Group #20243090 — subgroups

Subgroups — #338×D₄₇ #20243090

Order 6016.

372 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 135 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×M₁₆×D₄₇	C₂	1	3	yes	maximal
2	C₄₇⋊#338	C₂	1	3	yes	maximal, complemented
3	C₄₇×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
5	C₂×#10625329	C₂²	1	3	yes	—
6	C₂×#10625324	C₄	1	6	yes	—
7	M₁₆×D₄₇	—	2	6	no	—
8	M₁₆×D₄₇	—	2	6	no	—
9	C₂×C₈×D₄₇	C₄	1	6	yes	—
10	C₂×M₁₆×C₄₇	C₂²	1	3	yes	—
11	C₂³×D₄₇	Q₈	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
13	C₂²×Dic₄₇	Q₈	1	1	yes	characteristic
14	C₂×C₄×D₄₇	C₂×C₄	1	3	yes	—
15	C₂×C₄×D₄₇	C₂×C₄	1	3	yes	—
16	C₂×C₄×D₄₇	D₄	1	3	yes	—
17	C₂×C₄×D₄₇	D₄	1	3	yes	—
18	M₁₆×C₄₇	—	2	6	no	—
19	C₂×C₈×C₄₇	C₂×C₄	1	6	yes	—
20	#10625329	—	2	6	no	—
21	C₂×C₄₇⋊C₈	C₂×C₄	1	6	yes	—
22	#10625324	—	2	12	no	—
23	C₈×D₄₇	—	2	6	no	—
24	C₈×D₄₇	—	2	6	no	—
25	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
26	C₂²×D₄₇	—	4	2	no	—
27	C₂²×D₄₇	C₄⋊C₄	1	3	yes	—
28	C₂²×D₄₇	C₄⋊C₄	1	3	yes	—
29	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
30	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
31	C₂×Dic₄₇	C₄⋊C₄	1	3	yes	—
32	C₂×Dic₄₇	C₄⋊C₄	1	3	yes	—
33	C₄×D₄₇	C₄²	1	3	yes	—
34	C₄×D₄₇	C₄²	1	1	yes	characteristic
35	C₄×D₄₇	C₂²⋊C₄	1	3	yes	—
36	C₄×D₄₇	C₂²⋊C₄	1	3	yes	—
37	C₄×D₄₇	C₂²⋊C₄	1	6	yes	—
38	C₈×C₄₇	—	2	6	no	—
39	C₄₇⋊C₈	—	2	6	no	—
40	C₂²×C₄₇	—	4	1	no	—
41	C₂²×C₄₇	C₂×C₄⋊C₄	1	3	yes	—
42	C₂×D₄₇	—	2	6	no	—
43	C₂×D₄₇	—	4	3	no	—
44	C₂×D₄₇	#95	1	3	yes	—
45	C₂×D₄₇	#95	1	1	yes	characteristic
46	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
47	C₄×C₄₇	C₂×C₂²⋊C₄	1	3	yes	—
48	Dic₄₇	#95	1	1	yes	characteristic
49	Dic₄₇	#95	1	3	yes	—
50	C₂×#338	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	—	2	3	no	—
52	C₂×C₄₇	C₂×#95	1	1	yes	characteristic
53	D₄₇	—	2	3	no	—
54	D₄₇	#338	1	2	yes	direct product factor
55	C₂²×M₁₆	—	47	3	no	—
56	#338	—	47	3	no	—
57	#338	D₄₇	1	1	yes	characteristic, direct product factor
58	C₄₇	C₂×#338	1	1	yes	characteristic, complemented, Sylow
59	C₂³×C₄	—	47	1	no	—
60	C₂×M₁₆	—	47	3	no	—
61	C₂×M₁₆	—	47	6	no	—
62	C₂×M₁₆	—	94	6	no	—
63	C₂×M₁₆	—	94	6	no	—
64	C₂×M₁₆	C₂×D₄₇	1	3	yes	—
65	C₂²×C₈	—	47	6	no	—
66	C₂⁴	—	47	1	no	—
67	C₂²×C₄	—	47	1	no	—
68	C₂²×C₄	—	47	3	no	—
69	C₂²×C₄	—	47	3	no	—
70	C₂²×C₄	—	47	3	no	—
71	C₂²×C₄	—	47	3	no	—
72	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
73	M₁₆	—	2	6	no	—
74	M₁₆	—	94	12	no	—
75	M₁₆	—	94	6	no	—
76	C₂×C₈	—	47	6	no	—
77	C₂×C₈	—	94	6	no	—
78	C₂×C₈	—	94	6	no	—
79	C₂×C₈	C₄×D₄₇	1	6	yes	—
80	C₂³	—	47	3	no	—
81	C₂³	—	47	3	no	—
82	C₂³	—	188	2	no	—
83	C₂³	Q₈×D₄₇	1	1	yes	characteristic
84	C₂×C₄	—	47	3	no	—
85	C₂×C₄	—	47	3	no	—
86	C₂×C₄	—	47	1	no	—
87	C₂×C₄	—	47	3	no	—
88	C₂×C₄	—	47	3	no	—
89	C₂×C₄	—	47	3	no	—
90	C₂×C₄	—	47	6	no	—
91	C₂×C₄	C₂×C₄×D₄₇	1	3	yes	—
92	C₂×C₄	D₄×D₄₇	1	3	yes	—
93	C₈	—	2	6	no	—
94	C₈	—	94	6	no	—
95	C₂²	—	4	1	no	—
96	C₂²	—	47	1	no	—
97	C₂²	—	47	3	no	—
98	C₂²	—	94	6	no	—
99	C₂²	—	188	3	no	—
100	C₂²	C₄⋊C₄×D₄₇	1	3	yes	—
101	C₄	—	47	1	no	—
102	C₄	—	47	3	no	—
103	C₄	C₄²×D₄₇	1	1	yes	characteristic
104	C₄	C₂²⋊C₄×D₄₇	1	3	yes	—
105	C₂	—	2	3	no	—
106	C₂	—	47	2	no	—
107	C₂	—	94	3	no	—
108	C₂	#95×D₄₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×M₁₆×D₄₇

C₂

yes

maximal

C₄₇⋊#338

C₂

yes

maximal, complemented

C₄₇×#338

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

—

C₂×#10625324

C₄

yes

—

M₁₆×D₄₇

—

M₁₆×D₄₇

—

C₂×C₈×D₄₇

C₄

yes

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂³×D₄₇

Q₈

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

Q₈

yes

characteristic

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

C₂×C₄

yes

—

C₂×C₄×D₄₇

D₄

yes

—

C₂×C₄×D₄₇

D₄

yes

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

#10625329

—

C₂×C₄₇⋊C₈

C₂×C₄

yes

—

#10625324

—

C₈×D₄₇

—

C₈×D₄₇

—

C₂³×C₄₇

C₂×Q₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

C₄⋊C₄

yes

—

C₂²×D₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₄×D₄₇

C₄²

yes

—

C₄×D₄₇

C₄²

yes

characteristic

C₄×D₄₇

C₂²⋊C₄

yes

—

C₄×D₄₇

C₂²⋊C₄

yes

—

C₄×D₄₇

C₂²⋊C₄

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

#95

yes

—

C₂×D₄₇

#95

yes

characteristic

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

C₂×C₂²⋊C₄

yes

—

Dic₄₇

#95

yes

characteristic

Dic₄₇

#95

yes

—

C₂×#338

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×#95

yes

characteristic

D₄₇

—

D₄₇

#338

yes

direct product factor

C₂²×M₁₆

—

#338

—

#338

D₄₇

yes

characteristic, direct product factor

C₄₇

C₂×#338

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

—

C₂³

—

C₂³

—

C₂³

—

188

—

C₂³

Q₈×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₄

D₄×D₄₇

yes

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

188

—

100

C₂²

C₄⋊C₄×D₄₇

yes

—

101

C₄

—

102

C₄

—

103

C₄

C₄²×D₄₇

yes

characteristic

104

C₄

C₂²⋊C₄×D₄₇

yes

—

105

C₂

—

106

C₂

—

107

C₂

—

108

C₂

#95×D₄₇

yes

characteristic

	subgroup	G/H
center	C₄	C₄²×D₄₇
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#338	C₂
socle	C₂×C₄₇	C₂×#95
hypercenter	#338	D₄₇
hypocenter	C₄₇	C₂×#338
LCS	G ▷ C₄×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ #338

subgroup

G/H

center

C₄

C₄²×D₄₇

commutator

C₄×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#338

C₂

socle

C₂×C₄₇

C₂×#95

D₄₇

C₄₇

G ▷ C₄×C₄₇ ▷ C₄₇

C₁ ◁ C₄ ◁ #338

N	H ≅ G/N	type
2. C₄₇⋊#338	C₂	semidirect
3. C₄₇×#338	C₂	semidirect
54. D₄₇	#338	direct (N × H)
57. #338	D₄₇	direct (N × H)
58. C₄₇	C₂×#338	semidirect

H ≅ G/N

type

2. C₄₇⋊#338

C₂

semidirect

3. C₄₇×#338

C₂

semidirect

54. D₄₇

#338

direct (N × H)

57. #338

D₄₇

direct (N × H)

58. C₄₇

C₂×#338

semidirect

Subgroups — #338×D₄₇ #20243090

Conjugacy classes of subgroups

Complements

Subgroups — #338×D47 #20243090

Conjugacy classes of subgroups

Complements

Subgroups — #338×D₄₇ #20243090