Group #24905356 — subgroups

Subgroups — #24905356

Order 10624.

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

normal subgroups only

This group has 172 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	#19127758	C₂	1	1	yes	maximal, characteristic
2	C₄×#13050574	C₂	1	1	yes	maximal, characteristic
3	#376×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#13050574	—	2	1	no	—
5	C₄⋊(C₈₃⋊C₈)	C₄	1	2	yes	complemented
6	C₂²⋊(C₈₃⋊C₈)	—	2	1	no	—
7	#14581703	—	2	1	no	—
8	#14581703	C₄	1	2	yes	complemented
9	C₄×C₈₃⋊C₈	—	2	1	no	—
10	C₂×C₄²×C₈₃	—	2	1	no	—
11	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
12	#95×C₈₃	—	2	1	no	—
13	#95×C₈₃	C₄	1	2	yes	—
14	#13050574	—	2	4	no	—
15	C₂×C₈₃⋊C₈	—	2	2	no	—
16	C₂×C₈₃⋊C₈	—	2	2	no	—
17	C₂²×C₄×C₈₃	—	2	2	no	—
18	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₈₃	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₈₃	D₄	1	1	yes	characteristic
21	C₄²×C₈₃	—	2	4	no	—
22	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₈₃	D₄	1	1	yes	characteristic
25	C₄²×C₈₃	Q₈	1	1	yes	characteristic
26	C₂³×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₈₃	—	2	2	no	—
28	C₂×C₄×C₈₃	—	2	2	no	—
29	C₂×C₄×C₈₃	—	2	4	no	—
30	C₂×C₄×C₈₃	—	4	1	no	—
31	C₂×C₄×C₈₃	—	4	2	no	—
32	C₂×C₄×C₈₃	—	4	2	no	—
33	C₂×C₄×C₈₃	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₈₃	C₄⋊C₄	1	1	yes	characteristic
39	C₈₃⋊C₈	—	2	4	no	—
40	C₈₃⋊C₈	—	4	2	no	—
41	C₂²×C₈₃	—	2	1	no	—
42	C₂²×C₈₃	—	2	1	no	—
43	C₂²×C₈₃	#95	1	1	yes	characteristic
44	C₂²×C₈₃	#104	1	2	yes	—
45	C₄×C₈₃	—	2	1	no	—
46	C₄×C₈₃	—	2	1	no	—
47	C₄×C₈₃	—	2	1	no	—
48	C₄×C₈₃	—	2	1	no	—
49	C₄×C₈₃	—	2	1	no	—
50	C₄×C₈₃	—	4	4	no	—
51	C₄×C₈₃	#104	1	2	yes	—
52	C₂×C₈₃	—	2	2	no	—
53	C₂×C₈₃	#339	1	1	yes	characteristic
54	C₂×C₈₃	#339	1	1	yes	characteristic
55	C₂×C₈₃	#344	1	1	yes	characteristic
56	#1300	—	83	1	no	maximal, Sylow
57	C₈₃	#1300	1	1	yes	characteristic, complemented, Sylow
58	#432	—	83	1	no	—
59	C₄×M₁₆	—	83	1	no	—
60	#376	D₈₃	1	1	yes	characteristic
61	C₂×M₁₆	—	166	1	no	—
62	C₂×C₄²	—	2	1	no	—
63	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic
64	C₄⋊C₈	—	83	2	no	—
65	C₂²⋊C₈	—	166	1	no	—
66	#97	—	83	2	no	—
67	#97	—	166	1	no	—
68	C₄×C₈	—	166	1	no	—
69	#95	—	2	1	no	—
70	#95	Dic₈₃	1	2	yes	—
71	C₂²×C₄	—	2	2	no	—
72	C₂²×C₄	C₂×Dic₈₃	1	1	yes	characteristic
73	C₂²×C₄	C₂²⋊D₈₃	1	1	yes	characteristic
74	C₂²×C₄	C₂²⋊D₈₃	1	1	yes	characteristic
75	M₁₆	—	166	4	no	—
76	C₂×C₈	—	166	2	no	—
77	C₂×C₈	—	166	2	no	—
78	C₄²	—	2	4	no	—
79	C₄²	Dic₁₆₆	1	1	yes	characteristic
80	C₄²	C₄×D₈₃	1	1	yes	characteristic
81	C₄²	C₄×D₈₃	1	1	yes	characteristic
82	C₄²	D₃₃₂	1	1	yes	characteristic
83	C₂³	C₂²⋊Dic₈₃	1	1	yes	characteristic
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	C₄×Dic₈₃	1	1	yes	characteristic
91	C₂×C₄	(C₂×D₈₃)⋊C₄	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	Dic₈₃⋊C₄	1	1	yes	characteristic
95	C₂×C₄	C₄⋊Dic₈₃	1	1	yes	characteristic
96	C₈	—	332	2	no	—
97	C₈	—	166	4	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	C₈₃⋊#95	1	1	yes	characteristic
101	C₂²	#14581719	1	2	yes	—
102	C₄	—	2	1	no	—
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	—	4	4	no	—
108	C₄	#14581720	1	2	yes	—
109	C₂	—	2	2	no	—
110	C₂	#19127460	1	1	yes	characteristic
111	C₂	#19127461	1	1	yes	characteristic
112	C₂	#19127471	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19127758

C₂

yes

maximal, characteristic

C₄×#13050574

C₂

yes

maximal, characteristic

#376×C₈₃

C₂

yes

maximal, characteristic

C₂×#13050574

—

C₄⋊(C₈₃⋊C₈)

C₄

yes

complemented

C₂²⋊(C₈₃⋊C₈)

—

#14581703

—

#14581703

C₄

yes

complemented

C₄×C₈₃⋊C₈

—

C₂×C₄²×C₈₃

—

C₂×C₄²×C₈₃

C₂²

yes

characteristic

#95×C₈₃

—

#95×C₈₃

C₄

yes

—

#13050574

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

—

C₂²×C₄×C₈₃

—

C₂²×C₄×C₈₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₈₃

D₄

yes

characteristic

C₂²×C₄×C₈₃

D₄

yes

characteristic

C₄²×C₈₃

—

C₄²×C₈₃

C₂×C₄

yes

characteristic

C₄²×C₈₃

C₂×C₄

yes

characteristic

C₄²×C₈₃

D₄

yes

characteristic

C₄²×C₈₃

Q₈

yes

characteristic

C₂³×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

—

C₂×C₄×C₈₃

C₄²

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₈₃

C₄⋊C₄

yes

characteristic

C₈₃⋊C₈

—

C₈₃⋊C₈

—

C₂²×C₈₃

—

C₂²×C₈₃

—

C₂²×C₈₃

#95

yes

characteristic

C₂²×C₈₃

#104

yes

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

—

C₄×C₈₃

#104

yes

—

C₂×C₈₃

—

C₂×C₈₃

yes

C₂×C₈₃

yes

C₂×C₈₃

yes

—

C₈₃

yes

characteristic, complemented, Sylow

#432

—

C₄×M₁₆

—

#376

D₈₃

yes

characteristic

C₂×M₁₆

—

166

—

C₂×C₄²

—

C₂×C₄²

C₂×D₈₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

166

—

#97

—

#97

—

166

—

C₄×C₈

—

166

—

#95

—

#95

Dic₈₃

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₈₃

yes

characteristic

C₂²×C₄

C₂²⋊D₈₃

yes

characteristic

C₂²×C₄

C₂²⋊D₈₃

yes

characteristic

M₁₆

—

166

—

C₂×C₈

—

166

—

C₂×C₈

—

166

—

C₄²

—

C₄²

Dic₁₆₆

yes

characteristic

C₄²

C₄×D₈₃

yes

characteristic

C₄²

C₄×D₈₃

yes

characteristic

C₄²

D₃₃₂

yes

characteristic

C₂³

C₂²⋊Dic₈₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₈₃

yes

characteristic

C₂×C₄

(C₂×D₈₃)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₈₃)⋊C₄

yes

characteristic

C₂×C₄

Dic₈₃⋊C₄

yes

characteristic

C₂×C₄

Dic₈₃⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₈₃

yes

characteristic

C₈

—

332

—

C₈

—

166

—

C₂²

—

C₂²

—

100

C₂²

C₈₃⋊#95

yes

characteristic

101

C₂²

#14581719

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

#14581720

yes

—

109

C₂

—

110

C₂

#19127460

yes

characteristic

111

C₂

#19127461

yes

characteristic

112

C₂

#19127471

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₈₃)⋊C₄
commutator	C₂×C₄×C₈₃	C₄²
Frattini	C₂×C₄²	C₂×D₈₃
Fitting	#376×C₈₃	C₂
socle	C₂²×C₈₃	#95
prime radical	C₂³×C₈₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₈₃	C₂²
hypercenter	#376	D₈₃
hypocenter	C₈₃	#1300
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #376

subgroup

G/H

center

C₂×C₄

(C₂×D₈₃)⋊C₄

commutator

C₂×C₄×C₈₃

C₄²

Frattini

C₂×C₄²

C₂×D₈₃

Fitting

#376×C₈₃

C₂

socle

C₂²×C₈₃

#95

prime radical

C₂³×C₈₃

C₂²⋊C₄

cosocle

C₂×C₄²×C₈₃

C₂²

D₈₃

C₈₃

G ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #376

N	H ≅ G/N	type
5. C₄⋊(C₈₃⋊C₈)	C₄	semidirect
8. #14581703	C₄	semidirect
57. C₈₃	#1300	semidirect

H ≅ G/N

type

5. C₄⋊(C₈₃⋊C₈)

C₄

semidirect

8. #14581703

C₄

semidirect

57. C₈₃

#1300

semidirect

Subgroups — #24905356

Conjugacy classes of subgroups

Complements