Finite Group Databasebeta

← #16019773

Subgroups — #16019773

Order 3328.

580 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13126523C211yesmaximal, characteristic, complemented
2#13117070C211yesmaximal, characteristic, complemented
3#13117038C211yesmaximal, characteristic, complemented
4#13117027C211yesmaximal, characteristic, complemented
5#13116990C211yesmaximal, characteristic, complemented
6#13116930C211yesmaximal, characteristic, complemented
7#13116920C211yesmaximal, characteristic, complemented
8#13116891C211yesmaximal, characteristic, complemented
9#13116757C211yesmaximal, characteristic, complemented
10#13116747C211yesmaximal, characteristic, complemented
11C4×#88066C211yesmaximal, characteristic, complemented
12D4×#6090C211yesmaximal, characteristic, complemented
13#13116541C211yesmaximal, characteristic, complemented
14C2×#11718083C211yesmaximal, characteristic, complemented
15C13×#3339C211yesmaximal, characteristic, complemented
16C13×#553—21no—
17C2×#88158C2211yescharacteristic
18C22×D104C2211yescharacteristic
19#11719255—21no—
20C13×#499C2211yescharacteristic, complemented
21C13×#482—21no—
22C13×#481—21no—
23C13×#478—21no—
24C13×#466C2211yescharacteristic
25C13×#466C2211yescharacteristic, complemented
26C4×C13×D8C2211yescharacteristic, complemented
27C8×D4×C13C2211yescharacteristic
28C13×#427C2211yescharacteristic, complemented
29C2×C13×#107C2211yescharacteristic
30C2×#88067C2211yescharacteristic, complemented
31C2×#88066C2211yescharacteristic
32C2×#88066C2211yescharacteristic
33#11718777C2211yescharacteristic
34#11718776C2211yescharacteristic
35C22×#6090C2211yescharacteristic
36C22×#6090C2211yescharacteristic, complemented
37#11718505—21no—
38#11718395—21no—
39#11718392—21no—
40#11718357C2211yescharacteristic
41C4×D104C2211yescharacteristic
42#11718154C2211yescharacteristic, complemented
43C22⋊#6090C2211yescharacteristic
44C22⋊#6090C2211yescharacteristic, complemented
45#11718084C2211yescharacteristic, complemented
46#11718084C2211yescharacteristic, complemented
47#11718084C2211yescharacteristic, complemented
48#11718083C2211yescharacteristic
49#11718083C2211yescharacteristic
50#11718083C2211yescharacteristic
51#11718083C2211yescharacteristic
52#11718083C2211yescharacteristic
53#11718083C2211yescharacteristic
54#11718082C2211yescharacteristic, complemented
55#11718081C2211yescharacteristic, complemented
56#11718081C2211yescharacteristic, complemented
57C4⋊#6090C2211yescharacteristic, complemented
58C4×#6090C2211yescharacteristic, complemented
59C2×#6127—21no—
60C22×D52—21no—
61C2×C13×D8C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×#126—41no—
65C13×#125—21no—
66C13×#123—41no—
67C13×#121—21no—
68C13×#121—21no—
69C13×#121—41no—
70C4×D4×C13—21no—
71C4×D4×C13—41no—
72C4×D4×C13D411yescharacteristic
73C13×#117—21no—
74C2×C13×C4⋊C4—21no—
75#88191—41no—
76#88184—21no—
77#88178—21no—
78C2×Dic52C2311yescharacteristic
79#88158—22no—
80#88158—41no—
81C2×D104—22no—
82C2×D104—21no—
83C2×D104—41no—
84C2×D104C2311yescharacteristic
85C2×D104C2311yescharacteristic
86C2×#6095—21no—
87C2×#6095—21no—
88#88148—41no—
89#88138—41no—
90C22⋊C4×D13—41no—
91#88129—21no—
92C4×D52—21no—
93C13×#107—21no—
94C13×#107C2311yescharacteristic
95C13×#107C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#106—21no—
98C13×#106—21no—
99C13×C4⋊C8D411yescharacteristic
100C13×#102—21no—
101C13×#102—21no—
102C13×#102—21no—
103C13×C22⋊C8D411yescharacteristic
104C13×C22⋊C8D411yescharacteristic
105C4×C8×C13C2311yescharacteristic
106#88067—41no—
107#88066—22no—
108#88066—41no—
109#88061—21no—
110#88061—21no—
111#88058C2311yescharacteristic
112#88056—21no—
113C2×#6090—41no—
114C2×#6090—41no—
115C2×#6090C2311yescharacteristic
116C2×#6090C2311yescharacteristic
117C2×#6090C2311yescharacteristic
118C2×#6090C2311yescharacteristic
119#33864—131nomaximal, Sylow
120C23×D13—41no—
121C2×D4×C13—21no—
122C2×D4×C13—41no—
123C2×D4×C13—41no—
124C2×D4×C13D811yescharacteristic
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C2×C22⋊D13—41no—
130C2×C22⋊D13—41no—
131#6127—42no—
132#6127—81no—
133C2×D52—21no—
134C2×D52—21no—
135C2×D52—42no—
136C2×D52—41no—
137C2×D52—81no—
138C2×C4×D13—41no—
139C2×C4×D13—41no—
140C2×Dic26—21no—
141C13×D8—21no—
142C13×D8—21no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13C2×D411yescharacteristic
148C2×C8×C13C2×D411yescharacteristic
149C2×C8×C13C2×D411yescharacteristic
150C2×C8×C13C2411yescharacteristic
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—41no—
155C13×C4⋊C4—41no—
156C13×C4⋊C4—41no—
157C13×C4⋊C4D811yescharacteristic
158C13×C22⋊C4—41no—
159C13×C22⋊C4—41no—
160C13×C22⋊C4—41no—
161C13×C22⋊C4—41no—
162C13×C22⋊C4D811yescharacteristic
163C13×C22⋊C4D811yescharacteristic
164C42×C13—41no—
165C42×C13C2×D411yescharacteristic
166C22⋊Dic13—41no—
167#6103—41no—
168#6103—41no—
169#6103—41no—
170#6103—41no—
171C4⋊Dic13—21no—
172#6101—41no—
173Dic52—21no—
174Dic52—21no—
175D104—21no—
176D104—21no—
177D104—21no—
178D104—42no—
179D104#4112yes—
180#6095—42no—
181#6095—81no—
182#6090—21no—
183#6090—21no—
184#6090—21no—
185#6090—21no—
186#3339D1311yescharacteristic, complemented
187#3280—131no—
188#2242—131no—
189#2236—131no—
190#2234—131no—
191#2228—131no—
192#2217—131no—
193#2215—131no—
194#2210—131no—
195#2186—131no—
196#2184—131no—
197C4×D16—131no—
198D4×C16—131no—
199#2138—131no—
200C2×#357—131no—
201C23×C13—41no—
202C23×C13C2×D811yescharacteristic
203C23×C13C2×D811yescharacteristic
204C22×D13—41no—
205C22×D13—41no—
206C22×D13—82no—
207C22×D13—82no—
208C22×D13—161no—
209D4×C13—22no—
210D4×C13—41no—
211D4×C13—41no—
212D4×C13—82no—
213D4×C13—161no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—161no—
222C2×C4×C13—161no—
223C2×C4×C13C2×D811yescharacteristic
224C2×C4×C13C2×D811yescharacteristic
225C2×C4×C13C2×D811yescharacteristic
226C2×C4×C13C2×D811yescharacteristic
227C2×C4×C13C22×D411yescharacteristic
228C22⋊D13—82no—
229C22⋊D13—161no—
230C2×Dic13—41no—
231C2×Dic13—41no—
232D52—22no—
233D52—41no—
234D52—41no—
235D52—41no—
236D52—82no—
237C4×D13—82no—
238C4×D13—161no—
239Dic26—41no—
240Dic26—41no—
241C8×C13—21no—
242C8×C13—21no—
243C8×C13—21no—
244C8×C13C2×#4111yescharacteristic
245C8×C13H(5,𝔽2)11yescharacteristic
246C2×#135—131no—
247C22×D8—131no—
248#553—21no—
249#546—261no—
250C2×SD32—131no—
251C2×D16—131no—
252C2×D16—131no—
253C22×C16—131no—
254C22×C16—131no—
255#499C2×D1311yescharacteristic, complemented
256#495—131no—
257#482—21no—
258#481—21no—
259#478—21no—
260#467—131no—
261#466—131no—
262#466C2×D1311yescharacteristic
263#466C2×D1311yescharacteristic, complemented
264#463—261no—
265#450—261no—
266#449—261no—
267C4×D8—131no—
268C4×D8C2×D1311yescharacteristic, complemented
269C8×D4C2×D1311yescharacteristic
270#427C2×D1311yescharacteristic, complemented
271C2×#107C2×D1311yescharacteristic
272#367—131no—
273#366—131no—
274#366—131no—
275C4⋊C16—131no—
276#358—131no—
277#358—131no—
278#358—131no—
279#357—131no—
280#357—131no—
281#357—131no—
282#357—131no—
283#357—131no—
284#357—131no—
285#357—131no—
286C22⋊C16—131no—
287C22⋊C16—131no—
288C4×C16—131no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—21no—
294C22×C13—81no—
295C22×C13—81no—
296C22×C13—81no—
297C22×C13#50812yes—
298C22×C13C22×D811yescharacteristic
299C2×D13—42no—
300C2×D13—81no—
301C2×D13—81no—
302C2×D13—81no—
303C2×D13—81no—
304C2×D13—81no—
305C2×D13—164no—
306C4×C13—21no—
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—81no—
311C4×C13—81no—
312C4×C13—81no—
313C4×C13#54611yescharacteristic
314C4×C13#57711yescharacteristic
315Dic13—81no—
316Dic13—81no—
317C2×#41—261no—
318C22×D4—261no—
319#135—262no—
320#135—521no—
321C2×Q16—131no—
322C2×SD16—261no—
323C2×SD16—261no—
324C2×D8—131no—
325C2×D8—131no—
326C2×D8—262no—
327C2×D8—261no—
328C2×D8—521no—
329C2×D8C22×D1311yescharacteristic
330C22×C8C22×D1311yescharacteristic
331C22×C8C22×D1311yescharacteristic
332#126—41no—
333#125—21no—
334#124—261no—
335#123—41no—
336#123—521no—
337C22⋊Q8—261no—
338#121—21no—
339#121—21no—
340#121—41no—
341#121—261no—
342#121—521no—
343#120—521no—
344C4×D4—21no—
345C4×D4—41no—
346C4×D4—261no—
347C4×D4C22⋊D1311yescharacteristic
348#117—21no—
349C2×C4⋊C4—21no—
350C2×C22⋊C4—521no—
351SD32—521no—
352D16—262no—
353D16—521no—
354C2×C16—131no—
355C2×C16—131no—
356C2×C16—131no—
357C2×C16—131no—
358C2×C16—521no—
359C2×C16—521no—
360#107—21no—
361#107—131no—
362#107C22×D1311yescharacteristic
363#107C22×D1311yescharacteristic
364#107C22×D1311yescharacteristic
365#106—21no—
366#106—21no—
367C4⋊C8C22⋊D1311yescharacteristic
368#103—261no—
369#102—21no—
370#102—21no—
371#102—21no—
372#102—261no—
373#102—261no—
374C22⋊C8C22⋊D1311yescharacteristic
375C22⋊C8C22⋊D1311yescharacteristic
376C4×C8C22×D1311yescharacteristic
377C2×C13—22no—
378C2×C13—41no—
379C2×C13—161no—
380C2×C13#329411yescharacteristic
381C2×C13C2×#50811yescharacteristic
382C2×C13#341511yescharacteristic
383D13—82no—
384D13—161no—
385C24—521no—
386#41—522no—
387#41—1041no—
388C2×Q8—261no—
389C2×D4—21no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—261no—
393C2×D4—261no—
394C2×D4—522no—
395C2×D4—521no—
396C2×D4—521no—
397C2×D4—521no—
398C2×D4—1041no—
399C2×D4#610411yescharacteristic
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—521no—
403C22×C4—521no—
404C22×C4C2×C22⋊D1311yescharacteristic
405C22×C4C2×C22⋊D1311yescharacteristic
406Q16—261no—
407Q16—261no—
408SD16—522no—
409SD16—1041no—
410D8—21no—
411D8—21no—
412D8—132no—
413D8—261no—
414D8—261no—
415D8—261no—
416D8—522no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8C2×C22⋊D1311yescharacteristic
422C2×C8C2×C22⋊D1311yescharacteristic
423C2×C8C2×C22⋊D1311yescharacteristic
424C2×C8C23×D1311yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—261no—
432C4⋊C4—521no—
433C4⋊C4#610411yescharacteristic
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—521no—
439C22⋊C4—521no—
440C22⋊C4—521no—
441C22⋊C4—521no—
442C22⋊C4—521no—
443C22⋊C4#610411yescharacteristic
444C22⋊C4#610411yescharacteristic
445C42—41no—
446C42C2×C22⋊D1311yescharacteristic
447C16—261no—
448C16—261no—
449C16—261no—
450C16—261no—
451C13#3386411yescharacteristic, complemented, Sylow
452C23—41no—
453C23—521no—
454C23—521no—
455C23—1042no—
456C23—1042no—
457C23—2081no—
458C23C2×#610411yescharacteristic
459C23C2×#610411yescharacteristic
460Q8—521no—
461Q8—521no—
462D4—22no—
463D4—41no—
464D4—41no—
465D4—82no—
466D4—161no—
467D4—262no—
468D4—521no—
469D4—521no—
470D4—521no—
471D4—1042no—
472D4—1042no—
473D4—2081no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—161no—
482C2×C4—161no—
483C2×C4—521no—
484C2×C4—521no—
485C2×C4—1042no—
486C2×C4—2081no—
487C2×C4C2×#610411yescharacteristic
488C2×C4C2×#610411yescharacteristic
489C2×C4C2×#610411yescharacteristic
490C2×C4C2×#610411yescharacteristic
491C2×C4C22×C22⋊D1311yescharacteristic
492C8—21no—
493C8—21no—
494C8—21no—
495C8#41×D1311yescharacteristic
496C8#8825611yescharacteristic
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—522no—
506C22—1041no—
507C22—1041no—
508C22—1041no—
509C22—1041no—
510C22—1041no—
511C22—2084no—
512C22#1171885512yes—
513C22C22×#610411yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4—1041no—
522C4—1041no—
523C4#1171953411yescharacteristic
524C4#1171954211yescharacteristic
525C2—22no—
526C2—41no—
527C2—161no—
528C2—1042no—
529C2—2081no—
530C2#1312664311yescharacteristic
531C2C2×#1171885511yescharacteristic
532C2#1312797511yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3339C2
socleC22×C13C22×D8
hypercenter#3339D13
hypocenterC13#33864
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #13126523C2semidirect
2. #13117070C2semidirect
3. #13117038C2semidirect
4. #13117027C2semidirect
5. #13116990C2semidirect
6. #13116930C2semidirect
7. #13116920C2semidirect
8. #13116891C2semidirect
9. #13116757C2semidirect
10. #13116747C2semidirect
11. C4×#88066C2semidirect
12. D4×#6090C2semidirect
13. #13116541C2semidirect
14. C2×#11718083C2semidirect
15. C13×#3339C2semidirect
20. C13×#499C22semidirect
25. C13×#466C22semidirect
26. C4×C13×D8C22semidirect
28. C13×#427C22semidirect
30. C2×#88067C22semidirect
36. C22×#6090C22semidirect
42. #11718154C22semidirect
44. C22⋊#6090C22semidirect
45. #11718084C22semidirect
46. #11718084C22semidirect
47. #11718084C22semidirect
54. #11718082C22semidirect
55. #11718081C22semidirect
56. #11718081C22semidirect
57. C4⋊#6090C22semidirect
58. C4×#6090C22semidirect
186. #3339D13semidirect
255. #499C2×D13semidirect
263. #466C2×D13semidirect
268. C4×D8C2×D13semidirect
270. #427C2×D13semidirect
451. C13#33864semidirect

Maximal subgroups

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

subgroupindex
#131265232
#131170702
#131170382
#131170272
#131169902
#131169302
#131169202
#131168912
#131167572
#131167472
C4×#880662
D4×#60902
#131165412
C2×#117180832
C13×#33392
#3386413