Group #21445574 — subgroups

Subgroups — #21445574

Order 7808.

200 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 105 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	#16839717	C₂	1	2	yes	maximal
2	#16839520	C₂	1	1	yes	maximal, characteristic
3	#16839519	C₂	1	1	yes	maximal, characteristic
4	#16839518	C₂	1	2	yes	maximal
5	C₆₁×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₂²	1	2	yes	—
7	#14519736	C₂²	1	2	yes	—
8	#14519687	C₄	1	4	yes	complemented
9	C₈×Dic₆₁	C₄	1	4	yes	complemented
10	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	#117×C₆₁	C₂²	1	1	yes	characteristic
13	#97×C₆₁	C₄	1	2	yes	complemented
14	C₄×C₈×C₆₁	C₄	1	2	yes	complemented
15	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
16	M₁₆×C₆₁	—	2	2	no	—
17	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄⋊C₄×C₆₁	—	2	1	no	—
23	C₂²⋊C₄×C₆₁	—	2	1	no	—
24	C₄²×C₆₁	C₂×C₄	1	2	yes	—
25	C₂²⋊Dic₆₁	—	2	2	no	—
26	C₄⋊Dic₆₁	—	2	2	no	—
27	C₄×Dic₆₁	C₂×C₄	1	4	yes	—
28	#11758194	—	2	2	no	—
29	#11758194	—	2	2	no	—
30	C₂×#92418	C₂×C₄	1	4	yes	—
31	C₂³×C₆₁	#41	1	1	yes	characteristic
32	C₂×C₄×C₆₁	—	2	2	no	—
33	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₆₁	#41	1	1	yes	characteristic
36	C₂×C₄×C₆₁	#41	1	2	yes	—
37	C₂×Dic₆₁	—	2	4	no	—
38	C₈×C₆₁	—	2	2	no	—
39	C₈×C₆₁	C₄²	1	2	yes	—
40	C₈×C₆₁	C₄²	1	1	yes	characteristic
41	C₈×C₆₁	C₄²	1	1	yes	characteristic
42	#92418	—	2	4	no	—
43	C₂²×C₆₁	—	4	1	no	—
44	C₂²×C₆₁	#117	1	2	yes	—
45	C₂²×C₆₁	#117	1	1	yes	characteristic
46	C₄×C₆₁	—	4	2	no	—
47	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₆₁	#117	1	2	yes	—
49	C₄×C₆₁	#117	1	1	yes	characteristic
50	Dic₆₁	—	4	4	no	—
51	#1747	—	61	1	no	maximal, Sylow
52	C₂×C₆₁	—	2	2	no	—
53	C₂×C₆₁	—	2	1	no	—
54	C₂×C₆₁	#376	1	1	yes	characteristic
55	#405	—	61	2	no	—
56	#405	D₆₁	1	1	yes	characteristic
57	#338	—	61	1	no	—
58	H(3,ℤ/4)	—	61	1	no	—
59	H(3,ℤ/4)	—	61	2	no	—
60	C₆₁	#1747	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	61	2	no	—
62	C₂×M₁₆	C₂×D₆₁	1	1	yes	characteristic
63	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
64	#117	—	61	2	no	—
65	#117	C₂×D₆₁	1	1	yes	characteristic
66	#97	—	61	4	no	—
67	#97	Dic₆₁	1	2	yes	complemented
68	C₄×C₈	—	61	4	no	—
69	C₄×C₈	Dic₆₁	1	2	yes	complemented
70	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	122	2	no	—
73	M₁₆	—	122	2	no	—
74	C₂×C₈	—	61	4	no	—
75	C₂×C₈	C₄×D₆₁	1	2	yes	—
76	C₂×C₈	C₄×D₆₁	1	2	yes	—
77	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
78	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
79	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
80	C₄⋊C₄	—	2	1	no	—
81	C₄⋊C₄	—	122	2	no	—
82	C₂²⋊C₄	—	2	1	no	—
83	C₂²⋊C₄	—	122	2	no	—
84	C₄²	—	61	4	no	—
85	C₄²	C₂×Dic₆₁	1	2	yes	—
86	C₂³	#11758222	1	1	yes	characteristic
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	122	4	no	—
89	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
90	C₂×C₄	#11758222	1	1	yes	characteristic
91	C₂×C₄	#11758222	1	2	yes	—
92	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
93	C₈	—	2	2	no	—
94	C₈	—	122	4	no	—
95	C₈	C₄×Dic₆₁	1	1	yes	characteristic
96	C₈	C₄×Dic₆₁	1	2	yes	—
97	C₈	C₄×Dic₆₁	1	1	yes	characteristic
98	C₂²	—	4	1	no	—
99	C₂²	#14519734	1	2	yes	—
100	C₂²	#14519736	1	1	yes	characteristic
101	C₄	—	4	2	no	—
102	C₄	—	244	4	no	—
103	C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
104	C₄	#14519734	1	2	yes	—
105	C₄	#14519736	1	1	yes	characteristic
106	C₂	—	2	1	no	—
107	C₂	—	2	2	no	—
108	C₂	#16839608	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16839717

C₂

yes

maximal

#16839520

C₂

yes

maximal, characteristic

#16839519

C₂

yes

maximal, characteristic

#16839518

C₂

yes

maximal

C₆₁×#405

C₂

yes

maximal, characteristic

C₂×#11758194

C₂²

yes

—

#14519736

C₂²

yes

—

#14519687

C₄

yes

complemented

C₈×Dic₆₁

C₄

yes

complemented

C₂×M₁₆×C₆₁

C₂²

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#117×C₆₁

C₂²

yes

characteristic

#97×C₆₁

C₄

yes

complemented

C₄×C₈×C₆₁

C₄

yes

complemented

C₂²×C₄×C₆₁

C₂³

yes

characteristic

M₁₆×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

C₂×C₄

yes

—

#11758194

—

#11758194

—

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

#41

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂²×C₄

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

C₄²

yes

—

C₈×C₆₁

C₄²

yes

characteristic

C₈×C₆₁

C₄²

yes

characteristic

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

#117

yes

—

C₂²×C₆₁

#117

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

#117

yes

—

C₄×C₆₁

#117

yes

characteristic

Dic₆₁

—

#1747

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

yes

—

D₆₁

yes

—

—

—

C₆₁

#1747

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

—

#117

C₂×D₆₁

yes

characteristic

#97

—

#97

Dic₆₁

yes

complemented

C₄×C₈

—

C₄×C₈

Dic₆₁

yes

complemented

C₂²×C₄

C₂²×D₆₁

yes

characteristic

M₁₆

—

M₁₆

—

122

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

C₂²⋊C₄

—

122

—

C₄²

—

C₄²

C₂×Dic₆₁

yes

—

C₂³

#11758222

yes

characteristic

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₂×C₄×D₆₁

yes

—

C₂×C₄

#11758222

yes

characteristic

C₂×C₄

#11758222

yes

—

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₈

—

C₈

—

122

—

C₈

C₄×Dic₆₁

yes

characteristic

C₈

C₄×Dic₆₁

yes

—

C₈

C₄×Dic₆₁

yes

characteristic

C₂²

—

C₂²

#14519734

yes

—

100

C₂²

#14519736

yes

characteristic

101

C₄

—

102

C₄

—

244

—

103

C₄

C₂×C₄×Dic₆₁

yes

characteristic

104

C₄

#14519734

yes

—

105

C₄

#14519736

yes

characteristic

106

C₂

—

107

C₂

—

108

C₂

#16839608

yes

characteristic

	subgroup	G/H
center	C₈	C₄×Dic₆₁
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#405	C₂
socle	C₂×C₆₁	#376
hypercenter	#405	D₆₁
hypocenter	C₆₁	#1747
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ #405

subgroup

G/H

center

C₈

C₄×Dic₆₁

commutator

C₄×C₆₁

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₆₁

Fitting

C₆₁×#405

C₂

C₂×C₆₁

D₆₁

C₆₁

G ▷ C₄×C₆₁ ▷ C₆₁

C₁ ◁ C₈ ◁ #405

N	H ≅ G/N	type
8. #14519687	C₄	semidirect
9. C₈×Dic₆₁	C₄	semidirect
13. #97×C₆₁	C₄	semidirect
14. C₄×C₈×C₆₁	C₄	semidirect
60. C₆₁	#1747	semidirect
67. #97	Dic₆₁	semidirect
69. C₄×C₈	Dic₆₁	semidirect

H ≅ G/N

type

8. #14519687

C₄

semidirect

9. C₈×Dic₆₁

C₄

semidirect

13. #97×C₆₁

C₄

semidirect

14. C₄×C₈×C₆₁

C₄

semidirect

60. C₆₁

#1747

semidirect

67. #97

Dic₆₁

semidirect

69. C₄×C₈

Dic₆₁

semidirect

Subgroups — #21445574

Conjugacy classes of subgroups

Complements