Group #22590391 — subgroups

Subgroups — #22590391

Order 9088.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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	2	yes	maximal
2	#17986379	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₂₈₄	C₂	1	1	yes	maximal, characteristic
4	#17985804	C₂	1	2	yes	maximal
5	C₄⋊C₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₈₄	—	2	1	no	—
7	C₂×Dic₂₈₄	C₂²	1	2	yes	—
8	C₂×Dic₂₈₄	C₂²	1	1	yes	characteristic
9	#14556128	—	2	1	no	—
10	C₄×Dic₁₄₂	—	2	1	no	—
11	Dic₅₆₈	—	2	4	no	—
12	#14556062	C₂²	1	1	yes	characteristic
13	#14556053	—	2	1	no	—
14	C₂×C₁₆×C₇₁	C₂²	1	2	yes	—
15	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₄₂	—	2	1	no	—
17	C₂×Dic₁₄₂	—	2	2	no	—
18	Dic₂₈₄	—	2	2	no	—
19	Dic₂₈₄	—	2	1	no	—
20	Dic₂₈₄	—	2	2	no	—
21	Dic₂₈₄	—	4	2	no	—
22	Dic₂₈₄	D₄	1	2	yes	—
23	C₄⋊Dic₇₁	—	2	1	no	—
24	C₄⋊Dic₇₁	—	4	1	no	—
25	C₄⋊Dic₇₁	—	4	1	no	—
26	Dic₇₁⋊C₄	—	4	1	no	—
27	C₄×Dic₇₁	—	4	1	no	—
28	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
29	C₂×C₈×C₇₁	C₂³	1	1	yes	characteristic
30	C₄²×C₇₁	D₄	1	1	yes	characteristic
31	C₁₆×C₇₁	—	2	2	no	—
32	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
33	C₂×C₄×C₇₁	D₈	1	1	yes	characteristic
34	C₂×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₇₁	—	4	1	no	—
36	C₂×Dic₇₁	—	4	1	no	—
37	C₂×Dic₇₁	—	4	2	no	—
38	Dic₁₄₂	—	2	2	no	—
39	Dic₁₄₂	—	4	1	no	—
40	Dic₁₄₂	—	4	2	no	—
41	Dic₁₄₂	—	4	2	no	—
42	C₈×C₇₁	—	2	1	no	—
43	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
44	C₈×C₇₁	#41	1	1	yes	characteristic
45	C₂²×C₇₁	C₂×D₈	1	1	yes	characteristic
46	C₄×C₇₁	—	2	1	no	—
47	C₄×C₇₁	Q₃₂	1	2	yes	complemented
48	C₄×C₇₁	#121	1	1	yes	characteristic
49	C₄×C₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
50	Dic₇₁	—	4	2	no	—
51	Dic₇₁	—	8	2	no	—
52	Dic₇₁	—	8	1	no	—
53	C₂×C₇₁	#459	1	1	yes	characteristic
54	C₂×C₇₁	C₂×Q₃₂	1	1	yes	characteristic
55	C₂×C₇₁	#510	1	1	yes	characteristic
56	#2209	—	71	1	no	maximal, Sylow
57	C₇₁	#2209	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₃₂	—	71	2	no	—
59	#494	—	71	1	no	—
60	C₄×Q₁₆	—	71	1	no	—
61	C₄⋊C₁₆	D₇₁	1	1	yes	characteristic
62	#358	—	71	2	no	—
63	C₂×Q₁₆	—	71	1	no	—
64	C₂×Q₁₆	—	71	2	no	—
65	C₂×Q₁₆	—	142	1	no	—
66	C₄⋊Q₈	—	142	1	no	—
67	C₄×Q₈	—	142	1	no	—
68	Q₃₂	—	142	4	no	—
69	C₂×C₁₆	C₂×D₇₁	1	2	yes	—
70	#107	—	71	1	no	—
71	#103	—	142	1	no	—
72	C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
73	C₂×Q₈	—	142	2	no	—
74	C₂×Q₈	—	142	1	no	—
75	Q₁₆	—	284	2	no	—
76	Q₁₆	—	71	2	no	—
77	Q₁₆	—	142	2	no	—
78	Q₁₆	—	142	2	no	—
79	Q₁₆	—	142	1	no	—
80	C₂×C₈	D₂₈₄	1	1	yes	characteristic
81	C₂×C₈	C₂²×D₇₁	1	1	yes	characteristic
82	C₄⋊C₄	—	284	1	no	—
83	C₄⋊C₄	—	284	1	no	—
84	C₄⋊C₄	—	284	1	no	—
85	C₄⋊C₄	—	142	1	no	—
86	C₄²	—	284	1	no	—
87	C₄²	D₂₈₄	1	1	yes	characteristic
88	C₁₆	—	2	2	no	—
89	Q₈	—	284	1	no	—
90	Q₈	—	284	2	no	—
91	Q₈	—	284	2	no	—
92	Q₈	—	142	2	no	—
93	C₂×C₄	—	284	1	no	—
94	C₂×C₄	—	284	1	no	—
95	C₂×C₄	—	284	2	no	—
96	C₂×C₄	D₅₆₈	1	1	yes	characteristic
97	C₂×C₄	D₅₆₈	1	1	yes	characteristic
98	C₂×C₄	C₂×D₂₈₄	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	D₄×D₇₁	1	1	yes	characteristic
101	C₈	#11765866	1	1	yes	characteristic
102	C₂²	C₂×D₅₆₈	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	284	2	no	—
105	C₄	—	568	1	no	—
106	C₄	—	568	2	no	—
107	C₄	Dic₅₆₈	1	2	yes	complemented
108	C₄	#14556103	1	1	yes	characteristic
109	C₄	#14556156	1	1	yes	characteristic
110	C₂	#17986195	1	1	yes	characteristic
111	C₂	C₂×Dic₅₆₈	1	1	yes	characteristic
112	C₂	#17986442	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₅₆₈

C₂

yes

maximal

#17986379

C₂

yes

maximal, characteristic

C₄×Dic₂₈₄

C₂

yes

maximal, characteristic

#17985804

C₂

yes

maximal

C₄⋊C₁₆×C₇₁

C₂

yes

maximal, characteristic

C₂×Dic₂₈₄

—

C₂×Dic₂₈₄

C₂²

yes

—

C₂×Dic₂₈₄

C₂²

yes

characteristic

#14556128

—

C₄×Dic₁₄₂

—

Dic₅₆₈

—

#14556062

C₂²

yes

characteristic

#14556053

—

C₂×C₁₆×C₇₁

C₂²

yes

—

C₄×C₈×C₇₁

C₂²

yes

characteristic

C₂×Dic₁₄₂

—

C₂×Dic₁₄₂

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

—

Dic₂₈₄

D₄

yes

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

C₄⋊Dic₇₁

—

Dic₇₁⋊C₄

—

C₄×Dic₇₁

—

C₂×C₈×C₇₁

D₄

yes

characteristic

C₂×C₈×C₇₁

C₂³

yes

characteristic

C₄²×C₇₁

D₄

yes

characteristic

C₁₆×C₇₁

—

C₂×C₄×C₇₁

D₈

yes

characteristic

C₂×C₄×C₇₁

D₈

yes

characteristic

C₂×C₄×C₇₁

C₂×D₄

yes

characteristic

C₂×Dic₇₁

—

C₂×Dic₇₁

—

C₂×Dic₇₁

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

—

Dic₁₄₂

—

C₈×C₇₁

—

C₈×C₇₁

C₂×D₄

yes

characteristic

C₈×C₇₁

#41

yes

characteristic

C₂²×C₇₁

C₂×D₈

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

Q₃₂

yes

C₄×C₇₁

yes

C₄×C₇₁

yes

Dic₇₁

—

Dic₇₁

—

Dic₇₁

—

C₂×C₇₁

#459

yes

characteristic

C₂×C₇₁

C₂×Q₃₂

yes

C₂×C₇₁

yes

—

C₇₁

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

#494

—

C₄×Q₁₆

—

C₄⋊C₁₆

D₇₁

yes

characteristic

#358

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

142

—

C₄⋊Q₈

—

142

—

C₄×Q₈

—

142

—

Q₃₂

—

142

—

C₂×C₁₆

C₂×D₇₁

yes

—

#107

—

#103

—

142

—

C₄×C₈

C₂×D₇₁

yes

characteristic

C₂×Q₈

—

142

—

C₂×Q₈

—

142

—

Q₁₆

—

284

—

Q₁₆

—

Q₁₆

—

142

—

Q₁₆

—

142

—

Q₁₆

—

142

—

C₂×C₈

D₂₈₄

yes

characteristic

C₂×C₈

C₂²×D₇₁

yes

characteristic

C₄⋊C₄

—

284

—

C₄⋊C₄

—

284

—

C₄⋊C₄

—

284

—

C₄⋊C₄

—

142

—

C₄²

—

284

—

C₄²

D₂₈₄

yes

characteristic

C₁₆

—

Q₈

—

284

—

Q₈

—

284

—

Q₈

—

284

—

Q₈

—

142

—

C₂×C₄

—

284

—

C₂×C₄

—

284

—

C₂×C₄

—

284

—

C₂×C₄

D₅₆₈

yes

characteristic

C₂×C₄

D₅₆₈

yes

characteristic

C₂×C₄

C₂×D₂₈₄

yes

characteristic

C₈

—

100

C₈

D₄×D₇₁

yes

characteristic

101

C₈

#11765866

yes

characteristic

102

C₂²

C₂×D₅₆₈

yes

characteristic

103

C₄

—

104

C₄

—

284

—

105

C₄

—

568

—

106

C₄

—

568

—

107

C₄

Dic₅₆₈

yes

complemented

108

C₄

#14556103

yes

characteristic

109

C₄

#14556156

yes

characteristic

110

C₂

#17986195

yes

characteristic

111

C₂

C₂×Dic₅₆₈

yes

characteristic

112

C₂

#17986442

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₅₆₈
commutator	C₂×C₈×C₇₁	C₂³
Frattini	C₂×C₈	C₂²×D₇₁
Fitting	C₄⋊C₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂×D₈
hypercenter	C₄⋊C₁₆	D₇₁
hypocenter	C₇₁	#2209
LCS	G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₅₆₈

commutator

C₂×C₈×C₇₁

C₂³

Frattini

C₂×C₈

C₂²×D₇₁

Fitting

C₄⋊C₁₆×C₇₁

C₂

socle

C₂²×C₇₁

C₂×D₈

hypercenter

C₄⋊C₁₆

D₇₁

hypocenter

C₇₁

#2209

LCS

G ▷ C₂×C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
47. C₄×C₇₁	Q₃₂	semidirect
57. C₇₁	#2209	semidirect
107. C₄	Dic₅₆₈	semidirect

H ≅ G/N

type

47. C₄×C₇₁

Q₃₂

semidirect

57. C₇₁

#2209

semidirect

107. C₄

Dic₅₆₈

semidirect

Subgroups — #22590391

Conjugacy classes of subgroups

Complements