Finite Group Databasebeta

← #44529854

Subgroups — #44529854

Order 31168.

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#29510261C211yesmaximal, characteristic, complemented
2#29510260C211yesmaximal, characteristic, complemented
3#29510243C211yesmaximal, characteristic, complemented
4#29510242C212yesmaximal, complemented
5#29510239C212yesmaximal, complemented
6#29510236C212yesmaximal, complemented
7#29510235C211yesmaximal, characteristic, complemented
8C2×#21441246C211yesmaximal, characteristic, complemented
9D8×D487C212yesmaximal, complemented
10#29510223C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C487C211yesmaximal, characteristic, complemented
12#21441262C2212yescomplemented
13#21441261—21no—
14#21441261C2211yescharacteristic
15#21441261C2211yescharacteristic, complemented
16#21441260—21no—
17#21441260C2212yescomplemented
18C2×D1948—21no—
19C2×D1948C2211yescharacteristic, complemented
20C2×C22⋊D487—22no—
21D4×D487—21no—
22D4×D487—22no—
23D4×D487C2212yescomplemented
24D4×D487C2212yescomplemented
25#21441251C2211yescharacteristic, complemented
26#21441250C2212yescomplemented
27#21441249C2211yescharacteristic, complemented
28#21441248C2211yescharacteristic, complemented
29D3896C2212yescomplemented
30#21441246C2211yescharacteristic, complemented
31#21441246C2212yescomplemented
32#21441246C2212yescomplemented
33#21441244C2212yescomplemented
34C2×C487⋊C8C2211yescharacteristic, complemented
35C8×D487C2212yescomplemented
36#41×C487C2211yescharacteristic, complemented
37C2×D4×C487C2211yescharacteristic, complemented
38SD16×C487C2212yescomplemented
39D8×C487C2212yescomplemented
40M16×C487C2211yescharacteristic, complemented
41C22×D487—21no—
42C22×D487—22no—
43C22×D487—22no—
44Dic974D411yescharacteristic
45Dic974C2311yescharacteristic
46D1948—22no—
47D1948—21no—
48D1948D411yescharacteristic
49D1948C2312yes—
50D1948C2311yescharacteristic
51C22⋊D487—21no—
52C22⋊D487—22no—
53C22⋊D487—22no—
54C22⋊D487—22no—
55C22⋊D487D412yes—
56C2×Dic487—22no—
57C4×D487—21no—
58C4×D487—22no—
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—22no—
77C2×D487—82no—
78C2×D487—82no—
79C2×D487—81no—
80C2×D487C2×D412yes—
81C4×C487—21no—
82C4×C487C2×D411yescharacteristic
83C4×C487C2411yescharacteristic
84Dic487—21no—
85Dic487C2×D412yes—
86C2×C487—21no—
87C2×C487—41no—
88C2×C487—42no—
89C2×C487C22×D411yescharacteristic
90D487—22no—
91D487—41no—
92D487—42no—
93C487#57611yescharacteristic, complemented, Sylow
94#576—4871nomaximal, Sylow
95H(5,𝔽2)—4871no—
96H(5,𝔽2)—4871no—
97AGL(1,ℤ/8)—4872no—
98AGL(1,ℤ/8)—4872no—
99AGL(1,ℤ/8)—4871no—
100AGL(1,ℤ/8)D48711yescharacteristic, complemented
101#135—4871no—
102#135—4872no—
103C2×D8—4871no—
104C2×D8—4872no—
105#131—4871no—
106#41—9741no—
107#41—9741no—
108#41—4872no—
109#41—4872no—
110#41—4871no—
111#41—4871no—
112#41C2×D48711yescharacteristic, complemented
113C2×D4—9741no—
114C2×D4—9742no—
115C2×D4—9741no—
116C2×D4—9742no—
117C2×D4—4872no—
118C2×D4—4872no—
119C2×D4—4871no—
120C2×D4C2×D48711yescharacteristic, complemented
121Q16—4871no—
122SD16—4871no—
123SD16—4871no—
124SD16—4872no—
125SD16C2×D48712yescomplemented
126D8—4872no—
127D8—4871no—
128D8—4872no—
129D8—4872no—
130D8C2×D48712yescomplemented
131M16—4872no—
132M16C2×D48711yescharacteristic, complemented
133C2×C8—4871no—
134C2×C8—4872no—
135C23—21no—
136C23—9742no—
137C23—9742no—
138C23—9741no—
139Q8—4871no—
140Q8—4871no—
141Q8C22×D48711yescharacteristic
142D4—21no—
143D4—21no—
144D4—9742no—
145D4—9742no—
146D4—9741no—
147D4—9742no—
148D4—9742no—
149D4—9741no—
150D4—4872no—
151D4—4871no—
152D4—4872no—
153D4—4871no—
154D4C22×D48712yes—
155D4C22×D48711yescharacteristic
156C2×C4—21no—
157C2×C4—9742no—
158C2×C4—9742no—
159C2×C4—9741no—
160C2×C4—4872no—
161C2×C4C22×D48711yescharacteristic
162C8—4871no—
163C8—4871no—
164C8C22×D48712yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—38961no—
169C22—38962no—
170C22—38962no—
171C22—9742no—
172C22—9741no—
173C22—4872no—
174C22D4×D48711yescharacteristic
175C4—21no—
176C4—9741no—
177C4—4872no—
178C4D4×D48711yescharacteristic
179C4C23×D48711yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—19482no—
184C2—19481no—
185C2—9742no—
186C2C2×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#576
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. #29510261C2semidirect
2. #29510260C2semidirect
3. #29510243C2semidirect
4. #29510242C2semidirect
5. #29510239C2semidirect
6. #29510236C2semidirect
7. #29510235C2semidirect
8. C2×#21441246C2semidirect
9. D8×D487C2semidirect
10. #29510223C2semidirect
11. AGL(1,ℤ/8)×C487C2semidirect
12. #21441262C22semidirect
15. #21441261C22semidirect
17. #21441260C22semidirect
19. C2×D1948C22semidirect
23. D4×D487C22semidirect
24. D4×D487C22semidirect
25. #21441251C22semidirect
26. #21441250C22semidirect
27. #21441249C22semidirect
28. #21441248C22semidirect
29. D3896C22semidirect
30. #21441246C22semidirect
31. #21441246C22semidirect
32. #21441246C22semidirect
33. #21441244C22semidirect
34. C2×C487⋊C8C22semidirect
35. C8×D487C22semidirect
36. #41×C487C22semidirect
37. C2×D4×C487C22semidirect
38. SD16×C487C22semidirect
39. D8×C487C22semidirect
40. M16×C487C22semidirect
93. C487#576semidirect
100. AGL(1,ℤ/8)D487semidirect
112. #41C2×D487semidirect
120. C2×D4C2×D487semidirect
125. SD16C2×D487semidirect
130. D8C2×D487semidirect
132. M16C2×D487semidirect

Maximal subgroups

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

subgroupindex
#295102612
#295102602
#295102432
#295102422
#295102392
#295102362
#295102352
C2×#214412462
D8×D4872
#295102232
AGL(1,ℤ/8)×C4872
#576487