Finite Group Databasebeta

← #44567088

Subgroups — #44567088

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#30632911C211yesmaximal, characteristic, complemented
2#30632910C211yesmaximal, characteristic, complemented
3#30632896C212yesmaximal, complemented
4#30632894C211yesmaximal, characteristic, complemented
5#30632889C211yesmaximal, characteristic, complemented
6#30632888C212yesmaximal, complemented
7#30632885C212yesmaximal, complemented
8C2×#22548872C211yesmaximal, characteristic, complemented
9SD16×D503C212yesmaximal, complemented
10#30632870C211yesmaximal, characteristic, complemented
11#135×C503C211yesmaximal, characteristic, complemented
12#22548884C2212yes—
13#22548883—21no—
14#22548883—21no—
15#22548883C2211yescharacteristic
16#22548882—22no—
17#22548882C2212yescomplemented
18C2×Dic1006—21no—
19C2×Dic1006C2211yescharacteristic, complemented
20Q8×D503C2212yescomplemented
21C2×D2012—21no—
22C2×D2012C2211yescharacteristic
23D4×D503—22no—
24D4×D503C2212yes—
25#22548873C2212yescomplemented
26#22548872C2212yescomplemented
27#22548872C2212yescomplemented
28#22548871C2212yescomplemented
29#22548870C2212yescomplemented
30#22548868C2212yescomplemented
31#22548867C2211yescharacteristic, complemented
32#22548866C2212yescomplemented
33C8×D503C2212yescomplemented
34#41×C503C2211yescharacteristic
35#41×C503C2211yescharacteristic, complemented
36Q16×C503C2211yescharacteristic, complemented
37SD16×C503C2211yescharacteristic, complemented
38SD16×C503C2211yescharacteristic, complemented
39D8×C503C2211yescharacteristic, complemented
40C2×C8×C503C2211yescharacteristic, complemented
41C22×D503—21no—
42C22×D503—22no—
43Dic1006—21no—
44Dic1006—22no—
45Dic1006D411yescharacteristic
46Dic1006C2312yes—
47D2012—22no—
48D2012—21no—
49D2012D411yescharacteristic
50D2012C2312yes—
51C22⋊D503—22no—
52C22⋊D503—22no—
53C22⋊D503D412yes—
54C2×Dic503—21no—
55C2×Dic503—22no—
56C4×D503—22no—
57C4×D503—22no—
58C4×D503C2312yes—
59C503⋊C8C2312yes—
60Q8×C503C2311yescharacteristic
61Q8×C503C2311yescharacteristic
62D4×C503—21no—
63D4×C503—21no—
64D4×C503C2311yescharacteristic
65D4×C503C2311yescharacteristic
66C2×C4×C503—21no—
67C2×C4×C503—21no—
68C2×C4×C503C2311yescharacteristic
69C8×C503C2311yescharacteristic
70C8×C503C2311yescharacteristic
71C22×C503—21no—
72C22×C503—21no—
73C22×C503C2×D411yescharacteristic
74C2×D503—22no—
75C2×D503—82no—
76C2×D503—81no—
77C2×D503C2×D412yes—
78C4×C503—21no—
79C4×C503—21no—
80C4×C503C2×D411yescharacteristic
81C4×C503C2411yescharacteristic
82Dic503—22no—
83Dic503C2×D412yes—
84C2×C503—21no—
85C2×C503—41no—
86C2×C503—41no—
87C2×C503C22×D411yescharacteristic
88D503—22no—
89D503—42no—
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#135D50311yescharacteristic, complemented
100C2×SD16—5032no—
101C2×SD16—5031no—
102#131—5031no—
103#41—10061no—
104#41—10061no—
105#41—10062no—
106#41—5032no—
107#41—5032no—
108#41—5031no—
109#41C2×D50311yescharacteristic
110#41C2×D50311yescharacteristic, complemented
111C2×Q8—10061no—
112C2×Q8—5032no—
113C2×Q8—5031no—
114C2×D4—10061no—
115C2×D4—10062no—
116C2×D4—5032no—
117C2×D4—5031no—
118Q16—5032no—
119Q16C2×D50311yescharacteristic, complemented
120SD16—5032no—
121SD16—5032no—
122SD16—5032no—
123SD16—5032no—
124SD16C2×D50311yescharacteristic, complemented
125SD16C2×D50311yescharacteristic, complemented
126D8—5032no—
127D8C2×D50311yescharacteristic, complemented
128M16—5031no—
129M16—5032no—
130C2×C8—5032no—
131C2×C8C2×D50311yescharacteristic, complemented
132C23—10062no—
133C23—10061no—
134Q8—10062no—
135Q8—10061no—
136Q8—5032no—
137Q8—5031no—
138Q8C22×D50311yescharacteristic
139Q8C22×D50311yescharacteristic
140D4—21no—
141D4—21no—
142D4—10062no—
143D4—10062no—
144D4—10062no—
145D4—10061no—
146D4—5032no—
147D4—5031no—
148D4—5032no—
149D4C22×D50311yescharacteristic
150D4C22×D50311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—10062no—
154C2×C4—10062no—
155C2×C4—10061no—
156C2×C4—10062no—
157C2×C4—5032no—
158C2×C4C22×D50311yescharacteristic
159C8—5032no—
160C8C22×D50311yescharacteristic
161C8C22×D50311yescharacteristic
162C22—21no—
163C22—21no—
164C22—40241no—
165C22—40242no—
166C22—10062no—
167C22—5032no—
168C22D4×D50311yescharacteristic
169C4—21no—
170C4—21no—
171C4—10062no—
172C4—5032no—
173C4D4×D50311yescharacteristic
174C4C23×D50311yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—20122no—
179C2—10062no—
180C2C2×D4×D50311yescharacteristic
subgroupG/H
centerC2C2×D4×D503
commutator, cosocleC4×C503C24
FrattiniC4C23×D503
Fitting#135×C503C2
socleC2×C503C22×D4
hypercenter#135D503
hypocenterC503#577
LCSG ▷ C4×C503 ▷ C2×C503 ▷ C503
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #30632911C2semidirect
2. #30632910C2semidirect
3. #30632896C2semidirect
4. #30632894C2semidirect
5. #30632889C2semidirect
6. #30632888C2semidirect
7. #30632885C2semidirect
8. C2×#22548872C2semidirect
9. SD16×D503C2semidirect
10. #30632870C2semidirect
11. #135×C503C2semidirect
17. #22548882C22semidirect
19. C2×Dic1006C22semidirect
20. Q8×D503C22semidirect
25. #22548873C22semidirect
26. #22548872C22semidirect
27. #22548872C22semidirect
28. #22548871C22semidirect
29. #22548870C22semidirect
30. #22548868C22semidirect
31. #22548867C22semidirect
32. #22548866C22semidirect
33. C8×D503C22semidirect
35. #41×C503C22semidirect
36. Q16×C503C22semidirect
37. SD16×C503C22semidirect
38. SD16×C503C22semidirect
39. D8×C503C22semidirect
40. C2×C8×C503C22semidirect
90. C503#577semidirect
99. #135D503semidirect
110. #41C2×D503semidirect
119. Q16C2×D503semidirect
124. SD16C2×D503semidirect
125. SD16C2×D503semidirect
127. D8C2×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
#306329112
#306329102
#306328962
#306328942
#306328892
#306328882
#306328852
C2×#225488722
SD16×D5032
#306328702
#135×C5032
#577503