Finite Group Databasebeta

← #13124102

Subgroups — #13124102

Order 1664.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88256C211yesmaximal, characteristic, complemented
2C13×#535C211yesmaximal, characteristic, complemented
3C2×#88186C211yesmaximal, characteristic, complemented
4C22×#6104C211yesmaximal, characteristic, complemented
5#11718895C211yesmaximal, characteristic, complemented
6#11718698C214yesmaximal, complemented
7#11718697C214yesmaximal, complemented
8#11718663C211yesmaximal, characteristic, complemented
9#11718662C211yesmaximal, characteristic, complemented
10C2×C13×#41C2211yescharacteristic
11C22×D4×C13C2211yescharacteristic, complemented
12#88256—24no—
13#88256—24no—
14C2×#6131—21no—
15C2×D4×D13—21no—
16C2×D4×D13—22no—
17C2×#6127C2211yescharacteristic
18C2×#6127C2212yescomplemented
19C22×D52C2211yescharacteristic
20C22×D52C2212yescomplemented
21C13×#127—21no—
22C13×#124—21no—
23C13×#121C2214yescomplemented
24C13×#120—22no—
25C13×#117C2211yescharacteristic, complemented
26C2×#6105C2212yescomplemented
27#88186—24no—
28C2×#6104—24no—
29C2×#6104C2212yescomplemented
30C2×#6104C2214yescomplemented
31C2×#6099C2211yescharacteristic, complemented
32C22×#1055C2211yescharacteristic, complemented
33C22⋊#1055C2214yescomplemented
34#88050C2212yescomplemented
35#88049C2214yescomplemented
36#88049C2212yescomplemented
37C24×C13—21no—
38C23×D13—21no—
39C23×D13—22no—
40C13×#41—22no—
41C13×#41—22no—
42C2×Q8×C13D411yescharacteristic
43C2×D4×C13—24no—
44C2×D4×C13—22no—
45C2×D4×C13—22no—
46C2×D4×C13—21no—
47C2×D4×C13D412yes—
48C2×D4×C13D411yescharacteristic
49C2×D4×C13C2312yes—
50C22×C4×C13C2312yes—
51C22×C4×C13C2311yescharacteristic
52C2×C22⋊D13—21no—
53C2×C22⋊D13—22no—
54#6131—28no—
55D4×D13—216no—
56D4×D13—28no—
57#6127—22no—
58#6127—24no—
59#6127—24no—
60#6127D414yescomplemented
61C2×D52—21no—
62C2×D52—22no—
63C2×D52—22no—
64C2×D52—24no—
65C2×D52—24no—
66C2×D52D414yescomplemented
67C2×D52C2312yes—
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—22no—
71C2×Dic26C2311yescharacteristic
72C13×C4⋊C4C2312yes—
73C13×C22⋊C4—21no—
74C13×C22⋊C4—24no—
75C42×C13—21no—
76#6105—24no—
77#6104—28no—
78#6104—24no—
79#6099—22no—
80C2×#1055—22no—
81C2×#1055C2312yes—
82C2×#1055C2312yes—
83#3008—131nomaximal, Sylow
84C23×C13—22no—
85C23×C13—42no—
86C23×C13—82no—
87C23×C13C2×D412yes—
88C23×C13C2×D411yescharacteristic
89C22×D13—21no—
90C22×D13—22no—
91C22×D13—28no—
92C22×D13—24no—
93C22×D13—82no—
94C22×D13—84no—
95Q8×C13—22no—
96D4×C13—24no—
97D4×C13—22no—
98D4×C13—22no—
99D4×C13—22no—
100D4×C13—42no—
101D4×C13—84no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13C2×D412yes—
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2×D412yes—
108C2×C4×C13C2×D412yes—
109C2×C4×C13C2411yescharacteristic
110C22⋊D13—28no—
111C22⋊D13—24no—
112C2×Dic13—21no—
113D52—28no—
114D52—24no—
115D52—21no—
116D52—22no—
117D52C2×D412yes—
118D52C2×D414yes—
119C4×D13—28no—
120C4×D13—24no—
121Dic26—21no—
122Dic26C2×D412yes—
123#1055—22no—
124#1055—22no—
125C2×H(5,𝔽2)—131no—
126C2×AGL(1,ℤ/8)—131no—
127C22×D8—131no—
128#535D1311yescharacteristic, complemented
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—42no—
138C22×C13—44no—
139C22×C13—84no—
140C22×C13#12012yes—
141C22×C13C22×D411yescharacteristic
142C2×D13—24no—
143C2×D13—22no—
144C2×D13—44no—
145C2×D13—42no—
146C2×D13—84no—
147C2×D13—88no—
148C4×C13—22no—
149C4×C13—42no—
150C4×C13#12012yes—
151C4×C13C22×D411yescharacteristic
152C4×C13C22×D411yescharacteristic
153Dic13—22no—
154H(5,𝔽2)—264no—
155H(5,𝔽2)—264no—
156C2×#41—131no—
157C2×#41—132no—
158C2×#41—261no—
159C2×#41C2×D1311yescharacteristic
160C22×D4—131no—
161C22×D4—132no—
162C22×D4—262no—
163C22×D4—261no—
164C22×D4C2×D1311yescharacteristic, complemented
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—21no—
173#124—21no—
174#121C2×D1314yescomplemented
175#120—22no—
176#117C2×D1311yescharacteristic, complemented
177#103—132no—
178#102—132no—
179#102—134no—
180C22⋊C8—134no—
181C2×C13—22no—
182C2×C13—42no—
183C2×C13—82no—
184C2×C13C2×#12011yescharacteristic
185C2×C13#57612yes—
186D13—44no—
187D13—42no—
188C24—21no—
189C24—262no—
190C24—261no—
191#41—22no—
192#41—22no—
193#41—134no—
194#41—264no—
195#41—264no—
196#41—268no—
197#41—262no—
198C2×Q8—131no—
199C2×Q8C22⋊D1311yescharacteristic
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—134no—
205C2×D4—132no—
206C2×D4—131no—
207C2×D4—264no—
208C2×D4—264no—
209C2×D4—2616no—
210C2×D4—268no—
211C2×D4—262no—
212C2×D4—261no—
213C2×D4—262no—
214C2×D4—262no—
215C2×D4—261no—
216C2×D4C22⋊D1312yes—
217C2×D4C22⋊D1311yescharacteristic
218C2×D4C22×D1312yes—
219C22×C4—262no—
220C22×C4—261no—
221C22×C4C22×D1312yes—
222C22×C4C22×D1311yescharacteristic
223SD16—264no—
224D8—268no—
225D8—264no—
226M16—262no—
227C2×C8—132no—
228C2×C8—132no—
229C2×C8—262no—
230C4⋊C4C22×D1312yes—
231C22⋊C4—21no—
232C22⋊C4—24no—
233C42—21no—
234C13#300811yescharacteristic, complemented, Sylow
235C23—22no—
236C23—42no—
237C23—82no—
238C23—268no—
239C23—262no—
240C23—261no—
241C23—264no—
242C23—1042no—
243C23—1044no—
244C23C2×C22⋊D1312yes—
245C23C2×C22⋊D1311yescharacteristic
246Q8—22no—
247Q8—132no—
248Q8—261no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—84no—
255D4—134no—
256D4—132no—
257D4—268no—
258D4—268no—
259D4—264no—
260D4—264no—
261D4—261no—
262D4—262no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—268no—
267C2×C4—261no—
268C2×C4—264no—
269C2×C4D4×D1312yes—
270C2×C4D4×D1312yes—
271C2×C4C2×C22⋊D1312yes—
272C2×C4C2×C22⋊D1311yescharacteristic
273C2×C4C23×D1311yescharacteristic
274C8—262no—
275C8—262no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—264no—
283C22—262no—
284C22—524no—
285C22—522no—
286C22—1044no—
287C22—1048no—
288C22#8819112yes—
289C22C22×C22⋊D1311yescharacteristic
290C4—22no—
291C4—42no—
292C4—262no—
293C4#8819112yes—
294C4C2×D4×D1311yescharacteristic
295C4C2×D4×D1311yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—524no—
300C2—522no—
301C2C2×#8819111yescharacteristic
302C2#1171954012yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#535C2
socleC22×C13C22×D4
hypercenter#535D13
hypocenterC13#3008
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#88256C2semidirect
2. C13×#535C2semidirect
3. C2×#88186C2semidirect
4. C22×#6104C2semidirect
5. #11718895C2semidirect
6. #11718698C2semidirect
7. #11718697C2semidirect
8. #11718663C2semidirect
9. #11718662C2semidirect
11. C22×D4×C13C22semidirect
18. C2×#6127C22semidirect
20. C22×D52C22semidirect
23. C13×#121C22semidirect
25. C13×#117C22semidirect
26. C2×#6105C22semidirect
29. C2×#6104C22semidirect
30. C2×#6104C22semidirect
31. C2×#6099C22semidirect
32. C22×#1055C22semidirect
33. C22⋊#1055C22semidirect
34. #88050C22semidirect
35. #88049C22semidirect
36. #88049C22semidirect
60. #6127D4semidirect
66. C2×D52D4semidirect
128. #535D13semidirect
164. C22×D4C2×D13semidirect
174. #121C2×D13semidirect
176. #117C2×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×#882562
C13×#5352
C2×#881862
C22×#61042
#117188952
#117186982
#117186972
#117186632
#117186622
#300813