Group #20249348 — subgroups

Subgroups — #20249348

Order 6016.

420 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 133 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	#15689052	C₂	1	6	yes	maximal, complemented
2	#15689047	C₂	1	2	yes	maximal, complemented
3	#15689025	C₂	1	3	yes	maximal
4	#15689021	C₂	1	3	yes	maximal, complemented
5	C₄₇×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
8	C₂×Dic₄₇⋊C₄	C₂²	1	6	yes	—
9	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	6	yes	—
10	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	6	yes	—
11	C₄₇⋊#95	C₂²	1	6	yes	—
12	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
13	#95×C₄₇	C₂²	1	1	yes	characteristic
14	#95×C₄₇	C₂²	1	3	yes	—
15	C₂³×D₄₇	C₂³	1	2	yes	—
16	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
18	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂²×Dic₄₇	C₂³	1	6	yes	—
20	C₂×D₁₈₈	—	2	6	no	—
21	C₄²×C₄₇	—	2	6	no	—
22	(C₂×D₄₇)⋊C₄	—	4	6	no	—
23	(C₂×D₄₇)⋊C₄	—	4	6	no	—
24	C₄⋊Dic₄₇	—	2	6	no	—
25	Dic₄₇⋊C₄	—	4	6	no	—
26	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
27	C₂²×D₄₇	—	2	6	no	—
28	C₂²×D₄₇	—	2	6	no	—
29	C₂²×D₄₇	—	2	2	no	—
30	C₂×C₄×C₄₇	—	2	3	no	—
31	C₂×C₄×C₄₇	—	2	3	no	—
32	C₂×C₄×C₄₇	—	2	3	no	—
33	C₂×C₄×C₄₇	—	2	3	no	—
34	C₂×C₄×C₄₇	—	2	3	no	—
35	C₂×C₄×C₄₇	—	2	3	no	—
36	C₂×C₄×C₄₇	#41	1	6	yes	—
37	C₂×Dic₄₇	—	2	6	no	—
38	C₂×Dic₄₇	—	2	6	no	—
39	C₂×Dic₄₇	—	2	6	no	—
40	D₁₈₈	—	4	4	no	—
41	C₂²×C₄₇	C₂×#41	1	3	yes	—
42	C₂²×C₄₇	H(5,𝔽₂)	1	3	yes	—
43	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
44	C₂×D₄₇	—	4	2	no	—
45	C₂×D₄₇	—	4	6	no	—
46	C₂×D₄₇	—	4	6	no	—
47	C₄×C₄₇	—	4	3	no	—
48	C₄×C₄₇	—	4	3	no	—
49	C₄×C₄₇	#126	1	4	yes	—
50	Dic₄₇	—	4	6	no	—
51	#2644	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	C₂×#126	1	1	yes	characteristic
53	C₂×C₄₇	#540	1	3	yes	—
54	C₂×C₄₇	#542	1	3	yes	—
55	D₄₇	—	8	2	no	—
56	#397	—	47	6	no	—
57	#396	—	47	2	no	—
58	#390	—	47	3	no	—
59	#389	—	47	3	no	—
60	#376	D₄₇	1	1	yes	characteristic, complemented
61	C₄₇	#2644	1	1	yes	characteristic, complemented, Sylow
62	C₂²×D₄	—	47	1	no	—
63	C₂×C₄⋊C₄	—	47	3	no	—
64	C₂×C₄⋊C₄	—	47	6	no	—
65	C₂×C₂²⋊C₄	—	47	6	no	—
66	C₂×C₂²⋊C₄	—	47	6	no	—
67	C₂×C₄²	C₂×D₄₇	1	3	yes	—
68	#95	—	47	6	no	—
69	#95	C₂×D₄₇	1	1	yes	characteristic
70	#95	C₂×D₄₇	1	3	yes	—
71	C₂⁴	—	47	2	no	—
72	C₂×D₄	—	94	6	no	—
73	C₂²×C₄	—	47	6	no	—
74	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
75	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
76	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
77	C₄⋊C₄	—	94	6	no	—
78	C₄⋊C₄	—	188	6	no	—
79	C₂²⋊C₄	—	188	6	no	—
80	C₂²⋊C₄	—	188	6	no	—
81	C₄²	—	2	6	no	—
82	C₂³	—	94	6	no	—
83	C₂³	—	94	6	no	—
84	C₂³	—	94	2	no	—
85	C₂³	C₂³×D₄₇	1	1	yes	characteristic
86	D₄	—	188	4	no	—
87	C₂×C₄	—	2	3	no	—
88	C₂×C₄	—	2	3	no	—
89	C₂×C₄	—	2	3	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	94	6	no	—
94	C₂×C₄	—	94	6	no	—
95	C₂×C₄	—	94	6	no	—
96	C₂×C₄	#10625350	1	6	yes	—
97	C₂²	—	188	6	no	—
98	C₂²	—	188	6	no	—
99	C₂²	—	188	2	no	—
100	C₂²	C₂×#10625350	1	3	yes	—
101	C₂²	#13094070	1	3	yes	—
102	C₂²	#13094071	1	1	yes	characteristic
103	C₄	—	4	3	no	—
104	C₄	—	4	3	no	—
105	C₄	—	188	6	no	—
106	C₄	#13094018	1	4	yes	—
107	C₂	—	376	2	no	—
108	C₂	C₂×#13094018	1	1	yes	characteristic
109	C₂	#15689728	1	3	yes	—
110	C₂	#15689744	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689052

C₂

yes

maximal, complemented

#15689047

C₂

yes

maximal, complemented

#15689025

C₂

yes

maximal

#15689021

C₂

yes

maximal, complemented

C₄₇×#376

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

characteristic

#95×C₄₇

C₂²

yes

—

C₂³×D₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂×D₁₈₈

—

C₄²×C₄₇

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#126

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#542

yes

—

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#2644

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

—

#95

—

#95

C₂×D₄₇

yes

characteristic

#95

C₂×D₄₇

yes

—

C₂⁴

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₄²

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₄₇

yes

characteristic

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10625350

yes

—

C₂²

—

188

—

C₂²

—

188

—

C₂²

—

188

—

100

C₂²

C₂×#10625350

yes

—

101

C₂²

#13094070

yes

—

102

C₂²

#13094071

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

—

188

—

106

C₄

#13094018

yes

—

107

C₂

—

376

—

108

C₂

C₂×#13094018

yes

characteristic

109

C₂

#15689728

yes

—

110

C₂

#15689744

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#376	C₂
hypercenter	#376	D₄₇
hypocenter	C₄₇	#2644
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#376

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
1. #15689052	C₂	semidirect
2. #15689047	C₂	semidirect
4. #15689021	C₂	semidirect
5. C₄₇×#376	C₂	semidirect
60. #376	D₄₇	semidirect
61. C₄₇	#2644	semidirect

H ≅ G/N

type

1. #15689052

C₂

semidirect

2. #15689047

C₂

semidirect

4. #15689021

C₂

semidirect

5. C₄₇×#376

C₂

semidirect

60. #376

D₄₇

semidirect

61. C₄₇

#2644

semidirect

Subgroups — #20249348

Conjugacy classes of subgroups

Complements