Group #15689891 — subgroups

Subgroups — C₂×D₈×D₄₇ #15689891

Order 3008.

338 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 111 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×D₄×D₄₇	C₂	1	2	yes	maximal, complemented
2	C₂×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10625334	C₂	1	2	yes	maximal, complemented
4	D₈×D₄₇	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄₇	—	2	2	no	—
8	C₂×D₄×C₄₇	C₂²	1	2	yes	complemented
9	C₂×C₂²⋊D₄₇	—	2	2	no	—
10	D₄×D₄₇	—	2	4	no	—
11	D₄×D₄₇	C₂²	1	8	yes	complemented
12	C₂×D₁₈₈	C₂²	1	2	yes	complemented
13	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
14	D₈×C₄₇	C₂²	1	4	yes	complemented
15	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
16	#10625334	C₂²	1	8	yes	complemented
17	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
18	D₃₇₆	C₂²	1	4	yes	complemented
19	C₈×D₄₇	C₂²	1	4	yes	complemented
20	C₂³×C₄₇	—	2	2	no	—
21	C₂²×D₄₇	—	2	2	no	—
22	C₂²×D₄₇	—	2	8	no	—
23	C₂²×D₄₇	—	4	8	no	—
24	C₂²×D₄₇	D₄	1	1	yes	characteristic
25	D₄×C₄₇	—	2	2	no	—
26	D₄×C₄₇	C₂³	1	4	yes	complemented
27	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
28	C₂²⋊D₄₇	—	2	8	no	—
29	C₂×Dic₄₇	D₄	1	1	yes	characteristic
30	D₁₈₈	—	2	2	no	—
31	D₁₈₈	C₂³	1	4	yes	complemented
32	C₄×D₄₇	D₄	1	2	yes	—
33	C₄×D₄₇	C₂³	1	2	yes	—
34	C₈×C₄₇	C₂³	1	2	yes	complemented
35	C₄₇⋊C₈	C₂³	1	2	yes	complemented
36	C₂²×C₄₇	—	2	4	no	—
37	C₂²×C₄₇	—	4	4	no	—
38	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₂×D₄₇	—	2	4	no	—
40	C₂×D₄₇	—	4	4	no	—
41	C₂×D₄₇	—	4	16	no	—
42	C₂×D₄₇	D₈	1	4	yes	direct product factor
43	C₂×D₄₇	C₂×D₄	1	2	yes	—
44	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
45	C₄×C₄₇	C₂⁴	1	1	yes	characteristic
46	Dic₄₇	C₂×D₄	1	2	yes	—
47	C₂×C₄₇	—	4	4	no	—
48	C₂×C₄₇	C₂×D₈	1	2	yes	complemented
49	C₂×C₄₇	C₂²×D₄	1	1	yes	characteristic
50	D₄₇	—	4	4	no	—
51	D₄₇	C₂×D₈	1	4	yes	direct product factor
52	C₂²×D₈	—	47	1	no	maximal, Sylow
53	C₄₇	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
54	C₂²×D₄	—	47	2	no	—
55	C₂×D₈	—	47	2	no	—
56	C₂×D₈	—	47	8	no	—
57	C₂×D₈	—	47	1	no	—
58	C₂×D₈	D₄₇	1	1	yes	characteristic, direct product factor
59	C₂²×C₈	—	47	1	no	—
60	C₂⁴	—	94	2	no	—
61	C₂×D₄	—	47	8	no	—
62	C₂×D₄	—	47	2	no	—
63	C₂×D₄	—	94	4	no	—
64	C₂×D₄	—	94	2	no	—
65	C₂×D₄	C₂×D₄₇	1	2	yes	complemented
66	C₂²×C₄	—	47	1	no	—
67	D₈	—	47	8	no	—
68	D₈	—	47	4	no	—
69	D₈	C₂×D₄₇	1	4	yes	direct product factor
70	C₂×C₈	—	47	1	no	—
71	C₂×C₈	—	47	4	no	—
72	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
73	C₂³	—	2	2	no	—
74	C₂³	—	47	1	no	—
75	C₂³	—	94	8	no	—
76	C₂³	—	94	2	no	—
77	C₂³	—	188	8	no	—
78	D₄	—	2	2	no	—
79	D₄	—	47	4	no	—
80	D₄	—	94	8	no	—
81	D₄	—	94	2	no	—
82	D₄	C₂²×D₄₇	1	4	yes	complemented
83	C₂×C₄	—	47	1	no	—
84	C₂×C₄	—	47	2	no	—
85	C₂×C₄	—	47	2	no	—
86	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
87	C₈	—	47	2	no	—
88	C₈	C₂²×D₄₇	1	2	yes	complemented
89	C₂²	—	2	4	no	—
90	C₂²	—	4	4	no	—
91	C₂²	—	47	4	no	—
92	C₂²	—	47	2	no	—
93	C₂²	—	94	4	no	—
94	C₂²	—	188	16	no	—
95	C₂²	—	188	4	no	—
96	C₂²	D₄×D₄₇	1	1	yes	characteristic
97	C₄	—	47	2	no	—
98	C₄	D₄×D₄₇	1	1	yes	characteristic
99	C₄	C₂³×D₄₇	1	1	yes	characteristic
100	C₂	—	4	4	no	—
101	C₂	—	47	4	no	—
102	C₂	—	188	4	no	—
103	C₂	D₈×D₄₇	1	2	yes	direct product factor
104	C₂	C₂×D₄×D₄₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₄×D₄₇

C₂

yes

maximal, complemented

C₂×D₃₇₆

C₂

yes

maximal, characteristic, complemented

C₂×#10625334

C₂

yes

maximal, complemented

D₈×D₄₇

C₂

yes

maximal, direct product factor

C₂×C₈×D₄₇

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂³×D₄₇

—

C₂×D₄×C₄₇

C₂²

yes

complemented

C₂×C₂²⋊D₄₇

—

D₄×D₄₇

—

D₄×D₄₇

C₂²

yes

complemented

C₂×D₁₈₈

C₂²

yes

complemented

C₂×C₄×D₄₇

C₂²

yes

characteristic

D₈×C₄₇

C₂²

yes

complemented

C₂×C₈×C₄₇

C₂²

yes

characteristic, complemented

#10625334

C₂²

yes

complemented

C₂×C₄₇⋊C₈

C₂²

yes

characteristic, complemented

D₃₇₆

C₂²

yes

complemented

C₈×D₄₇

C₂²

yes

complemented

C₂³×C₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

D₄

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

C₂³

yes

complemented

C₂×C₄×C₄₇

C₂³

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

D₄

yes

characteristic

D₁₈₈

—

D₁₈₈

C₂³

yes

complemented

C₄×D₄₇

D₄

yes

—

C₄×D₄₇

C₂³

yes

—

C₈×C₄₇

C₂³

yes

complemented

C₄₇⋊C₈

C₂³

yes

complemented

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

D₈

yes

direct product factor

C₂×D₄₇

C₂×D₄

yes

—

C₄×C₄₇

C₂×D₄

yes

characteristic

C₄×C₄₇

C₂⁴

yes

characteristic

Dic₄₇

C₂×D₄

yes

—

C₂×C₄₇

—

C₂×C₄₇

C₂×D₈

yes

complemented

C₂×C₄₇

C₂²×D₄

yes

characteristic

D₄₇

—

D₄₇

C₂×D₈

yes

direct product factor

C₂²×D₈

—

maximal, Sylow

C₄₇

C₂²×D₈

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

D₄₇

yes

characteristic, direct product factor

C₂²×C₈

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×D₄₇

yes

complemented

C₂²×C₄

—

D₈

—

D₈

—

D₈

C₂×D₄₇

yes

direct product factor

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×D₄₇

yes

characteristic, complemented

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

188

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

C₂²×D₄₇

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×D₄₇

yes

characteristic

C₈

—

C₈

C₂²×D₄₇

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

188

—

C₂²

—

188

—

C₂²

D₄×D₄₇

yes

characteristic

C₄

—

C₄

D₄×D₄₇

yes

characteristic

C₄

C₂³×D₄₇

yes

characteristic

100

C₂

—

101

C₂

—

102

C₂

—

188

—

103

C₂

D₈×D₄₇

yes

direct product factor

104

C₂

C₂×D₄×D₄₇

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator, cosocle	C₄×C₄₇	C₂⁴
Frattini	C₄	C₂³×D₄₇
Fitting	C₂×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
hypercenter	C₂×D₈	D₄₇
hypocenter	C₄₇	C₂²×D₈
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

subgroup

G/H

center

C₂²

D₄×D₄₇

commutator, cosocle

C₄×C₄₇

C₂⁴

Frattini

C₄

C₂³×D₄₇

Fitting

C₂×D₈×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₄

hypercenter

C₂×D₈

D₄₇

hypocenter

C₄₇

C₂²×D₈

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

N	H ≅ G/N	type
1. C₂×D₄×D₄₇	C₂	semidirect
2. C₂×D₃₇₆	C₂	semidirect
3. C₂×#10625334	C₂	semidirect
4. D₈×D₄₇	C₂	direct (N × H)
5. C₂×C₈×D₄₇	C₂	semidirect
6. C₂×D₈×C₄₇	C₂	semidirect
8. C₂×D₄×C₄₇	C₂²	semidirect
11. D₄×D₄₇	C₂²	semidirect
12. C₂×D₁₈₈	C₂²	semidirect
14. D₈×C₄₇	C₂²	semidirect
15. C₂×C₈×C₄₇	C₂²	semidirect
16. #10625334	C₂²	semidirect
17. C₂×C₄₇⋊C₈	C₂²	semidirect
18. D₃₇₆	C₂²	semidirect
19. C₈×D₄₇	C₂²	semidirect
26. D₄×C₄₇	C₂³	semidirect
31. D₁₈₈	C₂³	semidirect
34. C₈×C₄₇	C₂³	semidirect
35. C₄₇⋊C₈	C₂³	semidirect
42. C₂×D₄₇	D₈	direct (N × H)
48. C₂×C₄₇	C₂×D₈	semidirect
51. D₄₇	C₂×D₈	direct (N × H)
53. C₄₇	C₂²×D₈	semidirect
58. C₂×D₈	D₄₇	direct (N × H)
65. C₂×D₄	C₂×D₄₇	semidirect
69. D₈	C₂×D₄₇	direct (N × H)
72. C₂×C₈	C₂×D₄₇	semidirect
82. D₄	C₂²×D₄₇	semidirect
88. C₈	C₂²×D₄₇	semidirect
103. C₂	D₈×D₄₇	direct (N × H)

H ≅ G/N

type

1. C₂×D₄×D₄₇

C₂

semidirect

2. C₂×D₃₇₆

C₂

semidirect

3. C₂×#10625334

C₂

semidirect

4. D₈×D₄₇

C₂

direct (N × H)

5. C₂×C₈×D₄₇

C₂

semidirect

6. C₂×D₈×C₄₇

C₂

semidirect

8. C₂×D₄×C₄₇

C₂²

semidirect

11. D₄×D₄₇

C₂²

semidirect

12. C₂×D₁₈₈

C₂²

semidirect

14. D₈×C₄₇

C₂²

semidirect

15. C₂×C₈×C₄₇

C₂²

semidirect

16. #10625334

C₂²

semidirect

17. C₂×C₄₇⋊C₈

C₂²

semidirect

18. D₃₇₆

C₂²

semidirect

19. C₈×D₄₇

C₂²

semidirect

26. D₄×C₄₇

C₂³

semidirect

31. D₁₈₈

C₂³

semidirect

34. C₈×C₄₇

C₂³

semidirect

35. C₄₇⋊C₈

C₂³

semidirect

42. C₂×D₄₇

D₈

direct (N × H)

48. C₂×C₄₇

C₂×D₈

semidirect

51. D₄₇

C₂×D₈

direct (N × H)

53. C₄₇

C₂²×D₈

semidirect

58. C₂×D₈

D₄₇

direct (N × H)

65. C₂×D₄

C₂×D₄₇

semidirect

69. D₈

C₂×D₄₇

direct (N × H)

72. C₂×C₈

C₂×D₄₇

semidirect

82. D₄

C₂²×D₄₇

semidirect

88. C₈

C₂²×D₄₇

semidirect

103. C₂

D₈×D₄₇

direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₄×D₄₇	2
C₂×D₃₇₆	2
C₂×#10625334	2
D₈×D₄₇	2
C₂×C₈×D₄₇	2
C₂×D₈×C₄₇	2
C₂²×D₈	47

subgroup

index

C₂×D₄×D₄₇

C₂×D₃₇₆

C₂×#10625334

D₈×D₄₇

C₂×C₈×D₄₇

C₂×D₈×C₄₇

C₂²×D₈

Subgroups — C₂×D₈×D₄₇ #15689891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×D8×D47 #15689891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₈×D₄₇ #15689891