Finite Group Databasebeta

← #13126790

Subgroups — #13126790

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#11719316C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic, complemented
4#11718893C211yesmaximal, characteristic, complemented
5#11718832C211yesmaximal, characteristic, complemented
6#11718826C211yesmaximal, characteristic, complemented
7#11718817C211yesmaximal, characteristic, complemented
8#11718813C211yesmaximal, characteristic, complemented
9#11718700C211yesmaximal, characteristic, complemented
10#11718466C211yesmaximal, characteristic, complemented
11#11718456C211yesmaximal, characteristic, complemented
12D13×#102C211yesmaximal, characteristic, complemented
13#11718422C211yesmaximal, characteristic, complemented
14#11718396C211yesmaximal, characteristic, complemented
15#11718389C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6129—21no—
18C2×D4×D13C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic, complemented
20C2×C13×D8C2211yescharacteristic
21C13×#121C2211yescharacteristic, complemented
22#88201C2211yescharacteristic
23#88200C2211yescharacteristic
24#88193—21no—
25#88192C2211yescharacteristic
26#88191—21no—
27#88189—21no—
28D4×Dic13C2211yescharacteristic
29D4×Dic13C2211yescharacteristic, complemented
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88183—21no—
33C4×C22⋊D13C2211yescharacteristic
34C2×#6103—21no—
35C2×C4⋊Dic13C2211yescharacteristic, complemented
36C2×#6099C2211yescharacteristic, complemented
37C2×C8×D13C2211yescharacteristic
38C4⋊C4×D13C2211yescharacteristic
39#88142C2211yescharacteristic, complemented
40#88137—21no—
41#88132—21no—
42C13×#103C2211yescharacteristic, complemented
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic, complemented
45#88075C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic, complemented
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88060C2211yescharacteristic
53#88057C2211yescharacteristic, complemented
54#88057C2211yescharacteristic, complemented
55#88055C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88049C2211yescharacteristic
58#88048C2211yescharacteristic, complemented
59C23×D13—21no—
60C13×#41—22no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13C2311yescharacteristic
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76#6129—44no—
77D4×D13—22no—
78D4×D13—41no—
79C2×D52C2311yescharacteristic
80C2×C4×D13—21no—
81C2×C4×D13C2311yescharacteristic
82C2×Dic26—21no—
83C13×SD16—41no—
84C13×D8—22no—
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C22⋊C4—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13D411yescharacteristic
93#6104—41no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103D411yescharacteristic
99C4⋊Dic13—21no—
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101D411yescharacteristic
107C4×Dic13C2311yescharacteristic
108#6099—41no—
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C8×D13—41no—
112#3306—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13—21no—
115C23×C13C2×D411yescharacteristic
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—21no—
125D4×C13—21no—
126D4×C13—42no—
127D4×C13—42no—
128D4×C13#4112yescomplemented
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—42no—
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2411yescharacteristic
136C22⋊D13—22no—
137C22⋊D13—42no—
138C22⋊D13—42no—
139C22⋊D13—81no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—81no—
146C2×Dic13C2×D411yescharacteristic
147C2×Dic13C2×D411yescharacteristic
148C2×Dic13C2×D411yescharacteristic
149D52—21no—
150D52—21no—
151C4×D13—21no—
152C4×D13—21no—
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#449D1311yescharacteristic, complemented
169#447—131no—
170#442—131no—
171#435—131no—
172#417—131no—
173C2×#102—131no—
174C22×C13—22no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13C22×D411yescharacteristic
184C2×D13—21no—
185C2×D13—21no—
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×C13C2×#4111yescharacteristic
195C4×C13H(5,𝔽2)11yescharacteristic
196Dic13—21no—
197Dic13—21no—
198Dic13—21no—
199Dic13—41no—
200Dic13—41no—
201Dic13—41no—
202C2×#41—261no—
203C2×#41C2×D1311yescharacteristic
204C22×D4—131no—
205C2×SD16C2×D1311yescharacteristic, complemented
206C2×D8—131no—
207C2×D8C2×D1311yescharacteristic
208C2×M16—131no—
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—261no—
220#121C2×D1311yescharacteristic, complemented
221#120—261no—
222C4×D4—131no—
223C4×D4—131no—
224C4×D4—131no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C22⋊C4—261no—
228#106—131no—
229#106—131no—
230#106—131no—
231C4⋊C8—131no—
232#103—131no—
233#103—131no—
234#103C2×D1311yescharacteristic, complemented
235#102—131no—
236#102—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102C2×D1311yescharacteristic
242C22⋊C8—131no—
243C22⋊C8C2×D1311yescharacteristic, complemented
244#97—131no—
245C2×C13—42no—
246C2×C13—41no—
247C2×C13—81no—
248C2×C13#54611yescharacteristic
249C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
250C2×C13#57711yescharacteristic
251D13—22no—
252D13—81no—
253C24—261no—
254#41—22no—
255#41—41no—
256#41—524no—
257C2×Q8—261no—
258C2×Q8C22×D1311yescharacteristic
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—131no—
262C2×D4—131no—
263C2×D4—261no—
264C2×D4—262no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4—521no—
268C2×D4C22×D1311yescharacteristic
269C2×D4C22×D1311yescharacteristic
270C22×C4—21no—
271C22×C4—131no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4C22×D1311yescharacteristic
277SD16—41no—
278D8—22no—
279D8—521no—
280M16—521no—
281C2×C8—131no—
282C2×C8—131no—
283C2×C8—521no—
284C2×C8C22×D1311yescharacteristic
285C2×C8C22×D1311yescharacteristic
286C4⋊C4—131no—
287C4⋊C4—131no—
288C4⋊C4—131no—
289C4⋊C4—131no—
290C4⋊C4—261no—
291C4⋊C4—261no—
292C4⋊C4—261no—
293C4⋊C4—261no—
294C4⋊C4C22×D1311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—131no—
297C22⋊C4—131no—
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—21no—
309C23—131no—
310C23—261no—
311C23—522no—
312C23—522no—
313C23—1041no—
314C23D4×D1311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—522no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—262no—
324D4—261no—
325D4—261no—
326D4—522no—
327D4—522no—
328D4—1041no—
329D4#612912yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—131no—
336C2×C4—131no—
337C2×C4—131no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—522no—
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—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—132no—
363C22—261no—
364C22—261no—
365C22—521no—
366C22—521no—
367C22—521no—
368C22—1044no—
369C22C2×D4×D1311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—261no—
374C4—261no—
375C4—261no—
376C4—521no—
377C4—521no—
378C4—521no—
379C4C2×#612911yescharacteristic
380C4#8825111yescharacteristic
381C2—41no—
382C2—42no—
383C2—81no—
384C2—262no—
385C2—1041no—
386C2#1171929611yescharacteristic
387C2#1171947511yescharacteristic
388C2D13×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3306
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11719534C2semidirect
2. #11719316C2semidirect
3. C13×#449C2semidirect
4. #11718893C2semidirect
5. #11718832C2semidirect
6. #11718826C2semidirect
7. #11718817C2semidirect
8. #11718813C2semidirect
9. #11718700C2semidirect
10. #11718466C2semidirect
11. #11718456C2semidirect
12. D13×#102C2semidirect
13. #11718422C2semidirect
14. #11718396C2semidirect
15. #11718389C2semidirect
19. C2×C13×SD16C22semidirect
21. C13×#121C22semidirect
29. D4×Dic13C22semidirect
35. C2×C4⋊Dic13C22semidirect
36. C2×#6099C22semidirect
39. #88142C22semidirect
42. C13×#103C22semidirect
44. C13×C22⋊C8C22semidirect
45. #88075C22semidirect
46. #88075C22semidirect
49. #88072C22semidirect
53. #88057C22semidirect
54. #88057C22semidirect
55. #88055C22semidirect
56. #88054C22semidirect
58. #88048C22semidirect
128. D4×C13#41semidirect
168. #449D13semidirect
205. C2×SD16C2×D13semidirect
220. #121C2×D13semidirect
234. #103C2×D13semidirect
243. C22⋊C8C2×D13semidirect
306. C13#3306semidirect
329. D4#6129semidirect

Maximal subgroups

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

subgroupindex
#117195342
#117193162
C13×#4492
#117188932
#117188322
#117188262
#117188172
#117188132
#117187002
#117184662
#117184562
D13×#1022
#117184222
#117183962
#117183892
#330613