Finite Group Databasebeta

← #16809579

Subgroups — #16809579

Order 3328.

1930 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131766C213yesmaximal, complemented
2#13131763C213yesmaximal, complemented
3#13131758C213yesmaximal, complemented
4#13131754C211yesmaximal, characteristic, complemented
5#13131739C211yesmaximal, characteristic, complemented
6#13131738C211yesmaximal, characteristic, complemented
7#13131733C213yesmaximal, complemented
8#13131678C213yesmaximal, complemented
9#13131677C213yesmaximal, complemented
10#13131647C213yesmaximal, complemented
11#13131642C211yesmaximal, characteristic, complemented
12Q8×#6118C211yesmaximal, characteristic, complemented
13Q8×#6122C211yesmaximal, characteristic, complemented
14D13⋊#446C213yesmaximal, complemented
15#13128045C211yesmaximal, characteristic
16C2×#88254C411yescharacteristic
17C13×#519C411yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19#11719279C413yes—
20#11719279C411yescharacteristic
21C4×#6131C2211yescharacteristic
22C4×#6131C2213yes—
23#11719277C411yescharacteristic
24#11719277C413yes—
25C4×Q8×D13C2213yes—
26C4×Q8×D13C2211yescharacteristic
27#11719228C413yes—
28#11719228C413yes—
29#11719227C2213yes—
30#11719227C2213yes—
31#11719158C2213yes—
32#11719158C2213yes—
33#11719158C2213yes—
34#11719158C2213yes—
35Q8×#1057C2211yescharacteristic
36Q8×#1057C2211yescharacteristic
37Q8×#1057C2211yescharacteristic
38Q8×#1057C2211yescharacteristic
39#11719130C2213yes—
40#11719129C2213yes—
41#11719125C2213yes—
42C4×#6122C2213yes—
43#11719080C2213yes—
44#11719080C2213yes—
45#11719080C2213yes—
46#11719080C2213yes—
47#11719078C2213yes—
48#11719078C2216yes—
49#11719078C2213yes—
50#11719075C2213yes—
51#11719075C2213yes—
52#11719075C2216yes—
53#11719073C2213yes—
54#11719073C2213yes—
55#11719073C2213yes—
56#11719073C2213yes—
57#11719066C2211yescharacteristic
58#11719066C2213yes—
59#11719065C2213yes—
60#11719065C2213yes—
61#11719065C2216yes—
62#11719055C2216yes—
63#11719054C2216yes—
64#11719054C2213yes—
65#11719052C2213yes—
66#11719051C2213yes—
67#11719051C2213yes—
68D13⋊(C4⋊C8)C2213yes—
69D13⋊(C4⋊C8)C2216yes—
70#11719049C2213yes—
71C4×#6118C2213yes—
72#11719047C2216yes—
73C4×D13⋊C8C2213yes—
74C22×Q8×C13C2×C411yescharacteristic
75#88254—28no—
76C2×#6131C2×C413yes—
77C2×#6131C2×C411yescharacteristic
78C2×Q8×D13C2×C411yescharacteristic
79C2×Q8×D13C2×C413yes—
80C2×#6127C2×C413yes—
81C2×#6127C2×C413yes—
82C2×#6122C2311yescharacteristic
83C2×#6122C2313yes—
84C2×#6118C2311yescharacteristic
85C2×#6118C2313yes—
86C2×D13⋊C8C2313yes—
87C2×D13⋊C8C2313yes—
88C2×D13⋊C8C2316yes—
89C4×Q8×C13C2×C413yes—
90C4×Q8×C13C2×C411yescharacteristic
91C4×Q8×C13C2×C413yes—
92C4×Q8×C13C2×C411yescharacteristic
93C13×#117C2×C413yes—
94C13×#117C2×C413yes—
95Q8×Dic13C2×C413yes—
96Q8×Dic13C2×C411yescharacteristic
97Q8×Dic13C2311yescharacteristic
98Q8×Dic13C2313yes—
99C2×C4⋊Dic13C2×C413yes—
100C2×C4×Dic13C2313yes—
101#88147C2×C413yes—
102#88147C2×C413yes—
103#88147C2313yes—
104#88147C2313yes—
105#88146C2×C413yes—
106#88146C2×C416yes—
107#88146C2×C413yes—
108C4⋊C4×D13C2×C416yes—
109C4⋊C4×D13C2×C413yes—
110C4⋊C4×D13C2×C413yes—
111#88141C2×C413yes—
112#88141C2×C413yes—
113#88141C2313yes—
114#88141C2313yes—
115#88135C2×C413yes—
116#88135C2×C413yes—
117#88135C2×C416yes—
118#88135C2313yes—
119#88135C2311yescharacteristic
120C4×D52C2×C416yes—
121C4×D52C2×C413yes—
122C4×D52C2×C413yes—
123#88126C2×C413yes—
124#88126C2×C416yes—
125#88126C2×C413yes—
126C42×D13C2313yes—
127C42×D13C2316yes—
128C42×D13C2313yes—
129C4×Dic26C2×C413yes—
130C4×Dic26C2×C416yes—
131C4×Dic26C2×C413yes—
132C22⋊#1057C2311yescharacteristic
133C22⋊#1057C2313yes—
134#88112C2311yescharacteristic
135#88112C2313yes—
136#88112C2313yes—
137#88112C2316yes—
138#88112C2313yes—
139#88111C2313yes—
140#88111C2313yes—
141#88111C2311yescharacteristic
142#88111C2313yes—
143#88111C2316yes—
144#88110C2313yes—
145#88110C2313yes—
146#88110C2316yes—
147#88110C2316yes—
148#88110C2313yes—
149#88110C2313yes—
150C4⋊#1057C2313yes—
151C4⋊#1057C2316yes—
152C4⋊#1057C2313yes—
153C4⋊#1057C2313yes—
154C4⋊#1057C2313yes—
155C4⋊#1057C2313yes—
156C4⋊#1057C2313yes—
157C4×#1057C2311yescharacteristic
158C4×#1057C2313yes—
159C4×#1057C2313yes—
160C4×#1057C2313yes—
161C4×#1057C2313yes—
162C4×#1057C2313yes—
163#60343—131nomaximal, Sylow
164C2×Q8×C13—24no—
165C2×Q8×C13C22×C413yes—
166C2×Q8×C13C22×C411yescharacteristic
167C22×C4×C13C22×C413yes—
168C2×C22⋊D13C22×C413yes—
169C2×C22⋊D13C22×C411yescharacteristic
170C22×Dic13C22×C413yes—
171C22×Dic13C2411yescharacteristic
172#6131—212no—
173#6131M1618yescomplemented
174Q8×D13—24no—
175Q8×D13—212no—
176#6127—212no—
177#6127—212no—
178C2×D52C22×C413yes—
179C2×D52C22×C413yes—
180C2×C4×D13C22×C416yes—
181C2×C4×D13C22×C413yes—
182C2×C4×D13C22×C413yes—
183C2×C4×D13C22×C413yes—
184C2×C4×D13C22×C416yes—
185C2×C4×D13C22×C413yes—
186C2×C4×D13C2413yes—
187C2×C4×D13C2411yescharacteristic
188C2×Dic26C22×C413yes—
189C2×Dic26C22×C413yes—
190#6122—22no—
191#6122—43no—
192C2×#1057C2411yescharacteristic
193C2×#1057C2411yescharacteristic
194C2×#1057C2411yescharacteristic
195C2×#1057C2413yes—
196C2×#1057C2413yes—
197C2×#1057C2413yes—
198C2×#1057C2413yes—
199C2×#1057C2411yescharacteristic
200#6118—22no—
201#6118—43no—
202D13⋊C8—26no—
203D13⋊C8—43no—
204D13⋊C8—46no—
205C13×C4⋊C4C22×C413yes—
206C13×C4⋊C4C22×C413yes—
207C13×C4⋊C4C22×C413yes—
208C13×C4⋊C4C22×C413yes—
209C13×C22⋊C4C22×C413yes—
210C13×C22⋊C4C22×C411yescharacteristic
211C42×C13C22×C416yes—
212C42×C13C22×C413yes—
213C42×C13C22×C413yes—
214#6103C22×C411yescharacteristic
215#6103C22×C413yes—
216#6103C22×C413yes—
217#6103C22×C416yes—
218#6103C22×C413yes—
219C4⋊Dic13C22×C416yes—
220C4⋊Dic13C22×C413yes—
221C4⋊Dic13C22×C413yes—
222#6101C22×C413yes—
223#6101C22×C416yes—
224#6101C22×C413yes—
225#6101C22×C413yes—
226#6101C22×C411yescharacteristic
227C4×Dic13C22×C416yes—
228C4×Dic13C22×C413yes—
229C4×Dic13C22×C413yes—
230C4×Dic13C22×C413yes—
231C4×Dic13C22×C413yes—
232C4×Dic13C2413yes—
233C4×Dic13C2411yescharacteristic
234C4×Dic13C2413yes—
235C4×Dic13C2413yes—
236C4×2−1+4—131no—
237#2990—133no—
238#2990—133no—
239#2989—133no—
240#2988—131no—
241#2984—131no—
242#2984—131no—
243#2983—133no—
244#2970—133no—
245#2970—133no—
246#2965—133no—
247C8×#41—131no—
248Q8×M16—131no—
249Q8×M16—131no—
250C2×#446—133no—
251C23×C13C23×C411yescharacteristic
252C22×D13C23×C411yescharacteristic
253C22×D13C23×C413yes—
254Q8×C13—26no—
255Q8×C13C2×M1614yes—
256C2×C4×C13—26no—
257C2×C4×C13C23×C413yes—
258C2×C4×C13C23×C411yescharacteristic
259C2×C4×C13C23×C413yes—
260C2×C4×C13C23×C411yescharacteristic
261C2×C4×C13C23×C413yes—
262C2×C4×C13C23×C413yes—
263C22⋊D13—26no—
264C22⋊D13—22no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—43no—
268C2×Dic13C23×C411yescharacteristic
269C2×Dic13C23×C413yes—
270C2×Dic13C23×C413yes—
271C2×Dic13C23×C413yes—
272C2×Dic13C23×C411yescharacteristic
273C2×Dic13C2511yescharacteristic
274D52—26no—
275D52C2×M16112yes—
276C4×D13—212no—
277C4×D13—26no—
278C4×D13—23no—
279C4×D13—21no—
280C4×D13—23no—
281C4×D13—21no—
282C4×D13—43no—
283C4×D13—46no—
284C4×D13—43no—
285C4×D13C2×M16112yes—
286Dic26—26no—
287Dic26—26no—
288#1057—23no—
289#1057—21no—
290#1057—21no—
291#1057—21no—
292#1057—23no—
293#1057—23no—
294#1057—23no—
295#10572−1+412yescomplemented
296C2×2−1+4—131no—
297#520—131no—
298#520—133no—
299#520—133no—
300#520—133no—
301#519—133no—
302#519—131no—
303#519#26111yescharacteristic
304C4×#41—131no—
305C4×#41—133no—
306C4×#41—133no—
307C4×#41—133no—
308C2×C4×Q8—131no—
309C2×C4×Q8—133no—
310C2×C4×Q8—131no—
311#446—133no—
312#446—133no—
313#446—133no—
314#446—136no—
315#446—133no—
316#446—133no—
317#446—133no—
318#446—133no—
319#446—133no—
320#446—133no—
321#446—133no—
322C8×Q8—131no—
323C8×Q8—131no—
324C8×Q8—131no—
325C8×Q8—131no—
326#436—131no—
327#436—133no—
328#435—133no—
329#435—133no—
330#435—133no—
331#435—133no—
332#435—136no—
333#435—136no—
334C8×D4—133no—
335C8×D4—133no—
336C8×D4—133no—
337C8×D4—133no—
338#432—136no—
339#432—133no—
340#432—136no—
341#432—133no—
342#431—133no—
343#431—133no—
344#431—133no—
345#431—133no—
346#423—133no—
347#423—133no—
348C2×C4⋊C8—133no—
349C2×C4⋊C8—136no—
350C4×M16—133no—
351C4×M16—133no—
352C2×#97—136no—
353C2×C4×C8—133no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13—21no—
357C22×C13C24×C411yescharacteristic
358C2×D13—23no—
359C2×D13—23no—
360C2×D13—21no—
361C2×D13—21no—
362C2×D13—21no—
363C2×D13C22×M1616yes—
364C4×C13—23no—
365C4×C13—21no—
366C4×C13—23no—
367C4×C13—21no—
368C4×C13—23no—
369C4×C13C22×M1616yes—
370Dic13—21no—
371Dic13—23no—
372Dic13—23no—
373Dic13—23no—
374Dic13C22×M1612yes—
375Dic13C2×2−1+411yescharacteristic
376Dic13#58511yescharacteristic
3772−1+4—268no—
378C2×#41—131no—
379C2×#41—133no—
380C2×#41—133no—
381C2×#41—133no—
382C22×Q8—133no—
383C22×Q8—131no—
384C22×Q8C2×#26111yescharacteristic
385C2×M16—131no—
386C2×M16—131no—
387C2×M16—133no—
388C2×M16—133no—
389C22×C8—133no—
390C22×C8—133no—
391C22×C8—136no—
392C4×Q8—131no—
393C4×Q8—133no—
394C4×Q8—133no—
395C4×Q8—131no—
396C4×Q8—133no—
397C4×Q8—133no—
398C4×Q8—133no—
399C4×Q8—133no—
400C4×Q8—136no—
401C4×Q8—133no—
402C4×Q8—133no—
403C4×Q8C2×#26113yes—
404C4×Q8C2×#26111yescharacteristic
405C4×Q8C2×#26113yes—
406C4×Q8C2×#26111yescharacteristic
407C4×D4—133no—
408C4×D4—133no—
409C4×D4—133no—
410C4×D4—133no—
411C4×D4—133no—
412C4×D4—131no—
413C4×D4—133no—
414C4×D4—133no—
415C4×D4—136no—
416C4×D4—133no—
417C4×D4—133no—
418C4×D4—136no—
419#117—133no—
420#117—133no—
421#117—136no—
422#117—133no—
423#117—133no—
424#117—136no—
425#117C2×#26113yes—
426#117C2×#26113yes—
427C2×C4⋊C4—133no—
428C2×C4⋊C4—133no—
429C2×C4⋊C4—136no—
430C2×C4⋊C4—133no—
431C2×C42—133no—
432C2×C42—133no—
433C2×C42—136no—
434C2×C42—133no—
435C4⋊C8—133no—
436C4⋊C8—133no—
437C4⋊C8—133no—
438C4⋊C8—136no—
439C4⋊C8—133no—
440C4⋊C8—133no—
441C4⋊C8—133no—
442C4⋊C8—133no—
443C4⋊C8—133no—
444C4⋊C8—136no—
445C4⋊C8—131no—
446C4⋊C8—133no—
447C22⋊C8—131no—
448C22⋊C8—133no—
449C22⋊C8—133no—
450C22⋊C8—136no—
451C22⋊C8—133no—
452C22⋊C8—131no—
453C22⋊C8—133no—
454#97—133no—
455#97—133no—
456#97—136no—
457#97—136no—
458#97—133no—
459#97—133no—
460C4×C8—131no—
461C4×C8—133no—
462C4×C8—133no—
463C4×C8—133no—
464C4×C8—133no—
465C4×C8—133no—
466C2×C13—41no—
467C2×C13C4×2−1+411yescharacteristic
468C2×C13C23×M1611yescharacteristic
469C2×C13#357311yescharacteristic
470D13—26no—
471D13—41no—
472#41—138no—
473#41—2612no—
474#41—2612no—
475#41—2612no—
476C2×Q8—24no—
477C2×Q8—133no—
478C2×Q8—133no—
479C2×Q8—2612no—
480C2×Q8—264no—
481C2×Q8C22×#26113yes—
482C2×Q8C22×#26111yescharacteristic
483C2×D4—131no—
484C2×D4—133no—
485C2×D4—133no—
486C2×D4—133no—
487C22×C4—133no—
488C22×C4—131no—
489C22×C4—133no—
490C22×C4—133no—
491C22×C4—131no—
492C22×C4—136no—
493C22×C4—133no—
494C22×C4—133no—
495C22×C4—136no—
496C22×C4—133no—
497C22×C4C22×#26113yes—
498M16—262no—
499M16—262no—
500M16—523no—
501M16—523no—
502C2×C8—131no—
503C2×C8—131no—
504C2×C8—131no—
505C2×C8—131no—
506C2×C8—133no—
507C2×C8—133no—
508C2×C8—133no—
509C2×C8—133no—
510C2×C8—266no—
511C2×C8—523no—
512C2×C8—526no—
513C4⋊C4—133no—
514C4⋊C4—136no—
515C4⋊C4—133no—
516C4⋊C4—136no—
517C4⋊C4—133no—
518C4⋊C4—133no—
519C4⋊C4—131no—
520C4⋊C4—133no—
521C4⋊C4C22×#26113yes—
522C4⋊C4C22×#26113yes—
523C4⋊C4C22×#26113yes—
524C4⋊C4C22×#26113yes—
525C22⋊C4—133no—
526C22⋊C4—131no—
527C22⋊C4—136no—
528C22⋊C4—133no—
529C22⋊C4—133no—
530C22⋊C4C22×#26113yes—
531C22⋊C4C22×#26111yescharacteristic
532C42—131no—
533C42—133no—
534C42—133no—
535C42—133no—
536C42—133no—
537C42—133no—
538C42—133no—
539C42—136no—
540C42—133no—
541C42C22×#26116yes—
542C42C22×#26113yes—
543C42C22×#26113yes—
544C13#6034311yescharacteristic, complemented, Sylow
545C23—133no—
546C23—131no—
547C23C23×#26111yescharacteristic
548Q8—26no—
549Q8—266no—
550Q8—266no—
551Q8D13⋊M1614yes—
552D4—1312no—
553D4—266no—
554D4—262no—
555D4—266no—
556C2×C4—26no—
557C2×C4—131no—
558C2×C4—131no—
559C2×C4—1312no—
560C2×C4—131no—
561C2×C4—133no—
562C2×C4—133no—
563C2×C4—133no—
564C2×C4—263no—
565C2×C4—263no—
566C2×C4—261no—
567C2×C4—261no—
568C2×C4—2612no—
569C2×C4—261no—
570C2×C4—261no—
571C2×C4—266no—
572C2×C4—523no—
573C2×C4—526no—
574C2×C4—523no—
575C2×C4—523no—
576C2×C4C23×#26113yes—
577C2×C4C23×#26111yescharacteristic
578C2×C4C23×#26113yes—
579C2×C4C23×#26111yescharacteristic
580C2×C4C23×#26113yes—
581C2×C4C23×#26113yes—
582C8—132no—
583C8—263no—
584C8—261no—
585C8—263no—
586C8—263no—
587C8—263no—
588C8—261no—
589C8—261no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—136no—
594C22—263no—
595C22—263no—
596C22—261no—
597C22—261no—
598C22—261no—
599C22C24×#26111yescharacteristic
600C4—23no—
601C4—21no—
602C4—23no—
603C4—21no—
604C4—23no—
605C4—131no—
606C4—131no—
607C4—132no—
608C4—261no—
609C4—263no—
610C4—263no—
611C4—263no—
612C4C2×D13⋊M1616yes—
613C2—41no—
614C2—266no—
615C2—521no—
616C22−1+4×#26111yescharacteristic
617C2C22×D13⋊M1611yescharacteristic
618C2#1313183211yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#519C4
prime radicalC2×#88254C4
cosocleC2×Dic13C25
hypercenter#519#261
hypocenterC13#60343
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
1. #13131766C2semidirect
2. #13131763C2semidirect
3. #13131758C2semidirect
4. #13131754C2semidirect
5. #13131739C2semidirect
6. #13131738C2semidirect
7. #13131733C2semidirect
8. #13131678C2semidirect
9. #13131677C2semidirect
10. #13131647C2semidirect
11. #13131642C2semidirect
12. Q8×#6118C2semidirect
13. Q8×#6122C2semidirect
14. D13⋊#446C2semidirect
173. #6131M16semidirect
295. #10572−1+4semidirect
544. C13#60343semidirect

Maximal subgroups

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

subgroupindex
#131317662
#131317632
#131317582
#131317542
#131317392
#131317382
#131317332
#131316782
#131316772
#131316472
#131316422
Q8×#61182
Q8×#61222
D13⋊#4462
#131280452
#6034313