Finite Group Databasebeta

← #13125856

Subgroups — #13125856

Order 1664.

490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719184C211yesmaximal, characteristic, complemented
2C2×#88128C211yesmaximal, characteristic, complemented
3C13×#432C211yesmaximal, characteristic, complemented
4#11718509C212yesmaximal, complemented
5#11718504C212yesmaximal, complemented
6#11718393C212yesmaximal, complemented
7#11718392C212yesmaximal, complemented
8#11718374C212yesmaximal, complemented
9#11718373C212yesmaximal, complemented
10C22×D52—21no—
11C22×D52—21no—
12C22×D52C2212yes—
13C2×C42×C13C2211yescharacteristic
14#88184C2211yescharacteristic
15#88183—21no—
16C4×C22⋊D13—21no—
17#88178C2211yescharacteristic
18C2×D104C2214yescomplemented
19C2×#6095C2214yescomplemented
20#88130—21no—
21#88129C2211yescharacteristic, complemented
22#88128—21no—
23#88128—21no—
24#88128C2212yes—
25#88128C2212yes—
26C4×D52C2211yescharacteristic, complemented
27#88126—21no—
28#88124C2211yescharacteristic, complemented
29C4×Dic26C2211yescharacteristic, complemented
30C13×C4⋊C8C2212yescomplemented
31C13×C22⋊C8C2212yes—
32C13×#97C2212yescomplemented
33#88061C2214yescomplemented
34#88061C2214yescomplemented
35C23×D13—22no—
36C22×C4×C13D411yescharacteristic
37C22×C4×C13D411yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C2×C22⋊D13—21no—
40C2×D52—22no—
41C2×D52—22no—
42C2×D52—22no—
43C2×D52—22no—
44C2×D52—22no—
45C2×D52—44no—
46C2×D52—44no—
47C2×D52—44no—
48C2×D52C2311yescharacteristic
49C2×D52C2314yes—
50C2×C4×D13—21no—
51C2×Dic26C2311yescharacteristic
52C2×C8×C13C2314yes—
53C42×C13D411yescharacteristic
54C42×C13D411yescharacteristic
55C42×C13C2311yescharacteristic
56C42×C13C2311yescharacteristic
57C22⋊Dic13—21no—
58#6103—21no—
59#6103—21no—
60#6103—21no—
61#6103—21no—
62C4⋊Dic13C2311yescharacteristic
63C4⋊Dic13C2311yescharacteristic
64#6101—21no—
65#6101—21no—
66#6101—21no—
67#6101—21no—
68C4×Dic13—21no—
69D104—44no—
70#6095—44no—
71#3217—131nomaximal, Sylow
72C23×C13C2×D411yescharacteristic
73C22×D13—21no—
74C22×D13—24no—
75C22×D13—44no—
76C22×D13—44no—
77C22×D13—44no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13C2411yescharacteristic
87C22⋊D13—42no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91D52—24no—
92D52—22no—
93D52—24no—
94D52—44no—
95D52—44no—
96D52—44no—
97D52—44no—
98D52—44no—
99C4×D13—42no—
100Dic26—22no—
101C8×C13—24no—
102C2×#127—131no—
103#529—131no—
104#496—132no—
105#490—132no—
106#460—132no—
107#459—132no—
108#450—132no—
109#447—132no—
110#432D1311yescharacteristic, complemented
111C22×C13—21no—
112C22×C13—21no—
113C22×C13AGL(1,ℤ/8)12yes—
114C22×C13C22×D411yescharacteristic
115C2×D13—44no—
116C2×D13—41no—
117C2×D13—41no—
118C2×D13—44no—
119C2×D13—44no—
120C2×D13—41no—
121C2×D13—88no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13AGL(1,ℤ/8)12yes—
127C4×C13H(5,𝔽2)12yes—
128Dic13—41no—
129Dic13—41no—
130Dic13—41no—
131C22×D4—132no—
132C22×D4—261no—
133C22×D4—261no—
134C2×SD16—134no—
135C2×D8—134no—
136#127—132no—
137#127—132no—
138#127—261no—
139#127—261no—
140#126—261no—
141#125—131no—
142#124—131no—
143#123—261no—
144C22⋊Q8—131no—
145#121—131no—
146C4×Q8—131no—
147C4×D4—131no—
148C4×D4—261no—
149#117—261no—
150C2×C42C2×D1311yescharacteristic
151C4⋊C8C2×D1312yescomplemented
152#102—134no—
153#102—134no—
154C22⋊C8C2×D1312yes—
155#97C2×D1312yescomplemented
156C2×C13—22no—
157C2×C13#53511yescharacteristic
158C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
159C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
160D13—81no—
161D13—84no—
162C24—262no—
163C2×Q8—131no—
164C2×D4—134no—
165C2×D4—131no—
166C2×D4—261no—
167C2×D4—262no—
168C2×D4—262no—
169C2×D4—262no—
170C2×D4—262no—
171C2×D4—262no—
172C2×D4—524no—
173C2×D4—524no—
174C2×D4—524no—
175C22×C4—261no—
176C22×C4D5211yescharacteristic
177C22×C4D5211yescharacteristic
178C22×C4C22×D1311yescharacteristic
179SD16—524no—
180D8—524no—
181C2×C8C22×D1314yes—
182C4⋊C4—131no—
183C4⋊C4—131no—
184C4⋊C4—261no—
185C4⋊C4—261no—
186C4⋊C4—261no—
187C4⋊C4—261no—
188C22⋊C4—261no—
189C22⋊C4—261no—
190C22⋊C4—261no—
191C22⋊C4—261no—
192C22⋊C4—261no—
193C42—261no—
194C42D5211yescharacteristic
195C42D5211yescharacteristic
196C42C22×D1311yescharacteristic
197C42C22×D1311yescharacteristic
198C13#321711yescharacteristic, complemented, Sylow
199C23—261no—
200C23—264no—
201C23—524no—
202C23—524no—
203C23—524no—
204C23C2×D5211yescharacteristic
205Q8—262no—
206D4—262no—
207D4—264no—
208D4—264no—
209D4—524no—
210D4—524no—
211D4—524no—
212D4—524no—
213D4—522no—
214D4—524no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—261no—
219C2×C4—261no—
220C2×C4—261no—
221C2×C4—522no—
222C2×C4C2×D5211yescharacteristic
223C2×C4C2×D5211yescharacteristic
224C2×C4C2×D5211yescharacteristic
225C2×C4C2×D5211yescharacteristic
226C2×C4C2×D5211yescharacteristic
227C2×C4C23×D1311yescharacteristic
228C8—24no—
229C22—21no—
230C22—21no—
231C22—521no—
232C22—524no—
233C22—524no—
234C22—521no—
235C22—524no—
236C22—521no—
237C22—1048no—
238C22#8816212yes—
239C22C22×D5211yescharacteristic
240C4—21no—
241C4—21no—
242C4—21no—
243C4—21no—
244C4—521no—
245C4—521no—
246C4—521no—
247C4#8816212yes—
248C4#8825612yes—
249C2—22no—
250C2—1044no—
251C2—1041no—
252C2#1171923011yescharacteristic
253C2C2×#8816211yescharacteristic
254C2C2×#8816211yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#432C2
socleC22×C13C22×D4
hypercenter#432D13
hypocenterC13#3217
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #11719184C2semidirect
2. C2×#88128C2semidirect
3. C13×#432C2semidirect
4. #11718509C2semidirect
5. #11718504C2semidirect
6. #11718393C2semidirect
7. #11718392C2semidirect
8. #11718374C2semidirect
9. #11718373C2semidirect
18. C2×D104C22semidirect
19. C2×#6095C22semidirect
21. #88129C22semidirect
26. C4×D52C22semidirect
28. #88124C22semidirect
29. C4×Dic26C22semidirect
30. C13×C4⋊C8C22semidirect
32. C13×#97C22semidirect
33. #88061C22semidirect
34. #88061C22semidirect
110. #432D13semidirect
151. C4⋊C8C2×D13semidirect
155. #97C2×D13semidirect
198. C13#3217semidirect

Maximal subgroups

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

subgroupindex
#117191842
C2×#881282
C13×#4322
#117185092
#117185042
#117183932
#117183922
#117183742
#117183732
#321713