Group #20245185 — subgroups

Subgroups — #20245185

Order 6016.

160 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	Dic₄₇⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	(C₂×D₄₇)⋊C₁₆	C₂	1	2	yes	maximal
4	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₄₇	C₄	1	1	yes	characteristic
7	C₂×C₈×D₄₇	C₂²	1	1	yes	characteristic
8	C₄²×D₄₇	C₄	1	1	yes	characteristic
9	C₂×C₄₇⋊C₁₆	C₂²	1	2	yes	—
10	C₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
11	C₈×Dic₄₇	C₄	1	1	yes	characteristic
12	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄₇	C₈	1	1	yes	characteristic
16	C₂×C₄×D₄₇	C₈	1	1	yes	characteristic
17	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
20	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₄₇	C₈	1	1	yes	characteristic
22	C₄×Dic₄₇	C₈	1	1	yes	characteristic
23	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₈×D₄₇	—	2	2	no	—
27	C₈×D₄₇	—	2	2	no	—
28	C₁₆×C₄₇	—	2	2	no	—
29	C₄₇⋊C₁₆	—	2	2	no	—
30	C₂²×D₄₇	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
35	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
37	C₄×D₄₇	—	2	2	no	—
38	C₄×D₄₇	—	2	1	no	—
39	C₄×D₄₇	—	2	1	no	—
40	C₄×D₄₇	C₁₆	1	4	yes	complemented
41	C₈×C₄₇	M₁₆	1	2	yes	—
42	C₈×C₄₇	#41	1	2	yes	—
43	C₄₇⋊C₈	—	2	1	no	—
44	C₄₇⋊C₈	—	2	1	no	—
45	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
46	C₂×D₄₇	—	2	1	no	—
47	C₂×D₄₇	—	2	1	no	—
48	C₂×D₄₇	C₂×C₁₆	1	2	yes	—
49	C₄×C₄₇	C₂×C₁₆	1	2	yes	—
50	C₄×C₄₇	M₃₂	1	2	yes	—
51	C₄×C₄₇	#117	1	1	yes	characteristic
52	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
53	Dic₄₇	—	2	1	no	—
54	Dic₄₇	—	2	1	no	—
55	Dic₄₇	C₂×C₁₆	1	2	yes	—
56	#2162	—	47	1	no	maximal, Sylow
57	C₂×C₄₇	#431	1	1	yes	characteristic
58	C₂×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
59	C₂×C₄₇	C₂×M₃₂	1	1	yes	characteristic
60	D₄₇	—	2	2	no	—
61	C₂×C₄×C₈	—	47	1	no	—
62	C₄⋊C₁₆	—	47	2	no	—
63	C₂²⋊C₁₆	—	47	2	no	—
64	C₄×C₁₆	—	47	1	no	—
65	C₄×C₁₆	D₄₇	1	1	yes	characteristic, complemented
66	C₄₇	#2162	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₈	—	47	1	no	—
68	C₂²×C₈	—	47	1	no	—
69	C₂×C₄²	—	47	1	no	—
70	C₂×C₁₆	—	47	2	no	—
71	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
72	C₄×C₈	—	47	1	no	—
73	C₄×C₈	—	47	1	no	—
74	C₄×C₈	—	47	1	no	—
75	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
76	C₂²×C₄	—	47	1	no	—
77	C₂²×C₄	—	47	1	no	—
78	C₂²×C₄	—	47	1	no	—
79	C₂×C₈	—	47	1	no	—
80	C₂×C₈	—	47	1	no	—
81	C₂×C₈	—	94	2	no	—
82	C₂×C₈	—	94	2	no	—
83	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
84	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
85	C₄²	—	47	1	no	—
86	C₄²	—	47	1	no	—
87	C₄²	—	47	1	no	—
88	C₄²	C₄×D₄₇	1	1	yes	characteristic
89	C₁₆	—	2	2	no	—
90	C₁₆	—	94	2	no	—
91	C₂³	—	47	1	no	—
92	C₂×C₄	—	47	1	no	—
93	C₂×C₄	—	47	4	no	—
94	C₂×C₄	—	47	1	no	—
95	C₂×C₄	—	47	1	no	—
96	C₂×C₄	—	94	2	no	—
97	C₂×C₄	—	94	1	no	—
98	C₂×C₄	—	94	1	no	—
99	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
100	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
101	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
102	C₈	—	94	1	no	—
103	C₈	—	94	1	no	—
104	C₈	#10625324	1	2	yes	—
105	C₈	#10625350	1	2	yes	—
106	C₂²	—	47	2	no	—
107	C₂²	—	94	1	no	—
108	C₂²	—	94	1	no	—
109	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
110	C₄	—	47	2	no	—
111	C₄	—	94	1	no	—
112	C₄	—	94	1	no	—
113	C₄	C₁₆×D₄₇	1	2	yes	—
114	C₄	#13093963	1	2	yes	—
115	C₄	#13093981	1	1	yes	characteristic
116	C₄	C₂×#10625324	1	1	yes	characteristic
117	C₂	—	94	2	no	—
118	C₂	#15689174	1	1	yes	characteristic
119	C₂	C₂×C₁₆×D₄₇	1	1	yes	characteristic
120	C₂	C₂×#13093963	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×D₄₇

C₂

yes

maximal, characteristic

Dic₄₇⋊C₁₆

C₂

yes

maximal, complemented

(C₂×D₄₇)⋊C₁₆

C₂

yes

maximal

C₄×C₄₇⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₇

C₄

yes

characteristic

C₂×C₈×D₄₇

C₂²

yes

characteristic

C₄²×D₄₇

C₄

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

—

C₄×C₄₇⋊C₈

C₄

yes

characteristic

C₈×Dic₄₇

C₄

yes

characteristic

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄×D₄₇

C₈

yes

characteristic

C₂×C₄×D₄₇

C₈

yes

characteristic

C₂×C₄×D₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂×C₄

yes

characteristic

C₄×Dic₄₇

C₈

yes

characteristic

C₄×Dic₄₇

C₈

yes

characteristic

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₂×C₄₇⋊C₈

C₂×C₄

yes

characteristic

C₈×D₄₇

—

C₈×D₄₇

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂²×D₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

C₂×Dic₄₇

C₂×C₈

yes

characteristic

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

C₁₆

yes

complemented

C₈×C₄₇

M₁₆

yes

—

C₈×C₄₇

#41

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

C₂×C₁₆

yes

—

C₄×C₄₇

C₂×C₁₆

yes

—

C₄×C₄₇

M₃₂

yes

—

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

C₂×C₁₆

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂²×C₁₆

yes

characteristic

C₂×C₄₇

C₂×M₃₂

yes

characteristic

D₄₇

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

D₄₇

yes

characteristic, complemented

C₄₇

#2162

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄×D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₇

yes

characteristic

100

C₂×C₄

C₈×D₄₇

yes

characteristic

101

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

#10625324

yes

—

105

C₈

#10625350

yes

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₂×C₈×D₄₇

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

C₁₆×D₄₇

yes

—

114

C₄

#13093963

yes

—

115

C₄

#13093981

yes

characteristic

116

C₄

C₂×#10625324

yes

characteristic

117

C₂

—

118

C₂

#15689174

yes

characteristic

119

C₂

C₂×C₁₆×D₄₇

yes

characteristic

120

C₂

C₂×#13093963

yes

characteristic

	subgroup	G/H
center	C₄×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₂²×C₁₆
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₈
hypercenter	C₄×C₁₆	D₄₇
hypocenter	C₄₇	#2162
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₄×C₈

C₂×D₄₇

commutator

C₂×C₄₇

C₂²×C₁₆

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄×C₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂²×C₈

hypercenter

C₄×C₁₆

D₄₇

C₄₇

G ▷ C₂×C₄₇ ▷ C₄₇

C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. Dic₄₇⋊C₁₆	C₂	semidirect
4. C₄×C₄₇⋊C₁₆	C₂	semidirect
5. C₄×C₁₆×C₄₇	C₂	semidirect
40. C₄×D₄₇	C₁₆	semidirect
65. C₄×C₁₆	D₄₇	semidirect
66. C₄₇	#2162	semidirect

H ≅ G/N

type

2. Dic₄₇⋊C₁₆

C₂

semidirect

4. C₄×C₄₇⋊C₁₆

C₂

semidirect

5. C₄×C₁₆×C₄₇

C₂

semidirect

40. C₄×D₄₇

C₁₆

semidirect

65. C₄×C₁₆

D₄₇

semidirect

66. C₄₇

#2162

semidirect

Subgroups — #20245185

Conjugacy classes of subgroups

Complements