Finite Group Databasebeta

← D13×#3499 #16771327

Subgroups — D13×#3499 #16771327

Order 3328.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×2−1+4C212yesmaximal, complemented
2#13128621C211yesmaximal, characteristic, complemented
3#13128620C214yesmaximal, complemented
4#13128619C213yesmaximal, complemented
5#13128618C216yesmaximal, complemented
6#13128617C212yesmaximal, complemented
7#13128616C213yesmaximal, complemented
8#13128615C2112yesmaximal, complemented
9D4×Q8×D13C214yesmaximal, complemented
10D13×#547C2112yesmaximal, complemented
11D13×#536C216yesmaximal, complemented
12D13×#532C213yesmaximal, complemented
13C2×D13×C4⋊Q8C213yesmaximal, complemented
14C4×#41×D13C211yesmaximal, characteristic, complemented
15C13×#3499C211yesmaximal, characteristic, complemented
16C2×C13×2−1+4C2212yescomplemented
17D13×2−1+4—232no—
18C2×#88257C22112yescomplemented
19C2×#88257C2216yescomplemented
20C2×#88257C2212yescomplemented
21C2×#41×D13C22112yes—
22C2×#41×D13C2216yes—
23C2×#41×D13C2211yescharacteristic
24C2×#88254C2216yescomplemented
25C2×#88254C2214yescomplemented
26C22×Q8×D13C2214yes—
27C22×Q8×D13C2216yes—
28D4×Q8×C13C2214yescomplemented
29C13×#547C22112yescomplemented
30C13×#536C2216yescomplemented
31C13×#532C2213yescomplemented
32C2×C13×C4⋊Q8C2213yescomplemented
33C4×C13×#41C2211yescharacteristic, complemented
34#11719537C2216yescomplemented
35#41×Dic13C2211yescharacteristic, complemented
36#11719530C2216yescomplemented
37#11719529C22124yescomplemented
38#11719521C2216yescomplemented
39Q8×C22⋊D13C2218yescomplemented
40C2×#88198C2216yescomplemented
41#11719432C22112yescomplemented
42#11719431C22112yescomplemented
43#11719430C2213yescomplemented
44#11719429C22112yescomplemented
45D13×C4⋊Q8C22112yes—
46D13×C4⋊Q8C2213yes—
47D13×C4⋊Q8C2216yes—
48D13×C4⋊Q8C22112yescomplemented
49D13×C4⋊Q8C2216yescomplemented
50D13×C4⋊Q8C2216yescomplemented
51#11719421C2213yescomplemented
52D13×#127C2211yescharacteristic
53#11719380C22112yescomplemented
54D13×#124C2216yes—
55#11719373C2216yescomplemented
56#11719360C22148yescomplemented
57D13×#123C22124yes—
58#11719353C22124yescomplemented
59#11719337C22124yescomplemented
60#11719336C22124yescomplemented
61#11719333C22124yescomplemented
62D13×C22⋊Q8C22124yes—
63#11719316C22124yescomplemented
64D13×#121C22112yes—
65#11719301C22112yescomplemented
66Q8×D52C2214yescomplemented
67C4×#6131C2212yescomplemented
68C4×Q8×D13C2212yes—
69#11719260C22112yescomplemented
70#11719256C22112yescomplemented
71#11719253C22112yescomplemented
72C4×D4×D13C2216yes—
73C4×D4×D13C22112yes—
74D4×Dic26C22112yescomplemented
75C4×#6129C2216yescomplemented
76#11719231C2216yescomplemented
77#11719227C2213yescomplemented
78D13×#117C2213yes—
79#11719212C22124yescomplemented
80C2×C4⋊C4×D13C22112yes—
81C2×#88142C22112yescomplemented
82#11719182C2213yescomplemented
83C4×#6127C2213yescomplemented
84C2×C42×D13C2213yes—
85C2×#88123C2213yescomplemented
86C13×2−1+4—216no—
87C2×C13×#41C23112yes—
88C2×C13×#41C2316yes—
89C2×C13×#41C2311yescharacteristic
90C22×Q8×C13C2316yes—
91C22×Q8×C13C2314yes—
92#88257—216no—
93#88257—296no—
94#88257—248no—
95#41×D13—296no—
96#41×D13—248no—
97#41×D13D4116yescomplemented
98#88254—232no—
99#88254—248no—
100C2×#6131C2316yes—
101C2×#6131C23112yes—
102C2×#6131C2311yescharacteristic
103C2×Q8×D13—232no—
104C2×Q8×D13—248no—
105C2×Q8×D13C2316yes—
106C2×Q8×D13C23112yes—
107C2×Q8×D13C23112yes—
108C2×Q8×D13C23112yes—
109C2×Q8×D13C23112yes—
110C2×Q8×D13C2314yes—
111C2×Q8×D13C2311yescharacteristic
112C2×#6129C23112yes—
113C2×#6129C23112yes—
114C2×#6129C23124yes—
115C2×#6129C2316yes—
116C2×#6129C2313yes—
117C2×D4×D13C2314yes—
118C2×D4×D13C23112yes—
119C2×D4×D13C2312yes—
120C2×D4×D13C2313yes—
121C2×#6127C2316yes—
122C2×#6127C23124yes—
123C2×#6127C23112yes—
124C2×#6127C23112yes—
125C2×#6127C2313yes—
126C22×C4×D13C2316yes—
127C22×C4×D13C23112yes—
128C22×C4×D13C23112yes—
129C22×C4×D13C2313yes—
130C22×Dic26C2316yes—
131C22×Dic26C23112yes—
132C22×Dic26C23112yes—
133C13×C4⋊Q8C2313yes—
134C13×C4⋊Q8C2316yes—
135C13×C4⋊Q8C23112yes—
136C13×#127C2311yescharacteristic
137C13×#124C2316yes—
138C13×#123C23124yes—
139C13×C22⋊Q8C23124yes—
140C13×#121C23112yes—
141C4×Q8×C13C2312yes—
142C4×D4×C13C2316yes—
143C4×D4×C13C23112yes—
144C13×#117C2313yes—
145C2×C13×C4⋊C4C23112yes—
146C2×C42×C13C2313yes—
147#88201C2316yes—
148#88200C23124yes—
149Q8×Dic13C2312yes—
150#88198C2316yes—
151#88198C23112yes—
152#88198C23124yes—
153#88194C2314yes—
154#88194C2312yes—
155#88193C23124yes—
156#88192C23112yes—
157#88190C2316yes—
158#88189C23124yes—
159D4×Dic13C2316yes—
160D4×Dic13C23112yes—
161#88184C23112yes—
162#88183C23124yes—
163C4×C22⋊D13C23112yes—
164C4×C22⋊D13C23124yes—
165#88180C2313yes—
166C2×C4⋊Dic13C23112yes—
167#88178C23124yes—
168C2×#6101C23124yes—
169C2×C4×Dic13C2316yes—
170C2×C4×Dic13C2313yes—
171#88151C23124yes—
172#88150C23148yes—
173#88149C23112yes—
174#88148C23148yes—
175#88147C23112yes—
176#88147C2316yes—
177#88146C2316yes—
178C4⋊C4×D13C23112yes—
179C4⋊C4×D13C23124yes—
180C4⋊C4×D13C23124yes—
181C4⋊C4×D13C23124yes—
182C4⋊C4×D13C2316yes—
183#88142C23112yes—
184#88142C23124yes—
185#88142C23124yes—
186#88142C23124yes—
187#88141C2316yes—
188#88140C23124yes—
189#88139C23124yes—
190#88138C23124yes—
191#88137C23148yes—
192#88135C23112yes—
193#88135C23124yes—
194C22⋊C4×D13C2316yes—
195C22⋊C4×D13C23124yes—
196#88132C23148yes—
197#88131C2316yes—
198#88129C2316yes—
199#88128C2311yescharacteristic
200C4×D52C2316yes—
201C4×D52C23112yes—
202#88126C2316yes—
203C42×D13C2311yescharacteristic
204C42×D13C2313yes—
205C42×D13C2316yes—
206C42×D13C2313yes—
207C42×D13C2313yes—
208C42×D13C2316yes—
209#88123C2313yes—
210#88123C2316yes—
211#88123C23112yes—
212C4×Dic26C2316yes—
213C2×#3499—131nomaximal, Sylow
214C23×D13C2414yes—
215C23×D13C2413yes—
216C13×#41—248no—
217C13×#41—224no—
218C13×#41C2×D418yescomplemented
219C2×Q8×C13—216no—
220C2×Q8×C13—224no—
221C2×Q8×C13C2416yes—
222C2×Q8×C13C24112yes—
223C2×Q8×C13C2411yescharacteristic
224C2×D4×C13C2414yes—
225C2×D4×C13C24112yes—
226C2×D4×C13C2412yes—
227C2×D4×C13C2413yes—
228C22×C4×C13C2416yes—
229C22×C4×C13C24112yes—
230C22×C4×C13C24112yes—
231C22×C4×C13C2413yes—
232C2×C22⋊D13C2418yes—
233C2×C22⋊D13C24112yes—
234C2×C22⋊D13C2414yes—
235C2×C22⋊D13C24112yes—
236C2×C22⋊D13C2416yes—
237C22×Dic13C24112yes—
238C22×Dic13C2416yes—
239C22×Dic13C24112yes—
240C22×Dic13C2413yes—
241#6131—248no—
242#6131—224no—
243#6131C2×D418yescomplemented
244Q8×D13—216no—
245Q8×D13—248no—
246Q8×D13—224no—
247Q8×D13—248no—
248Q8×D13—248no—
249Q8×D13—248no—
250Q8×D13C2×D418yes—
251#6129—248no—
252#6129—296no—
253#6129—248no—
254#6129—224no—
255#6129C2×D4124yescomplemented
256D4×D13—248no—
257D4×D13—28no—
258D4×D13—216no—
259D4×D13C2×D4124yes—
260#6127—224no—
261#6127—296no—
262#6127—248no—
263#6127—248no—
264#6127C2×D4124yescomplemented
265C2×D52C2414yes—
266C2×D52C2412yes—
267C2×D52C24112yes—
268C2×D52C2413yes—
269C2×C4×D13—248no—
270C2×C4×D13—248no—
271C2×C4×D13—224no—
272C2×C4×D13C2×D4124yes—
273C2×C4×D13C2416yes—
274C2×C4×D13C2416yes—
275C2×C4×D13C2416yes—
276C2×C4×D13C24112yes—
277C2×C4×D13C24112yes—
278C2×C4×D13C24112yes—
279C2×C4×D13C24124yes—
280C2×C4×D13C2411yescharacteristic
281C2×C4×D13C2413yes—
282C2×C4×D13C2413yes—
283C2×C4×D13C2413yes—
284C2×C4×D13C2412yes—
285C2×Dic26—224no—
286C2×Dic26—248no—
287C2×Dic26—248no—
288C2×Dic26C2416yes—
289C2×Dic26C24112yes—
290C2×Dic26C24124yes—
291C2×Dic26C24112yes—
292C2×Dic26C2413yes—
293C13×C4⋊C4C2416yes—
294C13×C4⋊C4C24112yes—
295C13×C4⋊C4C24124yes—
296C13×C22⋊C4C2416yes—
297C13×C22⋊C4C24124yes—
298C42×C13C2416yes—
299C42×C13C2411yescharacteristic
300C42×C13C2413yes—
301C22⋊Dic13C2416yes—
302C22⋊Dic13C24124yes—
303#6103C24112yes—
304#6103C24124yes—
305#6103C24124yes—
306C4⋊Dic13C2416yes—
307C4⋊Dic13C24112yes—
308C4⋊Dic13C24124yes—
309#6101C24112yes—
310#6101C24148yes—
311#6101C24124yes—
312C4×Dic13C2416yes—
313C4×Dic13C2412yes—
314C4×Dic13C2411yescharacteristic
315C4×Dic13C2413yes—
316C4×Dic13C2416yes—
317C4×Dic13C2416yes—
318C4×Dic13C2416yes—
319C22×2−1+4—132no—
320#3499—132no—
321#3499—134no—
322#3499—1312no—
323#3499—136no—
324#3499—133no—
325#3499—133no—
326#3499—131no—
327#3499D1311yescharacteristic, direct product factor
328C2×D4×Q8—134no—
329C2×#547—1312no—
330C2×#536—136no—
331C2×#532—133no—
332C22×C4⋊Q8—133no—
333C2×C4×#41—131no—
334C23×C13C2514yes—
335C23×C13C2513yes—
336C22×D13—212no—
337C22×D13—28no—
338C22×D13—216no—
339C22×D13C22×D4112yes—
340C22×D13C2514yes—
341C22×D13C2513yes—
342C22×D13C2511yescharacteristic
343Q8×C13—212no—
344Q8×C13—224no—
345Q8×C13C22×D414yes—
346D4×C13—224no—
347D4×C13—24no—
348D4×C13—28no—
349D4×C13C22×D4112yes—
350C2×C4×C13—224no—
351C2×C4×C13—224no—
352C2×C4×C13—212no—
353C2×C4×C13C22×D4112yes—
354C2×C4×C13C2516yes—
355C2×C4×C13C25112yes—
356C2×C4×C13C2511yescharacteristic
357C2×C4×C13C2513yes—
358C2×C4×C13C2512yes—
359C22⋊D13—224no—
360C22⋊D13—224no—
361C22⋊D13—28no—
362C22⋊D13—216no—
363C22⋊D13C22×D4124yes—
364C2×Dic13—224no—
365C2×Dic13—224no—
366C2×Dic13—212no—
367C2×Dic13C22×D4112yes—
368C2×Dic13C2516yes—
369C2×Dic13C25112yes—
370C2×Dic13C2511yescharacteristic
371C2×Dic13C2513yes—
372C2×Dic13C2512yes—
373D52—224no—
374D52—24no—
375D52—28no—
376D52C22×D4112yes—
377C4×D13—224no—
378C4×D13—248no—
379C4×D13—212no—
380C4×D13—224no—
381C4×D13—212no—
382C4×D13—224no—
383C4×D13—212no—
384C4×D13C22×D4112yes—
385C4×D13C22×D414yes—
386C4×D13C22×D4112yes—
387C4×D13C22×D4112yes—
388C4×D132−1+418yescomplemented
389Dic26—212no—
390Dic26—224no—
391Dic26—224no—
392Dic26—248no—
393Dic26C22×D4112yes—
394C2×2−1+4—136no—
395C2×2−1+4—1312no—
396C2×2−1+4—132no—
397C2×2−1+4—134no—
398C2×2−1+4—136no—
399C2×2−1+4—2632no—
400C2×2−1+4C2×D1312yescomplemented
401C22×#41—131no—
402C22×#41—136no—
403C22×#41—1312no—
404C23×Q8—136no—
405C23×Q8—134no—
406D4×Q8—138no—
407D4×Q8—1312no—
408D4×Q8—1324no—
409D4×Q8—134no—
410D4×Q8—1312no—
411D4×Q8C2×D1314yescomplemented
412#547—1324no—
413#547—1312no—
414#547—1348no—
415#547—1324no—
416#547—1324no—
417#547—1312no—
418#547—1312no—
419#547—1324no—
420#547C2×D13112yescomplemented
421#536—136no—
422#536—136no—
423#536—1312no—
424#536—1312no—
425#536—1324no—
426#536—1324no—
427#536—136no—
428#536C2×D1316yescomplemented
429#532—136no—
430#532—133no—
431#532—133no—
432#532—136no—
433#532—1312no—
434#532—1312no—
435#532—133no—
436#532C2×D1313yescomplemented
437C2×C4⋊Q8—136no—
438C2×C4⋊Q8—133no—
439C2×C4⋊Q8—136no—
440C2×C4⋊Q8—1312no—
441C2×C4⋊Q8—136no—
442C2×C4⋊Q8—136no—
443C2×C4⋊Q8—1312no—
444C2×C4⋊Q8—1312no—
445C2×C4⋊Q8—133no—
446C2×C4⋊Q8C2×D1313yescomplemented
447C2×#127—131no—
448C2×#124—136no—
449C2×#123—1324no—
450C2×C22⋊Q8—1324no—
451C2×#121—1312no—
452C4×#41—131no—
453C4×#41—132no—
454C4×#41—136no—
455C4×#41—133no—
456C4×#41—133no—
457C4×#41C2×D1311yescharacteristic, complemented
458C2×C4×Q8—132no—
459C2×C4×D4—136no—
460C2×C4×D4—1312no—
461C2×#117—133no—
462C22×C4⋊C4—1312no—
463C22×C42—133no—
464C22×C13—26no—
465C22×C13—24no—
466C22×C13—28no—
467C22×C13C23×D416yes—
468C22×C13C2611yescharacteristic
469C2×D13—26no—
470C2×D13—224no—
471C2×D13—24no—
472C2×D13—28no—
473C2×D13—416no—
474C2×D13C23×D416yes—
475C2×D13C23×D412yes—
476C2×D13C2×2−1+414yes—
477C4×C13—212no—
478C4×C13—26no—
479C4×C13C23×D412yes—
480C4×C13C23×D416yes—
481C4×C13C2×2−1+414yescomplemented
482Dic13—212no—
483Dic13—26no—
484Dic13C23×D412yes—
485Dic13C23×D416yes—
486Dic13C2×2−1+414yescomplemented
4872−1+4—216no—
4882−1+4—2632no—
4892−1+4—2648no—
4902−1+4—2696no—
4912−1+4—2648no—
4922−1+4—2616no—
493C2×#41—1316no—
494C2×#41—131no—
495C2×#41—136no—
496C2×#41—1312no—
497C2×#41—133no—
498C2×#41—1312no—
499C2×#41—136no—
500C2×#41—1312no—
501C2×#41—1324no—
502C2×#41—133no—
503C2×#41—1312no—
504C2×#41—136no—
505C2×#41—1312no—
506C2×#41—1324no—
507C2×#41—2648no—
508C2×#41—2696no—
509C2×#41C22×D1316yes—
510C2×#41C22×D13112yes—
511C2×#41C22×D1311yescharacteristic
512C22×Q8—131no—
513C22×Q8—1312no—
514C22×Q8—136no—
515C22×Q8—1312no—
516C22×Q8—1312no—
517C22×Q8—1312no—
518C22×Q8—134no—
519C22×Q8—1312no—
520C22×Q8—136no—
521C22×Q8—1312no—
522C22×Q8—2648no—
523C22×Q8—2632no—
524C22×Q8C22×D1316yes—
525C22×Q8C22×D1314yes—
526C22×D4—133no—
527C22×D4—134no—
528C22×D4—1312no—
529C22×D4—132no—
530C23×C4—133no—
531C23×C4—136no—
532C23×C4—1312no—
533C23×C4—1312no—
534C4⋊Q8—136no—
535C4⋊Q8—1312no—
536C4⋊Q8—1324no—
537C4⋊Q8—1312no—
538C4⋊Q8—1324no—
539C4⋊Q8—1324no—
540C4⋊Q8—1324no—
541C4⋊Q8—133no—
542C4⋊Q8—136no—
543C4⋊Q8—1312no—
544C4⋊Q8C22×D1313yes—
545C4⋊Q8C22×D1316yes—
546C4⋊Q8C22×D13112yes—
547#127—132no—
548#127—134no—
549#127—131no—
550#127C22×D1311yescharacteristic
551#124—136no—
552#124—136no—
553#124—1324no—
554#124—136no—
555#124C22×D1316yes—
556#123—1324no—
557#123—1324no—
558#123—1348no—
559#123—1348no—
560#123—1324no—
561#123C22×D13124yes—
562C22⋊Q8—1324no—
563C22⋊Q8—1324no—
564C22⋊Q8—1348no—
565C22⋊Q8—1324no—
566C22⋊Q8—1348no—
567C22⋊Q8C22×D13124yes—
568#121—1312no—
569#121—1324no—
570#121—1312no—
571#121—1312no—
572#121—1324no—
573#121C22×D13112yes—
574C4×Q8—132no—
575C4×Q8—136no—
576C4×Q8—136no—
577C4×Q8C22×D1312yes—
578C4×D4—136no—
579C4×D4—1312no—
580C4×D4—1312no—
581C4×D4—1324no—
582C4×D4—136no—
583C4×D4—1312no—
584C4×D4—1312no—
585C4×D4—1324no—
586C4×D4—136no—
587C4×D4—1312no—
588C4×D4C22×D1316yes—
589C4×D4C22×D13112yes—
590#117—133no—
591#117—136no—
592#117—136no—
593#117—136no—
594#117C22×D1313yes—
595C2×C4⋊C4—1324no—
596C2×C4⋊C4—1312no—
597C2×C4⋊C4—1312no—
598C2×C4⋊C4—1324no—
599C2×C4⋊C4—1324no—
600C2×C4⋊C4—1324no—
601C2×C4⋊C4—136no—
602C2×C4⋊C4C22×D13112yes—
603C2×C22⋊C4—136no—
604C2×C22⋊C4—1324no—
605C2×C42—136no—
606C2×C42—133no—
607C2×C42—133no—
608C2×C42—136no—
609C2×C42—136no—
610C2×C42—133no—
611C2×C42—133no—
612C2×C42—131no—
613C2×C42C22×D1313yes—
614C2×C13—26no—
615C2×C13—44no—
616C2×C13C24×D411yescharacteristic
617C2×C13C22×2−1+412yes—
618D13—26no—
619D13—44no—
620D13#349914yesdirect product factor
621C24—133no—
622C24—134no—
623#41—248no—
624#41—224no—
625#41—138no—
626#41—1324no—
627#41—1324no—
628#41—2648no—
629#41—2696no—
630#41—2648no—
631#41—2648no—
632#41—2624no—
633#41—2624no—
634#41—2696no—
635#41—2648no—
636#41—2648no—
637#41—2624no—
638#41D4×D1318yescomplemented
639C2×Q8—216no—
640C2×Q8—224no—
641C2×Q8—138no—
642C2×Q8—133no—
643C2×Q8—1324no—
644C2×Q8—1312no—
645C2×Q8—1312no—
646C2×Q8—136no—
647C2×Q8—2648no—
648C2×Q8—2648no—
649C2×Q8—2624no—
650C2×Q8—2648no—
651C2×Q8—2648no—
652C2×Q8—2648no—
653C2×Q8—2648no—
654C2×Q8—2616no—
655C2×Q8—2624no—
656C2×Q8C23×D13112yes—
657C2×Q8C23×D1316yes—
658C2×Q8C23×D1311yescharacteristic
659C2×D4—136no—
660C2×D4—1324no—
661C2×D4—138no—
662C2×D4—1312no—
663C2×D4—1312no—
664C2×D4—134no—
665C2×D4—133no—
666C2×D4—134no—
667C2×D4—1312no—
668C2×D4—132no—
669C2×D4—268no—
670C2×D4—2616no—
671C2×D4—2648no—
672C2×D4C23×D1314yes—
673C2×D4C23×D13112yes—
674C2×D4C23×D1312yes—
675C2×D4C23×D1313yes—
676C22×C4—133no—
677C22×C4—1324no—
678C22×C4—132no—
679C22×C4—131no—
680C22×C4—133no—
681C22×C4—133no—
682C22×C4—133no—
683C22×C4—136no—
684C22×C4—1312no—
685C22×C4—1312no—
686C22×C4—136no—
687C22×C4—136no—
688C22×C4—136no—
689C22×C4—1312no—
690C22×C4—1324no—
691C22×C4—1312no—
692C22×C4—1312no—
693C22×C4—2648no—
694C22×C4—2624no—
695C22×C4—2648no—
696C22×C4C23×D1316yes—
697C22×C4C23×D13112yes—
698C22×C4C23×D13112yes—
699C22×C4C23×D1313yes—
700C4⋊C4—1324no—
701C4⋊C4—1312no—
702C4⋊C4—1348no—
703C4⋊C4—1324no—
704C4⋊C4—1312no—
705C4⋊C4—136no—
706C4⋊C4C23×D13112yes—
707C4⋊C4C23×D13124yes—
708C4⋊C4C23×D1316yes—
709C22⋊C4—136no—
710C22⋊C4—1324no—
711C22⋊C4—1312no—
712C22⋊C4—1324no—
713C22⋊C4—1324no—
714C22⋊C4C23×D1316yes—
715C22⋊C4C23×D13124yes—
716C42—131no—
717C42—132no—
718C42—136no—
719C42—133no—
720C42—136no—
721C42—136no—
722C42—136no—
723C42C23×D1311yescharacteristic
724C42C23×D1313yes—
725C42C23×D1316yes—
726C13C2×#349911yescharacteristic, complemented, Sylow
727C23—131no—
728C23—1312no—
729C23—133no—
730C23—134no—
731C23—2612no—
732C23—268no—
733C23—2616no—
734C23C24×D1314yes—
735C23C24×D1313yes—
736Q8—224no—
737Q8—212no—
738Q8—1312no—
739Q8—2624no—
740Q8—2648no—
741Q8—2624no—
742Q8—2612no—
743Q8C2×D4×D1314yes—
744D4—224no—
745D4—24no—
746D4—28no—
747D4—1324no—
748D4—1312no—
749D4—2624no—
750D4—2616no—
751D4—268no—
752D4—2624no—
753D4—2624no—
754D4—264no—
755D4—268no—
756D4C2×D4×D13112yes—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—212no—
760C2×C4—1312no—
761C2×C4—132no—
762C2×C4—131no—
763C2×C4—133no—
764C2×C4—134no—
765C2×C4—1312no—
766C2×C4—1312no—
767C2×C4—1312no—
768C2×C4—138no—
769C2×C4—136no—
770C2×C4—1312no—
771C2×C4—2612no—
772C2×C4—2624no—
773C2×C4—2612no—
774C2×C4—2624no—
775C2×C4—2648no—
776C2×C4—2612no—
777C2×C4—2624no—
778C2×C4—2624no—
779C2×C4—2624no—
780C2×C4—2612no—
781C2×C4C2×D4×D13112yes—
782C2×C4C24×D1316yes—
783C2×C4C24×D13112yes—
784C2×C4C24×D1311yescharacteristic
785C2×C4C24×D1313yes—
786C2×C4C24×D1312yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—132no—
791C22—134no—
792C22—136no—
793C22—2624no—
794C22—266no—
795C22—264no—
796C22—268no—
797C22—5216no—
798C22C22×D4×D1316yes—
799C22C25×D1311yescharacteristic
800C4—212no—
801C4—26no—
802C4—132no—
803C4—136no—
804C4—134no—
805C4—2612no—
806C4—266no—
807C4C22×D4×D1316yes—
808C4C22×D4×D1312yes—
809C4D13×2−1+414yescomplemented
810C2—26no—
811C2—44no—
812C2—134no—
813C2—266no—
814C2—524no—
815C2C23×D4×D1311yescharacteristic
816C2C2×D13×2−1+412yes—
subgroupG/H
center, FrattiniC22C25×D13
commutator, socle, cosocleC22×C13C26
FittingC13×#3499C2
hypercenter#3499D13
hypocenterC13C2×#3499
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×D13×2−1+4C2semidirect
2. #13128621C2semidirect
3. #13128620C2semidirect
4. #13128619C2semidirect
5. #13128618C2semidirect
6. #13128617C2semidirect
7. #13128616C2semidirect
8. #13128615C2semidirect
9. D4×Q8×D13C2semidirect
10. D13×#547C2semidirect
11. D13×#536C2semidirect
12. D13×#532C2semidirect
13. C2×D13×C4⋊Q8C2semidirect
14. C4×#41×D13C2semidirect
15. C13×#3499C2semidirect
16. C2×C13×2−1+4C22semidirect
18. C2×#88257C22semidirect
19. C2×#88257C22semidirect
20. C2×#88257C22semidirect
24. C2×#88254C22semidirect
25. C2×#88254C22semidirect
28. D4×Q8×C13C22semidirect
29. C13×#547C22semidirect
30. C13×#536C22semidirect
31. C13×#532C22semidirect
32. C2×C13×C4⋊Q8C22semidirect
33. C4×C13×#41C22semidirect
34. #11719537C22semidirect
35. #41×Dic13C22semidirect
36. #11719530C22semidirect
37. #11719529C22semidirect
38. #11719521C22semidirect
39. Q8×C22⋊D13C22semidirect
40. C2×#88198C22semidirect
41. #11719432C22semidirect
42. #11719431C22semidirect
43. #11719430C22semidirect
44. #11719429C22semidirect
48. D13×C4⋊Q8C22semidirect
49. D13×C4⋊Q8C22semidirect
50. D13×C4⋊Q8C22semidirect
51. #11719421C22semidirect
53. #11719380C22semidirect
55. #11719373C22semidirect
56. #11719360C22semidirect
58. #11719353C22semidirect
59. #11719337C22semidirect
60. #11719336C22semidirect
61. #11719333C22semidirect
63. #11719316C22semidirect
65. #11719301C22semidirect
66. Q8×D52C22semidirect
67. C4×#6131C22semidirect
69. #11719260C22semidirect
70. #11719256C22semidirect
71. #11719253C22semidirect
74. D4×Dic26C22semidirect
75. C4×#6129C22semidirect
76. #11719231C22semidirect
77. #11719227C22semidirect
79. #11719212C22semidirect
81. C2×#88142C22semidirect
82. #11719182C22semidirect
83. C4×#6127C22semidirect
85. C2×#88123C22semidirect
97. #41×D13D4semidirect
218. C13×#41C2×D4semidirect
243. #6131C2×D4semidirect
255. #6129C2×D4semidirect
264. #6127C2×D4semidirect
327. #3499D13direct (N × H)
388. C4×D132−1+4semidirect
400. C2×2−1+4C2×D13semidirect
411. D4×Q8C2×D13semidirect
420. #547C2×D13semidirect
428. #536C2×D13semidirect
436. #532C2×D13semidirect
446. C2×C4⋊Q8C2×D13semidirect
457. C4×#41C2×D13semidirect
481. C4×C13C2×2−1+4semidirect
486. Dic13C2×2−1+4semidirect
620. D13#3499direct (N × H)
638. #41D4×D13semidirect
726. C13C2×#3499semidirect
809. C4D13×2−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×D13×2−1+42
#131286212
#131286202
#131286192
#131286182
#131286172
#131286162
#131286152
D4×Q8×D132
D13×#5472
D13×#5362
D13×#5322
C2×D13×C4⋊Q82
C4×#41×D132
C13×#34992
C2×#349913