Finite Group Databasebeta

← #13125881

Subgroups — #13125881

Order 1664.

420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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#11719424C211yesmaximal, characteristic, complemented
2#11719379C211yesmaximal, characteristic, complemented
3C13×#496C211yesmaximal, characteristic, complemented
4#11718833C212yesmaximal, complemented
5#11718826C212yesmaximal, complemented
6#11718817C212yesmaximal, complemented
7#11718811C212yesmaximal, complemented
8#11718734C211yesmaximal, characteristic, complemented
9#11718717C211yesmaximal, characteristic, complemented
10#11718374C211yesmaximal, characteristic, complemented
11#11718370C211yesmaximal, characteristic, complemented
12C2×#6131C2211yescharacteristic
13C2×D4×D13C2211yescharacteristic
14C2×C13×SD16C2212yescomplemented
15C2×C13×D8C2212yes—
16C13×#127C2211yescharacteristic, complemented
17C13×#124C2211yescharacteristic
18#88201C2211yescharacteristic
19#88194C2211yescharacteristic
20#88193—22no—
21#88192C2212yes—
22#88189—22no—
23D4×Dic13C2212yescomplemented
24C2×#6104C2212yes—
25C2×#6104C2212yescomplemented
26#88138—22no—
27#88136—22no—
28#88128C2211yescharacteristic
29#88126C2211yescharacteristic
30#88124C2211yescharacteristic, complemented
31C13×#97C2211yescharacteristic, complemented
32#88075C2212yescomplemented
33#88072C2212yes—
34#88061C2212yes—
35#88061C2212yescomplemented
36#88060C2212yes—
37#88054C2212yescomplemented
38C4×#1055C2211yescharacteristic, complemented
39C23×D13—21no—
40C2×Q8×C13C2311yescharacteristic
41C2×D4×C13—22no—
42C2×D4×C13C2311yescharacteristic
43C2×D4×C13C2312yes—
44C2×C22⋊D13—22no—
45C2×C22⋊D13—21no—
46C2×C22⋊D13—22no—
47C22×Dic13—22no—
48#6131—42no—
49D4×D13—42no—
50C2×D52—21no—
51C2×D52—22no—
52C2×D52C2311yescharacteristic
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C2×C4×D13C2311yescharacteristic
56C13×SD16—42no—
57C13×D8—42no—
58C2×C8×C13C2312yes—
59C13×C22⋊C4—22no—
60C42×C13C2311yescharacteristic
61C22⋊Dic13—22no—
62C22⋊Dic13—22no—
63#6104—42no—
64#6104—42no—
65#6103—22no—
66#6103D412yes—
67C4⋊Dic13C2312yes—
68#6101—22no—
69#6101D412yes—
70C4×Dic13C2311yescharacteristic
71C2×#1055C2312yes—
72#3220—131nomaximal, Sylow
73C23×C13—22no—
74C23×C13—21no—
75C22×D13—21no—
76C22×D13—21no—
77C22×D13—42no—
78C22×D13—82no—
79C22×D13C2×D411yescharacteristic
80Q8×C13—22no—
81D4×C13—22no—
82D4×C13—22no—
83D4×C13—22no—
84D4×C13—82no—
85C2×C4×C13—21no—
86C2×C4×C13C2×D412yes—
87C2×C4×C13C2411yescharacteristic
88C22⋊D13—42no—
89C22⋊D13—82no—
90C22⋊D13—82no—
91C2×Dic13—22no—
92C2×Dic13—82no—
93C2×Dic13C2×D412yes—
94C2×Dic13C2×D411yescharacteristic
95D52—22no—
96D52—22no—
97D52—42no—
98D52—82no—
99C4×D13—22no—
100C4×D13—42no—
101C8×C13—22no—
102#1055—22no—
103#540—131no—
104#535—131no—
105#496D1311yescharacteristic, complemented
106#493—131no—
107#490—131no—
108#488—131no—
109#463—132no—
110#459—132no—
111#449—132no—
112#447—132no—
113#433—131no—
114C22×C13—41no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13C22×D411yescharacteristic
120C2×D13—21no—
121C2×D13—22no—
122C2×D13—41no—
123C2×D13—41no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13—84no—
127C4×C13—22no—
128C4×C13—41no—
129C4×C13H(5,𝔽2)12yes—
130Dic13—21no—
131Dic13—22no—
132Dic13—42no—
133C2×#41—131no—
134C22×D4—131no—
135C2×SD16C2×D1312yescomplemented
136C2×D8—132no—
137C2×D8—132no—
138C2×D8C2×D1312yes—
139#127—131no—
140#127—131no—
141#127C2×D1311yescharacteristic, complemented
142#125—131no—
143#124—131no—
144#124C2×D1311yescharacteristic
145#123—262no—
146#121—132no—
147#121—262no—
148#121—262no—
149#120—262no—
150C4×D4—132no—
151#117—131no—
152C4⋊C8—132no—
153#103—132no—
154#102—132no—
155#102—132no—
156#102—132no—
157C22⋊C8—132no—
158#97C2×D1311yescharacteristic, complemented
159C4×C8—131no—
160C2×C13—81no—
161C2×C13—82no—
162C2×C13#53511yescharacteristic
163C2×C13#57612yes—
164D13—41no—
165D13—81no—
166D13—81no—
167C24—261no—
168#41—522no—
169C2×Q8C22×D1311yescharacteristic
170C2×D4—22no—
171C2×D4—131no—
172C2×D4—131no—
173C2×D4—261no—
174C2×D4—261no—
175C2×D4—262no—
176C2×D4—262no—
177C2×D4—262no—
178C2×D4—522no—
179C2×D4C22×D1311yescharacteristic
180C2×D4C22×D1312yes—
181C22×C4—131no—
182C22×C4—261no—
183C22×C4—262no—
184SD16—42no—
185D8—42no—
186D8—522no—
187D8—522no—
188C2×C8—132no—
189C2×C8C22×D1312yes—
190C4⋊C4—132no—
191C4⋊C4—132no—
192C4⋊C4—262no—
193C22⋊C4—22no—
194C22⋊C4—132no—
195C22⋊C4—262no—
196C22⋊C4—262no—
197C22⋊C4—262no—
198C42—131no—
199C42C22×D1311yescharacteristic
200C13#322011yescharacteristic, complemented, Sylow
201C23—21no—
202C23—22no—
203C23—131no—
204C23—261no—
205C23—261no—
206C23—522no—
207C23—1042no—
208Q8—22no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—82no—
213D4—262no—
214D4—262no—
215D4—522no—
216D4—522no—
217D4—1042no—
218D4—1042no—
219D4—1042no—
220C2×C4—21no—
221C2×C4—132no—
222C2×C4—131no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—522no—
226C2×C4—1042no—
227C2×C4D4×D1312yes—
228C2×C4C23×D1311yescharacteristic
229C8—22no—
230C8—262no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—41no—
235C22—42no—
236C22—262no—
237C22—261no—
238C22—522no—
239C22—522no—
240C22—521no—
241C22—521no—
242C22—1044no—
243C22C2×D4×D1311yescharacteristic
244C4—22no—
245C4—41no—
246C4—262no—
247C4—261no—
248C4—522no—
249C4#8825112yes—
250C2—81no—
251C2—82no—
252C2—521no—
253C2—1041no—
254C2—1041no—
255C2#1171942011yescharacteristic
256C2#1171947912yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#496C2
socleC22×C13C22×D4
hypercenter#496D13
hypocenterC13#3220
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #11719424C2semidirect
2. #11719379C2semidirect
3. C13×#496C2semidirect
4. #11718833C2semidirect
5. #11718826C2semidirect
6. #11718817C2semidirect
7. #11718811C2semidirect
8. #11718734C2semidirect
9. #11718717C2semidirect
10. #11718374C2semidirect
11. #11718370C2semidirect
14. C2×C13×SD16C22semidirect
16. C13×#127C22semidirect
23. D4×Dic13C22semidirect
25. C2×#6104C22semidirect
30. #88124C22semidirect
31. C13×#97C22semidirect
32. #88075C22semidirect
35. #88061C22semidirect
37. #88054C22semidirect
38. C4×#1055C22semidirect
105. #496D13semidirect
135. C2×SD16C2×D13semidirect
141. #127C2×D13semidirect
158. #97C2×D13semidirect
200. C13#3220semidirect

Maximal subgroups

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

subgroupindex
#117194242
#117193792
C13×#4962
#117188332
#117188262
#117188172
#117188112
#117187342
#117187172
#117183742
#117183702
#322013