Finite Group Databasebeta

← #20252290

Subgroups — #20252290

Order 6016.

456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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#15689923C211yesmaximal, characteristic
2C2×#13094032C212yesmaximal, complemented
3#15689244C214yesmaximal, complemented
4#15689239C214yesmaximal, complemented
5#15689139C212yesmaximal, complemented
6#15689081C211yesmaximal, characteristic, complemented
7C47×#430C211yesmaximal, characteristic, complemented
8C2×#10625350C2212yes—
9#13094057C414yescomplemented
10#13094052C414yescomplemented
11#13094046C2214yes—
12#13094032—22no—
13#13094032—22no—
14#13094032C2214yescomplemented
15#13094032C2214yescomplemented
16C2×#10625324—22no—
17C22×C47⋊C8C2211yescharacteristic
18C2×C8×D47—22no—
19#13093983C2211yescharacteristic
20#13093950C2218yescomplemented
21#13093934C2212yescomplemented
22C8×Dic47C2212yescomplemented
23C2×M16×C47C2212yes—
24C2×M16×C47C2211yescharacteristic
25#108×C47C2214yescomplemented
26C22×C4×C47C2311yescharacteristic
27C2×C22⋊D47—22no—
28#10625350—22no—
29#10625350—22no—
30#10625350C2×C414yes—
31#10625350C2314yes—
32C2×D188C2×C412yes—
33C2×C4×D47—22no—
34C2×Dic94C2×C412yes—
35M16×C47—22no—
36M16×C47C2×C414yes—
37M16×C47C2314yes—
38C2×C8×C47—22no—
39C2×C8×C47C2312yes—
40C22⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4×Dic47C2312yes—
43C2×C47⋊C8D412yes—
44C2×C47⋊C8D412yes—
45C2×C47⋊C8C2311yescharacteristic
46C2×C47⋊C8C2311yescharacteristic
47Dic188C2×C414yes—
48D376C2×C414yes—
49#10625325C2×C418yes—
50#10625324—24no—
51#10625324—24no—
52C8×D47—24no—
53C8×D47—24no—
54C23×C47#4111yescharacteristic
55C22×D47—22no—
56C2×C4×C47C22×C412yes—
57C2×C4×C47C2×D412yes—
58C2×C4×C47#4111yescharacteristic
59C2×C4×C47C2411yescharacteristic
60C22⋊D47—24no—
61C22⋊D47—24no—
62C2×Dic47—22no—
63C2×Dic47—22no—
64D188—22no—
65D188C22×C414yes—
66C4×D47—24no—
67C4×D47—24no—
68Dic94—22no—
69Dic94C22×C414yes—
70C8×C47—24no—
71C8×C47C22×C414yes—
72C47⋊C8C2×D411yescharacteristic
73C47⋊C8C2×D412yes—
74C47⋊C8C2×D411yescharacteristic
75C22×C47—41no—
76C22×C47C4×D412yes—
77C22×C47C2×#4111yescharacteristic
78C2×D47—24no—
79C2×D47—44no—
80C4×C47C4×D412yes—
81C4×C47C23×C411yescharacteristic
82C4×C47C22×D411yescharacteristic
83Dic47—24no—
84Dic47—42no—
85#2955—471nomaximal, Sylow
86C2×C47—21no—
87C2×C47—22no—
88C2×C47C2×C4×D411yescharacteristic
89D47—44no—
90#575—471no—
91C2×#131—472no—
92#444—474no—
93#443—474no—
94#430D4711yescharacteristic, complemented
95#421—472no—
96#405—471no—
97C47#295511yescharacteristic, complemented, Sylow
98C2×#41—472no—
99#137—474no—
100AGL(1,ℤ/8)—474no—
101#135—474no—
102#131—474no—
103#131—474no—
104#131—942no—
105#131—942no—
106C2×M16—942no—
107C2×M16C2×D4712yes—
108C2×M16C2×D4711yescharacteristic
109C22×C8—471no—
110C22×C8—942no—
111#117—471no—
112#108C2×D4714yescomplemented
113#104—478no—
114#97—472no—
115C4×C8—472no—
116#41—474no—
117#41—474no—
118#41—942no—
119#41—942no—
120C2×Q8—472no—
121C2×D4—472no—
122C2×D4—942no—
123C22×C4—942no—
124C22×C4C22×D4711yescharacteristic
125Q16—474no—
126SD16—478no—
127D8—474no—
128M16—22no—
129M16—944no—
130M16—944no—
131M16C4×D4714yes—
132M16C22×D4714yes—
133C2×C8—22no—
134C2×C8—472no—
135C2×C8—472no—
136C2×C8—471no—
137C2×C8—471no—
138C2×C8—944no—
139C2×C8—944no—
140C2×C8C22×D4712yes—
141C4⋊C4—941no—
142C22⋊C4—941no—
143C42—472no—
144C23—942no—
145C23#1062535411yescharacteristic
146Q8—474no—
147Q8—942no—
148D4—474no—
149D4—944no—
150D4—944no—
151D4—942no—
152C2×C4—942no—
153C2×C4—944no—
154C2×C4—944no—
155C2×C4—942no—
156C2×C4C2×C4×D4712yes—
157C2×C4D4×D4712yes—
158C2×C4#1062535411yescharacteristic
159C2×C4C23×D4711yescharacteristic
160C8—24no—
161C8—471no—
162C8—472no—
163C8—471no—
164C8C2×C4×D4714yes—
165C22—41no—
166C22—944no—
167C22—1884no—
168C22#1309398612yes—
169C22C2×#1062535411yescharacteristic
170C4—944no—
171C4—1882no—
172C4#1309398612yes—
173C4C22×C4×D4711yescharacteristic
174C4C2×D4×D4711yescharacteristic
175C2—21no—
176C2—22no—
177C2—1884no—
178C2C2×#1309398611yescharacteristic
subgroupG/H
centerC4C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#430C2
socleC2×C47C2×C4×D4
hypercenter#430D47
hypocenterC47#2955
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
2. C2×#13094032C2semidirect
3. #15689244C2semidirect
4. #15689239C2semidirect
5. #15689139C2semidirect
6. #15689081C2semidirect
7. C47×#430C2semidirect
9. #13094057C4semidirect
10. #13094052C4semidirect
14. #13094032C22semidirect
15. #13094032C22semidirect
20. #13093950C22semidirect
21. #13093934C22semidirect
22. C8×Dic47C22semidirect
25. #108×C47C22semidirect
94. #430D47semidirect
97. C47#2955semidirect
112. #108C2×D47semidirect