Group #21448118 — subgroups

Subgroups — SD₆₄×D₆₁ #21448118

Order 7808.

112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 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	Q₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
3	#16839601	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839600	C₂	1	1	yes	maximal, characteristic, complemented
5	#16839599	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×SD₆₄	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₁₆×D₆₁	—	2	1	no	—
9	D₈×D₆₁	—	2	1	no	—
10	Dic₄₈₈	C₂²	1	1	yes	characteristic, complemented
11	#14519723	—	2	1	no	—
12	D₉₇₆	C₂²	1	1	yes	characteristic
13	#14519718	—	2	1	no	—
14	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
15	#14519683	C₂²	1	1	yes	characteristic, complemented
16	Q₃₂×C₆₁	C₂²	1	1	yes	characteristic, complemented
17	D₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₃₂×C₆₁	C₂²	1	1	yes	characteristic, complemented
19	Q₈×D₆₁	—	4	1	no	—
20	D₄×D₆₁	—	4	1	no	—
21	Q₁₆×C₆₁	—	2	1	no	—
22	D₈×C₆₁	—	2	1	no	—
23	#11758202	—	4	1	no	—
24	#11758199	—	4	1	no	—
25	Dic₂₄₄	—	2	1	no	—
26	D₄₈₈	—	2	1	no	—
27	C₈×D₆₁	D₄	1	1	yes	characteristic
28	C₁₆×C₆₁	C₂³	1	1	yes	characteristic
29	#11758185	D₄	1	1	yes	characteristic
30	C₂²×D₆₁	—	8	1	no	—
31	Q₈×C₆₁	—	4	1	no	—
32	D₄×C₆₁	—	4	1	no	—
33	C₂²⋊D₆₁	—	8	1	no	—
34	D₂₄₄	—	4	1	no	—
35	C₄×D₆₁	—	8	1	no	—
36	C₄×D₆₁	D₈	1	1	yes	characteristic
37	Dic₁₂₂	—	4	1	no	—
38	Dic₁₂₂	—	8	1	no	—
39	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
40	#92418	D₈	1	1	yes	characteristic
41	C₂²×C₆₁	—	8	1	no	—
42	C₂×D₆₁	—	8	1	no	—
43	C₂×D₆₁	—	16	2	no	—
44	C₂×D₆₁	D₁₆	1	1	yes	characteristic
45	C₄×C₆₁	—	8	1	no	—
46	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
47	Dic₆₁	—	8	1	no	—
48	Dic₆₁	D₁₆	1	1	yes	characteristic
49	C₂×SD₆₄	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	—	16	1	no	—
51	C₂×C₆₁	C₂×D₁₆	1	1	yes	characteristic
52	D₆₁	—	16	1	no	—
53	D₆₁	SD₆₄	1	2	yes	direct product factor
54	C₂×Q₃₂	—	61	1	no	—
55	C₂×D₁₆	—	61	1	no	—
56	SD₆₄	—	61	1	no	—
57	SD₆₄	—	61	1	no	—
58	SD₆₄	—	61	1	no	—
59	SD₆₄	D₆₁	1	1	yes	characteristic, direct product factor
60	C₂×C₃₂	—	61	1	no	—
61	C₆₁	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₁₆	—	122	1	no	—
63	C₂×D₈	—	122	1	no	—
64	Q₃₂	—	61	1	no	—
65	Q₃₂	—	122	1	no	—
66	Q₃₂	C₂×D₆₁	1	1	yes	characteristic, complemented
67	D₁₆	—	61	1	no	—
68	D₁₆	—	122	1	no	—
69	D₁₆	C₂×D₆₁	1	1	yes	characteristic
70	C₂×C₁₆	—	61	1	no	—
71	C₃₂	—	61	1	no	—
72	C₃₂	C₂×D₆₁	1	1	yes	characteristic, complemented
73	C₂×Q₈	—	244	1	no	—
74	C₂×D₄	—	244	1	no	—
75	Q₁₆	—	2	1	no	—
76	Q₁₆	—	122	1	no	—
77	Q₁₆	—	244	1	no	—
78	D₈	—	2	1	no	—
79	D₈	—	122	1	no	—
80	D₈	—	244	1	no	—
81	C₂×C₈	—	61	1	no	—
82	C₁₆	—	61	1	no	—
83	C₁₆	C₂²×D₆₁	1	1	yes	characteristic
84	C₂³	—	488	1	no	—
85	Q₈	—	4	1	no	—
86	Q₈	—	488	1	no	—
87	Q₈	—	244	1	no	—
88	D₄	—	4	1	no	—
89	D₄	—	488	1	no	—
90	D₄	—	244	1	no	—
91	C₂×C₄	—	61	1	no	—
92	C₂×C₄	—	488	1	no	—
93	C₈	—	61	1	no	—
94	C₈	D₄×D₆₁	1	1	yes	characteristic
95	C₂²	—	8	1	no	—
96	C₂²	—	61	1	no	—
97	C₂²	—	976	2	no	—
98	C₂²	—	488	1	no	—
99	C₄	—	8	1	no	—
100	C₄	—	61	1	no	—
101	C₄	—	488	1	no	—
102	C₄	D₈×D₆₁	1	1	yes	characteristic
103	C₂	—	16	1	no	—
104	C₂	—	61	2	no	—
105	C₂	—	976	1	no	—
106	C₂	D₁₆×D₆₁	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₃₂×D₆₁

C₂

yes

maximal, characteristic, complemented

D₁₆×D₆₁

C₂

yes

maximal, characteristic

#16839601

C₂

yes

maximal, characteristic, complemented

#16839600

C₂

yes

maximal, characteristic, complemented

#16839599

C₂

yes

maximal, characteristic, complemented

C₃₂×D₆₁

C₂

yes

maximal, characteristic, complemented

C₆₁×SD₆₄

C₂

yes

maximal, characteristic, complemented

Q₁₆×D₆₁

—

D₈×D₆₁

—

Dic₄₈₈

C₂²

yes

characteristic, complemented

#14519723

—

D₉₇₆

C₂²

yes

characteristic

#14519718

—

C₁₆×D₆₁

C₂²

yes

characteristic

#14519683

C₂²

yes

characteristic, complemented

Q₃₂×C₆₁

C₂²

yes

characteristic, complemented

D₁₆×C₆₁

C₂²

yes

characteristic

C₃₂×C₆₁

C₂²

yes

characteristic, complemented

Q₈×D₆₁

—

D₄×D₆₁

—

Q₁₆×C₆₁

—

D₈×C₆₁

—

#11758202

—

#11758199

—

Dic₂₄₄

—

D₄₈₈

—

C₈×D₆₁

D₄

yes

characteristic

C₁₆×C₆₁

C₂³

yes

characteristic

#11758185

D₄

yes

characteristic

C₂²×D₆₁

—

Q₈×C₆₁

—

D₄×C₆₁

—

C₂²⋊D₆₁

—

D₂₄₄

—

C₄×D₆₁

—

C₄×D₆₁

D₈

yes

characteristic

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

C₂×D₄

yes

characteristic

#92418

D₈

yes

characteristic

C₂²×C₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

D₁₆

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×D₈

yes

characteristic

Dic₆₁

—

Dic₆₁

D₁₆

yes

characteristic

C₂×SD₆₄

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×D₁₆

yes

characteristic

D₆₁

—

D₆₁

SD₆₄

yes

direct product factor

C₂×Q₃₂

—

C₂×D₁₆

—

SD₆₄

—

SD₆₄

—

SD₆₄

—

SD₆₄

D₆₁

yes

characteristic, direct product factor

C₂×C₃₂

—

C₆₁

C₂×SD₆₄

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

122

—

C₂×D₈

—

122

—

Q₃₂

—

Q₃₂

—

122

—

Q₃₂

C₂×D₆₁

yes

characteristic, complemented

D₁₆

—

D₁₆

—

122

—

D₁₆

C₂×D₆₁

yes

characteristic

C₂×C₁₆

—

C₃₂

—

C₃₂

C₂×D₆₁

yes

characteristic, complemented

C₂×Q₈

—

244

—

C₂×D₄

—

244

—

Q₁₆

—

Q₁₆

—

122

—

Q₁₆

—

244

—

D₈

—

D₈

—

122

—

D₈

—

244

—

C₂×C₈

—

C₁₆

—

C₁₆

C₂²×D₆₁

yes

characteristic

C₂³

—

488

—

Q₈

—

Q₈

—

488

—

Q₈

—

244

—

D₄

—

D₄

—

488

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

488

—

C₈

—

C₈

D₄×D₆₁

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

976

—

C₂²

—

488

—

C₄

—

100

C₄

—

101

C₄

—

488

—

102

C₄

D₈×D₆₁

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

—

976

—

106

C₂

D₁₆×D₆₁

yes

characteristic

	subgroup	G/H
center	C₂	D₁₆×D₆₁
commutator	C₁₆×C₆₁	C₂³
Frattini	C₁₆	C₂²×D₆₁
Fitting	C₆₁×SD₆₄	C₂
socle	C₂×C₆₁	C₂×D₁₆
hypercenter	SD₆₄	D₆₁
hypocenter	C₆₁	C₂×SD₆₄
LCS	G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

subgroup

G/H

center

C₂

D₁₆×D₆₁

commutator

C₁₆×C₆₁

C₂³

Frattini

C₁₆

C₂²×D₆₁

Fitting

C₆₁×SD₆₄

C₂

socle

C₂×C₆₁

C₂×D₁₆

hypercenter

SD₆₄

D₆₁

hypocenter

C₆₁

C₂×SD₆₄

LCS

G ▷ C₁₆×C₆₁ ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ SD₆₄

N	H ≅ G/N	type
1. Q₃₂×D₆₁	C₂	semidirect
3. #16839601	C₂	semidirect
4. #16839600	C₂	semidirect
5. #16839599	C₂	semidirect
6. C₃₂×D₆₁	C₂	semidirect
7. C₆₁×SD₆₄	C₂	semidirect
10. Dic₄₈₈	C₂²	semidirect
15. #14519683	C₂²	semidirect
16. Q₃₂×C₆₁	C₂²	semidirect
18. C₃₂×C₆₁	C₂²	semidirect
53. D₆₁	SD₆₄	direct (N × H)
59. SD₆₄	D₆₁	direct (N × H)
61. C₆₁	C₂×SD₆₄	semidirect
66. Q₃₂	C₂×D₆₁	semidirect
72. C₃₂	C₂×D₆₁	semidirect

H ≅ G/N

type

1. Q₃₂×D₆₁

C₂

semidirect

3. #16839601

C₂

semidirect

4. #16839600

C₂

semidirect

5. #16839599

C₂

semidirect

6. C₃₂×D₆₁

C₂

semidirect

7. C₆₁×SD₆₄

C₂

semidirect

10. Dic₄₈₈

C₂²

semidirect

15. #14519683

C₂²

semidirect

16. Q₃₂×C₆₁

C₂²

semidirect

18. C₃₂×C₆₁

C₂²

semidirect

53. D₆₁

SD₆₄

direct (N × H)

59. SD₆₄

D₆₁

direct (N × H)

61. C₆₁

C₂×SD₆₄

semidirect

66. Q₃₂

C₂×D₆₁

semidirect

72. C₃₂

C₂×D₆₁

semidirect

Subgroups — SD₆₄×D₆₁ #21448118

Conjugacy classes of subgroups

Complements

Subgroups — SD64×D61 #21448118

Conjugacy classes of subgroups

Complements

Subgroups — SD₆₄×D₆₁ #21448118