Group #24906056 — subgroups

Subgroups — #24906056

Order 10624.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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	#19128257	C₂	1	1	yes	maximal, characteristic
2	#19127653	C₂	1	2	yes	maximal
3	#19127443	C₂	1	1	yes	maximal, characteristic, complemented
4	#19127442	C₂	1	2	yes	maximal, complemented
5	#330×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13050573	—	2	2	no	—
7	#14581791	C₄	1	2	yes	—
8	#14581784	C₂²	1	1	yes	characteristic
9	#14581770	—	2	2	no	—
10	#14581757	—	2	2	no	—
11	#14581750	C₄	1	2	yes	—
12	C₄²×D₈₃	C₂²	1	1	yes	characteristic
13	#14581703	C₂²	1	2	yes	—
14	C₈×Dic₈₃	—	2	2	no	—
15	#125×C₈₃	C₂²	1	1	yes	characteristic
16	#97×C₈₃	C₂²	1	2	yes	—
17	C₂×Dic₁₆₆	—	2	2	no	—
18	C₂×C₄×D₈₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₈₃	D₄	1	2	yes	—
20	#13050573	—	2	8	no	—
21	C₂×C₈₃⋊C₈	—	2	2	no	—
22	C₄⋊Dic₈₃	C₂×C₄	1	2	yes	—
23	Dic₈₃⋊C₄	—	2	2	no	—
24	Dic₈₃⋊C₄	—	2	2	no	—
25	(C₂×D₈₃)⋊C₄	—	2	2	no	—
26	C₄×Dic₈₃	—	2	2	no	—
27	C₄×Dic₈₃	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₈₃	D₄	1	2	yes	—
29	C₂×C₈×C₈₃	—	2	2	no	—
30	C₄⋊C₄×C₈₃	—	2	2	no	—
31	C₄⋊C₄×C₈₃	C₂×C₄	1	2	yes	—
32	C₄²×C₈₃	C₂³	1	1	yes	characteristic
33	C₂²×D₈₃	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₈₃	—	2	2	no	—
35	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
37	C₂×Dic₈₃	—	2	2	no	—
38	C₂×Dic₈₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×Dic₈₃	C₂²⋊C₄	1	2	yes	—
40	C₄×D₈₃	—	2	2	no	—
41	C₄×D₈₃	—	2	4	no	—
42	Dic₁₆₆	—	4	4	no	—
43	C₈×C₈₃	—	2	4	no	—
44	C₈₃⋊C₈	—	2	4	no	—
45	C₂²×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×D₈₃	—	2	1	no	—
47	C₂×D₈₃	—	2	2	no	—
48	C₄×C₈₃	—	2	1	no	—
49	C₄×C₈₃	—	2	2	no	—
50	C₄×C₈₃	—	4	2	no	—
51	Dic₈₃	—	4	2	no	—
52	Dic₈₃	#101	1	2	yes	—
53	Dic₈₃	#104	1	4	yes	—
54	C₂×C₈₃	C₂×#101	1	1	yes	characteristic
55	C₂×C₈₃	C₂×#104	1	2	yes	—
56	D₈₃	—	4	1	no	—
57	#1526	—	83	1	no	maximal, Sylow
58	C₈₃	#1526	1	1	yes	characteristic, complemented, Sylow
59	#533	—	83	1	no	—
60	C₄×M₁₆	—	83	2	no	—
61	#330	—	83	1	no	—
62	#330	—	83	2	no	—
63	#330	D₈₃	1	1	yes	characteristic, complemented
64	C₂×M₁₆	—	166	2	no	—
65	C₄⋊Q₈	—	83	2	no	—
66	#125	—	83	1	no	—
67	#125	C₂×D₈₃	1	1	yes	characteristic
68	C₂²⋊Q₈	—	166	2	no	—
69	C₄×Q₈	—	166	2	no	—
70	#117	—	83	2	no	—
71	C₂×C₄²	—	83	1	no	—
72	#97	—	83	2	no	—
73	#97	C₂×D₈₃	1	2	yes	—
74	C₄×C₈	—	166	2	no	—
75	C₂×Q₈	—	166	2	no	—
76	C₂²×C₄	—	83	1	no	—
77	C₂²×C₄	—	83	2	no	—
78	M₁₆	—	166	8	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	166	2	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	83	2	no	—
83	C₄⋊C₄	—	166	2	no	—
84	C₄⋊C₄	—	166	2	no	—
85	C₄⋊C₄	C₄×D₈₃	1	2	yes	—
86	C₂²⋊C₄	—	166	2	no	—
87	C₄²	—	83	1	no	—
88	C₄²	—	83	2	no	—
89	C₄²	—	166	2	no	—
90	C₄²	C₂²×D₈₃	1	1	yes	characteristic
91	C₂³	—	83	1	no	—
92	Q₈	—	332	4	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	83	1	no	—
95	C₂×C₄	—	83	2	no	—
96	C₂×C₄	—	166	4	no	—
97	C₂×C₄	—	166	2	no	—
98	C₂×C₄	—	166	2	no	—
99	C₂×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
100	C₂×C₄	D₄×D₈₃	1	2	yes	—
101	C₈	—	2	4	no	—
102	C₈	—	166	4	no	—
103	C₂²	—	166	1	no	—
104	C₂²	—	166	2	no	—
105	C₂²	C₂²⋊C₄×D₈₃	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	2	no	—
108	C₄	—	4	2	no	—
109	C₄	—	332	2	no	—
110	C₄	—	83	2	no	—
111	C₄	—	83	4	no	—
112	C₂	—	332	1	no	—
113	C₂	#101×D₈₃	1	1	yes	characteristic
114	C₂	#104×D₈₃	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19128257

C₂

yes

maximal, characteristic

#19127653

C₂

yes

maximal

#19127443

C₂

yes

maximal, characteristic, complemented

#19127442

C₂

yes

maximal, complemented

#330×C₈₃

C₂

yes

maximal, characteristic, complemented

C₂×#13050573

—

#14581791

C₄

yes

—

#14581784

C₂²

yes

—

—

C₄

yes

—

C₄²×D₈₃

C₂²

yes

characteristic

#14581703

C₂²

yes

—

C₈×Dic₈₃

—

#125×C₈₃

C₂²

yes

characteristic

#97×C₈₃

C₂²

yes

—

C₂×Dic₁₆₆

—

C₂×C₄×D₈₃

C₂×C₄

yes

characteristic

C₂×C₄×D₈₃

D₄

yes

—

#13050573

—

C₂×C₈₃⋊C₈

—

C₄⋊Dic₈₃

C₂×C₄

yes

—

Dic₈₃⋊C₄

—

Dic₈₃⋊C₄

—

(C₂×D₈₃)⋊C₄

—

C₄×Dic₈₃

—

C₄×Dic₈₃

C₂×C₄

yes

characteristic

C₄×Dic₈₃

D₄

yes

—

C₂×C₈×C₈₃

—

C₄⋊C₄×C₈₃

—

C₄⋊C₄×C₈₃

C₂×C₄

yes

—

C₄²×C₈₃

C₂³

yes

characteristic

C₂²×D₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₈₃

C₂×D₄

yes

—

C₂×Dic₈₃

—

C₂×Dic₈₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₈₃

C₂²⋊C₄

yes

—

C₄×D₈₃

—

C₄×D₈₃

—

Dic₁₆₆

—

C₈×C₈₃

—

C₈₃⋊C₈

—

C₂²×C₈₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₈₃

—

C₂×D₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

Dic₈₃

—

Dic₈₃

#101

yes

—

Dic₈₃

#104

yes

—

C₂×C₈₃

C₂×#101

yes

characteristic

C₂×C₈₃

C₂×#104

yes

—

D₈₃

—

#1526

—

maximal, Sylow

C₈₃

#1526

yes

characteristic, complemented, Sylow

#533

—

C₄×M₁₆

—

#330

—

#330

—

#330

D₈₃

yes

characteristic, complemented

C₂×M₁₆

—

166

—

C₄⋊Q₈

—

#125

—

#125

C₂×D₈₃

yes

characteristic

C₂²⋊Q₈

—

166

—

C₄×Q₈

—

166

—

#117

—

C₂×C₄²

—

#97

—

#97

C₂×D₈₃

yes

—

C₄×C₈

—

166

—

C₂×Q₈

—

166

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

166

—

C₂×C₈

—

C₂×C₈

—

166

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

166

—

C₄⋊C₄

—

166

—

C₄⋊C₄

C₄×D₈₃

yes

—

C₂²⋊C₄

—

166

—

C₄²

—

C₄²

—

C₄²

—

166

—

C₄²

C₂²×D₈₃

yes

characteristic

C₂³

—

Q₈

—

332

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

—

166

—

C₂×C₄

C₂×C₄×D₈₃

yes

characteristic

100

C₂×C₄

D₄×D₈₃

yes

—

101

C₈

—

102

C₈

—

166

—

103

C₂²

—

166

—

104

C₂²

—

166

—

105

C₂²

C₂²⋊C₄×D₈₃

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

332

—

110

C₄

—

111

C₄

—

112

C₂

—

332

—

113

C₂

#101×D₈₃

yes

characteristic

114

C₂

#104×D₈₃

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂²×C₄
Frattini	C₄²	C₂²×D₈₃
Fitting	#330×C₈₃	C₂
socle	C₂²×C₈₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₈₃	C₂²⋊C₄
cosocle	C₄²×C₈₃	C₂³
hypercenter	#330	D₈₃
hypocenter	C₈₃	#1526
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₈₃

commutator

C₂×C₄×C₈₃

C₂²×C₄

Frattini

C₄²

C₂²×D₈₃

Fitting

#330×C₈₃

C₂

socle

C₂²×C₈₃

C₂×C₂²⋊C₄

prime radical

C₂²×D₈₃

C₂²⋊C₄

cosocle

C₄²×C₈₃

C₂³

D₈₃

C₈₃

G ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #19127443	C₂	semidirect
4. #19127442	C₂	semidirect
5. #330×C₈₃	C₂	semidirect
58. C₈₃	#1526	semidirect
63. #330	D₈₃	semidirect

H ≅ G/N

type

3. #19127443

C₂

semidirect

4. #19127442

C₂

semidirect

5. #330×C₈₃

C₂

semidirect

58. C₈₃

#1526

semidirect

63. #330

D₈₃

semidirect

Subgroups — #24906056

Conjugacy classes of subgroups

Complements