Group #20245620 — subgroups

Subgroups — #20245620

Order 6016.

138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689525	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689507	C₂	1	1	yes	maximal, characteristic
3	#15688928	C₂	1	2	yes	maximal, complemented
4	#15688925	C₂	1	2	yes	maximal
5	C₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
7	C₂×#10625325	—	2	1	no	—
8	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
9	#13094016	—	2	1	no	—
10	#13094012	—	2	1	no	—
11	#13093958	C₂²	1	2	yes	—
12	#13093956	—	2	1	no	—
13	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×D₁₈₈	—	2	1	no	—
16	C₂×Dic₉₄	—	2	1	no	—
17	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
19	C₄²×C₄₇	D₄	1	1	yes	characteristic
20	(C₂×D₄₇)⋊C₄	—	4	2	no	—
21	C₄⋊Dic₄₇	—	2	2	no	—
22	Dic₄₇⋊C₄	—	4	2	no	—
23	Dic₁₈₈	—	2	2	no	—
24	D₃₇₆	—	2	2	no	—
25	#10625325	—	4	2	no	—
26	C₁₆×C₄₇	—	2	2	no	—
27	C₂²×D₄₇	—	4	1	no	—
28	C₂×C₄×C₄₇	D₈	1	2	yes	—
29	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₄₇	—	4	2	no	—
31	C₂×Dic₄₇	—	4	1	no	—
32	D₁₈₈	—	4	1	no	—
33	D₁₈₈	—	4	1	no	—
34	Dic₉₄	—	4	1	no	—
35	Dic₉₄	—	4	1	no	—
36	C₈×C₄₇	SD₁₆	1	2	yes	—
37	C₈×C₄₇	#41	1	2	yes	—
38	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
39	C₂×D₄₇	—	8	1	no	—
40	C₂×D₄₇	—	8	2	no	—
41	C₄×C₄₇	—	2	2	no	—
42	C₄×C₄₇	#124	1	1	yes	characteristic
43	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
44	Dic₄₇	—	8	1	no	—
45	Dic₄₇	—	8	2	no	—
46	#2242	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	#486	1	1	yes	characteristic
48	C₂×C₄₇	#508	1	2	yes	—
49	D₄₇	—	16	1	no	—
50	#499	—	47	1	no	—
51	#495	—	47	1	no	—
52	#358	—	47	2	no	—
53	#357	—	47	2	no	—
54	C₄×C₁₆	D₄₇	1	1	yes	characteristic, complemented
55	C₄₇	#2242	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₁₆	—	47	1	no	—
57	C₂×SD₁₆	—	94	1	no	—
58	C₂×D₈	—	47	1	no	—
59	#125	—	94	1	no	—
60	#124	—	94	1	no	—
61	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
62	#107	—	47	2	no	—
63	#106	—	94	1	no	—
64	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
65	C₂×Q₈	—	94	1	no	—
66	C₂×D₄	—	94	1	no	—
67	Q₁₆	—	94	2	no	—
68	SD₁₆	—	188	2	no	—
69	D₈	—	94	2	no	—
70	C₂×C₈	D₁₈₈	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
72	C₄⋊C₄	—	94	2	no	—
73	C₄⋊C₄	—	188	2	no	—
74	C₂²⋊C₄	—	188	2	no	—
75	C₄²	D₁₈₈	1	1	yes	characteristic
76	C₁₆	—	2	2	no	—
77	C₂³	—	188	1	no	—
78	Q₈	—	188	1	no	—
79	Q₈	—	188	1	no	—
80	D₄	—	188	1	no	—
81	D₄	—	188	1	no	—
82	C₂×C₄	—	188	1	no	—
83	C₂×C₄	—	188	2	no	—
84	C₂×C₄	D₃₇₆	1	2	yes	—
85	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
86	C₈	#10625325	1	2	yes	—
87	C₈	#10625350	1	2	yes	—
88	C₂²	—	376	2	no	—
89	C₂²	—	376	1	no	—
90	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	376	2	no	—
93	C₄	—	376	1	no	—
94	C₄	#13094012	1	1	yes	characteristic
95	C₄	C₂×#10625325	1	1	yes	characteristic
96	C₂	—	752	1	no	—
97	C₂	#15689470	1	1	yes	characteristic
98	C₂	#15689555	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689525

C₂

yes

maximal, characteristic, complemented

#15689507

C₂

yes

maximal, characteristic

#15688928

C₂

yes

maximal, complemented

#15688925

C₂

yes

maximal

C₄×C₁₆×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₈₈

C₂²

yes

characteristic

C₂×#10625325

—

C₂×D₃₇₆

C₂²

yes

—

—

C₂²

yes

—

#13093956

—

C₂×C₁₆×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₁₈₈

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₁₈₈

—

D₃₇₆

—

#10625325

—

C₁₆×C₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

SD₁₆

yes

—

C₈×C₄₇

#41

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#124

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

—

—

—

—

C₄×C₁₆

D₄₇

yes

characteristic, complemented

C₄₇

#2242

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#125

—

#124

—

C₂×C₁₆

C₂×D₄₇

yes

—

#107

—

#106

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

SD₁₆

—

188

—

D₈

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₄²

D₁₈₈

yes

characteristic

C₁₆

—

C₂³

—

188

—

Q₈

—

188

—

Q₈

—

188

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

D₃₇₆

yes

—

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₈

#10625325

yes

—

C₈

#10625350

yes

—

C₂²

—

376

—

C₂²

—

376

—

C₂²

C₂×D₃₇₆

yes

characteristic

C₄

—

C₄

—

376

—

C₄

—

376

—

C₄

yes

C₄

yes

C₂

—

752

—

C₂

#15689470

yes

characteristic

C₂

#15689555

yes

—

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄×C₁₆	D₄₇
hypocenter	C₄₇	#2242
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂²

C₂×D₃₇₆

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄×C₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₄×C₁₆

D₄₇

hypocenter

C₄₇

#2242

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
1. #15689525	C₂	semidirect
3. #15688928	C₂	semidirect
5. C₄×C₁₆×C₄₇	C₂	semidirect
54. C₄×C₁₆	D₄₇	semidirect
55. C₄₇	#2242	semidirect

H ≅ G/N

type

1. #15689525

C₂

semidirect

3. #15688928

C₂

semidirect

5. C₄×C₁₆×C₄₇

C₂

semidirect

54. C₄×C₁₆

D₄₇

semidirect

55. C₄₇

#2242

semidirect

Subgroups — #20245620

Conjugacy classes of subgroups

Complements