Finite Group Databasebeta

← #15689930

Subgroups — #15689930

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#13094071C211yesmaximal, characteristic, complemented
2#13094070C211yesmaximal, characteristic, complemented
3#13094056C212yesmaximal, complemented
4#13094054C211yesmaximal, characteristic, complemented
5#13094049C211yesmaximal, characteristic, complemented
6#13094048C212yesmaximal, complemented
7#13094045C212yesmaximal, complemented
8C2×#10625325C211yesmaximal, characteristic, complemented
9SD16×D47C212yesmaximal, complemented
10#13094030C211yesmaximal, characteristic, complemented
11#135×C47C211yesmaximal, characteristic, complemented
12#41×C47C2211yescharacteristic
13#41×C47C2211yescharacteristic, complemented
14#10625354C2212yes—
15Q8×D47C2212yescomplemented
16#10625352—22no—
17#10625352C2212yescomplemented
18D4×D47—22no—
19D4×D47C2212yes—
20#10625350—21no—
21#10625350—21no—
22#10625350C2211yescharacteristic
23C2×D188—21no—
24C2×D188C2211yescharacteristic
25C2×Dic94—21no—
26C2×Dic94C2211yescharacteristic, complemented
27Q16×C47C2211yescharacteristic, complemented
28SD16×C47C2211yescharacteristic, complemented
29SD16×C47C2211yescharacteristic, complemented
30D8×C47C2211yescharacteristic, complemented
31C2×C8×C47C2211yescharacteristic, complemented
32#10625337C2212yescomplemented
33#10625336C2212yescomplemented
34#10625335C2212yescomplemented
35#10625334C2212yescomplemented
36#10625329C2211yescharacteristic, complemented
37#10625325C2212yescomplemented
38#10625325C2212yescomplemented
39#10625324C2212yescomplemented
40C8×D47C2212yescomplemented
41C22×D47—21no—
42C22×D47—22no—
43Q8×C47C2311yescharacteristic
44Q8×C47C2311yescharacteristic
45D4×C47—21no—
46D4×C47—21no—
47D4×C47C2311yescharacteristic
48D4×C47C2311yescharacteristic
49C2×C4×C47—21no—
50C2×C4×C47—21no—
51C2×C4×C47C2311yescharacteristic
52C22⋊D47—22no—
53C22⋊D47—22no—
54C22⋊D47D412yes—
55C2×Dic47—21no—
56C2×Dic47—22no—
57D188—22no—
58D188—21no—
59D188D411yescharacteristic
60D188C2312yes—
61C4×D47—22no—
62C4×D47—22no—
63C4×D47C2312yes—
64Dic94—21no—
65Dic94—22no—
66Dic94D411yescharacteristic
67Dic94C2312yes—
68C8×C47C2311yescharacteristic
69C8×C47C2311yescharacteristic
70C47⋊C8C2312yes—
71C22×C47—21no—
72C22×C47—21no—
73C22×C47C2×D411yescharacteristic
74C2×D47—22no—
75C2×D47—82no—
76C2×D47—81no—
77C2×D47C2×D412yes—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47C2×D411yescharacteristic
81C4×C47C2411yescharacteristic
82Dic47—22no—
83Dic47C2×D412yes—
84C2×C47—21no—
85C2×C47—41no—
86C2×C47—41no—
87C2×C47C22×D411yescharacteristic
88D47—22no—
89D47—42no—
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#135D4711yescharacteristic, complemented
100C2×SD16—472no—
101C2×SD16—471no—
102#131—471no—
103#41—471no—
104#41—472no—
105#41—472no—
106#41—941no—
107#41—941no—
108#41—942no—
109#41C2×D4711yescharacteristic
110#41C2×D4711yescharacteristic, complemented
111C2×Q8—472no—
112C2×Q8—471no—
113C2×Q8—941no—
114C2×D4—472no—
115C2×D4—471no—
116C2×D4—941no—
117C2×D4—942no—
118Q16—472no—
119Q16C2×D4711yescharacteristic, complemented
120SD16—472no—
121SD16—472no—
122SD16—472no—
123SD16—472no—
124SD16C2×D4711yescharacteristic, complemented
125SD16C2×D4711yescharacteristic, complemented
126D8—472no—
127D8C2×D4711yescharacteristic, complemented
128M16—471no—
129M16—472no—
130C2×C8—472no—
131C2×C8C2×D4711yescharacteristic, complemented
132C23—942no—
133C23—941no—
134Q8—471no—
135Q8—472no—
136Q8—942no—
137Q8—941no—
138Q8C22×D4711yescharacteristic
139Q8C22×D4711yescharacteristic
140D4—21no—
141D4—21no—
142D4—472no—
143D4—471no—
144D4—472no—
145D4—942no—
146D4—942no—
147D4—942no—
148D4—941no—
149D4C22×D4711yescharacteristic
150D4C22×D4711yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—472no—
154C2×C4—942no—
155C2×C4—942no—
156C2×C4—942no—
157C2×C4—941no—
158C2×C4C22×D4711yescharacteristic
159C8—472no—
160C8C22×D4711yescharacteristic
161C8C22×D4711yescharacteristic
162C22—21no—
163C22—21no—
164C22—472no—
165C22—942no—
166C22—3761no—
167C22—3762no—
168C22D4×D4711yescharacteristic
169C4—21no—
170C4—21no—
171C4—472no—
172C4—942no—
173C4D4×D4711yescharacteristic
174C4C23×D4711yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—942no—
179C2—1882no—
180C2C2×D4×D4711yescharacteristic
subgroupG/H
centerC2C2×D4×D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
Fitting#135×C47C2
socleC2×C47C22×D4
hypercenter#135D47
hypocenterC47#577
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #13094071C2semidirect
2. #13094070C2semidirect
3. #13094056C2semidirect
4. #13094054C2semidirect
5. #13094049C2semidirect
6. #13094048C2semidirect
7. #13094045C2semidirect
8. C2×#10625325C2semidirect
9. SD16×D47C2semidirect
10. #13094030C2semidirect
11. #135×C47C2semidirect
13. #41×C47C22semidirect
15. Q8×D47C22semidirect
17. #10625352C22semidirect
26. C2×Dic94C22semidirect
27. Q16×C47C22semidirect
28. SD16×C47C22semidirect
29. SD16×C47C22semidirect
30. D8×C47C22semidirect
31. C2×C8×C47C22semidirect
32. #10625337C22semidirect
33. #10625336C22semidirect
34. #10625335C22semidirect
35. #10625334C22semidirect
36. #10625329C22semidirect
37. #10625325C22semidirect
38. #10625325C22semidirect
39. #10625324C22semidirect
40. C8×D47C22semidirect
91. C47#577semidirect
99. #135D47semidirect
110. #41C2×D47semidirect
119. Q16C2×D47semidirect
124. SD16C2×D47semidirect
125. SD16C2×D47semidirect
127. D8C2×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
#130940712
#130940702
#130940562
#130940542
#130940492
#130940482
#130940452
C2×#106253252
SD16×D472
#130940302
#135×C472
#57747