Finite Group Databasebeta

← #44567091

Subgroups — #44567091

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#30632909C211yesmaximal, characteristic, complemented
3#30632897C211yesmaximal, characteristic, complemented
4#30632893C212yesmaximal, complemented
5#30632888C212yesmaximal, complemented
6#30632884C211yesmaximal, characteristic, complemented
7#30632883C212yesmaximal, complemented
8C2×#22548871C211yesmaximal, characteristic, complemented
9SD16×D503C212yesmaximal, complemented
10#30632872C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C503C211yesmaximal, characteristic, complemented
12#22548883—21no—
13#22548883C2211yescharacteristic
14#22548883C2211yescharacteristic
15#22548882—21no—
16#22548882—22no—
17#22548882C2212yes—
18#22548882C2212yescomplemented
19C2×Dic1006—21no—
20C2×Dic1006C2211yescharacteristic, complemented
21Q8×D503C2212yescomplemented
22C2×C22⋊D503—22no—
23D4×D503—21no—
24D4×D503C2212yes—
25Dic2012C2212yescomplemented
26#22548873C2211yescharacteristic, complemented
27#22548872C2212yescomplemented
28#22548871C2212yescomplemented
29#22548871C2212yescomplemented
30#22548871C2211yescharacteristic, complemented
31#22548870C2211yescharacteristic, complemented
32#22548868C2211yescharacteristic, complemented
33#22548866C2212yescomplemented
34C2×C503⋊C8C2211yescharacteristic, complemented
35C8×D503C2212yescomplemented
36#41×C503C2211yescharacteristic, complemented
37C2×D4×C503C2211yescharacteristic
38SD16×C503C2212yescomplemented
39D8×C503C2212yescomplemented
40M16×C503C2211yescharacteristic, complemented
41C22×D503—22no—
42Dic1006—21no—
43Dic1006—22no—
44Dic1006D411yescharacteristic
45Dic1006C2312yes—
46Dic1006C2311yescharacteristic
47D2012D411yescharacteristic
48D2012C2311yescharacteristic
49C22⋊D503—21no—
50C22⋊D503—22no—
51C22⋊D503—22no—
52C22⋊D503—22no—
53C22⋊D503D412yes—
54C2×Dic503—21no—
55C2×Dic503—22no—
56C2×Dic503—22no—
57C4×D503—22no—
58C4×D503—21no—
59C4×D503C2312yes—
60C503⋊C8C2311yescharacteristic
61C503⋊C8C2311yescharacteristic
62C23×C503—21no—
63Q8×C503C2311yescharacteristic
64D4×C503—21no—
65D4×C503—21no—
66D4×C503C2311yescharacteristic
67D4×C503C2312yes—
68C2×C4×C503—21no—
69C2×C4×C503C2311yescharacteristic
70C8×C503C2312yes—
71C22×C503—21no—
72C22×C503—22no—
73C22×C503—81no—
74C22×C503C2×D411yescharacteristic
75C2×D503—21no—
76C2×D503—82no—
77C2×D503C2×D412yes—
78C4×C503—21no—
79C4×C503C2×D411yescharacteristic
80C4×C503C2411yescharacteristic
81Dic503—21no—
82Dic503—22no—
83Dic503C2×D412yes—
84C2×C503—21no—
85C2×C503—42no—
86C2×C503—41no—
87C2×C503C22×D411yescharacteristic
88D503—22no—
89D503—41no—
90C503#57711yescharacteristic, complemented, Sylow
91#577—5031nomaximal, Sylow
922−1+4—5031no—
93H(5,𝔽2)—5031no—
94#137—5032no—
95#137—5031no—
96AGL(1,ℤ/8)—5032no—
97AGL(1,ℤ/8)D50311yescharacteristic, complemented
98#135—5031no—
99#135—5032no—
100C2×SD16—5031no—
101C2×SD16—5032no—
102#131—5031no—
103#41—10061no—
104#41—10061no—
105#41—10062no—
106#41—5032no—
107#41—5032no—
108#41—5031no—
109#41—5031no—
110#41C2×D50311yescharacteristic, complemented
111C2×Q8—10061no—
112C2×Q8—5032no—
113C2×Q8—5031no—
114C2×D4—10061no—
115C2×D4—10062no—
116C2×D4—5032no—
117C2×D4C2×D50311yescharacteristic
118Q16—5031no—
119Q16—5032no—
120SD16—5031no—
121SD16—5032no—
122SD16—5032no—
123SD16—5031no—
124SD16—5032no—
125SD16C2×D50312yescomplemented
126D8—5031no—
127D8C2×D50312yescomplemented
128M16—5032no—
129M16C2×D50311yescharacteristic, complemented
130C2×C8—5031no—
131C2×C8—5032no—
132C23—21no—
133C23—10062no—
134Q8—10062no—
135Q8—10061no—
136Q8—5032no—
137Q8—5031no—
138Q8—5031no—
139Q8C22×D50311yescharacteristic
140D4—21no—
141D4—21no—
142D4—10062no—
143D4—10062no—
144D4—10061no—
145D4—10062no—
146D4—5032no—
147D4—5031no—
148D4—5031no—
149D4C22×D50311yescharacteristic
150D4C22×D50312yes—
151C2×C4—21no—
152C2×C4—10062no—
153C2×C4—10061no—
154C2×C4—10062no—
155C2×C4—10062no—
156C2×C4—10061no—
157C2×C4—5032no—
158C2×C4C22×D50311yescharacteristic
159C8—5031no—
160C8—5031no—
161C8C22×D50312yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—40242no—
166C22—10061no—
167C22—5032no—
168C22D4×D50311yescharacteristic
169C4—21no—
170C4—10061no—
171C4—10062no—
172C4—5032no—
173C4D4×D50311yescharacteristic
174C4C23×D50311yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—20121no—
179C2—10062no—
180C2C2×D4×D50311yescharacteristic
subgroupG/H
centerC2C2×D4×D503
commutator, cosocleC4×C503C24
FrattiniC4C23×D503
FittingAGL(1,ℤ/8)×C503C2
socleC2×C503C22×D4
hypercenterAGL(1,ℤ/8)D503
hypocenterC503#577
LCSG ▷ C4×C503 ▷ C2×C503 ▷ C503
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30632911C2semidirect
2. #30632909C2semidirect
3. #30632897C2semidirect
4. #30632893C2semidirect
5. #30632888C2semidirect
6. #30632884C2semidirect
7. #30632883C2semidirect
8. C2×#22548871C2semidirect
9. SD16×D503C2semidirect
10. #30632872C2semidirect
11. AGL(1,ℤ/8)×C503C2semidirect
18. #22548882C22semidirect
20. C2×Dic1006C22semidirect
21. Q8×D503C22semidirect
25. Dic2012C22semidirect
26. #22548873C22semidirect
27. #22548872C22semidirect
28. #22548871C22semidirect
29. #22548871C22semidirect
30. #22548871C22semidirect
31. #22548870C22semidirect
32. #22548868C22semidirect
33. #22548866C22semidirect
34. C2×C503⋊C8C22semidirect
35. C8×D503C22semidirect
36. #41×C503C22semidirect
38. SD16×C503C22semidirect
39. D8×C503C22semidirect
40. M16×C503C22semidirect
90. C503#577semidirect
97. AGL(1,ℤ/8)D503semidirect
110. #41C2×D503semidirect
125. SD16C2×D503semidirect
127. D8C2×D503semidirect
129. M16C2×D503semidirect

Maximal subgroups

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

subgroupindex
#306329112
#306329092
#306328972
#306328932
#306328882
#306328842
#306328832
C2×#225488712
SD16×D5032
#306328722
AGL(1,ℤ/8)×C5032
#577503