Finite Group Databasebeta

← D13×#3548 #16770708

Subgroups — D13×#3548 #16770708

Order 3328.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129236C211yesmaximal, characteristic, complemented
2#13129235C214yesmaximal, complemented
3#13129234C212yesmaximal, complemented
4#13129233C214yesmaximal, complemented
5#13129232C214yesmaximal, complemented
6#13129231C218yesmaximal, complemented
7#13129230C214yesmaximal, complemented
8#13129229C214yesmaximal, complemented
9D13×#562C214yesmaximal, complemented
10D13×#554C214yesmaximal, complemented
11D13×#550C214yesmaximal, complemented
12D13×#547C214yesmaximal, complemented
13D13×#540C214yesmaximal, complemented
14D13×#537C218yesmaximal, complemented
15D13×#533C211yesmaximal, characteristic, complemented
16D13×#532C212yesmaximal, complemented
17C13×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D13C2218yes—
19C2×#41×D13C2214yes—
20C13×#562C2214yescomplemented
21C13×#554C2214yescomplemented
22C13×#550C2214yescomplemented
23C13×#547C2214yescomplemented
24C13×#540C2214yescomplemented
25C13×#537C2218yescomplemented
26C13×#533C2211yescharacteristic, complemented
27C13×#532C2212yescomplemented
28#11719539C2218yescomplemented
29#11719538C2218yescomplemented
30#11719538C2218yescomplemented
31#11719537C2214yescomplemented
32#11719529C2218yescomplemented
33#11719435C2214yescomplemented
34#11719433C2212yescomplemented
35#11719431C2214yescomplemented
36#11719430C2212yescomplemented
37D13×C4⋊Q8C2212yes—
38D13×C4⋊Q8C2212yes—
39#11719424C2214yescomplemented
40#11719423C2218yescomplemented
41#11719423C2214yescomplemented
42#11719421C2212yescomplemented
43D13×#127C2212yes—
44D13×#127C2214yes—
45#11719405C2214yescomplemented
46#11719403C2214yescomplemented
47#11719395C2218yescomplemented
48#11719393C2212yescomplemented
49D13×#125C2214yes—
50D13×#125C2212yes—
51#11719389C2218yescomplemented
52D13×#124C2214yes—
53#11719373C2214yescomplemented
54#11719372C22116yescomplemented
55#11719368C22116yescomplemented
56#11719360C22116yescomplemented
57D13×#123C22116yes—
58#11719352C22116yescomplemented
59#11719341C22116yescomplemented
60#11719340C2218yescomplemented
61#11719336C2218yescomplemented
62#11719334C2218yescomplemented
63#11719334C22116yescomplemented
64#11719334C2218yescomplemented
65D13×C22⋊Q8C2218yes—
66D13×C22⋊Q8C22116yes—
67D13×C22⋊Q8C2214yes—
68#11719327C2214yescomplemented
69#11719326C22116yescomplemented
70#11719324C2218yescomplemented
71#11719320C22116yescomplemented
72#11719316C2218yescomplemented
73#11719313C2218yescomplemented
74#11719313C22116yescomplemented
75#11719313C2218yescomplemented
76D13×#121C2218yes—
77D13×#121C22116yes—
78D13×#121C2214yes—
79D13×#121C2214yes—
80D13×#121C22116yes—
81#11719304C22116yescomplemented
82#11719304C2218yescomplemented
83#11719302C22116yescomplemented
84#11719302C22116yescomplemented
85#11719301C2214yescomplemented
86#11719301C2214yescomplemented
87#11719284C2214yescomplemented
88#11719283C2214yescomplemented
89#11719282C2214yescomplemented
90C4×Q8×D13C2214yes—
91#11719267C2218yescomplemented
92#11719260C2214yescomplemented
93#11719258C2218yescomplemented
94#11719258C2214yescomplemented
95#11719256C2214yescomplemented
96#11719253C2214yescomplemented
97#11719253C2214yescomplemented
98C4×D4×D13C2214yes—
99C4×D4×D13C2214yes—
100C4×D4×D13C2218yes—
101#11719248C2214yescomplemented
102#11719244C2218yescomplemented
103#11719240C2214yescomplemented
104D13×#117C2212yes—
105#11719222C2212yescomplemented
106#11719216C2218yescomplemented
107#11719215C2218yescomplemented
108#11719212C2218yescomplemented
109C2×C4⋊C4×D13C2218yes—
110#11719182C2212yescomplemented
111C2×C42×D13C2211yescharacteristic
112#11719175C2211yescharacteristic, complemented
113C2×C13×#41C2318yes—
114C2×C13×#41C2314yes—
115#41×D13—416no—
116#41×D13—432no—
117C2×#6131C2314yes—
118C2×#6131C2318yes—
119C2×Q8×D13C2314yes—
120C2×Q8×D13C2314yes—
121C2×#6129C2318yes—
122C2×#6129C2318yes—
123C2×#6129C2314yes—
124C2×#6129C23116yes—
125C2×D4×D13C2314yes—
126C2×D4×D13C2314yes—
127C2×D4×D13C2318yes—
128C2×D4×D13C23116yes—
129C2×D4×D13C2314yes—
130C2×#6127C2314yes—
131C2×#6127C23116yes—
132C2×#6127C2318yes—
133C2×#6127C2318yes—
134C22×C4×D13C2311yescharacteristic
135C22×C4×D13C2312yes—
136C22×C4×D13C2318yes—
137C22×C4×D13C23116yes—
138C13×C4⋊Q8C2312yes—
139C13×C4⋊Q8C2312yes—
140C13×#127C2314yes—
141C13×#127C2312yes—
142C13×#125C2312yes—
143C13×#125C2314yes—
144C13×#124C2314yes—
145C13×#123C23116yes—
146C13×C22⋊Q8C2314yes—
147C13×C22⋊Q8C2318yes—
148C13×C22⋊Q8C23116yes—
149C13×#121C2314yes—
150C13×#121C2314yes—
151C13×#121C23116yes—
152C13×#121C23116yes—
153C13×#121C2318yes—
154C4×Q8×C13C2314yes—
155C4×D4×C13C2318yes—
156C4×D4×C13C2314yes—
157C4×D4×C13C2314yes—
158C13×#117C2312yes—
159C2×C13×C4⋊C4C2318yes—
160C2×C42×C13C2311yescharacteristic
161#88201C2314yes—
162#88200C2318yes—
163#88200C2314yes—
164#88200C23116yes—
165Q8×Dic13C2314yes—
166#88198C2314yes—
167#88198C2314yes—
168#88194C2314yes—
169#88194C2314yes—
170#88194C2318yes—
171#88194C2314yes—
172#88194C23116yes—
173#88193C23116yes—
174#88193C23116yes—
175#88193C2318yes—
176#88193C2318yes—
177#88193C23116yes—
178#88193C23116yes—
179#88193C23116yes—
180#88192C2314yes—
181#88192C2314yes—
182#88192C2318yes—
183#88192C23116yes—
184#88192C23116yes—
185#88190C2314yes—
186#88189C23116yes—
187D4×Dic13C2318yes—
188D4×Dic13C2314yes—
189D4×Dic13C2314yes—
190#88184C2314yes—
191#88184C2314yes—
192#88184C2318yes—
193#88184C23116yes—
194#88184C23116yes—
195#88183C23116yes—
196C4×C22⋊D13C2318yes—
197C4×C22⋊D13C2318yes—
198C4×C22⋊D13C23116yes—
199#88180C2312yes—
200C2×C4⋊Dic13C2318yes—
201#88178C2314yes—
202#88178C23116yes—
203#88178C2318yes—
204C2×#6101C23116yes—
205C2×C4×Dic13C2311yescharacteristic
206C2×C4×Dic13C2312yes—
207#88151C2314yes—
208#88151C2318yes—
209#88151C23116yes—
210#88150C23116yes—
211#88150C23116yes—
212#88150C2318yes—
213#88150C23116yes—
214#88149C2314yes—
215#88149C2314yes—
216#88149C2318yes—
217#88149C23116yes—
218#88149C23116yes—
219#88148C23116yes—
220#88148C23116yes—
221#88147C2314yes—
222#88147C2314yes—
223#88147C2318yes—
224#88146C2314yes—
225C4⋊C4×D13C2314yes—
226C4⋊C4×D13C2314yes—
227C4⋊C4×D13C2314yes—
228C4⋊C4×D13C2314yes—
229C4⋊C4×D13C2318yes—
230C4⋊C4×D13C2318yes—
231C4⋊C4×D13C23116yes—
232C4⋊C4×D13C23116yes—
233C4⋊C4×D13C2318yes—
234#88144C2314yes—
235#88144C2318yes—
236#88143C23116yes—
237#88143C2318yes—
238#88142C2314yes—
239#88142C2314yes—
240#88142C2314yes—
241#88142C2314yes—
242#88141C2314yes—
243#88141C2318yes—
244#88140C23116yes—
245#88139C2318yes—
246#88139C2318yes—
247#88138C23116yes—
248#88138C2318yes—
249#88138C2318yes—
250#88138C23116yes—
251#88138C23116yes—
252#88138C23116yes—
253#88138C23116yes—
254#88137C23116yes—
255#88137C23116yes—
256#88135C2318yes—
257#88135C2318yes—
258#88135C23116yes—
259C22⋊C4×D13C2314yes—
260C22⋊C4×D13C23116yes—
261C22⋊C4×D13C2318yes—
262C22⋊C4×D13C2318yes—
263#88132C2318yes—
264#88132C23116yes—
265#88132C23116yes—
266#88132C23116yes—
267#88131C2314yes—
268#88129C2314yes—
269#88128C2312yes—
270#88128C2314yes—
271C4×D52C2314yes—
272C4×D52C2314yes—
273C4×D52C2318yes—
274#88126C2314yes—
275C42×D13C2311yescharacteristic
276C42×D13C2312yes—
277C42×D13C2312yes—
278C42×D13C2311yescharacteristic
279C42×D13C2311yescharacteristic
280C42×D13C2311yescharacteristic
281C42×D13C2314yes—
282#88124C2314yes—
283#88124C2312yes—
284#88123C2312yes—
285#88123C2312yes—
286C4×Dic26C2314yes—
287C4×Dic26C2318yes—
288C2×#3548—131nomaximal, Sylow
289C23×D13C2411yescharacteristic
290C23×D13C2418yes—
291C13×#41—48no—
292C13×#41—416no—
293C2×Q8×C13C2414yes—
294C2×Q8×C13C2414yes—
295C2×D4×C13C2414yes—
296C2×D4×C13C2414yes—
297C2×D4×C13C24116yes—
298C2×D4×C13C2414yes—
299C2×D4×C13C2418yes—
300C22×C4×C13C2412yes—
301C22×C4×C13C2411yescharacteristic
302C22×C4×C13C2418yes—
303C22×C4×C13C24116yes—
304C2×C22⋊D13C2418yes—
305C2×C22⋊D13C2418yes—
306C2×C22⋊D13C24116yes—
307C2×C22⋊D13C2418yes—
308C2×C22⋊D13C2418yes—
309C2×C22⋊D13C24116yes—
310C2×C22⋊D13C2418yes—
311C22×Dic13C2411yescharacteristic
312C22×Dic13C2412yes—
313C22×Dic13C2418yes—
314C22×Dic13C24116yes—
315#6131—48no—
316#6131—416no—
317Q8×D13—216no—
318Q8×D13—48no—
319#6129—416no—
320#6129—432no—
321#6129—416no—
322#6129—48no—
323D4×D13—216no—
324D4×D13—216no—
325D4×D13—416no—
326D4×D13—48no—
327D4×D13—432no—
328#6127—432no—
329#6127—416no—
330#6127—416no—
331#6127—48no—
332C2×D52C2414yes—
333C2×D52C2414yes—
334C2×D52C2414yes—
335C2×D52C24116yes—
336C2×D52C2418yes—
337C2×C4×D13—232no—
338C2×C4×D13—28no—
339C2×C4×D13—24no—
340C2×C4×D13—432no—
341C2×C4×D13C2411yescharacteristic
342C2×C4×D13C2411yescharacteristic
343C2×C4×D13C2412yes—
344C2×C4×D13C2411yescharacteristic
345C2×C4×D13C2412yes—
346C2×C4×D13C2412yes—
347C2×C4×D13C2418yes—
348C2×C4×D13C2418yes—
349C2×C4×D13C2418yes—
350C2×C4×D13C2418yes—
351C2×C4×D13C24116yes—
352C2×C4×D13C24116yes—
353C2×C4×D13C2412yes—
354C2×C4×D13C2411yescharacteristic
355C2×Dic26C2414yes—
356C2×Dic26C2418yes—
357C2×Dic26C2414yes—
358C2×Dic26C2418yes—
359C13×C4⋊C4C2414yes—
360C13×C4⋊C4C2418yes—
361C13×C4⋊C4C2414yes—
362C13×C4⋊C4C2414yes—
363C13×C4⋊C4C2414yes—
364C13×C4⋊C4C24116yes—
365C13×C22⋊C4C2414yes—
366C13×C22⋊C4C24116yes—
367C13×C22⋊C4C2418yes—
368C13×C22⋊C4C2418yes—
369C42×C13C2412yes—
370C42×C13C2414yes—
371C42×C13C2411yescharacteristic
372C42×C13C2411yescharacteristic
373C22⋊Dic13C2414yes—
374C22⋊Dic13C24116yes—
375C22⋊Dic13C2418yes—
376C22⋊Dic13C2418yes—
377#6103C2418yes—
378#6103C2418yes—
379#6103C2418yes—
380#6103C24116yes—
381#6103C2418yes—
382#6103C2418yes—
383#6103C24116yes—
384C4⋊Dic13C2414yes—
385C4⋊Dic13C2418yes—
386C4⋊Dic13C2414yes—
387C4⋊Dic13C2414yes—
388C4⋊Dic13C2414yes—
389C4⋊Dic13C24116yes—
390#6101C2418yes—
391#6101C2418yes—
392#6101C2418yes—
393#6101C24116yes—
394#6101C2418yes—
395#6101C2418yes—
396#6101C24116yes—
397#6101C2418yes—
398C4×Dic13C2412yes—
399C4×Dic13C2414yes—
400C4×Dic13C2411yescharacteristic
401C4×Dic13C2412yes—
402C4×Dic13C2411yescharacteristic
403C4×Dic13C2412yes—
404C4×Dic13C2412yes—
405C4×Dic13C2412yes—
406C4×Dic13C2418yes—
407#3548—134no—
408#3548—134no—
409#3548—134no—
410#3548—134no—
411#3548—134no—
412#3548—138no—
413#3548—131no—
414#3548—132no—
415#3548D1311yescharacteristic, direct product factor
416C2×#562—134no—
417C2×#554—134no—
418C2×#550—134no—
419C2×#547—134no—
420C2×#540—134no—
421C2×#537—138no—
422C2×#533—131no—
423C2×#532—132no—
424C23×C13C2511yescharacteristic
425C23×C13C2518yes—
426C22×D13—24no—
427C22×D13—216no—
428C22×D13—216no—
429C22×D13—22no—
430C22×D13—216no—
431C22×D13C2511yescharacteristic
432C22×D13C2518yes—
433C22×D13C2511yescharacteristic
434Q8×C13—28no—
435Q8×C13—44no—
436D4×C13—28no—
437D4×C13—28no—
438D4×C13—416no—
439D4×C13—44no—
440D4×C13—48no—
441C2×C4×C13—24no—
442C2×C4×C13—216no—
443C2×C4×C13—22no—
444C2×C4×C13—416no—
445C2×C4×C13C2512yes—
446C2×C4×C13C2511yescharacteristic
447C2×C4×C13C2518yes—
448C2×C4×C13C2518yes—
449C2×C4×C13C2512yes—
450C2×C4×C13C2511yescharacteristic
451C22⋊D13—216no—
452C22⋊D13—216no—
453C22⋊D13—416no—
454C22⋊D13—416no—
455C22⋊D13—48no—
456C22⋊D13—48no—
457C22⋊D13—48no—
458C2×Dic13—24no—
459C2×Dic13—216no—
460C2×Dic13—22no—
461C2×Dic13—416no—
462C2×Dic13C2511yescharacteristic
463C2×Dic13C2512yes—
464C2×Dic13C2518yes—
465C2×Dic13C2518yes—
466C2×Dic13C2512yes—
467C2×Dic13C2511yescharacteristic
468D52—28no—
469D52—28no—
470D52—416no—
471D52—44no—
472D52—48no—
473C4×D13—216no—
474C4×D13—24no—
475C4×D13—216no—
476C4×D13—22no—
477C4×D13—24no—
478C4×D13—216no—
479C4×D13—22no—
480C4×D13—216no—
481C4×D13—24no—
482C4×D13—22no—
483C4×D13—416no—
484C4×D13—416no—
485C4×D13H(5,𝔽2)18yes—
486C4×D132−1+414yes—
487Dic26—28no—
488Dic26—216no—
489Dic26—48no—
490Dic26—44no—
491C22×#41—134no—
492C22×#41—138no—
493#562—134no—
494#562—138no—
495#562—1316no—
496#562—1316no—
497#562—1316no—
498#562C2×D1314yescomplemented
499#554—134no—
500#554—138no—
501#554—138no—
502#554—1316no—
503#554—134no—
504#554—138no—
505#554—134no—
506#554—138no—
507#554C2×D1314yescomplemented
508#550—138no—
509#550—138no—
510#550—134no—
511#550—138no—
512#550—1316no—
513#550—134no—
514#550—138no—
515#550—134no—
516#550C2×D1314yescomplemented
517#547—138no—
518#547—134no—
519#547—1316no—
520#547—138no—
521#547—138no—
522#547—134no—
523#547—134no—
524#547—138no—
525#547C2×D1314yescomplemented
526#540—134no—
527#540—134no—
528#540—1316no—
529#540—1316no—
530#540—138no—
531#540—138no—
532#540—134no—
533#540C2×D1314yescomplemented
534#537—138no—
535#537—138no—
536#537—138no—
537#537—1316no—
538#537—138no—
539#537—1316no—
540#537—1316no—
541#537—138no—
542#537—1316no—
543#537—138no—
544#537—138no—
545#537C2×D1318yescomplemented
546#533—132no—
547#533—132no—
548#533—134no—
549#533—134no—
550#533—132no—
551#533—131no—
552#533C2×D1311yescharacteristic, complemented
553#532—134no—
554#532—132no—
555#532—132no—
556#532—134no—
557#532—134no—
558#532—134no—
559#532—134no—
560#532—134no—
561#532—132no—
562#532C2×D1312yescomplemented
563C2×C4⋊Q8—132no—
564C2×C4⋊Q8—132no—
565C2×#127—132no—
566C2×#127—134no—
567C2×#125—132no—
568C2×#125—134no—
569C2×#124—134no—
570C2×#123—1316no—
571C2×C22⋊Q8—134no—
572C2×C22⋊Q8—138no—
573C2×C22⋊Q8—1316no—
574C2×#121—134no—
575C2×#121—134no—
576C2×#121—1316no—
577C2×#121—138no—
578C2×#121—1316no—
579C2×C4×Q8—134no—
580C2×C4×D4—134no—
581C2×C4×D4—134no—
582C2×C4×D4—138no—
583C2×#117—132no—
584C22×C4⋊C4—138no—
585C22×C42—131no—
586C22×C13—22no—
587C22×C13—28no—
588C22×C13—28no—
589C22×C13—21no—
590C22×C13—28no—
591C22×C13C2611yescharacteristic
592C2×D13—22no—
593C2×D13—28no—
594C2×D13—28no—
595C2×D13—21no—
596C2×D13—28no—
597C2×D13—44no—
598C2×D13—432no—
599C2×D13C2×H(5,𝔽2)14yes—
600C2×D13C2×2−1+412yes—
601C4×C13—28no—
602C4×C13—22no—
603C4×C13—28no—
604C4×C13—21no—
605C4×C13C2×H(5,𝔽2)14yes—
606C4×C13C2×2−1+412yes—
607Dic13—28no—
608Dic13—22no—
609Dic13—28no—
610Dic13—21no—
611Dic13C2×H(5,𝔽2)14yes—
612Dic13C2×2−1+412yes—
613C2×#41—134no—
614C2×#41—138no—
615C2×#41—138no—
616C2×#41—134no—
617C2×#41—1316no—
618C2×#41—138no—
619C2×#41—138no—
620C2×#41—134no—
621C2×#41—1316no—
622C2×#41—138no—
623C2×#41—5216no—
624C2×#41—5232no—
625C2×#41C22×D1314yes—
626C2×#41C22×D1318yes—
627C22×Q8—134no—
628C22×Q8—134no—
629C22×D4—134no—
630C22×D4—134no—
631C22×D4—138no—
632C22×D4—1316no—
633C22×D4—134no—
634C23×C4—138no—
635C23×C4—131no—
636C23×C4—132no—
637C23×C4—1316no—
638C4⋊Q8—134no—
639C4⋊Q8—134no—
640C4⋊Q8—134no—
641C4⋊Q8—134no—
642C4⋊Q8—134no—
643C4⋊Q8—134no—
644C4⋊Q8—132no—
645C4⋊Q8—132no—
646C4⋊Q8C22×D1312yes—
647C4⋊Q8C22×D1312yes—
648#127—134no—
649#127—134no—
650#127—134no—
651#127—1316no—
652#127—138no—
653#127—132no—
654#127—134no—
655#127C22×D1312yes—
656#127C22×D1314yes—
657#125—138no—
658#125—134no—
659#125—1316no—
660#125—138no—
661#125—132no—
662#125—134no—
663#125C22×D1312yes—
664#125C22×D1314yes—
665#124—134no—
666#124—134no—
667#124—138no—
668#124—138no—
669#124—134no—
670#124C22×D1314yes—
671#123—1316no—
672#123—1316no—
673#123—1316no—
674#123—1316no—
675#123—1316no—
676#123—1316no—
677#123—1316no—
678#123C22×D13116yes—
679C22⋊Q8—134no—
680C22⋊Q8—138no—
681C22⋊Q8—1316no—
682C22⋊Q8—134no—
683C22⋊Q8—138no—
684C22⋊Q8—1316no—
685C22⋊Q8—138no—
686C22⋊Q8—134no—
687C22⋊Q8—1316no—
688C22⋊Q8—138no—
689C22⋊Q8—1316no—
690C22⋊Q8—1316no—
691C22⋊Q8—1316no—
692C22⋊Q8—138no—
693C22⋊Q8—1316no—
694C22⋊Q8—1316no—
695C22⋊Q8—1316no—
696C22⋊Q8C22×D1314yes—
697C22⋊Q8C22×D1318yes—
698C22⋊Q8C22×D13116yes—
699#121—134no—
700#121—138no—
701#121—134no—
702#121—138no—
703#121—1316no—
704#121—1316no—
705#121—1316no—
706#121—138no—
707#121—1316no—
708#121—1316no—
709#121—1316no—
710#121—1316no—
711#121—134no—
712#121—134no—
713#121—1316no—
714#121—138no—
715#121—1316no—
716#121—134no—
717#121—134no—
718#121—1316no—
719#121—138no—
720#121—1316no—
721#121—138no—
722#121—138no—
723#121—1316no—
724#121—1316no—
725#121—1316no—
726#121—1316no—
727#121—1316no—
728#121C22×D1314yes—
729#121C22×D1314yes—
730#121C22×D13116yes—
731#121C22×D1318yes—
732#121C22×D13116yes—
733C4×Q8—134no—
734C4×Q8—138no—
735C4×Q8—134no—
736C4×Q8—138no—
737C4×Q8—134no—
738C4×Q8C22×D1314yes—
739C4×D4—134no—
740C4×D4—134no—
741C4×D4—138no—
742C4×D4—138no—
743C4×D4—138no—
744C4×D4—1316no—
745C4×D4—134no—
746C4×D4—134no—
747C4×D4—138no—
748C4×D4—138no—
749C4×D4—138no—
750C4×D4—1316no—
751C4×D4—134no—
752C4×D4—134no—
753C4×D4—138no—
754C4×D4C22×D1314yes—
755C4×D4C22×D1314yes—
756C4×D4C22×D1318yes—
757#117—132no—
758#117—134no—
759#117—134no—
760#117—134no—
761#117C22×D1312yes—
762C2×C4⋊C4—1316no—
763C2×C4⋊C4—138no—
764C2×C4⋊C4—134no—
765C2×C4⋊C4—134no—
766C2×C4⋊C4—1316no—
767C2×C4⋊C4—1316no—
768C2×C4⋊C4—138no—
769C2×C4⋊C4—138no—
770C2×C4⋊C4—134no—
771C2×C4⋊C4—134no—
772C2×C4⋊C4—138no—
773C2×C4⋊C4C22×D1318yes—
774C2×C22⋊C4—134no—
775C2×C22⋊C4—1316no—
776C2×C22⋊C4—138no—
777C2×C22⋊C4—138no—
778C2×C42—132no—
779C2×C42—131no—
780C2×C42—134no—
781C2×C42—131no—
782C2×C42—132no—
783C2×C42—131no—
784C2×C42—131no—
785C2×C42—132no—
786C2×C42—131no—
787C2×C42C22×D1311yescharacteristic
788C2×C13—41no—
789C2×C13—48no—
790C2×C13C22×H(5,𝔽2)12yes—
791C2×C13C22×2−1+411yescharacteristic
792D13—41no—
793D13—48no—
794D13#354814yesdirect product factor
795C24—131no—
796C24—138no—
797#41—48no—
798#41—416no—
799#41—5216no—
800#41—528no—
801#41—5216no—
802#41—5232no—
803#41—5216no—
804#41—528no—
805#41—528no—
806#41—5216no—
807#41—5232no—
808#41—5216no—
809C2×Q8—138no—
810C2×Q8—134no—
811C2×Q8—138no—
812C2×Q8—134no—
813C2×Q8—2616no—
814C2×Q8—528no—
815C2×Q8C23×D1314yes—
816C2×Q8C23×D1314yes—
817C2×D4—138no—
818C2×D4—138no—
819C2×D4—138no—
820C2×D4—138no—
821C2×D4—1316no—
822C2×D4—1316no—
823C2×D4—138no—
824C2×D4—134no—
825C2×D4—134no—
826C2×D4—138no—
827C2×D4—1316no—
828C2×D4—134no—
829C2×D4—2616no—
830C2×D4—2616no—
831C2×D4—5216no—
832C2×D4—528no—
833C2×D4—5232no—
834C2×D4C23×D1314yes—
835C2×D4C23×D1314yes—
836C2×D4C23×D1318yes—
837C2×D4C23×D13116yes—
838C2×D4C23×D1314yes—
839C22×C4—131no—
840C22×C4—132no—
841C22×C4—131no—
842C22×C4—132no—
843C22×C4—138no—
844C22×C4—1316no—
845C22×C4—131no—
846C22×C4—132no—
847C22×C4—131no—
848C22×C4—131no—
849C22×C4—132no—
850C22×C4—132no—
851C22×C4—138no—
852C22×C4—138no—
853C22×C4—138no—
854C22×C4—138no—
855C22×C4—1316no—
856C22×C4—1316no—
857C22×C4—2632no—
858C22×C4—268no—
859C22×C4—264no—
860C22×C4—5232no—
861C22×C4C23×D1311yescharacteristic
862C22×C4C23×D1312yes—
863C22×C4C23×D1318yes—
864C22×C4C23×D13116yes—
865C4⋊C4—138no—
866C4⋊C4—134no—
867C4⋊C4—138no—
868C4⋊C4—134no—
869C4⋊C4—1316no—
870C4⋊C4—1316no—
871C4⋊C4—1316no—
872C4⋊C4—138no—
873C4⋊C4—134no—
874C4⋊C4—138no—
875C4⋊C4—134no—
876C4⋊C4—138no—
877C4⋊C4—138no—
878C4⋊C4—138no—
879C4⋊C4C23×D1314yes—
880C4⋊C4C23×D1314yes—
881C4⋊C4C23×D13116yes—
882C4⋊C4C23×D1314yes—
883C4⋊C4C23×D1314yes—
884C4⋊C4C23×D1318yes—
885C22⋊C4—134no—
886C22⋊C4—1316no—
887C22⋊C4—138no—
888C22⋊C4—138no—
889C22⋊C4—138no—
890C22⋊C4—1316no—
891C22⋊C4—1316no—
892C22⋊C4—138no—
893C22⋊C4—138no—
894C22⋊C4—138no—
895C22⋊C4—138no—
896C22⋊C4C23×D1314yes—
897C22⋊C4C23×D13116yes—
898C22⋊C4C23×D1318yes—
899C22⋊C4C23×D1318yes—
900C42—131no—
901C42—132no—
902C42—132no—
903C42—132no—
904C42—132no—
905C42—132no—
906C42—131no—
907C42—138no—
908C42—134no—
909C42C23×D1311yescharacteristic
910C42C23×D1312yes—
911C42C23×D1311yescharacteristic
912C42C23×D1314yes—
913C13C2×#354811yescharacteristic, complemented, Sylow
914C23—131no—
915C23—131no—
916C23—138no—
917C23—264no—
918C23—2616no—
919C23—262no—
920C23—2616no—
921C23—2616no—
922C23C24×D1311yescharacteristic
923C23C24×D1318yes—
924Q8—28no—
925Q8—44no—
926Q8—2616no—
927Q8—268no—
928Q8—528no—
929Q8—524no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—2616no—
936D4—2616no—
937D4—268no—
938D4—268no—
939D4—528no—
940D4—524no—
941D4—5216no—
942D4—528no—
943D4—528no—
944D4—528no—
945D4—5216no—
946D4—5216no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—131no—
952C2×C4—132no—
953C2×C4—138no—
954C2×C4—134no—
955C2×C4—131no—
956C2×C4—132no—
957C2×C4—138no—
958C2×C4—138no—
959C2×C4—262no—
960C2×C4—2616no—
961C2×C4—264no—
962C2×C4—262no—
963C2×C4—2616no—
964C2×C4—264no—
965C2×C4—2616no—
966C2×C4—262no—
967C2×C4—2616no—
968C2×C4—264no—
969C2×C4—2616no—
970C2×C4—264no—
971C2×C4—262no—
972C2×C4—5216no—
973C2×C4—5216no—
974C2×C4—5216no—
975C2×C4C24×D1311yescharacteristic
976C2×C4C24×D1312yes—
977C2×C4C24×D1318yes—
978C2×C4C24×D1318yes—
979C2×C4C24×D1312yes—
980C2×C4C24×D1311yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—134no—
987C22—132no—
988C22—262no—
989C22—268no—
990C22—268no—
991C22—261no—
992C22—268no—
993C22—524no—
994C22—5232no—
995C22C25×D1311yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—134no—
1001C4—132no—
1002C4—268no—
1003C4—262no—
1004C4—268no—
1005C4—261no—
1006C4D13×H(5,𝔽2)14yes—
1007C4D13×2−1+412yes—
1008C2—41no—
1009C2—48no—
1010C2—134no—
1011C2—521no—
1012C2—528no—
1013C2C2×D13×H(5,𝔽2)12yes—
1014C2C2×D13×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D13
commutator, socle, cosocleC22×C13C26
FittingC13×#3548C2
hypercenter#3548D13
hypocenterC13C2×#3548
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #13129236C2semidirect
2. #13129235C2semidirect
3. #13129234C2semidirect
4. #13129233C2semidirect
5. #13129232C2semidirect
6. #13129231C2semidirect
7. #13129230C2semidirect
8. #13129229C2semidirect
9. D13×#562C2semidirect
10. D13×#554C2semidirect
11. D13×#550C2semidirect
12. D13×#547C2semidirect
13. D13×#540C2semidirect
14. D13×#537C2semidirect
15. D13×#533C2semidirect
16. D13×#532C2semidirect
17. C13×#3548C2semidirect
20. C13×#562C22semidirect
21. C13×#554C22semidirect
22. C13×#550C22semidirect
23. C13×#547C22semidirect
24. C13×#540C22semidirect
25. C13×#537C22semidirect
26. C13×#533C22semidirect
27. C13×#532C22semidirect
28. #11719539C22semidirect
29. #11719538C22semidirect
30. #11719538C22semidirect
31. #11719537C22semidirect
32. #11719529C22semidirect
33. #11719435C22semidirect
34. #11719433C22semidirect
35. #11719431C22semidirect
36. #11719430C22semidirect
39. #11719424C22semidirect
40. #11719423C22semidirect
41. #11719423C22semidirect
42. #11719421C22semidirect
45. #11719405C22semidirect
46. #11719403C22semidirect
47. #11719395C22semidirect
48. #11719393C22semidirect
51. #11719389C22semidirect
53. #11719373C22semidirect
54. #11719372C22semidirect
55. #11719368C22semidirect
56. #11719360C22semidirect
58. #11719352C22semidirect
59. #11719341C22semidirect
60. #11719340C22semidirect
61. #11719336C22semidirect
62. #11719334C22semidirect
63. #11719334C22semidirect
64. #11719334C22semidirect
68. #11719327C22semidirect
69. #11719326C22semidirect
70. #11719324C22semidirect
71. #11719320C22semidirect
72. #11719316C22semidirect
73. #11719313C22semidirect
74. #11719313C22semidirect
75. #11719313C22semidirect
81. #11719304C22semidirect
82. #11719304C22semidirect
83. #11719302C22semidirect
84. #11719302C22semidirect
85. #11719301C22semidirect
86. #11719301C22semidirect
87. #11719284C22semidirect
88. #11719283C22semidirect
89. #11719282C22semidirect
91. #11719267C22semidirect
92. #11719260C22semidirect
93. #11719258C22semidirect
94. #11719258C22semidirect
95. #11719256C22semidirect
96. #11719253C22semidirect
97. #11719253C22semidirect
101. #11719248C22semidirect
102. #11719244C22semidirect
103. #11719240C22semidirect
105. #11719222C22semidirect
106. #11719216C22semidirect
107. #11719215C22semidirect
108. #11719212C22semidirect
110. #11719182C22semidirect
112. #11719175C22semidirect
415. #3548D13direct (N × H)
498. #562C2×D13semidirect
507. #554C2×D13semidirect
516. #550C2×D13semidirect
525. #547C2×D13semidirect
533. #540C2×D13semidirect
545. #537C2×D13semidirect
552. #533C2×D13semidirect
562. #532C2×D13semidirect
794. D13#3548direct (N × H)
913. C13C2×#3548semidirect

Maximal subgroups

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

subgroupindex
#131292362
#131292352
#131292342
#131292332
#131292322
#131292312
#131292302
#131292292
D13×#5622
D13×#5542
D13×#5502
D13×#5472
D13×#5402
D13×#5372
D13×#5332
D13×#5322
C13×#35482
C2×#354813