Group #21447660 — subgroups

Subgroups — #21447660

Order 7808.

144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 63 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	#16840180	C₂	1	2	yes	maximal, complemented
2	#16839880	C₂	1	1	yes	maximal, characteristic
3	#16839547	C₂	1	2	yes	maximal, complemented
4	#16839538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
6	#14519799	C₄	1	1	yes	characteristic
7	#14519783	C₂²	1	2	yes	—
8	#14519716	—	2	2	no	—
9	C₂×#11758185	C₂²	1	1	yes	characteristic
10	C₂×#11758185	C₂²	1	1	yes	characteristic
11	C₁₆×D₆₁	—	2	2	no	—
12	#14519713	C₄	1	1	yes	characteristic
13	#14519705	C₄	1	2	yes	—
14	M₃₂×C₆₁	C₂²	1	2	yes	—
15	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	#11758222	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
19	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
20	#11758194	C₂×C₄	1	2	yes	—
21	Dic₂₄₄	C₈	1	1	yes	characteristic
22	D₄₈₈	C₈	1	1	yes	characteristic
23	#11758190	C₈	1	2	yes	—
24	#11758189	—	2	2	no	—
25	C₈×D₆₁	—	2	2	no	—
26	C₁₆×C₆₁	—	2	2	no	—
27	#11758185	—	2	1	no	—
28	#11758185	D₄	1	2	yes	—
29	C₂×C₄×C₆₁	—	2	1	no	—
30	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
31	C₂²⋊D₆₁	—	2	2	no	—
32	D₂₄₄	C₂×C₈	1	2	yes	—
33	C₄×D₆₁	—	2	2	no	—
34	Dic₁₂₂	C₂×C₈	1	2	yes	—
35	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
36	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
37	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
38	C₈×C₆₁	#41	1	1	yes	characteristic
39	#92418	—	2	2	no	—
40	C₂²×C₆₁	#131	1	1	yes	characteristic
41	C₂×D₆₁	—	2	2	no	—
42	C₄×C₆₁	—	4	1	no	—
43	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
44	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
45	Dic₆₁	—	2	2	no	—
46	#2171	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	—	2	1	no	—
48	C₂×C₆₁	C₈×D₄	1	1	yes	characteristic
49	D₆₁	—	4	2	no	—
50	#504	—	61	2	no	—
51	#443	—	61	1	no	—
52	#364	D₆₁	1	1	yes	characteristic, complemented
53	#350	—	61	2	no	—
54	#346	—	61	1	no	—
55	C₆₁	#2171	1	1	yes	characteristic, complemented, Sylow
56	#135	—	61	1	no	—
57	#131	—	61	2	no	—
58	M₃₂	—	122	2	no	—
59	M₃₂	C₂×D₆₁	1	2	yes	—
60	C₂×C₁₆	—	61	1	no	—
61	C₂×C₁₆	—	61	1	no	—
62	C₂×C₁₆	—	122	2	no	—
63	#108	—	61	1	no	—
64	#104	—	61	2	no	—
65	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
66	#41	—	61	2	no	—
67	Q₁₆	—	61	1	no	—
68	SD₁₆	—	61	2	no	—
69	D₈	—	61	1	no	—
70	M₁₆	—	61	2	no	—
71	M₁₆	—	122	2	no	—
72	C₂×C₈	—	122	2	no	—
73	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
75	C₄²	C₄×D₆₁	1	1	yes	characteristic
76	C₁₆	—	2	2	no	—
77	C₁₆	—	61	2	no	—
78	C₁₆	—	122	1	no	—
79	Q₈	—	61	2	no	—
80	D₄	—	61	2	no	—
81	D₄	—	122	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	122	2	no	—
84	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
85	C₈	—	122	2	no	—
86	C₈	C₈×D₆₁	1	1	yes	characteristic
87	C₈	C₈×D₆₁	1	1	yes	characteristic
88	C₈	D₄×D₆₁	1	1	yes	characteristic
89	C₈	#11758226	1	1	yes	characteristic
90	C₂²	—	122	2	no	—
91	C₂²	#14519785	1	1	yes	characteristic
92	C₄	—	4	1	no	—
93	C₄	—	122	2	no	—
94	C₄	#14519739	1	1	yes	characteristic
95	C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	244	2	no	—
98	C₂	#16839827	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840180

C₂

yes

maximal, complemented

#16839880

C₂

yes

maximal, characteristic

#16839547

C₂

yes

maximal, complemented

#16839538

C₂

yes

maximal, characteristic, complemented

C₆₁×#364

C₂

yes

maximal, characteristic, complemented

#14519799

C₄

yes

characteristic

#14519783

C₂²

yes

—

#14519716

—

C₂×#11758185

C₂²

yes

characteristic

C₂×#11758185

C₂²

yes

characteristic

C₁₆×D₆₁

—

#14519713

C₄

yes

characteristic

#14519705

C₄

yes

—

M₃₂×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

#11758222

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758194

C₂×C₄

yes

—

Dic₂₄₄

C₈

yes

characteristic

D₄₈₈

C₈

yes

characteristic

#11758190

C₈

yes

—

#11758189

—

C₈×D₆₁

—

C₁₆×C₆₁

—

#11758185

—

#11758185

D₄

yes

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂²⋊D₆₁

—

D₂₄₄

C₂×C₈

yes

—

C₄×D₆₁

—

Dic₁₂₂

C₂×C₈

yes

—

C₈×C₆₁

C₂×C₈

yes

characteristic

C₈×C₆₁

C₂×C₈

yes

characteristic

C₈×C₆₁

C₂×D₄

yes

C₈×C₆₁

yes

—

C₂²×C₆₁

#131

yes

characteristic

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

C₄×D₄

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

#2171

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₈×D₄

yes

characteristic

D₆₁

—

#504

—

#443

—

#364

D₆₁

yes

characteristic, complemented

#350

—

#346

—

C₆₁

#2171

yes

characteristic, complemented, Sylow

#135

—

#131

—

M₃₂

—

122

—

M₃₂

C₂×D₆₁

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

122

—

#108

—

#104

—

C₄×C₈

C₂×D₆₁

yes

characteristic

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

122

—

Q₈

—

D₄

—

D₄

—

122

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

122

—

C₈

C₈×D₆₁

yes

characteristic

C₈

C₈×D₆₁

yes

characteristic

C₈

D₄×D₆₁

yes

characteristic

C₈

#11758226

yes

characteristic

C₂²

—

122

—

C₂²

#14519785

yes

characteristic

C₄

—

C₄

—

122

—

C₄

#14519739

yes

characteristic

C₄

C₂×C₈×D₆₁

yes

characteristic

C₂

—

C₂

—

244

—

C₂

#16839827

yes

characteristic

	subgroup	G/H
center	C₈	D₄×D₆₁
commutator	C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#364	C₂
socle	C₂×C₆₁	C₈×D₄
hypercenter	#364	D₆₁
hypocenter	C₆₁	#2171
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

subgroup

G/H

center

C₈

D₄×D₆₁

commutator

C₄×C₆₁

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#364

C₂

socle

C₂×C₆₁

C₈×D₄

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ #364

N	H ≅ G/N	type
1. #16840180	C₂	semidirect
3. #16839547	C₂	semidirect
4. #16839538	C₂	semidirect
5. C₆₁×#364	C₂	semidirect
52. #364	D₆₁	semidirect
55. C₆₁	#2171	semidirect

H ≅ G/N

type

1. #16840180

C₂

semidirect

3. #16839547

C₂

semidirect

4. #16839538

C₂

semidirect

5. C₆₁×#364

C₂

semidirect

52. #364

D₆₁

semidirect

55. C₆₁

#2171

semidirect

Subgroups — #21447660

Conjugacy classes of subgroups

Complements