Group #21462218 — subgroups

Subgroups — #21462218

Order 7808.

146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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	#16840804	C₂	1	2	yes	maximal, complemented
2	#16840690	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840676	C₂	1	2	yes	maximal, complemented
4	C₁₆×#6923	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840191	C₂	1	1	yes	maximal, characteristic
6	#14519864	—	2	2	no	—
7	D₆₁⋊C₁₆	C₂²	1	1	yes	characteristic
8	#14519848	C₂²	1	2	yes	—
9	#14519841	—	2	2	no	—
10	C₈×#6923	C₂²	1	1	yes	characteristic
11	#14519796	C₂²	1	2	yes	—
12	Dic₄₈₈	C₄	1	1	yes	characteristic, complemented
13	#14519721	C₄	1	2	yes	complemented
14	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
15	D₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
16	#11758224	—	2	2	no	—
17	#11758217	—	4	2	no	—
18	C₂×#92420	—	4	2	no	—
19	C₄×#6923	D₄	1	1	yes	characteristic
20	#11758213	—	2	2	no	—
21	D₆₁⋊C₈	D₄	1	1	yes	characteristic
22	D₈×C₆₁	C₂×C₄	1	2	yes	—
23	#11758200	—	2	2	no	—
24	Dic₂₄₄	C₂×C₄	1	2	yes	—
25	C₈×D₆₁	C₂³	1	1	yes	characteristic
26	#11758187	—	2	1	no	—
27	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
28	#11758185	C₂×C₄	1	1	yes	characteristic
29	C₂×#6923	—	2	1	no	—
30	D₄×C₆₁	—	2	2	no	—
31	C₂²⋊D₆₁	—	4	2	no	—
32	C₂×Dic₆₁	—	4	2	no	—
33	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
34	Dic₁₂₂	—	2	2	no	—
35	#92420	—	4	2	no	—
36	#92420	D₈	1	1	yes	characteristic
37	#92420	D₈	1	1	yes	characteristic
38	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
39	#92418	#41	1	1	yes	characteristic
40	C₂²×C₆₁	—	4	2	no	—
41	C₂×D₆₁	#135	1	1	yes	characteristic
42	#6923	—	2	2	no	—
43	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
44	Dic₆₁	—	4	2	no	—
45	Dic₆₁	C₂×D₈	1	1	yes	characteristic
46	#2178	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	—	8	2	no	—
48	C₂×C₆₁	C₄×D₈	1	1	yes	characteristic
49	D₆₁	—	2	1	no	—
50	#508	—	61	1	no	—
51	#443	—	61	2	no	—
52	#368	—	61	1	no	—
53	#359	—	61	2	no	—
54	C₄×C₁₆	—	61	1	no	—
55	C₆₁	#2178	1	1	yes	characteristic, complemented, Sylow
56	#135	—	61	2	no	—
57	#131	—	122	2	no	—
58	Q₃₂	—	61	1	no	—
59	SD₃₂	—	61	2	no	—
60	D₁₆	#6923	1	1	yes	characteristic, complemented
61	C₂×C₁₆	—	61	1	no	—
62	C₂×C₁₆	—	61	1	no	—
63	#108	—	61	2	no	—
64	#104	—	122	2	no	—
65	C₄×C₈	—	61	1	no	—
66	#41	—	122	2	no	—
67	Q₁₆	—	61	2	no	—
68	SD₁₆	—	122	2	no	—
69	D₈	C₂×#6923	1	2	yes	—
70	M₁₆	—	122	2	no	—
71	M₁₆	—	244	2	no	—
72	C₂×C₈	—	61	1	no	—
73	C₂×C₈	—	61	1	no	—
74	C₂×C₈	—	244	2	no	—
75	C₄²	—	61	1	no	—
76	C₁₆	—	61	1	no	—
77	C₁₆	—	122	1	no	—
78	C₁₆	C₂×#6923	1	1	yes	characteristic
79	Q₈	—	122	2	no	—
80	D₄	—	2	2	no	—
81	D₄	—	244	2	no	—
82	C₂×C₄	—	61	1	no	—
83	C₂×C₄	—	122	1	no	—
84	C₂×C₄	—	244	2	no	—
85	C₈	—	61	1	no	—
86	C₈	—	61	1	no	—
87	C₈	—	61	1	no	—
88	C₈	—	244	2	no	—
89	C₈	C₂²×#6923	1	1	yes	characteristic
90	C₂²	—	4	2	no	—
91	C₂²	—	61	1	no	—
92	C₄	—	61	1	no	—
93	C₄	—	122	2	no	—
94	C₄	—	244	2	no	—
95	C₄	D₄×#6923	1	1	yes	characteristic
96	C₂	—	8	2	no	—
97	C₂	—	122	1	no	—
98	C₂	D₈×#6923	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840804

C₂

yes

maximal, complemented

#16840690

C₂

yes

maximal, characteristic, complemented

#16840676

C₂

yes

maximal, complemented

C₁₆×#6923

C₂

yes

maximal, characteristic, complemented

#16840191

C₂

yes

maximal, characteristic

#14519864

—

D₆₁⋊C₁₆

C₂²

yes

characteristic

#14519848

C₂²

yes

—

#14519841

—

C₈×#6923

C₂²

yes

characteristic

#14519796

C₂²

yes

—

Dic₄₈₈

C₄

yes

characteristic, complemented

#14519721

C₄

yes

complemented

C₁₆×D₆₁

C₂²

yes

characteristic

D₁₆×C₆₁

C₄

yes

characteristic, complemented

—

—

—

D₄

yes

characteristic

#11758213

—

D₆₁⋊C₈

D₄

yes

characteristic

D₈×C₆₁

C₂×C₄

yes

—

#11758200

—

Dic₂₄₄

C₂×C₄

yes

—

C₈×D₆₁

C₂³

yes

characteristic

#11758187

—

C₁₆×C₆₁

C₂×C₄

yes

characteristic

#11758185

C₂×C₄

yes

characteristic

C₂×#6923

—

D₄×C₆₁

—

C₂²⋊D₆₁

—

C₂×Dic₆₁

—

C₄×D₆₁

C₂×D₄

yes

characteristic

Dic₁₂₂

—

#92420

—

#92420

D₈

yes

characteristic

#92420

D₈

yes

characteristic

C₈×C₆₁

C₂²×C₄

yes

yes

C₂²×C₆₁

—

C₂×D₆₁

#135

yes

characteristic

#6923

—

C₄×C₆₁

C₄×D₄

yes

characteristic

Dic₆₁

—

Dic₆₁

C₂×D₈

yes

characteristic

#2178

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₄×D₈

yes

characteristic

D₆₁

—

—

—

—

—

C₄×C₁₆

—

C₆₁

#2178

yes

characteristic, complemented, Sylow

#135

—

#131

—

122

—

Q₃₂

—

SD₃₂

—

D₁₆

#6923

yes

characteristic, complemented

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#104

—

122

—

C₄×C₈

—

#41

—

122

—

Q₁₆

—

SD₁₆

—

122

—

D₈

C₂×#6923

yes

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

244

—

C₄²

—

C₁₆

—

C₁₆

—

122

—

C₁₆

C₂×#6923

yes

characteristic

Q₈

—

122

—

D₄

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

—

244

—

C₈

—

C₈

—

C₈

—

C₈

—

244

—

C₈

C₂²×#6923

yes

characteristic

C₂²

—

C₂²

—

C₄

—

C₄

—

122

—

C₄

—

244

—

C₄

D₄×#6923

yes

characteristic

C₂

—

C₂

—

122

—

C₂

D₈×#6923

yes

characteristic

	subgroup	G/H
center	C₂	D₈×#6923
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₈	C₂²×#6923
Fitting	D₁₆×C₆₁	C₄
socle	C₂×C₆₁	C₄×D₈
hypercenter	D₁₆	#6923
hypocenter	C₆₁	#2178
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

subgroup

G/H

center

C₂

D₈×#6923

commutator

C₈×C₆₁

C₂²×C₄

Frattini

C₈

C₂²×#6923

Fitting

D₁₆×C₆₁

C₄

socle

C₂×C₆₁

C₄×D₈

D₁₆

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

N	H ≅ G/N	type
1. #16840804	C₂	semidirect
2. #16840690	C₂	semidirect
3. #16840676	C₂	semidirect
4. C₁₆×#6923	C₂	semidirect
12. Dic₄₈₈	C₄	semidirect
13. #14519721	C₄	semidirect
15. D₁₆×C₆₁	C₄	semidirect
55. C₆₁	#2178	semidirect
60. D₁₆	#6923	semidirect

H ≅ G/N

type

1. #16840804

C₂

semidirect

2. #16840690

C₂

semidirect

3. #16840676

C₂

semidirect

4. C₁₆×#6923

C₂

semidirect

12. Dic₄₈₈

C₄

semidirect

13. #14519721

C₄

semidirect

15. D₁₆×C₆₁

C₄

semidirect

55. C₆₁

#2178

semidirect

60. D₁₆

#6923

semidirect

Subgroups — #21462218

Conjugacy classes of subgroups

Complements