Group #20245516 — subgroups

Subgroups — #20245516

Order 6016.

144 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 47 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	C₂×#13093968	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689540	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689398	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688952	C₂	1	1	yes	maximal, characteristic, complemented
5	#15688938	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#472	C₂	1	1	yes	maximal, characteristic
8	#13094054	—	2	1	no	—
9	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
10	#13093968	—	2	1	no	—
11	#13093968	—	2	1	no	—
12	#13093964	—	2	1	no	—
13	#13093964	C₂²	1	1	yes	characteristic
14	C₂×C₄₇⋊C₁₆	—	2	1	no	—
15	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
16	#13093960	C₂²	1	1	yes	characteristic
17	#13093942	—	2	1	no	—
18	AGL(1,ℤ/8)×C₄₇	—	2	1	no	—
19	C₂×D₈×C₄₇	C₂²	1	1	yes	characteristic
20	#131×C₄₇	C₂²	1	1	yes	characteristic
21	#108×C₄₇	C₂²	1	1	yes	characteristic
22	#100×C₄₇	—	2	1	no	—
23	#41×C₄₇	D₄	1	1	yes	characteristic
24	C₂×D₄×C₄₇	—	2	1	no	—
25	C₂×Dic₉₄	—	2	1	no	—
26	SD₁₆×C₄₇	—	4	1	no	—
27	D₈×C₄₇	—	2	1	no	—
28	D₈×C₄₇	—	2	1	no	—
29	D₈×C₄₇	—	4	1	no	—
30	M₁₆×C₄₇	—	2	1	no	—
31	M₁₆×C₄₇	—	2	1	no	—
32	M₁₆×C₄₇	D₄	1	1	yes	characteristic
33	C₂×C₈×C₄₇	—	2	1	no	—
34	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
35	#10625337	—	4	1	no	—
36	#10625335	—	4	1	no	—
37	#10625329	—	2	1	no	—
38	Dic₁₈₈	—	2	1	no	—
39	Dic₁₈₈	—	2	1	no	—
40	C₄₇⋊C₁₆	—	2	1	no	—
41	C₄₇⋊C₁₆	D₄	1	1	yes	characteristic
42	C₄₇⋊C₁₆	D₄	1	1	yes	characteristic
43	C₂³×C₄₇	—	4	1	no	—
44	Q₈×C₄₇	D₈	1	1	yes	characteristic
45	D₄×C₄₇	—	2	1	no	—
46	D₄×C₄₇	—	4	1	no	—
47	D₄×C₄₇	—	4	1	no	—
48	D₄×C₄₇	D₈	1	1	yes	characteristic
49	C₂×C₄×C₄₇	—	2	1	no	—
50	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₄₇	—	4	1	no	—
52	Dic₉₄	—	4	1	no	—
53	Dic₉₄	—	4	1	no	—
54	C₈×C₄₇	—	2	1	no	—
55	C₈×C₄₇	—	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	C₂²×C₄₇	—	2	1	no	—
60	C₂²×C₄₇	—	8	1	no	—
61	C₂²×C₄₇	—	16	1	no	—
62	C₂²×C₄₇	#135	1	1	yes	characteristic
63	C₄×C₄₇	—	2	1	no	—
64	C₄×C₄₇	#121	1	1	yes	characteristic
65	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
66	Dic₄₇	—	8	1	no	—
67	#2223	—	47	1	no	maximal, Sylow
68	C₂×C₄₇	—	2	1	no	—
69	C₂×C₄₇	—	4	1	no	—
70	C₂×C₄₇	—	16	1	no	—
71	C₂×C₄₇	#466	1	1	yes	characteristic
72	C₂×SD₃₂	—	47	1	no	—
73	#504	—	47	1	no	—
74	#473	—	47	1	no	—
75	#472	D₄₇	1	1	yes	characteristic
76	#368	—	47	1	no	—
77	#362	—	47	1	no	—
78	#361	—	47	1	no	—
79	C₄₇	#2223	1	1	yes	characteristic, complemented, Sylow
80	#137	—	94	1	no	—
81	AGL(1,ℤ/8)	—	2	1	no	—
82	C₂×Q₁₆	—	47	1	no	—
83	C₂×D₈	C₂×D₄₇	1	1	yes	characteristic
84	#131	C₂×D₄₇	1	1	yes	characteristic
85	SD₃₂	—	94	1	no	—
86	SD₃₂	—	94	1	no	—
87	M₃₂	—	47	1	no	—
88	M₃₂	—	94	1	no	—
89	C₂×C₁₆	—	47	1	no	—
90	C₂×C₁₆	—	94	1	no	—
91	#108	—	47	1	no	—
92	#108	C₂×D₄₇	1	1	yes	characteristic
93	#101	—	94	1	no	—
94	#100	—	2	1	no	—
95	#41	C₂²⋊D₄₇	1	1	yes	characteristic
96	C₂×Q₈	—	94	1	no	—
97	C₂×D₄	—	2	1	no	—
98	Q₁₆	—	94	1	no	—
99	Q₁₆	—	94	1	no	—
100	Q₁₆	—	188	1	no	—
101	SD₁₆	—	4	1	no	—
102	SD₁₆	—	188	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	2	1	no	—
105	D₈	—	4	1	no	—
106	M₁₆	—	2	1	no	—
107	M₁₆	—	2	1	no	—
108	M₁₆	—	94	1	no	—
109	M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
112	C₁₆	—	47	1	no	—
113	C₁₆	—	47	1	no	—
114	C₁₆	—	94	1	no	—
115	C₂³	—	4	1	no	—
116	Q₈	—	188	1	no	—
117	Q₈	—	188	1	no	—
118	Q₈	#10625334	1	1	yes	characteristic
119	D₄	—	2	1	no	—
120	D₄	—	4	1	no	—
121	D₄	—	4	1	no	—
122	D₄	#10625334	1	1	yes	characteristic
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	188	1	no	—
125	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
126	C₈	—	2	1	no	—
127	C₈	—	4	1	no	—
128	C₈	—	188	1	no	—
129	C₈	D₄×D₄₇	1	1	yes	characteristic
130	C₈	#10625352	1	1	yes	characteristic
131	C₂²	—	2	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	—	16	1	no	—
134	C₂²	#13094044	1	1	yes	characteristic
135	C₄	—	2	1	no	—
136	C₄	—	376	1	no	—
137	C₄	#13093996	1	1	yes	characteristic
138	C₄	C₂×#10625334	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	1	no	—
141	C₂	—	16	1	no	—
142	C₂	#15689357	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093968

C₂

yes

maximal, characteristic, complemented

#15689540

C₂

yes

maximal, characteristic, complemented

#15689398

C₂

yes

maximal, characteristic, complemented

#15688952

C₂

yes

maximal, characteristic, complemented

#15688938

C₂

yes

maximal, characteristic, complemented

#15688936

C₂

yes

maximal, characteristic, complemented

C₄₇×#472

C₂

yes

maximal, characteristic

#13094054

—

C₂×Dic₁₈₈

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093960

C₂²

yes

characteristic

#13093942

—

AGL(1,ℤ/8)×C₄₇

—

C₂×D₈×C₄₇

C₂²

yes

characteristic

#131×C₄₇

C₂²

yes

characteristic

#108×C₄₇

C₂²

yes

characteristic

#100×C₄₇

—

#41×C₄₇

D₄

yes

characteristic

C₂×D₄×C₄₇

—

C₂×Dic₉₄

—

SD₁₆×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

—

D₈×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

—

—

—

Dic₁₈₈

—

Dic₁₈₈

—

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

D₄

yes

characteristic

C₄₇⋊C₁₆

D₄

yes

characteristic

C₂³×C₄₇

—

Q₈×C₄₇

D₈

yes

characteristic

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#135

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

#121

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

—

#2223

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#466

yes

characteristic

C₂×SD₃₂

—

#504

—

#473

—

#472

D₄₇

yes

—

—

—

C₄₇

#2223

yes

characteristic, complemented, Sylow

#137

—

AGL(1,ℤ/8)

—

C₂×Q₁₆

—

C₂×D₈

C₂×D₄₇

yes

characteristic

#131

C₂×D₄₇

yes

characteristic

SD₃₂

—

SD₃₂

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#108

C₂×D₄₇

yes

—

—

C₂²⋊D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

100

Q₁₆

—

188

—

101

SD₁₆

—

102

SD₁₆

—

188

—

103

D₈

—

104

D₈

—

105

D₈

—

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

109

M₁₆

C₂²⋊D₄₇

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

C₂²×D₄₇

yes

characteristic

112

C₁₆

—

113

C₁₆

—

114

C₁₆

—

115

C₂³

—

116

Q₈

—

188

—

117

Q₈

—

188

—

118

Q₈

#10625334

yes

characteristic

119

D₄

—

120

D₄

—

121

D₄

—

122

D₄

#10625334

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

188

—

125

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

126

C₈

—

127

C₈

—

128

C₈

—

188

—

129

C₈

D₄×D₄₇

yes

characteristic

130

C₈

#10625352

yes

characteristic

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

#13094044

yes

characteristic

135

C₄

—

136

C₄

—

376

—

137

C₄

#13093996

yes

characteristic

138

C₄

C₂×#10625334

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

142

C₂

#15689357

yes

characteristic

	subgroup	G/H
center	C₂	#15689357
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#472	C₂
socle	C₂×C₄₇	#466
hypercenter	#472	D₄₇
hypocenter	C₄₇	#2223
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

subgroup

G/H

center

C₂

#15689357

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#472

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

N	H ≅ G/N	type
1. C₂×#13093968	C₂	semidirect
2. #15689540	C₂	semidirect
3. #15689398	C₂	semidirect
4. #15688952	C₂	semidirect
5. #15688938	C₂	semidirect
6. #15688936	C₂	semidirect
79. C₄₇	#2223	semidirect

H ≅ G/N

type

1. C₂×#13093968

C₂

semidirect

2. #15689540

C₂

semidirect

3. #15689398

C₂

semidirect

4. #15688952

C₂

semidirect

5. #15688938

C₂

semidirect

6. #15688936

C₂

semidirect

79. C₄₇

#2223

semidirect

Subgroups — #20245516

Conjugacy classes of subgroups

Complements