Group #20256601 — subgroups

Subgroups — 2₋¹⁺⁴×Dic₄₇ #20256601

Order 6016.

1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.

normal subgroups only

This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 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	#15689606	C₂	1	10	yes	maximal, complemented
2	#15689601	C₂	1	5	yes	maximal, complemented
3	#41×Dic₄₇	C₂	1	10	yes	maximal, complemented
4	C₂×Q₈×Dic₄₇	C₂	1	5	yes	maximal, complemented
5	C₂×2₋¹⁺⁴×C₄₇	C₂	1	1	yes	maximal, characteristic
6	Q₈×Dic₄₇	C₂²	1	10	yes	—
7	Q₈×Dic₄₇	C₂²	1	20	yes	—
8	Q₈×Dic₄₇	C₂²	1	10	yes	—
9	D₄×Dic₄₇	C₂²	1	10	yes	—
10	D₄×Dic₄₇	C₂²	1	30	yes	—
11	#13093983	C₂²	1	30	yes	—
12	C₂×C₄⋊Dic₄₇	C₂²	1	15	yes	—
13	C₂×C₄×Dic₄₇	C₂²	1	15	yes	—
14	2₋¹⁺⁴×C₄₇	C₄	1	16	yes	complemented
15	C₂×#41×C₄₇	C₂²	1	10	yes	—
16	C₂²×Q₈×C₄₇	C₂²	1	5	yes	—
17	#41×C₄₇	C₂×C₄	1	80	yes	complemented
18	C₂×Q₈×C₄₇	C₂×C₄	1	40	yes	complemented
19	C₂×Q₈×C₄₇	C₂³	1	10	yes	—
20	C₂×D₄×C₄₇	C₂³	1	10	yes	—
21	C₂²×C₄×C₄₇	C₂³	1	15	yes	—
22	C₂²×Dic₄₇	C₂³	1	5	yes	—
23	C₂²×Dic₄₇	C₂³	1	15	yes	—
24	C₂²⋊Dic₄₇	C₂³	1	20	yes	—
25	C₄⋊Dic₄₇	C₂³	1	30	yes	—
26	C₄⋊Dic₄₇	C₂³	1	10	yes	—
27	C₄×Dic₄₇	C₂³	1	10	yes	—
28	C₄×Dic₄₇	C₂³	1	30	yes	—
29	C₂³×C₄₇	C₂⁴	1	5	yes	—
30	Q₈×C₄₇	C₂²×C₄	1	40	yes	—
31	D₄×C₄₇	C₂²×C₄	1	40	yes	—
32	C₂×C₄×C₄₇	C₂²×C₄	1	60	yes	—
33	C₂×C₄×C₄₇	C₂⁴	1	10	yes	—
34	C₂×Dic₄₇	—	2	10	no	—
35	C₂×Dic₄₇	—	4	15	no	—
36	C₂×Dic₄₇	C₂⁴	1	5	yes	—
37	C₂×Dic₄₇	C₂⁴	1	10	yes	—
38	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
39	C₂²×C₄₇	—	2	5	no	—
40	C₂²×C₄₇	—	2	5	no	—
41	C₂²×C₄₇	C₂³×C₄	1	10	yes	—
42	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
43	C₄×C₄₇	C₂³×C₄	1	20	yes	—
44	Dic₄₇	—	2	5	no	—
45	Dic₄₇	—	2	10	no	—
46	Dic₄₇	2₋¹⁺⁴	1	2	yes	direct product factor
47	C₄×2₋¹⁺⁴	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	—	2	10	no	—
49	C₂×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
50	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
51	C₂×C₄₇	#585	1	1	yes	characteristic
52	C₂×2₋¹⁺⁴	D₄₇	1	1	yes	characteristic
53	#520	—	47	10	no	—
54	#519	—	47	5	no	—
55	C₄×#41	—	47	10	no	—
56	C₂×C₄×Q₈	—	47	5	no	—
57	C₄₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
58	2₋¹⁺⁴	Dic₄₇	1	16	yes	direct product factor
59	C₂×#41	C₂×D₄₇	1	10	yes	—
60	C₂²×Q₈	C₂×D₄₇	1	5	yes	—
61	C₄×Q₈	—	47	10	no	—
62	C₄×Q₈	—	47	20	no	—
63	C₄×Q₈	—	47	10	no	—
64	C₄×D₄	—	47	10	no	—
65	C₄×D₄	—	47	30	no	—
66	#117	—	47	30	no	—
67	C₂×C₄⋊C₄	—	47	15	no	—
68	C₂×C₄²	—	47	15	no	—
69	#41	C₂×Dic₄₇	1	80	yes	complemented
70	C₂×Q₈	C₂×Dic₄₇	1	40	yes	complemented
71	C₂×Q₈	C₂²×D₄₇	1	10	yes	—
72	C₂×D₄	C₂²×D₄₇	1	10	yes	—
73	C₂²×C₄	—	47	5	no	—
74	C₂²×C₄	—	47	15	no	—
75	C₂²×C₄	C₂²×D₄₇	1	15	yes	—
76	C₄⋊C₄	—	47	30	no	—
77	C₄⋊C₄	—	47	10	no	—
78	C₂²⋊C₄	—	47	20	no	—
79	C₄²	—	47	10	no	—
80	C₄²	—	47	30	no	—
81	C₂³	C₂³×D₄₇	1	5	yes	—
82	Q₈	C₂²×Dic₄₇	1	40	yes	—
83	D₄	C₂²×Dic₄₇	1	40	yes	—
84	C₂×C₄	—	47	1	no	—
85	C₂×C₄	—	47	5	no	—
86	C₂×C₄	—	47	10	no	—
87	C₂×C₄	—	94	10	no	—
88	C₂×C₄	—	188	15	no	—
89	C₂×C₄	C₂²×Dic₄₇	1	60	yes	—
90	C₂×C₄	C₂³×D₄₇	1	10	yes	—
91	C₂²	—	2	5	no	—
92	C₂²	—	2	5	no	—
93	C₂²	C₂³×Dic₄₇	1	10	yes	—
94	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
95	C₄	—	47	2	no	—
96	C₄	—	94	5	no	—
97	C₄	—	94	10	no	—
98	C₄	C₂³×Dic₄₇	1	20	yes	—
99	C₂	—	2	10	no	—
100	C₂	C₂⁴×Dic₄₇	1	1	yes	characteristic
101	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
102	C₂	#15689960	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689606

C₂

yes

maximal, complemented

#15689601

C₂

yes

maximal, complemented

#41×Dic₄₇

C₂

yes

maximal, complemented

C₂×Q₈×Dic₄₇

C₂

yes

maximal, complemented

C₂×2₋¹⁺⁴×C₄₇

C₂

yes

maximal, characteristic

Q₈×Dic₄₇

C₂²

yes

—

Q₈×Dic₄₇

C₂²

yes

—

Q₈×Dic₄₇

C₂²

yes

—

D₄×Dic₄₇

C₂²

yes

—

D₄×Dic₄₇

C₂²

yes

—

#13093983

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

2₋¹⁺⁴×C₄₇

C₄

yes

complemented

C₂×#41×C₄₇

C₂²

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

—

#41×C₄₇

C₂×C₄

yes

complemented

C₂×Q₈×C₄₇

C₂×C₄

yes

complemented

C₂×Q₈×C₄₇

C₂³

yes

—

C₂×D₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²⋊Dic₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₂³×C₄₇

C₂⁴

yes

—

Q₈×C₄₇

C₂²×C₄

yes

—

D₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂⁴

yes

—

C₂×Dic₄₇

C₂⁴

yes

—

C₂×Dic₄₇

C₂⁴

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂³×C₄

yes

—

C₂²×C₄₇

C₂⁵

yes

characteristic

C₄×C₄₇

C₂³×C₄

yes

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

2₋¹⁺⁴

yes

direct product factor

C₄×2₋¹⁺⁴

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂⁴×C₄

yes

characteristic

C₂×C₄₇

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₄₇

#585

yes

characteristic

C₂×2₋¹⁺⁴

D₄₇

yes

characteristic

#520

—

#519

—

C₄×#41

—

C₂×C₄×Q₈

—

C₄₇

C₄×2₋¹⁺⁴

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

Dic₄₇

yes

direct product factor

C₂×#41

C₂×D₄₇

yes

—

C₂²×Q₈

C₂×D₄₇

yes

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×D₄

—

C₄×D₄

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

#41

C₂×Dic₄₇

yes

complemented

C₂×Q₈

C₂×Dic₄₇

yes

complemented

C₂×Q₈

C₂²×D₄₇

yes

—

C₂×D₄

C₂²×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₂³

C₂³×D₄₇

yes

—

Q₈

C₂²×Dic₄₇

yes

—

D₄

C₂²×Dic₄₇

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂²×Dic₄₇

yes

—

C₂×C₄

C₂³×D₄₇

yes

—

C₂²

—

C₂²

—

C₂²

C₂³×Dic₄₇

yes

—

C₂²

C₂⁴×D₄₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₂³×Dic₄₇

yes

—

C₂

—

100

C₂

C₂⁴×Dic₄₇

yes

characteristic

101

C₂

2₋¹⁺⁴×D₄₇

yes

characteristic

102

C₂

#15689960

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator	C₂×C₄₇	C₂⁴×C₄
Fitting	C₂×2₋¹⁺⁴×C₄₇	C₂
socle	C₂²×C₄₇	C₂⁵
hypercenter	C₂×2₋¹⁺⁴	D₄₇
hypocenter	C₄₇	C₄×2₋¹⁺⁴
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×2₋¹⁺⁴

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₄₇

commutator

C₂×C₄₇

C₂⁴×C₄

Fitting

C₂×2₋¹⁺⁴×C₄₇

C₂

socle

C₂²×C₄₇

C₂⁵

hypercenter

C₂×2₋¹⁺⁴

D₄₇

hypocenter

C₄₇

C₄×2₋¹⁺⁴

LCS

G ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×2₋¹⁺⁴

N	H ≅ G/N	type
1. #15689606	C₂	semidirect
2. #15689601	C₂	semidirect
3. #41×Dic₄₇	C₂	semidirect
4. C₂×Q₈×Dic₄₇	C₂	semidirect
14. 2₋¹⁺⁴×C₄₇	C₄	semidirect
17. #41×C₄₇	C₂×C₄	semidirect
18. C₂×Q₈×C₄₇	C₂×C₄	semidirect
46. Dic₄₇	2₋¹⁺⁴	direct (N × H)
57. C₄₇	C₄×2₋¹⁺⁴	semidirect
58. 2₋¹⁺⁴	Dic₄₇	direct (N × H)
69. #41	C₂×Dic₄₇	semidirect
70. C₂×Q₈	C₂×Dic₄₇	semidirect

H ≅ G/N

type

1. #15689606

C₂

semidirect

2. #15689601

C₂

semidirect

3. #41×Dic₄₇

C₂

semidirect

4. C₂×Q₈×Dic₄₇

C₂

semidirect

14. 2₋¹⁺⁴×C₄₇

C₄

semidirect

17. #41×C₄₇

C₂×C₄

semidirect

18. C₂×Q₈×C₄₇

C₂×C₄

semidirect

46. Dic₄₇

2₋¹⁺⁴

direct (N × H)

57. C₄₇

C₄×2₋¹⁺⁴

semidirect

58. 2₋¹⁺⁴

Dic₄₇

direct (N × H)

69. #41

C₂×Dic₄₇

semidirect

70. C₂×Q₈

C₂×Dic₄₇

semidirect

Subgroups — 2₋¹⁺⁴×Dic₄₇ #20256601

Conjugacy classes of subgroups

Complements

Subgroups — 2−1+4×Dic47 #20256601

Conjugacy classes of subgroups

Complements

Subgroups — 2₋¹⁺⁴×Dic₄₇ #20256601