Group #21461268 — subgroups

Subgroups — D₆₁⋊#330 #21461268

Order 7808.

232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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	#16840721	C₂	1	2	yes	maximal
2	#16840619	C₂	1	4	yes	maximal, complemented
3	#125×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×D₆₁⋊C₈	—	2	2	no	—
5	#14519832	—	2	2	no	—
6	#14519832	C₂²	1	4	yes	—
7	#14519769	C₄	1	1	yes	characteristic
8	#14519768	C₂²	1	2	yes	—
9	#14519767	—	2	2	no	—
10	C₄⋊C₄×D₆₁	—	2	2	no	—
11	C₄⋊C₄×D₆₁	C₄	1	2	yes	—
12	C₄²×D₆₁	C₂²	1	1	yes	characteristic
13	#125×C₆₁	C₄	1	1	yes	characteristic
14	C₂×C₄×D₆₁	—	2	2	no	—
15	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×D₆₁	D₄	1	2	yes	—
17	C₂×#92420	—	2	4	no	—
18	D₆₁⋊C₈	—	2	8	no	—
19	C₄⋊C₄×C₆₁	—	2	2	no	—
20	C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
21	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄⋊Dic₆₁	—	2	2	no	—
23	C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
24	#11758196	—	2	2	no	—
25	#11758196	—	2	2	no	—
26	#11758196	—	2	2	no	—
27	C₄×Dic₆₁	D₄	1	2	yes	—
28	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
29	C₂²×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	—	2	2	no	—
31	C₂×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₆₁	—	2	2	no	—
34	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	C₂×D₄	1	2	yes	—
36	C₄×D₆₁	—	2	2	no	—
37	C₄×D₆₁	—	2	4	no	—
38	C₄×D₆₁	—	4	4	no	—
39	#92420	—	2	8	no	—
40	C₂²×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂×D₆₁	#101	1	2	yes	—
42	C₂×D₆₁	#104	1	4	yes	—
43	C₄×C₆₁	—	2	1	no	—
44	C₄×C₆₁	—	2	2	no	—
45	C₄×C₆₁	—	4	2	no	—
46	Dic₆₁	—	2	1	no	—
47	Dic₆₁	—	2	2	no	—
48	Dic₆₁	—	4	2	no	—
49	C₂×#330	—	61	1	no	maximal, Sylow
50	C₂×C₆₁	C₂×#101	1	1	yes	characteristic
51	C₂×C₆₁	C₂×#104	1	2	yes	—
52	D₆₁	#330	1	4	yes	complemented
53	C₂×#125	—	61	1	no	—
54	C₂×#97	—	61	2	no	—
55	#330	—	61	4	no	—
56	C₆₁	C₂×#330	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	—	122	2	no	—
58	#125	—	61	2	no	—
59	#125	—	61	1	no	—
60	#125	—	122	2	no	—
61	#125	#6923	1	1	yes	characteristic
62	C₂×C₄⋊C₄	—	61	2	no	—
63	C₂×C₄⋊C₄	—	122	2	no	—
64	C₂×C₄²	—	61	1	no	—
65	#97	—	61	4	no	—
66	#97	—	122	2	no	—
67	C₂²×C₄	—	61	2	no	—
68	C₂²×C₄	—	61	1	no	—
69	C₂²×C₄	—	122	2	no	—
70	C₂×C₈	—	122	4	no	—
71	C₂×C₈	—	122	8	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	61	2	no	—
74	C₄⋊C₄	—	122	2	no	—
75	C₄⋊C₄	—	122	2	no	—
76	C₄⋊C₄	—	122	2	no	—
77	C₄⋊C₄	—	122	2	no	—
78	C₄⋊C₄	C₂×#6923	1	2	yes	—
79	C₄²	—	61	2	no	—
80	C₄²	—	61	1	no	—
81	C₄²	C₂×#6923	1	1	yes	characteristic
82	C₂³	—	61	1	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	61	1	no	—
85	C₂×C₄	—	61	2	no	—
86	C₂×C₄	—	122	4	no	—
87	C₂×C₄	—	122	2	no	—
88	C₂×C₄	—	122	2	no	—
89	C₂×C₄	—	244	4	no	—
90	C₂×C₄	C₂²⋊#6923	1	2	yes	—
91	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
92	C₈	—	122	8	no	—
93	C₂²	—	61	2	no	—
94	C₂²	—	61	4	no	—
95	C₂²	C₂×C₂²⋊#6923	1	1	yes	characteristic
96	C₄	—	2	1	no	—
97	C₄	—	2	2	no	—
98	C₄	—	4	2	no	—
99	C₄	—	122	1	no	—
100	C₄	—	122	2	no	—
101	C₄	—	244	2	no	—
102	C₂	—	61	4	no	—
103	C₂	D₆₁⋊#101	1	1	yes	characteristic
104	C₂	D₆₁⋊#104	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840721

C₂

yes

maximal

#16840619

C₂

yes

maximal, complemented

#125×D₆₁

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

—

#14519832

—

#14519832

C₂²

yes

—

#14519769

C₄

yes

characteristic

#14519768

C₂²

yes

—

#14519767

—

C₄⋊C₄×D₆₁

—

C₄⋊C₄×D₆₁

C₄

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

#125×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

—

C₂×#92420

—

D₆₁⋊C₈

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂×C₄

yes

—

#11758196

—

#11758196

—

#11758196

—

C₄×Dic₆₁

D₄

yes

—

C₄×Dic₆₁

C₂³

yes

characteristic

C₂²×D₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂×D₄

yes

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

#92420

—

C₂²×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₆₁

#101

yes

—

C₂×D₆₁

#104

yes

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

#330

yes

complemented

C₂×#125

—

C₂×#97

—

#330

—

C₆₁

C₂×#330

yes

characteristic, complemented, Sylow

C₂²×C₈

—

122

—

#125

—

#125

—

#125

—

122

—

#125

#6923

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

122

—

C₂×C₄²

—

#97

—

#97

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₂×C₄

C₂²⋊#6923

yes

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

122

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊#6923

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

122

—

100

C₄

—

122

—

101

C₄

—

244

—

102

C₂

—

103

C₂

D₆₁⋊#101

yes

characteristic

104

C₂

D₆₁⋊#104

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#125×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₂²⋊C₄
hypercenter	#125	#6923
hypocenter	C₆₁	C₂×#330
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

subgroup

G/H

center

C₂²

C₂×C₂²⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

#125×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₂²⋊C₄

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #125

N	H ≅ G/N	type
2. #16840619	C₂	semidirect
52. D₆₁	#330	semidirect
56. C₆₁	C₂×#330	semidirect

H ≅ G/N

type

2. #16840619

C₂

semidirect

52. D₆₁

#330

semidirect

56. C₆₁

C₂×#330

semidirect

Subgroups — D₆₁⋊#330 #21461268

Conjugacy classes of subgroups

Complements

Subgroups — D61⋊#330 #21461268

Conjugacy classes of subgroups

Complements

Subgroups — D₆₁⋊#330 #21461268