Finite Group Databasebeta

← #15689927

Subgroups — #15689927

Order 3008.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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#13094070C211yesmaximal, characteristic, complemented
2#13094069C211yesmaximal, characteristic, complemented
3#13094052C211yesmaximal, characteristic, complemented
4#13094051C212yesmaximal, complemented
5#13094048C212yesmaximal, complemented
6#13094045C212yesmaximal, complemented
7#13094044C211yesmaximal, characteristic, complemented
8C2×#10625334C211yesmaximal, characteristic, complemented
9D8×D47C212yesmaximal, complemented
10#13094032C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
12#41×C47C2211yescharacteristic, complemented
13C2×D4×C47C2211yescharacteristic, complemented
14C2×C22⋊D47—22no—
15#10625354C2212yescomplemented
16#10625352—21no—
17#10625352C2212yescomplemented
18D4×D47—22no—
19D4×D47—21no—
20D4×D47C2212yescomplemented
21D4×D47C2212yescomplemented
22#10625350—21no—
23#10625350C2211yescharacteristic
24#10625350C2211yescharacteristic, complemented
25C2×D188—21no—
26C2×D188C2211yescharacteristic, complemented
27SD16×C47C2212yescomplemented
28D8×C47C2212yescomplemented
29M16×C47C2211yescharacteristic, complemented
30#10625337C2211yescharacteristic, complemented
31#10625336C2211yescharacteristic, complemented
32#10625335C2211yescharacteristic, complemented
33#10625334C2211yescharacteristic, complemented
34#10625334C2212yescomplemented
35#10625334C2212yescomplemented
36C2×C47⋊C8C2211yescharacteristic, complemented
37D376C2212yescomplemented
38#10625325C2212yescomplemented
39#10625324C2212yescomplemented
40C8×D47C2212yescomplemented
41C23×C47—21no—
42C22×D47—21no—
43C22×D47—22no—
44C22×D47—22no—
45Q8×C47C2311yescharacteristic
46D4×C47—21no—
47D4×C47—21no—
48D4×C47C2312yes—
49D4×C47C2311yescharacteristic
50C2×C4×C47—21no—
51C2×C4×C47C2311yescharacteristic
52C22⋊D47—21no—
53C22⋊D47—22no—
54C22⋊D47—22no—
55C22⋊D47—22no—
56C22⋊D47D412yes—
57C2×Dic47—22no—
58D188—22no—
59D188—21no—
60D188D411yescharacteristic
61D188C2312yes—
62D188C2311yescharacteristic
63C4×D47—21no—
64C4×D47—22no—
65C4×D47C2312yes—
66Dic94D411yescharacteristic
67Dic94C2311yescharacteristic
68C8×C47C2312yes—
69C47⋊C8C2311yescharacteristic
70C47⋊C8C2311yescharacteristic
71C22×C47—22no—
72C22×C47—21no—
73C22×C47—81no—
74C22×C47C2×D411yescharacteristic
75C2×D47—22no—
76C2×D47—21no—
77C2×D47—82no—
78C2×D47—82no—
79C2×D47—81no—
80C2×D47C2×D412yes—
81C4×C47—21no—
82C4×C47C2×D411yescharacteristic
83C4×C47C2411yescharacteristic
84Dic47—21no—
85Dic47C2×D412yes—
86C2×C47—21no—
87C2×C47—41no—
88C2×C47—42no—
89C2×C47C22×D411yescharacteristic
90D47—22no—
91D47—42no—
92D47—41no—
93#576—471nomaximal, Sylow
94C47#57611yescharacteristic, complemented, Sylow
95H(5,𝔽2)—471no—
96H(5,𝔽2)—471no—
97AGL(1,ℤ/8)—472no—
98AGL(1,ℤ/8)—472no—
99AGL(1,ℤ/8)—471no—
100AGL(1,ℤ/8)D4711yescharacteristic, complemented
101#135—471no—
102#135—472no—
103C2×D8—471no—
104C2×D8—472no—
105#131—471no—
106#41—471no—
107#41—472no—
108#41—472no—
109#41—471no—
110#41—941no—
111#41—941no—
112#41C2×D4711yescharacteristic, complemented
113C2×D4—472no—
114C2×D4—472no—
115C2×D4—471no—
116C2×D4—941no—
117C2×D4—942no—
118C2×D4—941no—
119C2×D4—942no—
120C2×D4C2×D4711yescharacteristic, complemented
121Q16—471no—
122SD16—471no—
123SD16—471no—
124SD16—472no—
125SD16C2×D4712yescomplemented
126D8—472no—
127D8—471no—
128D8—472no—
129D8—472no—
130D8C2×D4712yescomplemented
131M16—472no—
132M16C2×D4711yescharacteristic, complemented
133C2×C8—471no—
134C2×C8—472no—
135C23—21no—
136C23—942no—
137C23—942no—
138C23—941no—
139Q8—471no—
140Q8—471no—
141Q8C22×D4711yescharacteristic
142D4—21no—
143D4—21no—
144D4—472no—
145D4—471no—
146D4—472no—
147D4—471no—
148D4—942no—
149D4—942no—
150D4—942no—
151D4—942no—
152D4—941no—
153D4—941no—
154D4C22×D4712yes—
155D4C22×D4711yescharacteristic
156C2×C4—21no—
157C2×C4—472no—
158C2×C4—942no—
159C2×C4—942no—
160C2×C4—941no—
161C2×C4C22×D4711yescharacteristic
162C8—471no—
163C8—471no—
164C8C22×D4712yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—472no—
169C22—942no—
170C22—941no—
171C22—3761no—
172C22—3762no—
173C22—3762no—
174C22D4×D4711yescharacteristic
175C4—21no—
176C4—472no—
177C4—941no—
178C4D4×D4711yescharacteristic
179C4C23×D4711yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—942no—
184C2—1882no—
185C2—1881no—
186C2C2×D4×D4711yescharacteristic
subgroupG/H
centerC2C2×D4×D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
FittingAGL(1,ℤ/8)×C47C2
socleC2×C47C22×D4
hypercenterAGL(1,ℤ/8)D47
hypocenterC47#576
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #13094070C2semidirect
2. #13094069C2semidirect
3. #13094052C2semidirect
4. #13094051C2semidirect
5. #13094048C2semidirect
6. #13094045C2semidirect
7. #13094044C2semidirect
8. C2×#10625334C2semidirect
9. D8×D47C2semidirect
10. #13094032C2semidirect
11. AGL(1,ℤ/8)×C47C2semidirect
12. #41×C47C22semidirect
13. C2×D4×C47C22semidirect
15. #10625354C22semidirect
17. #10625352C22semidirect
20. D4×D47C22semidirect
21. D4×D47C22semidirect
24. #10625350C22semidirect
26. C2×D188C22semidirect
27. SD16×C47C22semidirect
28. D8×C47C22semidirect
29. M16×C47C22semidirect
30. #10625337C22semidirect
31. #10625336C22semidirect
32. #10625335C22semidirect
33. #10625334C22semidirect
34. #10625334C22semidirect
35. #10625334C22semidirect
36. C2×C47⋊C8C22semidirect
37. D376C22semidirect
38. #10625325C22semidirect
39. #10625324C22semidirect
40. C8×D47C22semidirect
94. C47#576semidirect
100. AGL(1,ℤ/8)D47semidirect
112. #41C2×D47semidirect
120. C2×D4C2×D47semidirect
125. SD16C2×D47semidirect
130. D8C2×D47semidirect
132. M16C2×D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130940702
#130940692
#130940522
#130940512
#130940482
#130940452
#130940442
C2×#106253342
D8×D472
#130940322
AGL(1,ℤ/8)×C472
#57647