Group #24905424 — subgroups

Subgroups — #24905424

Order 10624.

110 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 49 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×C₈₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#19127454	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₈×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈₃⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
6	C₂×D₈×C₈₃	C₄	1	1	yes	characteristic
7	C₄×D₄×C₈₃	—	2	1	no	—
8	#107×C₈₃	C₄	1	1	yes	characteristic
9	#102×C₈₃	—	2	1	no	—
10	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
11	C₂×C₈₃⋊C₈	—	4	1	no	—
12	C₈₃⋊C₁₆	—	2	2	no	—
13	C₂×D₄×C₈₃	—	2	1	no	—
14	C₂²×C₄×C₈₃	—	4	1	no	—
15	D₈×C₈₃	—	2	1	no	—
16	D₈×C₈₃	C₈	1	2	yes	complemented
17	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
19	C₄⋊C₄×C₈₃	—	2	1	no	—
20	C₂²⋊C₄×C₈₃	—	4	1	no	—
21	C₄²×C₈₃	D₄	1	1	yes	characteristic
22	C₂³×C₈₃	—	4	1	no	—
23	D₄×C₈₃	—	2	2	no	—
24	D₄×C₈₃	—	4	1	no	—
25	C₂×C₄×C₈₃	—	4	1	no	—
26	C₂×C₄×C₈₃	—	8	1	no	—
27	C₂×C₄×C₈₃	—	8	1	no	—
28	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
31	C₈×C₈₃	—	2	1	no	—
32	C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₈₃	M₁₆	1	1	yes	characteristic
34	C₈₃⋊C₈	—	8	1	no	—
35	C₂²×C₈₃	—	4	2	no	—
36	C₂²×C₈₃	—	8	1	no	—
37	C₂²×C₈₃	—	8	1	no	—
38	C₂²×C₈₃	#102	1	1	yes	characteristic
39	C₄×C₈₃	—	2	1	no	—
40	C₄×C₈₃	—	8	1	no	—
41	C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₈₃	#104	1	1	yes	characteristic
43	C₄×C₈₃	D₁₆	1	1	yes	characteristic
44	C₄×C₈₃	SD₃₂	1	1	yes	characteristic
45	C₂×C₈₃	—	8	2	no	—
46	C₂×C₈₃	D₄⋊C₈	1	1	yes	characteristic
47	C₂×C₈₃	#357	1	1	yes	characteristic
48	C₂×C₈₃	#359	1	1	yes	characteristic
49	#1331	—	83	1	no	maximal, Sylow
50	C₈₃	#1331	1	1	yes	characteristic, complemented, Sylow
51	C₄×D₈	D₈₃	1	1	yes	characteristic
52	C₄×C₁₆	—	83	1	no	—
53	#335	—	83	1	no	—
54	C₂×D₈	Dic₈₃	1	1	yes	characteristic
55	C₄×D₄	—	2	1	no	—
56	C₂×C₁₆	—	166	1	no	—
57	#107	Dic₈₃	1	1	yes	characteristic
58	C₄⋊C₈	—	166	1	no	—
59	#102	—	2	1	no	—
60	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
61	C₂×D₄	—	2	1	no	—
62	C₂²×C₄	—	4	1	no	—
63	D₈	—	2	1	no	—
64	D₈	C₈₃⋊C₈	1	2	yes	complemented
65	C₂×C₈	—	332	1	no	—
66	C₂×C₈	C₂×Dic₈₃	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₄²	C₂²⋊D₈₃	1	1	yes	characteristic
71	C₁₆	—	166	2	no	—
72	C₂³	—	4	1	no	—
73	D₄	—	2	2	no	—
74	D₄	—	4	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	8	1	no	—
77	C₂×C₄	—	8	1	no	—
78	C₂×C₄	C₂²⋊Dic₈₃	1	1	yes	characteristic
79	C₂×C₄	#13050575	1	1	yes	characteristic
80	C₂×C₄	#13050578	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	664	1	no	—
83	C₈	C₂×C₈₃⋊C₈	1	1	yes	characteristic
84	C₈	#13050574	1	1	yes	characteristic
85	C₂²	—	4	2	no	—
86	C₂²	—	8	1	no	—
87	C₂²	—	8	1	no	—
88	C₂²	#14581713	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	8	1	no	—
91	C₄	C₂²⋊(C₈₃⋊C₈)	1	1	yes	characteristic
92	C₄	#14581719	1	1	yes	characteristic
93	C₄	#14581733	1	1	yes	characteristic
94	C₄	#14581736	1	1	yes	characteristic
95	C₂	—	8	2	no	—
96	C₂	D₄⋊(C₈₃⋊C₈)	1	1	yes	characteristic
97	C₂	#19127502	1	1	yes	characteristic
98	C₂	#19127508	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#19127454

C₂

yes

maximal, characteristic, complemented

C₄×D₈×C₈₃

C₂

yes

maximal, characteristic

C₂×C₈₃⋊C₁₆

—

C₄⋊(C₈₃⋊C₈)

—

C₂×D₈×C₈₃

C₄

yes

characteristic

C₄×D₄×C₈₃

—

#107×C₈₃

C₄

yes

characteristic

#102×C₈₃

—

C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂×C₈₃⋊C₈

—

C₈₃⋊C₁₆

—

C₂×D₄×C₈₃

—

C₂²×C₄×C₈₃

—

D₈×C₈₃

—

D₈×C₈₃

C₈

yes

complemented

C₂×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

D₄

yes

characteristic

C₄⋊C₄×C₈₃

—

C₂²⋊C₄×C₈₃

—

C₄²×C₈₃

D₄

yes

characteristic

C₂³×C₈₃

—

D₄×C₈₃

—

D₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

D₈

yes

characteristic

C₂×C₄×C₈₃

SD₁₆

yes

characteristic

C₈×C₈₃

—

C₈×C₈₃

C₂×C₈

yes

characteristic

C₈×C₈₃

M₁₆

yes

characteristic

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

#102

yes

characteristic

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

C₂²⋊C₈

yes

characteristic

C₄×C₈₃

#104

yes

characteristic

C₄×C₈₃

D₁₆

yes

characteristic

C₄×C₈₃

SD₃₂

yes

characteristic

C₂×C₈₃

—

C₂×C₈₃

D₄⋊C₈

yes

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₈₃

yes

characteristic, complemented, Sylow

C₄×D₈

D₈₃

yes

characteristic

C₄×C₁₆

—

#335

—

C₂×D₈

Dic₈₃

yes

characteristic

C₄×D₄

—

C₂×C₁₆

—

166

—

#107

Dic₈₃

yes

characteristic

C₄⋊C₈

—

166

—

#102

—

C₄×C₈

C₂×D₈₃

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

C₈₃⋊C₈

yes

complemented

C₂×C₈

—

332

—

C₂×C₈

C₂×Dic₈₃

yes

characteristic

C₂×C₈

C₂²⋊D₈₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₈₃

yes

characteristic

C₁₆

—

166

—

C₂³

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₈₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

664

—

C₈

C₂×C₈₃⋊C₈

yes

characteristic

C₈

#13050574

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

#14581713

yes

characteristic

C₄

—

C₄

—

C₄

C₂²⋊(C₈₃⋊C₈)

yes

C₄

yes

C₄

yes

C₄

yes

C₂

—

C₂

D₄⋊(C₈₃⋊C₈)

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	#13050575
commutator	C₈×C₈₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₈₃
Fitting	C₄×D₈×C₈₃	C₂
socle	C₂²×C₈₃	#102
prime radical	C₂×D₈×C₈₃	C₄
cosocle	C₄×C₈×C₈₃	C₂²
hypercenter	C₄×D₈	D₈₃
hypocenter	C₈₃	#1331
LCS	G ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

subgroup

G/H

center

C₂×C₄

#13050575

commutator

C₈×C₈₃

C₂×C₈

Frattini

C₄×C₈

C₂×D₈₃

Fitting

C₄×D₈×C₈₃

C₂

socle

C₂²×C₈₃

#102

prime radical

C₂×D₈×C₈₃

C₄

cosocle

C₄×C₈×C₈₃

C₂²

hypercenter

C₄×D₈

D₈₃

hypocenter

C₈₃

#1331

LCS

G ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

N	H ≅ G/N	type
1. C₄×C₈₃⋊C₁₆	C₂	semidirect
2. #19127454	C₂	semidirect
16. D₈×C₈₃	C₈	semidirect
50. C₈₃	#1331	semidirect
64. D₈	C₈₃⋊C₈	semidirect

H ≅ G/N

type

1. C₄×C₈₃⋊C₁₆

C₂

semidirect

2. #19127454

C₂

semidirect

16. D₈×C₈₃

C₈

semidirect

50. C₈₃

#1331

semidirect

64. D₈

C₈₃⋊C₈

semidirect

Subgroups — #24905424

Conjugacy classes of subgroups

Complements