Group #21447624 — subgroups

Subgroups — #21447624

Order 7808.

138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 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	#16839716	C₂	1	1	yes	maximal, characteristic
2	#16839580	C₂	1	2	yes	maximal, complemented
3	#16839541	C₂	1	2	yes	maximal
4	#16839538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11758189	C₄	1	1	yes	characteristic
7	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
8	#14519734	C₄	1	1	yes	characteristic
9	C₂×#11758185	C₂²	1	2	yes	—
10	#14519688	C₄	1	1	yes	characteristic
11	#14519687	C₄	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
18	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
19	#11758198	C₈	1	2	yes	—
20	#11758196	C₈	1	2	yes	—
21	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×#92418	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	C₂×C₄	1	1	yes	characteristic
24	#11758189	—	2	2	no	—
25	C₈×D₆₁	—	2	2	no	—
26	C₁₆×C₆₁	—	2	2	no	—
27	#11758185	—	2	2	no	—
28	C₂²×D₆₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₆₁	C₂×C₈	1	2	yes	—
32	C₂×Dic₆₁	C₂×C₈	1	1	yes	characteristic
33	C₄×D₆₁	—	2	1	no	—
34	C₄×D₆₁	—	2	1	no	—
35	C₈×C₆₁	M₁₆	1	2	yes	—
36	C₈×C₆₁	#41	1	2	yes	—
37	#92418	—	2	1	no	—
38	#92418	—	2	1	no	—
39	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
40	C₂×D₆₁	—	2	1	no	—
41	C₂×D₆₁	—	2	2	no	—
42	C₄×C₆₁	—	2	2	no	—
43	C₄×C₆₁	#117	1	1	yes	characteristic
44	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
45	Dic₆₁	—	2	1	no	—
46	Dic₆₁	—	2	2	no	—
47	#2164	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	#431	1	1	yes	characteristic
49	C₂×C₆₁	#504	1	2	yes	—
50	D₆₁	—	4	1	no	—
51	#405	—	61	1	no	—
52	C₄⋊C₁₆	—	61	2	no	—
53	C₂²⋊C₁₆	—	61	2	no	—
54	#346	—	61	1	no	—
55	C₄×C₁₆	D₆₁	1	1	yes	characteristic, complemented
56	C₆₁	#2164	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	61	1	no	—
58	C₂²×C₈	—	61	1	no	—
59	#117	—	61	1	no	—
60	C₂×C₁₆	—	61	2	no	—
61	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
62	#97	—	61	1	no	—
63	#97	—	61	1	no	—
64	C₄×C₈	—	61	1	no	—
65	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
66	C₂²×C₄	—	61	1	no	—
67	M₁₆	—	122	2	no	—
68	C₂×C₈	—	61	1	no	—
69	C₂×C₈	—	61	1	no	—
70	C₂×C₈	—	122	2	no	—
71	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
73	C₄⋊C₄	—	61	2	no	—
74	C₂²⋊C₄	—	61	2	no	—
75	C₄²	—	61	1	no	—
76	C₄²	C₄×D₆₁	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	122	2	no	—
79	C₂³	—	61	1	no	—
80	C₂×C₄	—	61	2	no	—
81	C₂×C₄	—	61	1	no	—
82	C₂×C₄	—	122	1	no	—
83	C₂×C₄	—	122	1	no	—
84	C₂×C₄	C₈×D₆₁	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
86	C₈	—	122	1	no	—
87	C₈	—	122	1	no	—
88	C₈	#11758189	1	2	yes	—
89	C₈	#11758222	1	2	yes	—
90	C₂²	—	122	1	no	—
91	C₂²	—	122	2	no	—
92	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	122	1	no	—
95	C₄	—	122	2	no	—
96	C₄	#14519734	1	1	yes	characteristic
97	C₄	C₂×#11758189	1	1	yes	characteristic
98	C₂	—	244	1	no	—
99	C₂	#16839813	1	1	yes	characteristic
100	C₂	#16840178	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16839716

C₂

yes

maximal, characteristic

#16839580

C₂

yes

maximal, complemented

#16839541

C₂

yes

maximal

#16839538

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₆₁

C₂

yes

maximal, characteristic, complemented

C₂×#11758189

C₄

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519734

C₄

yes

characteristic

C₂×#11758185

C₂²

yes

—

#14519688

C₄

yes

characteristic

#14519687

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₂×C₁₆×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758198

C₈

yes

—

#11758196

C₈

yes

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

#11758189

—

C₈×D₆₁

—

C₁₆×C₆₁

—

#11758185

—

C₂²×D₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

C₂×C₈

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₈×C₆₁

M₁₆

yes

—

C₈×C₆₁

#41

yes

—

#92418

—

#92418

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

—

D₆₁

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

D₆₁

yes

characteristic, complemented

C₆₁

#2164

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₆₁

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₄×D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₆₁

yes

characteristic

C₁₆

—

C₁₆

—

122

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

122

—

C₂×C₄

C₈×D₆₁

yes

—

C₂×C₄

C₂×C₄×D₆₁

yes

characteristic

C₈

—

122

—

C₈

—

122

—

C₈

#11758189

yes

—

C₈

#11758222

yes

—

C₂²

—

122

—

C₂²

—

122

—

C₂²

C₂×C₈×D₆₁

yes

characteristic

C₄

—

C₄

—

122

—

C₄

—

122

—

C₄

yes

C₄

yes

C₂

—

244

—

C₂

#16839813

yes

characteristic

100

C₂

#16840178

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₄×C₁₆×C₆₁	C₂
hypercenter	C₄×C₁₆	D₆₁
hypocenter	C₆₁	#2164
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₆₁

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₄×C₁₆×C₆₁

C₂

hypercenter

C₄×C₁₆

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. #16839580	C₂	semidirect
4. #16839538	C₂	semidirect
5. C₄×C₁₆×C₆₁	C₂	semidirect
55. C₄×C₁₆	D₆₁	semidirect
56. C₆₁	#2164	semidirect

H ≅ G/N

type

2. #16839580

C₂

semidirect

4. #16839538

C₂

semidirect

5. C₄×C₁₆×C₆₁

C₂

semidirect

55. C₄×C₁₆

D₆₁

semidirect

56. C₆₁

#2164

semidirect

Subgroups — #21447624

Conjugacy classes of subgroups

Complements