Group #20243074 — subgroups

Subgroups — #20243074

Order 6016.

328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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×#13093935	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093934	C₂	1	2	yes	maximal
3	C₂×C₈×Dic₄₇	C₂	1	2	yes	maximal
4	#15688969	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
8	#13093935	C₄	1	4	yes	complemented
9	#13093934	C₄	1	8	yes	complemented
10	C₈×Dic₄₇	C₄	1	8	yes	complemented
11	C₄₇⋊#95	C₄	1	4	yes	—
12	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₇	C₄	1	4	yes	complemented
16	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₇	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
23	C₄²×C₄₇	C₂×C₄	1	2	yes	—
24	C₄²×C₄₇	C₂×C₄	1	2	yes	—
25	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
26	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
27	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
28	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
29	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
30	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	—	2	4	no	—
32	C₂×C₄×C₄₇	C₄²	1	4	yes	—
33	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
35	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₄₇	—	2	8	no	—
38	C₂×Dic₄₇	C₄²	1	8	yes	—
39	C₈×C₄₇	C₄²	1	4	yes	—
40	C₈×C₄₇	C₄²	1	4	yes	—
41	C₄₇⋊C₈	C₄²	1	8	yes	—
42	C₂²×C₄₇	C₂×C₄²	1	2	yes	—
43	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₄₇	#131	1	4	yes	—
45	C₄×C₄₇	—	2	4	no	—
46	C₄×C₄₇	C₂×C₄²	1	2	yes	—
47	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
48	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
49	Dic₄₇	—	2	8	no	—
50	#1726	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	C₄³	1	1	yes	characteristic
52	C₂×C₄₇	#405	1	4	yes	—
53	C₂×C₄₇	#405	1	2	yes	—
54	C₂×#97	—	47	2	no	—
55	C₂×#97	—	47	1	no	—
56	C₂×C₄×C₈	—	47	2	no	—
57	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
58	#376	—	47	1	no	—
59	C₄₇	#1726	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	47	2	no	—
61	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
62	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
63	C₂×C₄²	—	47	2	no	—
64	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
65	#97	—	47	8	no	—
66	#97	—	47	4	no	—
67	C₄×C₈	—	47	8	no	—
68	C₄×C₈	Dic₄₇	1	4	yes	complemented
69	#95	—	47	4	no	—
70	C₂²×C₄	—	47	4	no	—
71	C₂²×C₄	C₄×D₄₇	1	2	yes	—
72	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
73	C₂×C₈	—	47	4	no	—
74	C₂×C₈	—	47	4	no	—
75	C₂×C₈	—	47	4	no	—
76	C₂×C₈	C₄×D₄₇	1	4	yes	—
77	C₂×C₈	C₄×D₄₇	1	4	yes	—
78	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
79	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
80	C₄²	—	47	4	no	—
81	C₄²	—	47	4	no	—
82	C₄²	C₄×D₄₇	1	2	yes	—
83	C₄²	C₂×Dic₄₇	1	2	yes	—
84	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	47	8	no	—
87	C₂×C₄	—	94	8	no	—
88	C₂×C₄	C₄×Dic₄₇	1	4	yes	—
89	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
90	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
91	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
92	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
93	C₈	—	47	8	no	—
94	C₈	C₄×Dic₄₇	1	4	yes	—
95	C₈	C₄×Dic₄₇	1	4	yes	—
96	C₂²	C₄²×D₄₇	1	2	yes	—
97	C₂²	C₂×C₄×Dic₄₇	1	1	yes	characteristic
98	C₂²	#13094030	1	4	yes	—
99	C₄	—	2	4	no	—
100	C₄	—	94	8	no	—
101	C₄	C₄²×D₄₇	1	2	yes	—
102	C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
103	C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
104	C₂	C₄²×Dic₄₇	1	1	yes	characteristic
105	C₂	#15689077	1	4	yes	—
106	C₂	#15689078	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093935

C₂

yes

maximal, characteristic

C₂×#13093934

C₂

yes

maximal

C₂×C₈×Dic₄₇

C₂

yes

maximal

#15688969

C₂

yes

maximal, characteristic

C₂×C₄×C₈×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

#13093935

C₄

yes

complemented

#13093934

C₄

yes

complemented

C₈×Dic₄₇

C₄

yes

complemented

C₄₇⋊#95

C₄

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄²

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

C₄²

yes

—

C₈×C₄₇

C₄²

yes

—

C₈×C₄₇

C₄²

yes

—

C₄₇⋊C₈

C₄²

yes

—

C₂²×C₄₇

C₂×C₄²

yes

—

C₂²×C₄₇

C₂×C₄²

yes

characteristic

C₂²×C₄₇

#131

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄²

yes

—

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

C₂×C₄²

yes

characteristic

Dic₄₇

—

#1726

—

maximal, Sylow

C₂×C₄₇

C₄³

yes

characteristic

C₂×C₄₇

#405

yes

—

C₂×C₄₇

#405

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₄₇

yes

characteristic

#376

—

C₄₇

#1726

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#97

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₄₇

yes

complemented

#95

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₄²

—

C₄²

—

C₄²

C₄×D₄₇

yes

—

C₄²

C₂×Dic₄₇

yes

—

C₂³

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₄₇

yes

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

—

C₈

C₄×Dic₄₇

yes

—

C₈

C₄×Dic₄₇

yes

—

C₂²

C₄²×D₄₇

yes

—

C₂²

C₂×C₄×Dic₄₇

yes

characteristic

C₂²

#13094030

yes

—

C₄

—

100

C₄

—

101

C₄

C₄²×D₄₇

yes

—

102

C₄

C₂×C₄×Dic₄₇

yes

characteristic

103

C₄

C₂×C₄×Dic₄₇

yes

characteristic

104

C₂

C₄²×Dic₄₇

yes

characteristic

105

C₂

#15689077

yes

—

106

C₂

#15689078

yes

—

	subgroup	G/H
center	C₂²×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₄³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	#1726
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂²×C₈

C₂×D₄₇

commutator

C₂×C₄₇

C₄³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×C₄×C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂²×C₄

hypercenter

C₂×C₄×C₈

D₄₇

C₄₇

G ▷ C₂×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
8. #13093935	C₄	semidirect
9. #13093934	C₄	semidirect
10. C₈×Dic₄₇	C₄	semidirect
15. C₄×C₈×C₄₇	C₄	semidirect
59. C₄₇	#1726	semidirect
68. C₄×C₈	Dic₄₇	semidirect

H ≅ G/N

type

8. #13093935

C₄

semidirect

9. #13093934

C₄

semidirect

10. C₈×Dic₄₇

C₄

semidirect

15. C₄×C₈×C₄₇

C₄

semidirect

59. C₄₇

#1726

semidirect

68. C₄×C₈

Dic₄₇

semidirect

Subgroups — #20243074

Conjugacy classes of subgroups

Complements