Finite Group Databasebeta

← #15689922

Subgroups — #15689922

Order 3008.

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

normal subgroups only

This group has 262 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
1C2×#10625354C211yesmaximal, characteristic, complemented
2#41×D47C211yesmaximal, characteristic, complemented
3#13094056C212yesmaximal, complemented
4#13094055C211yesmaximal, characteristic, complemented
5#13094052C211yesmaximal, characteristic, complemented
6#13094051C212yesmaximal, complemented
7#13094049C211yesmaximal, characteristic, complemented
8#13094047C212yesmaximal, complemented
9#13094045C212yesmaximal, complemented
10M16×D47C211yesmaximal, characteristic, complemented
11#137×C47C211yesmaximal, characteristic, complemented
12#41×C47C2211yescharacteristic
13C2×Q8×C47C2211yescharacteristic, complemented
14#10625354—21no—
15#10625354—21no—
16#10625354C2212yes—
17#10625354C2212yescomplemented
18#10625354C2211yescharacteristic, complemented
19Q8×D47C2211yescharacteristic, complemented
20#10625352—21no—
21#10625352C2211yescharacteristic, complemented
22D4×D47—21no—
23D4×D47C2211yescharacteristic, complemented
24#10625350—21no—
25#10625350C2211yescharacteristic
26C2×D188—21no—
27C2×D188C2211yescharacteristic, complemented
28C2×C4×D47—21no—
29C2×C4×D47—21no—
30C2×C4×D47C2211yescharacteristic
31Q16×C47C2212yescomplemented
32SD16×C47C2212yescomplemented
33M16×C47C2211yescharacteristic, complemented
34#10625337C2212yescomplemented
35#10625336C2212yescomplemented
36#10625336C2212yescomplemented
37#10625334C2212yescomplemented
38#10625329C2211yescharacteristic, complemented
39D376C2212yescomplemented
40#10625325C2212yescomplemented
41#10625324C2212yescomplemented
42C8×D47C2212yescomplemented
43C22×D47—21no—
44C22×D47—21no—
45C22×D47D411yescharacteristic
46Q8×C47—21no—
47Q8×C47C2311yescharacteristic
48Q8×C47C2312yes—
49D4×C47—21no—
50D4×C47C2311yescharacteristic
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47C2311yescharacteristic
54C22⋊D47—21no—
55C22⋊D47—21no—
56C22⋊D47—21no—
57C2×Dic47—21no—
58C2×Dic47D411yescharacteristic
59D188—22no—
60D188—22no—
61D188—21no—
62D188—21no—
63D188C2312yes—
64D188C2311yescharacteristic
65C4×D47—21no—
66C4×D47—21no—
67C4×D47—21no—
68C4×D47—22no—
69C4×D47—22no—
70C4×D47D411yescharacteristic
71C4×D47D411yescharacteristic
72C4×D47C2311yescharacteristic
73C4×D47C2311yescharacteristic
74Dic94—21no—
75Dic94C2311yescharacteristic
76C8×C47C2312yes—
77C47⋊C8C2312yes—
78C22×C47—21no—
79C22×C47C2×D411yescharacteristic
80C2×D47—22no—
81C2×D47—21no—
82C2×D47—41no—
83C2×D47—42no—
84C2×D47—42no—
85C2×D47C2×D411yescharacteristic
86C2×D47C2×D411yescharacteristic
87C4×C47—21no—
88C4×C47—22no—
89C4×C47C2×D411yescharacteristic
90C4×C47C2411yescharacteristic
91Dic47—21no—
92Dic47C2×D411yescharacteristic
93Dic47C2×D411yescharacteristic
94C2×C47—21no—
95C2×C47—41no—
96C2×C47C22×D411yescharacteristic
97D47—21no—
98D47—21no—
99D47—42no—
100D47—41no—
101#575—471nomaximal, Sylow
102C47#57511yescharacteristic, complemented, Sylow
103C2×#41—471no—
104C2×#41—471no—
105#137—471no—
106#137—472no—
107#137D4711yescharacteristic, complemented
108AGL(1,ℤ/8)—471no—
109AGL(1,ℤ/8)—472no—
110AGL(1,ℤ/8)—471no—
111#135—472no—
112#135—472no—
113C2×M16—471no—
114#41—472no—
115#41—471no—
116#41—472no—
117#41—471no—
118#41—471no—
119#41—941no—
120#41—941no—
121#41—941no—
122#41—941no—
123#41C2×D4711yescharacteristic
124C2×Q8—471no—
125C2×Q8C2×D4711yescharacteristic, complemented
126C2×D4—471no—
127C2×D4—471no—
128C2×D4—941no—
129C2×D4—941no—
130C22×C4—471no—
131C22×C4—941no—
132C22×C4—941no—
133Q16—472no—
134Q16C2×D4712yescomplemented
135SD16—472no—
136SD16—472no—
137SD16—472no—
138SD16C2×D4712yescomplemented
139D8—472no—
140D8—472no—
141M16—471no—
142M16—472no—
143M16C2×D4711yescharacteristic, complemented
144C2×C8—472no—
145C23—471no—
146C23—941no—
147C23—941no—
148Q8—21no—
149Q8—471no—
150Q8—941no—
151Q8C22×D4711yescharacteristic
152Q8C22×D4712yes—
153D4—21no—
154D4—472no—
155D4—471no—
156D4—941no—
157D4—942no—
158D4—942no—
159D4—941no—
160D4—941no—
161D4—941no—
162D4—941no—
163D4C22×D4711yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—471no—
167C2×C4—471no—
168C2×C4—471no—
169C2×C4—471no—
170C2×C4—471no—
171C2×C4—941no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—941no—
175C2×C4—941no—
176C2×C4—941no—
177C2×C4C22×D4711yescharacteristic
178C8—472no—
179C8C22×D4712yes—
180C22—21no—
181C22—471no—
182C22—471no—
183C22—942no—
184C22—941no—
185C22—1881no—
186C22—1882no—
187C22—1882no—
188C22D4×D4711yescharacteristic
189C4—21no—
190C4—22no—
191C4—471no—
192C4—471no—
193C4—941no—
194C4D4×D4711yescharacteristic
195C4C23×D4711yescharacteristic
196C2—21no—
197C2—41no—
198C2—941no—
199C2—941no—
200C2—1882no—
201C2—1881no—
202C2C2×D4×D4711yescharacteristic
subgroupG/H
centerC2C2×D4×D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
Fitting#137×C47C2
socleC2×C47C22×D4
hypercenter#137D47
hypocenterC47#575
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#10625354C2semidirect
2. #41×D47C2semidirect
3. #13094056C2semidirect
4. #13094055C2semidirect
5. #13094052C2semidirect
6. #13094051C2semidirect
7. #13094049C2semidirect
8. #13094047C2semidirect
9. #13094045C2semidirect
10. M16×D47C2semidirect
11. #137×C47C2semidirect
13. C2×Q8×C47C22semidirect
17. #10625354C22semidirect
18. #10625354C22semidirect
19. Q8×D47C22semidirect
21. #10625352C22semidirect
23. D4×D47C22semidirect
27. C2×D188C22semidirect
31. Q16×C47C22semidirect
32. SD16×C47C22semidirect
33. M16×C47C22semidirect
34. #10625337C22semidirect
35. #10625336C22semidirect
36. #10625336C22semidirect
37. #10625334C22semidirect
38. #10625329C22semidirect
39. D376C22semidirect
40. #10625325C22semidirect
41. #10625324C22semidirect
42. C8×D47C22semidirect
102. C47#575semidirect
107. #137D47semidirect
125. C2×Q8C2×D47semidirect
134. Q16C2×D47semidirect
138. SD16C2×D47semidirect
143. M16C2×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#106253542
#41×D472
#130940562
#130940552
#130940522
#130940512
#130940492
#130940472
#130940452
M16×D472
#137×C472
#57547