Group #20244980 — subgroups

Subgroups — M₃₂×Dic₄₇ #20244980

Order 6016.

196 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13093964	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#15688898	C₂	1	2	yes	maximal, complemented
4	C₁₆×Dic₄₇	C₂	1	2	yes	maximal, complemented
5	C₂×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₄₇	C₄	1	1	yes	characteristic
8	#13093964	C₄	1	4	yes	complemented
9	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
10	C₈×Dic₄₇	C₄	1	1	yes	characteristic
11	C₈×Dic₄₇	C₄	1	1	yes	characteristic
12	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	M₃₂×C₄₇	C₄	1	4	yes	complemented
16	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₄₇	C₈	1	2	yes	—
19	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
23	C₄×Dic₄₇	C₈	1	2	yes	—
24	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄₇⋊C₈	C₈	1	4	yes	—
27	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
30	C₄₇⋊C₁₆	C₂×C₄	1	4	yes	complemented
31	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₄²	1	2	yes	—
33	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
35	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₄₇	—	2	4	no	—
37	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
38	C₂×Dic₄₇	C₂×C₈	1	2	yes	—
39	C₈×C₄₇	C₄²	1	2	yes	—
40	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
42	C₄₇⋊C₈	C₂×C₈	1	2	yes	—
43	C₄₇⋊C₈	C₂×C₈	1	2	yes	—
44	C₂²×C₄₇	—	2	2	no	—
45	C₂²×C₄₇	C₄×C₈	1	2	yes	—
46	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
47	C₄×C₄₇	C₄×C₈	1	2	yes	—
48	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
49	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
50	Dic₄₇	—	2	2	no	—
51	Dic₄₇	M₃₂	1	4	yes	direct product factor
52	C₄×M₃₂	—	47	1	no	maximal, Sylow
53	C₂×C₄₇	—	2	2	no	—
54	C₂×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
55	C₂×C₄₇	C₂×M₃₂	1	2	yes	—
56	C₂×M₃₂	—	47	1	no	—
57	C₂×M₃₂	D₄₇	1	1	yes	characteristic
58	C₂×C₄×C₈	—	47	1	no	—
59	#346	—	47	2	no	—
60	C₄×C₁₆	—	47	2	no	—
61	C₄₇	C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	47	1	no	—
63	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
64	C₂×C₄²	—	47	1	no	—
65	M₃₂	—	47	4	no	—
66	M₃₂	Dic₄₇	1	4	yes	direct product factor
67	C₂×C₁₆	—	47	2	no	—
68	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
69	C₄×C₈	—	47	1	no	—
70	C₄×C₈	—	47	1	no	—
71	C₄×C₈	—	47	1	no	—
72	C₄×C₈	—	47	1	no	—
73	C₂²×C₄	—	47	2	no	—
74	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
75	C₂×C₈	—	47	4	no	—
76	C₂×C₈	—	47	1	no	—
77	C₂×C₈	—	47	1	no	—
78	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
79	C₂×C₈	C₄×D₄₇	1	2	yes	—
80	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
81	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
82	C₄²	—	47	2	no	—
83	C₄²	—	47	1	no	—
84	C₄²	—	47	1	no	—
85	C₁₆	—	47	4	no	—
86	C₁₆	C₂×Dic₄₇	1	4	yes	complemented
87	C₂³	C₈×D₄₇	1	1	yes	characteristic
88	C₂×C₄	—	47	2	no	—
89	C₂×C₄	—	47	2	no	—
90	C₂×C₄	—	94	4	no	—
91	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
92	C₂×C₄	C₈×D₄₇	1	2	yes	—
93	C₂×C₄	C₄×Dic₄₇	1	2	yes	—
94	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
95	C₈	—	47	2	no	—
96	C₈	—	47	2	no	—
97	C₈	C₄×Dic₄₇	1	2	yes	—
98	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
99	C₈	C₂²×Dic₄₇	1	1	yes	characteristic
100	C₂²	—	2	2	no	—
101	C₂²	C₈×Dic₄₇	1	2	yes	—
102	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
103	C₄	—	47	4	no	—
104	C₄	—	94	2	no	—
105	C₄	C₈×Dic₄₇	1	2	yes	—
106	C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
107	C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
108	C₂	—	2	2	no	—
109	C₂	C₂×C₈×Dic₄₇	1	1	yes	characteristic
110	C₂	M₃₂×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093964

C₂

yes

maximal, characteristic

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic

#15688898

C₂

yes

maximal, complemented

C₁₆×Dic₄₇

C₂

yes

maximal, complemented

C₂×M₃₂×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₄

yes

characteristic

#13093964

C₄

yes

complemented

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₈×Dic₄₇

C₄

yes

characteristic

C₈×Dic₄₇

C₄

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

C₄

yes

complemented

C₂×C₁₆×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₈

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄×Dic₄₇

C₈

yes

—

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₈

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₁₆×C₄₇

C₂×C₄

yes

complemented

C₄₇⋊C₁₆

C₂×C₄

yes

complemented

C₂³×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₄²

yes

—

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₈×C₄₇

C₄²

yes

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₄₇⋊C₈

C₂×C₈

yes

—

C₄₇⋊C₈

C₂×C₈

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄×C₈

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₄×C₄₇

C₄×C₈

yes

—

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

C₂²×C₈

yes

characteristic

Dic₄₇

—

Dic₄₇

M₃₂

yes

direct product factor

C₄×M₃₂

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×C₄×C₈

yes

characteristic

C₂×C₄₇

C₂×M₃₂

yes

—

C₂×M₃₂

—

C₂×M₃₂

D₄₇

yes

characteristic

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₄₇

C₄×M₃₂

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

Dic₄₇

yes

direct product factor

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

C₂×Dic₄₇

yes

complemented

C₂³

C₈×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₇

yes

characteristic

C₂×C₄

C₈×D₄₇

yes

—

C₂×C₄

C₄×Dic₄₇

yes

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₈

—

C₈

—

C₈

C₄×Dic₄₇

yes

—

C₈

C₂×C₄×D₄₇

yes

characteristic

C₈

C₂²×Dic₄₇

yes

characteristic

100

C₂²

—

101

C₂²

C₈×Dic₄₇

yes

—

102

C₂²

C₂×C₈×D₄₇

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

C₈×Dic₄₇

yes

—

106

C₄

C₂×C₄×Dic₄₇

yes

characteristic

107

C₄

C₂×C₈×D₄₇

yes

characteristic

108

C₂

—

109

C₂

C₂×C₈×Dic₄₇

yes

characteristic

110

C₂

M₃₂×D₄₇

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₇
commutator	C₂×C₄₇	C₂×C₄×C₈
Fitting	C₂×M₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₈
hypercenter	C₂×M₃₂	D₄₇
hypocenter	C₄₇	C₄×M₃₂
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₇

commutator

C₂×C₄₇

C₂×C₄×C₈

Fitting

C₂×M₃₂×C₄₇

C₂

socle

C₂²×C₄₇

C₂²×C₈

hypercenter

C₂×M₃₂

D₄₇

hypocenter

C₄₇

C₄×M₃₂

LCS

G ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #15688898	C₂	semidirect
4. C₁₆×Dic₄₇	C₂	semidirect
8. #13093964	C₄	semidirect
15. M₃₂×C₄₇	C₄	semidirect
29. C₁₆×C₄₇	C₂×C₄	semidirect
30. C₄₇⋊C₁₆	C₂×C₄	semidirect
51. Dic₄₇	M₃₂	direct (N × H)
61. C₄₇	C₄×M₃₂	semidirect
66. M₃₂	Dic₄₇	direct (N × H)
86. C₁₆	C₂×Dic₄₇	semidirect

H ≅ G/N

type

3. #15688898

C₂

semidirect

4. C₁₆×Dic₄₇

C₂

semidirect

8. #13093964

C₄

semidirect

15. M₃₂×C₄₇

C₄

semidirect

29. C₁₆×C₄₇

C₂×C₄

semidirect

30. C₄₇⋊C₁₆

C₂×C₄

semidirect

51. Dic₄₇

M₃₂

direct (N × H)

61. C₄₇

C₄×M₃₂

semidirect

66. M₃₂

Dic₄₇

direct (N × H)

86. C₁₆

C₂×Dic₄₇

semidirect

Subgroups — M₃₂×Dic₄₇ #20244980

Conjugacy classes of subgroups

Complements

Subgroups — M32×Dic47 #20244980

Conjugacy classes of subgroups

Complements

Subgroups — M₃₂×Dic₄₇ #20244980