Finite Group Databasebeta

← #20245344

Subgroups — #20245344

Order 6016.

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

normal subgroups only

This group has 220 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.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689924C211yesmaximal, characteristic, complemented
2#15689559C211yesmaximal, characteristic, complemented
3#15689390C211yesmaximal, characteristic, complemented
4#15688936C211yesmaximal, characteristic, complemented
5#15688931C211yesmaximal, characteristic, complemented
6#15688906C211yesmaximal, characteristic, complemented
7C2×D16×C47C211yesmaximal, characteristic, complemented
8#13094069—21no—
9#13094050—21no—
10#13094050—21no—
11#13094048—22no—
12#13094046C2211yescharacteristic
13#13094043—21no—
14D8×D47—21no—
15#13094030C2211yescharacteristic
16#13093968—21no—
17#13093965—21no—
18#13093964C2211yescharacteristic, complemented
19#13093960C2211yescharacteristic, complemented
20#13093941—21no—
21C2×D8×C47C2211yescharacteristic
22C2×D8×C47C2211yescharacteristic, complemented
23D16×C47—22no—
24C2×C16×C47C2211yescharacteristic, complemented
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×C22⋊D47—42no—
28#10625352—22no—
29#10625352—41no—
30D4×D47—22no—
31D4×D47—41no—
32#10625350—21no—
33#10625350D411yescharacteristic
34D8×C47—21no—
35D8×C47—21no—
36D8×C47—21no—
37D8×C47D412yes—
38C2×C8×C47C2311yescharacteristic
39#10625335—22no—
40#10625335—41no—
41#10625334—22no—
42#10625334—41no—
43#10625329—21no—
44#10625329D411yescharacteristic
45Dic188D411yescharacteristic
46D376D411yescharacteristic
47#10625325—21no—
48#10625324—21no—
49C8×D47—21no—
50C16×C47—21no—
51C47⋊C16—21no—
52C23×C47—41no—
53C23×C47—41no—
54C22×D47—42no—
55D4×C47—22no—
56D4×C47—41no—
57D4×C47—41no—
58D4×C47—41no—
59C2×C4×C47C2×D411yescharacteristic
60C22⋊D47—21no—
61C22⋊D47—42no—
62C22⋊D47—42no—
63C22⋊D47—41no—
64C2×Dic47—42no—
65D188—21no—
66D188D811yescharacteristic
67C4×D47—21no—
68C4×D47—41no—
69Dic94—21no—
70Dic94D811yescharacteristic
71C8×C47C2×D411yescharacteristic
72C8×C47C2×D411yescharacteristic
73C47⋊C8—21no—
74C47⋊C8—41no—
75C22×C47—42no—
76C22×C47—81no—
77C22×C47—161no—
78C22×C47—161no—
79C22×C47AGL(1,ℤ/8)11yescharacteristic
80C2×D47—21no—
81C2×D47—41no—
82C2×D47—162no—
83C4×C47#12011yescharacteristic
84C4×C47C2×D811yescharacteristic
85Dic47—21no—
86Dic47—41no—
87#2192—471nomaximal, Sylow
88C2×C47—21no—
89C2×C47—82no—
90C2×C47—161no—
91C2×C47#44711yescharacteristic
92D47—41no—
93D47—81no—
94#576—471no—
95#509—471no—
96C2×D16D4711yescharacteristic, complemented
97#472—471no—
98#361—471no—
99#359—471no—
100#350—471no—
101C47#219211yescharacteristic, complemented, Sylow
102H(5,𝔽2)—941no—
103AGL(1,ℤ/8)—941no—
104AGL(1,ℤ/8)—942no—
105AGL(1,ℤ/8)—941no—
106#135—471no—
107#135—941no—
108C2×D8—941no—
109C2×D8C2×D4711yescharacteristic
110C2×D8C2×D4711yescharacteristic, complemented
111#131—471no—
112SD32—941no—
113D16—22no—
114D16—941no—
115M32—471no—
116C2×C16C2×D4711yescharacteristic, complemented
117#108—471no—
118#100—941no—
119#41—471no—
120#41—942no—
121#41—941no—
122#41—1881no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—942no—
126C2×D4—1881no—
127C2×D4—1882no—
128Q16—471no—
129SD16—942no—
130SD16—941no—
131SD16—1881no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—471no—
136D8—942no—
137D8—1881no—
138D8C22⋊D4712yes—
139M16—471no—
140M16—941no—
141M16—941no—
142C2×C8—941no—
143C2×C8C22×D4711yescharacteristic
144C16—21no—
145C16—941no—
146C23—41no—
147C23—41no—
148C23—1882no—
149Q8—471no—
150Q8—941no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—471no—
156D4—941no—
157D4—941no—
158D4—1882no—
159D4—1882no—
160D4—1881no—
161C2×C4—941no—
162C2×C4—1882no—
163C2×C4—1881no—
164C2×C4D4×D4711yescharacteristic
165C8—941no—
166C8—1881no—
167C8D4×D4711yescharacteristic
168C8C2×C22⋊D4711yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—941no—
174C22—1881no—
175C22—7522no—
176C22#1309404811yescharacteristic
177C4—941no—
178C4—1881no—
179C4#1309399211yescharacteristic
180C4D8×D4711yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—3761no—
185C2—1881no—
186C2#1568925511yescharacteristic
subgroupG/H
centerC2#15689255
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC2×D16×C47C2
socleC2×C47#447
hypercenterC2×D16D47
hypocenterC47#2192
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689924C2semidirect
2. #15689559C2semidirect
3. #15689390C2semidirect
4. #15688936C2semidirect
5. #15688931C2semidirect
6. #15688906C2semidirect
7. C2×D16×C47C2semidirect
18. #13093964C22semidirect
19. #13093960C22semidirect
22. C2×D8×C47C22semidirect
24. C2×C16×C47C22semidirect
96. C2×D16D47semidirect
101. C47#2192semidirect
110. C2×D8C2×D47semidirect
116. C2×C16C2×D47semidirect