Group #24913423 — subgroups

Subgroups — #24913423

Order 10624.

420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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	#19127630	C₂	1	6	yes	maximal, complemented
2	#19127625	C₂	1	2	yes	maximal, complemented
3	#19127603	C₂	1	3	yes	maximal
4	#19127599	C₂	1	3	yes	maximal, complemented
5	#376×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₈₃	C₂²	1	3	yes	—
8	C₂×Dic₈₃⋊C₄	C₂²	1	6	yes	—
9	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	6	yes	—
10	C₂×(C₂×D₈₃)⋊C₄	C₂²	1	6	yes	—
11	C₈₃⋊#95	C₂²	1	6	yes	—
12	C₂×C₄²×C₈₃	C₂²	1	3	yes	—
13	#95×C₈₃	C₂²	1	1	yes	characteristic
14	#95×C₈₃	C₂²	1	3	yes	—
15	C₂³×D₈₃	C₂³	1	2	yes	—
16	C₂×D₃₃₂	—	2	6	no	—
17	C₂²×Dic₈₃	C₂³	1	6	yes	—
18	C₄⋊Dic₈₃	—	2	6	no	—
19	Dic₈₃⋊C₄	—	4	6	no	—
20	(C₂×D₈₃)⋊C₄	—	4	6	no	—
21	(C₂×D₈₃)⋊C₄	—	4	6	no	—
22	C₂²×C₄×C₈₃	C₂³	1	3	yes	—
23	C₂²×C₄×C₈₃	C₂³	1	3	yes	—
24	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
25	C₄²×C₈₃	—	2	6	no	—
26	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
27	C₂²×D₈₃	—	2	6	no	—
28	C₂²×D₈₃	—	2	6	no	—
29	C₂²×D₈₃	—	2	2	no	—
30	C₂×C₄×C₈₃	—	2	3	no	—
31	C₂×C₄×C₈₃	—	2	3	no	—
32	C₂×C₄×C₈₃	—	2	3	no	—
33	C₂×C₄×C₈₃	—	2	3	no	—
34	C₂×C₄×C₈₃	—	2	3	no	—
35	C₂×C₄×C₈₃	—	2	3	no	—
36	C₂×C₄×C₈₃	#41	1	6	yes	—
37	C₂×Dic₈₃	—	2	6	no	—
38	C₂×Dic₈₃	—	2	6	no	—
39	C₂×Dic₈₃	—	2	6	no	—
40	D₃₃₂	—	4	4	no	—
41	C₂²×C₈₃	C₂×#41	1	3	yes	—
42	C₂²×C₈₃	H(5,𝔽₂)	1	3	yes	—
43	C₂²×C₈₃	2₋¹⁺⁴	1	1	yes	characteristic
44	C₂×D₈₃	—	4	2	no	—
45	C₂×D₈₃	—	4	6	no	—
46	C₂×D₈₃	—	4	6	no	—
47	C₄×C₈₃	—	4	3	no	—
48	C₄×C₈₃	—	4	3	no	—
49	C₄×C₈₃	#126	1	4	yes	—
50	Dic₈₃	—	4	6	no	—
51	C₂×C₈₃	C₂×#126	1	1	yes	characteristic
52	C₂×C₈₃	#540	1	3	yes	—
53	C₂×C₈₃	#542	1	3	yes	—
54	D₈₃	—	8	2	no	—
55	#2644	—	83	1	no	maximal, Sylow
56	C₈₃	#2644	1	1	yes	characteristic, complemented, Sylow
57	#397	—	83	6	no	—
58	#396	—	83	2	no	—
59	#390	—	83	3	no	—
60	#389	—	83	3	no	—
61	#376	D₈₃	1	1	yes	characteristic, complemented
62	C₂²×D₄	—	83	1	no	—
63	C₂×C₄⋊C₄	—	83	6	no	—
64	C₂×C₄⋊C₄	—	83	3	no	—
65	C₂×C₂²⋊C₄	—	83	6	no	—
66	C₂×C₂²⋊C₄	—	83	6	no	—
67	C₂×C₄²	C₂×D₈₃	1	3	yes	—
68	#95	—	83	6	no	—
69	#95	C₂×D₈₃	1	1	yes	characteristic
70	#95	C₂×D₈₃	1	3	yes	—
71	C₂⁴	—	83	2	no	—
72	C₂×D₄	—	166	6	no	—
73	C₂²×C₄	—	83	6	no	—
74	C₂²×C₄	C₂²×D₈₃	1	3	yes	—
75	C₂²×C₄	C₂²×D₈₃	1	3	yes	—
76	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
77	C₄⋊C₄	—	332	6	no	—
78	C₄⋊C₄	—	166	6	no	—
79	C₂²⋊C₄	—	332	6	no	—
80	C₂²⋊C₄	—	332	6	no	—
81	C₄²	—	2	6	no	—
82	C₂³	—	166	6	no	—
83	C₂³	—	166	6	no	—
84	C₂³	—	166	2	no	—
85	C₂³	C₂³×D₈₃	1	1	yes	characteristic
86	D₄	—	332	4	no	—
87	C₂×C₄	—	2	3	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	166	6	no	—
94	C₂×C₄	—	166	6	no	—
95	C₂×C₄	—	166	6	no	—
96	C₂×C₄	#13050590	1	6	yes	—
97	C₂²	—	332	6	no	—
98	C₂²	—	332	2	no	—
99	C₂²	—	332	6	no	—
100	C₂²	C₂×#13050590	1	3	yes	—
101	C₂²	#14581838	1	3	yes	—
102	C₂²	#14581839	1	1	yes	characteristic
103	C₄	—	4	3	no	—
104	C₄	—	4	3	no	—
105	C₄	—	332	6	no	—
106	C₄	#14581786	1	4	yes	—
107	C₂	—	664	2	no	—
108	C₂	C₂×#14581786	1	1	yes	characteristic
109	C₂	#19128306	1	3	yes	—
110	C₂	#19128322	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19127630

C₂

yes

maximal, complemented

#19127625

C₂

yes

maximal, complemented

#19127603

C₂

yes

maximal

#19127599

C₂

yes

maximal, complemented

#376×C₈₃

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₃₂

C₂²

yes

characteristic

C₂×C₄⋊Dic₈₃

C₂²

yes

—

C₂×Dic₈₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₈₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₈₃)⋊C₄

C₂²

yes

—

C₈₃⋊#95

C₂²

yes

—

C₂×C₄²×C₈₃

C₂²

yes

—

#95×C₈₃

C₂²

yes

characteristic

#95×C₈₃

C₂²

yes

—

C₂³×D₈₃

C₂³

yes

—

C₂×D₃₃₂

—

C₂²×Dic₈₃

C₂³

yes

—

C₄⋊Dic₈₃

—

Dic₈₃⋊C₄

—

(C₂×D₈₃)⋊C₄

—

(C₂×D₈₃)⋊C₄

—

C₂²×C₄×C₈₃

C₂³

yes

—

C₂²×C₄×C₈₃

C₂³

yes

—

C₂²×C₄×C₈₃

C₂³

yes

characteristic

C₄²×C₈₃

—

C₂³×C₈₃

C₂⁴

yes

characteristic

C₂²×D₈₃

—

C₂²×D₈₃

—

C₂²×D₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

#41

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₂×Dic₈₃

—

D₃₃₂

—

C₂²×C₈₃

C₂×#41

yes

—

C₂²×C₈₃

H(5,𝔽₂)

yes

—

C₂²×C₈₃

2₋¹⁺⁴

yes

characteristic

C₂×D₈₃

—

C₂×D₈₃

—

C₂×D₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

#126

yes

—

Dic₈₃

—

C₂×C₈₃

C₂×#126

yes

characteristic

C₂×C₈₃

#540

yes

—

C₂×C₈₃

#542

yes

—

D₈₃

—

#2644

—

maximal, Sylow

C₈₃

#2644

yes

characteristic, complemented, Sylow

—

—

—

—

D₈₃

yes

characteristic, complemented

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₈₃

yes

—

#95

—

#95

C₂×D₈₃

yes

characteristic

#95

C₂×D₈₃

yes

—

C₂⁴

—

C₂×D₄

—

166

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₈₃

yes

—

C₂²×C₄

C₂²×D₈₃

yes

—

C₂²×C₄

C₂²×D₈₃

yes

characteristic

C₄⋊C₄

—

332

—

C₄⋊C₄

—

166

—

C₂²⋊C₄

—

332

—

C₂²⋊C₄

—

332

—

C₄²

—

C₂³

—

166

—

C₂³

—

166

—

C₂³

—

166

—

C₂³

C₂³×D₈₃

yes

characteristic

D₄

—

332

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

#13050590

yes

—

C₂²

—

332

—

C₂²

—

332

—

C₂²

—

332

—

100

C₂²

C₂×#13050590

yes

—

101

C₂²

#14581838

yes

—

102

C₂²

#14581839

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

332

—

106

C₄

#14581786

yes

—

107

C₂

—

664

—

108

C₂

C₂×#14581786

yes

characteristic

109

C₂

#19128306

yes

—

110

C₂

#19128322

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₈₃
commutator, socle, cosocle	C₂³×C₈₃	C₂⁴
Fitting	#376×C₈₃	C₂
prime radical	C₂²×D₃₃₂	C₂²
hypercenter	#376	D₈₃
hypocenter	C₈₃	#2644
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₈₃

commutator, socle, cosocle

C₂³×C₈₃

C₂⁴

Fitting

#376×C₈₃

C₂

prime radical

C₂²×D₃₃₂

C₂²

D₈₃

C₈₃

G ▷ C₂³×C₈₃ ▷ C₈₃

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
1. #19127630	C₂	semidirect
2. #19127625	C₂	semidirect
4. #19127599	C₂	semidirect
5. #376×C₈₃	C₂	semidirect
56. C₈₃	#2644	semidirect
61. #376	D₈₃	semidirect

H ≅ G/N

type

1. #19127630

C₂

semidirect

2. #19127625

C₂

semidirect

4. #19127599

C₂

semidirect

5. #376×C₈₃

C₂

semidirect

56. C₈₃

#2644

semidirect

61. #376

D₈₃

semidirect

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

subgroup	index
#19127630	2
#19127625	2
#19127603	2
#19127599	2
#376×C₈₃	2
#2644	83

subgroup

index

#376×C₈₃

Subgroups — #24913423

Conjugacy classes of subgroups

Complements

Maximal subgroups