Group #20243535 — subgroups

Subgroups — #20243535

Order 6016.

162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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	M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#15688893	C₂	1	2	yes	maximal
3	#15688882	C₂	1	2	yes	maximal
4	C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic
5	C₄₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	2	yes	—
7	C₂×#10625329	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	#13093934	C₄	1	2	yes	complemented
10	C₈×Dic₄₇	C₄	1	2	yes	complemented
11	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	#117×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
14	C₂²×Dic₄₇	—	2	1	no	—
15	M₁₆×C₄₇	—	2	2	no	—
16	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
17	C₄⋊C₄×C₄₇	—	2	2	no	—
18	C₂²⋊C₄×C₄₇	—	2	2	no	—
19	C₄²×C₄₇	—	2	2	no	—
20	C₄×Dic₄₇	—	2	1	no	—
21	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
23	#10625329	—	2	2	no	—
24	#10625329	—	2	2	no	—
25	#10625329	—	2	2	no	—
26	C₂×C₄₇⋊C₈	—	2	2	no	—
27	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
28	C₂³×C₄₇	#41	1	1	yes	characteristic
29	C₂×C₄×C₄₇	—	4	2	no	—
30	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	#41	1	2	yes	—
32	C₂×C₄×C₄₇	#41	1	2	yes	—
33	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
34	C₂×Dic₄₇	—	2	1	no	—
35	C₂×Dic₄₇	—	2	1	no	—
36	C₂×Dic₄₇	—	4	2	no	—
37	C₈×C₄₇	—	2	2	no	—
38	C₄₇⋊C₈	—	2	2	no	—
39	C₄₇⋊C₈	—	4	2	no	—
40	C₂²×C₄₇	—	4	1	no	—
41	C₂²×C₄₇	#117	1	1	yes	characteristic
42	C₂²×C₄₇	#126	1	2	yes	—
43	C₄×C₄₇	—	8	2	no	—
44	C₄×C₄₇	#117	1	1	yes	characteristic
45	C₄×C₄₇	#117	1	1	yes	characteristic
46	C₄×C₄₇	#126	1	2	yes	—
47	Dic₄₇	—	2	2	no	—
48	Dic₄₇	—	4	1	no	—
49	#1841	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	—	2	1	no	—
51	C₂×C₄₇	—	2	2	no	—
52	C₂×C₄₇	#383	1	1	yes	characteristic
53	C₄×M₁₆	—	47	1	no	—
54	#344	—	47	2	no	—
55	#339	—	47	2	no	—
56	#338	—	47	1	no	—
57	H(3,ℤ/4)	D₄₇	1	1	yes	characteristic
58	C₄₇	#1841	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	47	1	no	—
60	C₂×M₁₆	—	47	2	no	—
61	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
62	#117	C₂×D₄₇	1	2	yes	—
63	C₂×C₄²	—	47	1	no	—
64	#97	—	47	2	no	—
65	C₄×C₈	—	47	2	no	—
66	C₂²×C₄	—	94	1	no	—
67	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	94	2	no	—
70	M₁₆	—	94	2	no	—
71	M₁₆	—	94	2	no	—
72	C₂×C₈	—	47	2	no	—
73	C₂×C₈	—	94	2	no	—
74	C₂×C₈	C₄×D₄₇	1	2	yes	—
75	C₄⋊C₄	—	2	2	no	—
76	C₂²⋊C₄	—	2	2	no	—
77	C₄²	—	2	2	no	—
78	C₄²	—	47	1	no	—
79	C₄²	—	47	1	no	—
80	C₄²	—	94	1	no	—
81	C₂³	#10625352	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	94	1	no	—
84	C₂×C₄	—	94	1	no	—
85	C₂×C₄	—	188	2	no	—
86	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
87	C₂×C₄	#10625350	1	2	yes	—
88	C₂×C₄	#10625352	1	2	yes	—
89	C₂×C₄	#10625354	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	94	2	no	—
92	C₈	—	188	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#13093982	1	1	yes	characteristic
95	C₂²	#13094017	1	2	yes	—
96	C₄	—	8	2	no	—
97	C₄	—	94	2	no	—
98	C₄	—	188	1	no	—
99	C₄	#13093980	1	1	yes	characteristic
100	C₄	#13093981	1	1	yes	characteristic
101	C₄	#13094019	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	—	2	1	no	—
104	C₂	#15688990	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

M₁₆×Dic₄₇

C₂

yes

maximal, characteristic

#15688893

C₂

yes

maximal

#15688882

C₂

yes

maximal

C₄₇⋊#338

C₂

yes

maximal, characteristic

C₄₇×H(3,ℤ/4)

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

C₂×#10625329

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093934

C₄

yes

complemented

C₈×Dic₄₇

C₄

yes

complemented

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₄×Dic₄₇

C₂×C₄

yes

—

—

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

#117

yes

characteristic

C₂²×C₄₇

#126

yes

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

Dic₄₇

—

#1841

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#383

yes

characteristic

C₄×M₁₆

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#1841

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

#117

C₂×D₄₇

yes

—

C₂×C₄²

—

#97

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

#10625352

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

#10625350

yes

—

C₂×C₄

#10625352

yes

—

C₂×C₄

#10625354

yes

characteristic

C₈

—

C₈

—

C₈

—

188

—

C₂²

—

C₂²

#13093982

yes

characteristic

C₂²

#13094017

yes

—

C₄

—

C₄

—

C₄

—

188

—

C₄

#13093980

yes

characteristic

100

C₄

#13093981

yes

characteristic

101

C₄

#13094019

yes

—

102

C₂

—

103

C₂

—

104

C₂

#15688990

yes

characteristic

	subgroup	G/H
center	C₄	#13093981
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×H(3,ℤ/4)	C₂
socle	C₂×C₄₇	#383
hypercenter	H(3,ℤ/4)	D₄₇
hypocenter	C₄₇	#1841
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#13093981

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×H(3,ℤ/4)

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
9. #13093934	C₄	semidirect
10. C₈×Dic₄₇	C₄	semidirect
58. C₄₇	#1841	semidirect

H ≅ G/N

type

9. #13093934

C₄

semidirect

10. C₈×Dic₄₇

C₄

semidirect

58. C₄₇

#1841

semidirect

Subgroups — #20243535

Conjugacy classes of subgroups

Complements