Finite Group Databasebeta

← #44567080

Subgroups — #44567080

Order 32192.

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

normal subgroups only

This group has 262 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
1C2×#22548884C211yesmaximal, characteristic, complemented
2#41×D503C211yesmaximal, characteristic, complemented
3#30632896C212yesmaximal, complemented
4#30632895C211yesmaximal, characteristic, complemented
5#30632892C211yesmaximal, characteristic, complemented
6#30632891C212yesmaximal, complemented
7#30632889C211yesmaximal, characteristic, complemented
8#30632887C212yesmaximal, complemented
9#30632885C212yesmaximal, complemented
10M16×D503C211yesmaximal, characteristic, complemented
11#137×C503C211yesmaximal, characteristic, complemented
12#22548884—21no—
13#22548884—21no—
14#22548884C2212yes—
15#22548884C2212yescomplemented
16#22548884C2211yescharacteristic, complemented
17#22548883—21no—
18#22548883C2211yescharacteristic
19#22548882—21no—
20#22548882C2211yescharacteristic, complemented
21Q8×D503C2211yescharacteristic, complemented
22C2×D2012—21no—
23C2×D2012C2211yescharacteristic, complemented
24D4×D503—21no—
25D4×D503C2211yescharacteristic, complemented
26C2×C4×D503—21no—
27C2×C4×D503—21no—
28C2×C4×D503C2211yescharacteristic
29#22548873C2212yescomplemented
30#22548872C2212yescomplemented
31#22548870C2212yescomplemented
32#22548870C2212yescomplemented
33D4024C2212yescomplemented
34#22548868C2212yescomplemented
35#22548867C2211yescharacteristic, complemented
36#22548866C2212yescomplemented
37C8×D503C2212yescomplemented
38#41×C503C2211yescharacteristic
39C2×Q8×C503C2211yescharacteristic, complemented
40Q16×C503C2212yescomplemented
41SD16×C503C2212yescomplemented
42M16×C503C2211yescharacteristic, complemented
43C22×D503—21no—
44C22×D503—21no—
45C22×D503D411yescharacteristic
46Dic1006—21no—
47Dic1006C2311yescharacteristic
48D2012—21no—
49D2012—22no—
50D2012—22no—
51D2012—21no—
52D2012C2312yes—
53D2012C2311yescharacteristic
54C22⋊D503—21no—
55C22⋊D503—21no—
56C22⋊D503—21no—
57C2×Dic503—21no—
58C2×Dic503D411yescharacteristic
59C4×D503—21no—
60C4×D503—21no—
61C4×D503—21no—
62C4×D503—22no—
63C4×D503—22no—
64C4×D503D411yescharacteristic
65C4×D503D411yescharacteristic
66C4×D503C2311yescharacteristic
67C4×D503C2311yescharacteristic
68C503⋊C8C2312yes—
69Q8×C503—21no—
70Q8×C503C2312yes—
71Q8×C503C2311yescharacteristic
72D4×C503—21no—
73D4×C503C2311yescharacteristic
74C2×C4×C503—21no—
75C2×C4×C503—21no—
76C2×C4×C503C2311yescharacteristic
77C8×C503C2312yes—
78C22×C503—21no—
79C22×C503C2×D411yescharacteristic
80C2×D503—21no—
81C2×D503—22no—
82C2×D503—41no—
83C2×D503—42no—
84C2×D503—42no—
85C2×D503C2×D411yescharacteristic
86C2×D503C2×D411yescharacteristic
87C4×C503—21no—
88C4×C503—22no—
89C4×C503C2×D411yescharacteristic
90C4×C503C2411yescharacteristic
91Dic503—21no—
92Dic503C2×D411yescharacteristic
93Dic503C2×D411yescharacteristic
94C2×C503—21no—
95C2×C503—41no—
96C2×C503C22×D411yescharacteristic
97D503—21no—
98D503—21no—
99D503—41no—
100D503—42no—
101C503#57511yescharacteristic, complemented, Sylow
102#575—5031nomaximal, Sylow
103C2×#41—5031no—
104C2×#41—5031no—
105#137—5031no—
106#137—5032no—
107#137D50311yescharacteristic, complemented
108AGL(1,ℤ/8)—5031no—
109AGL(1,ℤ/8)—5032no—
110AGL(1,ℤ/8)—5031no—
111#135—5032no—
112#135—5032no—
113C2×M16—5031no—
114#41—10061no—
115#41—10061no—
116#41—10061no—
117#41—10061no—
118#41—5031no—
119#41—5032no—
120#41—5032no—
121#41—5031no—
122#41—5031no—
123#41C2×D50311yescharacteristic
124C2×Q8—5031no—
125C2×Q8C2×D50311yescharacteristic, complemented
126C2×D4—10061no—
127C2×D4—10061no—
128C2×D4—5031no—
129C2×D4—5031no—
130C22×C4—10061no—
131C22×C4—10061no—
132C22×C4—5031no—
133Q16—5032no—
134Q16C2×D50312yescomplemented
135SD16—5032no—
136SD16—5032no—
137SD16—5032no—
138SD16C2×D50312yescomplemented
139D8—5032no—
140D8—5032no—
141M16—5031no—
142M16—5032no—
143M16C2×D50311yescharacteristic, complemented
144C2×C8—5032no—
145C23—10061no—
146C23—10061no—
147C23—5031no—
148Q8—21no—
149Q8—10061no—
150Q8—5031no—
151Q8C22×D50311yescharacteristic
152Q8C22×D50312yes—
153D4—21no—
154D4—10061no—
155D4—10062no—
156D4—10062no—
157D4—10061no—
158D4—10061no—
159D4—10061no—
160D4—10061no—
161D4—5032no—
162D4—5031no—
163D4C22×D50311yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—10061no—
167C2×C4—10061no—
168C2×C4—10062no—
169C2×C4—10062no—
170C2×C4—10061no—
171C2×C4—10061no—
172C2×C4—5031no—
173C2×C4—5031no—
174C2×C4—5031no—
175C2×C4—5031no—
176C2×C4—5031no—
177C2×C4C22×D50311yescharacteristic
178C8—5032no—
179C8C22×D50312yes—
180C22—21no—
181C22—20122no—
182C22—20121no—
183C22—20122no—
184C22—10062no—
185C22—10061no—
186C22—5031no—
187C22—5031no—
188C22D4×D50311yescharacteristic
189C4—21no—
190C4—22no—
191C4—10061no—
192C4—5031no—
193C4—5031no—
194C4D4×D50311yescharacteristic
195C4C23×D50311yescharacteristic
196C2—21no—
197C2—41no—
198C2—20122no—
199C2—20121no—
200C2—10061no—
201C2—10061no—
202C2C2×D4×D50311yescharacteristic
subgroupG/H
centerC2C2×D4×D503
commutator, cosocleC4×C503C24
FrattiniC4C23×D503
Fitting#137×C503C2
socleC2×C503C22×D4
hypercenter#137D503
hypocenterC503#575
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. C2×#22548884C2semidirect
2. #41×D503C2semidirect
3. #30632896C2semidirect
4. #30632895C2semidirect
5. #30632892C2semidirect
6. #30632891C2semidirect
7. #30632889C2semidirect
8. #30632887C2semidirect
9. #30632885C2semidirect
10. M16×D503C2semidirect
11. #137×C503C2semidirect
15. #22548884C22semidirect
16. #22548884C22semidirect
20. #22548882C22semidirect
21. Q8×D503C22semidirect
23. C2×D2012C22semidirect
25. D4×D503C22semidirect
29. #22548873C22semidirect
30. #22548872C22semidirect
31. #22548870C22semidirect
32. #22548870C22semidirect
33. D4024C22semidirect
34. #22548868C22semidirect
35. #22548867C22semidirect
36. #22548866C22semidirect
37. C8×D503C22semidirect
39. C2×Q8×C503C22semidirect
40. Q16×C503C22semidirect
41. SD16×C503C22semidirect
42. M16×C503C22semidirect
101. C503#575semidirect
107. #137D503semidirect
125. C2×Q8C2×D503semidirect
134. Q16C2×D503semidirect
138. SD16C2×D503semidirect
143. M16C2×D503semidirect

Maximal subgroups

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

subgroupindex
C2×#225488842
#41×D5032
#306328962
#306328952
#306328922
#306328912
#306328892
#306328872
#306328852
M16×D5032
#137×C5032
#575503