Group #20245678 — subgroups

Subgroups — M₆₄×D₄₇ #20245678

Order 6016.

112 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 67 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×C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#15688957	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688956	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₄₇	C₂	1	2	yes	maximal, complemented
5	C₄₇×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₄₇	C₄	1	1	yes	characteristic
7	C₂×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
8	C₁₆×D₄₇	C₄	1	1	yes	characteristic
9	C₁₆×D₄₇	C₄	1	1	yes	characteristic
10	C₁₆×D₄₇	C₂²	1	1	yes	characteristic
11	C₁₆×D₄₇	C₂²	1	1	yes	characteristic
12	C₄₇⋊C₃₂	C₂²	1	2	yes	complemented
13	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₃₂×C₄₇	C₂²	1	2	yes	complemented
15	C₂×C₄×D₄₇	C₈	1	1	yes	characteristic
16	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄₇⋊C₈	C₈	1	1	yes	characteristic
18	C₈×D₄₇	C₈	1	1	yes	characteristic
19	C₈×D₄₇	C₈	1	1	yes	characteristic
20	C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
21	C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
22	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₄₇	C₂³	1	1	yes	characteristic
24	C₄₇⋊C₁₆	C₂×C₄	1	1	yes	characteristic
25	C₄₇⋊C₁₆	C₂×C₄	1	1	yes	characteristic
26	C₂²×D₄₇	C₁₆	1	1	yes	characteristic
27	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₄₇	C₁₆	1	1	yes	characteristic
29	C₄×D₄₇	C₁₆	1	1	yes	characteristic
30	C₄×D₄₇	C₁₆	1	1	yes	characteristic
31	C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
32	C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
33	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
34	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₄₇⋊C₈	C₂×C₈	1	1	yes	characteristic
36	C₄₇⋊C₈	C₂×C₈	1	1	yes	characteristic
37	C₂²×C₄₇	C₂×C₁₆	1	1	yes	characteristic
38	C₂×D₄₇	—	2	2	no	—
39	C₂×D₄₇	C₂×C₁₆	1	1	yes	characteristic
40	C₂×D₄₇	C₂×C₁₆	1	1	yes	characteristic
41	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
42	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
43	Dic₄₇	C₂×C₁₆	1	1	yes	characteristic
44	Dic₄₇	C₂×C₁₆	1	1	yes	characteristic
45	C₂×M₆₄	—	47	1	no	maximal, Sylow
46	C₂×C₄₇	—	2	1	no	—
47	C₂×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
48	D₄₇	—	2	1	no	—
49	D₄₇	M₆₄	1	2	yes	direct product factor
50	C₂²×C₁₆	—	47	1	no	—
51	M₆₄	—	47	1	no	—
52	M₆₄	—	47	2	no	—
53	M₆₄	D₄₇	1	1	yes	characteristic, direct product factor
54	C₂×C₃₂	—	47	2	no	—
55	C₄₇	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₈	—	47	1	no	—
57	C₂×C₁₆	—	47	1	no	—
58	C₂×C₁₆	—	47	1	no	—
59	C₂×C₁₆	—	47	1	no	—
60	C₂×C₁₆	—	47	1	no	—
61	C₂×C₁₆	—	47	1	no	—
62	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
63	C₃₂	—	47	2	no	—
64	C₃₂	C₂×D₄₇	1	2	yes	complemented
65	C₂²×C₄	—	47	1	no	—
66	C₂×C₈	—	47	1	no	—
67	C₂×C₈	—	47	1	no	—
68	C₂×C₈	—	47	1	no	—
69	C₂×C₈	—	47	1	no	—
70	C₂×C₈	—	47	1	no	—
71	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
72	C₁₆	—	47	1	no	—
73	C₁₆	—	47	1	no	—
74	C₁₆	C₄×D₄₇	1	1	yes	characteristic
75	C₁₆	C₂²×D₄₇	1	1	yes	characteristic
76	C₂³	—	47	1	no	—
77	C₂×C₄	—	47	1	no	—
78	C₂×C₄	—	47	1	no	—
79	C₂×C₄	—	47	1	no	—
80	C₂×C₄	—	47	1	no	—
81	C₂×C₄	—	47	1	no	—
82	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
83	C₈	—	47	1	no	—
84	C₈	—	47	1	no	—
85	C₈	C₈×D₄₇	1	1	yes	characteristic
86	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
87	C₂²	—	47	1	no	—
88	C₂²	—	47	1	no	—
89	C₂²	—	94	2	no	—
90	C₂²	C₁₆×D₄₇	1	1	yes	characteristic
91	C₄	—	47	1	no	—
92	C₄	—	47	1	no	—
93	C₄	C₁₆×D₄₇	1	1	yes	characteristic
94	C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
95	C₂	—	2	1	no	—
96	C₂	—	47	2	no	—
97	C₂	—	94	1	no	—
98	C₂	C₂×C₁₆×D₄₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₄₇

C₂

yes

maximal, characteristic

#15688957

C₂

yes

maximal, characteristic, complemented

#15688956

C₂

yes

maximal, complemented

C₃₂×D₄₇

C₂

yes

maximal, complemented

C₄₇×M₆₄

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₇

C₄

yes

characteristic

C₂×C₄₇⋊C₁₆

C₄

yes

characteristic

C₁₆×D₄₇

C₄

yes

characteristic

C₁₆×D₄₇

C₄

yes

characteristic

C₁₆×D₄₇

C₂²

yes

characteristic

C₁₆×D₄₇

C₂²

yes

characteristic

C₄₇⋊C₃₂

C₂²

yes

complemented

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₃₂×C₄₇

C₂²

yes

complemented

C₂×C₄×D₄₇

C₈

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₈

yes

characteristic

C₈×D₄₇

C₈

yes

characteristic

C₈×D₄₇

C₈

yes

characteristic

C₈×D₄₇

C₂×C₄

yes

characteristic

C₈×D₄₇

C₂×C₄

yes

characteristic

C₁₆×C₄₇

C₂×C₄

yes

characteristic

C₁₆×C₄₇

C₂³

yes

characteristic

C₄₇⋊C₁₆

C₂×C₄

yes

characteristic

C₄₇⋊C₁₆

C₂×C₄

yes

characteristic

C₂²×D₄₇

C₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×Dic₄₇

C₁₆

yes

characteristic

C₄×D₄₇

C₁₆

yes

characteristic

C₄×D₄₇

C₁₆

yes

characteristic

C₄×D₄₇

C₂×C₈

yes

characteristic

C₄×D₄₇

C₂×C₈

yes

characteristic

C₈×C₄₇

C₂×C₈

yes

characteristic

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₄₇⋊C₈

C₂×C₈

yes

characteristic

C₄₇⋊C₈

C₂×C₈

yes

characteristic

C₂²×C₄₇

C₂×C₁₆

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

C₂×C₁₆

yes

characteristic

C₂×D₄₇

C₂×C₁₆

yes

characteristic

C₄×C₄₇

C₂×C₁₆

yes

characteristic

C₄×C₄₇

C₂²×C₈

yes

characteristic

Dic₄₇

C₂×C₁₆

yes

characteristic

Dic₄₇

C₂×C₁₆

yes

characteristic

C₂×M₆₄

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂²×C₁₆

yes

characteristic

D₄₇

—

D₄₇

M₆₄

yes

direct product factor

C₂²×C₁₆

—

M₆₄

—

M₆₄

—

M₆₄

D₄₇

yes

characteristic, direct product factor

C₂×C₃₂

—

C₄₇

C₂×M₆₄

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

C₃₂

—

C₃₂

C₂×D₄₇

yes

complemented

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

C₄×D₄₇

yes

characteristic

C₁₆

C₂²×D₄₇

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₇

yes

characteristic

C₈

—

C₈

—

C₈

C₈×D₄₇

yes

characteristic

C₈

C₂×C₄×D₄₇

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

C₁₆×D₄₇

yes

characteristic

C₄

—

C₄

—

C₄

C₁₆×D₄₇

yes

characteristic

C₄

C₂×C₈×D₄₇

yes

characteristic

C₂

—

C₂

—

C₂

—

C₂

C₂×C₁₆×D₄₇

yes

characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₄₇
commutator, socle	C₂×C₄₇	C₂²×C₁₆
Fitting	C₄₇×M₆₄	C₂
hypercenter	M₆₄	D₄₇
hypocenter	C₄₇	C₂×M₆₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₁₆ ◁ M₆₄

subgroup

G/H

center, Frattini

C₁₆

C₂²×D₄₇

commutator, socle

C₂×C₄₇

C₂²×C₁₆

Fitting

C₄₇×M₆₄

C₂

hypercenter

M₆₄

D₄₇

hypocenter

C₄₇

C₂×M₆₄

LCS

G ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₁₆ ◁ M₆₄

N	H ≅ G/N	type
2. #15688957	C₂	semidirect
3. #15688956	C₂	semidirect
4. C₃₂×D₄₇	C₂	semidirect
5. C₄₇×M₆₄	C₂	semidirect
12. C₄₇⋊C₃₂	C₂²	semidirect
14. C₃₂×C₄₇	C₂²	semidirect
49. D₄₇	M₆₄	direct (N × H)
53. M₆₄	D₄₇	direct (N × H)
55. C₄₇	C₂×M₆₄	semidirect
64. C₃₂	C₂×D₄₇	semidirect

H ≅ G/N

type

2. #15688957

C₂

semidirect

3. #15688956

C₂

semidirect

4. C₃₂×D₄₇

C₂

semidirect

5. C₄₇×M₆₄

C₂

semidirect

12. C₄₇⋊C₃₂

C₂²

semidirect

14. C₃₂×C₄₇

C₂²

semidirect

49. D₄₇

M₆₄

direct (N × H)

53. M₆₄

D₄₇

direct (N × H)

55. C₄₇

C₂×M₆₄

semidirect

64. C₃₂

C₂×D₄₇

semidirect

Subgroups — M₆₄×D₄₇ #20245678

Conjugacy classes of subgroups

Complements

Subgroups — M64×D47 #20245678

Conjugacy classes of subgroups

Complements

Subgroups — M₆₄×D₄₇ #20245678