Group #24905340 — subgroups

Subgroups — #24905340

Order 10624.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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	#19127665	C₂	1	2	yes	maximal
2	C₂×C₂²⋊C₈×C₈₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#13050574	—	2	2	no	—
4	C₂²⋊(C₈₃⋊C₈)	—	2	2	no	—
5	C₂²⋊(C₈₃⋊C₈)	C₄	1	4	yes	—
6	C₂³×C₄×C₈₃	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₈₃	C₄	1	2	yes	—
8	C₂²⋊C₈×C₈₃	—	2	2	no	—
9	#13050574	—	4	4	no	—
10	C₂×C₈₃⋊C₈	—	2	4	no	—
11	C₂⁴×C₈₃	Q₈	1	1	yes	characteristic
12	C₂²×C₄×C₈₃	—	4	2	no	—
13	C₂²×C₄×C₈₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₈₃	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₈₃	D₄	1	2	yes	—
17	C₂×C₈×C₈₃	—	2	2	no	—
18	C₂×C₈×C₈₃	—	4	2	no	—
19	C₂³×C₈₃	—	2	2	no	—
20	C₂³×C₈₃	—	4	1	no	—
21	C₂³×C₈₃	—	4	1	no	—
22	C₂³×C₈₃	C₄⋊C₄	1	2	yes	—
23	C₂³×C₈₃	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₈₃	—	2	2	no	—
25	C₂×C₄×C₈₃	—	2	4	no	—
26	C₂×C₄×C₈₃	—	4	2	no	—
27	C₂×C₄×C₈₃	—	4	1	no	—
28	C₂×C₄×C₈₃	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₈₃	C₂²⋊C₄	1	2	yes	—
30	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₈×C₈₃	—	4	2	no	—
32	C₈₃⋊C₈	—	4	4	no	—
33	C₂²×C₈₃	—	2	1	no	—
34	C₂²×C₈₃	—	2	1	no	—
35	C₂²×C₈₃	—	2	2	no	—
36	C₂²×C₈₃	—	2	2	no	—
37	C₂²×C₈₃	—	2	2	no	—
38	C₂²×C₈₃	—	4	4	no	—
39	C₂²×C₈₃	#95	1	1	yes	characteristic
40	C₂²×C₈₃	#108	1	2	yes	—
41	C₄×C₈₃	—	2	2	no	—
42	C₄×C₈₃	—	2	1	no	—
43	C₄×C₈₃	#99	1	2	yes	—
44	C₂×C₈₃	—	2	2	no	—
45	C₂×C₈₃	—	4	2	no	—
46	C₂×C₈₃	#338	1	1	yes	characteristic
47	C₂×C₈₃	#341	1	1	yes	characteristic
48	C₂×C₈₃	#342	1	1	yes	characteristic
49	#1293	—	83	1	no	maximal, Sylow
50	C₈₃	#1293	1	1	yes	characteristic, complemented, Sylow
51	#407	—	83	2	no	—
52	C₂×C₂²⋊C₈	D₈₃	1	1	yes	characteristic
53	C₂³×C₄	C₂×D₈₃	1	1	yes	characteristic
54	C₂×M₁₆	—	166	2	no	—
55	C₂²×C₈	Dic₈₃	1	2	yes	—
56	C₂²⋊C₈	—	2	2	no	—
57	C₂²⋊C₈	—	83	4	no	—
58	C₂²⋊C₈	—	166	2	no	—
59	C₂⁴	Dic₁₆₆	1	1	yes	characteristic
60	C₂²×C₄	—	4	2	no	—
61	C₂²×C₄	C₄×D₈₃	1	2	yes	—
62	C₂²×C₄	D₃₃₂	1	1	yes	characteristic
63	C₂²×C₄	C₂×Dic₈₃	1	1	yes	characteristic
64	C₂²×C₄	C₂²⋊D₈₃	1	2	yes	—
65	M₁₆	—	332	4	no	—
66	C₂×C₈	—	2	2	no	—
67	C₂×C₈	—	4	2	no	—
68	C₂×C₈	—	166	4	no	—
69	C₂³	—	2	2	no	—
70	C₂³	—	4	1	no	—
71	C₂³	—	4	1	no	—
72	C₂³	Dic₈₃⋊C₄	1	2	yes	—
73	C₂³	C₄⋊Dic₈₃	1	1	yes	characteristic
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	C₄×Dic₈₃	1	1	yes	characteristic
79	C₂×C₄	(C₂×D₈₃)⋊C₄	1	2	yes	—
80	C₂×C₄	C₂²⋊Dic₈₃	1	1	yes	characteristic
81	C₈	—	4	2	no	—
82	C₈	—	332	4	no	—
83	C₂²	—	2	1	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	2	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	4	4	no	—
89	C₂²	C₈₃⋊#95	1	1	yes	characteristic
90	C₂²	#14581728	1	2	yes	—
91	C₄	—	2	2	no	—
92	C₄	—	2	1	no	—
93	C₄	#14581707	1	2	yes	—
94	C₂	—	2	2	no	—
95	C₂	—	4	2	no	—
96	C₂	C₈₃⋊#338	1	1	yes	characteristic
97	C₂	#19127466	1	1	yes	characteristic
98	C₂	#19127468	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19127665

C₂

yes

maximal

C₂×C₂²⋊C₈×C₈₃

C₂

yes

maximal, characteristic

C₂×#13050574

—

C₂²⋊(C₈₃⋊C₈)

—

C₂²⋊(C₈₃⋊C₈)

C₄

yes

—

C₂³×C₄×C₈₃

C₂²

yes

characteristic

C₂²×C₈×C₈₃

C₄

yes

—

C₂²⋊C₈×C₈₃

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₂⁴×C₈₃

Q₈

yes

characteristic

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×C₄

yes

—

C₂²×C₄×C₈₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₈₃

D₄

yes

characteristic

C₂²×C₄×C₈₃

D₄

yes

—

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

—

C₂³×C₈₃

C₄⋊C₄

yes

—

C₂³×C₈₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₄²

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊C₄

yes

—

C₂×C₄×C₈₃

C₂²⋊C₄

yes

characteristic

C₈×C₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

#95

yes

characteristic

C₂²×C₈₃

#108

yes

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

#99

yes

—

C₂×C₈₃

—

C₂×C₈₃

—

C₂×C₈₃

yes

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₈₃

yes

characteristic, complemented, Sylow

#407

—

C₂×C₂²⋊C₈

D₈₃

yes

characteristic

C₂³×C₄

C₂×D₈₃

yes

characteristic

C₂×M₁₆

—

166

—

C₂²×C₈

Dic₈₃

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

166

—

C₂⁴

Dic₁₆₆

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄×D₈₃

yes

—

C₂²×C₄

D₃₃₂

yes

characteristic

C₂²×C₄

C₂×Dic₈₃

yes

characteristic

C₂²×C₄

C₂²⋊D₈₃

yes

—

M₁₆

—

332

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

166

—

C₂³

—

C₂³

—

C₂³

—

C₂³

Dic₈₃⋊C₄

yes

—

C₂³

C₄⋊Dic₈₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₈₃

yes

characteristic

C₂×C₄

(C₂×D₈₃)⋊C₄

yes

—

C₂×C₄

C₂²⋊Dic₈₃

yes

characteristic

C₈

—

C₈

—

332

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₈₃⋊#95

yes

characteristic

C₂²

#14581728

yes

—

C₄

—

C₄

—

C₄

#14581707

yes

—

C₂

—

C₂

—

C₂

C₈₃⋊#338

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	C₈₃⋊#95
commutator	C₂×C₄×C₈₃	C₄²
Frattini	C₂³×C₄	C₂×D₈₃
Fitting	C₂×C₂²⋊C₈×C₈₃	C₂
socle	C₂²×C₈₃	#95
prime radical	C₂⁴×C₈₃	Q₈
cosocle	C₂³×C₄×C₈₃	C₂²
hypercenter	C₂×C₂²⋊C₈	D₈₃
hypocenter	C₈₃	#1293
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center

C₂²

C₈₃⋊#95

commutator

C₂×C₄×C₈₃

C₄²

Frattini

C₂³×C₄

C₂×D₈₃

Fitting

C₂×C₂²⋊C₈×C₈₃

C₂

socle

C₂²×C₈₃

#95

prime radical

C₂⁴×C₈₃

Q₈

cosocle

C₂³×C₄×C₈₃

C₂²

hypercenter

C₂×C₂²⋊C₈

D₈₃

hypocenter

C₈₃

#1293

LCS

G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
50. C₈₃	#1293	semidirect

H ≅ G/N

type

50. C₈₃

#1293

semidirect

Subgroups — #24905340

Conjugacy classes of subgroups

Complements