Finite Group Databasebeta

← #16018027

Subgroups — #16018027

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125475C211yesmaximal, characteristic, complemented
2#13117044C211yesmaximal, characteristic, complemented
3#13117027C211yesmaximal, characteristic, complemented
4#13116983C211yesmaximal, characteristic, complemented
5#13116973C211yesmaximal, characteristic, complemented
6#13116891C211yesmaximal, characteristic, complemented
7#13116891C211yesmaximal, characteristic, complemented
8#13116765C211yesmaximal, characteristic, complemented
9#13116748C211yesmaximal, characteristic
10#13116710C211yesmaximal, characteristic, complemented
11#13116700C211yesmaximal, characteristic, complemented
12C4×#88067C211yesmaximal, characteristic, complemented
13C4×#88066C211yesmaximal, characteristic, complemented
14#13116643C211yesmaximal, characteristic, complemented
15C13×#2948C211yesmaximal, characteristic, complemented
16C22×C13×D8C2211yescharacteristic
17C13×#518—21no—
18#11719239—21no—
19C13×#442—21no—
20C13×#442—21no—
21C4×C13×D8C2211yescharacteristic
22C4×C13×D8C2211yescharacteristic
23C4×C13×D8C2211yescharacteristic
24C4×C13×D8C2211yescharacteristic
25C13×#427C2211yescharacteristic
26C13×#418—21no—
27C13×#405C2211yescharacteristic
28C2×#88067C2211yescharacteristic
29C2×#88067C2211yescharacteristic
30C2×#88066C2211yescharacteristic
31C2×#88066C2211yescharacteristic
32#11718795—21no—
33#11718777C2211yescharacteristic
34#11718776C2211yescharacteristic
35#11718375—21no—
36#11718371—21no—
37C4×Dic52C2211yescharacteristic, complemented
38#11718357C2211yescharacteristic, complemented
39C4×D104C2211yescharacteristic, complemented
40#11718343C2211yescharacteristic, complemented
41#11718154C2211yescharacteristic
42#11718154C2211yescharacteristic
43#11718154C2211yescharacteristic
44#11718154C2211yescharacteristic
45C22⋊#6090C2211yescharacteristic
46C22⋊#6090C2211yescharacteristic
47#11718084C2211yescharacteristic, complemented
48#11718084C2211yescharacteristic, complemented
49#11718083C2211yescharacteristic, complemented
50#11718083C2211yescharacteristic, complemented
51#11718082C2211yescharacteristic, complemented
52#11718082C2211yescharacteristic, complemented
53#11718081C2211yescharacteristic, complemented
54#11718081C2211yescharacteristic, complemented
55C4⋊#6090C2211yescharacteristic, complemented
56C4⋊#6090C2211yescharacteristic, complemented
57#11718053C2211yescharacteristic, complemented
58C4×#6090C2211yescharacteristic, complemented
59C22×D4×C13—21no—
60C2×C13×D8—22no—
61C2×C13×D8—22no—
62C2×C13×D8—21no—
63C2×C13×D8C2311yescharacteristic
64C2×C13×D8C2311yescharacteristic
65C2×C13×M16D411yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C4×D4×C13—21no—
68C4×D4×C13—21no—
69C4×D4×C13—21no—
70C4×D4×C13—21no—
71C4×D4×C13—41no—
72C4×D4×C13—41no—
73C13×#117—21no—
74C13×#117D411yescharacteristic
75C2×C13×C22⋊C4—41no—
76C2×C13×C22⋊C4—41no—
77#88184—21no—
78#88178—21no—
79C2×Dic52C2311yescharacteristic
80C2×D104C2311yescharacteristic
81C2×#6095—21no—
82#88152—41no—
83#88150—41no—
84#88139—41no—
85#88137—41no—
86#88129—21no—
87C4×D52—21no—
88#88123—21no—
89C4×Dic26—21no—
90C13×#107C2311yescharacteristic
91C13×#107C2311yescharacteristic
92C13×#106—21no—
93C13×#102—21no—
94C13×#102—21no—
95C13×#102—21no—
96C13×#102—21no—
97C13×#97D411yescharacteristic
98C13×#97D411yescharacteristic
99C4×C8×C13C2311yescharacteristic
100C4×C8×C13C2311yescharacteristic
101#88067—22no—
102#88067—22no—
103#88066—22no—
104#88066—22no—
105#88061—21no—
106#88061—21no—
107#88058—21no—
108#88058C2311yescharacteristic
109#88058C2311yescharacteristic
110#88056—21no—
111#88056—21no—
112C2×#6090C2311yescharacteristic
113C2×#6090C2311yescharacteristic
114C2×#6090C2311yescharacteristic
115C2×#6090C2311yescharacteristic
116#33678—131nomaximal, Sylow
117C24×C13—41no—
118C2×D4×C13—24no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—42no—
122C2×D4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13C2×D411yescharacteristic
128C2×C22⋊D13—41no—
129C2×D52—21no—
130C2×C4×D13—41no—
131C2×Dic26—21no—
132C2×Dic26—41no—
133C13×D8—24no—
134C13×D8—21no—
135C13×D8—21no—
136C13×D8#4112yes—
137C13×D8#4112yes—
138C13×M16—41no—
139C2×C8×C13—21no—
140C2×C8×C13—21no—
141C2×C8×C13C2×D411yescharacteristic
142C2×C8×C13C2×D411yescharacteristic
143C2×C8×C13C2×D411yescharacteristic
144C2×C8×C13C2411yescharacteristic
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4D811yescharacteristic
148C13×C4⋊C4D811yescharacteristic
149C13×C22⋊C4—41no—
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4D811yescharacteristic
155C13×C22⋊C4D811yescharacteristic
156C42×C13—41no—
157C42×C13C2×D411yescharacteristic
158C42×C13C2×D411yescharacteristic
159C22⋊Dic13—41no—
160#6103—41no—
161#6103—41no—
162#6103—41no—
163#6103—41no—
164C4⋊Dic13—21no—
165C4⋊Dic13—21no—
166C4⋊Dic13—41no—
167#6101—41no—
168#6101—41no—
169C4×Dic13—41no—
170Dic52—21no—
171Dic52—21no—
172D104—21no—
173D104—21no—
174#6095—42no—
175#6090—21no—
176#6090—21no—
177#6090—21no—
178#6090—21no—
179#3175—131no—
180#2948D1311yescharacteristic, complemented
181#2237—131no—
182#2234—131no—
183#2226—131no—
184#2224—131no—
185#2210—131no—
186#2210—131no—
187#2187—131no—
188#2184—131no—
189#2177—131no—
190#2175—131no—
191C4×SD32—131no—
192C4×D16—131no—
193#2164—131no—
194C23×C13—44no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13—161no—
198C23×C13—161no—
199C23×C13C2×D811yescharacteristic
200C22×D13—41no—
201D4×C13—22no—
202D4×C13—22no—
203D4×C13—44no—
204D4×C13—41no—
205D4×C13—41no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—161no—
211C2×C4×C13—161no—
212C2×C4×C13—161no—
213C2×C4×C13—161no—
214C2×C4×C13C2×D811yescharacteristic
215C2×C4×C13C2×D811yescharacteristic
216C2×C4×C13C2×D811yescharacteristic
217C2×C4×C13C2×D811yescharacteristic
218C2×C4×C13C2×D811yescharacteristic
219C2×C4×C13C22×D411yescharacteristic
220C22⋊D13—161no—
221C2×Dic13—41no—
222C2×Dic13—41no—
223C2×Dic13—41no—
224D52—41no—
225D52—41no—
226C4×D13—161no—
227Dic26—41no—
228Dic26—41no—
229Dic26—161no—
230C8×C13—21no—
231C8×C13—21no—
232C8×C13—21no—
233C8×C13C2×#4111yescharacteristic
234C8×C13C2×#4111yescharacteristic
235C22×D8C2×D1311yescharacteristic
236#542—261no—
237#518—21no—
238C2×SD32—131no—
239C2×SD32—131no—
240C2×D16—131no—
241C2×D16—131no—
242#500—131no—
243#495—131no—
244#489—261no—
245#468—261no—
246#467—131no—
247#466—131no—
248#442—21no—
249#442—21no—
250#440—261no—
251C4×Q16—131no—
252C4×D8—131no—
253C4×D8C2×D1311yescharacteristic
254C4×D8C2×D1311yescharacteristic
255C4×D8C2×D1311yescharacteristic
256C4×D8C2×D1311yescharacteristic
257#427C2×D1311yescharacteristic
258#418—21no—
259#405C2×D1311yescharacteristic
260#367—131no—
261#367—131no—
262#366—131no—
263#366—131no—
264C4⋊C16—131no—
265C4⋊C16—131no—
266#358—131no—
267#358—131no—
268#357—131no—
269#357—131no—
270#357—131no—
271#357—131no—
272#357—131no—
273#357—131no—
274C22⋊C16—131no—
275C22⋊C16—131no—
276#346—131no—
277C4×C16—131no—
278C22×C13—21no—
279C22×C13—21no—
280C22×C13—21no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—81no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13—164no—
288C22×C13C22×D811yescharacteristic
289C2×D13—81no—
290C2×D13—81no—
291C2×D13—81no—
292C4×C13—21no—
293C4×C13—21no—
294C4×C13—21no—
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—81no—
298C4×C13—81no—
299C4×C13#52511yescharacteristic
300C4×C13#57511yescharacteristic
301Dic13—81no—
302Dic13—81no—
303Dic13—81no—
304C22×D4—21no—
305C2×Q16—131no—
306C2×SD16—261no—
307C2×D8—22no—
308C2×D8—22no—
309C2×D8—21no—
310C2×D8—131no—
311C2×D8C22×D1311yescharacteristic
312C2×D8C22×D1311yescharacteristic
313C2×M16C22⋊D1311yescharacteristic
314C22×C8C22×D1311yescharacteristic
315C4⋊Q8—261no—
316#126—521no—
317#124—261no—
318#124—521no—
319#123—521no—
320C22⋊Q8—261no—
321C22⋊Q8—521no—
322#121—261no—
323C4×Q8—261no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—41no—
329C4×D4—41no—
330C4×D4—261no—
331#117—21no—
332#117C22⋊D1311yescharacteristic
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335SD32—262no—
336SD32—262no—
337D16—262no—
338D16—262no—
339C2×C16—131no—
340C2×C16—131no—
341C2×C16—131no—
342C2×C16—131no—
343#107—131no—
344#107—131no—
345#107—261no—
346#107C22×D1311yescharacteristic
347#107C22×D1311yescharacteristic
348#106—21no—
349#103—261no—
350#103—261no—
351#102—21no—
352#102—21no—
353#102—21no—
354#102—21no—
355#102—261no—
356#102—261no—
357#97C22⋊D1311yescharacteristic
358#97C22⋊D1311yescharacteristic
359C4×C8C22×D1311yescharacteristic
360C4×C8C22×D1311yescharacteristic
361C2×C13—41no—
362C2×C13—82no—
363C2×C13—82no—
364C2×C13#310011yescharacteristic
365C2×C13#341511yescharacteristic
366C2×C13#341611yescharacteristic
367D13—161no—
368C24—41no—
369C2×Q8—261no—
370C2×Q8—521no—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—42no—
375C2×D4—41no—
376C2×D4—261no—
377C2×D4—521no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—521no—
383C22×C4C2×C22⋊D1311yescharacteristic
384Q16—261no—
385Q16—261no—
386SD16—522no—
387D8—24no—
388D8—21no—
389D8—21no—
390D8—261no—
391D8—261no—
392D8#612712yes—
393D8#612712yes—
394M16—41no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8C2×C22⋊D1311yescharacteristic
398C2×C8C2×C22⋊D1311yescharacteristic
399C2×C8C2×C22⋊D1311yescharacteristic
400C2×C8C23×D1311yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—261no—
404C4⋊C4—261no—
405C4⋊C4—521no—
406C4⋊C4—521no—
407C4⋊C4—521no—
408C4⋊C4#610411yescharacteristic
409C4⋊C4#610411yescharacteristic
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—521no—
416C22⋊C4—521no—
417C22⋊C4—521no—
418C22⋊C4—521no—
419C22⋊C4—521no—
420C22⋊C4#610411yescharacteristic
421C22⋊C4#610411yescharacteristic
422C42—41no—
423C42—521no—
424C42C2×C22⋊D1311yescharacteristic
425C42C2×C22⋊D1311yescharacteristic
426C16—261no—
427C16—261no—
428C16—261no—
429C16—261no—
430C13#3367811yescharacteristic, complemented, Sylow
431C23—44no—
432C23—41no—
433C23—41no—
434C23—161no—
435C23—161no—
436C23—521no—
437C23C2×#610411yescharacteristic
438Q8—521no—
439Q8—521no—
440Q8—2081no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—521no—
447D4—521no—
448D4—2081no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—161no—
454C2×C4—161no—
455C2×C4—161no—
456C2×C4—161no—
457C2×C4—521no—
458C2×C4—521no—
459C2×C4—521no—
460C2×C4—2081no—
461C2×C4C2×#610411yescharacteristic
462C2×C4C2×#610411yescharacteristic
463C2×C4C2×#610411yescharacteristic
464C2×C4C2×#610411yescharacteristic
465C2×C4C2×#610411yescharacteristic
466C2×C4C22×C22⋊D1311yescharacteristic
467C8—21no—
468C8—21no—
469C8—21no—
470C8C2×#612711yescharacteristic
471C8C2×#612711yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—164no—
482C22—1041no—
483C22—1041no—
484C22—1041no—
485C22C22×#610411yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—81no—
492C4—81no—
493C4—1041no—
494C4—1041no—
495C4—1041no—
496C4#1171949611yescharacteristic
497C4#1171952711yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—2081no—
502C2#1312483611yescharacteristic
503C2#1312797511yescharacteristic
504C2#1312798311yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2948C2
socleC22×C13C22×D8
prime radical#13116748C2
hypercenter#2948D13
hypocenterC13#33678
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2948

Complements

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

NH ≅ G/Ntype
1. #13125475C2semidirect
2. #13117044C2semidirect
3. #13117027C2semidirect
4. #13116983C2semidirect
5. #13116973C2semidirect
6. #13116891C2semidirect
7. #13116891C2semidirect
8. #13116765C2semidirect
10. #13116710C2semidirect
11. #13116700C2semidirect
12. C4×#88067C2semidirect
13. C4×#88066C2semidirect
14. #13116643C2semidirect
15. C13×#2948C2semidirect
37. C4×Dic52C22semidirect
38. #11718357C22semidirect
39. C4×D104C22semidirect
40. #11718343C22semidirect
47. #11718084C22semidirect
48. #11718084C22semidirect
49. #11718083C22semidirect
50. #11718083C22semidirect
51. #11718082C22semidirect
52. #11718082C22semidirect
53. #11718081C22semidirect
54. #11718081C22semidirect
55. C4⋊#6090C22semidirect
56. C4⋊#6090C22semidirect
57. #11718053C22semidirect
58. C4×#6090C22semidirect
180. #2948D13semidirect
430. C13#33678semidirect

Maximal subgroups

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

subgroupindex
#131254752
#131170442
#131170272
#131169832
#131169732
#131168912
#131167652
#131167482
#131167102
#131167002
C4×#880672
C4×#880662
#131166432
C13×#29482
#3367813