Group #20239272 — subgroups

Subgroups — C₄₇×#1662 #20239272

Order 6016.

196 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 60 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×#562	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#491	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#489	C₂	1	2	yes	maximal, complemented
4	C₄₇×#330	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#329	C₂	1	2	yes	maximal, complemented
6	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
7	#125×C₄₇	C₂²	1	1	yes	characteristic
8	#124×C₄₇	C₂²	1	2	yes	—
9	#123×C₄₇	—	2	2	no	—
10	C₂²⋊Q₈×C₄₇	—	2	2	no	—
11	#121×C₄₇	—	2	2	no	—
12	#103×C₄₇	—	2	2	no	—
13	#103×C₄₇	—	2	2	no	—
14	#102×C₄₇	—	2	2	no	—
15	#97×C₄₇	C₂²	1	2	yes	—
16	#97×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₇	—	2	1	no	—
18	C₂×Q₈×C₄₇	D₄	1	2	yes	—
19	C₂×D₄×C₄₇	—	2	2	no	—
20	C₂×D₄×C₄₇	D₄	1	2	yes	—
21	C₂²×C₄×C₄₇	—	2	2	no	—
22	C₂×C₈×C₄₇	—	2	1	no	—
23	C₂×C₈×C₄₇	—	2	2	no	—
24	C₄⋊C₄×C₄₇	—	2	2	no	—
25	C₄⋊C₄×C₄₇	—	2	2	no	—
26	C₄⋊C₄×C₄₇	—	2	2	no	—
27	C₄⋊C₄×C₄₇	D₄	1	2	yes	—
28	C₂²⋊C₄×C₄₇	—	2	2	no	—
29	C₂²⋊C₄×C₄₇	—	2	2	no	—
30	C₂²⋊C₄×C₄₇	—	2	2	no	—
31	C₄²×C₄₇	C₂³	1	1	yes	characteristic
32	C₂³×C₄₇	—	2	2	no	—
33	Q₈×C₄₇	—	4	2	no	—
34	Q₈×C₄₇	—	4	2	no	—
35	D₄×C₄₇	—	4	2	no	—
36	D₄×C₄₇	—	8	2	no	—
37	C₂×C₄×C₄₇	—	2	2	no	—
38	C₂×C₄×C₄₇	—	2	2	no	—
39	C₂×C₄×C₄₇	—	4	1	no	—
40	C₂×C₄×C₄₇	—	8	2	no	—
41	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
43	C₈×C₄₇	—	4	1	no	—
44	C₈×C₄₇	—	4	2	no	—
45	C₂²×C₄₇	—	4	2	no	—
46	C₂²×C₄₇	—	4	2	no	—
47	C₂²×C₄₇	—	4	2	no	—
48	C₂²×C₄₇	#120	1	1	yes	characteristic
49	C₄×C₄₇	—	2	1	no	—
50	C₄×C₄₇	—	2	2	no	—
51	C₄×C₄₇	—	4	2	no	—
52	C₄×C₄₇	—	4	2	no	—
53	C₄×C₄₇	—	8	1	no	—
54	#1662	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂×C₄₇	—	8	2	no	—
56	C₂×C₄₇	#454	1	1	yes	characteristic
57	C₂×C₄₇	#455	1	2	yes	—
58	#562	C₂×C₄₇	1	1	yes	characteristic
59	#491	C₂×C₄₇	1	1	yes	characteristic, complemented
60	#489	C₂×C₄₇	1	2	yes	complemented
61	#330	C₂×C₄₇	1	1	yes	characteristic, complemented
62	#329	C₂×C₄₇	1	2	yes	complemented
63	C₄₇	#1662	1	1	yes	characteristic, direct product factor, Sylow
64	C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
65	#125	C₂²×C₄₇	1	1	yes	characteristic
66	#124	C₂²×C₄₇	1	2	yes	—
67	#123	—	2	2	no	—
68	C₂²⋊Q₈	—	2	2	no	—
69	#121	—	2	2	no	—
70	#103	—	2	2	no	—
71	#103	—	2	2	no	—
72	#102	—	2	2	no	—
73	#97	C₂²×C₄₇	1	1	yes	characteristic
74	#97	C₂²×C₄₇	1	2	yes	—
75	C₂×Q₈	—	2	1	no	—
76	C₂×Q₈	D₄×C₄₇	1	2	yes	—
77	C₂×D₄	—	2	2	no	—
78	C₂×D₄	D₄×C₄₇	1	2	yes	—
79	C₂²×C₄	—	2	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	2	1	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	2	2	no	—
84	C₄⋊C₄	—	2	2	no	—
85	C₄⋊C₄	D₄×C₄₇	1	2	yes	—
86	C₂²⋊C₄	—	2	2	no	—
87	C₂²⋊C₄	—	2	2	no	—
88	C₂²⋊C₄	—	2	2	no	—
89	C₄²	C₂³×C₄₇	1	1	yes	characteristic
90	C₂³	—	2	2	no	—
91	Q₈	—	4	2	no	—
92	Q₈	—	4	2	no	—
93	D₄	—	4	2	no	—
94	D₄	—	8	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	8	2	no	—
99	C₂×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
100	C₂×C₄	C₂×D₄×C₄₇	1	2	yes	—
101	C₈	—	4	1	no	—
102	C₈	—	4	2	no	—
103	C₂²	—	4	2	no	—
104	C₂²	—	4	2	no	—
105	C₂²	—	4	2	no	—
106	C₂²	#120×C₄₇	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	2	no	—
109	C₄	—	4	2	no	—
110	C₄	—	4	2	no	—
111	C₄	—	8	1	no	—
112	C₂	—	8	2	no	—
113	C₂	C₄₇×#454	1	1	yes	characteristic
114	C₂	C₄₇×#455	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₇×#562

C₂

yes

maximal, characteristic

C₄₇×#491

C₂

yes

maximal, characteristic, complemented

C₄₇×#489

C₂

yes

maximal, complemented

C₄₇×#330

C₂

yes

maximal, characteristic, complemented

C₄₇×#329

C₂

yes

maximal, complemented

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

#125×C₄₇

C₂²

yes

characteristic

#124×C₄₇

C₂²

yes

—

#123×C₄₇

—

C₂²⋊Q₈×C₄₇

—

#121×C₄₇

—

#103×C₄₇

—

#103×C₄₇

—

#102×C₄₇

—

#97×C₄₇

C₂²

yes

—

#97×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

D₄

yes

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

C₂³×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#120

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

#1662

C₄₇

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₄₇

—

C₂×C₄₇

#454

yes

characteristic

C₂×C₄₇

#455

yes

—

#562

C₂×C₄₇

yes

characteristic

#491

C₂×C₄₇

yes

characteristic, complemented

#489

C₂×C₄₇

yes

complemented

#330

C₂×C₄₇

yes

characteristic, complemented

#329

C₂×C₄₇

yes

complemented

C₄₇

#1662

yes

characteristic, direct product factor, Sylow

C₄⋊Q₈

C₂²×C₄₇

yes

characteristic

#125

C₂²×C₄₇

yes

characteristic

#124

C₂²×C₄₇

yes

—

#123

—

C₂²⋊Q₈

—

—

—

—

—

C₂²×C₄₇

yes

characteristic

#97

C₂²×C₄₇

yes

—

C₂×Q₈

—

C₂×Q₈

D₄×C₄₇

yes

—

C₂×D₄

—

C₂×D₄

D₄×C₄₇

yes

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₄₇

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂³×C₄₇

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₄₇

yes

characteristic

100

C₂×C₄

C₂×D₄×C₄₇

yes

—

101

C₈

—

102

C₈

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

#120×C₄₇

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₂

—

113

C₂

C₄₇×#454

yes

characteristic

114

C₂

C₄₇×#455

yes

—

	subgroup	G/H
center, socle	C₂²×C₄₇	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₄₇
prime radical	C₄₇×#562	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

subgroup

G/H

center, socle

C₂²×C₄₇

#120

commutator, Frattini, cosocle

C₄²

C₂³×C₄₇

prime radical

C₄₇×#562

C₂

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

N	H ≅ G/N	type
2. C₄₇×#491	C₂	semidirect
3. C₄₇×#489	C₂	semidirect
4. C₄₇×#330	C₂	semidirect
5. C₄₇×#329	C₂	semidirect
54. #1662	C₄₇	direct (N × H)
59. #491	C₂×C₄₇	semidirect
60. #489	C₂×C₄₇	semidirect
61. #330	C₂×C₄₇	semidirect
62. #329	C₂×C₄₇	semidirect
63. C₄₇	#1662	direct (N × H)

H ≅ G/N

type

2. C₄₇×#491

C₂

semidirect

3. C₄₇×#489

C₂

semidirect

4. C₄₇×#330

C₂

semidirect

5. C₄₇×#329

C₂

semidirect

54. #1662

C₄₇

direct (N × H)

59. #491

C₂×C₄₇

semidirect

60. #489

C₂×C₄₇

semidirect

61. #330

C₂×C₄₇

semidirect

62. #329

C₂×C₄₇

semidirect

63. C₄₇

#1662

direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₇×#562	2
C₄₇×#491	2
C₄₇×#489	2
C₄₇×#330	2
C₄₇×#329	2
#1662	47

subgroup

index

C₄₇×#562

C₄₇×#491

C₄₇×#489

C₄₇×#330

C₄₇×#329

#1662

Subgroups — C₄₇×#1662 #20239272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C47×#1662 #20239272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#1662 #20239272