Group #21461023 — subgroups

Subgroups — #21461023

Order 7808.

212 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 106 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	#16840780	C₂	1	2	yes	maximal
2	#16840603	C₂	1	2	yes	maximal, complemented
3	C₈×#92420	C₂	1	2	yes	maximal, complemented
4	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
5	#14519844	C₄	1	4	yes	—
6	#14519834	C₄	1	4	yes	—
7	C₄×#92420	C₂²	1	4	yes	—
8	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
9	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
10	C₄²×D₆₁	C₂²	1	1	yes	characteristic
11	C₄×#92418	C₄	1	1	yes	characteristic
12	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
15	C₂×C₄×D₆₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×#92420	C₂×C₄	1	8	yes	—
18	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
22	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
23	C₂×#92418	C₂×C₄	1	1	yes	characteristic
24	C₂×#92418	C₂×C₄	1	1	yes	characteristic
25	C₈×D₆₁	C₈	1	4	yes	complemented
26	C₈×D₆₁	C₈	1	4	yes	complemented
27	C₂²×D₆₁	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₄²	1	2	yes	—
29	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
31	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
32	C₄×D₆₁	—	2	4	no	—
33	C₄×D₆₁	C₂×C₈	1	2	yes	—
34	C₄×D₆₁	C₂×C₈	1	2	yes	—
35	#92420	—	2	8	no	—
36	C₈×C₆₁	C₂×C₈	1	2	yes	—
37	C₈×C₆₁	C₂×C₈	1	2	yes	—
38	#92418	C₂×C₈	1	2	yes	—
39	#92418	C₂×C₈	1	2	yes	—
40	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
41	C₂×D₆₁	—	2	2	no	—
42	C₂×D₆₁	C₄×C₈	1	2	yes	—
43	C₄×C₆₁	—	2	2	no	—
44	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
45	C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
46	Dic₆₁	C₄×C₈	1	2	yes	—
47	Dic₆₁	#131	1	4	yes	—
48	#1450	—	61	1	no	maximal, Sylow
49	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
50	C₂×C₆₁	#405	1	2	yes	—
51	D₆₁	—	2	2	no	—
52	#431	—	61	2	no	—
53	C₂×C₄×C₈	—	61	1	no	—
54	#322	—	61	2	no	—
55	C₈²	—	61	2	no	—
56	C₆₁	#1450	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	—	61	1	no	—
58	C₂²×C₈	—	61	1	no	—
59	C₂×C₄²	—	61	1	no	—
60	C₄⋊C₈	—	61	4	no	—
61	C₂²⋊C₈	—	61	4	no	—
62	C₄×C₈	—	61	4	no	—
63	C₄×C₈	—	61	1	no	—
64	C₄×C₈	—	61	1	no	—
65	C₄×C₈	—	61	1	no	—
66	C₄×C₈	#6923	1	1	yes	characteristic
67	C₂²×C₄	—	61	1	no	—
68	C₂²×C₄	—	61	2	no	—
69	C₂×C₈	—	61	1	no	—
70	C₂×C₈	—	61	1	no	—
71	C₂×C₈	—	61	4	no	—
72	C₂×C₈	—	61	4	no	—
73	C₂×C₈	—	61	8	no	—
74	C₂×C₈	C₂×#6923	1	1	yes	characteristic
75	C₂×C₈	C₂×#6923	1	1	yes	characteristic
76	C₄²	—	61	2	no	—
77	C₄²	—	61	1	no	—
78	C₄²	C₂×#6923	1	1	yes	characteristic
79	C₂³	—	61	1	no	—
80	C₂×C₄	—	61	1	no	—
81	C₂×C₄	—	61	2	no	—
82	C₂×C₄	—	61	2	no	—
83	C₂×C₄	—	61	2	no	—
84	C₂×C₄	—	122	4	no	—
85	C₂×C₄	C₄×#6923	1	2	yes	—
86	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
87	C₈	—	61	2	no	—
88	C₈	—	61	2	no	—
89	C₈	—	122	8	no	—
90	C₈	D₆₁⋊C₈	1	2	yes	—
91	C₈	D₆₁⋊C₈	1	2	yes	—
92	C₂²	—	61	2	no	—
93	C₂²	—	122	2	no	—
94	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	61	2	no	—
97	C₄	—	61	4	no	—
98	C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
99	C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
100	C₂	—	122	2	no	—
101	C₂	C₄×D₆₁⋊C₈	1	1	yes	characteristic
102	C₂	#16840725	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840780

C₂

yes

maximal

#16840603

C₂

yes

maximal, complemented

C₈×#92420

C₂

yes

maximal, complemented

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

#14519844

C₄

yes

—

#14519834

C₄

yes

—

C₄×#92420

C₂²

yes

—

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₄

yes

characteristic

C₄²×D₆₁

C₂²

yes

characteristic

C₄×#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₄×C₈×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×#92420

C₂×C₄

yes

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

C₈

yes

complemented

C₈×D₆₁

C₈

yes

complemented

C₂²×D₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₂²×C₄

yes

—

C₄×D₆₁

—

C₄×D₆₁

C₂×C₈

yes

—

C₄×D₆₁

C₂×C₈

yes

—

#92420

—

C₈×C₆₁

C₂×C₈

yes

—

C₈×C₆₁

C₂×C₈

yes

—

#92418

C₂×C₈

yes

—

#92418

C₂×C₈

yes

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

C₄×C₈

yes

—

C₄×C₆₁

—

C₄×C₆₁

C₂²×C₈

yes

characteristic

C₄×C₆₁

C₂²×C₈

yes

characteristic

Dic₆₁

C₄×C₈

yes

—

Dic₆₁

#131

yes

—

#1450

—

maximal, Sylow

C₂×C₆₁

C₂×C₄×C₈

yes

characteristic

C₂×C₆₁

#405

yes

—

D₆₁

—

#431

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₆₁

#1450

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

122

—

C₂×C₄

C₄×#6923

yes

—

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

C₈

—

C₈

—

122

—

C₈

D₆₁⋊C₈

yes

—

C₈

D₆₁⋊C₈

yes

—

C₂²

—

C₂²

—

122

—

C₂²

C₂×C₄×#6923

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₂×D₆₁⋊C₈

yes

characteristic

C₄

C₂×D₆₁⋊C₈

yes

characteristic

100

C₂

—

122

—

101

C₂

C₄×D₆₁⋊C₈

yes

characteristic

102

C₂

#16840725

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×#6923
commutator	C₂×C₆₁	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄²
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1450
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

subgroup

G/H

center

C₂×C₈

C₂×#6923

commutator

C₂×C₆₁

C₂×C₄×C₈

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₄×C₈×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄²

C₄×C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₈ ◁ C₄×C₈

N	H ≅ G/N	type
2. #16840603	C₂	semidirect
3. C₈×#92420	C₂	semidirect
25. C₈×D₆₁	C₈	semidirect
26. C₈×D₆₁	C₈	semidirect
56. C₆₁	#1450	semidirect

H ≅ G/N

type

2. #16840603

C₂

semidirect

3. C₈×#92420

C₂

semidirect

25. C₈×D₆₁

C₈

semidirect

26. C₈×D₆₁

C₈

semidirect

56. C₆₁

#1450

semidirect

Subgroups — #21461023

Conjugacy classes of subgroups

Complements