Finite Group Databasebeta

← #13126791

Subgroups — #13126791

Order 1664.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#547C211yesmaximal, characteristic, complemented
2#11719255C211yesmaximal, characteristic, complemented
3#11718750C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718702C211yesmaximal, characteristic, complemented
6#11718700C211yesmaximal, characteristic, complemented
7#11718698C211yesmaximal, characteristic, complemented
8#11718697C211yesmaximal, characteristic, complemented
9#11718677C211yesmaximal, characteristic, complemented
10#11718675C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic, complemented
12#11718632C211yesmaximal, characteristic, complemented
13#11718629C211yesmaximal, characteristic, complemented
14#11718627C211yesmaximal, characteristic, complemented
15C2×#88049C211yesmaximal, characteristic, complemented
16C2×C13×#41—21no—
17C2×#6127C2211yescharacteristic
18C22×D52C2211yescharacteristic
19C13×C4⋊Q8C2211yescharacteristic, complemented
20C13×#123—21no—
21C13×#123—21no—
22C13×C22⋊Q8—21no—
23C13×#121C2211yescharacteristic
24C13×#121C2211yescharacteristic, complemented
25C4×D4×C13C2211yescharacteristic
26C4×D4×C13C2211yescharacteristic, complemented
27C2×C13×C4⋊C4C2211yescharacteristic
28C2×C13×C4⋊C4C2211yescharacteristic, complemented
29#88191—21no—
30C2×#6105C2211yescharacteristic, complemented
31C2×#6104C2211yescharacteristic
32C2×#6104C2211yescharacteristic
33#88184C2211yescharacteristic
34#88178C2211yescharacteristic
35C2×#6099C2211yescharacteristic, complemented
36C22×#1055C2211yescharacteristic
37#88148—21no—
38#88138—21no—
39C22⋊C4×D13—21no—
40#88129C2211yescharacteristic
41C4×D52C2211yescharacteristic
42#88072C2211yescharacteristic, complemented
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic, complemented
45#88050C2211yescharacteristic, complemented
46#88050C2211yescharacteristic, complemented
47#88050C2211yescharacteristic, complemented
48#88049C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic, complemented
55#88048C2211yescharacteristic, complemented
56#88048C2211yescharacteristic, complemented
57C4⋊#1055C2211yescharacteristic, complemented
58#88043C2211yescharacteristic, complemented
59C23×D13—21no—
60C13×#41—44no—
61C2×Q8×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13D411yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73#6127—22no—
74#6127—41no—
75C2×D52—22no—
76C2×D52—21no—
77C2×D52—41no—
78C2×D52C2311yescharacteristic
79C2×D52C2311yescharacteristic
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×Dic26C2311yescharacteristic
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4D411yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C4⋊C4C2311yescharacteristic
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C13×C22⋊C4—21no—
93C13×C22⋊C4D411yescharacteristic
94C13×C22⋊C4D411yescharacteristic
95C42×C13C2311yescharacteristic
96C22⋊Dic13—21no—
97#6105—41no—
98#6104—22no—
99#6104—41no—
100#6103—21no—
101#6103—21no—
102#6103—21no—
103#6103—21no—
104C4⋊Dic13C2311yescharacteristic
105#6101—21no—
106#6099—41no—
107C2×#1055—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112#3306—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C23×C13C2×D411yescharacteristic
116C22×D13—21no—
117C22×D13—21no—
118C22×D13—42no—
119C22×D13—42no—
120C22×D13—81no—
121Q8×C13—42no—
122D4×C13—22no—
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—42no—
126D4×C13—42no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2411yescharacteristic
142C22⋊D13—42no—
143C22⋊D13—81no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146D52—21no—
147D52—21no—
148D52—21no—
149D52—42no—
150D52#4112yescomplemented
151C4×D13—42no—
152C4×D13—81no—
153Dic26—21no—
154Dic26—21no—
155#1055—21no—
156#1055—21no—
157#1055—21no—
158#1055—21no—
159#547D1311yescharacteristic, complemented
160#546—131no—
161#489—131no—
162#483—131no—
163#481—131no—
164#476—131no—
165#469—131no—
166#465—131no—
167#463—131no—
168#449—131no—
169#447—131no—
170#442—131no—
171#435—131no—
172#417—131no—
173C2×#102—131no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13AGL(1,ℤ/8)12yes—
183C22×C13C22×D411yescharacteristic
184C2×D13—22no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—84no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13C2×#4111yescharacteristic
199C4×C13H(5,𝔽2)11yescharacteristic
200Dic13—41no—
201Dic13—41no—
202C2×#41—21no—
203C2×#41—131no—
204C22×D4—131no—
205C2×SD16—131no—
206C2×D8—131no—
207C2×D8—131no—
208C2×M16—131no—
209C22×C8—131no—
210C4⋊Q8C2×D1311yescharacteristic, complemented
211#124—131no—
212#123—21no—
213#123—21no—
214#123—261no—
215C22⋊Q8—21no—
216C22⋊Q8—131no—
217#121—131no—
218#121—261no—
219#121C2×D1311yescharacteristic
220#121C2×D1311yescharacteristic, complemented
221#120—261no—
222C4×D4—131no—
223C4×D4C2×D1311yescharacteristic
224C4×D4C2×D1311yescharacteristic, complemented
225C2×C4⋊C4C2×D1311yescharacteristic
226C2×C4⋊C4C2×D1311yescharacteristic, complemented
227C2×C22⋊C4—261no—
228#106—131no—
229#106—131no—
230#106—131no—
231C4⋊C8—131no—
232#103—131no—
233#103—131no—
234#103—131no—
235#102—131no—
236#102—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102—131no—
242C22⋊C8—131no—
243C22⋊C8—131no—
244#97—131no—
245C2×C13—22no—
246C2×C13—41no—
247C2×C13—81no—
248C2×C13#54611yescharacteristic
249C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
250C2×C13#57711yescharacteristic
251D13—42no—
252D13—81no—
253C24—261no—
254#41—44no—
255#41—262no—
256#41—521no—
257C2×Q8—21no—
258C2×Q8—131no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—131no—
262C2×D4—131no—
263C2×D4—262no—
264C2×D4—261no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4—521no—
268C2×D4C22⋊D1311yescharacteristic
269C2×D4C22×D1311yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4C22×D1311yescharacteristic
276C22×C4C22×D1311yescharacteristic
277SD16—521no—
278D8—262no—
279D8—521no—
280M16—521no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8—131no—
284C2×C8—131no—
285C2×C8—521no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—131no—
290C4⋊C4—261no—
291C4⋊C4C22⋊D1311yescharacteristic
292C4⋊C4C22×D1311yescharacteristic
293C4⋊C4C22×D1311yescharacteristic
294C4⋊C4C22×D1311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—261no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4C22⋊D1311yescharacteristic
304C22⋊C4C22⋊D1311yescharacteristic
305C42C22×D1311yescharacteristic
306C13#330611yescharacteristic, complemented, Sylow
307C23—21no—
308C23—261no—
309C23—261no—
310C23—522no—
311C23—522no—
312C23—1041no—
313C23C2×C22⋊D1311yescharacteristic
314C23C2×C22⋊D1311yescharacteristic
315Q8—42no—
316Q8—261no—
317Q8—261no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—132no—
324D4—261no—
325D4—261no—
326D4—261no—
327D4—522no—
328D4—522no—
329D4—1041no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—522no—
343C2×C4—1041no—
344C2×C4C2×C22⋊D1311yescharacteristic
345C2×C4C2×C22⋊D1311yescharacteristic
346C2×C4C2×C22⋊D1311yescharacteristic
347C2×C4C2×C22⋊D1311yescharacteristic
348C2×C4C23×D1311yescharacteristic
349C8—261no—
350C8—261no—
351C8—261no—
352C8—261no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—262no—
362C22—521no—
363C22—521no—
364C22—521no—
365C22—521no—
366C22—521no—
367C22—1044no—
368C22#8818612yes—
369C22C22×C22⋊D1311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—521no—
378C4—521no—
379C4#41×D1311yescharacteristic
380C4#8825611yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—522no—
385C2—1041no—
386C2C2×#8818611yescharacteristic
387C2#1171953411yescharacteristic
388C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3306
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C13×#547C2semidirect
2. #11719255C2semidirect
3. #11718750C2semidirect
4. #11718745C2semidirect
5. #11718702C2semidirect
6. #11718700C2semidirect
7. #11718698C2semidirect
8. #11718697C2semidirect
9. #11718677C2semidirect
10. #11718675C2semidirect
11. #11718672C2semidirect
12. #11718632C2semidirect
13. #11718629C2semidirect
14. #11718627C2semidirect
15. C2×#88049C2semidirect
19. C13×C4⋊Q8C22semidirect
24. C13×#121C22semidirect
26. C4×D4×C13C22semidirect
28. C2×C13×C4⋊C4C22semidirect
30. C2×#6105C22semidirect
35. C2×#6099C22semidirect
42. #88072C22semidirect
44. C22⋊#1055C22semidirect
45. #88050C22semidirect
46. #88050C22semidirect
47. #88050C22semidirect
54. #88048C22semidirect
55. #88048C22semidirect
56. #88048C22semidirect
57. C4⋊#1055C22semidirect
58. #88043C22semidirect
150. D52#41semidirect
159. #547D13semidirect
210. C4⋊Q8C2×D13semidirect
220. #121C2×D13semidirect
224. C4×D4C2×D13semidirect
226. C2×C4⋊C4C2×D13semidirect
306. C13#3306semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
#117192552
#117187502
#117187452
#117187022
#117187002
#117186982
#117186972
#117186772
#117186752
#117186722
#117186322
#117186292
#117186272
C2×#880492
#330613