Group #21460659 — subgroups

Subgroups — #21460659

Order 7808.

152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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	#16840778	C₂	1	2	yes	maximal
2	C₂×#14519687	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#92420	—	2	2	no	—
4	C₂²⋊#92420	C₄	1	4	yes	—
5	C₄×#92420	—	2	2	no	—
6	C₂²×#92418	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
8	#14519687	—	2	2	no	—
9	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
12	C₂×#92420	—	2	4	no	—
13	C₂×C₈×C₆₁	—	2	1	no	—
14	C₂×C₈×C₆₁	—	2	1	no	—
15	C₂×C₈×C₆₁	C₈	1	2	yes	complemented
16	C₄×Dic₆₁	D₄	1	1	yes	characteristic
17	C₄×Dic₆₁	D₄	1	2	yes	—
18	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
19	C₂×#92418	—	2	1	no	—
20	C₂×#92418	—	2	1	no	—
21	C₂×#92418	C₈	1	2	yes	complemented
22	C₂³×C₆₁	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
29	C₂×Dic₆₁	—	4	2	no	—
30	C₂×Dic₆₁	C₂²⋊C₄	1	2	yes	—
31	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
32	#92420	—	4	4	no	—
33	C₈×C₆₁	—	2	2	no	—
34	#92418	—	2	2	no	—
35	C₂²×C₆₁	—	2	2	no	—
36	C₂²×C₆₁	#95	1	1	yes	characteristic
37	C₂²×C₆₁	C₄×C₈	1	1	yes	characteristic
38	C₂²×C₆₁	#97	1	1	yes	characteristic
39	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
42	C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
43	Dic₆₁	—	2	2	no	—
44	Dic₆₁	—	2	2	no	—
45	#1281	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	—	2	1	no	—
47	C₂×C₆₁	—	2	1	no	—
48	C₂×C₆₁	#336	1	1	yes	characteristic
49	C₂×C₆₁	#344	1	2	yes	—
50	#431	—	61	2	no	—
51	C₂×#97	—	61	1	no	—
52	C₆₁	#1281	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₈	—	61	1	no	—
54	C₂²×C₈	#6923	1	1	yes	characteristic
55	C₂×C₄²	—	61	1	no	—
56	C₄⋊C₈	—	122	2	no	—
57	C₂²⋊C₈	—	61	4	no	—
58	#97	—	122	2	no	—
59	C₄×C₈	—	122	2	no	—
60	C₂²×C₄	—	61	2	no	—
61	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
62	C₂×C₈	—	2	1	no	—
63	C₂×C₈	—	2	1	no	—
64	C₂×C₈	—	61	2	no	—
65	C₂×C₈	—	122	1	no	—
66	C₂×C₈	—	122	1	no	—
67	C₂×C₈	—	122	4	no	—
68	C₂×C₈	#92420	1	2	yes	complemented
69	C₄²	—	61	1	no	—
70	C₄²	—	61	1	no	—
71	C₄²	—	61	2	no	—
72	C₂³	C₄×#6923	1	1	yes	characteristic
73	C₂×C₄	—	61	2	no	—
74	C₂×C₄	—	61	2	no	—
75	C₂×C₄	—	244	2	no	—
76	C₂×C₄	D₆₁⋊C₈	1	1	yes	characteristic
77	C₂×C₄	#11758213	1	1	yes	characteristic
78	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
79	C₂×C₄	C₂×#92420	1	1	yes	characteristic
80	C₂×C₄	#11758217	1	1	yes	characteristic
81	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	122	2	no	—
84	C₈	—	244	4	no	—
85	C₂²	—	2	2	no	—
86	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
87	C₂²	C₄×#92420	1	1	yes	characteristic
88	C₂²	#14519832	1	1	yes	characteristic
89	C₄	—	122	2	no	—
90	C₄	—	122	2	no	—
91	C₄	C₂²⋊#92420	1	1	yes	characteristic
92	C₄	#14519834	1	1	yes	characteristic
93	C₄	C₄⋊#92420	1	1	yes	characteristic
94	C₄	#14519844	1	1	yes	characteristic
95	C₂	—	2	1	no	—
96	C₂	—	2	1	no	—
97	C₂	#16840628	1	1	yes	characteristic
98	C₂	#16840644	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#16840778

C₂

yes

maximal

C₂×#14519687

C₂

yes

maximal, characteristic

C₄⋊#92420

—

C₂²⋊#92420

C₄

yes

—

C₄×#92420

—

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519687

—

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

—

C₂×#92420

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₈

yes

complemented

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

—

C₄×Dic₆₁

Q₈

yes

—

—

C₈

yes

complemented

C₂³×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

C₂×C₈

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

C₂²⋊C₄

yes

—

C₂×Dic₆₁

C₄⋊C₄

yes

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

#95

yes

characteristic

C₂²×C₆₁

C₄×C₈

yes

characteristic

C₂²×C₆₁

#97

yes

characteristic

C₄×C₆₁

C₂²⋊C₈

yes

characteristic

C₄×C₆₁

C₂²⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

C₄×C₆₁

C₄⋊C₈

yes

characteristic

Dic₆₁

—

Dic₆₁

—

#1281

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

—

C₂×C₆₁

#336

yes

characteristic

C₂×C₆₁

#344

yes

—

#431

—

C₂×#97

—

C₆₁

#1281

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

#6923

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

#97

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

#92420

yes

complemented

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

244

—

C₂×C₄

D₆₁⋊C₈

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊#6923

yes

characteristic

C₈

—

C₈

—

122

—

C₈

—

244

—

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

—

122

—

C₄

—

122

—

C₄

yes

C₄

yes

C₄

yes

C₄

yes

C₂

—

C₂

—

C₂

#16840628

yes

characteristic

C₂

#16840644

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#6923
commutator	C₂²×C₆₁	C₄×C₈
Frattini	C₂²×C₄	C₂×#6923
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	#1281
LCS	G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊#6923

commutator

C₂²×C₆₁

C₄×C₈

Frattini

C₂²×C₄

C₂×#6923

Fitting

C₂²×C₈×C₆₁

C₄

C₂²×C₆₁

C₂²×C₈

C₆₁

G ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
15. C₂×C₈×C₆₁	C₈	semidirect
21. C₂×#92418	C₈	semidirect
52. C₆₁	#1281	semidirect
68. C₂×C₈	#92420	semidirect

H ≅ G/N

type

15. C₂×C₈×C₆₁

C₈

semidirect

21. C₂×#92418

C₈

semidirect

52. C₆₁

#1281

semidirect

68. C₂×C₈

#92420

semidirect

Subgroups — #21460659

Conjugacy classes of subgroups

Complements