Group #24905482 — subgroups

Subgroups — #24905482

Order 10624.

104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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	#19127942	C₂	1	1	yes	maximal, characteristic
2	#19127466	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊C₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₃₂	C₄	1	1	yes	characteristic
5	C₂×#13050574	—	2	1	no	—
6	#14581771	—	2	1	no	—
7	#14581726	C₄	1	1	yes	characteristic
8	#14581717	—	2	1	no	—
9	C₂²×C₈×C₈₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₈₃	—	2	1	no	—
11	C₂×Dic₁₆₆	—	2	1	no	—
12	Dic₃₃₂	—	4	1	no	—
13	#13050574	—	2	2	no	—
14	#13050574	—	4	1	no	—
15	C₂×C₈₃⋊C₈	—	4	1	no	—
16	C₄⋊Dic₈₃	—	2	1	no	—
17	Dic₈₃⋊C₄	—	4	1	no	—
18	C₂²⋊Dic₈₃	—	4	1	no	—
19	C₂²×C₄×C₈₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₈₃	—	4	1	no	—
21	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
23	C₁₆×C₈₃	—	4	1	no	—
24	C₂³×C₈₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₈₃	—	2	1	no	—
26	C₂×C₄×C₈₃	—	2	1	no	—
27	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
29	C₂×Dic₈₃	—	4	1	no	—
30	C₂×Dic₈₃	—	4	1	no	—
31	Dic₁₆₆	—	4	1	no	—
32	Dic₁₆₆	—	4	1	no	—
33	C₈×C₈₃	—	2	1	no	—
34	C₈×C₈₃	—	2	1	no	—
35	C₈₃⋊C₈	—	4	2	no	—
36	C₂²×C₈₃	—	2	1	no	—
37	C₂²×C₈₃	—	2	1	no	—
38	C₂²×C₈₃	—	2	1	no	—
39	C₂²×C₈₃	#102	1	1	yes	characteristic
40	C₄×C₈₃	—	2	1	no	—
41	C₄×C₈₃	#99	1	1	yes	characteristic
42	C₄×C₈₃	#104	1	1	yes	characteristic
43	Dic₈₃	—	8	1	no	—
44	Dic₈₃	—	8	1	no	—
45	C₂×C₈₃	—	4	1	no	—
46	C₂×C₈₃	#327	1	1	yes	characteristic
47	C₂×C₈₃	#359	1	1	yes	characteristic
48	C₂×C₈₃	#362	1	1	yes	characteristic
49	#1350	—	83	1	no	maximal, Sylow
50	C₈₃	#1350	1	1	yes	characteristic, complemented, Sylow
51	#467	—	83	1	no	—
52	C₂²⋊C₁₆	D₈₃	1	1	yes	characteristic
53	#341	—	83	1	no	—
54	C₂×Q₁₆	—	83	1	no	—
55	C₂×M₁₆	—	166	1	no	—
56	C₂²×C₈	C₂×D₈₃	1	1	yes	characteristic
57	C₂²⋊Q₈	—	166	1	no	—
58	C₂×C₁₆	—	2	1	no	—
59	#107	—	83	1	no	—
60	#103	—	166	1	no	—
61	C₂×Q₈	—	166	1	no	—
62	C₂²×C₄	D₃₃₂	1	1	yes	characteristic
63	Q₁₆	—	332	1	no	—
64	M₁₆	—	332	1	no	—
65	M₁₆	—	166	2	no	—
66	C₂×C₈	—	4	1	no	—
67	C₂×C₈	—	332	1	no	—
68	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
69	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
70	C₄⋊C₄	—	332	1	no	—
71	C₄⋊C₄	—	166	1	no	—
72	C₂²⋊C₄	—	332	1	no	—
73	C₁₆	—	4	1	no	—
74	C₂³	#13050579	1	1	yes	characteristic
75	Q₈	—	332	1	no	—
76	Q₈	—	332	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	332	1	no	—
80	C₂×C₄	—	332	1	no	—
81	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
82	C₂×C₄	D₆₆₄	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₈	—	332	2	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	2	1	no	—
88	C₂²	—	2	1	no	—
89	C₂²	#14581714	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	664	1	no	—
92	C₄	—	664	1	no	—
93	C₄	#14581706	1	1	yes	characteristic
94	C₄	#14581718	1	1	yes	characteristic
95	C₂	—	4	1	no	—
96	C₂	#19127436	1	1	yes	characteristic
97	C₂	#19127509	1	1	yes	characteristic
98	C₂	#19127518	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19127942

C₂

yes

maximal, characteristic

#19127466

C₂

yes

maximal, characteristic

C₂²⋊C₁₆×C₈₃

C₂

yes

maximal, characteristic

C₂×Dic₃₃₂

C₄

yes

—

—

C₄

yes

characteristic

#14581717

—

C₂²×C₈×C₈₃

C₂²

yes

characteristic

C₂×C₁₆×C₈₃

—

C₂×Dic₁₆₆

—

Dic₃₃₂

—

#13050574

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

—

Dic₈₃⋊C₄

—

C₂²⋊Dic₈₃

—

C₂²×C₄×C₈₃

D₄

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

D₄

yes

characteristic

C₁₆×C₈₃

—

C₂³×C₈₃

SD₁₆

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

D₈

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

#102

yes

characteristic

C₄×C₈₃

—

C₄×C₈₃

yes

C₄×C₈₃

yes

Dic₈₃

—

Dic₈₃

—

C₂×C₈₃

—

C₂×C₈₃

yes

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₈₃

yes

characteristic, complemented, Sylow

#467

—

C₂²⋊C₁₆

D₈₃

yes

characteristic

#341

—

C₂×Q₁₆

—

C₂×M₁₆

—

166

—

C₂²×C₈

C₂×D₈₃

yes

characteristic

C₂²⋊Q₈

—

166

—

C₂×C₁₆

—

#107

—

#103

—

166

—

C₂×Q₈

—

166

—

C₂²×C₄

D₃₃₂

yes

characteristic

Q₁₆

—

332

—

M₁₆

—

332

—

M₁₆

—

166

—

C₂×C₈

—

C₂×C₈

—

332

—

C₂×C₈

C₄×D₈₃

yes

characteristic

C₂×C₈

C₂²⋊D₈₃

yes

characteristic

C₄⋊C₄

—

332

—

C₄⋊C₄

—

166

—

C₂²⋊C₄

—

332

—

C₁₆

—

C₂³

#13050579

yes

characteristic

Q₈

—

332

—

Q₈

—

332

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

332

—

C₂×C₄

—

332

—

C₂×C₄

(C₂×D₈₃)⋊C₄

yes

characteristic

C₂×C₄

D₆₆₄

yes

characteristic

C₈

—

C₈

—

C₈

—

332

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#14581714

yes

characteristic

C₄

—

C₄

—

664

—

C₄

—

664

—

C₄

yes

C₄

yes

C₂

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	#14581714
commutator	C₂×C₈×C₈₃	C₂×C₄
Frattini	C₂²×C₈	C₂×D₈₃
Fitting	C₂²⋊C₁₆×C₈₃	C₂
socle	C₂²×C₈₃	#102
prime radical	C₂³×C₈₃	SD₁₆
cosocle	C₂²×C₈×C₈₃	C₂²
hypercenter	C₂²⋊C₁₆	D₈₃
hypocenter	C₈₃	#1350
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂²

#14581714

commutator

C₂×C₈×C₈₃

C₂×C₄

Frattini

C₂²×C₈

C₂×D₈₃

Fitting

C₂²⋊C₁₆×C₈₃

C₂

socle

C₂²×C₈₃

#102

prime radical

C₂³×C₈₃

SD₁₆

cosocle

C₂²×C₈×C₈₃

C₂²

hypercenter

C₂²⋊C₁₆

D₈₃

hypocenter

C₈₃

#1350

LCS

G ▷ C₂×C₈×C₈₃ ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
50. C₈₃	#1350	semidirect

H ≅ G/N

type

50. C₈₃

#1350

semidirect

Subgroups — #24905482

Conjugacy classes of subgroups

Complements