Finite Group Databasebeta

← #13124104

Subgroups — #13124104

Order 1664.

784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×C13×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#11719535C211yesmaximal, characteristic, complemented
3C2×#88203C211yesmaximal, characteristic, complemented
4C22×#6104C211yesmaximal, characteristic, complemented
5#11718899C214yesmaximal, complemented
6#11718895C211yesmaximal, characteristic, complemented
7#11718894C211yesmaximal, characteristic, complemented
8#11718878C214yesmaximal, complemented
9#11718876C211yesmaximal, characteristic, complemented
10C13×H(5,𝔽2)—24no—
11C13×H(5,𝔽2)—24no—
12C2×C13×#41—21no—
13C2×C13×#41C2211yescharacteristic
14C2×C13×#41C2211yescharacteristic
15C2×C13×#41C2212yescomplemented
16C22×D4×C13—21no—
17C22×D4×C13—22no—
18C22×D4×C13C2211yescharacteristic
19C22×D4×C13C2212yescomplemented
20C22×D52C2211yescharacteristic, complemented
21#88203—24no—
22#88201—21no—
23C2×#6106C2212yescomplemented
24#88194—21no—
25#88191—22no—
26C2×#6104—24no—
27C2×#6104C2214yescomplemented
28C2×#6104C2212yescomplemented
29#88184C2214yescomplemented
30#88180C2211yescharacteristic, complemented
31C2×#6099C2211yescharacteristic, complemented
32C22×#1055C2211yescharacteristic, complemented
33#88075C2212yescomplemented
34#88072C2214yescomplemented
35#88072C2212yescomplemented
36C22⋊#1055C2214yescomplemented
37C24×C13—21no—
38C24×C13—22no—
39C23×D13—21no—
40C13×#41—28no—
41C13×#41—24no—
42C13×#41—24no—
43C13×#41—22no—
44C13×#41—22no—
45C13×#41—22no—
46C13×#41D414yescomplemented
47C2×Q8×C13D411yescharacteristic
48C2×Q8×C13C2311yescharacteristic
49C2×D4×C13—216no—
50C2×D4×C13—28no—
51C2×D4×C13—21no—
52C2×D4×C13—22no—
53C2×D4×C13—24no—
54C2×D4×C13—24no—
55C2×D4×C13—21no—
56C2×D4×C13—22no—
57C2×D4×C13—22no—
58C2×D4×C13D412yes—
59C2×D4×C13D411yescharacteristic
60C2×D4×C13D414yescomplemented
61C2×D4×C13C2312yes—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13C2312yes—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—24no—
68C2×D52—22no—
69C2×D52—22no—
70C2×D52—21no—
71C2×D52C2312yes—
72C22⋊Dic13—21no—
73#6106—24no—
74#6104—28no—
75#6104—24no—
76#6103—24no—
77C4⋊Dic13C2312yes—
78C4×Dic13—21no—
79#6099—22no—
80C2×#1055—22no—
81C2×#1055C2312yes—
82C2×#1055C2312yes—
83#3008—131nomaximal, Sylow
84C23×C13—28no—
85C23×C13—21no—
86C23×C13—22no—
87C23×C13—24no—
88C23×C13—82no—
89C23×C13—84no—
90C23×C13C2×D412yes—
91C23×C13C2×D411yescharacteristic
92C22×D13—22no—
93C22×D13—42no—
94C22×D13—82no—
95Q8×C13—22no—
96Q8×C13—21no—
97Q8×C13C2×D412yes—
98D4×C13—28no—
99D4×C13—28no—
100D4×C13—24no—
101D4×C13—24no—
102D4×C13—22no—
103D4×C13—24no—
104D4×C13—22no—
105D4×C13—21no—
106D4×C13C2×D412yes—
107D4×C13C2×D414yes—
108C2×C4×C13—28no—
109C2×C4×C13—21no—
110C2×C4×C13—24no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13C2×D412yes—
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D412yes—
116C2×C4×C13C2×D412yes—
117C2×C4×C13C2411yescharacteristic
118C22⋊D13—84no—
119C2×Dic13—22no—
120D52—22no—
121D52—22no—
122D52—42no—
123#1055—22no—
124#1055—22no—
125C2×H(5,𝔽2)D1311yescharacteristic, complemented
126C2×AGL(1,ℤ/8)—131no—
127C22×D8—131no—
128#535—131no—
129#449—134no—
130#447—134no—
131#418—131no—
132#416—131no—
133#408—131no—
134C22×C13—22no—
135C22×C13—22no—
136C22×C13—24no—
137C22×C13—22no—
138C22×C13—24no—
139C22×C13—44no—
140C22×C13—42no—
141C22×C13—84no—
142C22×C13—88no—
143C22×C13#12012yes—
144C22×C13C22×D411yescharacteristic
145C2×D13—42no—
146C2×D13—44no—
147C2×D13—84no—
148C4×C13—22no—
149C4×C13—22no—
150C4×C13#12012yes—
151C4×C13C22×D411yescharacteristic
152C4×C13C22×D411yescharacteristic
153Dic13—42no—
154H(5,𝔽2)—24no—
155H(5,𝔽2)—24no—
156C2×#41—21no—
157C2×#41C2×D1311yescharacteristic
158C2×#41C2×D1311yescharacteristic
159C2×#41C2×D1312yescomplemented
160C22×D4—21no—
161C22×D4—22no—
162C22×D4—131no—
163C22×D4C2×D1311yescharacteristic
164C22×D4C2×D1312yescomplemented
165AGL(1,ℤ/8)—264no—
166C2×SD16—132no—
167C2×D8—134no—
168C2×D8—132no—
169C2×D8—264no—
170C2×M16—131no—
171C22×C8—131no—
172#127—261no—
173#124—261no—
174#121—134no—
175#120—262no—
176#117—131no—
177#103—132no—
178#102—132no—
179#102—134no—
180C22⋊C8—134no—
181C2×C13—22no—
182C2×C13—42no—
183C2×C13—44no—
184C2×C13—42no—
185C2×C13C2×#12011yescharacteristic
186C2×C13#57612yes—
187D13—82no—
188C24—21no—
189C24—22no—
190C24—261no—
191#41—28no—
192#41—24no—
193#41—24no—
194#41—22no—
195#41—22no—
196#41—22no—
197#41C22⋊D1314yescomplemented
198C2×Q8C22⋊D1311yescharacteristic
199C2×Q8C22×D1311yescharacteristic
200C2×D4—216no—
201C2×D4—28no—
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—24no—
205C2×D4—24no—
206C2×D4—21no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—132no—
210C2×D4—264no—
211C2×D4—262no—
212C2×D4—262no—
213C2×D4—261no—
214C2×D4C22⋊D1312yes—
215C2×D4C22⋊D1311yescharacteristic
216C2×D4C22⋊D1314yescomplemented
217C2×D4C22×D1312yes—
218C2×D4C22×D1311yescharacteristic
219C22×C4—21no—
220C22×C4—22no—
221C22×C4C22×D1312yes—
222C22×C4C22×D1311yescharacteristic
223SD16—264no—
224D8—268no—
225D8—264no—
226M16—262no—
227C2×C8—132no—
228C2×C8—132no—
229C2×C8—262no—
230C4⋊C4—132no—
231C22⋊C4—261no—
232C22⋊C4—264no—
233C42—261no—
234C13#300811yescharacteristic, complemented, Sylow
235C23—28no—
236C23—21no—
237C23—22no—
238C23—24no—
239C23—82no—
240C23—84no—
241C23—262no—
242C23—522no—
243C23—1042no—
244C23C2×C22⋊D1312yes—
245C23C2×C22⋊D1311yescharacteristic
246Q8—22no—
247Q8—21no—
248Q8C2×C22⋊D1312yes—
249D4—28no—
250D4—28no—
251D4—24no—
252D4—24no—
253D4—22no—
254D4—24no—
255D4—22no—
256D4—21no—
257D4—262no—
258D4—262no—
259D4—522no—
260D4—1044no—
261D4C2×C22⋊D1312yes—
262D4C2×C22⋊D1314yes—
263C2×C4—28no—
264C2×C4—21no—
265C2×C4—24no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—262no—
269C2×C4C2×C22⋊D1312yes—
270C2×C4C2×C22⋊D1311yescharacteristic
271C2×C4C2×C22⋊D1312yes—
272C2×C4C2×C22⋊D1312yes—
273C2×C4C23×D1311yescharacteristic
274C8—262no—
275C8—262no—
276C22—22no—
277C22—24no—
278C22—22no—
279C22—24no—
280C22—22no—
281C22—44no—
282C22—42no—
283C22—84no—
284C22—88no—
285C22—524no—
286C22—522no—
287C22—1044no—
288C22#8820712yes—
289C22C22×C22⋊D1311yescharacteristic
290C4—22no—
291C4—22no—
292C4—522no—
293C4#8820712yes—
294C4C22×C22⋊D1311yescharacteristic
295C4C22×C22⋊D1311yescharacteristic
296C2—22no—
297C2—42no—
298C2—44no—
299C2—42no—
300C2—1042no—
301C2#1171954012yes—
302C2C2×#8820711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×H(5,𝔽2)C2
socleC22×C13C22×D4
hypercenterC2×H(5,𝔽2)D13
hypocenterC13#3008
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×C13×H(5,𝔽2)C2semidirect
2. #11719535C2semidirect
3. C2×#88203C2semidirect
4. C22×#6104C2semidirect
5. #11718899C2semidirect
6. #11718895C2semidirect
7. #11718894C2semidirect
8. #11718878C2semidirect
9. #11718876C2semidirect
15. C2×C13×#41C22semidirect
19. C22×D4×C13C22semidirect
20. C22×D52C22semidirect
23. C2×#6106C22semidirect
27. C2×#6104C22semidirect
28. C2×#6104C22semidirect
29. #88184C22semidirect
30. #88180C22semidirect
31. C2×#6099C22semidirect
32. C22×#1055C22semidirect
33. #88075C22semidirect
34. #88072C22semidirect
35. #88072C22semidirect
36. C22⋊#1055C22semidirect
46. C13×#41D4semidirect
60. C2×D4×C13D4semidirect
125. C2×H(5,𝔽2)D13semidirect
159. C2×#41C2×D13semidirect
164. C22×D4C2×D13semidirect
197. #41C22⋊D13semidirect
216. C2×D4C22⋊D13semidirect
234. C13#3008semidirect

Maximal subgroups

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

subgroupindex
C2×C13×H(5,𝔽2)2
#117195352
C2×#882032
C22×#61042
#117188992
#117188952
#117188942
#117188782
#117188762
#300813