Finite Group Databasebeta

← #44529857

Subgroups — #44529857

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#29510261C211yesmaximal, characteristic, complemented
3#29510247C212yesmaximal, complemented
4#29510245C211yesmaximal, characteristic, complemented
5#29510240C211yesmaximal, characteristic, complemented
6#29510239C212yesmaximal, complemented
7#29510236C212yesmaximal, complemented
8C2×#21441250C211yesmaximal, characteristic, complemented
9SD16×D487C212yesmaximal, complemented
10#29510221C211yesmaximal, characteristic, complemented
11#135×C487C211yesmaximal, characteristic, complemented
12#21441262C2212yes—
13#21441261—21no—
14#21441261—21no—
15#21441261C2211yescharacteristic
16#21441260—22no—
17#21441260C2212yescomplemented
18C2×Dic974—21no—
19C2×Dic974C2211yescharacteristic, complemented
20Q8×D487C2212yescomplemented
21C2×D1948—21no—
22C2×D1948C2211yescharacteristic
23D4×D487—22no—
24D4×D487C2212yes—
25#21441251C2212yescomplemented
26#21441250C2212yescomplemented
27#21441250C2212yescomplemented
28#21441249C2212yescomplemented
29#21441248C2212yescomplemented
30#21441246C2212yescomplemented
31#21441245C2211yescharacteristic, complemented
32#21441244C2212yescomplemented
33C8×D487C2212yescomplemented
34#41×C487C2211yescharacteristic
35#41×C487C2211yescharacteristic, complemented
36Q16×C487C2211yescharacteristic, complemented
37SD16×C487C2211yescharacteristic, complemented
38SD16×C487C2211yescharacteristic, complemented
39D8×C487C2211yescharacteristic, complemented
40C2×C8×C487C2211yescharacteristic, complemented
41C22×D487—21no—
42C22×D487—22no—
43Dic974—21no—
44Dic974—22no—
45Dic974D411yescharacteristic
46Dic974C2312yes—
47D1948—22no—
48D1948—21no—
49D1948D411yescharacteristic
50D1948C2312yes—
51C22⋊D487—22no—
52C22⋊D487—22no—
53C22⋊D487D412yes—
54C2×Dic487—21no—
55C2×Dic487—22no—
56C4×D487—22no—
57C4×D487—22no—
58C4×D487C2312yes—
59C487⋊C8C2312yes—
60Q8×C487C2311yescharacteristic
61Q8×C487C2311yescharacteristic
62D4×C487—21no—
63D4×C487—21no—
64D4×C487C2311yescharacteristic
65D4×C487C2311yescharacteristic
66C2×C4×C487—21no—
67C2×C4×C487—21no—
68C2×C4×C487C2311yescharacteristic
69C8×C487C2311yescharacteristic
70C8×C487C2311yescharacteristic
71C22×C487—21no—
72C22×C487—21no—
73C22×C487C2×D411yescharacteristic
74C2×D487—22no—
75C2×D487—82no—
76C2×D487—81no—
77C2×D487C2×D412yes—
78C4×C487—21no—
79C4×C487—21no—
80C4×C487C2×D411yescharacteristic
81C4×C487C2411yescharacteristic
82Dic487—22no—
83Dic487C2×D412yes—
84C2×C487—21no—
85C2×C487—41no—
86C2×C487—41no—
87C2×C487C22×D411yescharacteristic
88D487—22no—
89D487—42no—
90C487#57711yescharacteristic, complemented, Sylow
91#577—4871nomaximal, Sylow
922−1+4—4871no—
93H(5,𝔽2)—4871no—
94#137—4871no—
95#137—4872no—
96AGL(1,ℤ/8)—4871no—
97AGL(1,ℤ/8)—4872no—
98#135—4872no—
99#135D48711yescharacteristic, complemented
100C2×SD16—4872no—
101C2×SD16—4871no—
102#131—4871no—
103#41—9741no—
104#41—9741no—
105#41—9742no—
106#41—4872no—
107#41—4872no—
108#41—4871no—
109#41C2×D48711yescharacteristic
110#41C2×D48711yescharacteristic, complemented
111C2×Q8—9741no—
112C2×Q8—4872no—
113C2×Q8—4871no—
114C2×D4—9741no—
115C2×D4—9742no—
116C2×D4—4872no—
117C2×D4—4871no—
118Q16—4872no—
119Q16C2×D48711yescharacteristic, complemented
120SD16—4872no—
121SD16—4872no—
122SD16—4872no—
123SD16—4872no—
124SD16C2×D48711yescharacteristic, complemented
125SD16C2×D48711yescharacteristic, complemented
126D8—4872no—
127D8C2×D48711yescharacteristic, complemented
128M16—4871no—
129M16—4872no—
130C2×C8—4872no—
131C2×C8C2×D48711yescharacteristic, complemented
132C23—9742no—
133C23—9741no—
134Q8—9742no—
135Q8—9741no—
136Q8—4872no—
137Q8—4871no—
138Q8C22×D48711yescharacteristic
139Q8C22×D48711yescharacteristic
140D4—21no—
141D4—21no—
142D4—9742no—
143D4—9742no—
144D4—9742no—
145D4—9741no—
146D4—4872no—
147D4—4871no—
148D4—4872no—
149D4C22×D48711yescharacteristic
150D4C22×D48711yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—9742no—
154C2×C4—9742no—
155C2×C4—9741no—
156C2×C4—9742no—
157C2×C4—4872no—
158C2×C4C22×D48711yescharacteristic
159C8—4872no—
160C8C22×D48711yescharacteristic
161C8C22×D48711yescharacteristic
162C22—21no—
163C22—21no—
164C22—38961no—
165C22—38962no—
166C22—9742no—
167C22—4872no—
168C22D4×D48711yescharacteristic
169C4—21no—
170C4—21no—
171C4—9742no—
172C4—4872no—
173C4D4×D48711yescharacteristic
174C4C23×D48711yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—19482no—
179C2—9742no—
180C2C2×D4×D48711yescharacteristic
subgroupG/H
centerC2C2×D4×D487
commutator, cosocleC4×C487C24
FrattiniC4C23×D487
Fitting#135×C487C2
socleC2×C487C22×D4
hypercenter#135D487
hypocenterC487#577
LCSG ▷ C4×C487 ▷ C2×C487 ▷ C487
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #29510262C2semidirect
2. #29510261C2semidirect
3. #29510247C2semidirect
4. #29510245C2semidirect
5. #29510240C2semidirect
6. #29510239C2semidirect
7. #29510236C2semidirect
8. C2×#21441250C2semidirect
9. SD16×D487C2semidirect
10. #29510221C2semidirect
11. #135×C487C2semidirect
17. #21441260C22semidirect
19. C2×Dic974C22semidirect
20. Q8×D487C22semidirect
25. #21441251C22semidirect
26. #21441250C22semidirect
27. #21441250C22semidirect
28. #21441249C22semidirect
29. #21441248C22semidirect
30. #21441246C22semidirect
31. #21441245C22semidirect
32. #21441244C22semidirect
33. C8×D487C22semidirect
35. #41×C487C22semidirect
36. Q16×C487C22semidirect
37. SD16×C487C22semidirect
38. SD16×C487C22semidirect
39. D8×C487C22semidirect
40. C2×C8×C487C22semidirect
90. C487#577semidirect
99. #135D487semidirect
110. #41C2×D487semidirect
119. Q16C2×D487semidirect
124. SD16C2×D487semidirect
125. SD16C2×D487semidirect
127. D8C2×D487semidirect
131. C2×C8C2×D487semidirect

Maximal subgroups

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

subgroupindex
#295102622
#295102612
#295102472
#295102452
#295102402
#295102392
#295102362
C2×#214412502
SD16×D4872
#295102212
#135×C4872
#577487