Finite Group Databasebeta

← #13124107

Subgroups — #13124107

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
2C2×#88203C211yesmaximal, characteristic, complemented
3C22×D104C211yesmaximal, characteristic, complemented
4#11719230C211yesmaximal, characteristic, complemented
5C13×#416C211yesmaximal, characteristic, complemented
6#11718771C211yesmaximal, characteristic, complemented
7#11718662C211yesmaximal, characteristic, complemented
8#11718472C214yesmaximal, complemented
9#11718434C214yesmaximal, complemented
10C2×C13×#41C2211yescharacteristic
11#88256—24no—
12#88256—24no—
13C2×#6131C2212yescomplemented
14C2×D4×D13—22no—
15C2×D4×D13C2212yescomplemented
16C2×#6127—21no—
17C2×#6127C2211yescharacteristic
18C22×D52—21no—
19C22×D52C2211yescharacteristic
20C22×D52C2211yescharacteristic, complemented
21C22×C8×C13C2211yescharacteristic, complemented
22C13×#117C2211yescharacteristic, complemented
23#88203—24no—
24C2×#6106C2212yescomplemented
25C2×#6104C2212yescomplemented
26C2×#6099C2211yescharacteristic, complemented
27C2×D104—24no—
28C2×D104C2214yescomplemented
29#88149C2214yescomplemented
30#88136—22no—
31#88129—21no—
32#88128—21no—
33C13×#103C2212yescomplemented
34C13×#102C2212yescomplemented
35#88060C2214yescomplemented
36#88049C2214yescomplemented
37C23×D13—21no—
38C23×D13—22no—
39C23×D13—21no—
40C13×#41—22no—
41C13×#41D414yescomplemented
42C2×Q8×C13C2311yescharacteristic
43C2×D4×C13—21no—
44C2×D4×C13C2311yescharacteristic
45C22×C4×C13—21no—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—22no—
48C2×C22⋊D13D412yes—
49#6131—24no—
50#6131—24no—
51D4×D13—216no—
52D4×D13—24no—
53D4×D13—24no—
54#6127—28no—
55#6127—22no—
56#6127—22no—
57C2×D52—28no—
58C2×D52—22no—
59C2×D52—21no—
60C2×D52—22no—
61C2×D52—22no—
62C2×D52—22no—
63C2×D52—21no—
64C2×D52—24no—
65C2×D52D411yescharacteristic
66C2×D52D414yescomplemented
67C2×D52C2312yes—
68C2×D52C2312yes—
69C2×C4×D13—22no—
70C2×C4×D13C2312yes—
71C2×Dic26D411yescharacteristic
72C2×C8×C13—22no—
73C2×C8×C13C2312yes—
74C13×C4⋊C4C2312yes—
75C13×C22⋊C4—21no—
76C42×C13—21no—
77#6106—24no—
78#6104—24no—
79#6103—24no—
80#6099—22no—
81C2×#1055C2312yes—
82D104—28no—
83#3008—131nomaximal, Sylow
84C23×C13—21no—
85C23×C13C2×D411yescharacteristic
86C22×D13—22no—
87C22×D13—28no—
88C22×D13—24no—
89C22×D13—22no—
90C22×D13—42no—
91C22×D13—84no—
92C22×D13—82no—
93C22×D13—82no—
94C22×D13C2×D412yes—
95Q8×C13—21no—
96Q8×C13C2×D412yes—
97D4×C13—24no—
98D4×C13—21no—
99D4×C13C2×D412yes—
100C2×C4×C13—21no—
101C2×C4×C13—24no—
102C2×C4×C13—22no—
103C2×C4×C13C2×D411yescharacteristic
104C2×C4×C13C2×D412yes—
105C2×C4×C13C2×D412yes—
106C2×C4×C13C2411yescharacteristic
107C22⋊D13—28no—
108C22⋊D13—24no—
109C2×Dic13C2×D412yes—
110D52—28no—
111D52—22no—
112D52—24no—
113D52—22no—
114D52—22no—
115D52—22no—
116D52—42no—
117D52—84no—
118D52C2×D414yes—
119C4×D13—28no—
120C4×D13—22no—
121C4×D13—22no—
122Dic26—22no—
123C8×C13—22no—
124#1055—22no—
125C2×H(5,𝔽2)—131no—
126C2×AGL(1,ℤ/8)—131no—
127C22×D8—131no—
128#535—131no—
129#449—134no—
130#447—134no—
131#418—131no—
132#416D1311yescharacteristic, complemented
133#408—131no—
134C22×C13—22no—
135C22×C13—22no—
136C22×C13—42no—
137C22×C13#12012yes—
138C22×C13C22×D411yescharacteristic
139C2×D13—22no—
140C2×D13—24no—
141C2×D13—24no—
142C2×D13—44no—
143C2×D13—42no—
144C2×D13—44no—
145C2×D13—84no—
146C2×D13—88no—
147C2×D13—84no—
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—132no—
161C22×D4—131no—
162C22×D4—131no—
163C22×D4—261no—
164C22×D4—262no—
165AGL(1,ℤ/8)—264no—
166C2×SD16—132no—
167C2×D8—132no—
168C2×D8—134no—
169C2×D8—264no—
170C2×M16—131no—
171C22×C8C2×D1311yescharacteristic, complemented
172#127—261no—
173#124—261no—
174#121—134no—
175#120—262no—
176#117C2×D1311yescharacteristic, complemented
177#103C2×D1312yescomplemented
178#102—134no—
179#102C2×D1312yescomplemented
180C22⋊C8—134no—
181C2×C13—22no—
182C2×C13—42no—
183C2×C13C2×#12011yescharacteristic
184C2×C13#57612yes—
185D13—42no—
186D13—44no—
187D13—82no—
188C24—262no—
189C24—261no—
190C24—261no—
191#41—22no—
192#41—268no—
193#41—264no—
194#41—264no—
195#41—262no—
196#41—262no—
197#41D5214yescomplemented
198C2×Q8—131no—
199C2×Q8C22×D1311yescharacteristic
200C2×D4—21no—
201C2×D4—132no—
202C2×D4—134no—
203C2×D4—131no—
204C2×D4—132no—
205C2×D4—132no—
206C2×D4—262no—
207C2×D4—268no—
208C2×D4—264no—
209C2×D4—262no—
210C2×D4—264no—
211C2×D4—2616no—
212C2×D4—264no—
213C2×D4—262no—
214C2×D4—262no—
215C2×D4—261no—
216C2×D4—262no—
217C2×D4—261no—
218C2×D4C22×D1311yescharacteristic
219C22×C4—21no—
220C22×C4—132no—
221C22×C4—262no—
222C22×C4C22×D1311yescharacteristic
223SD16—264no—
224D8—268no—
225D8—264no—
226M16—262no—
227C2×C8—22no—
228C2×C8—132no—
229C2×C8C22×D1312yes—
230C4⋊C4C22×D1312yes—
231C22⋊C4—21no—
232C22⋊C4—264no—
233C42—21no—
234C13#300811yescharacteristic, complemented, Sylow
235C23—21no—
236C23—132no—
237C23—268no—
238C23—262no—
239C23—264no—
240C23—262no—
241C23—522no—
242C23—1042no—
243C23—1042no—
244C23—1044no—
245C23D4×D1311yescharacteristic
246Q8—21no—
247Q8—262no—
248Q8C2×D5212yes—
249D4—24no—
250D4—21no—
251D4—134no—
252D4—268no—
253D4—268no—
254D4—264no—
255D4—264no—
256D4—262no—
257D4—262no—
258D4—262no—
259D4—262no—
260D4—522no—
261D4—1044no—
262D4C2×D5212yes—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—132no—
267C2×C4—268no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4C2×D5212yes—
271C2×C4D4×D1311yescharacteristic
272C2×C4D4×D1312yes—
273C2×C4C23×D1311yescharacteristic
274C8—22no—
275C8—262no—
276C22—22no—
277C22—22no—
278C22—42no—
279C22—264no—
280C22—262no—
281C22—264no—
282C22—524no—
283C22—522no—
284C22—524no—
285C22—1044no—
286C22—1044no—
287C22—1048no—
288C22#8813612yes—
289C22C2×D4×D1311yescharacteristic
290C4—22no—
291C4—42no—
292C4—262no—
293C4#8813612yes—
294C4C22×D5211yescharacteristic
295C4C2×D4×D1311yescharacteristic
296C2—22no—
297C2—42no—
298C2—522no—
299C2—524no—
300C2—1042no—
301C2C2×#8813611yescharacteristic
302C2#1171947412yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#416C2
socleC22×C13C22×D4
hypercenter#416D13
hypocenterC13#3008
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#88256C2semidirect
2. C2×#88203C2semidirect
3. C22×D104C2semidirect
4. #11719230C2semidirect
5. C13×#416C2semidirect
6. #11718771C2semidirect
7. #11718662C2semidirect
8. #11718472C2semidirect
9. #11718434C2semidirect
13. C2×#6131C22semidirect
15. C2×D4×D13C22semidirect
20. C22×D52C22semidirect
21. C22×C8×C13C22semidirect
22. C13×#117C22semidirect
24. C2×#6106C22semidirect
25. C2×#6104C22semidirect
26. C2×#6099C22semidirect
28. C2×D104C22semidirect
29. #88149C22semidirect
33. C13×#103C22semidirect
34. C13×#102C22semidirect
35. #88060C22semidirect
36. #88049C22semidirect
41. C13×#41D4semidirect
66. C2×D52D4semidirect
132. #416D13semidirect
171. C22×C8C2×D13semidirect
176. #117C2×D13semidirect
177. #103C2×D13semidirect
179. #102C2×D13semidirect
197. #41D52semidirect
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
C2×#882032
C22×D1042
#117192302
C13×#4162
#117187712
#117186622
#117184722
#117184342
#300813