Group #21445969 — subgroups

Subgroups — #21445969

Order 7808.

162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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	M₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
2	#16839534	C₂	1	2	yes	maximal
3	#16839523	C₂	1	2	yes	maximal
4	#16839519	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#338	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	1	yes	characteristic
7	#14519736	C₂²	1	2	yes	—
8	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
9	#14519687	C₄	1	2	yes	complemented
10	C₈×Dic₆₁	C₄	1	2	yes	complemented
11	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
12	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
14	C₂²×Dic₆₁	—	2	1	no	—
15	M₁₆×C₆₁	—	2	2	no	—
16	M₁₆×C₆₁	—	2	2	no	—
17	M₁₆×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	—	2	2	no	—
19	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
20	C₂²⋊Dic₆₁	—	2	2	no	—
21	C₄⋊Dic₆₁	—	2	2	no	—
22	C₄×Dic₆₁	—	2	1	no	—
23	C₄×Dic₆₁	—	2	2	no	—
24	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
26	#11758194	—	2	2	no	—
27	C₂×#92418	C₂×C₄	1	2	yes	—
28	C₂³×C₆₁	#41	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	#41	1	2	yes	—
31	C₂×C₄×C₆₁	#41	1	2	yes	—
32	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
33	C₂×Dic₆₁	—	2	1	no	—
34	C₂×Dic₆₁	—	2	1	no	—
35	C₂×Dic₆₁	—	4	2	no	—
36	C₂×Dic₆₁	—	4	2	no	—
37	C₈×C₆₁	—	2	2	no	—
38	C₈×C₆₁	—	4	2	no	—
39	#92418	—	2	2	no	—
40	C₂²×C₆₁	—	4	1	no	—
41	C₂²×C₆₁	#117	1	1	yes	characteristic
42	C₂²×C₆₁	#126	1	2	yes	—
43	C₄×C₆₁	#117	1	1	yes	characteristic
44	C₄×C₆₁	#117	1	1	yes	characteristic
45	C₄×C₆₁	#126	1	2	yes	—
46	Dic₆₁	—	2	2	no	—
47	Dic₆₁	—	4	1	no	—
48	Dic₆₁	—	8	2	no	—
49	#1841	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	—	2	1	no	—
51	C₂×C₆₁	—	2	2	no	—
52	C₂×C₆₁	#383	1	1	yes	characteristic
53	C₄×M₁₆	—	61	1	no	—
54	#344	—	61	2	no	—
55	#339	—	61	2	no	—
56	#338	D₆₁	1	1	yes	characteristic
57	H(3,ℤ/4)	—	61	1	no	—
58	C₆₁	#1841	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	61	1	no	—
60	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
61	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
62	#117	—	61	2	no	—
63	C₂×C₄²	—	61	1	no	—
64	#97	—	61	2	no	—
65	C₄×C₈	—	61	2	no	—
66	C₂²×C₄	—	122	1	no	—
67	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	122	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	61	2	no	—
74	C₂×C₈	C₄×D₆₁	1	2	yes	—
75	C₄⋊C₄	—	122	2	no	—
76	C₂²⋊C₄	—	122	2	no	—
77	C₄²	—	61	1	no	—
78	C₄²	—	61	1	no	—
79	C₄²	—	122	1	no	—
80	C₄²	—	122	2	no	—
81	C₂³	#11758226	1	1	yes	characteristic
82	C₂×C₄	—	122	1	no	—
83	C₂×C₄	—	122	1	no	—
84	C₂×C₄	—	244	2	no	—
85	C₂×C₄	—	244	2	no	—
86	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
87	C₂×C₄	#11758222	1	2	yes	—
88	C₂×C₄	#11758224	1	2	yes	—
89	C₂×C₄	#11758224	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	4	2	no	—
92	C₈	—	122	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#14519735	1	1	yes	characteristic
95	C₂²	#14519772	1	2	yes	—
96	C₄	—	122	2	no	—
97	C₄	—	488	2	no	—
98	C₄	—	244	1	no	—
99	C₄	#14519733	1	1	yes	characteristic
100	C₄	#14519734	1	1	yes	characteristic
101	C₄	#14519770	1	2	yes	—
102	C₂	—	2	1	no	—
103	C₂	—	2	2	no	—
104	C₂	#16839629	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₁₆×Dic₆₁

C₂

yes

maximal, characteristic

#16839534

C₂

yes

maximal

#16839523

C₂

yes

maximal

#16839519

C₂

yes

maximal, characteristic

C₆₁×#338

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

characteristic

#14519736

C₂²

yes

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519687

C₄

yes

complemented

C₈×Dic₆₁

C₄

yes

complemented

C₂×M₁₆×C₆₁

C₂²

yes

—

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂³

yes

characteristic

C₂²×Dic₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

#11758194

—

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

#41

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₁

#41

yes

—

C₂×C₄×C₆₁

#41

yes

—

C₂×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

#117

yes

characteristic

C₂²×C₆₁

#126

yes

—

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

#1841

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#383

yes

characteristic

C₄×M₁₆

—

#344

—

#339

—

#338

D₆₁

yes

characteristic

H(3,ℤ/4)

—

C₆₁

#1841

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

#117

—

C₂×C₄²

—

#97

—

C₄×C₈

—

C₂²×C₄

—

122

—

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

122

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₄²

—

122

—

C₂³

#11758226

yes

characteristic

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

—

244

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₂×C₄

#11758222

yes

—

C₂×C₄

#11758224

yes

—

C₂×C₄

#11758224

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₂²

—

C₂²

#14519735

yes

characteristic

C₂²

#14519772

yes

—

C₄

—

122

—

C₄

—

488

—

C₄

—

244

—

C₄

#14519733

yes

characteristic

100

C₄

#14519734

yes

characteristic

101

C₄

#14519770

yes

—

102

C₂

—

103

C₂

—

104

C₂

#16839629

yes

characteristic

	subgroup	G/H
center	C₄	#14519734
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#338	C₂
socle	C₂×C₆₁	#383
hypercenter	#338	D₆₁
hypocenter	C₆₁	#1841
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

subgroup

G/H

center

C₄

#14519734

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#338

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #338

N	H ≅ G/N	type
9. #14519687	C₄	semidirect
10. C₈×Dic₆₁	C₄	semidirect
58. C₆₁	#1841	semidirect

H ≅ G/N

type

9. #14519687

C₄

semidirect

10. C₈×Dic₆₁

C₄

semidirect

58. C₆₁

#1841

semidirect

Subgroups — #21445969

Conjugacy classes of subgroups

Complements