Group #20242691 — subgroups

Subgroups — #20242691

Order 6016.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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	1	yes	maximal, characteristic, complemented
2	#15689489	C₂	1	1	yes	maximal, characteristic
3	#15689488	C₂	1	2	yes	maximal
4	#15688864	C₂	1	2	yes	maximal, complemented
5	C₄₇×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094021	C₂²	1	1	yes	characteristic
7	#13094016	C₂²	1	2	yes	—
8	#13094015	—	2	2	no	—
9	#13094014	—	2	2	no	—
10	#13094014	—	2	2	no	—
11	#13093946	—	2	2	no	—
12	#13093946	—	2	2	no	—
13	#13093944	—	2	2	no	—
14	#13093935	C₂²	1	1	yes	characteristic
15	#125×C₄₇	C₂²	1	1	yes	characteristic
16	#97×C₄₇	C₂²	1	2	yes	—
17	C₂×D₁₈₈	—	2	1	no	—
18	C₂×D₁₈₈	—	2	2	no	—
19	C₂×C₈×C₄₇	—	2	2	no	—
20	C₄⋊C₄×C₄₇	—	2	2	no	—
21	C₄⋊C₄×C₄₇	D₄	1	2	yes	—
22	C₄²×C₄₇	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₇	—	2	2	no	—
24	C₄⋊Dic₄₇	D₄	1	2	yes	—
25	C₄⋊Dic₄₇	D₄	1	2	yes	—
26	Dic₄₇⋊C₄	—	2	2	no	—
27	Dic₄₇⋊C₄	—	2	2	no	—
28	Dic₄₇⋊C₄	—	2	2	no	—
29	Dic₄₇⋊C₄	—	2	2	no	—
30	C₄×Dic₄₇	—	2	2	no	—
31	C₂×C₄₇⋊C₈	—	2	1	no	—
32	C₂²×D₄₇	—	4	1	no	—
33	C₂×C₄×C₄₇	—	2	2	no	—
34	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
36	C₂×Dic₄₇	—	2	2	no	—
37	C₂×Dic₄₇	—	2	2	no	—
38	D₁₈₈	—	4	2	no	—
39	D₁₈₈	—	4	4	no	—
40	C₈×C₄₇	—	4	2	no	—
41	C₄₇⋊C₈	—	4	1	no	—
42	C₂²×C₄₇	#120	1	1	yes	characteristic
43	C₂×D₄₇	—	8	2	no	—
44	C₂×D₄₇	—	8	1	no	—
45	C₄×C₄₇	—	2	1	no	—
46	C₄×C₄₇	—	2	2	no	—
47	C₄×C₄₇	—	4	2	no	—
48	Dic₄₇	—	4	2	no	—
49	Dic₄₇	—	4	2	no	—
50	#1658	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	#454	1	2	yes	—
52	C₂×C₄₇	#454	1	1	yes	characteristic
53	D₄₇	—	16	1	no	—
54	#564	—	47	1	no	—
55	#490	—	47	1	no	—
56	#490	—	47	2	no	—
57	#330	—	47	2	no	—
58	#330	D₄₇	1	1	yes	characteristic, complemented
59	C₄₇	#1658	1	1	yes	characteristic, complemented, Sylow
60	#127	—	47	1	no	—
61	#125	—	47	2	no	—
62	#125	—	94	2	no	—
63	#125	—	94	2	no	—
64	#125	—	94	2	no	—
65	#125	C₂×D₄₇	1	1	yes	characteristic
66	#102	—	94	2	no	—
67	#102	—	94	2	no	—
68	#102	—	94	2	no	—
69	#97	—	47	1	no	—
70	#97	C₂×D₄₇	1	2	yes	—
71	C₂×D₄	—	94	1	no	—
72	C₂×D₄	—	94	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	94	1	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	47	2	no	—
77	C₄⋊C₄	—	47	2	no	—
78	C₄⋊C₄	—	94	2	no	—
79	C₄⋊C₄	—	94	2	no	—
80	C₄⋊C₄	—	94	2	no	—
81	C₄⋊C₄	—	94	2	no	—
82	C₄⋊C₄	—	94	2	no	—
83	C₄⋊C₄	D₁₈₈	1	2	yes	—
84	C₄²	—	94	2	no	—
85	C₄²	C₂²×D₄₇	1	1	yes	characteristic
86	C₂³	—	188	1	no	—
87	D₄	—	188	4	no	—
88	D₄	—	188	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	94	2	no	—
91	C₂×C₄	—	94	2	no	—
92	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
93	C₂×C₄	D₄×D₄₇	1	2	yes	—
94	C₈	—	4	2	no	—
95	C₈	—	188	1	no	—
96	C₂²	—	376	2	no	—
97	C₂²	—	376	1	no	—
98	C₂²	#13093994	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	—	188	2	no	—
103	C₄	—	188	2	no	—
104	C₂	—	752	1	no	—
105	C₂	#15689297	1	2	yes	—
106	C₂	#15689298	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₇⋊#564

C₂

yes

maximal, characteristic, complemented

#15689489

C₂

yes

maximal, characteristic

#15689488

C₂

yes

maximal

#15688864

C₂

yes

maximal, complemented

C₄₇×#330

C₂

yes

maximal, characteristic, complemented

#13094021

C₂²

yes

characteristic

#13094016

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

#125×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₂²

yes

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

—

C₄⋊Dic₄₇

D₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

#120

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#1658

—

maximal, Sylow

C₂×C₄₇

#454

yes

—

C₂×C₄₇

#454

yes

characteristic

D₄₇

—

—

—

—

—

D₄₇

yes

characteristic, complemented

C₄₇

#1658

yes

characteristic, complemented, Sylow

—

—

—

—

—

C₂×D₄₇

yes

—

—

—

—

C₂×D₄₇

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₈₈

yes

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

188

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₂×C₄

D₄×D₄₇

yes

—

C₈

—

C₈

—

188

—

C₂²

—

376

—

C₂²

—

376

—

C₂²

#13093994

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

188

—

103

C₄

—

188

—

104

C₂

—

752

—

105

C₂

#15689297

yes

—

106

C₂

#15689298

yes

characteristic

	subgroup	G/H
center	C₂²	#13093994
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#330	C₂
socle	C₂²×C₄₇	#120
hypercenter	#330	D₄₇
hypocenter	C₄₇	#1658
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#13093994

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#330

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
1. C₄₇⋊#564	C₂	semidirect
4. #15688864	C₂	semidirect
5. C₄₇×#330	C₂	semidirect
58. #330	D₄₇	semidirect
59. C₄₇	#1658	semidirect

H ≅ G/N

type

1. C₄₇⋊#564

C₂

semidirect

4. #15688864

C₂

semidirect

5. C₄₇×#330

C₂

semidirect

58. #330

D₄₇

semidirect

59. C₄₇

#1658

semidirect

Subgroups — #20242691

Conjugacy classes of subgroups

Complements