Group #20243133 — subgroups

Subgroups — #20243133

Order 6016.

296 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 173 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×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#15688877	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄×Dic₄₇	C₄	1	2	yes	—
7	C₂×C₄×Dic₄₇	C₄	1	2	yes	—
8	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
9	C₄×C₄₇⋊C₈	C₄	1	4	yes	complemented
10	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
11	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₄₇	C₄	1	4	yes	complemented
13	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₇	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₄₇	—	2	4	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
19	C₄²×C₄₇	C₂×C₄	1	2	yes	—
20	C₄²×C₄₇	C₂×C₄	1	2	yes	—
21	C₄×Dic₄₇	—	2	4	no	—
22	C₄×Dic₄₇	—	2	4	no	—
23	C₄×Dic₄₇	C₈	1	8	yes	complemented
24	C₂×C₄₇⋊C₈	—	2	4	no	—
25	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
26	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₄₇	C₄²	1	2	yes	—
28	C₂×C₄×C₄₇	C₄²	1	2	yes	—
29	C₂×C₄×C₄₇	C₂×C₈	1	4	yes	—
30	C₂×C₄×C₄₇	M₁₆	1	4	yes	—
31	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	#41	1	4	yes	—
34	C₂×Dic₄₇	—	2	4	no	—
35	C₂×Dic₄₇	—	2	4	no	—
36	C₂×Dic₄₇	C₂×C₈	1	8	yes	—
37	C₈×C₄₇	—	2	4	no	—
38	C₄₇⋊C₈	—	2	4	no	—
39	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
40	C₂²×C₄₇	#117	1	2	yes	—
41	C₂²×C₄₇	C₂²×C₈	1	2	yes	—
42	C₂²×C₄₇	C₂×M₁₆	1	2	yes	—
43	C₄×C₄₇	C₄×C₈	1	4	yes	—
44	C₄×C₄₇	#97	1	4	yes	—
45	C₄×C₄₇	#117	1	2	yes	—
46	C₄×C₄₇	#117	1	2	yes	—
47	Dic₄₇	—	2	8	no	—
48	#1744	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	#376	1	1	yes	characteristic
50	C₂×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
51	C₂×C₄₇	C₂×#97	1	1	yes	characteristic
52	C₂×C₄₇	#431	1	4	yes	—
53	C₂×C₄×C₈	—	47	1	no	—
54	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
55	C₄³	—	47	1	no	—
56	#336	—	47	4	no	—
57	C₄₇	#1744	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₈	—	47	2	no	—
59	C₂²×C₈	C₂×D₄₇	1	2	yes	—
60	C₂×C₄²	—	47	2	no	—
61	C₂×C₄²	—	47	2	no	—
62	C₂×C₄²	—	47	2	no	—
63	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
64	C₄×C₈	—	47	4	no	—
65	C₄×C₈	Dic₄₇	1	4	yes	complemented
66	C₂²×C₄	—	47	4	no	—
67	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
68	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
69	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
70	C₂×C₈	—	2	4	no	—
71	C₂×C₈	—	47	4	no	—
72	C₂×C₈	—	94	4	no	—
73	C₂×C₈	C₂×Dic₄₇	1	4	yes	—
74	C₄²	—	47	8	no	—
75	C₄²	—	94	4	no	—
76	C₄²	—	94	4	no	—
77	C₄²	C₄×D₄₇	1	2	yes	—
78	C₄²	C₂×Dic₄₇	1	2	yes	—
79	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
80	C₂×C₄	—	47	8	no	—
81	C₂×C₄	—	94	4	no	—
82	C₂×C₄	—	94	4	no	—
83	C₂×C₄	C₈×D₄₇	1	4	yes	—
84	C₂×C₄	#10625324	1	4	yes	—
85	C₂×C₄	C₄×Dic₄₇	1	2	yes	—
86	C₂×C₄	C₄×Dic₄₇	1	2	yes	—
87	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
88	C₂×C₄	#10625350	1	4	yes	—
89	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
90	C₈	—	2	4	no	—
91	C₈	—	94	4	no	—
92	C₂²	C₂×C₄×Dic₄₇	1	1	yes	characteristic
93	C₂²	#13093981	1	2	yes	—
94	C₂²	C₂×C₈×D₄₇	1	2	yes	—
95	C₂²	C₂×#10625324	1	2	yes	—
96	C₄	—	94	8	no	—
97	C₄	C₈×Dic₄₇	1	4	yes	—
98	C₄	#13093934	1	4	yes	—
99	C₄	#13093981	1	2	yes	—
100	C₄	#13093983	1	2	yes	—
101	C₂	#15688969	1	1	yes	characteristic
102	C₂	C₂×C₈×Dic₄₇	1	1	yes	characteristic
103	C₂	C₂×#13093934	1	1	yes	characteristic
104	C₂	#15689174	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₄₇⋊C₈

C₂

yes

maximal, characteristic

C₄²×Dic₄₇

C₂

yes

maximal, characteristic

#15688877

C₂

yes

maximal

C₂×C₄×C₈×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₇

C₄

yes

—

C₂×C₄×Dic₄₇

C₄

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄×C₄₇⋊C₈

C₄

yes

complemented

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₈

yes

complemented

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₄²

yes

—

C₂×C₄×C₄₇

C₄²

yes

—

C₂×C₄×C₄₇

C₂×C₈

yes

—

C₂×C₄×C₄₇

M₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×C₈

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₄²

yes

characteristic

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

C₂²×C₈

yes

—

C₂²×C₄₇

C₂×M₁₆

yes

—

C₄×C₄₇

C₄×C₈

yes

—

C₄×C₄₇

#97

yes

—

C₄×C₄₇

#117

yes

—

C₄×C₄₇

#117

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×C₄×C₈

yes

characteristic

C₂×C₄₇

C₂×#97

yes

characteristic

C₂×C₄₇

#431

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₄₇

yes

characteristic

C₄³

—

#336

—

C₄₇

#1744

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄×C₈

—

C₄×C₈

Dic₄₇

yes

complemented

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₄₇

yes

—

C₄²

C₂×Dic₄₇

yes

—

C₂³

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₇

yes

—

C₂×C₄

#10625324

yes

—

C₂×C₄

C₄×Dic₄₇

yes

—

C₂×C₄

C₄×Dic₄₇

yes

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

#10625350

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

—

C₈

—

C₂²

C₂×C₄×Dic₄₇

yes

characteristic

C₂²

#13093981

yes

—

C₂²

C₂×C₈×D₄₇

yes

—

C₂²

C₂×#10625324

yes

—

C₄

—

C₄

C₈×Dic₄₇

yes

—

C₄

#13093934

yes

—

C₄

#13093981

yes

—

100

C₄

#13093983

yes

—

101

C₂

#15688969

yes

characteristic

102

C₂

C₂×C₈×Dic₄₇

yes

characteristic

103

C₂

C₂×#13093934

yes

characteristic

104

C₂

#15689174

yes

—

	subgroup	G/H
center	C₂×C₄²	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	#1744
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄²

C₂×D₄₇

commutator

C₂×C₄₇

C₂×C₄×C₈

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 ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
9. C₄×C₄₇⋊C₈	C₄	semidirect
12. C₄×C₈×C₄₇	C₄	semidirect
23. C₄×Dic₄₇	C₈	semidirect
57. C₄₇	#1744	semidirect
65. C₄×C₈	Dic₄₇	semidirect

H ≅ G/N

type

9. C₄×C₄₇⋊C₈

C₄

semidirect

12. C₄×C₈×C₄₇

C₄

semidirect

23. C₄×Dic₄₇

C₈

semidirect

57. C₄₇

#1744

semidirect

65. C₄×C₈

Dic₄₇

semidirect

Subgroups — #20243133

Conjugacy classes of subgroups

Complements