Group #24913414 — subgroups

Subgroups — #24913414

Order 10624.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14581792	C₂	1	1	yes	maximal, characteristic
2	#19127640	C₂	1	8	yes	maximal
3	#19127606	C₂	1	4	yes	maximal
4	#19127547	C₂	1	1	yes	maximal, characteristic
5	C₂×#125×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₆₆	C₂²	1	2	yes	—
7	#14581792	—	2	4	no	—
8	C₂×C₄⋊Dic₈₃	C₂²	1	4	yes	—
9	C₂×C₄×Dic₈₃	C₂²	1	2	yes	—
10	C₈₃⋊#95	C₂²	1	16	yes	—
11	C₈₃⋊#95	C₂²	1	4	yes	—
12	#125×C₈₃	—	2	4	no	—
13	C₂×C₄⋊C₄×C₈₃	C₂²	1	2	yes	—
14	C₂×C₄⋊C₄×C₈₃	C₂²	1	4	yes	—
15	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₆₆	—	2	4	no	—
17	C₂×Dic₁₆₆	—	2	8	no	—
18	C₂²×Dic₈₃	C₂³	1	4	yes	—
19	C₂²×Dic₈₃	C₂³	1	4	yes	—
20	C₄⋊Dic₈₃	—	2	8	no	—
21	C₄×Dic₈₃	—	2	4	no	—
22	C₂²×C₄×C₈₃	C₂³	1	4	yes	—
23	C₂²×C₄×C₈₃	C₂³	1	2	yes	—
24	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₈₃	—	2	8	no	—
26	C₄⋊C₄×C₈₃	—	2	4	no	—
27	C₄²×C₈₃	D₄	1	4	yes	—
28	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₈₃	—	2	4	no	—
30	C₂×C₄×C₈₃	—	2	4	no	—
31	C₂×C₄×C₈₃	—	2	8	no	—
32	C₂×C₄×C₈₃	C₂×D₄	1	4	yes	—
33	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₈₃	#41	1	4	yes	—
35	C₂×Dic₈₃	—	2	4	no	—
36	C₂×Dic₈₃	—	2	4	no	—
37	C₂×Dic₈₃	—	2	8	no	—
38	C₂×Dic₈₃	—	2	8	no	—
39	Dic₁₆₆	—	4	8	no	—
40	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
41	C₂²×C₈₃	C₂×#41	1	2	yes	—
42	C₂²×C₈₃	2₋¹⁺⁴	1	4	yes	—
43	C₄×C₈₃	—	2	4	no	—
44	C₄×C₈₃	—	4	4	no	—
45	C₄×C₈₃	#124	1	4	yes	—
46	Dic₈₃	—	4	4	no	—
47	Dic₈₃	—	4	4	no	—
48	C₂×C₈₃	C₂×#124	1	1	yes	characteristic
49	C₂×C₈₃	#536	1	2	yes	—
50	C₂×C₈₃	#541	1	4	yes	—
51	#2642	—	83	1	no	maximal, Sylow
52	C₈₃	#2642	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₄⋊Q₈	—	83	1	no	—
54	C₂×#125	D₈₃	1	1	yes	characteristic
55	#400	—	83	8	no	—
56	#391	—	83	4	no	—
57	#376	—	83	1	no	—
58	C₂²×Q₈	—	83	2	no	—
59	C₄⋊Q₈	—	166	4	no	—
60	#125	—	2	4	no	—
61	C₂×C₄⋊C₄	—	83	4	no	—
62	C₂×C₄⋊C₄	C₂×D₈₃	1	2	yes	—
63	C₂×C₄⋊C₄	C₂×D₈₃	1	4	yes	—
64	C₂×C₄²	—	83	2	no	—
65	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic
66	#95	—	83	4	no	—
67	#95	—	83	16	no	—
68	C₂×Q₈	—	166	4	no	—
69	C₂×Q₈	—	166	8	no	—
70	C₂²×C₄	—	83	4	no	—
71	C₂²×C₄	—	83	4	no	—
72	C₂²×C₄	C₂²×D₈₃	1	4	yes	—
73	C₂²×C₄	C₂²×D₈₃	1	2	yes	—
74	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
75	C₄⋊C₄	—	2	8	no	—
76	C₄⋊C₄	—	2	4	no	—
77	C₄⋊C₄	—	166	8	no	—
78	C₄²	—	166	4	no	—
79	C₄²	C₂²⋊D₈₃	1	4	yes	—
80	C₂³	C₂³×D₈₃	1	1	yes	characteristic
81	Q₈	—	332	8	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	—	2	8	no	—
85	C₂×C₄	—	166	4	no	—
86	C₂×C₄	—	166	4	no	—
87	C₂×C₄	—	166	8	no	—
88	C₂×C₄	—	166	8	no	—
89	C₂×C₄	C₂×C₂²⋊D₈₃	1	4	yes	—
90	C₂×C₄	C₂×C₂²⋊D₈₃	1	2	yes	—
91	C₂×C₄	#13050591	1	4	yes	—
92	C₂²	C₂²×C₂²⋊D₈₃	1	1	yes	characteristic
93	C₂²	C₂×#13050591	1	2	yes	—
94	C₂²	#14581839	1	4	yes	—
95	C₄	—	2	4	no	—
96	C₄	—	4	4	no	—
97	C₄	—	332	4	no	—
98	C₄	—	332	4	no	—
99	C₄	#14581781	1	4	yes	—
100	C₂	C₂×#14581781	1	1	yes	characteristic
101	C₂	#19128272	1	2	yes	—
102	C₂	#19128314	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14581792

C₂

yes

maximal, characteristic

#19127640

C₂

yes

maximal

#19127606

C₂

yes

maximal

#19127547

C₂

yes

maximal, characteristic

C₂×#125×C₈₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₆₆

C₂²

yes

—

#14581792

—

C₂×C₄⋊Dic₈₃

C₂²

yes

—

C₂×C₄×Dic₈₃

C₂²

yes

—

C₈₃⋊#95

C₂²

yes

—

C₈₃⋊#95

C₂²

yes

—

#125×C₈₃

—

C₂×C₄⋊C₄×C₈₃

C₂²

yes

—

C₂×C₄⋊C₄×C₈₃

C₂²

yes

—

C₂×C₄²×C₈₃

C₂²

yes

characteristic

C₂×Dic₁₆₆

—

C₂×Dic₁₆₆

—

C₂²×Dic₈₃

C₂³

yes

—

C₂²×Dic₈₃

C₂³

yes

—

C₄⋊Dic₈₃

—

C₄×Dic₈₃

—

C₂²×C₄×C₈₃

C₂³

yes

—

C₂²×C₄×C₈₃

C₂³

yes

—

C₂²×C₄×C₈₃

C₂³

yes

characteristic

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄²×C₈₃

D₄

yes

—

C₂³×C₈₃

C₂⁴

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂×D₄

yes

—

C₂×C₄×C₈₃

C₂×D₄

yes

—

C₂×C₄×C₈₃

#41

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

Dic₁₆₆

—

C₂²×C₈₃

C₂²×D₄

yes

characteristic

C₂²×C₈₃

C₂×#41

yes

—

C₂²×C₈₃

2₋¹⁺⁴

yes

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

#124

yes

—

Dic₈₃

—

Dic₈₃

—

C₂×C₈₃

C₂×#124

yes

characteristic

C₂×C₈₃

#536

yes

—

C₂×C₈₃

#541

yes

—

#2642

—

maximal, Sylow

C₈₃

#2642

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

C₂×#125

D₈₃

yes

—

—

—

C₂²×Q₈

—

C₄⋊Q₈

—

166

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₈₃

yes

—

C₂×C₄⋊C₄

C₂×D₈₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₈₃

yes

characteristic

#95

—

#95

—

C₂×Q₈

—

166

—

C₂×Q₈

—

166

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₈₃

yes

—

C₂²×C₄

C₂²×D₈₃

yes

—

C₂²×C₄

C₂²×D₈₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

166

—

C₄²

—

166

—

C₄²

C₂²⋊D₈₃

yes

—

C₂³

C₂³×D₈₃

yes

characteristic

Q₈

—

332

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

C₂×C₂²⋊D₈₃

yes

—

C₂×C₄

C₂×C₂²⋊D₈₃

yes

—

C₂×C₄

#13050591

yes

—

C₂²

C₂²×C₂²⋊D₈₃

yes

characteristic

C₂²

C₂×#13050591

yes

—

C₂²

#14581839

yes

—

C₄

—

C₄

—

C₄

—

332

—

C₄

—

332

—

C₄

#14581781

yes

—

100

C₂

C₂×#14581781

yes

characteristic

101

C₂

#19128272

yes

—

102

C₂

#19128314

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₈₃
commutator, socle, prime radical, cosocle	C₂³×C₈₃	C₂⁴
Fitting	C₂×#125×C₈₃	C₂
hypercenter	C₂×#125	D₈₃
hypocenter	C₈₃	#2642
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₈₃

commutator, socle, prime radical, cosocle

C₂³×C₈₃

C₂⁴

Fitting

C₂×#125×C₈₃

C₂

D₈₃

C₈₃

G ▷ C₂³×C₈₃ ▷ C₈₃

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
52. C₈₃	#2642	semidirect

H ≅ G/N

type

52. C₈₃

#2642

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#14581792	2
#19127640	2
#19127606	2
#19127547	2
C₂×#125×C₈₃	2
#2642	83

subgroup

index

C₂×#125×C₈₃

Subgroups — #24913414

Conjugacy classes of subgroups

Complements

Maximal subgroups