Finite Group Databasebeta

← #15689929

Subgroups — #15689929

Order 3008.

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

normal subgroups only

This group has 258 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#13094072C211yesmaximal, characteristic, complemented
2#13094069C211yesmaximal, characteristic, complemented
3#13094055C211yesmaximal, characteristic, complemented
4#13094053C212yesmaximal, complemented
5#13094051C212yesmaximal, complemented
6#13094050C211yesmaximal, characteristic, complemented
7#13094046C211yesmaximal, characteristic, complemented
8#13094045C212yesmaximal, complemented
9SD16×D47C212yesmaximal, complemented
10#13094030C211yesmaximal, characteristic, complemented
11C2×SD16×C47C211yesmaximal, characteristic, complemented
12C2×Q8×C47C2211yescharacteristic, complemented
13C2×D4×C47C2211yescharacteristic
14C2×C22⋊D47—22no—
15#10625354—21no—
16#10625354C2212yescomplemented
17Q8×D47—21no—
18Q8×D47C2212yescomplemented
19#10625352—21no—
20#10625352C2212yes—
21D4×D47—21no—
22D4×D47C2212yes—
23#10625350—22no—
24#10625350C2211yescharacteristic
25#10625350C2211yescharacteristic
26#10625350C2211yescharacteristic, complemented
27SD16×C47C2212yescomplemented
28SD16×C47C2212yescomplemented
29C2×C8×C47C2211yescharacteristic, complemented
30#10625337C2212yescomplemented
31#10625336C2212yescomplemented
32#10625335C2212yescomplemented
33#10625334C2212yescomplemented
34#10625329C2211yescharacteristic, complemented
35Dic188C2211yescharacteristic, complemented
36D376C2211yescharacteristic, complemented
37#10625325C2211yescharacteristic, complemented
38#10625325C2211yescharacteristic, complemented
39#10625324C2212yescomplemented
40C8×D47C2212yescomplemented
41C23×C47—21no—
42C22×D47—22no—
43Q8×C47—21no—
44Q8×C47C2312yes—
45D4×C47—21no—
46D4×C47C2312yes—
47C2×C4×C47—21no—
48C2×C4×C47C2311yescharacteristic
49C22⋊D47—21no—
50C22⋊D47—21no—
51C22⋊D47—22no—
52C22⋊D47—22no—
53C22⋊D47D412yes—
54C2×Dic47—22no—
55D188—22no—
56D188D411yescharacteristic
57D188C2311yescharacteristic
58D188C2311yescharacteristic
59C4×D47—22no—
60C4×D47—21no—
61C4×D47—21no—
62C4×D47—22no—
63C4×D47C2312yes—
64Dic94—22no—
65Dic94D411yescharacteristic
66Dic94C2311yescharacteristic
67Dic94C2311yescharacteristic
68C8×C47C2311yescharacteristic
69C8×C47C2311yescharacteristic
70C47⋊C8C2312yes—
71C22×C47—22no—
72C22×C47—81no—
73C22×C47C2×D411yescharacteristic
74C2×D47—21no—
75C2×D47—21no—
76C2×D47—82no—
77C2×D47C2×D412yes—
78C4×C47—22no—
79C4×C47C2×D411yescharacteristic
80C4×C47C2411yescharacteristic
81Dic47—21no—
82Dic47—21no—
83Dic47C2×D412yes—
84C2×C47—21no—
85C2×C47—42no—
86C2×C47C22×D411yescharacteristic
87D47—22no—
88D47—41no—
89D47—41no—
90#577—471nomaximal, Sylow
91C47#57711yescharacteristic, complemented, Sylow
922−1+4—471no—
93H(5,𝔽2)—471no—
94#137—471no—
95#137—472no—
96AGL(1,ℤ/8)—471no—
97AGL(1,ℤ/8)—472no—
98#135—472no—
99#135—471no—
100C2×SD16—472no—
101C2×SD16D4711yescharacteristic, complemented
102#131—471no—
103#41—471no—
104#41—472no—
105#41—472no—
106#41—471no—
107#41—471no—
108#41—942no—
109#41—941no—
110#41—941no—
111C2×Q8—472no—
112C2×Q8—941no—
113C2×Q8C2×D4711yescharacteristic, complemented
114C2×D4—472no—
115C2×D4—941no—
116C2×D4—942no—
117C2×D4C2×D4711yescharacteristic
118Q16—472no—
119Q16—471no—
120SD16—472no—
121SD16—472no—
122SD16—471no—
123SD16—471no—
124SD16C2×D4712yescomplemented
125SD16C2×D4712yescomplemented
126D8—472no—
127D8—471no—
128M16—471no—
129M16—472no—
130C2×C8—472no—
131C2×C8C2×D4711yescharacteristic, complemented
132C23—21no—
133C23—942no—
134Q8—21no—
135Q8—471no—
136Q8—471no—
137Q8—471no—
138Q8—942no—
139Q8C22×D4712yes—
140D4—21no—
141D4—472no—
142D4—471no—
143D4—471no—
144D4—471no—
145D4—942no—
146D4—942no—
147D4—942no—
148D4—941no—
149D4—941no—
150D4C22×D4712yes—
151C2×C4—21no—
152C2×C4—472no—
153C2×C4—942no—
154C2×C4—942no—
155C2×C4—942no—
156C2×C4—941no—
157C2×C4—941no—
158C2×C4C22×D4711yescharacteristic
159C8—472no—
160C8C22×D4711yescharacteristic
161C8C22×D4711yescharacteristic
162C22—22no—
163C22—81no—
164C22—472no—
165C22—941no—
166C22—941no—
167C22—3762no—
168C22D4×D4711yescharacteristic
169C4—22no—
170C4—472no—
171C4—941no—
172C4—941no—
173C4D4×D4711yescharacteristic
174C4C23×D4711yescharacteristic
175C2—21no—
176C2—42no—
177C2—942no—
178C2—1881no—
179C2—1881no—
180C2C2×D4×D4711yescharacteristic
subgroupG/H
centerC2C2×D4×D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
FittingC2×SD16×C47C2
socleC2×C47C22×D4
hypercenterC2×SD16D47
hypocenterC47#577
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #13094072C2semidirect
2. #13094069C2semidirect
3. #13094055C2semidirect
4. #13094053C2semidirect
5. #13094051C2semidirect
6. #13094050C2semidirect
7. #13094046C2semidirect
8. #13094045C2semidirect
9. SD16×D47C2semidirect
10. #13094030C2semidirect
11. C2×SD16×C47C2semidirect
12. C2×Q8×C47C22semidirect
16. #10625354C22semidirect
18. Q8×D47C22semidirect
26. #10625350C22semidirect
27. SD16×C47C22semidirect
28. SD16×C47C22semidirect
29. C2×C8×C47C22semidirect
30. #10625337C22semidirect
31. #10625336C22semidirect
32. #10625335C22semidirect
33. #10625334C22semidirect
34. #10625329C22semidirect
35. Dic188C22semidirect
36. D376C22semidirect
37. #10625325C22semidirect
38. #10625325C22semidirect
39. #10625324C22semidirect
40. C8×D47C22semidirect
91. C47#577semidirect
101. C2×SD16D47semidirect
113. C2×Q8C2×D47semidirect
124. SD16C2×D47semidirect
125. SD16C2×D47semidirect
131. C2×C8C2×D47semidirect

Maximal subgroups

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

subgroupindex
#130940722
#130940692
#130940552
#130940532
#130940512
#130940502
#130940462
#130940452
SD16×D472
#130940302
C2×SD16×C472
#57747