Group #20243524 — subgroups

Subgroups — #20243524

Order 6016.

188 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 81 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	#15689146	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#15688888	C₂	1	1	yes	maximal, characteristic
4	#15688887	C₂	1	2	yes	maximal
5	C₄₇×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	Dic₄₇⋊C₈	—	2	4	no	—
10	C₈×Dic₄₇	C₄	1	2	yes	—
11	C₈×Dic₄₇	C₄	1	2	yes	—
12	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
15	C₂²×Dic₄₇	Q₈	1	2	yes	—
16	M₁₆×C₄₇	—	2	2	no	—
17	M₁₆×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	—	2	2	no	—
19	C₂×C₈×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
21	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₄₇	D₄	1	2	yes	—
24	#10625329	—	2	2	no	—
25	#10625329	—	2	2	no	—
26	C₂×C₄₇⋊C₈	—	2	2	no	—
27	C₂×C₄₇⋊C₈	—	2	2	no	—
28	C₂×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
29	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	#41	1	2	yes	—
33	C₂×C₄×C₄₇	#41	1	2	yes	—
34	C₂×Dic₄₇	—	2	4	no	—
35	C₂×Dic₄₇	C₄⋊C₄	1	2	yes	—
36	C₂×Dic₄₇	C₄⋊C₄	1	2	yes	—
37	C₈×C₄₇	—	2	2	no	—
38	C₈×C₄₇	—	4	2	no	—
39	C₄₇⋊C₈	—	2	2	no	—
40	C₄₇⋊C₈	—	4	2	no	—
41	C₂²×C₄₇	—	2	2	no	—
42	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₄₇	#125	1	2	yes	—
44	C₄×C₄₇	#117	1	1	yes	characteristic
45	C₄×C₄₇	#117	1	1	yes	characteristic
46	C₄×C₄₇	#124	1	2	yes	—
47	Dic₄₇	—	2	2	no	—
48	Dic₄₇	#108	1	4	yes	—
49	#1837	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	—	2	2	no	—
51	C₂×C₄₇	#382	1	1	yes	characteristic
52	C₂×C₄₇	C₂×#108	1	2	yes	—
53	#423	—	47	2	no	—
54	C₂×C₄×C₈	—	47	1	no	—
55	#341	—	47	2	no	—
56	#341	—	47	1	no	—
57	#341	D₄₇	1	1	yes	characteristic
58	C₄₇	#1837	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	47	2	no	—
60	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
61	C₂²×C₈	—	47	1	no	—
62	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
63	C₂×C₄²	—	47	1	no	—
64	C₄⋊C₈	—	94	4	no	—
65	C₄×C₈	—	47	2	no	—
66	C₄×C₈	—	47	2	no	—
67	C₂²×C₄	—	47	2	no	—
68	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	94	2	no	—
72	M₁₆	—	94	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	47	2	no	—
76	C₂×C₈	—	94	2	no	—
77	C₂×C₈	—	94	2	no	—
78	C₂×C₈	C₄×D₄₇	1	2	yes	—
79	C₄²	—	47	1	no	—
80	C₄²	—	47	1	no	—
81	C₄²	—	47	2	no	—
82	C₂³	Q₈×D₄₇	1	1	yes	characteristic
83	C₂×C₄	—	47	2	no	—
84	C₂×C₄	—	47	2	no	—
85	C₂×C₄	—	94	4	no	—
86	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
87	C₂×C₄	#10625350	1	2	yes	—
88	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
89	C₂×C₄	#10625352	1	2	yes	—
90	C₈	—	2	2	no	—
91	C₈	—	4	2	no	—
92	C₈	—	94	2	no	—
93	C₈	—	188	2	no	—
94	C₂²	—	2	2	no	—
95	C₂²	C₄⋊C₄×D₄₇	1	1	yes	characteristic
96	C₂²	#13094014	1	2	yes	—
97	C₄	—	47	4	no	—
98	C₄	—	94	2	no	—
99	C₄	#13093980	1	1	yes	characteristic
100	C₄	#13093981	1	1	yes	characteristic
101	C₄	#13094010	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	#15688987	1	1	yes	characteristic
104	C₂	#108×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689146

C₂

yes

maximal

C₂×C₈×Dic₄₇

C₂

yes

maximal, characteristic

#15688888

C₂

yes

maximal, characteristic

#15688887

C₂

yes

maximal

C₄₇×#341

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

—

C₂²×C₄₇⋊C₈

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

Dic₄₇⋊C₈

—

C₈×Dic₄₇

C₄

yes

—

C₈×Dic₄₇

C₄

yes

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

Q₈

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₄×Dic₄₇

D₄

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

#125

yes

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

Dic₄₇

#108

yes

—

#1837

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#382

yes

characteristic

C₂×C₄₇

C₂×#108

yes

—

#423

—

C₂×C₄×C₈

—

#341

—

#341

—

#341

D₄₇

yes

characteristic

C₄₇

#1837

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

—

C₄²

—

C₄²

—

C₄²

—

C₂³

Q₈×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

#10625350

yes

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₂×C₄

#10625352

yes

—

C₈

—

C₈

—

C₈

—

C₈

—

188

—

C₂²

—

C₂²

C₄⋊C₄×D₄₇

yes

characteristic

C₂²

#13094014

yes

—

C₄

—

C₄

—

C₄

#13093980

yes

characteristic

100

C₄

#13093981

yes

characteristic

101

C₄

#13094010

yes

—

102

C₂

—

103

C₂

#15688987

yes

characteristic

104

C₂

#108×D₄₇

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#341	C₂
socle	C₂²×C₄₇	C₂×C₄⋊C₄
hypercenter	#341	D₄₇
hypocenter	C₄₇	#1837
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#341

C₂

socle

C₂²×C₄₇

C₂×C₄⋊C₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
58. C₄₇	#1837	semidirect

H ≅ G/N

type

58. C₄₇

#1837

semidirect

Subgroups — #20243524

Conjugacy classes of subgroups

Complements