Finite Group Databasebeta

← #13126550

Subgroups — #13126550

Order 1664.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D13C211yesmaximal, characteristic, complemented
2C2×#88158C211yesmaximal, characteristic, complemented
3#11719338C211yesmaximal, characteristic, complemented
4#11719317C211yesmaximal, characteristic, complemented
5C13×#465C211yesmaximal, characteristic, complemented
6#11718829C211yesmaximal, characteristic, complemented
7C8×C22⋊D13C211yesmaximal, characteristic, complemented
8#11718708C211yesmaximal, characteristic, complemented
9#11718698C211yesmaximal, characteristic, complemented
10#11718525C211yesmaximal, characteristic, complemented
11#11718513C211yesmaximal, characteristic, complemented
12#11718480C211yesmaximal, characteristic, complemented
13#11718469C211yesmaximal, characteristic, complemented
14#11718434C211yesmaximal, characteristic, complemented
15#11718428C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×#6127C2211yescharacteristic
19C2×#6127C2211yescharacteristic, complemented
20C2×C13×SD16C2211yescharacteristic
21C22×C8×C13C2211yescharacteristic, complemented
22C13×C22⋊Q8C2211yescharacteristic, complemented
23C13×#121C2211yescharacteristic
24#88201C2211yescharacteristic, complemented
25C2×#6107C2211yescharacteristic, complemented
26C2×#6106C2211yescharacteristic
27#88192—21no—
28#88191—21no—
29#88190C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31C2×#6104C2211yescharacteristic
32C4×C22⋊D13C2211yescharacteristic
33SD16×D13—24no—
34C2×Dic52C2211yescharacteristic, complemented
35#88158—24no—
36C2×D104C2211yescharacteristic
37C2×#6095C2211yescharacteristic
38C2×#6095C2211yescharacteristic, complemented
39C2×C8×D13C2211yescharacteristic
40#88151C2211yescharacteristic
41#88150—21no—
42#88149C2211yescharacteristic
43#88147—21no—
44#88147C2211yescharacteristic
45#88141C2211yescharacteristic, complemented
46#88139—21no—
47#88138—21no—
48#88137—21no—
49C22⋊C4×D13—21no—
50C13×#106C2211yescharacteristic, complemented
51C13×#103C2211yescharacteristic, complemented
52C13×#102C2211yescharacteristic
53C22⋊#1055C2211yescharacteristic, complemented
54#88060C2211yescharacteristic
55#88054C2211yescharacteristic, complemented
56C8×Dic13C2211yescharacteristic, complemented
57#88050C2211yescharacteristic, complemented
58#88050C2211yescharacteristic, complemented
59#88049C2211yescharacteristic
60#88049C2211yescharacteristic, complemented
61C23×D13—21no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13D411yescharacteristic
70Q8×D13—22no—
71Q8×D13—41no—
72D4×D13—22no—
73D4×D13—41no—
74#6127—22no—
75#6127—22no—
76#6127—41no—
77#6127—41no—
78C2×D52—21no—
79C2×D52C2311yescharacteristic
80C2×D52C2311yescharacteristic
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C2×C4×D13—21no—
84C2×C4×D13—21no—
85C2×C4×D13C2311yescharacteristic
86C2×Dic26—21no—
87C2×Dic26C2311yescharacteristic
88C2×Dic26C2311yescharacteristic
89C13×SD16—22no—
90C2×C8×C13—22no—
91C2×C8×C13C2311yescharacteristic
92C2×C8×C13C2311yescharacteristic
93C13×C4⋊C4—21no—
94C13×C4⋊C4C2311yescharacteristic
95C13×C4⋊C4C2311yescharacteristic
96C13×C22⋊C4—21no—
97C13×C22⋊C4—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13—21no—
100C22⋊Dic13D411yescharacteristic
101#6107—41no—
102#6106—22no—
103#6105—22no—
104#6104—41no—
105#6103—21no—
106#6103—21no—
107#6103—21no—
108#6103—21no—
109#6103—21no—
110#6103D411yescharacteristic
111C4⋊Dic13—21no—
112#6101—21no—
113#6101D411yescharacteristic
114C4×Dic13—21no—
115C4×Dic13C2311yescharacteristic
116C2×#1055C2311yescharacteristic
117C2×#1055C2311yescharacteristic
118Dic52—22no—
119D104—22no—
120#6095—22no—
121#6095D414yescomplemented
122C8×D13—22no—
123#3282—131nomaximal, Sylow
124C23×C13—21no—
125C23×C13C2×D411yescharacteristic
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—42no—
129C22×D13—42no—
130C22×D13—81no—
131C22×D13C2×D411yescharacteristic
132Q8×C13—21no—
133Q8×C13—21no—
134D4×C13—21no—
135D4×C13—21no—
136D4×C13—81no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13C2×D411yescharacteristic
143C2×C4×C13C2411yescharacteristic
144C22⋊D13—22no—
145C22⋊D13—42no—
146C22⋊D13—42no—
147C22⋊D13—42no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13C2×D411yescharacteristic
151C2×Dic13C2×D411yescharacteristic
152C2×Dic13C2×D411yescharacteristic
153D52—21no—
154D52—21no—
155D52—21no—
156D52—42no—
157D52C2×D412yes—
158C4×D13—21no—
159C4×D13—21no—
160C4×D13—42no—
161C4×D13—42no—
162C4×D13—42no—
163C4×D13—81no—
164Dic26—21no—
165Dic26—21no—
166Dic26—21no—
167Dic26—42no—
168Dic26C2×D412yes—
169C8×C13—21no—
170C8×C13C2×D412yes—
171#1055—21no—
172#1055—21no—
173C2×#135—131no—
174C22×SD16—131no—
175#548—131no—
176#546—131no—
177#495—131no—
178#465—131no—
179#465D1311yescharacteristic, complemented
180#464—131no—
181#463—131no—
182#452—131no—
183#451—131no—
184#449—131no—
185#447—131no—
186C4×SD16—131no—
187C8×D4—131no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13C22×D411yescharacteristic
195C2×D13—21no—
196C2×D13—21no—
197C2×D13—22no—
198C2×D13—41no—
199C2×D13—41no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—84no—
204C2×D13#13512yescomplemented
205C4×C13—21no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—41no—
209C4×C13C22×D411yescharacteristic
210C4×C13H(5,𝔽2)11yescharacteristic
211Dic13—22no—
212Dic13—21no—
213Dic13—21no—
214Dic13—21no—
215Dic13—41no—
216C2×#41—131no—
217C2×#41—131no—
218C22×Q8—131no—
219C22×D4—131no—
220#135—264no—
221C2×Q16—131no—
222C2×Q16—131no—
223C2×SD16—131no—
224C2×SD16—131no—
225C2×SD16—131no—
226C2×SD16—131no—
227C2×SD16—264no—
228C2×SD16C2×D1311yescharacteristic
229C2×D8—131no—
230C2×D8—131no—
231C22×C8—131no—
232C22×C8C2×D1311yescharacteristic, complemented
233#124—131no—
234#124—131no—
235#124—261no—
236#123—261no—
237C22⋊Q8—131no—
238C22⋊Q8—261no—
239C22⋊Q8C2×D1311yescharacteristic, complemented
240#121—131no—
241#121—261no—
242#121—261no—
243#121C2×D1311yescharacteristic
244#120—261no—
245C4×Q8—131no—
246C4×D4—131no—
247C4×D4—131no—
248C4×D4—261no—
249C2×C22⋊C4—261no—
250#106C2×D1311yescharacteristic, complemented
251C4⋊C8—131no—
252#103—131no—
253#103—131no—
254#103C2×D1311yescharacteristic, complemented
255#102—131no—
256#102—131no—
257#102C2×D1311yescharacteristic
258C22⋊C8—131no—
259C22⋊C8—131no—
260C4×C8—131no—
261C2×C13—41no—
262C2×C13—81no—
263C2×C13D4211yescharacteristic
264C2×C13C2×#13511yescharacteristic
265C2×C13#57711yescharacteristic
266D13—22no—
267D13—42no—
268D13—81no—
269C24—261no—
270#41—262no—
271#41—262no—
272#41—521no—
273#41—521no—
274C2×Q8—131no—
275C2×Q8—131no—
276C2×Q8—261no—
277C2×Q8—262no—
278C2×Q8—521no—
279C2×Q8C22×D1311yescharacteristic
280C2×D4—21no—
281C2×D4—131no—
282C2×D4—131no—
283C2×D4—131no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—262no—
287C2×D4—261no—
288C2×D4—261no—
289C2×D4—521no—
290C2×D4C22×D1311yescharacteristic
291C22×C4—131no—
292C22×C4—261no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4C22×D1311yescharacteristic
297Q16—262no—
298Q16—521no—
299SD16—22no—
300SD16—134no—
301SD16—262no—
302SD16—262no—
303SD16—262no—
304D8—262no—
305D8—521no—
306C2×C8—22no—
307C2×C8—131no—
308C2×C8—131no—
309C2×C8—262no—
310C2×C8C22×D1311yescharacteristic
311C2×C8C22×D1311yescharacteristic
312C4⋊C4—21no—
313C4⋊C4—131no—
314C4⋊C4—261no—
315C4⋊C4—261no—
316C4⋊C4C22×D1311yescharacteristic
317C4⋊C4C22×D1311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—131no—
321C22⋊C4—131no—
322C22⋊C4—261no—
323C22⋊C4—261no—
324C22⋊C4—261no—
325C22⋊C4—261no—
326C22⋊C4—261no—
327C22⋊C4—261no—
328C22⋊C4—261no—
329C42—131no—
330C42—261no—
331C13#328211yescharacteristic, complemented, Sylow
332C23—21no—
333C23—131no—
334C23—261no—
335C23—261no—
336C23—522no—
337C23—522no—
338C23—1041no—
339C23D4×D1311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—132no—
343Q8—261no—
344Q8—261no—
345Q8—261no—
346Q8—522no—
347D4—21no—
348D4—21no—
349D4—81no—
350D4—132no—
351D4—262no—
352D4—261no—
353D4—261no—
354D4—261no—
355D4—522no—
356D4—522no—
357D4—522no—
358D4—522no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—131no—
365C2×C4—131no—
366C2×C4—131no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—522no—
372C2×C4—522no—
373C2×C4—522no—
374C2×C4—1041no—
375C2×C4D4×D1311yescharacteristic
376C2×C4C23×D1311yescharacteristic
377C8—21no—
378C8—261no—
379C8—261no—
380C8D4×D1312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—132no—
388C22—261no—
389C22—261no—
390C22—262no—
391C22—521no—
392C22—521no—
393C22—521no—
394C22—521no—
395C22—521no—
396C22—1044no—
397C22C2×D4×D1311yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—261no—
403C4—261no—
404C4—261no—
405C4—262no—
406C4—521no—
407C4C2×D4×D1311yescharacteristic
408C4#8825611yescharacteristic
409C2—41no—
410C2—81no—
411C2—262no—
412C2—522no—
413C2—1041no—
414C2#1171931411yescharacteristic
415C2#1171946711yescharacteristic
416C2D13×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
hypercenter#465D13
hypocenterC13#3282
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D13C2semidirect
2. C2×#88158C2semidirect
3. #11719338C2semidirect
4. #11719317C2semidirect
5. C13×#465C2semidirect
6. #11718829C2semidirect
7. C8×C22⋊D13C2semidirect
8. #11718708C2semidirect
9. #11718698C2semidirect
10. #11718525C2semidirect
11. #11718513C2semidirect
12. #11718480C2semidirect
13. #11718469C2semidirect
14. #11718434C2semidirect
15. #11718428C2semidirect
19. C2×#6127C22semidirect
21. C22×C8×C13C22semidirect
22. C13×C22⋊Q8C22semidirect
24. #88201C22semidirect
25. C2×#6107C22semidirect
34. C2×Dic52C22semidirect
38. C2×#6095C22semidirect
45. #88141C22semidirect
50. C13×#106C22semidirect
51. C13×#103C22semidirect
53. C22⋊#1055C22semidirect
55. #88054C22semidirect
56. C8×Dic13C22semidirect
57. #88050C22semidirect
58. #88050C22semidirect
60. #88049C22semidirect
121. #6095D4semidirect
179. #465D13semidirect
204. C2×D13#135semidirect
232. C22×C8C2×D13semidirect
239. C22⋊Q8C2×D13semidirect
250. #106C2×D13semidirect
254. #103C2×D13semidirect
331. C13#3282semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D132
C2×#881582
#117193382
#117193172
C13×#4652
#117188292
C8×C22⋊D132
#117187082
#117186982
#117185252
#117185132
#117184802
#117184692
#117184342
#117184282
#328213