Group #21447626 — subgroups

Subgroups — #21447626

Order 7808.

138 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₄⋊#11758185	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11758185	C₂	1	2	yes	maximal
3	#16839538	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#11758185	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758185	C₂²	1	2	yes	—
7	C₂×#11758185	C₂²	1	2	yes	—
8	C₂×M₁₆×C₆₁	C₄	1	1	yes	characteristic
9	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	#117×C₆₁	C₄	1	1	yes	characteristic
11	#97×C₆₁	C₄	1	1	yes	characteristic
12	#97×C₆₁	C₄	1	1	yes	characteristic
13	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
16	M₁₆×C₆₁	—	2	2	no	—
17	C₂×C₈×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₆₁	C₈	1	2	yes	—
23	C₂²⋊C₄×C₆₁	C₈	1	2	yes	—
24	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
26	#11758185	—	2	2	no	—
27	#11758185	—	2	2	no	—
28	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₆₁	—	2	1	no	—
30	C₂×C₄×C₆₁	—	2	1	no	—
31	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₆₁	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₆₁	—	2	1	no	—
36	C₈×C₆₁	—	2	1	no	—
37	C₈×C₆₁	M₁₆	1	2	yes	—
38	C₈×C₆₁	#41	1	2	yes	—
39	C₂²×C₆₁	—	2	1	no	—
40	C₂²×C₆₁	—	2	2	no	—
41	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₆₁	—	2	1	no	—
43	C₄×C₆₁	—	2	2	no	—
44	C₄×C₆₁	—	2	2	no	—
45	C₄×C₆₁	#117	1	1	yes	characteristic
46	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
47	#2164	—	61	1	no	maximal, Sylow
48	C₂×C₆₁	—	4	1	no	—
49	C₂×C₆₁	#431	1	1	yes	characteristic
50	C₂×C₆₁	#504	1	2	yes	—
51	#405	D₆₁	1	1	yes	characteristic
52	C₄⋊C₁₆	—	61	2	no	—
53	C₂²⋊C₁₆	—	61	2	no	—
54	#346	—	61	1	no	—
55	C₄×C₁₆	—	61	1	no	—
56	C₆₁	#2164	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	Dic₆₁	1	1	yes	characteristic
58	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
59	#117	Dic₆₁	1	1	yes	characteristic
60	C₂×C₁₆	—	61	2	no	—
61	C₂×C₁₆	—	61	2	no	—
62	#97	Dic₆₁	1	1	yes	characteristic
63	#97	Dic₆₁	1	1	yes	characteristic
64	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
65	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
66	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
70	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
71	C₂×C₈	C₂×Dic₆₁	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
73	C₄⋊C₄	#92418	1	2	yes	—
74	C₂²⋊C₄	#92418	1	2	yes	—
75	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
76	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
77	C₁₆	—	122	2	no	—
78	C₁₆	—	122	2	no	—
79	C₂³	C₂×#92418	1	1	yes	characteristic
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	C₂×#92418	1	2	yes	—
83	C₂×C₄	C₂×#92418	1	2	yes	—
84	C₂×C₄	C₂×#92418	1	1	yes	characteristic
85	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	2	1	no	—
88	C₈	#11758194	1	2	yes	—
89	C₈	#11758222	1	2	yes	—
90	C₂²	—	2	1	no	—
91	C₂²	—	2	2	no	—
92	C₂²	C₂²×#92418	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	2	2	no	—
96	C₄	#14519736	1	1	yes	characteristic
97	C₄	C₂×#11758194	1	1	yes	characteristic
98	C₂	—	4	1	no	—
99	C₂	#16839815	1	1	yes	characteristic
100	C₂	#16840179	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#11758185

C₂

yes

maximal, complemented

C₂²⋊#11758185

C₂

yes

maximal

#16839538

C₂

yes

maximal, characteristic, complemented

C₄×#11758185

C₂

yes

maximal, characteristic, complemented

C₆₁×#405

C₂

yes

maximal, characteristic

C₂×#11758185

C₂²

yes

—

C₂×#11758185

C₂²

yes

—

C₂×M₁₆×C₆₁

C₄

yes

characteristic

C₂²×C₈×C₆₁

C₂²

yes

characteristic

#117×C₆₁

C₄

yes

characteristic

#97×C₆₁

C₄

yes

characteristic

#97×C₆₁

C₄

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄⋊C₄×C₆₁

C₈

yes

—

C₂²⋊C₄×C₆₁

C₈

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

#11758185

—

#11758185

—

C₂³×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

—

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

—

C₈×C₆₁

#41

yes

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

—

C₄×C₆₁

#117

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

#2164

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

#431

yes

characteristic

C₂×C₆₁

#504

yes

—

#405

D₆₁

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₆₁

#2164

yes

characteristic, complemented, Sylow

C₂×M₁₆

Dic₆₁

yes

characteristic

C₂²×C₈

C₂×D₆₁

yes

characteristic

#117

Dic₆₁

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

#97

Dic₆₁

yes

characteristic

#97

Dic₆₁

yes

characteristic

C₄×C₈

C₂×D₆₁

yes

characteristic

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂²×C₄

C₂×Dic₆₁

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂×Dic₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

#92418

yes

—

C₂²⋊C₄

#92418

yes

—

C₄²

C₂×Dic₆₁

yes

characteristic

C₄²

C₂×Dic₆₁

yes

characteristic

C₁₆

—

122

—

C₁₆

—

122

—

C₂³

C₂×#92418

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#92418

yes

—

C₂×C₄

C₂×#92418

yes

—

C₂×C₄

C₂×#92418

yes

characteristic

C₂×C₄

C₂²×Dic₆₁

yes

characteristic

C₈

—

C₈

—

C₈

#11758194

yes

—

C₈

#11758222

yes

—

C₂²

—

C₂²

—

C₂²

C₂²×#92418

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

#16839815

yes

characteristic

100

C₂

#16840179

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₆₁×#405	C₂
hypercenter	#405	D₆₁
hypocenter	C₆₁	#2164
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ #405

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₆₁

commutator, socle

C₂²×C₆₁

C₂²×C₈

Fitting

C₆₁×#405

C₂

D₆₁

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ #405

N	H ≅ G/N	type
1. C₄⋊#11758185	C₂	semidirect
3. #16839538	C₂	semidirect
4. C₄×#11758185	C₂	semidirect
56. C₆₁	#2164	semidirect

H ≅ G/N

type

1. C₄⋊#11758185

C₂

semidirect

3. #16839538

C₂

semidirect

4. C₄×#11758185

C₂

semidirect

56. C₆₁

#2164

semidirect

Subgroups — #21447626

Conjugacy classes of subgroups

Complements