇₁

hypocenter

C₇₁

#2219

LCS

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
1. C₂×Dic₅₆₈	C₂	semidirect
3. #17985827	C₂	semidirect
4. #17985804	C₂	semidirect
52. C₇₁	#2219	semidirect

H ≅ G/N

type

1. C₂×Dic₅₆₈

C₂

semidirect

3. #17985827

C₂

semidirect

4. #17985804

C₂

semidirect

52. C₇₁

#2219

semidirect

Subgroups — #22590448

Conjugacy classes of subgroups

Complements