Finite Group Databasebeta

← #45656037

Subgroups — #45656037

Order 32576.

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×#22550862C211yesmaximal, characteristic, complemented
2#41×D509C211yesmaximal, characteristic, complemented
3#30654247C212yesmaximal, complemented
4#30654246C211yesmaximal, characteristic, complemented
5#30654243C211yesmaximal, characteristic, complemented
6#30654242C212yesmaximal, complemented
7#30654240C211yesmaximal, characteristic, complemented
8#30654238C212yesmaximal, complemented
9#30654236C212yesmaximal, complemented
10M16×D509C211yesmaximal, characteristic, complemented
11#137×C509C211yesmaximal, characteristic, complemented
12#22550862—21no—
13#22550862—21no—
14#22550862C2212yes—
15#22550862C2212yescomplemented
16#22550862C2211yescharacteristic, complemented
17#22550861—21no—
18#22550861C2211yescharacteristic
19#22550860—21no—
20#22550860C2211yescharacteristic, complemented
21Q8×D509C2211yescharacteristic, complemented
22C2×D2036—21no—
23C2×D2036C2211yescharacteristic, complemented
24D4×D509—21no—
25D4×D509C2211yescharacteristic, complemented
26C2×C4×D509—21no—
27C2×C4×D509—21no—
28C2×C4×D509C2211yescharacteristic
29#22550851C2212yescomplemented
30#22550850C2212yescomplemented
31#22550848C2212yescomplemented
32#22550848C2212yescomplemented
33D4072C2212yescomplemented
34#22550846C2212yescomplemented
35#22550845C2211yescharacteristic, complemented
36#22550844C2212yescomplemented
37C8×D509C2212yescomplemented
38#41×C509C2211yescharacteristic
39C2×Q8×C509C2211yescharacteristic, complemented
40Q16×C509C2212yescomplemented
41SD16×C509C2212yescomplemented
42M16×C509C2211yescharacteristic, complemented
43C22×D509—21no—
44C22×D509—21no—
45C22×D509D411yescharacteristic
46Dic1018—21no—
47Dic1018C2311yescharacteristic
48D2036—21no—
49D2036—22no—
50D2036—22no—
51D2036—21no—
52D2036C2312yes—
53D2036C2311yescharacteristic
54C22⋊D509—21no—
55C22⋊D509—21no—
56C22⋊D509—21no—
57C2×Dic509—21no—
58C2×Dic509D411yescharacteristic
59C4×D509—21no—
60C4×D509—21no—
61C4×D509—21no—
62C4×D509—22no—
63C4×D509—22no—
64C4×D509D411yescharacteristic
65C4×D509D411yescharacteristic
66C4×D509C2311yescharacteristic
67C4×D509C2311yescharacteristic
68#16861325C2312yes—
69Q8×C509—21no—
70Q8×C509C2312yes—
71Q8×C509C2311yescharacteristic
72D4×C509—21no—
73D4×C509C2311yescharacteristic
74C2×C4×C509—21no—
75C2×C4×C509—21no—
76C2×C4×C509C2311yescharacteristic
77C8×C509C2312yes—
78C22×C509—21no—
79C22×C509C2×D411yescharacteristic
80C2×D509—21no—
81C2×D509—22no—
82C2×D509—41no—
83C2×D509—42no—
84C2×D509—42no—
85C2×D509C2×D411yescharacteristic
86C2×D509C2×D411yescharacteristic
87C4×C509—21no—
88C4×C509—22no—
89C4×C509C2×D411yescharacteristic
90C4×C509C2411yescharacteristic
91Dic509—21no—
92Dic509C2×D411yescharacteristic
93Dic509C2×D411yescharacteristic
94C2×C509—21no—
95C2×C509—41no—
96C2×C509C22×D411yescharacteristic
97D509—21no—
98D509—21no—
99D509—41no—
100D509—42no—
101C509#57511yescharacteristic, complemented, Sylow
102#575—5091nomaximal, Sylow
103C2×#41—5091no—
104C2×#41—5091no—
105#137—5091no—
106#137—5092no—
107#137D50911yescharacteristic, complemented
108AGL(1,ℤ/8)—5091no—
109AGL(1,ℤ/8)—5092no—
110AGL(1,ℤ/8)—5091no—
111#135—5092no—
112#135—5092no—
113C2×M16—5091no—
114#41—10181no—
115#41—10181no—
116#41—10181no—
117#41—10181no—
118#41—5092no—
119#41—5091no—
120#41—5092no—
121#41—5091no—
122#41—5091no—
123#41C2×D50911yescharacteristic
124C2×Q8—5091no—
125C2×Q8C2×D50911yescharacteristic, complemented
126C2×D4—10181no—
127C2×D4—10181no—
128C2×D4—5091no—
129C2×D4—5091no—
130C22×C4—10181no—
131C22×C4—10181no—
132C22×C4—5091no—
133Q16—5092no—
134Q16C2×D50912yescomplemented
135SD16—5092no—
136SD16—5092no—
137SD16—5092no—
138SD16C2×D50912yescomplemented
139D8—5092no—
140D8—5092no—
141M16—5091no—
142M16—5092no—
143M16C2×D50911yescharacteristic, complemented
144C2×C8—5092no—
145C23—10181no—
146C23—10181no—
147C23—5091no—
148Q8—21no—
149Q8—10181no—
150Q8—5091no—
151Q8C22×D50911yescharacteristic
152Q8C22×D50912yes—
153D4—21no—
154D4—10181no—
155D4—10182no—
156D4—10182no—
157D4—10181no—
158D4—10181no—
159D4—10181no—
160D4—10181no—
161D4—5092no—
162D4—5091no—
163D4C22×D50911yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—10181no—
167C2×C4—10181no—
168C2×C4—10182no—
169C2×C4—10182no—
170C2×C4—10181no—
171C2×C4—10181no—
172C2×C4—5091no—
173C2×C4—5091no—
174C2×C4—5091no—
175C2×C4—5091no—
176C2×C4—5091no—
177C2×C4C22×D50911yescharacteristic
178C8—5092no—
179C8C22×D50912yes—
180C22—21no—
181C22—20362no—
182C22—20361no—
183C22—20362no—
184C22—10182no—
185C22—10181no—
186C22—5091no—
187C22—5091no—
188C22D4×D50911yescharacteristic
189C4—21no—
190C4—22no—
191C4—10181no—
192C4—5091no—
193C4—5091no—
194C4D4×D50911yescharacteristic
195C4C23×D50911yescharacteristic
196C2—21no—
197C2—41no—
198C2—20362no—
199C2—20361no—
200C2—10181no—
201C2—10181no—
202C2C2×D4×D50911yescharacteristic
subgroupG/H
centerC2C2×D4×D509
commutator, cosocleC4×C509C24
FrattiniC4C23×D509
Fitting#137×C509C2
socleC2×C509C22×D4
hypercenter#137D509
hypocenterC509#575
LCSG ▷ C4×C509 ▷ C2×C509 ▷ C509
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#22550862C2semidirect
2. #41×D509C2semidirect
3. #30654247C2semidirect
4. #30654246C2semidirect
5. #30654243C2semidirect
6. #30654242C2semidirect
7. #30654240C2semidirect
8. #30654238C2semidirect
9. #30654236C2semidirect
10. M16×D509C2semidirect
11. #137×C509C2semidirect
15. #22550862C22semidirect
16. #22550862C22semidirect
20. #22550860C22semidirect
21. Q8×D509C22semidirect
23. C2×D2036C22semidirect
25. D4×D509C22semidirect
29. #22550851C22semidirect
30. #22550850C22semidirect
31. #22550848C22semidirect
32. #22550848C22semidirect
33. D4072C22semidirect
34. #22550846C22semidirect
35. #22550845C22semidirect
36. #22550844C22semidirect
37. C8×D509C22semidirect
39. C2×Q8×C509C22semidirect
40. Q16×C509C22semidirect
41. SD16×C509C22semidirect
42. M16×C509C22semidirect
101. C509#575semidirect
107. #137D509semidirect
125. C2×Q8C2×D509semidirect
134. Q16C2×D509semidirect
138. SD16C2×D509semidirect
143. M16C2×D509semidirect

Maximal subgroups

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

subgroupindex
C2×#225508622
#41×D5092
#306542472
#306542462
#306542432
#306542422
#306542402
#306542382
#306542362
M16×D5092
#137×C5092
#575509