Finite Group Databasebeta

← #44567087

Subgroups — #44567087

Order 32192.

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#30632912C211yesmaximal, characteristic, complemented
2#30632909C211yesmaximal, characteristic, complemented
3#30632895C211yesmaximal, characteristic, complemented
4#30632893C212yesmaximal, complemented
5#30632891C212yesmaximal, complemented
6#30632890C211yesmaximal, characteristic, complemented
7#30632886C211yesmaximal, characteristic, complemented
8#30632885C212yesmaximal, complemented
9SD16×D503C212yesmaximal, complemented
10#30632870C211yesmaximal, characteristic, complemented
11C2×SD16×C503C211yesmaximal, characteristic, complemented
12#22548884—21no—
13#22548884C2212yescomplemented
14#22548883—22no—
15#22548883C2211yescharacteristic
16#22548883C2211yescharacteristic
17#22548883C2211yescharacteristic, complemented
18#22548882—21no—
19#22548882C2212yes—
20Q8×D503—21no—
21Q8×D503C2212yescomplemented
22C2×C22⋊D503—22no—
23D4×D503—21no—
24D4×D503C2212yes—
25Dic2012C2211yescharacteristic, complemented
26#22548873C2212yescomplemented
27#22548872C2211yescharacteristic, complemented
28#22548872C2211yescharacteristic, complemented
29#22548871C2212yescomplemented
30#22548870C2212yescomplemented
31D4024C2211yescharacteristic, complemented
32#22548868C2212yescomplemented
33#22548867C2211yescharacteristic, complemented
34#22548866C2212yescomplemented
35C8×D503C2212yescomplemented
36C2×Q8×C503C2211yescharacteristic, complemented
37C2×D4×C503C2211yescharacteristic
38SD16×C503C2212yescomplemented
39SD16×C503C2212yescomplemented
40C2×C8×C503C2211yescharacteristic, complemented
41C22×D503—22no—
42Dic1006—22no—
43Dic1006D411yescharacteristic
44Dic1006C2311yescharacteristic
45Dic1006C2311yescharacteristic
46D2012—22no—
47D2012D411yescharacteristic
48D2012C2311yescharacteristic
49D2012C2311yescharacteristic
50C22⋊D503—21no—
51C22⋊D503—21no—
52C22⋊D503—22no—
53C22⋊D503—22no—
54C22⋊D503D412yes—
55C2×Dic503—22no—
56C4×D503—22no—
57C4×D503—21no—
58C4×D503—21no—
59C4×D503—22no—
60C4×D503C2312yes—
61C503⋊C8C2312yes—
62C23×C503—21no—
63Q8×C503—21no—
64Q8×C503C2312yes—
65D4×C503—21no—
66D4×C503C2312yes—
67C2×C4×C503—21no—
68C2×C4×C503C2311yescharacteristic
69C8×C503C2311yescharacteristic
70C8×C503C2311yescharacteristic
71C22×C503—22no—
72C22×C503—81no—
73C22×C503C2×D411yescharacteristic
74C2×D503—21no—
75C2×D503—21no—
76C2×D503—82no—
77C2×D503C2×D412yes—
78C4×C503—22no—
79C4×C503C2×D411yescharacteristic
80C4×C503C2411yescharacteristic
81Dic503—21no—
82Dic503—21no—
83Dic503C2×D412yes—
84C2×C503—21no—
85C2×C503—42no—
86C2×C503C22×D411yescharacteristic
87D503—22no—
88D503—41no—
89D503—41no—
90C503#57711yescharacteristic, complemented, Sylow
91#577—5031nomaximal, Sylow
922−1+4—5031no—
93H(5,𝔽2)—5031no—
94#137—5031no—
95#137—5032no—
96AGL(1,ℤ/8)—5031no—
97AGL(1,ℤ/8)—5032no—
98#135—5032no—
99#135—5031no—
100C2×SD16—5032no—
101C2×SD16D50311yescharacteristic, complemented
102#131—5031no—
103#41—10062no—
104#41—10061no—
105#41—10061no—
106#41—5032no—
107#41—5032no—
108#41—5031no—
109#41—5031no—
110#41—5031no—
111C2×Q8—10061no—
112C2×Q8—5032no—
113C2×Q8C2×D50311yescharacteristic, complemented
114C2×D4—10061no—
115C2×D4—10062no—
116C2×D4—5032no—
117C2×D4C2×D50311yescharacteristic
118Q16—5032no—
119Q16—5031no—
120SD16—5032no—
121SD16—5032no—
122SD16—5031no—
123SD16—5031no—
124SD16C2×D50312yescomplemented
125SD16C2×D50312yescomplemented
126D8—5032no—
127D8—5031no—
128M16—5031no—
129M16—5032no—
130C2×C8—5032no—
131C2×C8C2×D50311yescharacteristic, complemented
132C23—21no—
133C23—10062no—
134Q8—21no—
135Q8—10062no—
136Q8—5031no—
137Q8—5031no—
138Q8—5031no—
139Q8C22×D50312yes—
140D4—21no—
141D4—10062no—
142D4—10062no—
143D4—10061no—
144D4—10061no—
145D4—10062no—
146D4—5032no—
147D4—5031no—
148D4—5031no—
149D4—5031no—
150D4C22×D50312yes—
151C2×C4—21no—
152C2×C4—10062no—
153C2×C4—10062no—
154C2×C4—10062no—
155C2×C4—10061no—
156C2×C4—10061no—
157C2×C4—5032no—
158C2×C4C22×D50311yescharacteristic
159C8—5032no—
160C8C22×D50311yescharacteristic
161C8C22×D50311yescharacteristic
162C22—22no—
163C22—81no—
164C22—40242no—
165C22—10061no—
166C22—10061no—
167C22—5032no—
168C22D4×D50311yescharacteristic
169C4—22no—
170C4—10061no—
171C4—10061no—
172C4—5032no—
173C4D4×D50311yescharacteristic
174C4C23×D50311yescharacteristic
175C2—21no—
176C2—42no—
177C2—20121no—
178C2—20121no—
179C2—10062no—
180C2C2×D4×D50311yescharacteristic
subgroupG/H
centerC2C2×D4×D503
commutator, cosocleC4×C503C24
FrattiniC4C23×D503
FittingC2×SD16×C503C2
socleC2×C503C22×D4
hypercenterC2×SD16D503
hypocenterC503#577
LCSG ▷ C4×C503 ▷ C2×C503 ▷ C503
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #30632912C2semidirect
2. #30632909C2semidirect
3. #30632895C2semidirect
4. #30632893C2semidirect
5. #30632891C2semidirect
6. #30632890C2semidirect
7. #30632886C2semidirect
8. #30632885C2semidirect
9. SD16×D503C2semidirect
10. #30632870C2semidirect
11. C2×SD16×C503C2semidirect
13. #22548884C22semidirect
17. #22548883C22semidirect
21. Q8×D503C22semidirect
25. Dic2012C22semidirect
26. #22548873C22semidirect
27. #22548872C22semidirect
28. #22548872C22semidirect
29. #22548871C22semidirect
30. #22548870C22semidirect
31. D4024C22semidirect
32. #22548868C22semidirect
33. #22548867C22semidirect
34. #22548866C22semidirect
35. C8×D503C22semidirect
36. C2×Q8×C503C22semidirect
38. SD16×C503C22semidirect
39. SD16×C503C22semidirect
40. C2×C8×C503C22semidirect
90. C503#577semidirect
101. C2×SD16D503semidirect
113. C2×Q8C2×D503semidirect
124. SD16C2×D503semidirect
125. SD16C2×D503semidirect
131. C2×C8C2×D503semidirect

Maximal subgroups

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

subgroupindex
#306329122
#306329092
#306328952
#306328932
#306328912
#306328902
#306328862
#306328852
SD16×D5032
#306328702
C2×SD16×C5032
#577503