Group #20245657 — subgroups

Subgroups — #20245657

Order 6016.

178 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 57 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×#13093970	C₂	1	2	yes	maximal, complemented
2	C₂×#13093967	C₂	1	2	yes	maximal
3	#15689507	C₂	1	1	yes	maximal, characteristic
4	#15688899	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#494	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	#13094012	—	2	1	no	—
10	#13093970	—	2	4	no	—
11	#13093967	—	2	4	no	—
12	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
13	C₂×Q₁₆×C₄₇	—	2	1	no	—
14	C₂×Q₁₆×C₄₇	C₂²	1	2	yes	—
15	C₄⋊Q₈×C₄₇	—	2	1	no	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₇	—	2	2	no	—
18	C₂×D₁₈₈	—	2	1	no	—
19	C₂×Dic₉₄	—	2	1	no	—
20	Q₁₆×C₄₇	—	2	2	no	—
21	Q₁₆×C₄₇	—	2	2	no	—
22	Q₁₆×C₄₇	—	4	2	no	—
23	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
25	C₄⋊C₄×C₄₇	—	4	2	no	—
26	C₄²×C₄₇	D₄	1	1	yes	characteristic
27	(C₂×D₄₇)⋊C₄	—	4	2	no	—
28	Dic₁₈₈	—	2	2	no	—
29	D₃₇₆	—	2	2	no	—
30	#10625325	—	4	2	no	—
31	C₄₇⋊C₁₆	D₄	1	4	yes	—
32	C₂²×D₄₇	—	4	1	no	—
33	Q₈×C₄₇	—	4	2	no	—
34	Q₈×C₄₇	—	4	2	no	—
35	C₂×C₄×C₄₇	—	4	2	no	—
36	C₂×C₄×C₄₇	D₈	1	2	yes	—
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₄₇	—	4	1	no	—
39	D₁₈₈	—	4	1	no	—
40	D₁₈₈	—	4	1	no	—
41	Dic₉₄	—	4	1	no	—
42	Dic₉₄	—	4	1	no	—
43	C₈×C₄₇	D₈	1	2	yes	—
44	C₈×C₄₇	C₂×D₄	1	2	yes	—
45	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
46	C₂×D₄₇	—	8	1	no	—
47	C₂×D₄₇	—	8	2	no	—
48	C₄×C₄₇	—	2	2	no	—
49	C₄×C₄₇	—	8	2	no	—
50	C₄×C₄₇	#127	1	1	yes	characteristic
51	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
52	Dic₄₇	—	8	1	no	—
53	#2251	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	#493	1	1	yes	characteristic
55	C₂×C₄₇	#510	1	2	yes	—
56	D₄₇	—	16	1	no	—
57	C₂×Q₃₂	—	47	2	no	—
58	C₂×SD₃₂	—	47	2	no	—
59	#495	—	47	1	no	—
60	#494	D₄₇	1	1	yes	characteristic, complemented
61	#346	—	47	1	no	—
62	C₄₇	#2251	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₁₆	—	2	1	no	—
64	C₂×Q₁₆	—	47	1	no	—
65	C₂×Q₁₆	C₂×D₄₇	1	2	yes	—
66	C₂×SD₁₆	—	94	1	no	—
67	C₂×D₈	—	47	1	no	—
68	C₄⋊Q₈	—	2	1	no	—
69	#124	—	94	1	no	—
70	Q₃₂	—	94	4	no	—
71	SD₃₂	—	94	4	no	—
72	C₂×C₁₆	—	47	2	no	—
73	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
74	C₂×Q₈	—	2	2	no	—
75	C₂×Q₈	—	94	1	no	—
76	C₂×D₄	—	94	1	no	—
77	Q₁₆	—	2	2	no	—
78	Q₁₆	—	2	2	no	—
79	Q₁₆	—	4	2	no	—
80	Q₁₆	—	94	2	no	—
81	SD₁₆	—	188	2	no	—
82	D₈	—	94	2	no	—
83	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
85	C₄⋊C₄	—	4	2	no	—
86	C₂²⋊C₄	—	188	2	no	—
87	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
88	C₁₆	—	47	4	no	—
89	C₂³	—	188	1	no	—
90	Q₈	—	4	2	no	—
91	Q₈	—	4	2	no	—
92	Q₈	—	188	1	no	—
93	Q₈	—	188	1	no	—
94	D₄	—	188	1	no	—
95	D₄	—	188	1	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	188	1	no	—
98	C₂×C₄	#10625334	1	2	yes	—
99	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
100	C₈	#10625334	1	2	yes	—
101	C₈	D₄×D₄₇	1	2	yes	—
102	C₂²	—	376	1	no	—
103	C₂²	—	376	2	no	—
104	C₂²	C₂×#10625334	1	1	yes	characteristic
105	C₄	—	2	2	no	—
106	C₄	—	8	2	no	—
107	C₄	—	376	1	no	—
108	C₄	#13094020	1	1	yes	characteristic
109	C₄	C₂×#10625334	1	1	yes	characteristic
110	C₂	—	752	1	no	—
111	C₂	#15689499	1	1	yes	characteristic
112	C₂	#15689564	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093970

C₂

yes

maximal, complemented

C₂×#13093967

C₂

yes

maximal

#15689507

C₂

yes

maximal, characteristic

#15688899

C₂

yes

maximal, characteristic, complemented

C₄₇×#494

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₈₈

C₂²

yes

characteristic

C₂×#10625325

—

C₂×D₃₇₆

C₂²

yes

—

—

—

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×D₁₈₈

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

Dic₁₈₈

—

D₃₇₆

—

#10625325

—

C₄₇⋊C₁₆

D₄

yes

—

C₂²×D₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

D₈

yes

—

C₈×C₄₇

C₂×D₄

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#127

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

C₂×Q₃₂

—

C₂×SD₃₂

—

#495

—

#494

D₄₇

yes

characteristic, complemented

#346

—

C₄₇

#2251

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₇

yes

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#124

—

Q₃₂

—

SD₃₂

—

C₂×C₁₆

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

188

—

D₈

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

188

—

C₄²

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

C₂³

—

188

—

Q₈

—

Q₈

—

Q₈

—

188

—

Q₈

—

188

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

#10625334

yes

—

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

100

C₈

#10625334

yes

—

101

C₈

D₄×D₄₇

yes

—

102

C₂²

—

376

—

103

C₂²

—

376

—

104

C₂²

C₂×#10625334

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

376

—

108

C₄

#13094020

yes

characteristic

109

C₄

C₂×#10625334

yes

characteristic

110

C₂

—

752

—

111

C₂

#15689499

yes

characteristic

112

C₂

#15689564

yes

—

	subgroup	G/H
center	C₂²	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#494	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#494	D₄₇
hypocenter	C₄₇	#2251
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

subgroup

G/H

center

C₂²

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#494

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

N	H ≅ G/N	type
1. C₂×#13093970	C₂	semidirect
4. #15688899	C₂	semidirect
5. C₄₇×#494	C₂	semidirect
60. #494	D₄₇	semidirect
62. C₄₇	#2251	semidirect

H ≅ G/N

type

1. C₂×#13093970

C₂

semidirect

4. #15688899

C₂

semidirect

5. C₄₇×#494

C₂

semidirect

60. #494

D₄₇

semidirect

62. C₄₇

#2251

semidirect

Subgroups — #20245657

Conjugacy classes of subgroups

Complements