Finite Group Databasebeta

← #13125646

Subgroups — #13125646

Order 1664.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C13×#525C211yesmaximal, characteristic, complemented
2C2×#88184C211yesmaximal, characteristic, complemented
3#11718899C212yesmaximal, complemented
4#11718868C211yesmaximal, characteristic, complemented
5#11718710C212yesmaximal, complemented
6#11718707C211yesmaximal, characteristic, complemented
7#11718704C211yesmaximal, characteristic, complemented
8#11718700C212yesmaximal, complemented
9#11718697C211yesmaximal, characteristic, complemented
10#11718694C211yesmaximal, characteristic, complemented
11#11718664C212yesmaximal, complemented
12C2×C13×#41C2211yescharacteristic, complemented
13C23×C4×C13C2211yescharacteristic
14C22×C22⋊D13—21no—
15C22×D52C2211yescharacteristic
16C13×#123—21no—
17C13×C22⋊Q8C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic, complemented
19C13×#121C2211yescharacteristic
20C13×#121C2211yescharacteristic, complemented
21C13×#120—21no—
22C4×D4×C13—21no—
23C4×D4×C13—21no—
24C13×#117C2211yescharacteristic, complemented
25C2×#6106C2212yescomplemented
26C2×#6104C2212yescomplemented
27#88184—21no—
28#88184—21no—
29#88184C2212yes—
30#88184C2212yes—
31C2×#6103—21no—
32C2×C4⋊Dic13C2211yescharacteristic
33C2×#6099C2212yescomplemented
34#88075C2212yescomplemented
35#88072C2212yescomplemented
36C22⋊#1055C2211yescharacteristic
37C22⋊#1055C2211yescharacteristic
38C22⋊#1055C2212yescomplemented
39#88049C2212yescomplemented
40#88049C2212yescomplemented
41#88048C2212yescomplemented
42#88047C2212yescomplemented
43C24×C13D411yescharacteristic
44C23×D13—21no—
45C13×#41—42no—
46C2×Q8×C13C2311yescharacteristic
47C2×D4×C13—21no—
48C2×D4×C13—21no—
49C2×D4×C13—21no—
50C2×D4×C13C2311yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—42no—
53C22×C4×C13D411yescharacteristic
54C22×C4×C13D411yescharacteristic
55C22×C4×C13D411yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C2×C22⋊D13—22no—
60C2×C22⋊D13—22no—
61C2×C22⋊D13—44no—
62C22×Dic13—21no—
63C2×D52—21no—
64C2×D52—42no—
65C2×D52C2312yes—
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4C2311yescharacteristic
69C13×C4⋊C4C2311yescharacteristic
70C13×C22⋊C4—21no—
71C13×C22⋊C4—21no—
72C13×C22⋊C4—21no—
73C13×C22⋊C4—21no—
74C13×C22⋊C4—21no—
75C42×C13—21no—
76#6106—42no—
77#6104—42no—
78#6103—22no—
79#6103—22no—
80C4⋊Dic13—21no—
81C4⋊Dic13C2312yes—
82#6099—42no—
83C2×#1055C2312yes—
84C2×#1055C2312yes—
85#3194—131nomaximal, Sylow
86C23×C13—22no—
87C23×C13—21no—
88C23×C13—41no—
89C23×C13—41no—
90C23×C13C2×D411yescharacteristic
91C23×C13C2×D411yescharacteristic
92C23×C13C2×D411yescharacteristic
93C22×D13—22no—
94C22×D13—42no—
95C22×D13—42no—
96C22×D13—42no—
97Q8×C13—22no—
98D4×C13—22no—
99D4×C13—42no—
100D4×C13—42no—
101D4×C13—42no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2411yescharacteristic
116C22⋊D13—44no—
117C22⋊D13—44no—
118C2×Dic13—22no—
119C2×Dic13—42no—
120D52—22no—
121D52—22no—
122D52—42no—
123#1055—22no—
124#1055—22no—
125#525D1311yescharacteristic, complemented
126C2×#121—131no—
127#483—131no—
128#482—132no—
129#480—131no—
130#469—132no—
131#468—132no—
132#450—131no—
133#449—132no—
134#447—131no—
135#407—131no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—44no—
145C22×C13—41no—
146C22×C13—41no—
147C22×C13—41no—
148C22×C13AGL(1,ℤ/8)12yes—
149C22×C13C22×D411yescharacteristic
150C2×D13—42no—
151C2×D13—42no—
152C2×D13—42no—
153C2×D13—84no—
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13H(5,𝔽2)12yes—
161Dic13—42no—
162C2×#41C2×D1311yescharacteristic, complemented
163C22×D4—131no—
164C22×D4—261no—
165C23×C4C2×D1311yescharacteristic
166C2×SD16—132no—
167C2×D8—132no—
168C2×M16—132no—
169#123—21no—
170C22⋊Q8C2×D1311yescharacteristic
171C22⋊Q8C2×D1311yescharacteristic, complemented
172#121—132no—
173#121—132no—
174#121—261no—
175#121—261no—
176#121C2×D1311yescharacteristic
177#121C2×D1311yescharacteristic, complemented
178#120—21no—
179C4×D4—21no—
180C4×D4—21no—
181#117C2×D1311yescharacteristic, complemented
182C2×C4⋊C4—131no—
183C2×C22⋊C4—261no—
184#107—132no—
185#106—132no—
186#103—132no—
187#102—132no—
188#102—132no—
189#102—132no—
190C22⋊C8—131no—
191C22⋊C8—131no—
192C22⋊C8—132no—
193C2×C13—22no—
194C2×C13—41no—
195C2×C13—41no—
196C2×C13—81no—
197C2×C13#53411yescharacteristic
198C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C13#57511yescharacteristic
200D13—82no—
201C24—261no—
202C24C22⋊D1311yescharacteristic
203#41—42no—
204C2×Q8C22×D1311yescharacteristic
205C2×D4—21no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—132no—
209C2×D4—262no—
210C2×D4—262no—
211C2×D4—261no—
212C2×D4—522no—
213C2×D4—524no—
214C2×D4C22×D1311yescharacteristic
215C22×C4—21no—
216C22×C4—42no—
217C22×C4—261no—
218C22×C4C22⋊D1311yescharacteristic
219C22×C4C22⋊D1311yescharacteristic
220C22×C4C22⋊D1311yescharacteristic
221C22×C4C22×D1311yescharacteristic
222C22×C4C22×D1311yescharacteristic
223C22×C4C22×D1311yescharacteristic
224SD16—522no—
225D8—522no—
226M16—522no—
227C2×C8—132no—
228C2×C8—132no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—132no—
232C4⋊C4—261no—
233C4⋊C4C22×D1311yescharacteristic
234C4⋊C4C22×D1311yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—21no—
240C22⋊C4—262no—
241C22⋊C4—262no—
242C42—21no—
243C13#319411yescharacteristic, complemented, Sylow
244C23—22no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23—262no—
249C23—522no—
250C23—522no—
251C23—522no—
252C23C2×C22⋊D1311yescharacteristic
253C23C2×C22⋊D1311yescharacteristic
254C23C2×C22⋊D1311yescharacteristic
255Q8—22no—
256D4—22no—
257D4—42no—
258D4—42no—
259D4—42no—
260D4—262no—
261D4—262no—
262D4—522no—
263D4—524no—
264D4—524no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—262no—
276C2×C4—522no—
277C2×C4C2×C22⋊D1311yescharacteristic
278C2×C4C2×C22⋊D1311yescharacteristic
279C2×C4C2×C22⋊D1311yescharacteristic
280C2×C4C23×D1311yescharacteristic
281C8—262no—
282C8—262no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—522no—
296C22—522no—
297C22—522no—
298C22—1044no—
299C22#8820312yes—
300C22C22×C22⋊D1311yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—522no—
308C4#8825112yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—81no—
313C2—1042no—
314C2#1171950911yescharacteristic
315C2C2×#8820311yescharacteristic
316C2#1171952711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#525C2
socleC22×C13C22×D4
hypercenter#525D13
hypocenterC13#3194
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C13×#525C2semidirect
2. C2×#88184C2semidirect
3. #11718899C2semidirect
4. #11718868C2semidirect
5. #11718710C2semidirect
6. #11718707C2semidirect
7. #11718704C2semidirect
8. #11718700C2semidirect
9. #11718697C2semidirect
10. #11718694C2semidirect
11. #11718664C2semidirect
12. C2×C13×#41C22semidirect
18. C13×C22⋊Q8C22semidirect
20. C13×#121C22semidirect
24. C13×#117C22semidirect
25. C2×#6106C22semidirect
26. C2×#6104C22semidirect
33. C2×#6099C22semidirect
34. #88075C22semidirect
35. #88072C22semidirect
38. C22⋊#1055C22semidirect
39. #88049C22semidirect
40. #88049C22semidirect
41. #88048C22semidirect
42. #88047C22semidirect
125. #525D13semidirect
162. C2×#41C2×D13semidirect
171. C22⋊Q8C2×D13semidirect
177. #121C2×D13semidirect
181. #117C2×D13semidirect
243. C13#3194semidirect

Maximal subgroups

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

subgroupindex
C13×#5252
C2×#881842
#117188992
#117188682
#117187102
#117187072
#117187042
#117187002
#117186972
#117186942
#117186642
#319413