Group #35308913 — subgroups

Subgroups — #35308913

Order 21248.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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	#24907596	C₂	1	3	yes	maximal
2	#24905344	C₂	1	3	yes	maximal
3	C₈₃×#2845	C₂	1	1	yes	maximal, characteristic
4	C₂×#14581703	C₂²	1	3	yes	—
5	#19127571	C₂²	1	1	yes	characteristic
6	#19127463	—	2	6	no	—
7	#398×C₈₃	—	2	6	no	—
8	#382×C₈₃	C₂²	1	3	yes	—
9	C₂²×C₈₃⋊C₈	—	2	3	no	—
10	C₂×C₄⋊Dic₈₃	—	2	3	no	—
11	#14581703	—	2	3	no	—
12	#14581703	Q₈	1	6	yes	—
13	C₂×C₄⋊C₄×C₈₃	—	2	6	no	—
14	C₂×C₄⋊C₄×C₈₃	D₄	1	6	yes	—
15	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
16	#95×C₈₃	—	2	2	no	—
17	#95×C₈₃	—	2	6	no	—
18	C₂²×Dic₈₃	—	4	1	no	—
19	C₂×C₈₃⋊C₈	—	2	6	no	—
20	C₂×C₈₃⋊C₈	—	4	3	no	—
21	C₂×C₈₃⋊C₈	—	4	3	no	—
22	C₄⋊Dic₈₃	—	4	6	no	—
23	C₂²×C₄×C₈₃	—	2	6	no	—
24	C₂²×C₄×C₈₃	C₂×D₄	1	3	yes	—
25	C₄⋊C₄×C₈₃	—	4	6	no	—
26	C₄⋊C₄×C₈₃	—	8	6	no	—
27	C₄²×C₈₃	C₂×Q₈	1	3	yes	—
28	C₄²×C₈₃	#41	1	1	yes	characteristic
29	C₂³×C₈₃	#120	1	1	yes	characteristic
30	C₂×C₄×C₈₃	—	2	3	no	—
31	C₂×C₄×C₈₃	—	2	3	no	—
32	C₂×C₄×C₈₃	—	4	6	no	—
33	C₂×C₄×C₈₃	—	4	6	no	—
34	C₂×C₄×C₈₃	—	4	6	no	—
35	C₂×C₄×C₈₃	C₂²⋊Q₈	1	3	yes	—
36	C₂×C₄×C₈₃	C₄⋊Q₈	1	3	yes	—
37	C₂×Dic₈₃	—	8	3	no	—
38	C₈₃⋊C₈	—	4	6	no	—
39	C₂²×C₈₃	#395	1	1	yes	characteristic
40	C₂²×C₈₃	#454	1	3	yes	—
41	C₂²×C₈₃	#455	1	3	yes	—
42	C₄×C₈₃	—	2	3	no	—
43	C₄×C₈₃	—	2	3	no	—
44	C₄×C₈₃	—	8	6	no	—
45	Dic₈₃	—	16	1	no	—
46	#10586	—	83	1	no	maximal, Sylow
47	C₂×C₈₃	#1658	1	1	yes	characteristic
48	C₂×C₈₃	#1662	1	3	yes	—
49	C₂×C₈₃	#2061	1	3	yes	—
50	#2845	D₈₃	1	1	yes	characteristic
51	#1836	—	83	3	no	—
52	#1295	—	83	3	no	—
53	C₈₃	#10586	1	1	yes	characteristic, complemented, Sylow
54	C₂×#97	—	83	3	no	—
55	#398	—	2	6	no	—
56	#384	—	83	1	no	—
57	#382	C₂×D₈₃	1	3	yes	—
58	#340	—	166	6	no	—
59	C₂²×C₈	—	166	3	no	—
60	C₂×C₄⋊C₄	—	2	6	no	—
61	C₂×C₄⋊C₄	—	166	3	no	—
62	C₂×C₄⋊C₄	C₂²⋊D₈₃	1	6	yes	—
63	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
64	#97	—	83	6	no	—
65	#97	—	166	3	no	—
66	#95	—	2	2	no	—
67	#95	—	2	6	no	—
68	C₂²×C₄	—	2	6	no	—
69	C₂²×C₄	—	332	1	no	—
70	C₂²×C₄	C₂×C₂²⋊D₈₃	1	3	yes	—
71	C₂×C₈	—	332	3	no	—
72	C₂×C₈	—	332	3	no	—
73	C₂×C₈	—	166	6	no	—
74	C₄⋊C₄	—	4	6	no	—
75	C₄⋊C₄	—	8	6	no	—
76	C₄⋊C₄	—	332	6	no	—
77	C₄²	Q₈×D₈₃	1	3	yes	—
78	C₄²	#13050591	1	1	yes	characteristic
79	C₂³	#14581761	1	1	yes	characteristic
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	4	6	no	—
85	C₂×C₄	—	664	3	no	—
86	C₂×C₄	#14581768	1	3	yes	—
87	C₂×C₄	#14581790	1	3	yes	—
88	C₈	—	332	6	no	—
89	C₂²	#19127620	1	1	yes	characteristic
90	C₂²	#19127874	1	3	yes	—
91	C₂²	#19127879	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	1328	1	no	—
96	C₂	#24906765	1	1	yes	characteristic
97	C₂	#24906786	1	3	yes	—
98	C₂	#24908810	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#24907596

C₂

yes

maximal

#24905344

C₂

yes

maximal

C₈₃×#2845

C₂

yes

maximal, characteristic

C₂×#14581703

C₂²

yes

—

#19127571

C₂²

yes

characteristic

#19127463

—

#398×C₈₃

—

#382×C₈₃

C₂²

yes

—

C₂²×C₈₃⋊C₈

—

C₂×C₄⋊Dic₈₃

—

#14581703

—

#14581703

Q₈

yes

—

C₂×C₄⋊C₄×C₈₃

—

C₂×C₄⋊C₄×C₈₃

D₄

yes

—

C₂×C₄²×C₈₃

C₂³

yes

characteristic

#95×C₈₃

—

#95×C₈₃

—

C₂²×Dic₈₃

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×D₄

yes

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄²×C₈₃

C₂×Q₈

yes

—

C₄²×C₈₃

yes

C₂³×C₈₃

yes

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₃

C₄⋊Q₈

yes

—

C₂×Dic₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

#395

yes

characteristic

C₂²×C₈₃

#454

yes

—

C₂²×C₈₃

#455

yes

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

Dic₈₃

—

—

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₂×C₈₃

#2061

yes

—

#2845

D₈₃

yes

characteristic

#1836

—

#1295

—

C₈₃

#10586

yes

characteristic, complemented, Sylow

C₂×#97

—

#398

—

#384

—

#382

C₂×D₈₃

yes

—

#340

—

166

—

C₂²×C₈

—

166

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

166

—

C₂×C₄⋊C₄

C₂²⋊D₈₃

yes

—

C₂×C₄²

C₂²×D₈₃

yes

characteristic

#97

—

#97

—

166

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

—

332

—

C₂²×C₄

C₂×C₂²⋊D₈₃

yes

—

C₂×C₈

—

332

—

C₂×C₈

—

332

—

C₂×C₈

—

166

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

332

—

C₄²

Q₈×D₈₃

yes

—

C₄²

yes

C₂³

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

664

—

C₂×C₄

#14581768

yes

—

C₂×C₄

#14581790

yes

—

C₈

—

332

—

C₂²

#19127620

yes

characteristic

C₂²

#19127874

yes

—

C₂²

#19127879

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

1328

—

C₂

#24906765

yes

characteristic

C₂

#24906786

yes

—

C₂

#24908810

yes

—

	subgroup	G/H
center	C₂³	#14581761
commutator, cosocle	C₂×C₄²×C₈₃	C₂³
Frattini	C₂×C₄²	C₂²×D₈₃
Fitting	C₈₃×#2845	C₂
socle, prime radical	C₂³×C₈₃	#120
hypercenter	#2845	D₈₃
hypocenter	C₈₃	#10586
LCS	G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

subgroup

G/H

center

C₂³

#14581761

commutator, cosocle

C₂×C₄²×C₈₃

C₂³

Frattini

C₂×C₄²

C₂²×D₈₃

Fitting

C₈₃×#2845

C₂

C₂³×C₈₃

D₈₃

C₈₃

G ▷ C₂×C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

N	H ≅ G/N	type
53. C₈₃	#10586	semidirect

H ≅ G/N

type

53. C₈₃

#10586

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#24907596	2
#24905344	2
C₈₃×#2845	2
#10586	83

subgroup

index

#24907596

#24905344

C₈₃×#2845

#10586

Subgroups — #35308913

Conjugacy classes of subgroups

Complements

Maximal subgroups