Group #24905546 — subgroups

Subgroups — #24905546

Order 10624.

140 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14581732	C₂	1	1	yes	maximal, characteristic
2	C₂×#14581702	C₂	1	1	yes	maximal, characteristic
3	C₂×M₃₂×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	#14581732	—	2	1	no	—
7	#14581732	C₄	1	2	yes	complemented
8	C₂×C₈₃⋊C₁₆	—	2	1	no	—
9	#14581702	—	2	1	no	—
10	#14581702	—	2	1	no	—
11	C₂²×C₈×C₈₃	C₂²	1	1	yes	characteristic
12	M₃₂×C₈₃	—	2	1	no	—
13	M₃₂×C₈₃	C₄	1	2	yes	complemented
14	C₂×C₁₆×C₈₃	—	2	1	no	—
15	C₂²×Dic₈₃	C₈	1	2	yes	—
16	C₂×C₈₃⋊C₈	—	2	1	no	—
17	C₂×C₈₃⋊C₈	—	2	1	no	—
18	C₂×C₈₃⋊C₈	C₈	1	2	yes	—
19	C₄×Dic₈₃	—	2	1	no	—
20	C₄×Dic₈₃	—	2	1	no	—
21	C₈₃⋊C₁₆	—	2	2	no	—
22	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
26	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
27	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
28	C₂×C₈×C₈₃	Q₈	1	1	yes	characteristic
29	C₁₆×C₈₃	—	2	2	no	—
30	C₂³×C₈₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₈₃	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₈₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₈₃	M₁₆	1	1	yes	characteristic
36	C₂×C₄×C₈₃	M₁₆	1	1	yes	characteristic
37	C₂×Dic₈₃	—	2	2	no	—
38	C₂×Dic₈₃	—	4	2	no	—
39	C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
42	C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
43	C₈₃⋊C₈	—	2	2	no	—
44	C₂²×C₈₃	—	2	2	no	—
45	C₂²×C₈₃	C₄×C₈	1	1	yes	characteristic
46	C₂²×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
47	C₂²×C₈₃	C₄⋊C₈	1	1	yes	characteristic
48	C₄×C₈₃	#95	1	1	yes	characteristic
49	C₄×C₈₃	#97	1	1	yes	characteristic
50	C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₈₃	C₄⋊C₈	1	1	yes	characteristic
52	Dic₈₃	—	4	2	no	—
53	C₂×C₈₃	—	2	1	no	—
54	C₂×C₈₃	—	2	1	no	—
55	C₂×C₈₃	#336	1	1	yes	characteristic
56	C₂×C₈₃	#349	1	2	yes	—
57	#1377	—	83	1	no	maximal, Sylow
58	C₈₃	#1377	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₃₂	—	83	1	no	—
60	C₂×M₃₂	D₈₃	1	1	yes	characteristic
61	C₂×#97	—	83	1	no	—
62	C₂²×C₈	—	83	1	no	—
63	C₂²×C₈	C₂×D₈₃	1	1	yes	characteristic
64	C₂×C₄²	—	83	1	no	—
65	M₃₂	—	2	1	no	—
66	M₃₂	—	83	2	no	—
67	M₃₂	—	166	1	no	—
68	M₃₂	Dic₈₃	1	2	yes	complemented
69	C₂×C₁₆	—	2	1	no	—
70	C₂×C₁₆	—	166	1	no	—
71	#97	—	166	1	no	—
72	#97	—	166	1	no	—
73	C₂²×C₄	—	83	2	no	—
74	C₂²×C₄	C₄×D₈₃	1	1	yes	characteristic
75	C₂×C₈	—	83	2	no	—
76	C₂×C₈	—	166	1	no	—
77	C₂×C₈	—	166	1	no	—
78	C₂×C₈	Dic₁₆₆	1	1	yes	characteristic
79	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
80	C₂×C₈	D₃₃₂	1	1	yes	characteristic
81	C₂×C₈	C₂×Dic₈₃	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
83	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
84	C₄²	—	166	1	no	—
85	C₄²	—	166	1	no	—
86	C₁₆	—	2	2	no	—
87	C₁₆	—	166	2	no	—
88	C₂³	C₈×D₈₃	1	1	yes	characteristic
89	C₂×C₄	—	332	2	no	—
90	C₂×C₄	—	166	2	no	—
91	C₂×C₄	C₄×Dic₈₃	1	1	yes	characteristic
92	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
93	C₂×C₄	Dic₈₃⋊C₄	1	1	yes	characteristic
94	C₂×C₄	C₈×D₈₃	1	1	yes	characteristic
95	C₂×C₄	#13050573	1	1	yes	characteristic
96	C₂×C₄	#13050573	1	1	yes	characteristic
97	C₈	—	166	2	no	—
98	C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
99	C₈	C₂²⋊Dic₈₃	1	1	yes	characteristic
100	C₈	Dic₈₃⋊C₄	1	1	yes	characteristic
101	C₈	C₄⋊Dic₈₃	1	1	yes	characteristic
102	C₂²	—	2	2	no	—
103	C₂²	C₈×Dic₈₃	1	1	yes	characteristic
104	C₂²	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
105	C₂²	Dic₈₃⋊C₈	1	1	yes	characteristic
106	C₄	—	332	2	no	—
107	C₄	C₈₃⋊#95	1	1	yes	characteristic
108	C₄	#14581702	1	1	yes	characteristic
109	C₄	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
110	C₄	Dic₈₃⋊C₈	1	1	yes	characteristic
111	C₂	—	2	1	no	—
112	C₂	—	2	1	no	—
113	C₂	#19127455	1	1	yes	characteristic
114	C₂	#19127482	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14581732

C₂

yes

maximal, characteristic

C₂×#14581702

C₂

yes

maximal, characteristic

C₂×M₃₂×C₈₃

C₂

yes

maximal, characteristic

C₂²×C₈₃⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₈₃

C₄

yes

characteristic

#14581732

—

#14581732

C₄

yes

complemented

C₂×C₈₃⋊C₁₆

—

#14581702

—

#14581702

—

C₂²×C₈×C₈₃

C₂²

yes

characteristic

M₃₂×C₈₃

—

M₃₂×C₈₃

C₄

yes

complemented

C₂×C₁₆×C₈₃

—

C₂²×Dic₈₃

C₈

yes

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

C₈

yes

—

C₄×Dic₈₃

—

C₄×Dic₈₃

—

C₈₃⋊C₁₆

—

C₂²×C₄×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

D₄

yes

characteristic

C₂×C₈×C₈₃

D₄

yes

characteristic

C₂×C₈×C₈₃

D₄

yes

characteristic

C₂×C₈×C₈₃

Q₈

yes

characteristic

C₁₆×C₈₃

—

C₂³×C₈₃

C₂×C₈

yes

characteristic

C₂×C₄×C₈₃

C₄²

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₂×C₈

yes

characteristic

C₂×C₄×C₈₃

M₁₆

yes

characteristic

C₂×C₄×C₈₃

M₁₆

yes

characteristic

C₂×Dic₈₃

—

C₂×Dic₈₃

—

C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₈×C₈₃

C₂²⋊C₄

yes

characteristic

C₈×C₈₃

C₄⋊C₄

yes

characteristic

C₈×C₈₃

C₄⋊C₄

yes

characteristic

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

C₄×C₈

yes

characteristic

C₂²×C₈₃

C₂²⋊C₈

yes

characteristic

C₂²×C₈₃

C₄⋊C₈

yes

C₄×C₈₃

yes

C₄×C₈₃

yes

C₄×C₈₃

C₂²⋊C₈

yes

characteristic

C₄×C₈₃

C₄⋊C₈

yes

characteristic

Dic₈₃

—

C₂×C₈₃

—

C₂×C₈₃

—

C₂×C₈₃

#336

yes

characteristic

C₂×C₈₃

#349

yes

—

#1377

—

maximal, Sylow

C₈₃

#1377

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

D₈₃

yes

characteristic

C₂×#97

—

C₂²×C₈

—

C₂²×C₈

C₂×D₈₃

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

166

—

M₃₂

Dic₈₃

yes

complemented

C₂×C₁₆

—

C₂×C₁₆

—

166

—

#97

—

166

—

#97

—

166

—

C₂²×C₄

—

C₂²×C₄

C₄×D₈₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

166

—

C₂×C₈

—

166

—

C₂×C₈

Dic₁₆₆

yes

characteristic

C₂×C₈

C₄×D₈₃

yes

characteristic

C₂×C₈

D₃₃₂

yes

characteristic

C₂×C₈

C₂×Dic₈₃

yes

characteristic

C₂×C₈

C₂²⋊D₈₃

yes

characteristic

C₂×C₈

C₂²⋊D₈₃

yes

characteristic

C₄²

—

166

—

C₄²

—

166

—

C₁₆

—

C₁₆

—

166

—

C₂³

C₈×D₈₃

yes

characteristic

C₂×C₄

—

332

—

C₂×C₄

—

166

—

C₂×C₄

C₄×Dic₈₃

yes

characteristic

C₂×C₄

(C₂×D₈₃)⋊C₄

yes

characteristic

C₂×C₄

Dic₈₃⋊C₄

yes

characteristic

C₂×C₄

C₈×D₈₃

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

166

—

C₈

(C₂×D₈₃)⋊C₄

yes

characteristic

C₈

C₂²⋊Dic₈₃

yes

characteristic

100

C₈

Dic₈₃⋊C₄

yes

characteristic

101

C₈

C₄⋊Dic₈₃

yes

characteristic

102

C₂²

—

103

C₂²

C₈×Dic₈₃

yes

characteristic

104

C₂²

(C₂×D₈₃)⋊C₈

yes

characteristic

105

C₂²

Dic₈₃⋊C₈

yes

characteristic

106

C₄

—

332

—

107

C₄

C₈₃⋊#95

yes

characteristic

108

C₄

#14581702

yes

characteristic

109

C₄

(C₂×D₈₃)⋊C₈

yes

characteristic

110

C₄

Dic₈₃⋊C₈

yes

characteristic

111

C₂

—

112

C₂

—

113

C₂

#19127455

yes

characteristic

114

C₂

#19127482

yes

—

	subgroup	G/H
center	C₂×C₄	(C₂×D₈₃)⋊C₄
commutator	C₂²×C₈₃	C₄×C₈
Frattini	C₂²×C₈	C₂×D₈₃
Fitting	C₂×M₃₂×C₈₃	C₂
socle	C₂²×C₈₃	C₂²⋊C₈
prime radical	C₂³×C₈₃	C₂×C₈
cosocle	C₂²×C₈×C₈₃	C₂²
hypercenter	C₂×M₃₂	D₈₃
hypocenter	C₈₃	#1377
LCS	G ▷ C₂²×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₄

(C₂×D₈₃)⋊C₄

commutator

C₂²×C₈₃

C₄×C₈

Frattini

C₂²×C₈

C₂×D₈₃

Fitting

C₂×M₃₂×C₈₃

C₂

socle

C₂²×C₈₃

C₂²⋊C₈

prime radical

C₂³×C₈₃

C₂×C₈

cosocle

C₂²×C₈×C₈₃

C₂²

hypercenter

C₂×M₃₂

D₈₃

hypocenter

C₈₃

#1377

LCS

G ▷ C₂²×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
7. #14581732	C₄	semidirect
13. M₃₂×C₈₃	C₄	semidirect
58. C₈₃	#1377	semidirect
68. M₃₂	Dic₈₃	semidirect

H ≅ G/N

type

7. #14581732

C₄

semidirect

13. M₃₂×C₈₃

C₄

semidirect

58. C₈₃

#1377

semidirect

68. M₃₂

Dic₈₃

semidirect

Subgroups — #24905546

Conjugacy classes of subgroups

Complements