Group #20243142 — subgroups

Subgroups — #20243142

Order 6016.

200 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 93 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	#15689081	C₂	1	1	yes	maximal, characteristic
2	#15689079	C₂	1	2	yes	maximal
3	C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic
4	#15688879	C₂	1	2	yes	maximal
5	C₄₇×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	#13093983	C₂²	1	1	yes	characteristic
9	#13093935	C₄	1	4	yes	complemented
10	#13093934	C₄	1	2	yes	complemented
11	C₄×C₄₇⋊C₈	C₄	1	4	yes	complemented
12	C₈×Dic₄₇	C₄	1	2	yes	complemented
13	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	#117×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	M₁₆×C₄₇	—	2	2	no	—
17	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
18	C₄⋊C₄×C₄₇	—	2	2	no	—
19	C₂²⋊C₄×C₄₇	—	2	2	no	—
20	C₄²×C₄₇	C₂×C₄	1	4	yes	—
21	C₂²⋊Dic₄₇	—	2	1	no	—
22	C₄⋊Dic₄₇	—	2	1	no	—
23	C₄×Dic₄₇	C₂×C₄	1	2	yes	—
24	#10625329	—	2	2	no	—
25	#10625329	—	2	2	no	—
26	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
27	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
29	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
31	C₂³×C₄₇	#41	1	1	yes	characteristic
32	C₂×C₄×C₄₇	—	2	4	no	—
33	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
34	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	#41	1	2	yes	—
36	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
37	C₂×Dic₄₇	—	2	2	no	—
38	C₈×C₄₇	—	2	2	no	—
39	C₄₇⋊C₈	—	2	4	no	—
40	C₄₇⋊C₈	C₄²	1	1	yes	characteristic
41	C₄₇⋊C₈	C₄²	1	1	yes	characteristic
42	C₄₇⋊C₈	C₄²	1	2	yes	—
43	C₂²×C₄₇	—	4	1	no	—
44	C₂²×C₄₇	#117	1	2	yes	—
45	C₂²×C₄₇	#117	1	1	yes	characteristic
46	C₄×C₄₇	—	4	4	no	—
47	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₄₇	#117	1	1	yes	characteristic
49	C₄×C₄₇	#117	1	2	yes	—
50	Dic₄₇	—	4	2	no	—
51	#1747	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	—	2	1	no	—
53	C₂×C₄₇	—	2	2	no	—
54	C₂×C₄₇	#376	1	1	yes	characteristic
55	#405	—	47	1	no	—
56	#405	—	47	2	no	—
57	#338	—	47	1	no	—
58	H(3,ℤ/4)	—	47	2	no	—
59	H(3,ℤ/4)	D₄₇	1	1	yes	characteristic
60	C₄₇	#1747	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	47	2	no	—
62	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
63	C₂²×C₈	—	47	1	no	—
64	#117	—	47	1	no	—
65	#117	C₂×D₄₇	1	2	yes	—
66	#97	—	47	2	no	—
67	#97	—	47	4	no	—
68	C₄×C₈	—	47	2	no	—
69	C₄×C₈	—	47	4	no	—
70	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	94	2	no	—
73	M₁₆	—	94	2	no	—
74	C₂×C₈	—	47	1	no	—
75	C₂×C₈	—	47	2	no	—
76	C₂×C₈	—	47	1	no	—
77	C₂×C₈	—	47	2	no	—
78	C₂×C₈	—	47	4	no	—
79	C₂×C₈	C₄×D₄₇	1	2	yes	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	—	94	1	no	—
82	C₂²⋊C₄	—	2	2	no	—
83	C₂²⋊C₄	—	94	1	no	—
84	C₄²	—	47	2	no	—
85	C₄²	C₄×D₄₇	1	4	yes	—
86	C₂³	#10625352	1	1	yes	characteristic
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	94	2	no	—
89	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
91	C₂×C₄	#10625352	1	2	yes	—
92	C₂×C₄	#10625354	1	1	yes	characteristic
93	C₈	—	2	2	no	—
94	C₈	—	47	1	no	—
95	C₈	—	47	1	no	—
96	C₈	—	47	2	no	—
97	C₈	—	94	4	no	—
98	C₂²	—	4	1	no	—
99	C₂²	#13093980	1	2	yes	—
100	C₂²	#13093982	1	1	yes	characteristic
101	C₄	—	4	4	no	—
102	C₄	—	188	2	no	—
103	C₄	C₄²×D₄₇	1	1	yes	characteristic
104	C₄	#13093980	1	1	yes	characteristic
105	C₄	#13093982	1	2	yes	—
106	C₂	—	2	2	no	—
107	C₂	—	2	1	no	—
108	C₂	#15688968	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689081

C₂

yes

maximal, characteristic

#15689079

C₂

yes

maximal

C₄₇⋊#338

C₂

yes

maximal, characteristic

#15688879

C₂

yes

maximal

C₄₇×H(3,ℤ/4)

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

#13093983

C₂²

yes

characteristic

#13093935

C₄

yes

complemented

#13093934

C₄

yes

complemented

C₄×C₄₇⋊C₈

C₄

yes

complemented

C₈×Dic₄₇

C₄

yes

complemented

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

C₄²

yes

characteristic

C₄₇⋊C₈

C₄²

yes

characteristic

C₄₇⋊C₈

C₄²

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

#117

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄²

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

#1747

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#1747

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

—

#117

—

#117

C₂×D₄₇

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₄₇

yes

—

C₂³

#10625352

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₄

#10625352

yes

—

C₂×C₄

#10625354

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#13093980

yes

—

100

C₂²

#13093982

yes

characteristic

101

C₄

—

102

C₄

—

188

—

103

C₄

C₄²×D₄₇

yes

characteristic

104

C₄

#13093980

yes

characteristic

105

C₄

#13093982

yes

—

106

C₂

—

107

C₂

—

108

C₂

#15688968

yes

characteristic

	subgroup	G/H
center	C₄	C₄²×D₄₇
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×H(3,ℤ/4)	C₂
socle	C₂×C₄₇	#376
hypercenter	H(3,ℤ/4)	D₄₇
hypocenter	C₄₇	#1747
LCS	G ▷ C₄×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

C₄²×D₄₇

commutator

C₄×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×H(3,ℤ/4)

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₄×C₄₇ ▷ C₄₇

C₁ ◁ C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
9. #13093935	C₄	semidirect
10. #13093934	C₄	semidirect
11. C₄×C₄₇⋊C₈	C₄	semidirect
12. C₈×Dic₄₇	C₄	semidirect
60. C₄₇	#1747	semidirect

H ≅ G/N

type

9. #13093935

C₄

semidirect

10. #13093934

C₄

semidirect

11. C₄×C₄₇⋊C₈

C₄

semidirect

12. C₈×Dic₄₇

C₄

semidirect

60. C₄₇

#1747

semidirect

Subgroups — #20243142

Conjugacy classes of subgroups

Complements