Group #20245286 — subgroups

Subgroups — #20245286

Order 6016.

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

normal subgroups only

This group has 154 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	#15689558	C₂	1	1	yes	maximal, characteristic
2	#15689236	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688947	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688935	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688933	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688901	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#444	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
9	C₄×D₁₈₈	—	2	1	no	—
10	#13093967	C₄	1	2	yes	complemented
11	#13093965	C₄	1	2	yes	complemented
12	#13093964	C₂²	1	1	yes	characteristic
13	#13093964	C₂²	1	1	yes	characteristic
14	#13093956	C₂²	1	1	yes	characteristic
15	#13093946	—	2	1	no	—
16	#135×C₄₇	C₂²	1	1	yes	characteristic
17	#131×C₄₇	—	2	1	no	—
18	#108×C₄₇	C₂²	1	1	yes	characteristic
19	#104×C₄₇	—	2	1	no	—
20	#97×C₄₇	C₂²	1	1	yes	characteristic
21	#41×C₄₇	—	2	1	no	—
22	C₂×D₁₈₈	—	2	1	no	—
23	C₂×C₄×D₄₇	—	4	1	no	—
24	Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
25	SD₁₆×C₄₇	—	2	1	no	—
26	D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
27	M₁₆×C₄₇	—	2	1	no	—
28	M₁₆×C₄₇	—	4	1	no	—
29	C₂×C₈×C₄₇	—	4	1	no	—
30	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
31	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
32	C₄²×C₄₇	D₄	1	1	yes	characteristic
33	(C₂×D₄₇)⋊C₄	—	4	1	no	—
34	C₄⋊Dic₄₇	—	2	1	no	—
35	D₃₇₆	—	2	1	no	—
36	D₃₇₆	C₂×C₄	1	2	yes	—
37	C₄₇⋊C₁₆	—	2	1	no	—
38	C₄₇⋊C₁₆	C₂×C₄	1	2	yes	complemented
39	C₂²×D₄₇	—	4	1	no	—
40	Q₈×C₄₇	—	2	1	no	—
41	D₄×C₄₇	—	2	1	no	—
42	D₄×C₄₇	—	4	1	no	—
43	C₂×C₄×C₄₇	—	2	1	no	—
44	C₂×C₄×C₄₇	—	4	1	no	—
45	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₄₇	—	4	1	no	—
47	D₁₈₈	—	2	2	no	—
48	D₁₈₈	—	4	1	no	—
49	C₄×D₄₇	—	8	2	no	—
50	C₈×C₄₇	—	2	1	no	—
51	C₈×C₄₇	—	4	1	no	—
52	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
53	C₈×C₄₇	#41	1	1	yes	characteristic
54	C₂²×C₄₇	—	4	1	no	—
55	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
56	C₂×D₄₇	—	4	2	no	—
57	C₂×D₄₇	—	8	1	no	—
58	C₂×D₄₇	—	8	1	no	—
59	C₄×C₄₇	—	4	1	no	—
60	C₄×C₄₇	—	4	1	no	—
61	C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
62	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
63	Dic₄₇	—	8	1	no	—
64	AGL(1,ℤ/16)	—	47	1	no	maximal, Sylow
65	C₂×C₄₇	—	2	1	no	—
66	C₂×C₄₇	—	8	1	no	—
67	C₂×C₄₇	#442	1	1	yes	characteristic
68	D₄₇	—	8	2	no	—
69	#509	—	47	1	no	—
70	#444	D₄₇	1	1	yes	characteristic, complemented
71	#442	—	47	1	no	—
72	#365	—	47	1	no	—
73	#361	—	47	1	no	—
74	#360	—	47	1	no	—
75	#347	—	47	1	no	—
76	C₄₇	AGL(1,ℤ/16)	1	1	yes	characteristic, complemented, Sylow
77	#135	C₂×D₄₇	1	1	yes	characteristic
78	C₂×D₈	—	47	1	no	—
79	#131	—	2	1	no	—
80	C₄×D₄	—	94	1	no	—
81	SD₃₂	—	47	2	no	—
82	D₁₆	—	47	2	no	—
83	M₃₂	—	47	1	no	—
84	M₃₂	—	47	1	no	—
85	#108	C₂×D₄₇	1	1	yes	characteristic
86	#106	—	47	1	no	—
87	#104	—	2	1	no	—
88	#102	—	94	1	no	—
89	#97	C₂×D₄₇	1	1	yes	characteristic
90	#41	—	2	1	no	—
91	C₂×D₄	—	94	1	no	—
92	C₂²×C₄	—	188	1	no	—
93	Q₁₆	C₄×D₄₇	1	1	yes	characteristic, complemented
94	SD₁₆	—	2	1	no	—
95	D₈	—	47	2	no	—
96	D₈	—	94	1	no	—
97	D₈	C₄×D₄₇	1	1	yes	characteristic, complemented
98	M₁₆	—	2	1	no	—
99	M₁₆	—	4	1	no	—
100	C₂×C₈	—	4	1	no	—
101	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
102	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
103	C₄⋊C₄	—	94	1	no	—
104	C₂²⋊C₄	—	188	1	no	—
105	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
106	C₁₆	—	47	2	no	—
107	C₁₆	—	94	1	no	—
108	C₂³	—	188	1	no	—
109	Q₈	—	2	1	no	—
110	D₄	—	2	1	no	—
111	D₄	—	4	1	no	—
112	D₄	—	94	2	no	—
113	D₄	—	188	1	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	—	376	2	no	—
117	C₂×C₄	—	188	1	no	—
118	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
119	C₈	—	2	1	no	—
120	C₈	—	4	1	no	—
121	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
122	C₈	#10625350	1	1	yes	characteristic
123	C₂²	—	4	1	no	—
124	C₂²	—	376	1	no	—
125	C₂²	—	376	1	no	—
126	C₂²	—	188	2	no	—
127	C₂²	#13094049	1	1	yes	characteristic
128	C₄	—	4	1	no	—
129	C₄	—	4	1	no	—
130	C₄	—	376	1	no	—
131	C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
132	C₄	#13094050	1	1	yes	characteristic
133	C₂	—	2	1	no	—
134	C₂	—	8	1	no	—
135	C₂	—	376	2	no	—
136	C₂	#15689233	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689558

C₂

yes

maximal, characteristic

#15689236

C₂

yes

maximal, characteristic, complemented

#15688947

C₂

yes

maximal, characteristic, complemented

#15688935

C₂

yes

maximal, characteristic, complemented

#15688933

C₂

yes

maximal, characteristic, complemented

#15688901

C₂

yes

maximal, characteristic, complemented

C₄₇×#444

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

C₂²

yes

characteristic

C₄×D₁₈₈

—

#13093967

C₄

yes

complemented

#13093965

C₄

yes

complemented

#13093964

C₂²

yes

characteristic

#13093964

C₂²

yes

characteristic

#13093956

C₂²

yes

characteristic

#13093946

—

#135×C₄₇

C₂²

yes

characteristic

#131×C₄₇

—

#108×C₄₇

C₂²

yes

characteristic

#104×C₄₇

—

#97×C₄₇

C₂²

yes

characteristic

#41×C₄₇

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

Q₁₆×C₄₇

C₂×C₄

yes

characteristic, complemented

SD₁₆×C₄₇

—

D₈×C₄₇

C₂×C₄

yes

characteristic, complemented

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

D₃₇₆

—

D₃₇₆

C₂×C₄

yes

—

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

C₂×C₄

yes

complemented

C₂²×D₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

AGL(1,ℤ/8)

yes

characteristic

Dic₄₇

—

AGL(1,ℤ/16)

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#442

yes

characteristic

D₄₇

—

#509

—

#444

D₄₇

yes

characteristic, complemented

—

—

—

—

—

C₄₇

AGL(1,ℤ/16)

yes

characteristic, complemented, Sylow

#135

C₂×D₄₇

yes

characteristic

C₂×D₈

—

#131

—

C₄×D₄

—

SD₃₂

—

D₁₆

—

M₃₂

—

M₃₂

—

#108

C₂×D₄₇

yes

—

—

—

C₂×D₄₇

yes

characteristic

#41

—

C₂×D₄

—

C₂²×C₄

—

188

—

Q₁₆

C₄×D₄₇

yes

characteristic, complemented

SD₁₆

—

D₈

—

D₈

—

D₈

C₄×D₄₇

yes

characteristic, complemented

M₁₆

—

M₁₆

—

100

C₂×C₈

—

101

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

102

C₂×C₈

C₂²×D₄₇

yes

characteristic

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

188

—

105

C₄²

C₂²⋊D₄₇

yes

characteristic

106

C₁₆

—

107

C₁₆

—

108

C₂³

—

188

—

109

Q₈

—

110

D₄

—

111

D₄

—

112

D₄

—

113

D₄

—

188

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

376

—

117

C₂×C₄

—

188

—

118

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

119

C₈

—

120

C₈

—

121

C₈

C₂×C₄×D₄₇

yes

characteristic

122

C₈

#10625350

yes

characteristic

123

C₂²

—

124

C₂²

—

376

—

125

C₂²

—

376

—

126

C₂²

—

188

—

127

C₂²

#13094049

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

376

—

131

C₄

C₄×C₂²⋊D₄₇

yes

characteristic

132

C₄

#13094050

yes

characteristic

133

C₂

—

134

C₂

—

135

C₂

—

376

—

136

C₂

#15689233

yes

characteristic

	subgroup	G/H
center	C₂	#15689233
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#444	C₂
socle	C₂×C₄₇	#442
hypercenter	#444	D₄₇
hypocenter	C₄₇	AGL(1,ℤ/16)
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #444

subgroup

G/H

center

C₂

#15689233

commutator

C₈×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#444

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #444

N	H ≅ G/N	type
2. #15689236	C₂	semidirect
3. #15688947	C₂	semidirect
4. #15688935	C₂	semidirect
5. #15688933	C₂	semidirect
6. #15688901	C₂	semidirect
7. C₄₇×#444	C₂	semidirect
10. #13093967	C₄	semidirect
11. #13093965	C₄	semidirect
24. Q₁₆×C₄₇	C₂×C₄	semidirect
26. D₈×C₄₇	C₂×C₄	semidirect
38. C₄₇⋊C₁₆	C₂×C₄	semidirect
70. #444	D₄₇	semidirect
76. C₄₇	AGL(1,ℤ/16)	semidirect
93. Q₁₆	C₄×D₄₇	semidirect
97. D₈	C₄×D₄₇	semidirect

H ≅ G/N

type

2. #15689236

C₂

semidirect

3. #15688947

C₂

semidirect

4. #15688935

C₂

semidirect

5. #15688933

C₂

semidirect

6. #15688901

C₂

semidirect

7. C₄₇×#444

C₂

semidirect

10. #13093967

C₄

semidirect

11. #13093965

C₄

semidirect

24. Q₁₆×C₄₇

C₂×C₄

semidirect

26. D₈×C₄₇

C₂×C₄

semidirect

38. C₄₇⋊C₁₆

C₂×C₄

semidirect

70. #444

D₄₇

semidirect

76. C₄₇

AGL(1,ℤ/16)

semidirect

93. Q₁₆

C₄×D₄₇

semidirect

97. D₈

C₄×D₄₇

semidirect

Subgroups — #20245286

Conjugacy classes of subgroups

Complements