Group #22590654 — subgroups

Subgroups — #22590654

Order 9088.

112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 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	#17986432	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₆×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#17985836	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₂₇₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#17985834	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985832	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₆₄×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#14556151	—	2	1	no	—
9	D₈×D₇₁	—	2	1	no	—
10	#14556071	—	2	1	no	—
11	D₁₁₃₆	C₂²	1	1	yes	characteristic
12	D₁₁₃₆	C₂²	1	1	yes	characteristic, complemented
13	#14556069	—	2	1	no	—
14	C₁₆×D₇₁	C₂²	1	1	yes	characteristic
15	C₇₁⋊C₃₂	C₂²	1	1	yes	characteristic, complemented
16	Q₃₂×C₇₁	C₂²	1	1	yes	characteristic, complemented
17	D₁₆×C₇₁	C₂²	1	1	yes	characteristic
18	C₃₂×C₇₁	C₂²	1	1	yes	characteristic, complemented
19	#11765866	—	4	1	no	—
20	D₄×D₇₁	—	4	1	no	—
21	#11765852	—	4	1	no	—
22	D₅₆₈	—	2	1	no	—
23	D₅₆₈	—	2	1	no	—
24	#11765850	—	4	1	no	—
25	C₈×D₇₁	D₄	1	1	yes	characteristic
26	C₇₁⋊C₁₆	D₄	1	1	yes	characteristic
27	Q₁₆×C₇₁	—	2	1	no	—
28	D₈×C₇₁	—	2	1	no	—
29	C₁₆×C₇₁	C₂³	1	1	yes	characteristic
30	C₂²×D₇₁	—	8	1	no	—
31	Q₈×C₇₁	—	4	1	no	—
32	D₄×C₇₁	—	4	1	no	—
33	C₂²⋊D₇₁	—	8	1	no	—
34	D₂₈₄	—	4	1	no	—
35	D₂₈₄	—	4	1	no	—
36	D₂₈₄	—	8	1	no	—
37	C₄×D₇₁	—	8	1	no	—
38	C₄×D₇₁	D₈	1	1	yes	characteristic
39	C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
40	C₇₁⋊C₈	D₈	1	1	yes	characteristic
41	C₂²×C₇₁	—	8	1	no	—
42	C₂×D₇₁	—	8	1	no	—
43	C₂×D₇₁	—	8	1	no	—
44	C₂×D₇₁	—	16	2	no	—
45	C₂×D₇₁	D₁₆	1	1	yes	characteristic
46	C₄×C₇₁	—	8	1	no	—
47	C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
48	Dic₇₁	D₁₆	1	1	yes	characteristic
49	C₂×C₇₁	—	16	1	no	—
50	C₂×C₇₁	C₂×D₁₆	1	1	yes	characteristic
51	D₇₁	—	2	1	no	—
52	D₇₁	—	16	1	no	—
53	D₇₁	—	16	1	no	—
54	#2263	—	71	1	no	maximal, Sylow
55	C₇₁	#2263	1	1	yes	characteristic, complemented, Sylow
56	#508	—	71	1	no	—
57	C₂×D₁₆	—	71	1	no	—
58	SD₆₄	—	71	1	no	—
59	SD₆₄	D₇₁	1	1	yes	characteristic, complemented
60	D₃₂	—	71	1	no	—
61	D₃₂	—	71	1	no	—
62	M₆₄	—	71	1	no	—
63	#135	—	142	1	no	—
64	C₂×D₈	—	142	1	no	—
65	Q₃₂	C₂×D₇₁	1	1	yes	characteristic, complemented
66	SD₃₂	—	142	1	no	—
67	D₁₆	—	71	1	no	—
68	D₁₆	—	71	1	no	—
69	D₁₆	—	142	1	no	—
70	D₁₆	C₂×D₇₁	1	1	yes	characteristic
71	C₂×C₁₆	—	71	1	no	—
72	C₃₂	—	71	1	no	—
73	C₃₂	C₂×D₇₁	1	1	yes	characteristic, complemented
74	#41	—	284	1	no	—
75	C₂×D₄	—	284	1	no	—
76	Q₁₆	—	2	1	no	—
77	SD₁₆	—	284	1	no	—
78	D₈	—	2	1	no	—
79	D₈	—	284	1	no	—
80	D₈	—	142	1	no	—
81	D₈	—	142	1	no	—
82	C₂×C₈	—	71	1	no	—
83	C₁₆	—	71	1	no	—
84	C₁₆	C₂²×D₇₁	1	1	yes	characteristic
85	C₂³	—	568	1	no	—
86	Q₈	—	4	1	no	—
87	D₄	—	4	1	no	—
88	D₄	—	284	1	no	—
89	D₄	—	284	1	no	—
90	D₄	—	568	1	no	—
91	D₄	—	568	1	no	—
92	C₂×C₄	—	568	1	no	—
93	C₂×C₄	—	71	1	no	—
94	C₈	—	71	1	no	—
95	C₈	D₄×D₇₁	1	1	yes	characteristic
96	C₂²	—	8	1	no	—
97	C₂²	—	568	1	no	—
98	C₂²	—	568	1	no	—
99	C₂²	—	71	1	no	—
100	C₂²	—	1136	2	no	—
101	C₄	—	8	1	no	—
102	C₄	—	71	1	no	—
103	C₄	D₈×D₇₁	1	1	yes	characteristic
104	C₂	—	16	1	no	—
105	C₂	—	1136	1	no	—
106	C₂	—	1136	1	no	—
107	C₂	—	142	1	no	—
108	C₂	D₁₆×D₇₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17986432

C₂

yes

maximal, characteristic, complemented

D₁₆×D₇₁

C₂

yes

maximal, characteristic, complemented

#17985836

C₂

yes

maximal, characteristic, complemented

D₂₂₇₂

C₂

yes

maximal, characteristic, complemented

#17985834

C₂

yes

maximal, characteristic, complemented

#17985832

C₂

yes

maximal, characteristic, complemented

SD₆₄×C₇₁

C₂

yes

maximal, characteristic, complemented

#14556151

—

D₈×D₇₁

—

#14556071

—

D₁₁₃₆

C₂²

yes

characteristic

D₁₁₃₆

C₂²

yes

characteristic, complemented

#14556069

—

C₁₆×D₇₁

C₂²

yes

characteristic

C₇₁⋊C₃₂

C₂²

yes

characteristic, complemented

Q₃₂×C₇₁

C₂²

yes

characteristic, complemented

D₁₆×C₇₁

C₂²

yes

characteristic

C₃₂×C₇₁

C₂²

yes

characteristic, complemented

#11765866

—

D₄×D₇₁

—

#11765852

—

D₅₆₈

—

D₅₆₈

—

#11765850

—

C₈×D₇₁

D₄

yes

characteristic

C₇₁⋊C₁₆

D₄

yes

characteristic

Q₁₆×C₇₁

—

D₈×C₇₁

—

C₁₆×C₇₁

C₂³

yes

characteristic

C₂²×D₇₁

—

Q₈×C₇₁

—

D₄×C₇₁

—

C₂²⋊D₇₁

—

D₂₈₄

—

D₂₈₄

—

D₂₈₄

—

C₄×D₇₁

—

C₄×D₇₁

D₈

yes

characteristic

C₈×C₇₁

C₂×D₄

yes

characteristic

C₇₁⋊C₈

D₈

yes

characteristic

C₂²×C₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

—

C₂×D₇₁

D₁₆

yes

characteristic

C₄×C₇₁

—

C₄×C₇₁

C₂×D₈

yes

characteristic

Dic₇₁

D₁₆

yes

characteristic

C₂×C₇₁

—

C₂×C₇₁

C₂×D₁₆

yes

characteristic

D₇₁

—

D₇₁

—

D₇₁

—

#2263

—

maximal, Sylow

C₇₁

#2263

yes

characteristic, complemented, Sylow

#508

—

C₂×D₁₆

—

SD₆₄

—

SD₆₄

D₇₁

yes

characteristic, complemented

D₃₂

—

D₃₂

—

M₆₄

—

#135

—

142

—

C₂×D₈

—

142

—

Q₃₂

C₂×D₇₁

yes

characteristic, complemented

SD₃₂

—

142

—

D₁₆

—

D₁₆

—

D₁₆

—

142

—

D₁₆

C₂×D₇₁

yes

characteristic

C₂×C₁₆

—

C₃₂

—

C₃₂

C₂×D₇₁

yes

characteristic, complemented

#41

—

284

—

C₂×D₄

—

284

—

Q₁₆

—

SD₁₆

—

284

—

D₈

—

D₈

—

284

—

D₈

—

142

—

D₈

—

142

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂²×D₇₁

yes

characteristic

C₂³

—

568

—

Q₈

—

D₄

—

D₄

—

284

—

D₄

—

284

—

D₄

—

568

—

D₄

—

568

—

C₂×C₄

—

568

—

C₂×C₄

—

C₈

—

C₈

D₄×D₇₁

yes

characteristic

C₂²

—

C₂²

—

568

—

C₂²

—

568

—

C₂²

—

100

C₂²

—

1136

—

101

C₄

—

102

C₄

—

103

C₄

D₈×D₇₁

yes

characteristic

104

C₂

—

105

C₂

—

1136

—

106

C₂

—

1136

—

107

C₂

—

142

—

108

C₂

D₁₆×D₇₁

yes

characteristic

	subgroup	G/H
center	C₂	D₁₆×D₇₁
commutator	C₁₆×C₇₁	C₂³
Frattini	C₁₆	C₂²×D₇₁
Fitting	SD₆₄×C₇₁	C₂
socle	C₂×C₇₁	C₂×D₁₆
hypercenter	SD₆₄	D₇₁
hypocenter	C₇₁	#2263
LCS	G ▷ C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

subgroup

G/H

center

C₂

D₁₆×D₇₁

commutator

C₁₆×C₇₁

C₂³

Frattini

C₁₆

C₂²×D₇₁

Fitting

SD₆₄×C₇₁

C₂

socle

C₂×C₇₁

C₂×D₁₆

hypercenter

SD₆₄

D₇₁

hypocenter

C₇₁

#2263

LCS

G ▷ C₁₆×C₇₁ ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

N	H ≅ G/N	type
1. #17986432	C₂	semidirect
2. D₁₆×D₇₁	C₂	semidirect
3. #17985836	C₂	semidirect
4. D₂₂₇₂	C₂	semidirect
5. #17985834	C₂	semidirect
6. #17985832	C₂	semidirect
7. SD₆₄×C₇₁	C₂	semidirect
12. D₁₁₃₆	C₂²	semidirect
15. C₇₁⋊C₃₂	C₂²	semidirect
16. Q₃₂×C₇₁	C₂²	semidirect
18. C₃₂×C₇₁	C₂²	semidirect
55. C₇₁	#2263	semidirect
59. SD₆₄	D₇₁	semidirect
65. Q₃₂	C₂×D₇₁	semidirect
73. C₃₂	C₂×D₇₁	semidirect

H ≅ G/N

type

1. #17986432

C₂

semidirect

2. D₁₆×D₇₁

C₂

semidirect

3. #17985836

C₂

semidirect

4. D₂₂₇₂

C₂

semidirect

5. #17985834

C₂

semidirect

6. #17985832

C₂

semidirect

7. SD₆₄×C₇₁

C₂

semidirect

12. D₁₁₃₆

C₂²

semidirect

15. C₇₁⋊C₃₂

C₂²

semidirect

16. Q₃₂×C₇₁

C₂²

semidirect

18. C₃₂×C₇₁

C₂²

semidirect

55. C₇₁

#2263

semidirect

59. SD₆₄

D₇₁

semidirect

65. Q₃₂

C₂×D₇₁

semidirect

73. C₃₂

C₂×D₇₁

semidirect

Subgroups — #22590654

Conjugacy classes of subgroups

Complements