Finite Group Databasebeta

← #15869748

Subgroups — #15869748

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×#11718485C211yesmaximal, characteristic, complemented
3#13123540C211yesmaximal, characteristic, complemented
4#13123535C211yesmaximal, characteristic, complemented
5C2×C4×#6099C211yesmaximal, characteristic, complemented
6#13115726C211yesmaximal, characteristic, complemented
7#13115588C211yesmaximal, characteristic, complemented
8#13115541C211yesmaximal, characteristic, complemented
9#13115537C211yesmaximal, characteristic, complemented
10#13115279C211yesmaximal, characteristic, complemented
11#13114876C211yesmaximal, characteristic, complemented
12#13114714C211yesmaximal, characteristic, complemented
13#13114681C211yesmaximal, characteristic, complemented
14#13114677C211yesmaximal, characteristic, complemented
15C13×#1896C211yesmaximal, characteristic, complemented
16C13×#525C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C2×#88204C2211yescharacteristic
19C2×#88202C2211yescharacteristic
20#11719496C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23C2×#88161C2211yescharacteristic
24C2×C13×#104C2211yescharacteristic
25C2×C13×#104C2211yescharacteristic
26C13×#407C2211yescharacteristic
27#11718895C2211yescharacteristic
28#11718894C2211yescharacteristic
29#11718868C2211yescharacteristic
30#11718790C2211yescharacteristic
31C2×#88062C2211yescharacteristic
32C2×#88062C2211yescharacteristic
33#11718783C2211yescharacteristic
34#11718780C2211yescharacteristic
35#11718713C412yescomplemented
36#11718710C412yescomplemented
37#11718703C412yescomplemented
38#11718700C412yescomplemented
39#11718673—22no—
40#11718672—22no—
41#11718663C2211yescharacteristic
42#11718660C2211yescharacteristic
43#11718659C2211yescharacteristic
44#11718658C2211yescharacteristic
45C2×#88045C2211yescharacteristic
46C2×#88045C2211yescharacteristic
47C4×#6099—24no—
48C2×#88043C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51C2×C4×#1055C2211yescharacteristic
52#11718485—24no—
53#11718390—22no—
54#11718389—22no—
55C13×#339C2211yescharacteristic
56C13×#339C2211yescharacteristic
57#11718150C2211yescharacteristic
58#11718150C2211yescharacteristic
59#11718115C2211yescharacteristic
60#11718115C2211yescharacteristic
61C2×C13×#41C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C2×#6127C2311yescharacteristic
65C2×C13×M16C2311yescharacteristic
66C2×C13×M16C2311yescharacteristic
67C13×#123—21no—
68C13×C22⋊Q8C2×C412yes—
69C13×#121C2×C412yes—
70C13×#120—21no—
71C4×D4×C13—22no—
72C13×#117C2311yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13—22no—
75C2×C42×C13—22no—
76C2×C42×C13C2311yescharacteristic
77C2×C42×C13C2311yescharacteristic
78#88207—21no—
79#88204—22no—
80#88204—22no—
81#88202—22no—
82#88202—22no—
83C2×#6107C2×C411yescharacteristic, complemented
84C2×#6106C2×C411yescharacteristic, complemented
85C2×#6105C2×C411yescharacteristic, complemented
86C2×#6104C2×C411yescharacteristic, complemented
87#88184C2×C412yes—
88#88183—21no—
89C4×C22⋊D13—22no—
90#88180C2311yescharacteristic
91#88178C2×C412yes—
92C2×#6099—22no—
93C2×#6099—22no—
94C2×#6099—21no—
95C2×#6099—22no—
96C2×#6099—22no—
97C2×#6099C2×C412yes—
98C2×#6099C2×C412yes—
99C2×#6099D412yes—
100C2×#6099D412yes—
101C2×#6099C2311yescharacteristic
102C2×#6099C2311yescharacteristic
103C22×#1055—21no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88161—22no—
109#88161—22no—
110C2×#6094—21no—
111C2×C8×D13—21no—
112C13×#104—22no—
113C13×#104—22no—
114C13×C22⋊C8—22no—
115#88075C2×C412yescomplemented
116#88072C2×C412yescomplemented
117C22⋊#1055—22no—
118C22⋊#1055—22no—
119#88062—22no—
120#88062—22no—
121#88060—22no—
122#88055—21no—
123#88054—22no—
124C8×Dic13—21no—
125#88050C2×C412yescomplemented
126#88049C2×C412yescomplemented
127#88048C2×C412yescomplemented
128#88047C2×C412yescomplemented
129#88045—22no—
130#88045—22no—
131C4⋊#1055—22no—
132#88043—21no—
133#88043—22no—
134#88043—22no—
135C4×#1055—22no—
136C4×#1055—21no—
137C4×#1055D414yescomplemented
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×C13—24no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—44no—
157C22×C4×C13C22×C412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13#4111yescharacteristic
160C22×C4×C13C2411yescharacteristic
161C2×C22⋊D13—21no—
162C2×C22⋊D13—22no—
163#6127—21no—
164#6127—21no—
165#6127—21no—
166#6127—21no—
167C2×D52C22×C411yescharacteristic
168C2×C4×D13—21no—
169C2×Dic26C22×C411yescharacteristic
170C13×M16—21no—
171C13×M16—21no—
172C13×M16—21no—
173C13×M16—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4C22×C412yes—
178C13×C22⋊C4—22no—
179C13×C22⋊C4—21no—
180C13×C22⋊C4—22no—
181C42×C13—24no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13C2×D412yes—
186C42×C13#4112yes—
187C22⋊Dic13—22no—
188C22⋊Dic13—21no—
189#6107—22no—
190#6106—22no—
191#6105—22no—
192#6104—22no—
193#6103—22no—
194C4⋊Dic13C22×C412yes—
195#6101—22no—
196C4×Dic13—21no—
197#6099—24no—
198#6099—24no—
199#6099—24no—
200#6099—24no—
201#6099—21no—
202#6099—21no—
203#6099—21no—
204#6099—21no—
205#6099—42no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—42no—
213C2×#1055C22×C412yes—
214C2×#1055C22×C411yescharacteristic
215C2×#1055C22×C411yescharacteristic
216C2×#1055C2×D412yes—
217C2×#1055C2×D412yes—
218C2×#1055C2×D411yescharacteristic
219C2×#1055C2×D411yescharacteristic
220C2×#1055C2×D412yes—
221C2×#1055#4112yes—
222C2×#1055#4112yes—
223#6094—42no—
224C8×D13—42no—
225#3054—131no—
226C2×#443—131no—
227#2930—131no—
228#2930—131no—
229C2×C4×M16—131no—
230#1975—131no—
231#1946—131no—
232#1937—131no—
233#1937—131no—
234#1896—131no—
235#1896D1311yescharacteristic, complemented
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—24no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—48no—
266C2×C4×C13—42no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13C4×D412yes—
270C2×C4×C13C23×C411yescharacteristic
271C2×C4×C13C22×D411yescharacteristic
272C2×C4×C13C22×D411yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C22⋊D13—41no—
277C22⋊D13—41no—
278C22⋊D13—82no—
279C2×Dic13—22no—
280C2×Dic13—21no—
281D52—21no—
282D52—21no—
283C4×D13—41no—
284C4×D13—41no—
285Dic26—21no—
286Dic26—21no—
287C8×C13—41no—
288C8×C13—41no—
289#1055—22no—
290#1055—22no—
291#1055—41no—
292#1055—41no—
293#1055C4×D412yes—
294#1055C4×D412yes—
295#1055#12112yes—
296#1055#12112yes—
297C2×#135—131no—
298C2×#131—131no—
299C2×#131—131no—
300C22×M16—131no—
301C22×M16—131no—
302#525—131no—
303#525C2×D1311yescharacteristic
304C22×C42C2×D1311yescharacteristic
305#470—132no—
306#469—132no—
307#468—132no—
308#468—132no—
309#443—264no—
310#436—262no—
311#436—262no—
312#435—262no—
313#435—262no—
314C2×#108—131no—
315C2×#108—131no—
316#427—131no—
317#424—131no—
318#424—131no—
319C2×#104—131no—
320C2×#104—131no—
321C2×#104C2×D1311yescharacteristic
322C2×#104C2×D1311yescharacteristic
323#416—131no—
324#416—131no—
325#408—131no—
326#408—131no—
327#407—131no—
328#407C2×D1311yescharacteristic
329#405—131no—
330#405—131no—
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#339C2×D1311yescharacteristic
341#339C2×D1311yescharacteristic
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—24no—
356C4×C13—22no—
357C4×C13—42no—
358C4×C13—42no—
359C4×C13—41no—
360C4×C13C2×C4×D411yescharacteristic
361C4×C13C4×#4111yescharacteristic
362C4×C13C2×#12111yescharacteristic
363C4×C13#53211yescharacteristic
364Dic13—42no—
365Dic13—41no—
366C2×#41—131no—
367C2×#41C22×D1311yescharacteristic
368C23×C4—21no—
369C23×C4C22×D1311yescharacteristic
370#135—262no—
371#135—262no—
372C2×Q16—131no—
373C2×SD16—131no—
374C2×SD16—131no—
375C2×D8—131no—
376#131—262no—
377#131—262no—
378#131—262no—
379#131—262no—
380C2×M16—132no—
381C2×M16—132no—
382C2×M16—132no—
383C2×M16—132no—
384C2×M16—131no—
385C2×M16—131no—
386C2×M16—261no—
387C2×M16—262no—
388C2×M16—262no—
389C2×M16—262no—
390C2×M16—262no—
391C2×M16—261no—
392C2×M16C22×D1311yescharacteristic
393C2×M16C22×D1311yescharacteristic
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—131no—
398C22×C8—261no—
399C22×C8—261no—
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—21no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42C22×D1311yescharacteristic
416C2×C42C22×D1311yescharacteristic
417#108—262no—
418#108—262no—
419#107—132no—
420#106—132no—
421C4⋊C8—262no—
422C4⋊C8—262no—
423#104—22no—
424#104—22no—
425#104—262no—
426#104—262no—
427#103—132no—
428#103—132no—
429#102—132no—
430#102—132no—
431C22⋊C8—22no—
432C22⋊C8—262no—
433C22⋊C8—262no—
434C22⋊C8—262no—
435#97—262no—
436#97—262no—
437#97—261no—
438#97—261no—
439C4×C8—134no—
440C4×C8—261no—
441C4×C8—261no—
442C4×C8—262no—
443C2×C13—21no—
444C2×C13—21no—
445C2×C13—42no—
446C2×C13—81no—
447C2×C13C4×#12111yescharacteristic
448C2×C13#295612yes—
449D13—81no—
450C24#612911yescharacteristic
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—24no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—44no—
476C22×C4—261no—
477C22×C4C2×C4×D1312yes—
478C22×C4D4×D1312yes—
479C22×C4#612911yescharacteristic
480C22×C4C23×D1311yescharacteristic
481Q16—262no—
482SD16—262no—
483SD16—262no—
484D8—262no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—264no—
490M16—264no—
491M16—264no—
492M16—264no—
493M16—261no—
494M16—261no—
495M16—261no—
496M16—261no—
497M16—522no—
498M16—522no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—131no—
502C2×C8—131no—
503C2×C8—132no—
504C2×C8—132no—
505C2×C8—131no—
506C2×C8—131no—
507C2×C8—132no—
508C2×C8—132no—
509C2×C8—132no—
510C2×C8—132no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—522no—
518C2×C8—522no—
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—24no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—261no—
534C42D4×D1312yes—
535C42#612912yes—
536C13#2154911yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—42no—
541C23—261no—
542C23#8813512yes—
543C23C2×#612911yescharacteristic
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—24no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—262no—
574C2×C4—261no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4#8813512yes—
578C2×C4C22×C4×D1311yescharacteristic
579C2×C4C2×D4×D1311yescharacteristic
580C2×C4C2×D4×D1311yescharacteristic
581C2×C4C2×#612911yescharacteristic
582C2×C4#41×D1311yescharacteristic
583C2×C4#41×D1311yescharacteristic
584C8—41no—
585C8—41no—
586C8—132no—
587C8—132no—
588C8—132no—
589C8—132no—
590C8—262no—
591C8—262no—
592C8—521no—
593C8—521no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—41no—
602C22—522no—
603C22—521no—
604C22C2×#8813511yescharacteristic
605C22#1171929111yescharacteristic
606C22#1171935411yescharacteristic
607C4—24no—
608C4—22no—
609C4—42no—
610C4—42no—
611C4—41no—
612C4—522no—
613C4—521no—
614C4C4×#612911yescharacteristic
615C4C4×D4×D1311yescharacteristic
616C4#1171930111yescharacteristic
617C4D13×#12111yescharacteristic
618C2—21no—
619C2—21no—
620C2—42no—
621C2—81no—
622C2—1041no—
623C2#1311734611yescharacteristic
624C2#1312374212yes—
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1896C2
socleC22×C13C2×C4×D4
prime radical#13124442C2
cosocleC22×C4×C13C24
hypercenter#1896D13
hypocenterC13#21549
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C2×#11718485C2semidirect
3. #13123540C2semidirect
4. #13123535C2semidirect
5. C2×C4×#6099C2semidirect
6. #13115726C2semidirect
7. #13115588C2semidirect
8. #13115541C2semidirect
9. #13115537C2semidirect
10. #13115279C2semidirect
11. #13114876C2semidirect
12. #13114714C2semidirect
13. #13114681C2semidirect
14. #13114677C2semidirect
15. C13×#1896C2semidirect
35. #11718713C4semidirect
36. #11718710C4semidirect
37. #11718703C4semidirect
38. #11718700C4semidirect
83. C2×#6107C2×C4semidirect
84. C2×#6106C2×C4semidirect
85. C2×#6105C2×C4semidirect
86. C2×#6104C2×C4semidirect
115. #88075C2×C4semidirect
116. #88072C2×C4semidirect
125. #88050C2×C4semidirect
126. #88049C2×C4semidirect
127. #88048C2×C4semidirect
128. #88047C2×C4semidirect
137. C4×#1055D4semidirect
235. #1896D13semidirect
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×#117184852
#131235402
#131235352
C2×C4×#60992
#131157262
#131155882
#131155412
#131155372
#131152792
#131148762
#131147142
#131146812
#131146772
C13×#18962
#2154913