Group #21447415 — subgroups

Subgroups — #21447415

Order 7808.

184 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 125 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	C₂×#14519717	C₂	1	1	yes	maximal, characteristic
2	#16839717	C₂	1	1	yes	maximal, characteristic
3	#16839537	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₆₁	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₄	1	1	yes	characteristic
7	#14519736	C₄	1	1	yes	characteristic
8	#14519717	C₄	1	4	yes	complemented
9	C₂×#11758185	C₂²	1	2	yes	—
10	#14519687	C₄	1	2	yes	—
11	C₈×Dic₆₁	C₂²	1	2	yes	—
12	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₆₁	C₄	1	4	yes	complemented
14	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
21	C₂²⋊Dic₆₁	C₈	1	2	yes	—
22	C₄⋊Dic₆₁	C₈	1	2	yes	—
23	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
24	#11758194	C₈	1	4	yes	—
25	C₂×#92418	C₂×C₄	1	2	yes	—
26	C₁₆×C₆₁	C₂×C₄	1	2	yes	—
27	C₁₆×C₆₁	C₂×C₄	1	2	yes	—
28	#11758185	C₂×C₄	1	4	yes	—
29	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₄²	1	2	yes	—
31	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	C₂×C₈	1	4	yes	—
35	C₈×C₆₁	C₄²	1	2	yes	—
36	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	#92418	C₂×C₈	1	4	yes	—
39	C₂²×C₆₁	—	2	2	no	—
40	C₂²×C₆₁	C₄×C₈	1	2	yes	—
41	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₆₁	C₄×C₈	1	2	yes	—
43	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
44	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
45	Dic₆₁	—	2	4	no	—
46	#2108	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	—	2	2	no	—
48	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
49	C₂×C₆₁	#504	1	2	yes	—
50	C₂×M₃₂	—	61	1	no	—
51	C₂²×C₁₆	D₆₁	1	1	yes	characteristic
52	#405	—	61	1	no	—
53	#346	—	61	2	no	—
54	C₄×C₁₆	—	61	2	no	—
55	C₆₁	#2108	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₁₆	—	61	1	no	—
57	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
58	#117	—	61	1	no	—
59	M₃₂	—	61	4	no	—
60	C₂×C₁₆	—	61	2	no	—
61	C₂×C₁₆	Dic₆₁	1	4	yes	complemented
62	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
63	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
64	#97	—	61	2	no	—
65	C₄×C₈	—	61	2	no	—
66	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
67	M₁₆	—	61	4	no	—
68	C₂×C₈	—	61	2	no	—
69	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
70	C₂×C₈	C₄×D₆₁	1	2	yes	—
71	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
72	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
73	C₄⋊C₄	—	61	2	no	—
74	C₂²⋊C₄	—	61	2	no	—
75	C₄²	—	61	2	no	—
76	C₁₆	—	61	4	no	—
77	C₁₆	C₂×Dic₆₁	1	2	yes	—
78	C₁₆	C₂×Dic₆₁	1	2	yes	—
79	C₂³	C₈×D₆₁	1	1	yes	characteristic
80	C₂×C₄	—	61	4	no	—
81	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
82	C₂×C₄	C₈×D₆₁	1	2	yes	—
83	C₂×C₄	C₄×Dic₆₁	1	2	yes	—
84	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
85	C₈	—	61	4	no	—
86	C₈	C₄×Dic₆₁	1	2	yes	—
87	C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
88	C₈	C₂²×Dic₆₁	1	1	yes	characteristic
89	C₂²	—	2	2	no	—
90	C₂²	C₈×Dic₆₁	1	2	yes	—
91	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
92	C₄	—	122	4	no	—
93	C₄	C₈×Dic₆₁	1	2	yes	—
94	C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
95	C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
96	C₂	—	2	2	no	—
97	C₂	C₂×C₈×Dic₆₁	1	1	yes	characteristic
98	C₂	#16840178	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519717

C₂

yes

maximal, characteristic

#16839717

C₂

yes

maximal, characteristic

#16839537

C₂

yes

maximal, complemented

C₁₆×Dic₆₁

C₂

yes

maximal, complemented

C₂²×C₁₆×C₆₁

C₂

yes

maximal, characteristic

C₂×#11758194

C₄

yes

characteristic

#14519736

C₄

yes

characteristic

#14519717

C₄

yes

complemented

C₂×#11758185

C₂²

yes

—

#14519687

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₄

yes

complemented

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₂²⋊Dic₆₁

C₈

yes

—

C₄⋊Dic₆₁

C₈

yes

—

C₄×Dic₆₁

C₂×C₄

yes

—

#11758194

C₈

yes

—

C₂×#92418

C₂×C₄

yes

—

C₁₆×C₆₁

C₂×C₄

yes

—

C₁₆×C₆₁

C₂×C₄

yes

—

#11758185

C₂×C₄

yes

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

—

C₈×C₆₁

C₄²

yes

—

C₈×C₆₁

C₂²×C₄

yes

characteristic

C₈×C₆₁

C₂²×C₄

yes

characteristic

#92418

C₂×C₈

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

C₄×C₈

yes

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

C₄×C₈

yes

—

C₄×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

—

#2108

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×C₄×C₈

yes

characteristic

C₂×C₆₁

#504

yes

—

C₂×M₃₂

—

C₂²×C₁₆

D₆₁

yes

characteristic

#405

—

#346

—

C₄×C₁₆

—

C₆₁

#2108

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

Dic₆₁

yes

complemented

C₂×C₁₆

C₂×D₆₁

yes

characteristic

C₂×C₁₆

C₂×D₆₁

yes

characteristic

#97

—

C₄×C₈

—

C₂²×C₄

C₄×D₆₁

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₄×D₆₁

yes

—

C₂×C₈

C₂×Dic₆₁

yes

—

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₁₆

C₂×Dic₆₁

yes

—

C₁₆

C₂×Dic₆₁

yes

—

C₂³

C₈×D₆₁

yes

characteristic

C₂×C₄

—

C₂×C₄

C₈×D₆₁

yes

characteristic

C₂×C₄

C₈×D₆₁

yes

—

C₂×C₄

C₄×Dic₆₁

yes

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

C₈

C₄×Dic₆₁

yes

—

C₈

C₂×C₄×D₆₁

yes

characteristic

C₈

C₂²×Dic₆₁

yes

characteristic

C₂²

—

C₂²

C₈×Dic₆₁

yes

—

C₂²

C₂×C₈×D₆₁

yes

characteristic

C₄

—

122

—

C₄

C₈×Dic₆₁

yes

—

C₄

C₂×C₄×Dic₆₁

yes

characteristic

C₄

C₂×C₈×D₆₁

yes

characteristic

C₂

—

C₂

C₂×C₈×Dic₆₁

yes

characteristic

C₂

#16840178

yes

—

	subgroup	G/H
center	C₂×C₁₆	C₂×D₆₁
commutator	C₂×C₆₁	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂²×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂²×C₈
hypercenter	C₂²×C₁₆	D₆₁
hypocenter	C₆₁	#2108
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

subgroup

G/H

center

C₂×C₁₆

C₂×D₆₁

commutator

C₂×C₆₁

C₂×C₄×C₈

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₂²×C₁₆×C₆₁

C₂

socle

C₂²×C₆₁

C₂²×C₈

hypercenter

C₂²×C₁₆

D₆₁

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

N	H ≅ G/N	type
3. #16839537	C₂	semidirect
4. C₁₆×Dic₆₁	C₂	semidirect
8. #14519717	C₄	semidirect
13. C₂×C₁₆×C₆₁	C₄	semidirect
55. C₆₁	#2108	semidirect
61. C₂×C₁₆	Dic₆₁	semidirect

H ≅ G/N

type

3. #16839537

C₂

semidirect

4. C₁₆×Dic₆₁

C₂

semidirect

8. #14519717

C₄

semidirect

13. C₂×C₁₆×C₆₁

C₄

semidirect

55. C₆₁

#2108

semidirect

61. C₂×C₁₆

Dic₆₁

semidirect

Subgroups — #21447415

Conjugacy classes of subgroups

Complements