Group #20257536 — subgroups

Subgroups — #20257536

Order 6016.

930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 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	#15689877	C₂	1	10	yes	maximal, complemented
2	#15689871	C₂	1	5	yes	maximal, complemented
3	#15689679	C₂	1	5	yes	maximal, complemented
4	#15689658	C₂	1	10	yes	maximal, complemented
5	C₄₇×#564	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094023	C₂²	1	10	yes	—
7	#13094019	C₂²	1	20	yes	—
8	#13094016	C₂²	1	5	yes	—
9	#13094012	C₂²	1	10	yes	—
10	#13094009	C₂²	1	20	yes	—
11	#13094004	C₂²	1	10	yes	—
12	#13094002	C₂²	1	20	yes	—
13	#13093999	C₂²	1	10	yes	—
14	#13093989	C₂²	1	10	yes	—
15	#13093986	C₂²	1	10	yes	—
16	#13093982	C₂²	1	10	yes	—
17	C₄²×D₄₇	C₂²	1	5	yes	—
18	#125×C₄₇	C₂²	1	5	yes	—
19	#125×C₄₇	C₂²	1	10	yes	—
20	C₂×D₁₈₈	C₂³	1	10	yes	—
21	C₂×C₄×D₄₇	C₂³	1	5	yes	—
22	C₂×C₄×D₄₇	C₂³	1	10	yes	—
23	C₂×Dic₉₄	C₂³	1	10	yes	—
24	C₄⋊C₄×C₄₇	C₂³	1	10	yes	—
25	C₄⋊C₄×C₄₇	C₂³	1	10	yes	—
26	C₄⋊C₄×C₄₇	C₂³	1	10	yes	—
27	C₄²×C₄₇	C₂³	1	5	yes	—
28	(C₂×D₄₇)⋊C₄	C₂³	1	20	yes	—
29	(C₂×D₄₇)⋊C₄	C₂³	1	20	yes	—
30	C₄⋊Dic₄₇	C₂³	1	10	yes	—
31	Dic₄₇⋊C₄	C₂³	1	20	yes	—
32	C₄×Dic₄₇	C₂³	1	10	yes	—
33	C₄×Dic₄₇	C₂³	1	5	yes	—
34	C₂²×D₄₇	C₂⁴	1	5	yes	—
35	C₂×C₄×C₄₇	C₂⁴	1	10	yes	—
36	C₂×C₄×C₄₇	C₂⁴	1	5	yes	—
37	C₂×Dic₄₇	C₂⁴	1	10	yes	—
38	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
39	D₁₈₈	—	4	10	no	—
40	C₄×D₄₇	—	2	10	no	—
41	C₄×D₄₇	—	4	10	no	—
42	Dic₉₄	—	4	10	no	—
43	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
44	C₂×D₄₇	—	2	5	no	—
45	C₂×D₄₇	—	2	10	no	—
46	C₄×C₄₇	—	2	5	no	—
47	C₄×C₄₇	—	2	10	no	—
48	Dic₄₇	—	2	10	no	—
49	Dic₄₇	2₋¹⁺⁴	1	2	yes	—
50	#3531	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
52	C₂×C₄₇	#585	1	2	yes	—
53	D₄₇	—	4	5	no	—
54	#564	D₄₇	1	1	yes	characteristic, complemented
55	#563	—	47	10	no	—
56	#562	—	47	5	no	—
57	#533	—	47	5	no	—
58	#529	—	47	10	no	—
59	C₄₇	#3531	1	1	yes	characteristic, complemented, Sylow
60	C₄⋊Q₈	—	47	10	no	—
61	#126	—	47	20	no	—
62	#125	—	47	5	no	—
63	#125	C₂×D₄₇	1	10	yes	—
64	#125	C₂×D₄₇	1	5	yes	—
65	#124	—	47	10	no	—
66	#123	—	47	20	no	—
67	C₂²⋊Q₈	—	47	10	no	—
68	C₂²⋊Q₈	—	47	20	no	—
69	#121	—	47	10	no	—
70	C₄×Q₈	—	47	10	no	—
71	C₄×D₄	—	47	10	no	—
72	#117	—	47	10	no	—
73	C₂×C₄²	—	47	5	no	—
74	C₂×Q₈	—	47	10	no	—
75	C₂×D₄	—	47	10	no	—
76	C₂²×C₄	—	47	5	no	—
77	C₂²×C₄	—	47	10	no	—
78	C₄⋊C₄	—	47	20	no	—
79	C₄⋊C₄	—	47	10	no	—
80	C₄⋊C₄	C₂²×D₄₇	1	10	yes	—
81	C₄⋊C₄	C₂²×D₄₇	1	10	yes	—
82	C₄⋊C₄	C₂²×D₄₇	1	10	yes	—
83	C₂²⋊C₄	—	47	20	no	—
84	C₂²⋊C₄	—	47	20	no	—
85	C₄²	—	47	10	no	—
86	C₄²	—	47	5	no	—
87	C₄²	C₂²×D₄₇	1	5	yes	—
88	C₂³	—	47	5	no	—
89	Q₈	—	188	10	no	—
90	D₄	—	188	10	no	—
91	C₂×C₄	—	47	1	no	—
92	C₂×C₄	—	47	10	no	—
93	C₂×C₄	—	94	10	no	—
94	C₂×C₄	—	188	10	no	—
95	C₂×C₄	C₂³×D₄₇	1	5	yes	—
96	C₂×C₄	C₂³×D₄₇	1	10	yes	—
97	C₂²	—	94	5	no	—
98	C₂²	—	94	10	no	—
99	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
100	C₄	—	2	5	no	—
101	C₄	—	2	10	no	—
102	C₄	—	47	2	no	—
103	C₄	—	94	10	no	—
104	C₂	—	188	5	no	—
105	C₂	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
106	C₂	#15689960	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689877

C₂

yes

maximal, complemented

#15689871

C₂

yes

maximal, complemented

#15689679

C₂

yes

maximal, complemented

#15689658

C₂

yes

maximal, complemented

C₄₇×#564

C₂

yes

maximal, characteristic, complemented

#13094023

C₂²

yes

—

#13094019

C₂²

yes

—

#13094016

C₂²

yes

—

#13094012

C₂²

yes

—

#13094009

C₂²

yes

—

#13094004

C₂²

yes

—

#13094002

C₂²

yes

—

#13093999

C₂²

yes

—

#13093989

C₂²

yes

—

#13093986

C₂²

yes

—

#13093982

C₂²

yes

—

C₄²×D₄₇

C₂²

yes

—

#125×C₄₇

C₂²

yes

—

#125×C₄₇

C₂²

yes

—

C₂×D₁₈₈

C₂³

yes

—

C₂×C₄×D₄₇

C₂³

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

—

(C₂×D₄₇)⋊C₄

C₂³

yes

—

(C₂×D₄₇)⋊C₄

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₄×Dic₄₇

C₂³

yes

—

C₂²×D₄₇

C₂⁴

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

—

C₂×Dic₄₇

C₂⁴

yes

—

C₂×Dic₄₇

C₂⁴

yes

characteristic

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₂²×C₄₇

C₂⁵

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

2₋¹⁺⁴

yes

—

#3531

—

maximal, Sylow

C₂×C₄₇

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₄₇

#585

yes

—

D₄₇

—

#564

D₄₇

yes

characteristic, complemented

—

—

—

—

C₄₇

#3531

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

#126

—

#125

—

#125

C₂×D₄₇

yes

—

#125

C₂×D₄₇

yes

—

#124

—

#123

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

C₂²×D₄₇

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₇

yes

—

C₂³

—

Q₈

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂³×D₄₇

yes

—

C₂×C₄

C₂³×D₄₇

yes

—

C₂²

—

C₂²

—

C₂²

C₂⁴×D₄₇

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₂

—

188

—

105

C₂

2₋¹⁺⁴×D₄₇

yes

characteristic

106

C₂

#15689960

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#564	C₂
hypercenter	#564	D₄₇
hypocenter	C₄₇	#3531
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. #15689877	C₂	semidirect
2. #15689871	C₂	semidirect
3. #15689679	C₂	semidirect
4. #15689658	C₂	semidirect
5. C₄₇×#564	C₂	semidirect
54. #564	D₄₇	semidirect
59. C₄₇	#3531	semidirect

H ≅ G/N

type

1. #15689877

C₂

semidirect

2. #15689871

C₂

semidirect

3. #15689679

C₂

semidirect

4. #15689658

C₂

semidirect

5. C₄₇×#564

C₂

semidirect

54. #564

D₄₇

semidirect

59. C₄₇

#3531

semidirect

Subgroups — #20257536

Conjugacy classes of subgroups

Complements