Finite Group Databasebeta

← #44567085

Subgroups — #44567085

Order 32192.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 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#30632910C211yesmaximal, characteristic, complemented
2#30632909C211yesmaximal, characteristic, complemented
3#30632892C211yesmaximal, characteristic, complemented
4#30632891C212yesmaximal, complemented
5#30632888C212yesmaximal, complemented
6#30632885C212yesmaximal, complemented
7#30632884C211yesmaximal, characteristic, complemented
8C2×#22548868C211yesmaximal, characteristic, complemented
9D8×D503C212yesmaximal, complemented
10#30632872C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C503C211yesmaximal, characteristic, complemented
12#22548884C2212yescomplemented
13#22548883—21no—
14#22548883C2211yescharacteristic
15#22548883C2211yescharacteristic, complemented
16#22548882—21no—
17#22548882C2212yescomplemented
18C2×D2012—21no—
19C2×D2012C2211yescharacteristic, complemented
20C2×C22⋊D503—22no—
21D4×D503—21no—
22D4×D503—22no—
23D4×D503C2212yescomplemented
24D4×D503C2212yescomplemented
25#22548873C2211yescharacteristic, complemented
26#22548872C2212yescomplemented
27#22548871C2211yescharacteristic, complemented
28#22548870C2211yescharacteristic, complemented
29D4024C2212yescomplemented
30#22548868C2211yescharacteristic, complemented
31#22548868C2212yescomplemented
32#22548868C2212yescomplemented
33#22548866C2212yescomplemented
34C2×C503⋊C8C2211yescharacteristic, complemented
35C8×D503C2212yescomplemented
36#41×C503C2211yescharacteristic, complemented
37C2×D4×C503C2211yescharacteristic, complemented
38SD16×C503C2212yescomplemented
39D8×C503C2212yescomplemented
40M16×C503C2211yescharacteristic, complemented
41C22×D503—21no—
42C22×D503—22no—
43C22×D503—22no—
44Dic1006D411yescharacteristic
45Dic1006C2311yescharacteristic
46D2012—22no—
47D2012—21no—
48D2012D411yescharacteristic
49D2012C2312yes—
50D2012C2311yescharacteristic
51C22⋊D503—21no—
52C22⋊D503—22no—
53C22⋊D503—22no—
54C22⋊D503—22no—
55C22⋊D503D412yes—
56C2×Dic503—22no—
57C4×D503—21no—
58C4×D503—22no—
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—22no—
77C2×D503—82no—
78C2×D503—82no—
79C2×D503—81no—
80C2×D503C2×D412yes—
81C4×C503—21no—
82C4×C503C2×D411yescharacteristic
83C4×C503C2411yescharacteristic
84Dic503—21no—
85Dic503C2×D412yes—
86C2×C503—21no—
87C2×C503—41no—
88C2×C503—42no—
89C2×C503C22×D411yescharacteristic
90D503—22no—
91D503—41no—
92D503—42no—
93C503#57611yescharacteristic, complemented, Sylow
94#576—5031nomaximal, Sylow
95H(5,𝔽2)—5031no—
96H(5,𝔽2)—5031no—
97AGL(1,ℤ/8)—5032no—
98AGL(1,ℤ/8)—5032no—
99AGL(1,ℤ/8)—5031no—
100AGL(1,ℤ/8)D50311yescharacteristic, complemented
101#135—5031no—
102#135—5032no—
103C2×D8—5031no—
104C2×D8—5032no—
105#131—5031no—
106#41—10061no—
107#41—10061no—
108#41—5032no—
109#41—5032no—
110#41—5031no—
111#41—5031no—
112#41C2×D50311yescharacteristic, complemented
113C2×D4—10061no—
114C2×D4—10062no—
115C2×D4—10061no—
116C2×D4—10062no—
117C2×D4—5032no—
118C2×D4—5032no—
119C2×D4—5031no—
120C2×D4C2×D50311yescharacteristic, complemented
121Q16—5031no—
122SD16—5031no—
123SD16—5031no—
124SD16—5032no—
125SD16C2×D50312yescomplemented
126D8—5032no—
127D8—5031no—
128D8—5032no—
129D8—5032no—
130D8C2×D50312yescomplemented
131M16—5032no—
132M16C2×D50311yescharacteristic, complemented
133C2×C8—5031no—
134C2×C8—5032no—
135C23—21no—
136C23—10062no—
137C23—10062no—
138C23—10061no—
139Q8—5031no—
140Q8—5031no—
141Q8C22×D50311yescharacteristic
142D4—21no—
143D4—21no—
144D4—10062no—
145D4—10062no—
146D4—10061no—
147D4—10062no—
148D4—10062no—
149D4—10061no—
150D4—5032no—
151D4—5031no—
152D4—5032no—
153D4—5031no—
154D4C22×D50312yes—
155D4C22×D50311yescharacteristic
156C2×C4—21no—
157C2×C4—10062no—
158C2×C4—10062no—
159C2×C4—10061no—
160C2×C4—5032no—
161C2×C4C22×D50311yescharacteristic
162C8—5031no—
163C8—5031no—
164C8C22×D50312yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—40241no—
169C22—40242no—
170C22—40242no—
171C22—10062no—
172C22—10061no—
173C22—5032no—
174C22D4×D50311yescharacteristic
175C4—21no—
176C4—10061no—
177C4—5032no—
178C4D4×D50311yescharacteristic
179C4C23×D50311yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—20122no—
184C2—20121no—
185C2—10062no—
186C2C2×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#576
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. #30632910C2semidirect
2. #30632909C2semidirect
3. #30632892C2semidirect
4. #30632891C2semidirect
5. #30632888C2semidirect
6. #30632885C2semidirect
7. #30632884C2semidirect
8. C2×#22548868C2semidirect
9. D8×D503C2semidirect
10. #30632872C2semidirect
11. AGL(1,ℤ/8)×C503C2semidirect
12. #22548884C22semidirect
15. #22548883C22semidirect
17. #22548882C22semidirect
19. C2×D2012C22semidirect
23. D4×D503C22semidirect
24. D4×D503C22semidirect
25. #22548873C22semidirect
26. #22548872C22semidirect
27. #22548871C22semidirect
28. #22548870C22semidirect
29. D4024C22semidirect
30. #22548868C22semidirect
31. #22548868C22semidirect
32. #22548868C22semidirect
33. #22548866C22semidirect
34. C2×C503⋊C8C22semidirect
35. C8×D503C22semidirect
36. #41×C503C22semidirect
37. C2×D4×C503C22semidirect
38. SD16×C503C22semidirect
39. D8×C503C22semidirect
40. M16×C503C22semidirect
93. C503#576semidirect
100. AGL(1,ℤ/8)D503semidirect
112. #41C2×D503semidirect
120. C2×D4C2×D503semidirect
125. SD16C2×D503semidirect
130. D8C2×D503semidirect
132. M16C2×D503semidirect

Maximal subgroups

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

subgroupindex
#306329102
#306329092
#306328922
#306328912
#306328882
#306328852
#306328842
C2×#225488682
D8×D5032
#306328722
AGL(1,ℤ/8)×C5032
#576503