Group #20245190 — subgroups

Subgroups — #20245190

Order 6016.

152 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₄₇)⋊C₁₆	C₂	1	2	yes	maximal
4	#15688898	C₂	1	2	yes	maximal, complemented
5	C₄₇×C₄⋊C₁₆	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	1	no	—
27	C₈×D₄₇	—	2	1	no	—
28	C₈×D₄₇	—	2	2	no	—
29	C₁₆×C₄₇	—	2	2	no	—
30	C₄₇⋊C₁₆	—	2	2	no	—
31	C₂²×D₄₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
36	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
37	C₂×Dic₄₇	C₂×C₈	1	1	yes	characteristic
38	C₄×D₄₇	—	2	2	no	—
39	C₄×D₄₇	—	2	2	no	—
40	C₄×D₄₇	—	2	1	no	—
41	C₄×D₄₇	—	2	1	no	—
42	C₈×C₄₇	—	2	1	no	—
43	C₈×C₄₇	#41	1	1	yes	characteristic
44	C₈×C₄₇	#41	1	1	yes	characteristic
45	C₄₇⋊C₈	—	2	1	no	—
46	C₄₇⋊C₈	M₁₆	1	2	yes	—
47	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
48	C₂×D₄₇	—	2	1	no	—
49	C₂×D₄₇	—	2	1	no	—
50	C₂×D₄₇	M₃₂	1	2	yes	—
51	C₄×C₄₇	—	2	1	no	—
52	C₄×C₄₇	M₃₂	1	2	yes	—
53	C₄×C₄₇	#117	1	1	yes	characteristic
54	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
55	Dic₄₇	—	2	1	no	—
56	Dic₄₇	—	2	1	no	—
57	Dic₄₇	—	2	1	no	—
58	#2163	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	#431	1	1	yes	characteristic
60	C₂×C₄₇	C₂×M₃₂	1	1	yes	characteristic
61	C₂×C₄₇	C₂×M₃₂	1	1	yes	characteristic
62	D₄₇	—	2	2	no	—
63	C₂×C₄×C₈	—	47	1	no	—
64	C₄⋊C₁₆	—	47	1	no	—
65	C₄⋊C₁₆	D₄₇	1	1	yes	characteristic, complemented
66	C₂²⋊C₁₆	—	47	2	no	—
67	#346	—	47	2	no	—
68	C₄₇	#2163	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	47	1	no	—
70	C₂²×C₈	—	47	1	no	—
71	C₂×C₄²	—	47	1	no	—
72	C₂×C₁₆	—	47	2	no	—
73	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
74	C₄×C₈	—	47	1	no	—
75	C₄×C₈	—	47	1	no	—
76	C₄×C₈	—	47	1	no	—
77	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
78	C₂²×C₄	—	47	1	no	—
79	C₂²×C₄	—	47	1	no	—
80	C₂²×C₄	—	47	1	no	—
81	C₂×C₈	—	47	1	no	—
82	C₂×C₈	—	47	1	no	—
83	C₂×C₈	—	94	2	no	—
84	C₂×C₈	—	94	1	no	—
85	C₂×C₈	—	94	1	no	—
86	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
87	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
88	C₄²	—	47	1	no	—
89	C₄²	—	47	1	no	—
90	C₄²	—	47	1	no	—
91	C₄²	C₄×D₄₇	1	1	yes	characteristic
92	C₁₆	—	2	2	no	—
93	C₁₆	—	94	2	no	—
94	C₂³	—	47	1	no	—
95	C₂×C₄	—	47	1	no	—
96	C₂×C₄	—	47	1	no	—
97	C₂×C₄	—	47	1	no	—
98	C₂×C₄	—	94	2	no	—
99	C₂×C₄	—	94	2	no	—
100	C₂×C₄	—	94	1	no	—
101	C₂×C₄	—	94	1	no	—
102	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
103	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
104	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	47	2	no	—
107	C₈	—	94	1	no	—
108	C₈	#10625352	1	1	yes	characteristic
109	C₈	#10625354	1	1	yes	characteristic
110	C₂²	—	47	2	no	—
111	C₂²	—	94	1	no	—
112	C₂²	—	94	1	no	—
113	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	94	1	no	—
116	C₄	—	94	1	no	—
117	C₄	—	94	1	no	—
118	C₄	#13093963	1	2	yes	—
119	C₄	#13093982	1	1	yes	characteristic
120	C₄	M₁₆×D₄₇	1	1	yes	characteristic
121	C₂	—	94	2	no	—
122	C₂	#15689175	1	1	yes	characteristic
123	C₂	M₃₂×D₄₇	1	1	yes	characteristic
124	C₂	C₂×#13093963	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₈×D₄₇

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

(C₂×D₄₇)⋊C₁₆

C₂

yes

maximal

#15688898

C₂

yes

maximal, complemented

C₄₇×C₄⋊C₁₆

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

—

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

—

C₈×C₄₇

—

C₈×C₄₇

yes

C₈×C₄₇

yes

C₄₇⋊C₈

—

C₄₇⋊C₈

M₁₆

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

M₃₂

yes

—

C₄×C₄₇

—

C₄×C₄₇

M₃₂

yes

—

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×M₃₂

yes

characteristic

C₂×C₄₇

C₂×M₃₂

yes

characteristic

D₄₇

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

D₄₇

yes

characteristic, complemented

C₂²⋊C₁₆

—

#346

—

C₄₇

#2163

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

—

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

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₈×D₄₇

yes

characteristic

103

C₂×C₄

C₈×D₄₇

yes

characteristic

104

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

#10625352

yes

characteristic

109

C₈

#10625354

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

C₂×C₈×D₄₇

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#13093963

yes

—

119

C₄

#13093982

yes

characteristic

120

C₄

M₁₆×D₄₇

yes

characteristic

121

C₂

—

122

C₂

#15689175

yes

characteristic

123

C₂

M₃₂×D₄₇

yes

characteristic

124

C₂

C₂×#13093963

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₈
Fitting	C₄₇×C₄⋊C₁₆	C₂
hypercenter	C₄⋊C₁₆	D₄₇
hypocenter	C₄₇	#2163
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₇

commutator, socle

C₂²×C₄₇

C₂²×C₈

Fitting

C₄₇×C₄⋊C₁₆

C₂

hypercenter

C₄⋊C₁₆

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
2. C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
4. #15688898	C₂	semidirect
5. C₄₇×C₄⋊C₁₆	C₂	semidirect
65. C₄⋊C₁₆	D₄₇	semidirect
68. C₄₇	#2163	semidirect

H ≅ G/N

type

2. C₄⋊(C₄₇⋊C₁₆)

C₂

semidirect

4. #15688898

C₂

semidirect

5. C₄₇×C₄⋊C₁₆

C₂

semidirect

65. C₄⋊C₁₆

D₄₇

semidirect

68. C₄₇

#2163

semidirect

Subgroups — #20245190

Conjugacy classes of subgroups

Complements