Group #21445122 — subgroups

Subgroups — #21445122

Order 7808.

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

normal subgroups only

This group has 182 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, complemented
2	#16840128	C₂	1	1	yes	maximal, characteristic
3	#16840127	C₂	1	2	yes	maximal
4	#16839503	C₂	1	2	yes	maximal, complemented
5	C₆₁×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	#14519774	C₂²	1	1	yes	characteristic
7	#14519769	C₂²	1	2	yes	—
8	#14519768	—	2	2	no	—
9	#14519767	—	2	2	no	—
10	#14519767	—	2	2	no	—
11	#14519699	—	2	2	no	—
12	#14519699	—	2	2	no	—
13	#14519697	—	2	2	no	—
14	#14519688	C₂²	1	1	yes	characteristic
15	#125×C₆₁	C₂²	1	1	yes	characteristic
16	#97×C₆₁	C₂²	1	2	yes	—
17	C₂×D₂₄₄	—	2	1	no	—
18	C₂×D₂₄₄	—	2	2	no	—
19	C₂×C₈×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	1	no	—
32	C₂²×D₆₁	—	4	1	no	—
33	C₂×C₄×C₆₁	—	2	2	no	—
34	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
36	C₂×Dic₆₁	—	2	2	no	—
37	C₂×Dic₆₁	—	2	2	no	—
38	D₂₄₄	—	4	2	no	—
39	D₂₄₄	—	4	4	no	—
40	C₈×C₆₁	—	4	2	no	—
41	#92418	—	4	1	no	—
42	C₂²×C₆₁	#120	1	1	yes	characteristic
43	C₂×D₆₁	—	8	2	no	—
44	C₂×D₆₁	—	8	1	no	—
45	C₄×C₆₁	—	2	1	no	—
46	C₄×C₆₁	—	2	2	no	—
47	C₄×C₆₁	—	4	2	no	—
48	Dic₆₁	—	4	2	no	—
49	Dic₆₁	—	4	2	no	—
50	#1658	—	61	1	no	maximal, Sylow
51	C₂×C₆₁	#454	1	2	yes	—
52	C₂×C₆₁	#454	1	1	yes	characteristic
53	D₆₁	—	16	1	no	—
54	#564	—	61	1	no	—
55	#490	—	61	1	no	—
56	#490	—	61	2	no	—
57	#330	—	61	2	no	—
58	#330	D₆₁	1	1	yes	characteristic, complemented
59	C₆₁	#1658	1	1	yes	characteristic, complemented, Sylow
60	#127	—	61	1	no	—
61	#125	—	61	2	no	—
62	#125	—	122	2	no	—
63	#125	—	122	2	no	—
64	#125	—	122	2	no	—
65	#125	C₂×D₆₁	1	1	yes	characteristic
66	#102	—	122	2	no	—
67	#102	—	122	2	no	—
68	#102	—	122	2	no	—
69	#97	—	61	1	no	—
70	#97	C₂×D₆₁	1	2	yes	—
71	C₂×D₄	—	122	1	no	—
72	C₂×D₄	—	122	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	122	1	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	61	2	no	—
77	C₄⋊C₄	—	61	2	no	—
78	C₄⋊C₄	—	122	2	no	—
79	C₄⋊C₄	—	122	2	no	—
80	C₄⋊C₄	—	122	2	no	—
81	C₄⋊C₄	—	122	2	no	—
82	C₄⋊C₄	—	122	2	no	—
83	C₄⋊C₄	D₂₄₄	1	2	yes	—
84	C₄²	—	122	2	no	—
85	C₄²	C₂²×D₆₁	1	1	yes	characteristic
86	C₂³	—	244	1	no	—
87	D₄	—	244	4	no	—
88	D₄	—	244	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	122	2	no	—
91	C₂×C₄	—	122	2	no	—
92	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
93	C₂×C₄	D₄×D₆₁	1	2	yes	—
94	C₈	—	4	2	no	—
95	C₈	—	244	1	no	—
96	C₂²	—	488	2	no	—
97	C₂²	—	488	1	no	—
98	C₂²	#14519747	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	—	244	2	no	—
103	C₄	—	244	2	no	—
104	C₂	—	976	1	no	—
105	C₂	#16839936	1	2	yes	—
106	C₂	#16839937	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₆₁⋊#564

C₂

yes

maximal, characteristic, complemented

#16840128

C₂

yes

maximal, characteristic

#16840127

C₂

yes

maximal

#16839503

C₂

yes

maximal, complemented

C₆₁×#330

C₂

yes

maximal, characteristic, complemented

#14519774

C₂²

yes

characteristic

#14519769

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

#125×C₆₁

C₂²

yes

characteristic

#97×C₆₁

C₂²

yes

—

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×C₈×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

—

C₂²×D₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#120

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

Dic₆₁

—

Dic₆₁

—

#1658

—

maximal, Sylow

C₂×C₆₁

#454

yes

—

C₂×C₆₁

#454

yes

characteristic

D₆₁

—

—

—

—

—

D₆₁

yes

characteristic, complemented

C₆₁

#1658

yes

characteristic, complemented, Sylow

#127

—

#125

—

#125

—

122

—

#125

—

122

—

#125

—

122

—

#125

C₂×D₆₁

yes

characteristic

#102

—

122

—

#102

—

122

—

#102

—

122

—

#97

—

#97

C₂×D₆₁

yes

—

C₂×D₄

—

122

—

C₂×D₄

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₄⋊C₄

D₂₄₄

yes

—

C₄²

—

122

—

C₄²

C₂²×D₆₁

yes

characteristic

C₂³

—

244

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₂×D₂₄₄

yes

characteristic

C₂×C₄

D₄×D₆₁

yes

—

C₈

—

C₈

—

244

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

#14519747

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

244

—

103

C₄

—

244

—

104

C₂

—

976

—

105

C₂

#16839936

yes

—

106

C₂

#16839937

yes

characteristic

	subgroup	G/H
center	C₂²	#14519747
commutator	C₄²×C₆₁	C₂³
Frattini	C₄²	C₂²×D₆₁
Fitting	C₆₁×#330	C₂
socle	C₂²×C₆₁	#120
hypercenter	#330	D₆₁
hypocenter	C₆₁	#1658
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#14519747

commutator

C₄²×C₆₁

C₂³

Frattini

C₄²

C₂²×D₆₁

Fitting

C₆₁×#330

C₂

C₂²×C₆₁

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
1. C₆₁⋊#564	C₂	semidirect
4. #16839503	C₂	semidirect
5. C₆₁×#330	C₂	semidirect
58. #330	D₆₁	semidirect
59. C₆₁	#1658	semidirect

H ≅ G/N

type

1. C₆₁⋊#564

C₂

semidirect

4. #16839503

C₂

semidirect

5. C₆₁×#330

C₂

semidirect

58. #330

D₆₁

semidirect

59. C₆₁

#1658

semidirect

Subgroups — #21445122

Conjugacy classes of subgroups

Complements