Finite Group Databasebeta

← #16019373

Subgroups — #16019373

Order 3328.

760 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718808C211yesmaximal, characteristic, complemented
2C22×#88066C211yesmaximal, characteristic, complemented
3#13126523C211yesmaximal, characteristic, complemented
4#13117100C211yesmaximal, characteristic, complemented
5#13116937C211yesmaximal, characteristic, complemented
6#13116930C211yesmaximal, characteristic, complemented
7#13116891C211yesmaximal, characteristic, complemented
8#13116868C211yesmaximal, characteristic, complemented
9#13116765C211yesmaximal, characteristic, complemented
10#13116757C211yesmaximal, characteristic, complemented
11#13116748C211yesmaximal, characteristic, complemented
12#13116747C211yesmaximal, characteristic, complemented
13#13116710C211yesmaximal, characteristic, complemented
14#13116662C211yesmaximal, characteristic, complemented
15D4×C13×D8C211yesmaximal, characteristic, complemented
16C22×C13×D8C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic, complemented
18D42×C13—21no—
19C2×#88158C2211yescharacteristic, complemented
20C22×D104C2211yescharacteristic, complemented
21#11719255—21no—
22C13×#493C2211yescharacteristic, complemented
23C13×#466C2211yescharacteristic
24C13×#466C2211yescharacteristic, complemented
25C13×#459—21no—
26C13×#447—21no—
27C13×#447—21no—
28C4×C13×D8C2211yescharacteristic, complemented
29C8×D4×C13C2211yescharacteristic
30C2×#88067C2211yescharacteristic, complemented
31C2×#88067C2211yescharacteristic, complemented
32C2×#88067C2211yescharacteristic, complemented
33#11718808—24no—
34C2×#88066—24no—
35C2×#88066C2211yescharacteristic
36C2×#88066C2211yescharacteristic
37C2×#88066C2211yescharacteristic, complemented
38C2×#88066C2211yescharacteristic, complemented
39C2×#88066C2211yescharacteristic, complemented
40C2×#88066C2211yescharacteristic, complemented
41#11718777C2211yescharacteristic, complemented
42#11718776C2211yescharacteristic, complemented
43C2×#88052C2211yescharacteristic, complemented
44C22×#6090C2211yescharacteristic, complemented
45#11718505—21no—
46#11718395—21no—
47#11718392—21no—
48#11718357C2211yescharacteristic, complemented
49C4×D104C2211yescharacteristic, complemented
50#11718154C2211yescharacteristic, complemented
51#11718154C2211yescharacteristic, complemented
52#11718154C2211yescharacteristic, complemented
53C22⋊#6090C2211yescharacteristic, complemented
54C22⋊#6090C2211yescharacteristic, complemented
55#11718084C2211yescharacteristic, complemented
56#11718083C2211yescharacteristic, complemented
57#11718083C2211yescharacteristic, complemented
58#11718082C2211yescharacteristic, complemented
59C4⋊#6090C2211yescharacteristic, complemented
60#11718053C2211yescharacteristic, complemented
61C22×D4×C13—21no—
62C22×D4×C13—21no—
63C22×D4×C13—41no—
64C2×#6127—21no—
65C22×D52—21no—
66C2×C13×D8—22no—
67C2×C13×D8—22no—
68C2×C13×D8—21no—
69C2×C13×D8—21no—
70C2×C13×D8—21no—
71C2×C13×D8—41no—
72C2×C13×D8—41no—
73C2×C13×D8C2311yescharacteristic
74C2×C13×D8C2311yescharacteristic
75C2×C13×D8C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C13×#127—21no—
79C13×#121—21no—
80C13×#121—21no—
81C13×#121—41no—
82C13×#120—41no—
83C13×#120—41no—
84C4×D4×C13—21no—
85C4×D4×C13D411yescharacteristic
86#88191—41no—
87#88184—21no—
88#88178—21no—
89C2×Dic52C2311yescharacteristic
90#88158—22no—
91#88158—41no—
92C2×D104—22no—
93C2×D104—21no—
94C2×D104—41no—
95C2×D104C2311yescharacteristic
96C2×D104C2311yescharacteristic
97C2×#6095—21no—
98C2×#6095—21no—
99#88148—41no—
100#88138—41no—
101C22⋊C4×D13—41no—
102#88129—21no—
103C4×D52—21no—
104C13×#107C2311yescharacteristic
105C13×C4⋊C8D411yescharacteristic
106C13×#102—21no—
107C13×#102—21no—
108C13×#102—21no—
109C13×C22⋊C8D411yescharacteristic
110C13×C22⋊C8D411yescharacteristic
111C4×C8×C13C2311yescharacteristic
112#88067—22no—
113#88067—22no—
114#88067—41no—
115#88066—22no—
116#88066—22no—
117#88066—22no—
118#88066—22no—
119#88066—41no—
120#88066D414yescomplemented
121#88061—21no—
122#88061—21no—
123#88058C2311yescharacteristic
124#88056—21no—
125#88052—22no—
126C2×#6090—22no—
127C2×#6090C2311yescharacteristic
128C2×#6090C2311yescharacteristic
129C2×#6090C2311yescharacteristic
130C2×#6090C2311yescharacteristic
131#33830—131nomaximal, Sylow
132C24×C13—41no—
133C24×C13—41no—
134C23×D13—41no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—42no—
139C2×D4×C13—42no—
140C2×D4×C13—41no—
141C2×D4×C13—41no—
142C2×D4×C13—41no—
143C2×D4×C13—41no—
144C2×D4×C13—41no—
145C2×D4×C13—41no—
146C2×D4×C13—81no—
147C2×D4×C13—81no—
148C2×D4×C13—84no—
149C2×D4×C13D811yescharacteristic
150C22×C4×C13—41no—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C2×C22⋊D13—41no—
154C2×C22⋊D13—41no—
155#6127—42no—
156#6127—81no—
157C2×D52—21no—
158C2×D52—21no—
159C2×D52—42no—
160C2×D52—41no—
161C2×D52—81no—
162C2×C4×D13—41no—
163C2×C4×D13—41no—
164C2×Dic26—21no—
165C13×D8—21no—
166C13×D8—21no—
167C13×D8—21no—
168C13×D8—21no—
169C13×D8—21no—
170C13×D8—42no—
171C13×D8—42no—
172C13×D8—81no—
173C13×D8C2×D412yes—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13C2×D411yescharacteristic
179C2×C8×C13C2×D411yescharacteristic
180C2×C8×C13C2×D411yescharacteristic
181C2×C8×C13C2411yescharacteristic
182C13×C4⋊C4—21no—
183C13×C4⋊C4D811yescharacteristic
184C13×C22⋊C4—41no—
185C13×C22⋊C4—41no—
186C13×C22⋊C4—41no—
187C13×C22⋊C4D811yescharacteristic
188C13×C22⋊C4D811yescharacteristic
189C42×C13C2×D411yescharacteristic
190C22⋊Dic13—41no—
191#6103—41no—
192#6103—41no—
193#6103—41no—
194#6103—41no—
195C4⋊Dic13—21no—
196#6101—41no—
197Dic52—21no—
198Dic52—21no—
199D104—21no—
200D104—21no—
201D104—21no—
202D104—42no—
203D104C2×D412yescomplemented
204#6095—42no—
205#6095—81no—
206#6090—21no—
207#6090—21no—
208#6090—21no—
209#6090C2×D412yescomplemented
210C2×#509—131no—
211C22×D16—131no—
212#3280—131no—
213D4×D8D1311yescharacteristic, complemented
214#2250—131no—
215#2218—131no—
216#2217—131no—
217#2210—131no—
218#2206—131no—
219#2187—131no—
220#2186—131no—
221#2184—131no—
222#2184—131no—
223#2177—131no—
224#2168—131no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—82no—
229C23×C13—82no—
230C23×C13—82no—
231C23×C13—82no—
232C23×C13—161no—
233C23×C13—161no—
234C23×C13C2×D811yescharacteristic
235C23×C13C2×D811yescharacteristic
236C22×D13—41no—
237C22×D13—41no—
238C22×D13—82no—
239C22×D13—82no—
240C22×D13—161no—
241D4×C13—22no—
242D4×C13—22no—
243D4×C13—41no—
244D4×C13—41no—
245D4×C13—41no—
246D4×C13—41no—
247D4×C13—41no—
248D4×C13—82no—
249D4×C13—82no—
250D4×C13—82no—
251D4×C13—82no—
252D4×C13—82no—
253D4×C13—161no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—41no—
259C2×C4×C13—82no—
260C2×C4×C13C2×D811yescharacteristic
261C2×C4×C13C2×D811yescharacteristic
262C2×C4×C13C2×D811yescharacteristic
263C2×C4×C13C2×D811yescharacteristic
264C2×C4×C13C22×D411yescharacteristic
265C22⋊D13—82no—
266C22⋊D13—161no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269D52—22no—
270D52—41no—
271D52—41no—
272D52—41no—
273D52—82no—
274C4×D13—82no—
275C4×D13—161no—
276Dic26—41no—
277Dic26—41no—
278C8×C13—21no—
279C8×C13—21no—
280C8×C13—21no—
281C8×C13C22×D411yescharacteristic
282C8×C13H(5,𝔽2)11yescharacteristic
283C2×#135—131no—
284C22×D8—131no—
285C22×D8C2×D1311yescharacteristic
286C22×D8C2×D1311yescharacteristic, complemented
287#546—261no—
288D42—21no—
289#509—264no—
290C2×SD32—131no—
291C2×SD32—131no—
292C2×SD32—131no—
293C2×D16—131no—
294C2×D16—131no—
295C2×D16—131no—
296C2×D16—131no—
297C2×D16—131no—
298C2×D16—131no—
299C2×D16—264no—
300C2×M32—131no—
301C22×C16—131no—
302#495—131no—
303#493C2×D1311yescharacteristic, complemented
304#467—131no—
305#466—131no—
306#466C2×D1311yescharacteristic
307#466C2×D1311yescharacteristic, complemented
308#463—261no—
309#459—21no—
310#450—261no—
311#449—261no—
312#447—21no—
313#447—21no—
314C4×D8—131no—
315C4×D8C2×D1311yescharacteristic, complemented
316C8×D4C2×D1311yescharacteristic
317#367—131no—
318C4⋊C16—131no—
319#358—131no—
320#357—131no—
321#357—131no—
322#357—131no—
323#357—131no—
324#357—131no—
325C22⋊C16—131no—
326C22⋊C16—131no—
327#346—131no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—42no—
334C22×C13—81no—
335C22×C13—81no—
336C22×C13—81no—
337C22×C13—81no—
338C22×C13—81no—
339C22×C13—81no—
340C22×C13—81no—
341C22×C13—81no—
342C22×C13—164no—
343C22×C13—164no—
344C22×C13#50912yescomplemented
345C22×C13C22×D811yescharacteristic
346C2×D13—42no—
347C2×D13—81no—
348C2×D13—81no—
349C2×D13—81no—
350C2×D13—81no—
351C2×D13—81no—
352C2×D13—164no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—21no—
357C4×C13—81no—
358C4×C13D4211yescharacteristic
359C4×C13#57611yescharacteristic
360Dic13—81no—
361Dic13—81no—
362C2×#41—261no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—41no—
366C22×D4—261no—
367#135—262no—
368#135—521no—
369C2×Q16—131no—
370C2×SD16—261no—
371C2×SD16—261no—
372C2×D8—22no—
373C2×D8—22no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×D8—41no—
378C2×D8—41no—
379C2×D8—131no—
380C2×D8—131no—
381C2×D8—262no—
382C2×D8—261no—
383C2×D8—521no—
384C2×D8C22×D1311yescharacteristic
385C2×D8C22×D1311yescharacteristic
386C2×D8C22×D1311yescharacteristic
387C22×C8C22×D1311yescharacteristic
388C22×C8C22×D1311yescharacteristic
389#127—21no—
390#124—261no—
391#123—521no—
392C22⋊Q8—261no—
393#121—21no—
394#121—21no—
395#121—41no—
396#121—261no—
397#121—521no—
398#120—41no—
399#120—41no—
400#120—521no—
401C4×D4—21no—
402C4×D4—261no—
403C4×D4C22⋊D1311yescharacteristic
404C2×C22⋊C4—521no—
405SD32—262no—
406SD32—262no—
407SD32—521no—
408D16—134no—
409D16—262no—
410D16—262no—
411D16—262no—
412D16—262no—
413D16—521no—
414M32—262no—
415C2×C16—131no—
416C2×C16—131no—
417C2×C16—131no—
418C2×C16—131no—
419C2×C16—262no—
420#107—131no—
421#107C22×D1311yescharacteristic
422C4⋊C8C22⋊D1311yescharacteristic
423#103—261no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—261no—
428#102—261no—
429C22⋊C8C22⋊D1311yescharacteristic
430C22⋊C8C22⋊D1311yescharacteristic
431C4×C8C22×D1311yescharacteristic
432C2×C13—22no—
433C2×C13—41no—
434C2×C13—82no—
435C2×C13—161no—
436C2×C13—161no—
437C2×C13D4×D811yescharacteristic
438C2×C13C2×#50911yescharacteristic
439C2×C13#341511yescharacteristic
440D13—82no—
441D13—161no—
442C24—41no—
443C24—41no—
444C24—521no—
445#41—522no—
446#41—1041no—
447C2×Q8—261no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4—84no—
462C2×D4—261no—
463C2×D4—261no—
464C2×D4—522no—
465C2×D4—521no—
466C2×D4—521no—
467C2×D4—521no—
468C2×D4—1041no—
469C2×D4#610411yescharacteristic
470C22×C4—41no—
471C22×C4—521no—
472C22×C4—521no—
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475Q16—261no—
476Q16—261no—
477SD16—522no—
478SD16—1041no—
479D8—21no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—42no—
485D8—42no—
486D8—81no—
487D8—132no—
488D8—261no—
489D8—261no—
490D8—261no—
491D8—522no—
492D8D4×D1312yes—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8C2×C22⋊D1311yescharacteristic
498C2×C8C2×C22⋊D1311yescharacteristic
499C2×C8C2×C22⋊D1311yescharacteristic
500C2×C8C23×D1311yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—261no—
503C4⋊C4—521no—
504C4⋊C4#610411yescharacteristic
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—521no—
509C22⋊C4—521no—
510C22⋊C4—521no—
511C22⋊C4—521no—
512C22⋊C4—521no—
513C22⋊C4#610411yescharacteristic
514C22⋊C4#610411yescharacteristic
515C42C2×C22⋊D1311yescharacteristic
516C16—132no—
517C16—261no—
518C16—261no—
519C16—261no—
520C13#3383011yescharacteristic, complemented, Sylow
521C23—41no—
522C23—41no—
523C23—41no—
524C23—82no—
525C23—82no—
526C23—82no—
527C23—82no—
528C23—161no—
529C23—161no—
530C23—521no—
531C23—521no—
532C23—1042no—
533C23—1042no—
534C23—2081no—
535C23C2×#610411yescharacteristic
536C23C2×#610411yescharacteristic
537Q8—521no—
538Q8—521no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—82no—
547D4—82no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4—161no—
552D4—262no—
553D4—521no—
554D4—521no—
555D4—521no—
556D4—1042no—
557D4—1042no—
558D4—2081no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—82no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—1042no—
568C2×C4—2081no—
569C2×C4C2×#610411yescharacteristic
570C2×C4C2×#610411yescharacteristic
571C2×C4C2×#610411yescharacteristic
572C2×C4C2×#610411yescharacteristic
573C2×C4C22×C22⋊D1311yescharacteristic
574C8—21no—
575C8—21no—
576C8—21no—
577C8C2×D4×D1311yescharacteristic
578C8#8825111yescharacteristic
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—164no—
594C22—164no—
595C22—522no—
596C22—1041no—
597C22—1041no—
598C22—1041no—
599C22—1041no—
600C22—1041no—
601C22—2084no—
602C22#1171880812yescomplemented
603C22C22×#610411yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—81no—
609C4—1041no—
610C4—1041no—
611C4D4×C22⋊D1311yescharacteristic
612C4#1171954011yescharacteristic
613C2—22no—
614C2—41no—
615C2—82no—
616C2—161no—
617C2—161no—
618C2—1042no—
619C2—2081no—
620C2D4×#610411yescharacteristic
621C2C2×#1171880811yescharacteristic
622C2#1312797511yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingD4×C13×D8C2
socleC22×C13C22×D8
hypercenterD4×D8D13
hypocenterC13#33830
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#11718808C2semidirect
2. C22×#88066C2semidirect
3. #13126523C2semidirect
4. #13117100C2semidirect
5. #13116937C2semidirect
6. #13116930C2semidirect
7. #13116891C2semidirect
8. #13116868C2semidirect
9. #13116765C2semidirect
10. #13116757C2semidirect
11. #13116748C2semidirect
12. #13116747C2semidirect
13. #13116710C2semidirect
14. #13116662C2semidirect
15. D4×C13×D8C2semidirect
17. C22×C13×D8C22semidirect
19. C2×#88158C22semidirect
20. C22×D104C22semidirect
22. C13×#493C22semidirect
24. C13×#466C22semidirect
28. C4×C13×D8C22semidirect
30. C2×#88067C22semidirect
31. C2×#88067C22semidirect
32. C2×#88067C22semidirect
37. C2×#88066C22semidirect
38. C2×#88066C22semidirect
39. C2×#88066C22semidirect
40. C2×#88066C22semidirect
41. #11718777C22semidirect
42. #11718776C22semidirect
43. C2×#88052C22semidirect
44. C22×#6090C22semidirect
48. #11718357C22semidirect
49. C4×D104C22semidirect
50. #11718154C22semidirect
51. #11718154C22semidirect
52. #11718154C22semidirect
53. C22⋊#6090C22semidirect
54. C22⋊#6090C22semidirect
55. #11718084C22semidirect
56. #11718083C22semidirect
57. #11718083C22semidirect
58. #11718082C22semidirect
59. C4⋊#6090C22semidirect
60. #11718053C22semidirect
120. #88066D4semidirect
203. D104C2×D4semidirect
209. #6090C2×D4semidirect
213. D4×D8D13semidirect
286. C22×D8C2×D13semidirect
303. #493C2×D13semidirect
307. #466C2×D13semidirect
315. C4×D8C2×D13semidirect
344. C22×C13#509semidirect
520. C13#33830semidirect
602. C22#11718808semidirect

Maximal subgroups

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

subgroupindex
C2×#117188082
C22×#880662
#131265232
#131171002
#131169372
#131169302
#131168912
#131168682
#131167652
#131167572
#131167482
#131167472
#131167102
#131166622
D4×C13×D82
#3383013