Finite Group Databasebeta

← #13126798

Subgroups — #13126798

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
1#11719534C211yesmaximal, characteristic, complemented
2#11719212C211yesmaximal, characteristic, complemented
3C13×#417C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718796C211yesmaximal, characteristic, complemented
6#11718788C211yesmaximal, characteristic, complemented
7#11718629C211yesmaximal, characteristic, complemented
8#11718480C211yesmaximal, characteristic, complemented
9#11718468C211yesmaximal, characteristic, complemented
10#11718466C211yesmaximal, characteristic, complemented
11#11718456C211yesmaximal, characteristic, complemented
12#11718446C211yesmaximal, characteristic, complemented
13#11718434C211yesmaximal, characteristic, complemented
14D13×#102C211yesmaximal, characteristic, complemented
15#11718422C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×#6127—21no—
19C2×C13×M16C2211yescharacteristic, complemented
20C2×C13×C4⋊C4C2211yescharacteristic, complemented
21#88201C2211yescharacteristic
22#88200C2211yescharacteristic
23C2×#6106C2211yescharacteristic, complemented
24#88193—21no—
25#88191—21no—
26D4×Dic13C2211yescharacteristic
27C2×#6104C2211yescharacteristic
28#88184C2211yescharacteristic
29#88184C2211yescharacteristic, complemented
30#88183—21no—
31#88183—21no—
32C4×C22⋊D13C2211yescharacteristic
33C2×#6103—21no—
34C2×D104C2211yescharacteristic
35C2×C8×D13C2211yescharacteristic
36#88150—21no—
37#88149C2211yescharacteristic
38#88148—21no—
39#88147C2211yescharacteristic, complemented
40C4⋊C4×D13C2211yescharacteristic
41#88142C2211yescharacteristic, complemented
42C13×#103C2211yescharacteristic, complemented
43C13×#103C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic, complemented
47#88072C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic, complemented
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic, complemented
51#88060C2211yescharacteristic
52#88057C2211yescharacteristic, complemented
53#88055C2211yescharacteristic, complemented
54#88054C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic, complemented
58#88048C2211yescharacteristic, complemented
59C23×D13—21no—
60C13×#41—22no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13D411yescharacteristic
72C22×Dic13—21no—
73D4×D13—22no—
74D4×D13—41no—
75#6127—44no—
76C2×D52—21no—
77C2×D52C2311yescharacteristic
78C2×D52C2311yescharacteristic
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13C2311yescharacteristic
82C2×Dic26—21no—
83C13×M16—41no—
84C2×C8×C13C2311yescharacteristic
85C2×C8×C13C2311yescharacteristic
86C13×C4⋊C4—21no—
87C13×C4⋊C4C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C22⋊Dic13—21no—
90C22⋊Dic13D411yescharacteristic
91#6106—41no—
92#6104—22no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100#6103D411yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101D411yescharacteristic
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110D104—41no—
111C8×D13—41no—
112#3306—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—42no—
118C22×D13—42no—
119C22×D13—81no—
120C22×D13C2×D411yescharacteristic
121Q8×C13—21no—
122Q8×C13—21no—
123D4×C13—21no—
124D4×C13—42no—
125D4×C13#4112yescomplemented
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2411yescharacteristic
135C22⋊D13—22no—
136C22⋊D13—42no—
137C22⋊D13—42no—
138C22⋊D13—81no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—81no—
142C2×Dic13C2×D411yescharacteristic
143C2×Dic13C2×D411yescharacteristic
144C2×Dic13C2×D411yescharacteristic
145D52—21no—
146D52—21no—
147D52—21no—
148D52—21no—
149D52—42no—
150C4×D13—21no—
151C4×D13—21no—
152C4×D13—42no—
153C4×D13—42no—
154Dic26—42no—
155C8×C13—21no—
156C8×C13—21no—
157#1055—21no—
158#1055—21no—
159#547—131no—
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#417D1311yescharacteristic, complemented
173C2×#102—131no—
174C22×C13—22no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13C22×D411yescharacteristic
181C2×D13—21no—
182C2×D13—21no—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—41no—
188C2×D13—41no—
189C2×D13—84no—
190C2×D13AGL(1,ℤ/8)12yes—
191C4×C13—21no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13C2×#4111yescharacteristic
196C4×C13H(5,𝔽2)11yescharacteristic
197Dic13—21no—
198Dic13—21no—
199Dic13—21no—
200Dic13—41no—
201Dic13—41no—
202C2×#41—261no—
203C2×#41C2×D1311yescharacteristic
204C22×D4—131no—
205C2×SD16—131no—
206C2×D8—131no—
207C2×D8—131no—
208C2×M16C2×D1311yescharacteristic, complemented
209C22×C8—131no—
210C4⋊Q8—131no—
211#124—131no—
212#123—261no—
213#123—261no—
214#123—261no—
215C22⋊Q8—131no—
216C22⋊Q8—261no—
217#121—131no—
218#121—131no—
219#121—131no—
220#121—261no—
221#120—261no—
222C4×D4—131no—
223C4×D4—131no—
224C4×D4—131no—
225C2×C4⋊C4—131no—
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#103C2×D1311yescharacteristic, complemented
234#103C2×D1311yescharacteristic, complemented
235#102—131no—
236#102—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102C2×D1311yescharacteristic
241#102C2×D1311yescharacteristic
242C22⋊C8—131no—
243C22⋊C8—131no—
244#97—131no—
245C2×C13—42no—
246C2×C13—41no—
247C2×C13#54611yescharacteristic
248C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
249C2×C13#57711yescharacteristic
250D13—22no—
251D13—81no—
252D13—81no—
253C24—261no—
254#41—22no—
255#41—41no—
256#41—524no—
257C2×Q8—261no—
258C2×Q8C22×D1311yescharacteristic
259C2×D4—21no—
260C2×D4—131no—
261C2×D4—131no—
262C2×D4—131no—
263C2×D4—261no—
264C2×D4—261no—
265C2×D4—262no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—521no—
269C2×D4C22×D1311yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—131no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4C22×D1311yescharacteristic
277SD16—521no—
278D8—262no—
279D8—521no—
280M16—41no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8—521no—
284C2×C8C22×D1311yescharacteristic
285C2×C8C22×D1311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—131no—
288C4⋊C4—131no—
289C4⋊C4—131no—
290C4⋊C4—261no—
291C4⋊C4—261no—
292C4⋊C4—261no—
293C4⋊C4C22×D1311yescharacteristic
294C4⋊C4C22×D1311yescharacteristic
295C22⋊C4—131no—
296C22⋊C4—131no—
297C22⋊C4—261no—
298C22⋊C4—261no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4—261no—
304C22⋊C4—261no—
305C42—131no—
306C13#330611yescharacteristic, complemented, Sylow
307C23—21no—
308C23—131no—
309C23—261no—
310C23—261no—
311C23—522no—
312C23—522no—
313C23—1041no—
314C23D4×D1311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—522no—
318D4—21no—
319D4—42no—
320D4—262no—
321D4—261no—
322D4—261no—
323D4—261no—
324D4—261no—
325D4—522no—
326D4—522no—
327D4—522no—
328D4—1041no—
329D4#612712yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—131no—
338C2×C4—131no—
339C2×C4—131no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—1041no—
347C2×C4D4×D1311yescharacteristic
348C2×C4C23×D1311yescharacteristic
349C8—21no—
350C8—21no—
351C8—261no—
352C8—261no—
353C22—21no—
354C22—22no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—132no—
360C22—261no—
361C22—261no—
362C22—521no—
363C22—521no—
364C22—521no—
365C22—521no—
366C22—521no—
367C22—521no—
368C22—1044no—
369C22C2×D4×D1311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—261no—
375C4—261no—
376C4—261no—
377C4—521no—
378C4—521no—
379C4C2×#612711yescharacteristic
380C4#8825111yescharacteristic
381C2—41no—
382C2—42no—
383C2—262no—
384C2—1041no—
385C2—1041no—
386C2#1171919511yescharacteristic
387C2D13×AGL(1,ℤ/8)11yescharacteristic
388C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#417C2
socleC22×C13C22×D4
hypercenter#417D13
hypocenterC13#3306
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #11719534C2semidirect
2. #11719212C2semidirect
3. C13×#417C2semidirect
4. #11718899C2semidirect
5. #11718796C2semidirect
6. #11718788C2semidirect
7. #11718629C2semidirect
8. #11718480C2semidirect
9. #11718468C2semidirect
10. #11718466C2semidirect
11. #11718456C2semidirect
12. #11718446C2semidirect
13. #11718434C2semidirect
14. D13×#102C2semidirect
15. #11718422C2semidirect
19. C2×C13×M16C22semidirect
20. C2×C13×C4⋊C4C22semidirect
23. C2×#6106C22semidirect
29. #88184C22semidirect
39. #88147C22semidirect
41. #88142C22semidirect
42. C13×#103C22semidirect
43. C13×#103C22semidirect
46. #88075C22semidirect
48. C22⋊#1055C22semidirect
50. #88061C22semidirect
52. #88057C22semidirect
53. #88055C22semidirect
54. #88054C22semidirect
57. #88048C22semidirect
58. #88048C22semidirect
125. D4×C13#41semidirect
172. #417D13semidirect
208. C2×M16C2×D13semidirect
226. C2×C4⋊C4C2×D13semidirect
233. #103C2×D13semidirect
234. #103C2×D13semidirect
306. C13#3306semidirect
329. D4#6127semidirect

Maximal subgroups

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

subgroupindex
#117195342
#117192122
C13×#4172
#117188992
#117187962
#117187882
#117186292
#117184802
#117184682
#117184662
#117184562
#117184462
#117184342
D13×#1022
#117184222
#330613