Group #24905402 — subgroups

Subgroups — #24905402

Order 10624.

108 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 43 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	C₂×Dic₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₈₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊C₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈₃⋊C₈	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₈₃	C₄	1	1	yes	characteristic
6	C₂×C₈₃⋊C₁₆	—	2	1	no	—
7	Dic₈₃⋊C₈	—	2	1	no	—
8	Dic₈₃⋊C₈	—	2	1	no	—
9	C₂²×C₈×C₈₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₈₃	—	2	1	no	—
11	C₂²×Dic₈₃	C₈	1	1	yes	characteristic
12	C₂²×Dic₈₃	C₈	1	1	yes	characteristic
13	C₂×C₈₃⋊C₈	—	2	1	no	—
14	C₂×C₈₃⋊C₈	—	4	1	no	—
15	C₄×Dic₈₃	—	2	1	no	—
16	C₄×Dic₈₃	—	2	1	no	—
17	C₈₃⋊C₁₆	—	4	1	no	—
18	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₈₃	—	4	1	no	—
20	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
22	C₁₆×C₈₃	—	4	1	no	—
23	C₂³×C₈₃	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₈₃	—	2	1	no	—
25	C₂×C₄×C₈₃	—	2	1	no	—
26	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₈₃	M₁₆	1	1	yes	characteristic
28	C₂×Dic₈₃	—	2	1	no	—
29	C₂×Dic₈₃	—	2	1	no	—
30	C₂×Dic₈₃	—	2	1	no	—
31	C₂×Dic₈₃	—	4	1	no	—
32	C₂×Dic₈₃	C₁₆	1	2	yes	complemented
33	C₈×C₈₃	—	2	1	no	—
34	C₈×C₈₃	—	2	1	no	—
35	C₈₃⋊C₈	—	4	1	no	—
36	C₂²×C₈₃	—	2	1	no	—
37	C₂²×C₈₃	—	2	1	no	—
38	C₂²×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
39	C₂²×C₈₃	C₂×C₁₆	1	1	yes	characteristic
40	C₂²×C₈₃	M₃₂	1	1	yes	characteristic
41	C₄×C₈₃	—	2	1	no	—
42	C₄×C₈₃	#99	1	1	yes	characteristic
43	C₄×C₈₃	#101	1	1	yes	characteristic
44	Dic₈₃	—	2	2	no	—
45	Dic₈₃	—	4	1	no	—
46	C₂×C₈₃	—	2	1	no	—
47	C₂×C₈₃	—	2	1	no	—
48	C₂×C₈₃	#324	1	1	yes	characteristic
49	C₂×C₈₃	C₂²⋊C₁₆	1	1	yes	characteristic
50	C₂×C₈₃	#349	1	1	yes	characteristic
51	#1322	—	83	1	no	maximal, Sylow
52	C₈₃	#1322	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₄⋊C₈	—	83	1	no	—
54	C₂²⋊C₁₆	—	83	1	no	—
55	C₂²⋊C₁₆	D₈₃	1	1	yes	characteristic
56	C₂²×C₈	—	83	1	no	—
57	C₂²×C₈	C₂×D₈₃	1	1	yes	characteristic
58	C₂×C₄²	—	83	1	no	—
59	C₂×C₁₆	—	2	1	no	—
60	C₂×C₁₆	—	166	1	no	—
61	C₄⋊C₈	—	166	1	no	—
62	C₄⋊C₈	—	166	1	no	—
63	C₂²×C₄	—	83	1	no	—
64	C₂²×C₄	—	83	1	no	—
65	C₂²×C₄	C₄×D₈₃	1	1	yes	characteristic
66	C₂×C₈	—	4	1	no	—
67	C₂×C₈	—	332	1	no	—
68	C₂×C₈	—	166	1	no	—
69	C₂×C₈	D₃₃₂	1	1	yes	characteristic
70	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
71	C₄²	—	166	1	no	—
72	C₄²	—	166	1	no	—
73	C₁₆	—	4	1	no	—
74	C₁₆	—	332	1	no	—
75	C₂³	C₈×D₈₃	1	1	yes	characteristic
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	332	1	no	—
79	C₂×C₄	—	83	2	no	—
80	C₂×C₄	—	166	1	no	—
81	C₂×C₄	—	166	1	no	—
82	C₂×C₄	—	166	1	no	—
83	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
84	C₂×C₄	#13050573	1	1	yes	characteristic
85	C₈	—	2	1	no	—
86	C₈	—	2	1	no	—
87	C₈	—	332	1	no	—
88	C₂²	—	2	1	no	—
89	C₂²	—	2	1	no	—
90	C₂²	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
91	C₂²	C₁₆×D₈₃	1	1	yes	characteristic
92	C₂²	#14581731	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	332	1	no	—
95	C₄	—	166	2	no	—
96	C₄	#14581706	1	1	yes	characteristic
97	C₄	#14581710	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	2	1	no	—
100	C₂	#19127426	1	1	yes	characteristic
101	C₂	(C₂×D₈₃)⋊C₁₆	1	1	yes	characteristic
102	C₂	#19127482	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₈₃⋊C₈

C₂

yes

maximal, characteristic

C₂²⋊(C₈₃⋊C₁₆)

C₂

yes

maximal, characteristic

C₂²⋊C₁₆×C₈₃

C₂

yes

maximal, characteristic

C₂²×C₈₃⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₈₃

C₄

yes

characteristic

C₂×C₈₃⋊C₁₆

—

Dic₈₃⋊C₈

—

Dic₈₃⋊C₈

—

C₂²×C₈×C₈₃

C₂²

yes

characteristic

C₂×C₁₆×C₈₃

—

C₂²×Dic₈₃

C₈

yes

characteristic

C₂²×Dic₈₃

C₈

yes

characteristic

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₈₃⋊C₁₆

—

C₂²×C₄×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

D₄

yes

characteristic

C₂×C₈×C₈₃

D₄

yes

characteristic

C₁₆×C₈₃

—

C₂³×C₈₃

C₂×C₈

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

M₁₆

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

C₁₆

yes

complemented

C₈×C₈₃

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

C₂²⋊C₈

yes

characteristic

C₂²×C₈₃

C₂×C₁₆

yes

characteristic

C₂²×C₈₃

M₃₂

yes

characteristic

C₄×C₈₃

—

C₄×C₈₃

yes

C₄×C₈₃

yes

Dic₈₃

—

Dic₈₃

—

C₂×C₈₃

—

C₂×C₈₃

—

C₂×C₈₃

#324

yes

characteristic

C₂×C₈₃

C₂²⋊C₁₆

yes

C₂×C₈₃

yes

—

C₈₃

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

D₈₃

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₈₃

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

166

—

C₄⋊C₈

—

166

—

C₄⋊C₈

—

166

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₈₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

332

—

C₂×C₈

—

166

—

C₂×C₈

D₃₃₂

yes

characteristic

C₂×C₈

C₂²⋊D₈₃

yes

characteristic

C₄²

—

166

—

C₄²

—

166

—

C₁₆

—

C₁₆

—

332

—

C₂³

C₈×D₈₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

332

—

C₂×C₄

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

(C₂×D₈₃)⋊C₄

yes

characteristic

C₂×C₄

#13050573

yes

characteristic

C₈

—

C₈

—

C₈

—

332

—

C₂²

—

C₂²

—

C₂²

(C₂×D₈₃)⋊C₈

yes

characteristic

C₂²

C₁₆×D₈₃

yes

characteristic

C₂²

#14581731

yes

characteristic

C₄

—

C₄

—

332

—

C₄

—

166

—

C₄

yes

C₄

yes

C₂

—

C₂

—

100

C₂

#19127426

yes

characteristic

101

C₂

(C₂×D₈₃)⋊C₁₆

yes

characteristic

102

C₂

#19127482

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₈₃)⋊C₄
commutator	C₂²×C₈₃	C₂×C₁₆
Frattini	C₂²×C₈	C₂×D₈₃
Fitting	C₂²⋊C₁₆×C₈₃	C₂
socle	C₂²×C₈₃	C₂²⋊C₈
prime radical	C₂³×C₈₃	C₂×C₈
cosocle	C₂²×C₈×C₈₃	C₂²
hypercenter	C₂²⋊C₁₆	D₈₃
hypocenter	C₈₃	#1322
LCS	G ▷ C₂²×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂×C₄

(C₂×D₈₃)⋊C₄

commutator

C₂²×C₈₃

C₂×C₁₆

Frattini

C₂²×C₈

C₂×D₈₃

Fitting

C₂²⋊C₁₆×C₈₃

C₂

socle

C₂²×C₈₃

C₂²⋊C₈

prime radical

C₂³×C₈₃

C₂×C₈

cosocle

C₂²×C₈×C₈₃

C₂²

hypercenter

C₂²⋊C₁₆

D₈₃

hypocenter

C₈₃

#1322

LCS

G ▷ C₂²×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
32. C₂×Dic₈₃	C₁₆	semidirect
52. C₈₃	#1322	semidirect

H ≅ G/N

type

32. C₂×Dic₈₃

C₁₆

semidirect

52. C₈₃

#1322

semidirect

Subgroups — #24905402

Conjugacy classes of subgroups

Complements