Finite Group Databasebeta

← #16019388

Subgroups — #16019388

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718808C211yesmaximal, characteristic, complemented
2C22×#88067C211yesmaximal, characteristic, complemented
3#13126579C211yesmaximal, characteristic, complemented
4#13117100C211yesmaximal, characteristic, complemented
5#13116947C211yesmaximal, characteristic, complemented
6#13116920C211yesmaximal, characteristic, complemented
7#13116891C211yesmaximal, characteristic, complemented
8#13116873C211yesmaximal, characteristic, complemented
9#13116765C211yesmaximal, characteristic, complemented
10#13116757C211yesmaximal, characteristic, complemented
11#13116752C211yesmaximal, characteristic, complemented
12#13116748C211yesmaximal, characteristic, complemented
13#13116700C211yesmaximal, characteristic, complemented
14#13116662C211yesmaximal, characteristic, complemented
15D4×C13×D8C211yesmaximal, characteristic, complemented
16C22×C13×D8C2211yescharacteristic
17C22×C13×D8C2211yescharacteristic
18D42×C13—21no—
19C22×Dic52C2211yescharacteristic, complemented
20C2×#88158C2211yescharacteristic, complemented
21#11719257—21no—
22C13×#493C2211yescharacteristic
23C13×#466C2211yescharacteristic
24C13×#466C2211yescharacteristic
25C13×#459—21no—
26C13×#447—21no—
27C13×#447—21no—
28C4×C13×D8C2211yescharacteristic
29C8×D4×C13C2211yescharacteristic
30C2×#88067—24no—
31C2×#88067C2211yescharacteristic
32C2×#88067C2211yescharacteristic
33C2×#88067C2211yescharacteristic, complemented
34C2×#88067C2211yescharacteristic, complemented
35C2×#88067C2211yescharacteristic, complemented
36C2×#88067C2211yescharacteristic, complemented
37#11718808—24no—
38C2×#88066C2211yescharacteristic
39C2×#88066C2211yescharacteristic, complemented
40C2×#88066C2211yescharacteristic, complemented
41#11718777C2211yescharacteristic, complemented
42#11718776C2211yescharacteristic, complemented
43C2×#88052C2211yescharacteristic, complemented
44C22×#6090C2211yescharacteristic, complemented
45#11718506—21no—
46#11718399—21no—
47#11718394—21no—
48C4×Dic52C2211yescharacteristic, complemented
49#11718357C2211yescharacteristic, complemented
50#11718154C2211yescharacteristic
51#11718154C2211yescharacteristic, complemented
52#11718154C2211yescharacteristic, complemented
53C22⋊#6090C2211yescharacteristic, complemented
54C22⋊#6090C2211yescharacteristic, complemented
55#11718084C2211yescharacteristic, complemented
56#11718084C2211yescharacteristic, complemented
57#11718083C2211yescharacteristic, complemented
58#11718081C2211yescharacteristic, complemented
59C4⋊#6090C2211yescharacteristic, complemented
60#11718053C2211yescharacteristic, complemented
61C22×D4×C13—21no—
62C22×D4×C13—21no—
63C22×D4×C13—41no—
64C2×#6127—21no—
65C22×Dic26—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#88193—41no—
87#88184—21no—
88#88178—21no—
89C2×Dic52—22no—
90C2×Dic52—21no—
91C2×Dic52—41no—
92C2×Dic52C2311yescharacteristic
93C2×Dic52C2311yescharacteristic
94#88158—22no—
95#88158—41no—
96C2×D104C2311yescharacteristic
97C2×#6095—21no—
98C2×#6095—21no—
99#88150—41no—
100#88139—41no—
101#88135—41no—
102#88129—21no—
103C4×Dic26—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—22no—
115#88067—22no—
116#88067—41no—
117#88067D414yescomplemented
118#88066—22no—
119#88066—22no—
120#88066—41no—
121#88061—21no—
122#88058C2311yescharacteristic
123#88056—21no—
124#88056—21no—
125#88052—22no—
126C2×#6090—22no—
127C2×#6090C2311yescharacteristic
128C2×#6090C2311yescharacteristic
129C2×#6090C2311yescharacteristic
130C2×#6090C2311yescharacteristic
131#33831—131nomaximal, Sylow
132C24×C13—41no—
133C24×C13—41no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—42no—
138C2×D4×C13—42no—
139C2×D4×C13—41no—
140C2×D4×C13—41no—
141C2×D4×C13—41no—
142C2×D4×C13—41no—
143C2×D4×C13—41no—
144C2×D4×C13—41no—
145C2×D4×C13—81no—
146C2×D4×C13—81no—
147C2×D4×C13—84no—
148C2×D4×C13D811yescharacteristic
149C22×C4×C13—41no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C2×C22⋊D13—41no—
153C2×C22⋊D13—41no—
154C22×Dic13—41no—
155#6127—42no—
156#6127—81no—
157C2×D52—21no—
158C2×C4×D13—41no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—42no—
162C2×Dic26—41no—
163C2×Dic26—81no—
164C13×D8—21no—
165C13×D8—21no—
166C13×D8—21no—
167C13×D8—21no—
168C13×D8—21no—
169C13×D8—42no—
170C13×D8—42no—
171C13×D8—81no—
172C13×D8C2×D412yes—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13C2×D411yescharacteristic
178C2×C8×C13C2×D411yescharacteristic
179C2×C8×C13C2×D411yescharacteristic
180C2×C8×C13C2411yescharacteristic
181C13×C4⋊C4—21no—
182C13×C4⋊C4D811yescharacteristic
183C13×C22⋊C4—41no—
184C13×C22⋊C4—41no—
185C13×C22⋊C4—41no—
186C13×C22⋊C4D811yescharacteristic
187C13×C22⋊C4D811yescharacteristic
188C42×C13C2×D411yescharacteristic
189C22⋊Dic13—41no—
190#6103—41no—
191#6103—41no—
192#6103—41no—
193C4⋊Dic13—21no—
194#6101—41no—
195#6101—41no—
196C4×Dic13—41no—
197Dic52—21no—
198Dic52—21no—
199Dic52—21no—
200Dic52—42no—
201Dic52C2×D412yescomplemented
202D104—21no—
203D104—21no—
204#6095—42no—
205#6095—81no—
206#6090—21no—
207#6090—21no—
208#6090—21no—
209#6090C2×D412yescomplemented
210C2×#509—131no—
211C22×SD32—131no—
212#3285—131no—
213D4×D8D1311yescharacteristic, complemented
214#2250—131no—
215#2220—131no—
216#2215—131no—
217#2210—131no—
218#2207—131no—
219#2187—131no—
220#2186—131no—
221#2185—131no—
222#2184—131no—
223#2175—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—
237D4×C13—22no—
238D4×C13—22no—
239D4×C13—41no—
240D4×C13—41no—
241D4×C13—41no—
242D4×C13—41no—
243D4×C13—41no—
244D4×C13—82no—
245D4×C13—82no—
246D4×C13—82no—
247D4×C13—82no—
248D4×C13—82no—
249D4×C13—161no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—41no—
255C2×C4×C13—82no—
256C2×C4×C13C2×D811yescharacteristic
257C2×C4×C13C2×D811yescharacteristic
258C2×C4×C13C2×D811yescharacteristic
259C2×C4×C13C2×D811yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C22⋊D13—82no—
262C22⋊D13—82no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—82no—
267D52—41no—
268D52—41no—
269C4×D13—82no—
270Dic26—22no—
271Dic26—41no—
272Dic26—41no—
273Dic26—41no—
274Dic26—82no—
275C8×C13—21no—
276C8×C13—21no—
277C8×C13—21no—
278C8×C13C22×D411yescharacteristic
279C8×C13H(5,𝔽2)11yescharacteristic
280C2×#135—131no—
281C22×Q16—131no—
282C22×D8C2×D1311yescharacteristic
283C22×D8C2×D1311yescharacteristic
284#548—261no—
285D42—21no—
286#509—264no—
287C2×SD32—131no—
288C2×SD32—131no—
289C2×SD32—131no—
290C2×SD32—131no—
291C2×SD32—131no—
292C2×SD32—131no—
293C2×SD32—264no—
294C2×D16—131no—
295C2×D16—131no—
296C2×D16—131no—
297C2×M32—131no—
298C22×C16—131no—
299#495—131no—
300#493C2×D1311yescharacteristic
301#467—131no—
302#466—131no—
303#466C2×D1311yescharacteristic
304#466C2×D1311yescharacteristic
305#464—261no—
306#459—21no—
307#452—261no—
308#448—261no—
309#447—21no—
310#447—21no—
311C4×Q16—131no—
312C4×D8C2×D1311yescharacteristic
313C8×D4C2×D1311yescharacteristic
314#366—131no—
315C4⋊C16—131no—
316#358—131no—
317#358—131no—
318#357—131no—
319#357—131no—
320#357—131no—
321#357—131no—
322C22⋊C16—131no—
323C22⋊C16—131no—
324#346—131no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—42no—
331C22×C13—81no—
332C22×C13—81no—
333C22×C13—81no—
334C22×C13—81no—
335C22×C13—81no—
336C22×C13—81no—
337C22×C13—81no—
338C22×C13—81no—
339C22×C13—164no—
340C22×C13—164no—
341C22×C13#50912yescomplemented
342C22×C13C22×D811yescharacteristic
343C2×D13—81no—
344C2×D13—81no—
345C2×D13—81no—
346C4×C13—21no—
347C4×C13—21no—
348C4×C13—21no—
349C4×C13—21no—
350C4×C13—81no—
351C4×C13D4211yescharacteristic
352C4×C13#57611yescharacteristic
353Dic13—42no—
354Dic13—81no—
355Dic13—81no—
356C2×#41—261no—
357C22×Q8—261no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—41no—
361#135—262no—
362#135—521no—
363C2×Q16—131no—
364C2×Q16—131no—
365C2×Q16—262no—
366C2×Q16—261no—
367C2×Q16—521no—
368C2×SD16—261no—
369C2×SD16—261no—
370C2×D8—22no—
371C2×D8—22no—
372C2×D8—21no—
373C2×D8—21no—
374C2×D8—21no—
375C2×D8—41no—
376C2×D8—41no—
377C2×D8—131no—
378C2×D8C22×D1311yescharacteristic
379C2×D8C22×D1311yescharacteristic
380C2×D8C22×D1311yescharacteristic
381C22×C8C22×D1311yescharacteristic
382C22×C8C22×D1311yescharacteristic
383#127—21no—
384#124—261no—
385#124—521no—
386C22⋊Q8—261no—
387C22⋊Q8—521no—
388#121—21no—
389#121—21no—
390#121—41no—
391#121—261no—
392#121—521no—
393#120—41no—
394#120—41no—
395C4×Q8—261no—
396C4×D4—21no—
397C4×D4—521no—
398C4×D4C22⋊D1311yescharacteristic
399SD32—134no—
400SD32—262no—
401SD32—262no—
402SD32—262no—
403SD32—262no—
404SD32—521no—
405D16—262no—
406D16—262no—
407D16—521no—
408M32—262no—
409C2×C16—131no—
410C2×C16—131no—
411C2×C16—131no—
412C2×C16—131no—
413C2×C16—262no—
414#107—131no—
415#107C22×D1311yescharacteristic
416C4⋊C8C22⋊D1311yescharacteristic
417#103—261no—
418#103—261no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—261no—
423C22⋊C8C22⋊D1311yescharacteristic
424C22⋊C8C22⋊D1311yescharacteristic
425C4×C8C22×D1311yescharacteristic
426C2×C13—22no—
427C2×C13—41no—
428C2×C13—82no—
429C2×C13—161no—
430C2×C13—161no—
431C2×C13D4×D811yescharacteristic
432C2×C13C2×#50911yescharacteristic
433C2×C13#341611yescharacteristic
434D13—161no—
435C24—41no—
436C24—41no—
437#41—522no—
438#41—1041no—
439C2×Q8—261no—
440C2×Q8—261no—
441C2×Q8—522no—
442C2×Q8—521no—
443C2×Q8—1041no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—81no—
456C2×D4—81no—
457C2×D4—84no—
458C2×D4—261no—
459C2×D4—521no—
460C2×D4—521no—
461C2×D4#610411yescharacteristic
462C22×C4—41no—
463C22×C4—521no—
464C22×C4—521no—
465C22×C4C2×C22⋊D1311yescharacteristic
466C22×C4C2×C22⋊D1311yescharacteristic
467Q16—132no—
468Q16—261no—
469Q16—261no—
470Q16—261no—
471Q16—522no—
472SD16—522no—
473SD16—1041no—
474D8—21no—
475D8—21no—
476D8—21no—
477D8—21no—
478D8—21no—
479D8—42no—
480D8—42no—
481D8—81no—
482D8—261no—
483D8—261no—
484D8D4×D1312yes—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8C2×C22⋊D1311yescharacteristic
490C2×C8C2×C22⋊D1311yescharacteristic
491C2×C8C2×C22⋊D1311yescharacteristic
492C2×C8C23×D1311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—261no—
495C4⋊C4—521no—
496C4⋊C4—521no—
497C4⋊C4#610411yescharacteristic
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—521no—
502C22⋊C4—521no—
503C22⋊C4—521no—
504C22⋊C4—521no—
505C22⋊C4#610411yescharacteristic
506C22⋊C4#610411yescharacteristic
507C42—521no—
508C42C2×C22⋊D1311yescharacteristic
509C16—132no—
510C16—261no—
511C16—261no—
512C16—261no—
513C13#3383111yescharacteristic, complemented, Sylow
514C23—41no—
515C23—41no—
516C23—41no—
517C23—82no—
518C23—82no—
519C23—82no—
520C23—82no—
521C23—161no—
522C23—161no—
523C23—521no—
524C23C2×#610411yescharacteristic
525C23C2×#610411yescharacteristic
526Q8—262no—
527Q8—521no—
528Q8—521no—
529Q8—521no—
530Q8—1042no—
531D4—22no—
532D4—22no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—82no—
539D4—82no—
540D4—82no—
541D4—82no—
542D4—82no—
543D4—161no—
544D4—521no—
545D4—521no—
546D4—1042no—
547D4—1042no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—82no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—1042no—
558C2×C4—1042no—
559C2×C4C2×#610411yescharacteristic
560C2×C4C2×#610411yescharacteristic
561C2×C4C2×#610411yescharacteristic
562C2×C4C2×#610411yescharacteristic
563C2×C4C22×C22⋊D1311yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8C2×D4×D1311yescharacteristic
568C8#8825111yescharacteristic
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—164no—
584C22—164no—
585C22—1041no—
586C22—1041no—
587C22—1041no—
588C22#1171880812yescomplemented
589C22C22×#610411yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—81no—
595C4—522no—
596C4—1041no—
597C4—1041no—
598C4D4×C22⋊D1311yescharacteristic
599C4#1171954011yescharacteristic
600C2—22no—
601C2—41no—
602C2—82no—
603C2—161no—
604C2—161no—
605C2—2081no—
606C2D4×#610411yescharacteristic
607C2C2×#1171880811yescharacteristic
608C2#1312798311yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingD4×C13×D8C2
socleC22×C13C22×D8
hypercenterD4×D8D13
hypocenterC13#33831
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×#88067C2semidirect
3. #13126579C2semidirect
4. #13117100C2semidirect
5. #13116947C2semidirect
6. #13116920C2semidirect
7. #13116891C2semidirect
8. #13116873C2semidirect
9. #13116765C2semidirect
10. #13116757C2semidirect
11. #13116752C2semidirect
12. #13116748C2semidirect
13. #13116700C2semidirect
14. #13116662C2semidirect
15. D4×C13×D8C2semidirect
19. C22×Dic52C22semidirect
20. C2×#88158C22semidirect
33. C2×#88067C22semidirect
34. C2×#88067C22semidirect
35. C2×#88067C22semidirect
36. C2×#88067C22semidirect
39. C2×#88066C22semidirect
40. C2×#88066C22semidirect
41. #11718777C22semidirect
42. #11718776C22semidirect
43. C2×#88052C22semidirect
44. C22×#6090C22semidirect
48. C4×Dic52C22semidirect
49. #11718357C22semidirect
51. #11718154C22semidirect
52. #11718154C22semidirect
53. C22⋊#6090C22semidirect
54. C22⋊#6090C22semidirect
55. #11718084C22semidirect
56. #11718084C22semidirect
57. #11718083C22semidirect
58. #11718081C22semidirect
59. C4⋊#6090C22semidirect
60. #11718053C22semidirect
117. #88067D4semidirect
201. Dic52C2×D4semidirect
209. #6090C2×D4semidirect
213. D4×D8D13semidirect
341. C22×C13#509semidirect
513. C13#33831semidirect
588. 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×#880672
#131265792
#131171002
#131169472
#131169202
#131168912
#131168732
#131167652
#131167572
#131167522
#131167482
#131167002
#131166622
D4×C13×D82
#3383113