Group #20245476 — subgroups

Subgroups — #20245476

Order 6016.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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	#15689361	C₂	1	2	yes	maximal
3	#15688949	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688927	C₂	1	2	yes	maximal, complemented
5	C₂×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
7	#13094000	—	2	2	no	—
8	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₁₆×D₄₇	—	2	2	no	—
10	#13093958	C₂²	1	2	yes	—
11	#13093948	—	2	2	no	—
12	C₂×Q₁₆×C₄₇	C₂²	1	2	yes	—
13	Q₃₂×C₄₇	—	2	2	no	—
14	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₄₇	—	2	2	no	—
16	C₂×C₄×D₄₇	D₄	1	1	yes	characteristic
17	Q₁₆×C₄₇	—	2	2	no	—
18	Q₁₆×C₄₇	—	2	2	no	—
19	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
20	(C₂×D₄₇)⋊C₄	—	4	2	no	—
21	C₄⋊Dic₄₇	—	2	2	no	—
22	Dic₄₇⋊C₄	—	4	2	no	—
23	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
24	C₈×D₄₇	—	2	1	no	—
25	C₈×D₄₇	—	2	1	no	—
26	C₁₆×C₄₇	D₄	1	2	yes	—
27	C₄₇⋊C₁₆	—	2	1	no	—
28	C₂²×D₄₇	D₈	1	1	yes	characteristic
29	Q₈×C₄₇	—	4	2	no	—
30	Q₈×C₄₇	—	4	2	no	—
31	C₂×C₄×C₄₇	—	4	2	no	—
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₄₇	—	4	2	no	—
34	C₂×Dic₄₇	D₈	1	1	yes	characteristic
35	C₄×D₄₇	—	2	1	no	—
36	C₄×D₄₇	—	2	1	no	—
37	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₈×C₄₇	#41	1	1	yes	characteristic
39	C₄₇⋊C₈	—	2	1	no	—
40	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
41	C₂×D₄₇	—	2	1	no	—
42	C₂×D₄₇	—	2	1	no	—
43	C₂×D₄₇	Q₃₂	1	2	yes	complemented
44	C₄×C₄₇	—	8	2	no	—
45	C₄×C₄₇	#121	1	1	yes	characteristic
46	C₄×C₄₇	#135	1	1	yes	characteristic
47	Dic₄₇	—	2	1	no	—
48	Dic₄₇	—	8	2	no	—
49	#2216	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	#466	1	1	yes	characteristic
51	C₂×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
52	C₂×C₄₇	#508	1	1	yes	characteristic
53	D₄₇	—	2	2	no	—
54	C₂×Q₃₂	D₄₇	1	1	yes	characteristic, complemented
55	C₂²×C₁₆	—	47	1	no	—
56	#467	—	47	2	no	—
57	#366	—	47	1	no	—
58	#358	—	47	2	no	—
59	C₄₇	#2216	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₁₆	C₂×D₄₇	1	2	yes	—
61	C₂²×C₈	—	47	1	no	—
62	C₂²⋊Q₈	—	94	2	no	—
63	Q₃₂	—	2	2	no	—
64	C₂×C₁₆	—	47	1	no	—
65	C₂×C₁₆	—	94	2	no	—
66	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
67	#107	—	47	2	no	—
68	#103	—	94	2	no	—
69	C₂×Q₈	—	2	2	no	—
70	C₂²×C₄	—	47	1	no	—
71	Q₁₆	—	2	2	no	—
72	Q₁₆	—	2	2	no	—
73	C₂×C₈	—	47	1	no	—
74	C₂×C₈	—	94	1	no	—
75	C₂×C₈	—	94	1	no	—
76	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
77	C₄⋊C₄	—	94	2	no	—
78	C₄⋊C₄	—	188	2	no	—
79	C₂²⋊C₄	—	188	2	no	—
80	C₁₆	—	94	1	no	—
81	C₁₆	C₂²⋊D₄₇	1	2	yes	—
82	C₂³	—	47	1	no	—
83	Q₈	—	4	2	no	—
84	Q₈	—	4	2	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	—	47	1	no	—
87	C₂×C₄	—	94	1	no	—
88	C₂×C₄	—	94	1	no	—
89	C₂×C₄	—	188	2	no	—
90	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
91	C₈	—	94	1	no	—
92	C₈	#10625352	1	1	yes	characteristic
93	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
94	C₂²	—	47	2	no	—
95	C₂²	—	94	1	no	—
96	C₂²	—	94	1	no	—
97	C₂²	D₈×D₄₇	1	1	yes	characteristic
98	C₄	—	8	2	no	—
99	C₄	—	94	1	no	—
100	C₄	—	376	2	no	—
101	C₄	#13093995	1	1	yes	characteristic
102	C₄	#13094043	1	1	yes	characteristic
103	C₂	—	94	2	no	—
104	C₂	#15689356	1	1	yes	characteristic
105	C₂	Q₃₂×D₄₇	1	1	yes	characteristic
106	C₂	#15689556	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₄₇

C₂

yes

maximal, characteristic

#15689361

C₂

yes

maximal

#15688949

C₂

yes

maximal, characteristic, complemented

#15688927

C₂

yes

maximal, complemented

C₂×Q₃₂×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₇

C₂²

yes

characteristic

#13094000

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₁₆×D₄₇

—

#13093958

C₂²

yes

—

#13093948

—

C₂×Q₁₆×C₄₇

C₂²

yes

—

Q₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×C₄×D₄₇

D₄

yes

characteristic

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

D₄

yes

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

D₈

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

Q₃₂

yes

complemented

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×Q₃₂

yes

characteristic

C₂×C₄₇

#508

yes

characteristic

D₄₇

—

C₂×Q₃₂

D₄₇

yes

characteristic, complemented

C₂²×C₁₆

—

#467

—

#366

—

#358

—

C₄₇

#2216

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₄₇

yes

—

C₂²×C₈

—

C₂²⋊Q₈

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

#107

—

#103

—

C₂×Q₈

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₁₆

—

C₁₆

C₂²⋊D₄₇

yes

—

C₂³

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₈

—

C₈

#10625352

yes

characteristic

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

D₈×D₄₇

yes

characteristic

C₄

—

C₄

—

100

C₄

—

376

—

101

C₄

#13093995

yes

characteristic

102

C₄

#13094043

yes

characteristic

103

C₂

—

104

C₂

#15689356

yes

characteristic

105

C₂

Q₃₂×D₄₇

yes

characteristic

106

C₂

#15689556

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×Q₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂×Q₃₂	D₄₇
hypocenter	C₄₇	#2216
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂×Q₃₂×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₂×Q₃₂

D₄₇

hypocenter

C₄₇

#2216

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

N	H ≅ G/N	type
3. #15688949	C₂	semidirect
4. #15688927	C₂	semidirect
5. C₂×Q₃₂×C₄₇	C₂	semidirect
43. C₂×D₄₇	Q₃₂	semidirect
54. C₂×Q₃₂	D₄₇	semidirect
59. C₄₇	#2216	semidirect

H ≅ G/N

type

3. #15688949

C₂

semidirect

4. #15688927

C₂

semidirect

5. C₂×Q₃₂×C₄₇

C₂

semidirect

43. C₂×D₄₇

Q₃₂

semidirect

54. C₂×Q₃₂

D₄₇

semidirect

59. C₄₇

#2216

semidirect

Subgroups — #20245476

Conjugacy classes of subgroups

Complements