Finite Group Databasebeta

← #44567090

Subgroups — #44567090

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#30632910C211yesmaximal, characteristic, complemented
3#30632896C212yesmaximal, complemented
4#30632892C211yesmaximal, characteristic, complemented
5#30632891C212yesmaximal, complemented
6#30632887C212yesmaximal, complemented
7#30632884C211yesmaximal, characteristic, complemented
8C2×#22548870C211yesmaximal, characteristic, complemented
9SD16×D503C212yesmaximal, complemented
10#30632872C211yesmaximal, characteristic, complemented
11#137×C503C211yesmaximal, characteristic, complemented
12#22548884—21no—
13#22548884C2212yes—
14#22548884C2212yescomplemented
15#22548883—21no—
16#22548883—22no—
17#22548883C2211yescharacteristic
18#22548883C2211yescharacteristic, complemented
19Q8×D503—21no—
20Q8×D503C2212yescomplemented
21C2×D2012—21no—
22C2×D2012C2211yescharacteristic
23D4×D503—22no—
24D4×D503C2212yes—
25#22548873C2211yescharacteristic, complemented
26#22548872C2212yescomplemented
27#22548871C2211yescharacteristic, complemented
28#22548870C2212yescomplemented
29#22548870C2212yescomplemented
30#22548870C2211yescharacteristic, complemented
31D4024C2212yescomplemented
32#22548868C2211yescharacteristic, complemented
33#22548866C2212yescomplemented
34C2×C503⋊C8C2211yescharacteristic, complemented
35C8×D503C2212yescomplemented
36#41×C503C2211yescharacteristic
37C2×Q8×C503C2211yescharacteristic, complemented
38Q16×C503C2212yescomplemented
39SD16×C503C2212yescomplemented
40M16×C503C2211yescharacteristic, complemented
41C22×D503—21no—
42C22×D503—22no—
43Dic1006—22no—
44Dic1006D411yescharacteristic
45Dic1006C2311yescharacteristic
46D2012—22no—
47D2012—22no—
48D2012—21no—
49D2012D411yescharacteristic
50D2012C2311yescharacteristic
51D2012C2312yes—
52C22⋊D503—21no—
53C22⋊D503—22no—
54C22⋊D503D412yes—
55C4×D503—22no—
56C4×D503—21no—
57C4×D503—22no—
58C4×D503—22no—
59C4×D503C2312yes—
60C503⋊C8C2311yescharacteristic
61C503⋊C8C2311yescharacteristic
62Q8×C503—21no—
63Q8×C503C2312yes—
64Q8×C503C2311yescharacteristic
65D4×C503—21no—
66D4×C503C2311yescharacteristic
67C2×C4×C503—21no—
68C2×C4×C503—21no—
69C2×C4×C503C2311yescharacteristic
70C8×C503C2312yes—
71C22×C503—21no—
72C22×C503C2×D411yescharacteristic
73C2×D503—21no—
74C2×D503—22no—
75C2×D503—82no—
76C2×D503—81no—
77C2×D503C2×D412yes—
78C4×C503—21no—
79C4×C503—22no—
80C4×C503C2×D411yescharacteristic
81C4×C503C2411yescharacteristic
82Dic503—21no—
83Dic503C2×D412yes—
84C2×C503—21no—
85C2×C503—41no—
86C2×C503C22×D411yescharacteristic
87D503—22no—
88D503—41no—
89D503—42no—
90C503#57711yescharacteristic, complemented, Sylow
91#577—5031nomaximal, Sylow
922−1+4—5031no—
93H(5,𝔽2)—5031no—
94#137—5032no—
95#137D50311yescharacteristic, complemented
96AGL(1,ℤ/8)—5032no—
97AGL(1,ℤ/8)—5031no—
98#135—5031no—
99#135—5032no—
100C2×SD16—5031no—
101C2×SD16—5032no—
102#131—5031no—
103#41—10061no—
104#41—10062no—
105#41—10061no—
106#41—5032no—
107#41—5032no—
108#41—5031no—
109#41—5031no—
110#41C2×D50311yescharacteristic
111C2×Q8—10061no—
112C2×Q8—5032no—
113C2×Q8C2×D50311yescharacteristic, complemented
114C2×D4—10061no—
115C2×D4—10062no—
116C2×D4—5032no—
117C2×D4—5031no—
118Q16—5031no—
119Q16C2×D50312yescomplemented
120SD16—5032no—
121SD16—5032no—
122SD16—5031no—
123SD16—5031no—
124SD16—5032no—
125SD16C2×D50312yescomplemented
126D8—5031no—
127D8—5032no—
128M16—5032no—
129M16C2×D50311yescharacteristic, complemented
130C2×C8—5031no—
131C2×C8—5032no—
132C23—10062no—
133C23—10061no—
134Q8—21no—
135Q8—10062no—
136Q8—5031no—
137Q8—5031no—
138Q8C22×D50312yes—
139Q8C22×D50311yescharacteristic
140D4—21no—
141D4—10062no—
142D4—10062no—
143D4—10061no—
144D4—10062no—
145D4—10061no—
146D4—5032no—
147D4—5031no—
148D4—5031no—
149D4—5032no—
150D4C22×D50311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—10062no—
154C2×C4—10062no—
155C2×C4—10062no—
156C2×C4—10061no—
157C2×C4—5032no—
158C2×C4C22×D50311yescharacteristic
159C8—5031no—
160C8—5031no—
161C8C22×D50312yes—
162C22—21no—
163C22—40241no—
164C22—40242no—
165C22—10061no—
166C22—10062no—
167C22—5032no—
168C22D4×D50311yescharacteristic
169C4—21no—
170C4—22no—
171C4—10061no—
172C4—5032no—
173C4D4×D50311yescharacteristic
174C4C23×D50311yescharacteristic
175C2—21no—
176C2—41no—
177C2—20122no—
178C2—20121no—
179C2—10062no—
180C2C2×D4×D50311yescharacteristic
subgroupG/H
centerC2C2×D4×D503
commutator, cosocleC4×C503C24
FrattiniC4C23×D503
Fitting#137×C503C2
socleC2×C503C22×D4
hypercenter#137D503
hypocenterC503#577
LCSG ▷ C4×C503 ▷ C2×C503 ▷ C503
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #30632912C2semidirect
2. #30632910C2semidirect
3. #30632896C2semidirect
4. #30632892C2semidirect
5. #30632891C2semidirect
6. #30632887C2semidirect
7. #30632884C2semidirect
8. C2×#22548870C2semidirect
9. SD16×D503C2semidirect
10. #30632872C2semidirect
11. #137×C503C2semidirect
14. #22548884C22semidirect
18. #22548883C22semidirect
20. Q8×D503C22semidirect
25. #22548873C22semidirect
26. #22548872C22semidirect
27. #22548871C22semidirect
28. #22548870C22semidirect
29. #22548870C22semidirect
30. #22548870C22semidirect
31. D4024C22semidirect
32. #22548868C22semidirect
33. #22548866C22semidirect
34. C2×C503⋊C8C22semidirect
35. C8×D503C22semidirect
37. C2×Q8×C503C22semidirect
38. Q16×C503C22semidirect
39. SD16×C503C22semidirect
40. M16×C503C22semidirect
90. C503#577semidirect
95. #137D503semidirect
113. C2×Q8C2×D503semidirect
119. Q16C2×D503semidirect
125. SD16C2×D503semidirect
129. M16C2×D503semidirect

Maximal subgroups

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

subgroupindex
#306329122
#306329102
#306328962
#306328922
#306328912
#306328872
#306328842
C2×#225488702
SD16×D5032
#306328722
#137×C5032
#577503