Group #20257882 — subgroups

Subgroups — #20257882

Order 6016.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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	C₄₇⋊#564	C₂	1	3	yes	maximal, complemented
2	#15689850	C₂	1	12	yes	maximal, complemented
3	#15689732	C₂	1	12	yes	maximal
4	#15689679	C₂	1	3	yes	maximal
5	C₄₇×#564	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094023	C₂²	1	12	yes	—
7	#13094023	C₂²	1	6	yes	—
8	#13094019	C₂²	1	12	yes	—
9	#13094018	C₂²	1	4	yes	—
10	#13094016	C₂²	1	3	yes	—
11	#13094015	C₂²	1	12	yes	—
12	#13094014	C₂²	1	12	yes	—
13	#13094014	C₂²	1	12	yes	—
14	#13094014	C₂²	1	12	yes	—
15	#13094002	C₂²	1	12	yes	—
16	C₄×Dic₉₄	C₂²	1	12	yes	—
17	#13093989	C₂²	1	12	yes	—
18	#13093989	C₂²	1	12	yes	—
19	#13093982	C₂²	1	6	yes	—
20	C₄²×D₄₇	C₂²	1	1	yes	characteristic
21	#125×C₄₇	C₂²	1	12	yes	—
22	#125×C₄₇	C₂²	1	3	yes	—
23	C₂×C₄×D₄₇	C₂³	1	3	yes	—
24	C₂×Dic₉₄	C₂³	1	12	yes	—
25	C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
26	C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
27	C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
28	C₄²×C₄₇	C₂³	1	1	yes	characteristic
29	C₄²×C₄₇	C₂³	1	4	yes	—
30	(C₂×D₄₇)⋊C₄	C₂³	1	12	yes	—
31	C₄⋊Dic₄₇	C₂³	1	6	yes	—
32	C₄⋊Dic₄₇	C₂³	1	12	yes	—
33	Dic₄₇⋊C₄	C₂³	1	12	yes	—
34	Dic₄₇⋊C₄	C₂³	1	12	yes	—
35	Dic₄₇⋊C₄	C₂³	1	12	yes	—
36	Dic₄₇⋊C₄	C₂³	1	12	yes	—
37	C₄×Dic₄₇	C₂³	1	3	yes	—
38	C₄×Dic₄₇	C₂³	1	12	yes	—
39	C₄×Dic₄₇	C₂³	1	12	yes	—
40	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
41	C₂×C₄×C₄₇	C₂⁴	1	12	yes	—
42	C₂×C₄×C₄₇	C₂⁴	1	3	yes	—
43	C₂×Dic₄₇	C₂⁴	1	12	yes	—
44	C₂×Dic₄₇	C₂⁴	1	3	yes	—
45	C₄×D₄₇	—	2	6	no	—
46	Dic₉₄	—	2	24	no	—
47	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
48	C₂×D₄₇	—	2	3	no	—
49	C₄×C₄₇	—	2	12	no	—
50	C₄×C₄₇	—	2	3	no	—
51	Dic₄₇	—	2	12	no	—
52	Dic₄₇	2₋¹⁺⁴	1	6	yes	—
53	#3556	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	C₂×2₋¹⁺⁴	1	3	yes	—
55	D₄₇	—	4	1	no	—
56	#564	—	47	3	no	—
57	#564	D₄₇	1	1	yes	characteristic, complemented
58	#557	—	47	12	no	—
59	#541	—	47	12	no	—
60	#533	—	47	3	no	—
61	C₄₇	#3556	1	1	yes	characteristic, complemented, Sylow
62	C₄⋊Q₈	—	47	6	no	—
63	C₄⋊Q₈	—	47	12	no	—
64	#126	—	47	12	no	—
65	#126	—	47	4	no	—
66	#125	—	47	12	no	—
67	#125	—	47	12	no	—
68	#125	—	47	12	no	—
69	#125	—	47	12	no	—
70	#125	—	47	3	no	—
71	#125	C₂×D₄₇	1	3	yes	—
72	#125	C₂×D₄₇	1	12	yes	—
73	C₂²⋊Q₈	—	47	12	no	—
74	C₄×Q₈	—	47	12	no	—
75	C₄×Q₈	—	47	12	no	—
76	C₄×Q₈	—	47	12	no	—
77	#117	—	47	6	no	—
78	C₂×C₄²	—	47	1	no	—
79	C₂×Q₈	—	47	12	no	—
80	C₂²×C₄	—	47	3	no	—
81	C₄⋊C₄	—	47	12	no	—
82	C₄⋊C₄	—	47	12	no	—
83	C₄⋊C₄	—	47	12	no	—
84	C₄⋊C₄	—	47	12	no	—
85	C₄⋊C₄	—	47	6	no	—
86	C₄⋊C₄	—	47	12	no	—
87	C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
88	C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
89	C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
90	C₂²⋊C₄	—	47	12	no	—
91	C₄²	—	47	3	no	—
92	C₄²	—	47	12	no	—
93	C₄²	—	47	12	no	—
94	C₄²	C₂²×D₄₇	1	1	yes	characteristic
95	C₄²	C₂²×D₄₇	1	4	yes	—
96	C₂³	—	47	1	no	—
97	Q₈	—	94	24	no	—
98	C₂×C₄	—	47	3	no	—
99	C₂×C₄	—	47	12	no	—
100	C₂×C₄	—	94	6	no	—
101	C₂×C₄	C₂³×D₄₇	1	12	yes	—
102	C₂×C₄	C₂³×D₄₇	1	3	yes	—
103	C₂²	—	94	3	no	—
104	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
105	C₄	—	2	3	no	—
106	C₄	—	2	12	no	—
107	C₄	—	47	6	no	—
108	C₄	—	94	12	no	—
109	C₂	—	188	1	no	—
110	C₂	2₋¹⁺⁴×D₄₇	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₇⋊#564

C₂

yes

maximal, complemented

#15689850

C₂

yes

maximal, complemented

#15689732

C₂

yes

maximal

#15689679

C₂

yes

maximal

C₄₇×#564

C₂

yes

maximal, characteristic, complemented

#13094023

C₂²

yes

—

#13094023

C₂²

yes

—

#13094019

C₂²

yes

—

#13094018

C₂²

yes

—

#13094016

C₂²

yes

—

#13094015

C₂²

yes

—

#13094014

C₂²

yes

—

#13094014

C₂²

yes

—

#13094014

C₂²

yes

—

#13094002

C₂²

yes

—

C₄×Dic₉₄

C₂²

yes

—

#13093989

C₂²

yes

—

#13093989

C₂²

yes

—

#13093982

C₂²

yes

—

C₄²×D₄₇

C₂²

yes

characteristic

#125×C₄₇

C₂²

yes

—

#125×C₄₇

C₂²

yes

—

C₂×C₄×D₄₇

C₂³

yes

—

C₂×Dic₉₄

C₂³

yes

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂³

yes

—

(C₂×D₄₇)⋊C₄

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

C₂³

yes

—

Dic₄₇⋊C₄

C₂³

yes

—

Dic₄₇⋊C₄

C₂³

yes

—

Dic₄₇⋊C₄

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₂²×D₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

C₂⁴

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

—

C₂×Dic₄₇

C₂⁴

yes

—

C₂×Dic₄₇

C₂⁴

yes

—

C₄×D₄₇

—

Dic₉₄

—

C₂²×C₄₇

C₂⁵

yes

characteristic

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

2₋¹⁺⁴

yes

—

#3556

—

maximal, Sylow

C₂×C₄₇

C₂×2₋¹⁺⁴

yes

—

D₄₇

—

#564

—

#564

D₄₇

yes

characteristic, complemented

#557

—

#541

—

#533

—

C₄₇

#3556

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

—

—

—

—

—

—

—

—

C₂×D₄₇

yes

—

#125

C₂×D₄₇

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

C₂²×D₄₇

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

C₄²

C₂²×D₄₇

yes

—

C₂³

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₂³×D₄₇

yes

—

102

C₂×C₄

C₂³×D₄₇

yes

—

103

C₂²

—

104

C₂²

C₂⁴×D₄₇

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₂

—

188

—

110

C₂

2₋¹⁺⁴×D₄₇

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#564	C₂
hypercenter	#564	D₄₇
hypocenter	C₄₇	#3556
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #564

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₄₇

commutator, socle

C₂²×C₄₇

C₂⁵

Fitting

C₄₇×#564

C₂

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂² ◁ #564

N	H ≅ G/N	type
1. C₄₇⋊#564	C₂	semidirect
2. #15689850	C₂	semidirect
5. C₄₇×#564	C₂	semidirect
57. #564	D₄₇	semidirect
61. C₄₇	#3556	semidirect

H ≅ G/N

type

1. C₄₇⋊#564

C₂

semidirect

2. #15689850

C₂

semidirect

5. C₄₇×#564

C₂

semidirect

57. #564

D₄₇

semidirect

61. C₄₇

#3556

semidirect

Subgroups — #20257882

Conjugacy classes of subgroups

Complements