Group #24906283 — subgroups

Subgroups — #24906283

Order 10624.

160 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₈×Dic₁₆₆	C₂	1	2	yes	maximal
2	C₄×Dic₃₃₂	C₂	1	1	yes	maximal, characteristic
3	#19127452	C₂	1	1	yes	maximal, characteristic
4	#19127433	C₂	1	2	yes	maximal
5	#322×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₃₂	C₄	1	1	yes	characteristic
7	C₄×Dic₁₆₆	C₂²	1	2	yes	—
8	#14581726	C₄	1	1	yes	characteristic
9	C₄⋊(C₈₃⋊C₈)	C₂²	1	2	yes	—
10	Dic₈₃⋊C₈	—	2	2	no	—
11	#14581717	C₄	1	2	yes	—
12	C₈×Dic₈₃	—	2	2	no	—
13	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₆₆	C₂×C₄	1	2	yes	—
17	Dic₃₃₂	C₈	1	4	yes	complemented
18	C₂×C₈₃⋊C₈	—	2	2	no	—
19	C₄⋊Dic₈₃	C₂×C₄	1	2	yes	—
20	Dic₈₃⋊C₄	—	2	2	no	—
21	C₄×Dic₈₃	—	2	2	no	—
22	C₂×C₈×C₈₃	—	2	1	no	—
23	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₈₃	D₄	1	2	yes	—
26	C₄²×C₈₃	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₈₃	#41	1	1	yes	characteristic
30	C₂×Dic₈₃	—	2	2	no	—
31	C₂×Dic₈₃	—	2	2	no	—
32	Dic₁₆₆	—	2	2	no	—
33	Dic₁₆₆	C₂×C₈	1	4	yes	—
34	C₈×C₈₃	—	2	1	no	—
35	C₈×C₈₃	—	2	2	no	—
36	C₈×C₈₃	—	4	1	no	—
37	C₈×C₈₃	C₂×C₈	1	2	yes	—
38	C₈₃⋊C₈	—	4	2	no	—
39	C₂²×C₈₃	C₄×D₄	1	1	yes	characteristic
40	C₄×C₈₃	—	2	1	no	—
41	C₄×C₈₃	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₈₃	#131	1	1	yes	characteristic
43	C₄×C₈₃	#137	1	2	yes	—
44	Dic₈₃	—	2	4	no	—
45	Dic₈₃	—	4	2	no	—
46	C₂×C₈₃	C₈×D₄	1	1	yes	characteristic
47	C₂×C₈₃	#441	1	1	yes	characteristic
48	C₂×C₈₃	#444	1	1	yes	characteristic
49	#1579	—	83	1	no	maximal, Sylow
50	C₈₃	#1579	1	1	yes	characteristic, complemented, Sylow
51	C₈×Q₈	—	83	2	no	—
52	C₄×Q₁₆	—	83	1	no	—
53	#334	—	83	1	no	—
54	Q₈⋊C₈	—	83	2	no	—
55	#322	D₈₃	1	1	yes	characteristic
56	C₂×Q₁₆	—	83	1	no	—
57	C₄×Q₈	—	83	2	no	—
58	#107	—	83	1	no	—
59	C₄⋊C₈	—	83	2	no	—
60	C₄⋊C₈	—	166	2	no	—
61	#103	—	83	2	no	—
62	C₄×C₈	—	166	2	no	—
63	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
64	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
65	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
66	C₂×Q₈	—	83	2	no	—
67	Q₁₆	—	83	4	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	166	2	no	—
70	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
71	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
72	C₂×C₈	D₃₃₂	1	2	yes	—
73	C₄⋊C₄	—	83	2	no	—
74	C₄⋊C₄	—	166	2	no	—
75	C₄²	—	166	2	no	—
76	C₄²	C₂²×D₈₃	1	1	yes	characteristic
77	Q₈	—	83	4	no	—
78	Q₈	—	166	2	no	—
79	C₂×C₄	—	166	2	no	—
80	C₂×C₄	—	166	2	no	—
81	C₂×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
82	C₂×C₄	C₂×D₃₃₂	1	1	yes	characteristic
83	C₂×C₄	#13050590	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	332	2	no	—
88	C₈	C₈×D₈₃	1	2	yes	—
89	C₂²	C₄×D₃₃₂	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	332	2	no	—
92	C₄	—	166	4	no	—
93	C₄	C₂×C₈×D₈₃	1	1	yes	characteristic
94	C₄	#14581798	1	1	yes	characteristic
95	C₄	#14581825	1	2	yes	—
96	C₂	C₈×D₃₃₂	1	1	yes	characteristic
97	C₂	#19127809	1	1	yes	characteristic
98	C₂	#19127824	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₁₆₆

C₂

yes

maximal

C₄×Dic₃₃₂

C₂

yes

maximal, characteristic

#19127452

C₂

yes

maximal, characteristic

#19127433

C₂

yes

maximal

#322×C₈₃

C₂

yes

maximal, characteristic

C₂×Dic₃₃₂

C₄

yes

characteristic

C₄×Dic₁₆₆

C₂²

yes

—

#14581726

C₄

yes

characteristic

C₄⋊(C₈₃⋊C₈)

C₂²

yes

—

Dic₈₃⋊C₈

—

#14581717

C₄

yes

—

C₈×Dic₈₃

—

C₄×C₈×C₈₃

C₂²

yes

characteristic

C₄×C₈×C₈₃

C₂²

yes

characteristic

C₄×C₈×C₈₃

C₂²

yes

characteristic

C₂×Dic₁₆₆

C₂×C₄

yes

—

Dic₃₃₂

C₈

yes

complemented

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

C₂×C₄

yes

—

Dic₈₃⋊C₄

—

C₄×Dic₈₃

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

D₄

yes

—

C₄²×C₈₃

C₂³

yes

characteristic

C₂×C₄×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₈₃

C₂×D₄

yes

characteristic

C₂×C₄×C₈₃

#41

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

Dic₁₆₆

C₂×C₈

yes

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

—

C₈×C₈₃

C₂×C₈

yes

—

C₈₃⋊C₈

—

C₂²×C₈₃

C₄×D₄

yes

characteristic

C₄×C₈₃

—

C₄×C₈₃

C₂²×C₈

yes

C₄×C₈₃

yes

C₄×C₈₃

yes

—

Dic₈₃

—

Dic₈₃

—

C₂×C₈₃

C₈×D₄

yes

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₈₃

yes

characteristic, complemented, Sylow

C₈×Q₈

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

D₈₃

yes

characteristic

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

166

—

#103

—

C₄×C₈

—

166

—

C₄×C₈

C₂×D₈₃

yes

characteristic

C₄×C₈

C₂×D₈₃

yes

characteristic

C₄×C₈

C₂×D₈₃

yes

characteristic

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

166

—

C₂×C₈

C₄×D₈₃

yes

characteristic

C₂×C₈

C₄×D₈₃

yes

characteristic

C₂×C₈

D₃₃₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

166

—

C₄²

—

166

—

C₄²

C₂²×D₈₃

yes

characteristic

Q₈

—

Q₈

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

C₂×C₄×D₈₃

yes

characteristic

C₂×C₄

C₂×D₃₃₂

yes

characteristic

C₂×C₄

#13050590

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

332

—

C₈

C₈×D₈₃

yes

—

C₂²

C₄×D₃₃₂

yes

characteristic

C₄

—

C₄

—

332

—

C₄

—

166

—

C₄

C₂×C₈×D₈₃

yes

C₄

yes

C₄

yes

—

C₂

C₈×D₃₃₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₃₃₂
commutator	C₄×C₈₃	C₂²×C₈
Frattini	C₄²	C₂²×D₈₃
Fitting	#322×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	C₄×D₄
cosocle	C₄²×C₈₃	C₂³
hypercenter	#322	D₈₃
hypocenter	C₈₃	#1579
LCS	G ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₃₃₂

commutator

C₄×C₈₃

C₂²×C₈

Frattini

C₄²

C₂²×D₈₃

Fitting

#322×C₈₃

C₂

socle, prime radical

C₂²×C₈₃

C₄×D₄

cosocle

C₄²×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
17. Dic₃₃₂	C₈	semidirect
50. C₈₃	#1579	semidirect

H ≅ G/N

type

17. Dic₃₃₂

C₈

semidirect

50. C₈₃

#1579

semidirect

Subgroups — #24906283

Conjugacy classes of subgroups

Complements