Group #20243071 — subgroups

Subgroups — #97×Dic₄₇ #20243071

Order 6016.

360 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 221 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	C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#97×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×Dic₄₇	C₄	1	4	yes	—
8	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
10	#13093935	C₄	1	4	yes	complemented
11	#13093934	C₄	1	8	yes	complemented
12	C₈×Dic₄₇	C₄	1	8	yes	complemented
13	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	#97×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	2	yes	—
19	C₂²×Dic₄₇	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
22	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
23	C₄²×C₄₇	C₂×C₄	1	2	yes	—
24	C₄²×C₄₇	C₂×C₄	1	2	yes	—
25	C₄×Dic₄₇	—	2	8	no	—
26	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
27	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
28	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
29	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
30	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
31	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	—	2	4	no	—
33	C₂×C₄×C₄₇	C₄²	1	4	yes	—
34	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
36	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₄₇	—	2	4	no	—
39	C₂×Dic₄₇	C₄²	1	4	yes	—
40	C₂×Dic₄₇	C₄²	1	4	yes	—
41	C₂×Dic₄₇	M₁₆	1	8	yes	—
42	C₈×C₄₇	C₄²	1	8	yes	complemented
43	C₄₇⋊C₈	C₄²	1	8	yes	complemented
44	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
45	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
46	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
47	C₂²×C₄₇	C₂×M₁₆	1	4	yes	—
48	C₄×C₄₇	—	2	4	no	—
49	C₄×C₄₇	C₂×C₄²	1	2	yes	—
50	C₄×C₄₇	C₂×C₄²	1	2	yes	—
51	Dic₄₇	—	2	4	no	—
52	Dic₄₇	#97	1	8	yes	direct product factor
53	C₄×#97	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	C₄³	1	1	yes	characteristic
55	C₂×C₄₇	C₂×#97	1	2	yes	—
56	C₂×C₄₇	C₄×M₁₆	1	2	yes	—
57	C₂×C₄₇	C₄×M₁₆	1	2	yes	—
58	C₂×#97	—	47	2	no	—
59	C₂×#97	—	47	1	no	—
60	C₂×#97	D₄₇	1	1	yes	characteristic
61	C₂×C₄×C₈	—	47	2	no	—
62	C₄³	—	47	1	no	—
63	C₄₇	C₄×#97	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₈	—	47	2	no	—
65	C₂²×C₈	C₂×D₄₇	1	2	yes	—
66	C₂×C₄²	—	47	1	no	—
67	C₂×C₄²	—	47	1	no	—
68	C₂×C₄²	—	47	4	no	—
69	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
70	#97	—	47	8	no	—
71	#97	—	47	4	no	—
72	#97	Dic₄₇	1	4	yes	direct product factor
73	C₄×C₈	—	47	8	no	—
74	C₂²×C₄	—	47	2	no	—
75	C₂²×C₄	—	47	2	no	—
76	C₂²×C₄	C₄×D₄₇	1	2	yes	—
77	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
78	C₂×C₈	—	47	4	no	—
79	C₂×C₈	—	47	4	no	—
80	C₂×C₈	—	47	4	no	—
81	C₂×C₈	C₄×D₄₇	1	4	yes	—
82	C₂×C₈	C₄×D₄₇	1	4	yes	—
83	C₂×C₈	C₂×Dic₄₇	1	4	yes	—
84	C₄²	—	47	4	no	—
85	C₄²	—	47	4	no	—
86	C₄²	—	94	8	no	—
87	C₄²	C₄×D₄₇	1	2	yes	—
88	C₄²	C₂×Dic₄₇	1	2	yes	—
89	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
90	C₂×C₄	—	2	4	no	—
91	C₂×C₄	—	47	4	no	—
92	C₂×C₄	—	47	8	no	—
93	C₂×C₄	—	47	4	no	—
94	C₂×C₄	—	94	4	no	—
95	C₂×C₄	C₄×Dic₄₇	1	4	yes	—
96	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
97	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
98	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
99	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
100	C₈	—	47	8	no	—
101	C₈	C₄×Dic₄₇	1	8	yes	complemented
102	C₂²	C₄²×D₄₇	1	1	yes	characteristic
103	C₂²	C₄²×D₄₇	1	1	yes	characteristic
104	C₂²	C₂×C₄×Dic₄₇	1	1	yes	characteristic
105	C₂²	M₁₆×D₄₇	1	4	yes	—
106	C₄	—	2	4	no	—
107	C₄	—	47	8	no	—
108	C₄	—	94	4	no	—
109	C₄	C₄²×D₄₇	1	2	yes	—
110	C₄	C₂×C₄×Dic₄₇	1	2	yes	—
111	C₂	C₄²×Dic₄₇	1	1	yes	characteristic
112	C₂	#97×D₄₇	1	2	yes	—
113	C₂	M₁₆×Dic₄₇	1	2	yes	—
114	C₂	#15689075	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

C₄²×Dic₄₇

C₂

yes

maximal, characteristic

C₂×#97×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₇

C₄

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

#13093935

C₄

yes

complemented

#13093934

C₄

yes

complemented

C₈×Dic₄₇

C₄

yes

complemented

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

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

—

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

—

C₂×Dic₄₇

C₄²

yes

—

C₂×Dic₄₇

M₁₆

yes

—

C₈×C₄₇

C₄²

yes

complemented

C₄₇⋊C₈

C₄²

yes

complemented

C₂²×C₄₇

C₂×C₄²

yes

characteristic

C₂²×C₄₇

C₂×C₄²

yes

characteristic

C₂²×C₄₇

C₂×C₄²

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄²

yes

—

C₄×C₄₇

C₂×C₄²

yes

—

Dic₄₇

—

Dic₄₇

#97

yes

direct product factor

C₄×#97

—

maximal, Sylow

C₂×C₄₇

C₄³

yes

characteristic

C₂×C₄₇

C₂×#97

yes

—

C₂×C₄₇

C₄×M₁₆

yes

—

C₂×C₄₇

C₄×M₁₆

yes

—

C₂×#97

—

C₂×#97

—

C₂×#97

D₄₇

yes

characteristic

C₂×C₄×C₈

—

C₄³

—

C₄₇

C₄×#97

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

—

—

Dic₄₇

yes

direct product factor

C₄×C₈

—

C₂²×C₄

—

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

—

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

—

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

100

C₈

—

101

C₈

C₄×Dic₄₇

yes

complemented

102

C₂²

C₄²×D₄₇

yes

characteristic

103

C₂²

C₄²×D₄₇

yes

characteristic

104

C₂²

C₂×C₄×Dic₄₇

yes

characteristic

105

C₂²

M₁₆×D₄₇

yes

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

C₄²×D₄₇

yes

—

110

C₄

C₂×C₄×Dic₄₇

yes

—

111

C₂

C₄²×Dic₄₇

yes

characteristic

112

C₂

#97×D₄₇

yes

—

113

C₂

M₁₆×Dic₄₇

yes

—

114

C₂

#15689075

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₇
commutator	C₂×C₄₇	C₄³
Fitting	C₂×#97×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	C₂×#97	D₄₇
hypocenter	C₄₇	C₄×#97
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₇

commutator

C₂×C₄₇

C₄³

Fitting

C₂×#97×C₄₇

C₂

socle

C₂³×C₄₇

C₂²×C₄

hypercenter

C₂×#97

D₄₇

hypocenter

C₄₇

C₄×#97

LCS

G ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
10. #13093935	C₄	semidirect
11. #13093934	C₄	semidirect
12. C₈×Dic₄₇	C₄	semidirect
15. #97×C₄₇	C₄	semidirect
42. C₈×C₄₇	C₄²	semidirect
43. C₄₇⋊C₈	C₄²	semidirect
52. Dic₄₇	#97	direct (N × H)
63. C₄₇	C₄×#97	semidirect
72. #97	Dic₄₇	direct (N × H)
101. C₈	C₄×Dic₄₇	semidirect

H ≅ G/N

type

10. #13093935

C₄

semidirect

11. #13093934

C₄

semidirect

12. C₈×Dic₄₇

C₄

semidirect

15. #97×C₄₇

C₄

semidirect

42. C₈×C₄₇

C₄²

semidirect

43. C₄₇⋊C₈

C₄²

semidirect

52. Dic₄₇

#97

direct (N × H)

63. C₄₇

C₄×#97

semidirect

72. #97

Dic₄₇

direct (N × H)

101. C₈

C₄×Dic₄₇

semidirect

Subgroups — #97×Dic₄₇ #20243071

Conjugacy classes of subgroups

Complements

Subgroups — #97×Dic47 #20243071

Conjugacy classes of subgroups

Complements

Subgroups — #97×Dic₄₇ #20243071