Group #21445145 — subgroups

Subgroups — #21445145

Order 7808.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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	C₆₁⋊#564	C₂	1	1	yes	maximal, characteristic
2	#16840168	C₂	1	2	yes	maximal
3	#16839504	C₂	1	1	yes	maximal, characteristic
4	#16839503	C₂	1	2	yes	maximal
5	C₆₁×#491	C₂	1	1	yes	maximal, characteristic
6	#14519769	C₂²	1	2	yes	—
7	#14519768	—	2	2	no	—
8	#14519767	—	2	2	no	—
9	#14519767	—	2	2	no	—
10	#14519710	—	2	2	no	—
11	#14519708	—	2	2	no	—
12	#14519688	C₂²	1	2	yes	—
13	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	#125×C₆₁	C₂²	1	1	yes	characteristic
15	#103×C₆₁	—	2	2	no	—
16	#97×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₆₁	—	2	1	no	—
18	C₂×C₈×C₆₁	—	2	1	no	—
19	C₄⋊C₄×C₆₁	—	2	2	no	—
20	C₄⋊C₄×C₆₁	—	2	2	no	—
21	C₄⋊C₄×C₆₁	D₄	1	2	yes	—
22	C₄²×C₆₁	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₆₁	—	2	2	no	—
24	C₄⋊Dic₆₁	D₄	1	2	yes	—
25	C₄⋊Dic₆₁	D₄	1	2	yes	—
26	#11758196	—	2	2	no	—
27	#11758196	—	2	2	no	—
28	#11758196	—	2	2	no	—
29	#11758196	—	2	2	no	—
30	C₄×Dic₆₁	—	2	2	no	—
31	C₂×#92418	—	2	2	no	—
32	Q₈×C₆₁	—	4	2	no	—
33	C₂×C₄×C₆₁	—	2	2	no	—
34	C₂×C₄×C₆₁	—	4	1	no	—
35	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₆₁	—	2	2	no	—
38	C₂×Dic₆₁	—	2	2	no	—
39	C₈×C₆₁	—	4	1	no	—
40	#92418	—	2	4	no	—
41	C₂²×C₆₁	#120	1	1	yes	characteristic
42	C₄×C₆₁	—	2	1	no	—
43	C₄×C₆₁	—	2	2	no	—
44	C₄×C₆₁	—	4	2	no	—
45	C₄×C₆₁	—	8	1	no	—
46	Dic₆₁	—	4	2	no	—
47	Dic₆₁	—	4	2	no	—
48	#1663	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	#454	1	1	yes	characteristic
50	C₂×C₆₁	#456	1	2	yes	—
51	#564	—	61	1	no	—
52	#501	—	61	2	no	—
53	#491	D₆₁	1	1	yes	characteristic
54	#330	—	61	1	no	—
55	#330	—	61	2	no	—
56	C₆₁	#1663	1	1	yes	characteristic, complemented, Sylow
57	C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
58	#125	—	61	2	no	—
59	#125	—	122	2	no	—
60	#125	—	122	2	no	—
61	#125	—	122	2	no	—
62	#125	C₂×D₆₁	1	1	yes	characteristic
63	#107	—	122	2	no	—
64	#106	—	122	2	no	—
65	#103	—	2	2	no	—
66	#97	—	61	2	no	—
67	#97	C₂×D₆₁	1	1	yes	characteristic
68	C₂×Q₈	—	2	1	no	—
69	C₂×C₈	—	2	1	no	—
70	C₂×C₈	—	122	2	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	61	2	no	—
74	C₄⋊C₄	—	61	2	no	—
75	C₄⋊C₄	—	122	2	no	—
76	C₄⋊C₄	—	122	2	no	—
77	C₄⋊C₄	—	122	2	no	—
78	C₄⋊C₄	—	122	2	no	—
79	C₄⋊C₄	—	122	2	no	—
80	C₄⋊C₄	C₂²⋊D₆₁	1	2	yes	—
81	C₄²	—	122	2	no	—
82	C₄²	C₂²×D₆₁	1	1	yes	characteristic
83	Q₈	—	4	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	—	122	2	no	—
87	C₂×C₄	—	122	2	no	—
88	C₂×C₄	D₄×D₆₁	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
90	C₈	—	4	1	no	—
91	C₈	—	122	4	no	—
92	C₂²	#14519745	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	2	1	no	—
95	C₄	—	4	2	no	—
96	C₄	—	8	1	no	—
97	C₄	—	244	2	no	—
98	C₄	—	244	2	no	—
99	C₂	#16839934	1	1	yes	characteristic
100	C₂	#16839943	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₆₁⋊#564

C₂

yes

maximal, characteristic

#16840168

C₂

yes

maximal

#16839504

C₂

yes

maximal, characteristic

#16839503

C₂

yes

maximal

C₆₁×#491

C₂

yes

maximal, characteristic

#14519769

C₂²

yes

—

—

—

—

—

—

C₂²

yes

—

C₄⋊Q₈×C₆₁

C₂²

yes

characteristic

#125×C₆₁

C₂²

yes

characteristic

#103×C₆₁

—

#97×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

D₄

yes

—

C₄²×C₆₁

C₂³

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

D₄

yes

—

C₄⋊Dic₆₁

D₄

yes

—

—

—

—

—

C₄×Dic₆₁

—

C₂×#92418

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#120

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

#564

—

#501

—

#491

D₆₁

yes

characteristic

#330

—

#330

—

C₆₁

#1663

yes

characteristic, complemented, Sylow

C₄⋊Q₈

C₂×D₆₁

yes

characteristic

#125

—

#125

—

122

—

#125

—

122

—

#125

—

122

—

#125

C₂×D₆₁

yes

characteristic

#107

—

122

—

#106

—

122

—

#103

—

#97

—

#97

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

C₂²⋊D₆₁

yes

—

C₄²

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

D₄×D₆₁

yes

—

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

—

C₈

—

122

—

C₂²

#14519745

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

244

—

C₄

—

244

—

C₂

#16839934

yes

characteristic

100

C₂

#16839943

yes

—

	subgroup	G/H
center	C₂²	#14519745
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#491	C₂
socle	C₂²×C₆₁	#120
hypercenter	#491	D₆₁
hypocenter	C₆₁	#1663
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #491

subgroup

G/H

center

C₂²

#14519745

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#491

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #491

N	H ≅ G/N	type
56. C₆₁	#1663	semidirect

H ≅ G/N

type

56. C₆₁

#1663

semidirect

Subgroups — #21445145

Conjugacy classes of subgroups

Complements