Group #20245277 — subgroups

Subgroups — #20245277

Order 6016.

142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689564	C₂	1	1	yes	maximal, characteristic
2	#15689246	C₂	1	1	yes	maximal, characteristic
3	#15688945	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688939	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688932	C₂	1	1	yes	maximal, characteristic
6	#15688901	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
8	#13094046	C₂²	1	1	yes	characteristic
9	#13094030	—	2	1	no	—
10	#13093970	C₄	1	2	yes	complemented
11	#13093967	C₄	1	2	yes	complemented
12	#13093964	C₂²	1	1	yes	characteristic
13	#13093964	C₂²	1	1	yes	characteristic
14	#13093960	C₂²	1	1	yes	characteristic
15	#13093952	—	2	1	no	—
16	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	C₄×Q₈×C₄₇	—	2	1	no	—
18	#106×C₄₇	C₂²	1	1	yes	characteristic
19	#103×C₄₇	—	2	1	no	—
20	#97×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×Q₈×C₄₇	—	2	1	no	—
22	#10625350	—	2	1	no	—
23	Q₁₆×C₄₇	—	2	1	no	—
24	Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
26	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₄₇	—	2	1	no	—
28	C₄⋊C₄×C₄₇	—	4	1	no	—
29	C₄²×C₄₇	—	4	1	no	—
30	C₄²×C₄₇	D₄	1	1	yes	characteristic
31	#10625329	—	2	1	no	—
32	Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
33	D₃₇₆	C₂×C₄	1	1	yes	characteristic
34	#10625325	—	2	1	no	—
35	#10625324	—	4	1	no	—
36	C₈×D₄₇	—	4	1	no	—
37	C₄₇⋊C₁₆	—	2	1	no	—
38	C₄₇⋊C₁₆	C₂×C₄	1	2	yes	—
39	Q₈×C₄₇	—	2	2	no	—
40	Q₈×C₄₇	—	4	1	no	—
41	C₂×C₄×C₄₇	—	2	1	no	—
42	C₂×C₄×C₄₇	—	4	1	no	—
43	C₂×C₄×C₄₇	—	4	1	no	—
44	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
45	C₂²⋊D₄₇	—	4	1	no	—
46	D₁₈₈	—	2	1	no	—
47	C₄×D₄₇	—	4	1	no	—
48	Dic₉₄	—	2	1	no	—
49	C₈×C₄₇	—	2	1	no	—
50	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
51	C₈×C₄₇	#41	1	1	yes	characteristic
52	C₄₇⋊C₈	—	4	1	no	—
53	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
54	C₂×D₄₇	—	4	1	no	—
55	C₄×C₄₇	—	4	1	no	—
56	C₄×C₄₇	—	4	2	no	—
57	C₄×C₄₇	—	8	1	no	—
58	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
59	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
60	Dic₄₇	—	4	1	no	—
61	#2180	—	47	1	no	maximal, Sylow
62	C₂×C₄₇	—	2	1	no	—
63	C₂×C₄₇	#442	1	1	yes	characteristic
64	D₄₇	—	8	1	no	—
65	#510	—	47	1	no	—
66	#444	—	47	1	no	—
67	#441	D₄₇	1	1	yes	characteristic, complemented
68	#365	—	47	1	no	—
69	#362	—	47	1	no	—
70	#360	—	47	1	no	—
71	#347	—	47	1	no	—
72	C₄₇	#2180	1	1	yes	characteristic, complemented, Sylow
73	#135	—	47	1	no	—
74	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
75	#131	—	94	1	no	—
76	C₄×Q₈	—	2	1	no	—
77	Q₃₂	—	47	2	no	—
78	SD₃₂	—	47	2	no	—
79	M₃₂	—	47	1	no	—
80	M₃₂	—	47	1	no	—
81	#108	—	47	1	no	—
82	#106	C₂×D₄₇	1	1	yes	characteristic
83	#104	—	94	1	no	—
84	#103	—	2	1	no	—
85	#97	C₂×D₄₇	1	1	yes	characteristic
86	#41	—	94	1	no	—
87	C₂×Q₈	—	2	1	no	—
88	Q₁₆	—	2	1	no	—
89	Q₁₆	—	47	1	no	—
90	Q₁₆	C₄×D₄₇	1	2	yes	—
91	SD₁₆	—	94	1	no	—
92	D₈	—	47	1	no	—
93	M₁₆	—	94	1	no	—
94	M₁₆	—	188	1	no	—
95	C₂×C₈	—	188	1	no	—
96	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
97	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
98	C₄⋊C₄	—	2	1	no	—
99	C₄⋊C₄	—	4	1	no	—
100	C₄²	—	4	1	no	—
101	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
102	C₁₆	—	47	2	no	—
103	C₁₆	—	94	1	no	—
104	Q₈	—	2	2	no	—
105	Q₈	—	4	1	no	—
106	Q₈	—	94	1	no	—
107	D₄	—	94	1	no	—
108	D₄	—	188	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	188	1	no	—
113	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
114	C₈	—	2	1	no	—
115	C₈	—	188	1	no	—
116	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
117	C₈	#10625350	1	1	yes	characteristic
118	C₂²	—	188	1	no	—
119	C₂²	#13094050	1	1	yes	characteristic
120	C₄	—	4	1	no	—
121	C₄	—	4	2	no	—
122	C₄	—	8	1	no	—
123	C₄	—	188	1	no	—
124	C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
125	C₄	#13094049	1	1	yes	characteristic
126	C₂	—	2	1	no	—
127	C₂	—	376	1	no	—
128	C₂	#15689233	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689564

C₂

yes

maximal, characteristic

#15689246

C₂

yes

maximal, characteristic

#15688945

C₂

yes

maximal, characteristic, complemented

#15688939

C₂

yes

maximal, characteristic, complemented

#15688932

C₂

yes

maximal, characteristic

#15688901

C₂

yes

maximal, characteristic, complemented

C₄₇×#441

C₂

yes

maximal, characteristic, complemented

#13094046

C₂²

yes

characteristic

#13094030

—

#13093970

C₄

yes

complemented

#13093967

C₄

yes

complemented

#13093964

C₂²

yes

characteristic

#13093964

C₂²

yes

characteristic

#13093960

C₂²

yes

characteristic

#13093952

—

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

—

#106×C₄₇

C₂²

yes

characteristic

#103×C₄₇

—

#97×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

#10625350

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

#10625329

—

Dic₁₈₈

C₂×C₄

yes

characteristic

D₃₇₆

C₂×C₄

yes

characteristic

#10625325

—

#10625324

—

C₈×D₄₇

—

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

C₂×C₄

yes

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

Dic₄₇

—

#2180

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#442

yes

characteristic

D₄₇

—

#510

—

#444

—

#441

D₄₇

yes

characteristic, complemented

—

—

—

—

C₄₇

#2180

yes

characteristic, complemented, Sylow

#135

—

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

#131

—

C₄×Q₈

—

Q₃₂

—

SD₃₂

—

M₃₂

—

M₃₂

—

#108

—

#106

C₂×D₄₇

yes

—

—

C₂×D₄₇

yes

characteristic

#41

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

C₄×D₄₇

yes

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

188

—

C₂×C₈

—

188

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄²

—

101

C₄²

C₂²⋊D₄₇

yes

characteristic

102

C₁₆

—

103

C₁₆

—

104

Q₈

—

105

Q₈

—

106

Q₈

—

107

D₄

—

108

D₄

—

188

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

188

—

113

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

114

C₈

—

115

C₈

—

188

—

116

C₈

C₂×C₄×D₄₇

yes

characteristic

117

C₈

#10625350

yes

characteristic

118

C₂²

—

188

—

119

C₂²

#13094050

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

188

—

124

C₄

C₄×C₂²⋊D₄₇

yes

characteristic

125

C₄

#13094049

yes

characteristic

126

C₂

—

127

C₂

—

376

—

128

C₂

#15689233

yes

characteristic

	subgroup	G/H
center	C₂	#15689233
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#441	C₂
socle	C₂×C₄₇	#442
hypercenter	#441	D₄₇
hypocenter	C₄₇	#2180
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #441

subgroup

G/H

center

C₂

#15689233

commutator

C₈×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#441

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #441

N	H ≅ G/N	type
3. #15688945	C₂	semidirect
4. #15688939	C₂	semidirect
6. #15688901	C₂	semidirect
7. C₄₇×#441	C₂	semidirect
10. #13093970	C₄	semidirect
11. #13093967	C₄	semidirect
67. #441	D₄₇	semidirect
72. C₄₇	#2180	semidirect

H ≅ G/N

type

3. #15688945

C₂

semidirect

4. #15688939

C₂

semidirect

6. #15688901

C₂

semidirect

7. C₄₇×#441

C₂

semidirect

10. #13093970

C₄

semidirect

11. #13093967

C₄

semidirect

67. #441

D₄₇

semidirect

72. C₄₇

#2180

semidirect

Subgroups — #20245277

Conjugacy classes of subgroups

Complements