Group #20245467 — subgroups

Subgroups — #20245467

Order 6016.

150 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 45 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	#15689563	C₂	1	1	yes	maximal, characteristic
2	#15689501	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689240	C₂	1	1	yes	maximal, characteristic
4	#15688943	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688940	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#510	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#10625337	—	2	1	no	—
10	#13094031	—	2	1	no	—
11	#13094022	—	2	1	no	—
12	#13093970	—	2	1	no	—
13	#13093968	—	2	1	no	—
14	#13093964	C₂²	1	1	yes	characteristic
15	#13093960	C₂²	1	1	yes	characteristic
16	#13093951	—	2	1	no	—
17	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
18	#135×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	Q₃₂×C₄₇	—	2	1	no	—
21	SD₃₂×C₄₇	—	2	1	no	—
22	M₃₂×C₄₇	C₂²	1	1	yes	characteristic
23	#41×C₄₇	—	2	1	no	—
24	C₂×Q₈×C₄₇	—	2	1	no	—
25	C₂×Dic₉₄	—	2	1	no	—
26	Q₁₆×C₄₇	—	2	1	no	—
27	Q₁₆×C₄₇	—	2	1	no	—
28	Q₁₆×C₄₇	D₄	1	1	yes	characteristic
29	SD₁₆×C₄₇	—	2	1	no	—
30	D₈×C₄₇	D₄	1	1	yes	characteristic
31	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
32	#10625337	—	4	1	no	—
33	#10625337	—	4	1	no	—
34	Dic₄₇⋊C₄	—	4	2	no	—
35	C₄×Dic₄₇	D₄	1	1	yes	characteristic
36	#10625329	—	2	1	no	—
37	#10625329	—	4	1	no	—
38	C₂×C₄₇⋊C₈	—	4	1	no	—
39	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
40	Dic₁₈₈	—	2	1	no	—
41	Dic₁₈₈	—	2	1	no	—
42	C₁₆×C₄₇	—	2	1	no	—
43	C₄₇⋊C₁₆	—	2	1	no	—
44	Q₈×C₄₇	—	2	1	no	—
45	Q₈×C₄₇	—	4	1	no	—
46	Q₈×C₄₇	—	4	1	no	—
47	D₄×C₄₇	—	2	1	no	—
48	D₄×C₄₇	—	4	1	no	—
49	C₂×C₄×C₄₇	—	4	1	no	—
50	C₂×C₄×C₄₇	—	4	1	no	—
51	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂×Dic₄₇	—	2	1	no	—
53	C₂×Dic₄₇	—	4	1	no	—
54	Dic₉₄	—	4	1	no	—
55	Dic₉₄	—	4	1	no	—
56	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₈×C₄₇	#41	1	1	yes	characteristic
58	C₄₇⋊C₈	—	4	1	no	—
59	C₄₇⋊C₈	D₈	1	1	yes	characteristic
60	C₄₇⋊C₈	D₈	1	1	yes	characteristic
61	C₂²×C₄₇	—	4	1	no	—
62	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
63	C₄×C₄₇	—	4	1	no	—
64	C₄×C₄₇	—	8	1	no	—
65	C₄×C₄₇	#121	1	1	yes	characteristic
66	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
67	Dic₄₇	—	2	2	no	—
68	Dic₄₇	—	8	1	no	—
69	#2214	—	47	1	no	maximal, Sylow
70	C₂×C₄₇	—	2	1	no	—
71	C₂×C₄₇	—	8	1	no	—
72	C₂×C₄₇	#459	1	1	yes	characteristic
73	#510	—	47	1	no	—
74	#510	D₄₇	1	1	yes	characteristic
75	#494	—	47	1	no	—
76	#443	—	47	1	no	—
77	#364	—	47	1	no	—
78	#362	—	47	1	no	—
79	#362	—	47	1	no	—
80	C₄₇	#2214	1	1	yes	characteristic, complemented, Sylow
81	#135	C₂×D₄₇	1	1	yes	characteristic
82	C₂×Q₁₆	—	47	1	no	—
83	C₂×Q₁₆	—	94	1	no	—
84	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
85	#131	—	94	1	no	—
86	C₄⋊Q₈	—	94	1	no	—
87	Q₃₂	—	2	1	no	—
88	Q₃₂	—	94	1	no	—
89	SD₃₂	—	2	1	no	—
90	SD₃₂	—	94	1	no	—
91	M₃₂	—	47	1	no	—
92	M₃₂	C₂×D₄₇	1	1	yes	characteristic
93	#108	—	47	1	no	—
94	#104	—	94	1	no	—
95	C₄×C₈	—	47	1	no	—
96	#41	—	2	1	no	—
97	C₂×Q₈	—	2	1	no	—
98	C₂×Q₈	—	94	1	no	—
99	Q₁₆	—	2	1	no	—
100	Q₁₆	—	2	1	no	—
101	Q₁₆	—	94	1	no	—
102	Q₁₆	—	94	1	no	—
103	Q₁₆	—	188	1	no	—
104	Q₁₆	—	188	1	no	—
105	Q₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
106	SD₁₆	—	2	1	no	—
107	D₈	C₂²⋊D₄₇	1	1	yes	characteristic
108	M₁₆	—	94	1	no	—
109	M₁₆	—	188	1	no	—
110	C₂×C₈	—	47	1	no	—
111	C₂×C₈	—	188	1	no	—
112	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
113	C₄⋊C₄	—	188	2	no	—
114	C₄²	—	47	1	no	—
115	C₁₆	—	2	1	no	—
116	C₁₆	—	94	1	no	—
117	Q₈	—	2	1	no	—
118	Q₈	—	4	1	no	—
119	Q₈	—	4	1	no	—
120	Q₈	—	188	1	no	—
121	Q₈	—	188	1	no	—
122	D₄	—	2	1	no	—
123	D₄	—	4	1	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	4	1	no	—
126	C₂×C₄	—	94	1	no	—
127	C₂×C₄	—	188	1	no	—
128	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
129	C₈	—	47	1	no	—
130	C₈	—	47	1	no	—
131	C₈	—	188	1	no	—
132	C₈	#10625352	1	1	yes	characteristic
133	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
134	C₂²	—	4	1	no	—
135	C₂²	#13094048	1	1	yes	characteristic
136	C₄	—	4	1	no	—
137	C₄	—	8	1	no	—
138	C₄	—	94	2	no	—
139	C₄	—	376	1	no	—
140	C₄	#13093996	1	1	yes	characteristic
141	C₄	D₈×D₄₇	1	1	yes	characteristic
142	C₂	—	2	1	no	—
143	C₂	—	8	1	no	—
144	C₂	#15689316	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689563

C₂

yes

maximal, characteristic

#15689501

C₂

yes

maximal, characteristic, complemented

#15689240

C₂

yes

maximal, characteristic

#15688943

C₂

yes

maximal, characteristic, complemented

#15688940

C₂

yes

maximal, characteristic, complemented

#15688939

C₂

yes

maximal, characteristic, complemented

C₄₇×#510

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

#13093960

C₂²

yes

characteristic

#13093951

—

C₈×Dic₄₇

C₂²

yes

characteristic

#135×C₄₇

C₂²

yes

characteristic

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

Q₃₂×C₄₇

—

SD₃₂×C₄₇

—

M₃₂×C₄₇

C₂²

yes

characteristic

#41×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

D₄

yes

characteristic

SD₁₆×C₄₇

—

D₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

#10625337

—

#10625337

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

characteristic

Dic₁₈₈

—

Dic₁₈₈

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₄₇⋊C₈

D₈

yes

characteristic

C₄₇⋊C₈

D₈

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#121

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2214

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

D₄₇

yes

—

—

—

—

—

C₄₇

#2214

yes

characteristic, complemented, Sylow

#135

C₂×D₄₇

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

#131

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

M₃₂

—

M₃₂

C₂×D₄₇

yes

characteristic

#108

—

#104

—

C₄×C₈

—

#41

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

100

Q₁₆

—

101

Q₁₆

—

102

Q₁₆

—

103

Q₁₆

—

188

—

104

Q₁₆

—

188

—

105

Q₁₆

C₂²⋊D₄₇

yes

characteristic

106

SD₁₆

—

107

D₈

C₂²⋊D₄₇

yes

characteristic

108

M₁₆

—

109

M₁₆

—

188

—

110

C₂×C₈

—

111

C₂×C₈

—

188

—

112

C₂×C₈

C₂²×D₄₇

yes

characteristic

113

C₄⋊C₄

—

188

—

114

C₄²

—

115

C₁₆

—

116

C₁₆

—

117

Q₈

—

118

Q₈

—

119

Q₈

—

120

Q₈

—

188

—

121

Q₈

—

188

—

122

D₄

—

123

D₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

188

—

128

C₂×C₄

D₄×D₄₇

yes

characteristic

129

C₈

—

130

C₈

—

131

C₈

—

188

—

132

C₈

#10625352

yes

characteristic

133

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

134

C₂²

—

135

C₂²

#13094048

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

376

—

140

C₄

#13093996

yes

characteristic

141

C₄

D₈×D₄₇

yes

characteristic

142

C₂

—

143

C₂

—

144

C₂

#15689316

yes

characteristic

	subgroup	G/H
center	C₂	#15689316
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#510	C₂
socle	C₂×C₄₇	#459
hypercenter	#510	D₄₇
hypocenter	C₄₇	#2214
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #510

subgroup

G/H

center

C₂

#15689316

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#510

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #510

N	H ≅ G/N	type
2. #15689501	C₂	semidirect
4. #15688943	C₂	semidirect
5. #15688940	C₂	semidirect
6. #15688939	C₂	semidirect
80. C₄₇	#2214	semidirect

H ≅ G/N

type

2. #15689501

C₂

semidirect

4. #15688943

C₂

semidirect

5. #15688940

C₂

semidirect

6. #15688939

C₂

semidirect

80. C₄₇

#2214

semidirect

Subgroups — #20245467

Conjugacy classes of subgroups

Complements