Finite Group Databasebeta

← #16771465

Subgroups — #16771465

Order 3328.

11346 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719652C212yesmaximal, complemented
2#13128630C212yesmaximal, complemented
3#13128625C216yesmaximal, complemented
4#13128619C213yesmaximal, complemented
5#13128614C211yesmaximal, characteristic, complemented
6#13128609C213yesmaximal, complemented
7#13128606C214yesmaximal, complemented
8#13128594C2112yesmaximal, complemented
9D4×#6131C214yesmaximal, complemented
10#13128323C2112yesmaximal, complemented
11#13128168C216yesmaximal, complemented
12C2×#11719430C213yesmaximal, complemented
13D13×#532C213yesmaximal, complemented
14C4×#41×D13C211yesmaximal, characteristic, complemented
15C13×#3499C211yesmaximal, characteristic, complemented
16C2×C13×2−1+4C2212yescomplemented
17#11719652—232no—
18C2×#88256C22112yescomplemented
19C2×#88256C2216yescomplemented
20C2×#88256C2212yescomplemented
21C2×#41×D13C2211yescharacteristic
22C2×#41×D13C22112yescomplemented
23C2×#41×D13C2216yescomplemented
24C2×#88254C2214yescomplemented
25C2×#88254C2216yescomplemented
26C22×#6131C2214yescomplemented
27C22×#6131C2216yescomplemented
28D4×Q8×C13C2214yescomplemented
29C13×#547C22112yescomplemented
30C13×#536C2216yescomplemented
31C13×#532C2213yescomplemented
32C2×C13×C4⋊Q8C2213yescomplemented
33C4×C13×#41C2211yescharacteristic, complemented
34#11719537C2216yescomplemented
35#11719535C2216yescomplemented
36#11719534C22124yescomplemented
37#41×Dic13C2211yescharacteristic, complemented
38#11719522C2218yescomplemented
39#11719521C2216yescomplemented
40C2×#88201C2216yescomplemented
41#11719432C22112yescomplemented
42#11719431C22112yescomplemented
43#11719430C22112yescomplemented
44#11719430C22112yescomplemented
45#11719430C2216yescomplemented
46#11719430C2213yescomplemented
47#11719430C2216yescomplemented
48#11719430C2216yescomplemented
49#11719429C22112yescomplemented
50D13×C4⋊Q8C2213yescomplemented
51#11719421C2211yescharacteristic, complemented
52D13×#127C2213yescomplemented
53#11719379C22112yescomplemented
54D13×#124C2216yescomplemented
55#11719373C2216yescomplemented
56#11719361C22124yescomplemented
57#11719359C22148yescomplemented
58#11719358C22124yescomplemented
59#11719338C22124yescomplemented
60#11719335C22124yescomplemented
61#11719334C22124yescomplemented
62#11719332C22124yescomplemented
63#11719314C22124yescomplemented
64D13×#121C22112yescomplemented
65#11719301C22112yescomplemented
66#11719282C2214yescomplemented
67C4×#6131C2212yescomplemented
68C4×Q8×D13C2212yescomplemented
69#11719258C22112yescomplemented
70D4×D52C22112yescomplemented
71D4×D52C22112yescomplemented
72#11719253C22112yescomplemented
73C4×D4×D13C2216yescomplemented
74C4×D4×D13C22112yescomplemented
75C4×#6129C2216yescomplemented
76#11719230C2216yescomplemented
77#11719227C2213yescomplemented
78D13×#117C2213yescomplemented
79#11719212C22124yescomplemented
80C2×#88149C22112yescomplemented
81C2×#88147C22112yescomplemented
82#11719182C2213yescomplemented
83C2×#88128C2213yescomplemented
84C4×#6127C2213yescomplemented
85C2×C42×D13C2213yescomplemented
86C13×2−1+4—216no—
87C2×C13×#41C23112yes—
88C2×C13×#41C2316yes—
89C2×C13×#41C2311yescharacteristic
90C22×Q8×C13C2316yes—
91C22×Q8×C13C2314yes—
92#88256—216no—
93#88256—296no—
94#88256—248no—
95#41×D13—296no—
96#41×D13—248no—
97#41×D13D4116yescomplemented
98#88254—232no—
99#88254—248no—
100C2×#6131—232no—
101C2×#6131—248no—
102C2×#6131C23112yes—
103C2×#6131C2316yes—
104C2×#6131C23112yes—
105C2×#6131C23112yes—
106C2×#6131C23112yes—
107C2×#6131C2314yes—
108C2×#6131C2311yescharacteristic
109C2×Q8×D13C2316yes—
110C2×Q8×D13C23112yes—
111C2×Q8×D13C2311yescharacteristic
112C2×#6129C23112yes—
113C2×#6129C2312yes—
114C2×#6129C2313yes—
115C2×D4×D13C23112yes—
116C2×D4×D13C23112yes—
117C2×D4×D13C23124yes—
118C2×D4×D13C2316yes—
119C2×D4×D13C23112yes—
120C2×D4×D13C2313yes—
121C2×#6127C2316yes—
122C2×#6127C23124yes—
123C2×#6127C23112yes—
124C2×#6127C23112yes—
125C2×#6127C2313yes—
126C22×D52C2316yes—
127C22×D52C23112yes—
128C22×D52C23112yes—
129C22×D52C23112yes—
130C22×C4×D13C23112yes—
131C22×C4×D13C23112yes—
132C22×C4×D13C2316yes—
133C22×C4×D13C2313yes—
134C13×C4⋊Q8C2313yes—
135C13×C4⋊Q8C2316yes—
136C13×C4⋊Q8C23112yes—
137C13×#127C2311yescharacteristic
138C13×#124C2316yes—
139C13×#123C23124yes—
140C13×C22⋊Q8C23124yes—
141C13×#121C23112yes—
142C4×Q8×C13C2312yes—
143C4×D4×C13C2316yes—
144C4×D4×C13C23112yes—
145C13×#117C2313yes—
146C2×C13×C4⋊C4C23112yes—
147C2×C42×C13C2313yes—
148#88201C23112yes—
149#88201C2316yes—
150#88201C23124yes—
151#88200C23124yes—
152Q8×Dic13C2312yes—
153#88198C2316yes—
154#88194C23112yes—
155#88194C2316yes—
156#88193C23124yes—
157#88192C2314yes—
158#88191C23124yes—
159#88190C2312yes—
160D4×Dic13C2316yes—
161D4×Dic13C2314yes—
162#88184C23112yes—
163#88184C23124yes—
164#88183C23124yes—
165C4×C22⋊D13C23112yes—
166C4×C22⋊D13C23124yes—
167C2×#6103C23124yes—
168#88180C2313yes—
169C2×C4×Dic13C2316yes—
170C2×C4×Dic13C2313yes—
171#88150C23148yes—
172#88149C23112yes—
173#88149C23124yes—
174#88149C23124yes—
175#88149C23124yes—
176#88149C23124yes—
177#88148C23148yes—
178#88147C23112yes—
179#88147C23124yes—
180#88147C23124yes—
181#88147C23124yes—
182#88147C2316yes—
183#88146C2316yes—
184C4⋊C4×D13C23112yes—
185C4⋊C4×D13C2316yes—
186#88142C23112yes—
187#88141C2316yes—
188#88139C23124yes—
189#88138C23124yes—
190#88138C23148yes—
191#88136C23124yes—
192#88136C23148yes—
193#88135C23112yes—
194#88135C23124yes—
195C22⋊C4×D13C2316yes—
196C22⋊C4×D13C23124yes—
197#88131C2316yes—
198#88129C2316yes—
199#88128C2313yes—
200#88128C2316yes—
201#88128C23112yes—
202C4×D52C2316yes—
203C4×D52C23112yes—
204#88126C2316yes—
205C42×D13C2313yes—
206C42×D13C2311yescharacteristic
207C42×D13C2313yes—
208C42×D13C2313yes—
209C42×D13C2316yes—
210C42×D13C2316yes—
211#88123C2311yescharacteristic
212C4×Dic26C2316yes—
213#62812—131nomaximal, Sylow
214C23×D13C24112yes—
215C23×D13C24112yes—
216C23×D13C2413yes—
217C13×#41—248no—
218C13×#41—224no—
219C13×#41C2×D418yescomplemented
220C2×Q8×C13—216no—
221C2×Q8×C13—224no—
222C2×Q8×C13C2416yes—
223C2×Q8×C13C24112yes—
224C2×Q8×C13C2411yescharacteristic
225C2×D4×C13C2414yes—
226C2×D4×C13C2412yes—
227C2×D4×C13C24112yes—
228C2×D4×C13C2413yes—
229C22×C4×C13C2416yes—
230C22×C4×C13C24112yes—
231C22×C4×C13C24112yes—
232C22×C4×C13C2413yes—
233C2×C22⋊D13C24112yes—
234C2×C22⋊D13C2414yes—
235C2×C22⋊D13C24112yes—
236C2×C22⋊D13C24124yes—
237C2×C22⋊D13C2416yes—
238C22×Dic13C2414yes—
239C22×Dic13C2416yes—
240C22×Dic13C2413yes—
241#6131—216no—
242#6131—248no—
243#6131—248no—
244#6131—224no—
245#6131—248no—
246#6131—248no—
247#6131C2×D418yescomplemented
248Q8×D13—224no—
249Q8×D13—248no—
250Q8×D13C2×D418yescomplemented
251#6129—248no—
252#6129—28no—
253#6129C2×D4124yescomplemented
254D4×D13—248no—
255D4×D13—248no—
256D4×D13—296no—
257D4×D13—224no—
258D4×D13—424no—
259D4×D13C2×D4124yescomplemented
260#6127—224no—
261#6127—296no—
262#6127—248no—
263#6127—248no—
264#6127C2×D4124yescomplemented
265C2×D52—248no—
266C2×D52—224no—
267C2×D52—248no—
268C2×D52—424no—
269C2×D52C24112yes—
270C2×D52C2416yes—
271C2×D52C24112yes—
272C2×D52C24124yes—
273C2×D52C24112yes—
274C2×D52C24124yes—
275C2×D52C2413yes—
276C2×C4×D13—248no—
277C2×C4×D13—248no—
278C2×C4×D13—412no—
279C2×C4×D13C2×D4124yescomplemented
280C2×C4×D13C2412yes—
281C2×C4×D13C2416yes—
282C2×C4×D13C24112yes—
283C2×C4×D13C24112yes—
284C2×C4×D13C24112yes—
285C2×C4×D13C24124yes—
286C2×C4×D13C2416yes—
287C2×C4×D13C2416yes—
288C2×C4×D13C2411yescharacteristic
289C2×C4×D13C2413yes—
290C2×C4×D13C2413yes—
291C2×C4×D13C2413yes—
292C2×Dic26C2412yes—
293C2×Dic26C24112yes—
294C2×Dic26C2413yes—
295C13×C4⋊C4C2416yes—
296C13×C4⋊C4C24112yes—
297C13×C4⋊C4C24124yes—
298C13×C22⋊C4C2416yes—
299C13×C22⋊C4C24124yes—
300C42×C13C2416yes—
301C42×C13C2411yescharacteristic
302C42×C13C2413yes—
303C22⋊Dic13C2416yes—
304C22⋊Dic13C2418yes—
305#6103C24112yes—
306#6103C24124yes—
307#6103C24124yes—
308#6103C24148yes—
309C4⋊Dic13C2416yes—
310C4⋊Dic13C2414yes—
311#6101C24112yes—
312#6101C24124yes—
313C4×Dic13C2416yes—
314C4×Dic13C2412yes—
315C4×Dic13C2411yescharacteristic
316C4×Dic13C2413yes—
317C4×Dic13C2416yes—
318C4×Dic13C2416yes—
319C4×Dic13C2416yes—
320C2×#585—132no—
321#3500—132no—
322#3500—136no—
323#3499—133no—
324#3499D1311yescharacteristic, complemented
325#3498—133no—
326#3498—131no—
327#3497—134no—
328#3496—1312no—
329D4×#41—134no—
330D4×#41—1312no—
331#3449—136no—
332C2×#532—133no—
333C2×#532—133no—
334C2×C4×#41—131no—
335C23×C13C2514yes—
336C23×C13C2513yes—
337C22×D13—224no—
338C22×D13—224no—
339C22×D13—46no—
340C22×D13—424no—
341C22×D13—424no—
342C22×D13C22×D4112yes—
343C22×D13C25112yes—
344C22×D13C2513yes—
345C22×D13C2511yescharacteristic
346Q8×C13—212no—
347Q8×C13—224no—
348Q8×C13C22×D414yes—
349D4×C13—224no—
350D4×C13—24no—
351D4×C13—28no—
352D4×C13C22×D4112yes—
353C2×C4×C13—224no—
354C2×C4×C13—224no—
355C2×C4×C13—212no—
356C2×C4×C13C22×D4112yes—
357C2×C4×C13C2516yes—
358C2×C4×C13C25112yes—
359C2×C4×C13C2511yescharacteristic
360C2×C4×C13C2513yes—
361C2×C4×C13C2512yes—
362C22⋊D13—224no—
363C22⋊D13—28no—
364C22⋊D13—224no—
365C22⋊D13—424no—
366C22⋊D13C22×D4124yes—
367C2×Dic13—28no—
368C2×Dic13—46no—
369C2×Dic13C22×D4112yes—
370C2×Dic13C2512yes—
371C2×Dic13C2516yes—
372C2×Dic13C2514yes—
373C2×Dic13C2511yescharacteristic
374C2×Dic13C2513yes—
375D52—248no—
376D52—224no—
377D52—212no—
378D52—224no—
379D52—224no—
380D52—424no—
381D52C22×D4112yes—
382C4×D13—224no—
383C4×D13—224no—
384C4×D13—24no—
385C4×D13—212no—
386C4×D13—224no—
387C4×D13—248no—
388C4×D13—46no—
389C4×D13—46no—
390C4×D13C22×D4112yes—
391C4×D13C22×D414yes—
392C4×D13C22×D4112yes—
393C4×D13C22×D4112yes—
394Dic26—24no—
395Dic26—224no—
396Dic26C22×D4112yes—
397#585—2632no—
398C2×2−1+4—134no—
399C2×2−1+4—136no—
400C2×2−1+4C2×D1312yescomplemented
401C2×H(5,𝔽2)—1312no—
402C2×H(5,𝔽2)—136no—
403C2×H(5,𝔽2)—132no—
404C22×#41—131no—
405C22×#41—136no—
406C22×#41—1312no—
407C22×#41—136no—
408C22×#41—134no—
409#550—134no—
410#550—1312no—
411D4×Q8—1312no—
412D4×Q8C2×D1314yescomplemented
413#548—138no—
414#548—1324no—
415#547—1312no—
416#547—1324no—
417#547C2×D13112yescomplemented
418#546—1324no—
419#546—1348no—
420#546—1324no—
421D42—1324no—
422D42—1312no—
423D42—1312no—
424#537—1324no—
425#536—136no—
426#536—1312no—
427#536C2×D1316yescomplemented
428#535—136no—
429#535—1312no—
430#535—136no—
431#534—1324no—
432#532—136no—
433#532—133no—
434#532—136no—
435#532—1312no—
436#532—1312no—
437#532—136no—
438#532—136no—
439#532—131no—
440#532—136no—
441#532—1312no—
442#532—1312no—
443#532—133no—
444#532C2×D1313yescomplemented
445C2×C4⋊Q8—133no—
446C2×C4⋊Q8C2×D1313yescomplemented
447C2×#127—133no—
448C2×#127—133no—
449C2×#124—136no—
450C2×#124—136no—
451#525—1324no—
452#525—1324no—
453C2×#121—1312no—
454C2×#121—1312no—
455C4×#41—131no—
456C4×#41—132no—
457C4×#41—136no—
458C4×#41—133no—
459C4×#41—133no—
460C4×#41C2×D1311yescharacteristic, complemented
461C2×C4×Q8—132no—
462C2×C4×D4—136no—
463C2×C4×D4—1312no—
464C2×C4×D4—1312no—
465C2×#117—133no—
466C22×C42—133no—
467C22×C13—26no—
468C22×C13—24no—
469C22×C13—28no—
470C22×C13C23×D416yes—
471C22×C13C2611yescharacteristic
472C2×D13—22no—
473C2×D13—26no—
474C2×D13—212no—
475C2×D13—224no—
476C2×D13—412no—
477C2×D13—824no—
478C2×D13—824no—
479C2×D13C23×D416yes—
480C2×D13C23×D412yes—
481C4×C13—212no—
482C4×C13—26no—
483C4×C13C23×D412yes—
484C4×C13C23×D416yes—
485C4×C13#58514yescomplemented
486Dic13—24no—
487Dic13—22no—
488Dic13—26no—
489Dic13C23×D416yes—
490Dic13C23×D412yes—
4912−1+4—216no—
4922−1+4—2632no—
4932−1+4—2648no—
494H(5,𝔽2)—2696no—
495H(5,𝔽2)—2648no—
496H(5,𝔽2)—2616no—
497C2×#41—1316no—
498C2×#41—131no—
499C2×#41—1312no—
500C2×#41—136no—
501C2×#41—1312no—
502C2×#41—1312no—
503C2×#41—1312no—
504C2×#41—134no—
505C2×#41—133no—
506C2×#41—1312no—
507C2×#41—132no—
508C2×#41—133no—
509C2×#41—136no—
510C2×#41—1312no—
511C2×#41—1324no—
512C2×#41—1312no—
513C2×#41—2648no—
514C2×#41—2648no—
515C2×#41—2632no—
516C2×#41—2696no—
517C2×#41C22×D1316yes—
518C2×#41C22×D13112yes—
519C2×#41C22×D1311yescharacteristic
520C22×Q8—131no—
521C22×Q8—136no—
522C22×Q8—1312no—
523C22×Q8C22×D1316yes—
524C22×Q8C22×D1314yes—
525C22×D4—133no—
526C22×D4—1312no—
527C22×D4—136no—
528C22×D4—1324no—
529C22×D4—1312no—
530C22×D4—1312no—
531C22×D4—1312no—
532C22×D4—136no—
533C22×D4—1312no—
534C22×D4—1312no—
535C23×C4—133no—
536C23×C4—1312no—
537C23×C4—1312no—
538C23×C4—136no—
539C4⋊Q8—136no—
540C4⋊Q8—1312no—
541C4⋊Q8—131no—
542C4⋊Q8C22×D1313yes—
543C4⋊Q8C22×D1316yes—
544C4⋊Q8C22×D13112yes—
545#127—136no—
546#127—1312no—
547#127—133no—
548#127—136no—
549#127—1312no—
550#127C22×D1311yescharacteristic
551#124—136no—
552#124—1312no—
553#124—1324no—
554#124—132no—
555#124—1324no—
556#124—136no—
557#124C22×D1316yes—
558#123—1324no—
559#123—1348no—
560#123C22×D13124yes—
561C22⋊Q8—1324no—
562C22⋊Q8—1348no—
563C22⋊Q8C22×D13124yes—
564#121—134no—
565#121—1324no—
566#121—1312no—
567#121—1324no—
568#121—1312no—
569#121—1324no—
570#121—1324no—
571#121—1324no—
572#121—1324no—
573#121—1324no—
574#121—1348no—
575#121C22×D13112yes—
576#120—1324no—
577#120—1348no—
578#120—1324no—
579C4×Q8—132no—
580C4×Q8—136no—
581C4×Q8—136no—
582C4×Q8C22×D1312yes—
583C4×D4—134no—
584C4×D4—136no—
585C4×D4—1312no—
586C4×D4—1324no—
587C4×D4—1312no—
588C4×D4—136no—
589C4×D4—1324no—
590C4×D4—1324no—
591C4×D4—1324no—
592C4×D4—1312no—
593C4×D4—1324no—
594C4×D4—136no—
595C4×D4—1312no—
596C4×D4C22×D1316yes—
597C4×D4C22×D13112yes—
598#117—133no—
599#117—136no—
600#117—136no—
601#117—136no—
602#117C22×D1313yes—
603C2×C4⋊C4—136no—
604C2×C4⋊C4—1312no—
605C2×C4⋊C4C22×D13112yes—
606C2×C22⋊C4—1324no—
607C2×C22⋊C4—136no—
608C2×C22⋊C4—1324no—
609C2×C42—136no—
610C2×C42—133no—
611C2×C42—133no—
612C2×C42—136no—
613C2×C42—136no—
614C2×C42—133no—
615C2×C42—133no—
616C2×C42—131no—
617C2×C42C22×D1313yes—
618C2×C13—26no—
619C2×C13—44no—
620C2×C13C24×D411yescharacteristic
621C2×C13C2×#58512yes—
622D13—22no—
623D13—26no—
624D13—412no—
625C24—133no—
626C24—1312no—
627C24—1312no—
628#41—248no—
629#41—224no—
630#41—138no—
631#41—1324no—
632#41—1324no—
633#41—2648no—
634#41—2696no—
635#41—2648no—
636#41—2648no—
637#41—268no—
638#41—2624no—
639#41—2648no—
640#41—2648no—
641#41—2648no—
642#41—2648no—
643#41—2616no—
644#41—2624no—
645#41D4×D1318yescomplemented
646C2×Q8—216no—
647C2×Q8—224no—
648C2×Q8—138no—
649C2×Q8—133no—
650C2×Q8—1312no—
651C2×Q8—132no—
652C2×Q8—2624no—
653C2×Q8—2648no—
654C2×Q8C23×D13112yes—
655C2×Q8C23×D1316yes—
656C2×Q8C23×D1311yescharacteristic
657C2×D4—136no—
658C2×D4—1324no—
659C2×D4—1312no—
660C2×D4—134no—
661C2×D4—1312no—
662C2×D4—1324no—
663C2×D4—133no—
664C2×D4—1312no—
665C2×D4—1324no—
666C2×D4—1312no—
667C2×D4—1312no—
668C2×D4—136no—
669C2×D4—1324no—
670C2×D4—2648no—
671C2×D4—2648no—
672C2×D4—2624no—
673C2×D4—2696no—
674C2×D4—2648no—
675C2×D4—2648no—
676C2×D4—2624no—
677C2×D4—5224no—
678C2×D4—5224no—
679C2×D4C23×D1314yes—
680C2×D4C23×D13112yes—
681C2×D4C23×D1312yes—
682C2×D4C23×D1313yes—
683C22×C4—133no—
684C22×C4—1324no—
685C22×C4—131no—
686C22×C4—133no—
687C22×C4—133no—
688C22×C4—133no—
689C22×C4—134no—
690C22×C4—136no—
691C22×C4—132no—
692C22×C4—136no—
693C22×C4—1312no—
694C22×C4—1312no—
695C22×C4—1324no—
696C22×C4—1312no—
697C22×C4—136no—
698C22×C4—136no—
699C22×C4—2648no—
700C22×C4—2648no—
701C22×C4—5212no—
702C22×C4C23×D1316yes—
703C22×C4C23×D13112yes—
704C22×C4C23×D13112yes—
705C22×C4C23×D1313yes—
706C4⋊C4—134no—
707C4⋊C4—1312no—
708C4⋊C4—136no—
709C4⋊C4—1324no—
710C4⋊C4C23×D13112yes—
711C4⋊C4C23×D1316yes—
712C4⋊C4C23×D13124yes—
713C22⋊C4—138no—
714C22⋊C4—136no—
715C22⋊C4—1324no—
716C22⋊C4—1312no—
717C22⋊C4—1348no—
718C22⋊C4—1324no—
719C22⋊C4C23×D1316yes—
720C22⋊C4C23×D13124yes—
721C42—132no—
722C42—131no—
723C42—136no—
724C42—133no—
725C42—136no—
726C42—136no—
727C42—136no—
728C42C23×D1311yescharacteristic
729C42C23×D1313yes—
730C42C23×D1316yes—
731C13#6281211yescharacteristic, complemented, Sylow
732C23—133no—
733C23—131no—
734C23—1312no—
735C23—1312no—
736C23—2624no—
737C23—2624no—
738C23—526no—
739C23—5224no—
740C23—5224no—
741C23C24×D1314yes—
742C23C24×D1313yes—
743Q8—224no—
744Q8—212no—
745Q8—1312no—
746Q8—2624no—
747Q8—264no—
748Q8C2×D4×D1314yes—
749D4—224no—
750D4—24no—
751D4—28no—
752D4—1324no—
753D4—1312no—
754D4—2624no—
755D4—2648no—
756D4—2624no—
757D4—268no—
758D4—2624no—
759D4—2624no—
760D4—2612no—
761D4—2624no—
762D4—5224no—
763D4—5224no—
764D4C2×D4×D13112yes—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—212no—
768C2×C4—1312no—
769C2×C4—131no—
770C2×C4—133no—
771C2×C4—134no—
772C2×C4—1312no—
773C2×C4—1312no—
774C2×C4—1312no—
775C2×C4—132no—
776C2×C4—136no—
777C2×C4—134no—
778C2×C4—2624no—
779C2×C4—2648no—
780C2×C4—2624no—
781C2×C4—268no—
782C2×C4—2624no—
783C2×C4—264no—
784C2×C4—2612no—
785C2×C4—526no—
786C2×C4—526no—
787C2×C4—526no—
788C2×C4C2×D4×D13112yes—
789C2×C4C24×D1316yes—
790C2×C4C24×D13112yes—
791C2×C4C24×D1311yescharacteristic
792C2×C4C24×D1313yes—
793C2×C4C24×D1312yes—
794C22—26no—
795C22—24no—
796C22—28no—
797C22—132no—
798C22—136no—
799C22—262no—
800C22—266no—
801C22—2612no—
802C22—2624no—
803C22—5212no—
804C22—10424no—
805C22—10424no—
806C22C22×D4×D1316yes—
807C22C25×D1311yescharacteristic
808C4—212no—
809C4—26no—
810C4—132no—
811C4—136no—
812C4—264no—
813C4—262no—
814C4—266no—
815C4C22×D4×D1316yes—
816C4C22×D4×D1312yes—
817C4#1171965214yescomplemented
818C2—26no—
819C2—44no—
820C2—262no—
821C2—266no—
822C2—5212no—
823C2C23×D4×D1311yescharacteristic
824C2C2×#1171965212yes—
subgroupG/H
center, FrattiniC22C25×D13
commutator, socle, cosocleC22×C13C26
FittingC13×#3499C2
hypercenter#3499D13
hypocenterC13#62812
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×#11719652C2semidirect
2. #13128630C2semidirect
3. #13128625C2semidirect
4. #13128619C2semidirect
5. #13128614C2semidirect
6. #13128609C2semidirect
7. #13128606C2semidirect
8. #13128594C2semidirect
9. D4×#6131C2semidirect
10. #13128323C2semidirect
11. #13128168C2semidirect
12. C2×#11719430C2semidirect
13. D13×#532C2semidirect
14. C4×#41×D13C2semidirect
15. C13×#3499C2semidirect
16. C2×C13×2−1+4C22semidirect
18. C2×#88256C22semidirect
19. C2×#88256C22semidirect
20. C2×#88256C22semidirect
22. C2×#41×D13C22semidirect
23. C2×#41×D13C22semidirect
24. C2×#88254C22semidirect
25. C2×#88254C22semidirect
26. C22×#6131C22semidirect
27. C22×#6131C22semidirect
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. #11719535C22semidirect
36. #11719534C22semidirect
37. #41×Dic13C22semidirect
38. #11719522C22semidirect
39. #11719521C22semidirect
40. C2×#88201C22semidirect
41. #11719432C22semidirect
42. #11719431C22semidirect
43. #11719430C22semidirect
44. #11719430C22semidirect
45. #11719430C22semidirect
46. #11719430C22semidirect
47. #11719430C22semidirect
48. #11719430C22semidirect
49. #11719429C22semidirect
50. D13×C4⋊Q8C22semidirect
51. #11719421C22semidirect
52. D13×#127C22semidirect
53. #11719379C22semidirect
54. D13×#124C22semidirect
55. #11719373C22semidirect
56. #11719361C22semidirect
57. #11719359C22semidirect
58. #11719358C22semidirect
59. #11719338C22semidirect
60. #11719335C22semidirect
61. #11719334C22semidirect
62. #11719332C22semidirect
63. #11719314C22semidirect
64. D13×#121C22semidirect
65. #11719301C22semidirect
66. #11719282C22semidirect
67. C4×#6131C22semidirect
68. C4×Q8×D13C22semidirect
69. #11719258C22semidirect
70. D4×D52C22semidirect
71. D4×D52C22semidirect
72. #11719253C22semidirect
73. C4×D4×D13C22semidirect
74. C4×D4×D13C22semidirect
75. C4×#6129C22semidirect
76. #11719230C22semidirect
77. #11719227C22semidirect
78. D13×#117C22semidirect
79. #11719212C22semidirect
80. C2×#88149C22semidirect
81. C2×#88147C22semidirect
82. #11719182C22semidirect
83. C2×#88128C22semidirect
84. C4×#6127C22semidirect
85. C2×C42×D13C22semidirect
97. #41×D13D4semidirect
219. C13×#41C2×D4semidirect
247. #6131C2×D4semidirect
250. Q8×D13C2×D4semidirect
253. #6129C2×D4semidirect
259. D4×D13C2×D4semidirect
264. #6127C2×D4semidirect
279. C2×C4×D13C2×D4semidirect
324. #3499D13semidirect
400. C2×2−1+4C2×D13semidirect
412. D4×Q8C2×D13semidirect
417. #547C2×D13semidirect
427. #536C2×D13semidirect
444. #532C2×D13semidirect
446. C2×C4⋊Q8C2×D13semidirect
460. C4×#41C2×D13semidirect
485. C4×C13#585semidirect
645. #41D4×D13semidirect
731. C13#62812semidirect
817. C4#11719652semidirect

Maximal subgroups

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

subgroupindex
C2×#117196522
#131286302
#131286252
#131286192
#131286142
#131286092
#131286062
#131285942
D4×#61312
#131283232
#131281682
C2×#117194302
D13×#5322
C4×#41×D132
C13×#34992
#6281213