Finite Group Databasebeta

← #15869747

Subgroups — #15869747

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124442C211yesmaximal, characteristic
2C2×#11718805C211yesmaximal, characteristic, complemented
3#13123539C211yesmaximal, characteristic, complemented
4C2×M16×Dic13C211yesmaximal, characteristic, complemented
5#13115728C211yesmaximal, characteristic, complemented
6#13115586C211yesmaximal, characteristic, complemented
7#13115543C211yesmaximal, characteristic, complemented
8#13115539C211yesmaximal, characteristic, complemented
9#13115280C211yesmaximal, characteristic, complemented
10#13115277C211yesmaximal, characteristic, complemented
11#13114876C211yesmaximal, characteristic, complemented
12#13114716C211yesmaximal, characteristic, complemented
13#13114682C211yesmaximal, characteristic, complemented
14#13114678C211yesmaximal, characteristic, complemented
15C13×#2930C211yesmaximal, characteristic, complemented
16C2×C13×#131C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C13×#525C2211yescharacteristic
19C2×#88204C2211yescharacteristic
20#11719496C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23C2×#88155C2211yescharacteristic
24C13×#436—22no—
25C13×#435—22no—
26C13×#424C2211yescharacteristic
27C13×#408C2211yescharacteristic
28C13×#407C2211yescharacteristic
29C13×#405C2211yescharacteristic
30C2×#88077C2211yescharacteristic
31C2×#88077C2211yescharacteristic
32#11718894C2211yescharacteristic
33#11718868C2211yescharacteristic
34#11718805—24no—
35C2×#88065C2211yescharacteristic
36C2×#88065C2211yescharacteristic
37#11718789—22no—
38#11718788—22no—
39C2×#88062C2211yescharacteristic
40C2×#88062C2211yescharacteristic
41M16×Dic13—24no—
42#11718771C2211yescharacteristic
43#11718763C2211yescharacteristic
44#11718762C2211yescharacteristic
45C2×#88055C2211yescharacteristic
46C2×#88055C2211yescharacteristic
47C2×C8×Dic13C2211yescharacteristic
48C2×C8×Dic13C2211yescharacteristic
49#11718713C412yescomplemented
50#11718710C412yescomplemented
51#11718703C412yescomplemented
52#11718700C412yescomplemented
53#11718663C2211yescharacteristic
54#11718659C2211yescharacteristic
55#11718150C2211yescharacteristic
56#11718150C2211yescharacteristic
57#11718147C2211yescharacteristic
58#11718147C2211yescharacteristic
59#11718124C2211yescharacteristic
60#11718124C2211yescharacteristic
61C2×C13×#41C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13—21no—
64C2×#6127C2311yescharacteristic
65C13×#131—22no—
66C13×#131—22no—
67C2×C13×M16—22no—
68C2×C13×M16—21no—
69C2×C13×M16—22no—
70C2×C13×M16D412yes—
71C2×C13×M16D412yes—
72C2×C13×M16C2311yescharacteristic
73C2×C13×M16C2311yescharacteristic
74C22×C8×C13—21no—
75C22×C8×C13C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C13×#123—21no—
78C13×C22⋊Q8C2×C412yes—
79C13×#121C2×C412yes—
80C13×#120—21no—
81C4×D4×C13—22no—
82C13×#117C2311yescharacteristic
83#88207—21no—
84#88204—22no—
85#88204—22no—
86C2×#6107C2×C411yescharacteristic, complemented
87C2×#6106C2×C411yescharacteristic, complemented
88C2×#6105C2×C411yescharacteristic, complemented
89C2×#6104C2×C411yescharacteristic, complemented
90#88184C2×C412yes—
91#88183—21no—
92C4×C22⋊D13—22no—
93#88180C2311yescharacteristic
94#88178C2×C412yes—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×#6099—22no—
101C2×#6099—22no—
102C2×#6099C2×C412yes—
103C2×#6099C2×C412yes—
104C2×#6099C2311yescharacteristic
105C2×#6099C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88155—22no—
109#88155—22no—
110C2×#6094—21no—
111C2×C8×D13—21no—
112C13×C4⋊C8—22no—
113C13×C22⋊C8—22no—
114C13×C22⋊C8—22no—
115C13×#97—21no—
116C4×C8×C13—21no—
117#88077—22no—
118#88077—22no—
119#88075C2×C412yescomplemented
120#88072C2×C412yescomplemented
121C22⋊#1055—22no—
122#88065—22no—
123#88065—22no—
124#88062—22no—
125#88062—22no—
126#88060—22no—
127#88055—22no—
128#88055—21no—
129#88055—22no—
130#88054—22no—
131C8×Dic13—21no—
132C8×Dic13—22no—
133C8×Dic13D414yescomplemented
134#88050C2×C412yescomplemented
135#88049C2×C412yescomplemented
136#88048C2×C412yescomplemented
137#88047C2×C412yescomplemented
138#21549—131nomaximal, Sylow
139C24×C13#4111yescharacteristic
140C13×#41—21no—
141C13×#41—21no—
142C13×#41—21no—
143C13×#41—21no—
144C2×Q8×C13C22×C411yescharacteristic
145C2×D4×C13—21no—
146C2×D4×C13—22no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C22×C412yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13#4111yescharacteristic
156C22×C4×C13C2411yescharacteristic
157C2×C22⋊D13—21no—
158C2×C22⋊D13—22no—
159C22×Dic13—21no—
160C22×Dic13—24no—
161C22×Dic13—21no—
162C22×Dic13—44no—
163#6127—21no—
164#6127—21no—
165#6127—21no—
166#6127—21no—
167C2×D52C22×C411yescharacteristic
168C2×C4×D13—21no—
169C2×Dic26C22×C411yescharacteristic
170C13×M16—24no—
171C13×M16—24no—
172C13×M16—21no—
173C13×M16—21no—
174C13×M16—21no—
175C13×M16—21no—
176C13×M16—42no—
177C2×C8×C13—21no—
178C2×C8×C13—21no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13—42no—
182C2×C8×C13C2×D412yes—
183C2×C8×C13C2×D412yes—
184C2×C8×C13C2×D411yescharacteristic
185C2×C8×C13C2×D411yescharacteristic
186C2×C8×C13#4112yes—
187C13×C4⋊C4—22no—
188C13×C4⋊C4C22×C412yes—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—22no—
192C42×C13—21no—
193C22⋊Dic13—22no—
194C22⋊Dic13—21no—
195#6107—22no—
196#6106—22no—
197#6105—22no—
198#6104—22no—
199#6103—22no—
200C4⋊Dic13C22×C412yes—
201#6101—22no—
202C4×Dic13—24no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13C2×D412yes—
207C4×Dic13#4112yes—
208#6099—24no—
209#6099—24no—
210#6099—21no—
211#6099—21no—
212#6099—21no—
213#6099—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055C22×C412yes—
219C2×#1055C22×C411yescharacteristic
220C2×#1055C22×C411yescharacteristic
221C2×#1055C2×D412yes—
222C2×#1055#4112yes—
223#6094—42no—
224C8×D13—42no—
225#3054—131no—
226C2×#443—131no—
227#2930—131no—
228#2930D1311yescharacteristic, complemented
229C2×C4×M16—131no—
230#1975—131no—
231#1946—131no—
232#1937—131no—
233#1937—131no—
234#1896—131no—
235#1896—131no—
236#1811—131no—
237#1772—131no—
238#1765—131no—
239#1765—131no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—42no—
244C23×C13C4×D412yes—
245C23×C13C2×#4111yescharacteristic
246C22×D13—21no—
247Q8×C13—21no—
248Q8×C13—21no—
249D4×C13—21no—
250D4×C13—21no—
251D4×C13—41no—
252D4×C13—41no—
253D4×C13—82no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—21no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13C4×D412yes—
265C2×C4×C13C23×C411yescharacteristic
266C2×C4×C13C22×D411yescharacteristic
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C22⋊D13—41no—
272C22⋊D13—41no—
273C22⋊D13—82no—
274C2×Dic13—24no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—21no—
278C2×Dic13—22no—
279C2×Dic13—48no—
280C2×Dic13—42no—
281D52—21no—
282D52—21no—
283C4×D13—41no—
284C4×D13—41no—
285Dic26—21no—
286Dic26—21no—
287C8×C13—22no—
288C8×C13—41no—
289C8×C13—41no—
290C8×C13#12112yes—
291C8×C13#12112yes—
292#1055—22no—
293#1055—41no—
294#1055—41no—
295#1055C4×D412yes—
296#1055C4×D412yes—
297C2×#135—131no—
298C2×#131—131no—
299C2×#131C2×D1311yescharacteristic
300C22×M16—131no—
301C22×M16C2×D1311yescharacteristic
302#525—131no—
303#525C2×D1311yescharacteristic
304C22×C42—131no—
305#470—132no—
306#469—132no—
307#468—132no—
308#468—132no—
309#443—264no—
310#436—22no—
311#436—262no—
312#435—22no—
313#435—262no—
314C2×#108—131no—
315C2×#108—131no—
316#427—131no—
317#424—131no—
318#424C2×D1311yescharacteristic
319C2×#104—131no—
320C2×#104—131no—
321C2×#104—131no—
322C2×#104—131no—
323#416—131no—
324#416—131no—
325#408—131no—
326#408C2×D1311yescharacteristic
327#407—131no—
328#407C2×D1311yescharacteristic
329#405—131no—
330#405C2×D1311yescharacteristic
331C4×M16—264no—
332C2×#97—131no—
333C2×#97—131no—
334C2×C4×C8—131no—
335C2×C4×C8—131no—
336#341—131no—
337#341—131no—
338#339—131no—
339#339—131no—
340#339—131no—
341#339—131no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—41no—
350C22×C13C2×C4×D411yescharacteristic
351C22×C13#52511yescharacteristic
352C22×C13#52911yescharacteristic
353C2×D13—42no—
354C2×D13—41no—
355C4×C13—22no—
356C4×C13—42no—
357C4×C13—41no—
358C4×C13C2×C4×D411yescharacteristic
359C4×C13C4×#4111yescharacteristic
360C4×C13C2×#12111yescharacteristic
361C4×C13#53211yescharacteristic
362Dic13—24no—
363Dic13—42no—
364Dic13—42no—
365Dic13—41no—
366C2×#41—131no—
367C2×#41C22×D1311yescharacteristic
368C23×C4—261no—
369C23×C4C22×D1311yescharacteristic
370#135—262no—
371#135—262no—
372C2×Q16—131no—
373C2×SD16—131no—
374C2×SD16—131no—
375C2×D8—131no—
376#131—22no—
377#131—22no—
378#131—262no—
379#131—262no—
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—21no—
383C2×M16—132no—
384C2×M16—132no—
385C2×M16—131no—
386C2×M16—131no—
387C2×M16—262no—
388C2×M16—262no—
389C2×M16—261no—
390C2×M16C22⋊D1312yes—
391C2×M16C22⋊D1312yes—
392C2×M16C22×D1311yescharacteristic
393C2×M16C22×D1311yescharacteristic
394C22×C8—21no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—261no—
398C22×C8C22×D1311yescharacteristic
399C22×C8C22×D1311yescharacteristic
400#123—21no—
401#123—261no—
402C22⋊Q8—132no—
403C22⋊Q8C4×D1312yes—
404#121—132no—
405#121C4×D1312yes—
406#120—21no—
407#120—261no—
408C4×D4—22no—
409C4×D4—262no—
410#117—131no—
411#117C22×D1311yescharacteristic
412C2×C42—131no—
413C2×C42—131no—
414C2×C42—262no—
415C2×C42—262no—
416C2×C42—261no—
417#108—262no—
418#108—262no—
419#107—132no—
420#106—132no—
421C4⋊C8—22no—
422C4⋊C8—262no—
423#104—262no—
424#104—262no—
425#104—262no—
426#104—262no—
427#103—132no—
428#103—132no—
429#102—132no—
430#102—132no—
431C22⋊C8—22no—
432C22⋊C8—22no—
433C22⋊C8—262no—
434C22⋊C8—262no—
435#97—21no—
436#97—262no—
437#97—262no—
438#97—261no—
439C4×C8—21no—
440C4×C8—134no—
441C4×C8—262no—
442C4×C8—261no—
443C2×C13—21no—
444C2×C13—21no—
445C2×C13—42no—
446C2×C13—81no—
447C2×C13C4×#12111yescharacteristic
448C2×C13#295612yes—
449D13—81no—
450C24#612711yescharacteristic
451#41—21no—
452#41—21no—
453#41—21no—
454#41—21no—
455#41—261no—
456#41—261no—
457#41—261no—
458#41—261no—
459C2×Q8—131no—
460C2×Q8C2×C4×D1311yescharacteristic
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—131no—
464C2×D4—261no—
465C2×D4—262no—
466C2×D4C2×C4×D1311yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—261no—
473C22×C4—264no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—524no—
477C22×C4C2×C4×D1312yes—
478C22×C4#612711yescharacteristic
479C22×C4C2×C22⋊D1312yes—
480C22×C4C23×D1311yescharacteristic
481Q16—262no—
482SD16—262no—
483SD16—262no—
484D8—262no—
485M16—24no—
486M16—24no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—42no—
492M16—264no—
493M16—264no—
494M16—261no—
495M16—261no—
496M16—261no—
497M16—261no—
498M16—522no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—42no—
504C2×C8—131no—
505C2×C8—131no—
506C2×C8—132no—
507C2×C8—132no—
508C2×C8—132no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—522no—
514C2×C8D4×D1312yes—
515C2×C8#612912yes—
516C2×C8C2×C22⋊D1312yes—
517C2×C8C2×C22⋊D1311yescharacteristic
518C2×C8C2×C22⋊D1311yescharacteristic
519C4⋊C4—22no—
520C4⋊C4—132no—
521C4⋊C4—262no—
522C4⋊C4C2×C4×D1312yes—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—262no—
527C22⋊C4—261no—
528C22⋊C4—262no—
529C42—21no—
530C42—132no—
531C42—132no—
532C42—264no—
533C42—261no—
534C42—261no—
535C42—261no—
536C13#2154911yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—42no—
541C23—261no—
542C23C4×C22⋊D1312yes—
543C23C2×#612711yescharacteristic
544Q8—21no—
545Q8—21no—
546Q8—261no—
547Q8—261no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—82no—
553D4—261no—
554D4—261no—
555D4—521no—
556D4—521no—
557D4—1042no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—264no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—261no—
572C2×C4—262no—
573C2×C4—528no—
574C2×C4—522no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4C4×C22⋊D1312yes—
578C2×C4C22×C4×D1311yescharacteristic
579C2×C4C2×D4×D1311yescharacteristic
580C2×C4C2×#612911yescharacteristic
581C2×C4#41×D1311yescharacteristic
582C2×C4#41×D1311yescharacteristic
583C2×C4C22×C22⋊D1311yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—132no—
588C8—132no—
589C8—262no—
590C8—521no—
591C8—521no—
592C8#8819312yes—
593C8#8819312yes—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—41no—
602C22—522no—
603C22—521no—
604C22#1171924311yescharacteristic
605C22#1171925211yescharacteristic
606C22C2×C4×C22⋊D1311yescharacteristic
607C4—22no—
608C4—42no—
609C4—41no—
610C4—264no—
611C4—522no—
612C4—522no—
613C4—521no—
614C4C4×#612911yescharacteristic
615C4C4×D4×D1311yescharacteristic
616C4C2×#8819311yescharacteristic
617C4#1171953711yescharacteristic
618C2—21no—
619C2—21no—
620C2—42no—
621C2—81no—
622C2—1041no—
623C2C4×#8819311yescharacteristic
624C2#1312374312yes—
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2930C2
socleC22×C13C2×C4×D4
prime radical#13124442C2
cosocleC22×C4×C13C24
hypercenter#2930D13
hypocenterC13#21549
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. C2×#11718805C2semidirect
3. #13123539C2semidirect
4. C2×M16×Dic13C2semidirect
5. #13115728C2semidirect
6. #13115586C2semidirect
7. #13115543C2semidirect
8. #13115539C2semidirect
9. #13115280C2semidirect
10. #13115277C2semidirect
11. #13114876C2semidirect
12. #13114716C2semidirect
13. #13114682C2semidirect
14. #13114678C2semidirect
15. C13×#2930C2semidirect
49. #11718713C4semidirect
50. #11718710C4semidirect
51. #11718703C4semidirect
52. #11718700C4semidirect
86. C2×#6107C2×C4semidirect
87. C2×#6106C2×C4semidirect
88. C2×#6105C2×C4semidirect
89. C2×#6104C2×C4semidirect
119. #88075C2×C4semidirect
120. #88072C2×C4semidirect
133. C8×Dic13D4semidirect
134. #88050C2×C4semidirect
135. #88049C2×C4semidirect
136. #88048C2×C4semidirect
137. #88047C2×C4semidirect
228. #2930D13semidirect
536. C13#21549semidirect

Maximal subgroups

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

subgroupindex
#131244422
C2×#117188052
#131235392
C2×M16×Dic132
#131157282
#131155862
#131155432
#131155392
#131152802
#131152772
#131148762
#131147162
#131146822
#131146782
C13×#29302
#2154913