Finite Group Databasebeta

← #44529860

Subgroups — #44529860

Order 31168.

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#29510262C211yesmaximal, characteristic, complemented
2#29510260C211yesmaximal, characteristic, complemented
3#29510248C211yesmaximal, characteristic, complemented
4#29510244C212yesmaximal, complemented
5#29510239C212yesmaximal, complemented
6#29510235C211yesmaximal, characteristic, complemented
7#29510234C212yesmaximal, complemented
8C2×#21441249C211yesmaximal, characteristic, complemented
9SD16×D487C212yesmaximal, complemented
10#29510223C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C487C211yesmaximal, characteristic, complemented
12#21441261—21no—
13#21441261C2211yescharacteristic
14#21441261C2211yescharacteristic
15#21441260—21no—
16#21441260—22no—
17#21441260C2212yes—
18#21441260C2212yescomplemented
19C2×Dic974—21no—
20C2×Dic974C2211yescharacteristic, complemented
21Q8×D487C2212yescomplemented
22C2×C22⋊D487—22no—
23D4×D487—21no—
24D4×D487C2212yes—
25Dic1948C2212yescomplemented
26#21441251C2211yescharacteristic, complemented
27#21441250C2212yescomplemented
28#21441249C2212yescomplemented
29#21441249C2212yescomplemented
30#21441249C2211yescharacteristic, complemented
31#21441248C2211yescharacteristic, complemented
32#21441246C2211yescharacteristic, complemented
33#21441244C2212yescomplemented
34C2×C487⋊C8C2211yescharacteristic, complemented
35C8×D487C2212yescomplemented
36#41×C487C2211yescharacteristic, complemented
37C2×D4×C487C2211yescharacteristic
38SD16×C487C2212yescomplemented
39D8×C487C2212yescomplemented
40M16×C487C2211yescharacteristic, complemented
41C22×D487—22no—
42Dic974—21no—
43Dic974—22no—
44Dic974D411yescharacteristic
45Dic974C2312yes—
46Dic974C2311yescharacteristic
47D1948D411yescharacteristic
48D1948C2311yescharacteristic
49C22⋊D487—21no—
50C22⋊D487—22no—
51C22⋊D487—22no—
52C22⋊D487—22no—
53C22⋊D487D412yes—
54C2×Dic487—21no—
55C2×Dic487—22no—
56C2×Dic487—22no—
57C4×D487—22no—
58C4×D487—21no—
59C4×D487C2312yes—
60C487⋊C8C2311yescharacteristic
61C487⋊C8C2311yescharacteristic
62C23×C487—21no—
63Q8×C487C2311yescharacteristic
64D4×C487—21no—
65D4×C487—21no—
66D4×C487C2311yescharacteristic
67D4×C487C2312yes—
68C2×C4×C487—21no—
69C2×C4×C487C2311yescharacteristic
70C8×C487C2312yes—
71C22×C487—21no—
72C22×C487—22no—
73C22×C487—81no—
74C22×C487C2×D411yescharacteristic
75C2×D487—21no—
76C2×D487—82no—
77C2×D487C2×D412yes—
78C4×C487—21no—
79C4×C487C2×D411yescharacteristic
80C4×C487C2411yescharacteristic
81Dic487—21no—
82Dic487—22no—
83Dic487C2×D412yes—
84C2×C487—21no—
85C2×C487—42no—
86C2×C487—41no—
87C2×C487C22×D411yescharacteristic
88D487—22no—
89D487—41no—
90C487#57711yescharacteristic, complemented, Sylow
91#577—4871nomaximal, Sylow
922−1+4—4871no—
93H(5,𝔽2)—4871no—
94#137—4872no—
95#137—4871no—
96AGL(1,ℤ/8)—4872no—
97AGL(1,ℤ/8)D48711yescharacteristic, complemented
98#135—4871no—
99#135—4872no—
100C2×SD16—4871no—
101C2×SD16—4872no—
102#131—4871no—
103#41—9741no—
104#41—9741no—
105#41—9742no—
106#41—4872no—
107#41—4872no—
108#41—4871no—
109#41—4871no—
110#41C2×D48711yescharacteristic, complemented
111C2×Q8—9741no—
112C2×Q8—4872no—
113C2×Q8—4871no—
114C2×D4—9741no—
115C2×D4—9742no—
116C2×D4—4872no—
117C2×D4C2×D48711yescharacteristic
118Q16—4871no—
119Q16—4872no—
120SD16—4871no—
121SD16—4872no—
122SD16—4872no—
123SD16—4871no—
124SD16—4872no—
125SD16C2×D48712yescomplemented
126D8—4871no—
127D8C2×D48712yescomplemented
128M16—4872no—
129M16C2×D48711yescharacteristic, complemented
130C2×C8—4871no—
131C2×C8—4872no—
132C23—21no—
133C23—9742no—
134Q8—9742no—
135Q8—9741no—
136Q8—4872no—
137Q8—4871no—
138Q8—4871no—
139Q8C22×D48711yescharacteristic
140D4—21no—
141D4—21no—
142D4—9742no—
143D4—9742no—
144D4—9741no—
145D4—9742no—
146D4—4872no—
147D4—4871no—
148D4—4871no—
149D4C22×D48711yescharacteristic
150D4C22×D48712yes—
151C2×C4—21no—
152C2×C4—9742no—
153C2×C4—9741no—
154C2×C4—9742no—
155C2×C4—9742no—
156C2×C4—9741no—
157C2×C4—4872no—
158C2×C4C22×D48711yescharacteristic
159C8—4871no—
160C8—4871no—
161C8C22×D48712yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—38962no—
166C22—9741no—
167C22—4872no—
168C22D4×D48711yescharacteristic
169C4—21no—
170C4—9741no—
171C4—9742no—
172C4—4872no—
173C4D4×D48711yescharacteristic
174C4C23×D48711yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—19481no—
179C2—9742no—
180C2C2×D4×D48711yescharacteristic
subgroupG/H
centerC2C2×D4×D487
commutator, cosocleC4×C487C24
FrattiniC4C23×D487
FittingAGL(1,ℤ/8)×C487C2
socleC2×C487C22×D4
hypercenterAGL(1,ℤ/8)D487
hypocenterC487#577
LCSG ▷ C4×C487 ▷ C2×C487 ▷ C487
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #29510262C2semidirect
2. #29510260C2semidirect
3. #29510248C2semidirect
4. #29510244C2semidirect
5. #29510239C2semidirect
6. #29510235C2semidirect
7. #29510234C2semidirect
8. C2×#21441249C2semidirect
9. SD16×D487C2semidirect
10. #29510223C2semidirect
11. AGL(1,ℤ/8)×C487C2semidirect
18. #21441260C22semidirect
20. C2×Dic974C22semidirect
21. Q8×D487C22semidirect
25. Dic1948C22semidirect
26. #21441251C22semidirect
27. #21441250C22semidirect
28. #21441249C22semidirect
29. #21441249C22semidirect
30. #21441249C22semidirect
31. #21441248C22semidirect
32. #21441246C22semidirect
33. #21441244C22semidirect
34. C2×C487⋊C8C22semidirect
35. C8×D487C22semidirect
36. #41×C487C22semidirect
38. SD16×C487C22semidirect
39. D8×C487C22semidirect
40. M16×C487C22semidirect
90. C487#577semidirect
97. AGL(1,ℤ/8)D487semidirect
110. #41C2×D487semidirect
125. SD16C2×D487semidirect
127. D8C2×D487semidirect
129. M16C2×D487semidirect

Maximal subgroups

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

subgroupindex
#295102622
#295102602
#295102482
#295102442
#295102392
#295102352
#295102342
C2×#214412492
SD16×D4872
#295102232
AGL(1,ℤ/8)×C4872
#577487