Finite Group Databasebeta

← #11685736

Subgroups — #11685736

Order 768.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87018C211yesmaximal, characteristic, complemented
2#86956C211yesmaximal, characteristic, complemented
3C3×#3381C211yesmaximal, characteristic, complemented
4#83698C211yesmaximal, characteristic, complemented
5#83630C211yesmaximal, characteristic, complemented
6#81930C212yesmaximal, complemented
7#81923C212yesmaximal, complemented
8#81903C211yesmaximal, characteristic, complemented
9#81896C211yesmaximal, characteristic, complemented
10#81224C212yesmaximal, complemented
11#81209C212yesmaximal, complemented
12#81179C212yesmaximal, complemented
13#81154C212yesmaximal, complemented
14#81104C211yesmaximal, characteristic, complemented
15#81095C211yesmaximal, characteristic, complemented
16#80993C211yesmaximal, characteristic, complemented
17#80972C211yesmaximal, characteristic, complemented
18#79925C211yesmaximal, characteristic, complemented
19#79922C211yesmaximal, characteristic, complemented
20#79698C212yesmaximal
21#79694C211yesmaximal, characteristic
22#79626C212yesmaximal, complemented
23#79623C211yesmaximal, characteristic, complemented
24#61858—31nomaximal, Sylow
25C3×#557C2211yescharacteristic
26C3×#554C2211yescharacteristic
27#5728C2211yescharacteristic
28#5727—21no—
29#5727C2211yescharacteristic
30D3×C4⋊Q8—21no—
31D3×C4⋊Q8C2211yescharacteristic
32#5722C2211yescharacteristic
33#5698C2212yes—
34#5690—22no—
35#5690C2212yes—
36#5689—22no—
37#5689C2212yes—
38#5685C2212yes—
39#5646—22no—
40#5641—21no—
41#5625—21no—
42#5625—22no—
43#5578—21no—
44#5578C2211yescharacteristic
45Q8×D12—21no—
46Q8×D12C2211yescharacteristic
47#5574C2212yes—
48C4×#239C2211yescharacteristic
49#5570C2211yescharacteristic
50#5570C2211yescharacteristic
51Q8×Dic6C2212yes—
52#5561C2212yes—
53#5557C2211yescharacteristic
54#5542C2212yes—
55#5542C2211yescharacteristic
56#5513—21no—
57#5500—21no—
58C3×#499C2212yes—
59C3×#498C2211yescharacteristic
60C3×#479C2212yes—
61C3×#478C2212yes—
62C3×#477C2211yescharacteristic
63C3×#474C2211yescharacteristic
64C3×C8×Q8C2211yescharacteristic
65C3×C4×SD16C2211yescharacteristic
66C3×C4×SD16C2212yes—
67#5172C2211yescharacteristic
68#5166C2212yes—
69#5166C2211yescharacteristic
70#5094C2211yescharacteristic
71#5093C2211yescharacteristic
72#5084C2211yescharacteristic
73#5080C2211yescharacteristic
74#5069C2212yes—
75#5066C2212yes—
76#5064C2212yes—
77#5063C2212yes—
78#5031C2211yescharacteristic
79#5031C2212yes—
80#5030C2212yes—
81C4×#216C2211yescharacteristic
82#5024C2211yescharacteristic
83#5014C2212yes—
84C4×#213C2211yescharacteristic
85#5008C2212yes—
86#5007C2211yescharacteristic
87#4889C2212yes—
88#4889C2212yes—
89#4888C2212yes—
90#4884C2212yes—
91#4877C2212yes—
92#4876C2212yes—
93#4876C2212yes—
94#4875C2212yes—
95#4871C2211yescharacteristic
96#4870C2212yes—
97#4868C2211yescharacteristic
98#4862C2212yes—
99#4862C2212yes—
100#4857C2212yes—
101#4855C2212yes—
102#4854C2212yes—
103#4854C2212yes—
104#4854C2212yes—
105#4852C2212yes—
106#4851C2212yes—
107#4851C2211yescharacteristic
108#4841C2212yes—
109#4841C2211yescharacteristic
110#4840C2212yes—
111#4835C2211yescharacteristic
112#4831C2211yescharacteristic
113#4828C2212yes—
114#4808C2211yescharacteristic
115#4808C2212yes—
116#4799C2211yescharacteristic
117#4791C2212yes—
118#4790C2212yes—
119#4789C2212yes—
120#4789C2212yes—
121#4787C2211yescharacteristic
122#4787C2212yes—
123#4779C2211yescharacteristic
124#4777C2212yes—
125#4768C2212yes—
126#4765C2212yes—
127#4765C2212yes—
128C4×#204C2212yes—
129C4×#204C2211yescharacteristic
130#4690C2212yes—
131#4685C2211yescharacteristic
132#4681C2212yes—
133#4681C2211yescharacteristic
134#4679C2212yes—
135C8×Dic6C2211yescharacteristic
136#3555—31no—
137#3503—31no—
138#3388—32no—
139#3387—32no—
140#3387—31no—
141#3384—31no—
142#3381D311yescharacteristic, complemented
143Q8×SD16—31no—
144#3376—32no—
145#3374—31no—
146#3369—32no—
147#3367—31no—
148#3364—31no—
149#3359—31no—
150#3244—32no—
151#3242—32no—
152#3239—31no—
153#3229—31no—
154#3125—32no—
155#3120—32no—
156#3116—31no—
157#3102—31no—
158#2985—31no—
159C2×#239C2311yescharacteristic
160C2×D3×Q8—21no—
161C2×D3×Q8—21no—
162C2×D3×Q8—21no—
163C2×C3×SD16C2311yescharacteristic
164C3×C4⋊Q8—21no—
165C3×C4⋊Q8C2311yescharacteristic
166C3×C4⋊Q8C2311yescharacteristic
167C3×#125—22no—
168C3×#125C2312yes—
169C3×#125C2312yes—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—22no—
172C3×C4×Q8—21no—
173C3×C4×Q8C2311yescharacteristic
174C3×C4×Q8C2312yes—
175C3×C4×Q8C2311yescharacteristic
176C3×C4×D4C2311yescharacteristic
177C3×C4×D4C2312yes—
178C2×C3×C4⋊C4—21no—
179#946—21no—
180#946—21no—
181#946D411yescharacteristic
182Q8×Dic3—21no—
183Q8×Dic3—21no—
184Q8×Dic3C2311yescharacteristic
185Q8×Dic3C2312yes—
186#944—22no—
187#944—21no—
188#944D411yescharacteristic
189C2×#216C2311yescharacteristic
190C2×#216C2312yes—
191#938C2311yescharacteristic
192#936C2311yescharacteristic
193#936C2312yes—
194C2×#213C2311yescharacteristic
195#929—22no—
196C4×#67—21no—
197#926—21no—
198#926—22no—
199#926—21no—
200#924—22no—
201#924—21no—
202#924—22no—
203C2×#204C2312yes—
204C2×#204C2311yescharacteristic
205#898—22no—
206#898—22no—
207#897—22no—
208#897—21no—
209#897—22no—
210#897—22no—
211#897D411yescharacteristic
212#897C2311yescharacteristic
213#897C2312yes—
214#896—22no—
215#896—22no—
216#896—22no—
217#896—22no—
218#896D412yes—
219#893—21no—
220#893—22no—
221#893C2312yes—
222#893C2311yescharacteristic
223#892—21no—
224#892—21no—
225#892C2311yescharacteristic
226D3×C4⋊C4—21no—
227D3×C4⋊C4—22no—
228D3×C4⋊C4—22no—
229D3×C4⋊C4C2312yes—
230#890—22no—
231#890—21no—
232#890—22no—
233#890—22no—
234#890—22no—
235#890—21no—
236#890C2311yescharacteristic
237#890C2312yes—
238#889—22no—
239#889—22no—
240#889—22no—
241#889D412yes—
242#888—22no—
243#888—21no—
244#888—22no—
245#888—22no—
246#888—22no—
247#888—21no—
248#888D411yescharacteristic
249#888C2312yes—
250#888C2312yes—
251#888C2312yes—
252#887—21no—
253#887—22no—
254#887C2312yes—
255#887C2312yes—
256#887C2312yes—
257#885—22no—
258#883—21no—
259#879—22no—
260#879—22no—
261#879—22no—
262#879—22no—
263#879—21no—
264C4×D12—21no—
265C4×D12—22no—
266C4×D12C2312yes—
267C4×D12C2311yescharacteristic
268#872—22no—
269#872C2312yes—
270C42×D3—21no—
271C42×D3C2311yescharacteristic
272#869—21no—
273#869—22no—
274#869C2312yes—
275#869C2311yescharacteristic
276#869C2312yes—
277#869C2311yescharacteristic
278C4×Dic6—22no—
279C4×Dic6—21no—
280C4×Dic6C2312yes—
281C4×Dic6C2311yescharacteristic
282C4×Dic6C2312yes—
283C4×Dic6C2311yescharacteristic
284C3×#107C2312yes—
285C3×#107C2312yes—
286C3×#106C2311yescharacteristic
287C3×#106C2312yes—
288C3×#106C2312yes—
289C3×C4⋊C8C2312yes—
290C3×C4⋊C8C2311yescharacteristic
291C3×#103C2312yes—
292C3×#103C2311yescharacteristic
293C3×#102C2312yes—
294C3×#102C2311yescharacteristic
295C3×C4×C8C2311yescharacteristic
296C3×C4×C8C2312yes—
297#835C2311yescharacteristic
298#832C2312yes—
299#832C2311yescharacteristic
300#821C2311yescharacteristic
301(C2×D3)⋊C8C2311yescharacteristic
302(C2×D3)⋊C8C2312yes—
303(C2×D3)⋊C8C2311yescharacteristic
304#817C2312yes—
305#817C2311yescharacteristic
306#816C2311yescharacteristic
307#816C2312yes—
308#816C2312yes—
309#816C2312yes—
310#816C2312yes—
311#815C2312yes—
312#815C2312yes—
313Dic3⋊C8C2312yes—
314Dic3⋊C8C2311yescharacteristic
315Dic3⋊C8C2312yes—
316Dic3⋊C8C2311yescharacteristic
317C8×Dic3C2312yes—
318#810C2311yescharacteristic
319#810C2312yes—
320#810C2312yes—
321#810C2312yes—
322#810C2312yes—
323#809C2312yes—
324#809C2311yescharacteristic
325#808C2312yes—
326#808C2312yes—
327#808C2312yes—
328#808C2312yes—
329#807C2311yescharacteristic
330#807C2311yescharacteristic
331#807C2312yes—
332C4⋊(C3⋊C8)C2311yescharacteristic
333C4⋊(C3⋊C8)C2312yes—
334#803C2312yes—
335C4×C3⋊C8C2311yescharacteristic
336#563—62no—
337Q82—31no—
338Q82—32no—
339#557—32no—
340#557—31no—
341#557—31no—
342#557C2×D311yescharacteristic
343#556—31no—
344#556—32no—
345#556—61no—
346#554—32no—
347#554—62no—
348#554C2×D311yescharacteristic
349#552—61no—
350D4×Q8—31no—
351D4×Q8—31no—
352D4×Q8—61no—
353D4×Q8—61no—
354#544—32no—
355#544—61no—
356#544—62no—
357#542—32no—
358#541—32no—
359#541—62no—
360#541—61no—
361#533—31no—
362#533—31no—
363#533—61no—
364C2×C4⋊Q8—31no—
365C2×C4⋊Q8—61no—
366#529—31no—
367#520—32no—
368C4×#41—31no—
369#501—32no—
370#501—32no—
371#501—32no—
372#499C2×D312yes—
373#498—31no—
374#498—32no—
375#498C2×D311yescharacteristic
376#491—32no—
377#489—32no—
378#489—32no—
379#488—32no—
380#487—31no—
381#487—31no—
382#487—32no—
383#485—32no—
384#485—31no—
385#484—32no—
386#483—32no—
387#483—32no—
388#482—31no—
389#481—32no—
390#479—32no—
391#479—32no—
392#479—32no—
393#479—31no—
394#479C2×D312yes—
395#478—32no—
396#478—31no—
397#478C2×D312yes—
398#477—32no—
399#477C2×D311yescharacteristic
400#476—31no—
401#476—32no—
402#476—32no—
403#475—31no—
404#475—32no—
405#475—32no—
406#475—32no—
407#475—31no—
408#475—32no—
409#475—32no—
410#474—31no—
411#474C2×D311yescharacteristic
412#464—31no—
413#464—32no—
414#463—31no—
415#463—32no—
416#462—31no—
417#462—32no—
418#461—31no—
419#461—32no—
420#452—31no—
421#452—32no—
422#449—31no—
423#446—31no—
424#446—31no—
425#446—32no—
426#446—32no—
427C8×Q8—31no—
428C8×Q8C2×D311yescharacteristic
429#442—32no—
430#441—32no—
431#441—32no—
432#441—32no—
433#440—32no—
434#440—32no—
435C4×Q16—31no—
436C4×Q16—32no—
437C4×SD16—32no—
438C4×SD16—31no—
439C4×SD16—32no—
440C4×SD16C2×D311yescharacteristic
441C4×SD16C2×D312yes—
442C4×D8—31no—
443#433—32no—
444#433—32no—
445#432—31no—
446#431—31no—
447C2×C3×Q8—21no—
448C2×C3×Q8—21no—
449C2×C3×Q8C2×D411yescharacteristic
450C2×C3×Q8C2411yescharacteristic
451C2×C3×D4C2411yescharacteristic
452C22×C3×C4—21no—
453C22×C3×C4—22no—
454C2×#67—21no—
455#239—22no—
456#239—22no—
457D3×Q8—82no—
458D3×Q8—82no—
459D3×Q8—82no—
460C2×D12—21no—
461C2×D12C2411yescharacteristic
462C2×C4×D3—21no—
463C2×C4×D3—21no—
464C2×C4×D3—21no—
465C2×C4×D3—22no—
466C2×C4×D3—22no—
467C2×C4×D3—22no—
468C2×C4×D3C2×D411yescharacteristic
469C2×C4×D3C2×D411yescharacteristic
470C2×C4×D3C2411yescharacteristic
471C2×Dic6—21no—
472C2×Dic6—22no—
473C2×Dic6—22no—
474C2×Dic6—22no—
475C2×Dic6—22no—
476C2×Dic6C2×D411yescharacteristic
477C2×Dic6C2×D412yes—
478C2×Dic6C2411yescharacteristic
479C2×Dic6C2412yes—
480C3×SD16—22no—
481C2×C3×C8C2411yescharacteristic
482C2×C3×C8C2411yescharacteristic
483C2×C3×C8C2412yes—
484C3×C4⋊C4—21no—
485C3×C4⋊C4—22no—
486C3×C4⋊C4—22no—
487C3×C4⋊C4—22no—
488C3×C4⋊C4—21no—
489C3×C4⋊C4—22no—
490C3×C4⋊C4—22no—
491C3×C4⋊C4—21no—
492C3×C4⋊C4C2×D411yescharacteristic
493C3×C4⋊C4C2×D412yes—
494C3×C4⋊C4C2411yescharacteristic
495C3×C4⋊C4C2411yescharacteristic
496C3×C4⋊C4C2412yes—
497C3×C4⋊C4C2412yes—
498C3×C22⋊C4—21no—
499C3×C22⋊C4—22no—
500C3×C42—21no—
501C3×C42—22no—
502C3×C42C2411yescharacteristic
503C3×C42C2412yes—
504#217—21no—
505#217—22no—
506#217—21no—
507#217—21no—
508#217—22no—
509#216—22no—
510#216—24no—
511#213—22no—
512(C2×D3)⋊C4—21no—
513(C2×D3)⋊C4—21no—
514(C2×D3)⋊C4—22no—
515(C2×D3)⋊C4—22no—
516(C2×D3)⋊C4—21no—
517(C2×D3)⋊C4—22no—
518(C2×D3)⋊C4—21no—
519(C2×D3)⋊C4C2×D412yes—
520(C2×D3)⋊C4C2×D412yes—
521C4⋊Dic3—22no—
522C4⋊Dic3—22no—
523C4⋊Dic3—21no—
524C4⋊Dic3—21no—
525C4⋊Dic3—22no—
526C4⋊Dic3—21no—
527C4⋊Dic3—21no—
528C4⋊Dic3—22no—
529C4⋊Dic3—22no—
530C4⋊Dic3—21no—
531C4⋊Dic3—22no—
532C4⋊Dic3—21no—
533C4⋊Dic3C2×D411yescharacteristic
534C4⋊Dic3C2×D412yes—
535C4⋊Dic3C2411yescharacteristic
536C4⋊Dic3C2412yes—
537C4⋊Dic3C2411yescharacteristic
538Dic3⋊C4—21no—
539Dic3⋊C4—22no—
540Dic3⋊C4—22no—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—21no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4C2×D412yes—
550Dic3⋊C4C2×D412yes—
551Dic3⋊C4C2×D412yes—
552Dic3⋊C4C2×D412yes—
553Dic3⋊C4C2×D412yes—
554C4×Dic3—22no—
555C4×Dic3—21no—
556C4×Dic3—21no—
557C4×Dic3—22no—
558C4×Dic3—21no—
559C4×Dic3—22no—
560C4×Dic3—22no—
561C4×Dic3—22no—
562C4×Dic3C2×D411yescharacteristic
563C4×Dic3C2×D411yescharacteristic
564C4×Dic3C2412yes—
565C4×Dic3C2411yescharacteristic
566C2×C3⋊C8C2411yescharacteristic
567C2×C3⋊C8C2411yescharacteristic
568C2×C3⋊C8C2412yes—
569#204—24no—
570#204—22no—
571C2×#41—31no—
572C22×Q8—61no—
573C22×Q8—61no—
574C22×Q8—61no—
575C2×Q16—31no—
576C2×Q16—32no—
577C2×SD16—31no—
578C2×SD16—32no—
579C2×SD16C22×D311yescharacteristic
580C2×D8—31no—
581C4⋊Q8—21no—
582C4⋊Q8—31no—
583C4⋊Q8—31no—
584C4⋊Q8—32no—
585C4⋊Q8—32no—
586C4⋊Q8—32no—
587C4⋊Q8—31no—
588C4⋊Q8—32no—
589C4⋊Q8—31no—
590C4⋊Q8—32no—
591C4⋊Q8—62no—
592C4⋊Q8—61no—
593C4⋊Q8—61no—
594C4⋊Q8—61no—
595C4⋊Q8—62no—
596C4⋊Q8—62no—
597C4⋊Q8—62no—
598C4⋊Q8—61no—
599C4⋊Q8—62no—
600C4⋊Q8—62no—
601C4⋊Q8C22×D311yescharacteristic
602C4⋊Q8C22×D311yescharacteristic
603#126—61no—
604#126—62no—
605#126—62no—
606#126—62no—
607#126—62no—
608#126—62no—
609#126—62no—
610#125—22no—
611#125—32no—
612#125—31no—
613#125—32no—
614#125—61no—
615#125—62no—
616#125—62no—
617#125—62no—
618#125—62no—
619#125—62no—
620#125—62no—
621#125—62no—
622#125—61no—
623#125C22×D312yes—
624#125C22×D312yes—
625#124—31no—
626#124—32no—
627#124—62no—
628#123—61no—
629#123—62no—
630C22⋊Q8—21no—
631C22⋊Q8—22no—
632C22⋊Q8—31no—
633C22⋊Q8—31no—
634C22⋊Q8—32no—
635C22⋊Q8—31no—
636C22⋊Q8—32no—
637C22⋊Q8—62no—
638C22⋊Q8—62no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—62no—
643C22⋊Q8—62no—
644C22⋊Q8—61no—
645C22⋊Q8—61no—
646C22⋊Q8—62no—
647C22⋊Q8—61no—
648C22⋊Q8—61no—
649C22⋊Q8—62no—
650#121—31no—
651C4×Q8—21no—
652C4×Q8—31no—
653C4×Q8—32no—
654C4×Q8—31no—
655C4×Q8—32no—
656C4×Q8—32no—
657C4×Q8—32no—
658C4×Q8—32no—
659C4×Q8—31no—
660C4×Q8—32no—
661C4×Q8—61no—
662C4×Q8—62no—
663C4×Q8—61no—
664C4×Q8—62no—
665C4×Q8—61no—
666C4×Q8—61no—
667C4×Q8C22×D311yescharacteristic
668C4×Q8C22×D312yes—
669C4×Q8C22×D311yescharacteristic
670C4×D4—31no—
671C4×D4—32no—
672C4×D4—31no—
673C4×D4—32no—
674C4×D4—62no—
675C4×D4—61no—
676C4×D4—62no—
677C4×D4—61no—
678C4×D4—61no—
679C4×D4C22×D311yescharacteristic
680C4×D4C22×D312yes—
681#117—32no—
682#117—31no—
683#117—62no—
684#117—61no—
685#117—61no—
686#117—61no—
687#117—62no—
688#117—61no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—32no—
691C2×C4⋊C4—62no—
692C2×C4⋊C4—62no—
693C2×C4⋊C4—61no—
694C2×C42—31no—
695C2×C42—61no—
696#107—31no—
697#107—32no—
698#107—31no—
699#107C22×D312yes—
700#107C22×D312yes—
701#106—32no—
702#106—31no—
703#106—32no—
704#106—32no—
705#106—32no—
706#106—32no—
707#106C22×D312yes—
708#106C22×D312yes—
709#106C22×D311yescharacteristic
710C4⋊C8—31no—
711C4⋊C8—31no—
712C4⋊C8—32no—
713C4⋊C8—32no—
714C4⋊C8—31no—
715C4⋊C8—32no—
716C4⋊C8C22×D311yescharacteristic
717C4⋊C8C22×D312yes—
718#103—31no—
719#103—31no—
720#103—32no—
721#103—32no—
722#103—32no—
723#103—32no—
724#103—32no—
725#103—31no—
726#103—32no—
727#103—32no—
728#103—32no—
729#103C22×D311yescharacteristic
730#103C22×D312yes—
731#102—31no—
732#102—32no—
733#102—31no—
734#102—31no—
735#102—32no—
736#102C22×D312yes—
737#102C22×D311yescharacteristic
738C22⋊C8—31no—
739C22⋊C8—31no—
740C22⋊C8—32no—
741#97—32no—
742#97—32no—
743#97—32no—
744C4×C8—32no—
745C4×C8—31no—
746C4×C8C22×D311yescharacteristic
747C4×C8C22×D312yes—
748C23×C3—21no—
749C22×D3—21no—
750C22×D3C22×D411yescharacteristic
751C3×Q8—22no—
752C3×Q8—21no—
753C3×Q8—42no—
754C3×Q8—81no—
755C3×Q82−1+412yes—
756C3×D4—21no—
757C3×D4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—22no—
761C2×C3×C4—21no—
762C2×C3×C4—22no—
763C2×C3×C4—42no—
764C2×C3×C4—82no—
765C2×C3×C4C22×D412yes—
766C2×C3×C4C22×D411yescharacteristic
767C2×C3×C4C22×D412yes—
768C2×C3×C4C22×D411yescharacteristic
769C2×C3×C4C2511yescharacteristic
770#67—81no—
771C2×Dic3—21no—
772C2×Dic3—22no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—22no—
776C2×Dic3C22×D411yescharacteristic
777C2×Dic3C22×D412yes—
778C2×Dic3C22×D411yescharacteristic
779C2×Dic3C22×D411yescharacteristic
780C2×Dic3C22×D412yes—
781D12—24no—
782D12—21no—
783D122−1+412yes—
784C4×D3—24no—
785C4×D3—22no—
786C4×D3—21no—
787C4×D3—21no—
788C4×D3—41no—
789C4×D3—42no—
790C4×D3—42no—
791C4×D3—82no—
792C4×D3—82no—
793C4×D3—82no—
794Dic6—22no—
795Dic6—22no—
796Dic6—21no—
797Dic6—21no—
798Dic6—22no—
799Dic6—42no—
800Dic6—42no—
801Dic6—82no—
802Dic6—82no—
803Dic6—82no—
804Dic6—82no—
805C3×C8—21no—
806C3×C8—22no—
807C3×C8—21no—
808C3⋊C8—21no—
809C3⋊C8—21no—
810C3⋊C8—22no—
811#41—62no—
812#41—62no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—31no—
816C2×Q8—32no—
817C2×Q8—31no—
818C2×Q8—32no—
819C2×Q8—62no—
820C2×Q8—62no—
821C2×Q8—62no—
822C2×Q8—61no—
823C2×Q8—62no—
824C2×Q8—242no—
825C2×Q8—242no—
826C2×Q8—242no—
827C2×Q8D3×D411yescharacteristic
828C2×Q8C23×D311yescharacteristic
829C2×D4—31no—
830C2×D4—61no—
831C2×D4—61no—
832C2×D4C23×D311yescharacteristic
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—31no—
836C22×C4—31no—
837C22×C4—31no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—62no—
841C22×C4—62no—
842C22×C4—61no—
843C22×C4—62no—
844Q16—62no—
845Q16—64no—
846SD16—22no—
847SD16—62no—
848SD16—64no—
849D8—62no—
850C2×C8—32no—
851C2×C8—31no—
852C2×C8—31no—
853C2×C8C23×D311yescharacteristic
854C2×C8C23×D311yescharacteristic
855C2×C8C23×D312yes—
856C4⋊C4—21no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—21no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—32no—
865C4⋊C4—32no—
866C4⋊C4—32no—
867C4⋊C4—31no—
868C4⋊C4—32no—
869C4⋊C4—32no—
870C4⋊C4—32no—
871C4⋊C4—32no—
872C4⋊C4—31no—
873C4⋊C4—31no—
874C4⋊C4—62no—
875C4⋊C4—62no—
876C4⋊C4—62no—
877C4⋊C4—62no—
878C4⋊C4—61no—
879C4⋊C4—61no—
880C4⋊C4—61no—
881C4⋊C4—61no—
882C4⋊C4—62no—
883C4⋊C4—62no—
884C4⋊C4—62no—
885C4⋊C4—62no—
886C4⋊C4—62no—
887C4⋊C4—62no—
888C4⋊C4—62no—
889C4⋊C4—61no—
890C4⋊C4—61no—
891C4⋊C4—62no—
892C4⋊C4—62no—
893C4⋊C4—61no—
894C4⋊C4—62no—
895C4⋊C4—61no—
896C4⋊C4—62no—
897C4⋊C4D3×D411yescharacteristic
898C4⋊C4D3×D412yes—
899C4⋊C4C23×D312yes—
900C4⋊C4C23×D311yescharacteristic
901C4⋊C4C23×D312yes—
902C4⋊C4C23×D311yescharacteristic
903C22⋊C4—21no—
904C22⋊C4—22no—
905C22⋊C4—32no—
906C22⋊C4—32no—
907C22⋊C4—61no—
908C22⋊C4—62no—
909C22⋊C4—61no—
910C22⋊C4—62no—
911C22⋊C4—61no—
912C22⋊C4—61no—
913C22⋊C4—61no—
914C22⋊C4—61no—
915C22⋊C4—62no—
916C22⋊C4—62no—
917C22⋊C4—61no—
918C22⋊C4—62no—
919C42—21no—
920C42—22no—
921C42—31no—
922C42—31no—
923C42—32no—
924C42—31no—
925C42—61no—
926C42—61no—
927C42—62no—
928C42—62no—
929C42—62no—
930C42—62no—
931C42—61no—
932C42—62no—
933C42C23×D311yescharacteristic
934C42C23×D312yes—
935C22×C3—41no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3C23×D411yescharacteristic
939C2×D3—21no—
940C2×D3—21no—
941C2×D3—22no—
942C2×D3—21no—
943C2×D3—41no—
944C2×D3—41no—
945C3×C4—22no—
946C3×C4—21no—
947C3×C4—22no—
948C3×C4—22no—
949C3×C4—42no—
950C3×C4—41no—
951C3×C4—42no—
952C3×C4—41no—
953C3×C4#57712yes—
954C3×C4C2×2−1+411yescharacteristic
955C3×C4C2×2−1+411yescharacteristic
956Dic3—21no—
957Dic3—22no—
958Dic3—21no—
959Dic3—22no—
960Dic3—21no—
961Dic3—41no—
962Dic3—42no—
963Dic3—41no—
964Dic3—42no—
965Dic3—41no—
966C23—21no—
967C23—31no—
968C23—61no—
969Q8—21no—
970Q8—22no—
971Q8—42no—
972Q8—62no—
973Q8—61no—
974Q8—62no—
975Q8—61no—
976Q8—62no—
977Q8—81no—
978Q8—122no—
979Q8—122no—
980Q8—242no—
981Q8—242no—
982Q8—242no—
983Q8—242no—
984Q8#100712yes—
985D4—21no—
986D4—21no—
987D4—32no—
988D4—64no—
989D4—61no—
990D4—241no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—31no—
997C2×C4—31no—
998C2×C4—31no—
999C2×C4—32no—
1000C2×C4—32no—
1001C2×C4—42no—
1002C2×C4—64no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—62no—
1011C2×C4—82no—
1012C2×C4—121no—
1013C2×C4—122no—
1014C2×C4—122no—
1015C2×C4—242no—
1016C2×C4—242no—
1017C2×C4—242no—
1018C2×C4C2×D3×D412yes—
1019C2×C4C2×D3×D411yescharacteristic
1020C2×C4C2×D3×D412yes—
1021C2×C4C2×D3×D411yescharacteristic
1022C2×C4C24×D311yescharacteristic
1023C8—21no—
1024C8—21no—
1025C8—22no—
1026C8—62no—
1027C8—61no—
1028C8—61no—
1029C2×C3—81no—
1030C2×C3#348611yescharacteristic
1031C2×C3C2×#57711yescharacteristic
1032C2×C3#358611yescharacteristic
1033D3—41no—
1034D3—42no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—61no—
1039C22—61no—
1040C22—62no—
1041C22—61no—
1042C22—121no—
1043C22—121no—
1044C22C22×D3×D411yescharacteristic
1045C4—22no—
1046C4—22no—
1047C4—21no—
1048C4—22no—
1049C4—41no—
1050C4—42no—
1051C4—42no—
1052C4—41no—
1053C4—61no—
1054C4—62no—
1055C4—61no—
1056C4—62no—
1057C4—61no—
1058C4—121no—
1059C4—122no—
1060C4—121no—
1061C4—122no—
1062C4—121no—
1063C4#577012yes—
1064C4C2×#100711yescharacteristic
1065C4D3×2−1+411yescharacteristic
1066C3#6185811yescharacteristic, complemented, Sylow
1067C2—81no—
1068C2—121no—
1069C2—122no—
1070C2#8675911yescharacteristic
1071C2C2×#577011yescharacteristic
1072C2#8720811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3381C2
socleC22×C3C23×D4
prime radical#5172C22
hypercenter#3381D3
hypocenterC3#61858
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3381

Complements

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

NH ≅ G/Ntype
1. #87018C2semidirect
2. #86956C2semidirect
3. C3×#3381C2semidirect
4. #83698C2semidirect
5. #83630C2semidirect
6. #81930C2semidirect
7. #81923C2semidirect
8. #81903C2semidirect
9. #81896C2semidirect
10. #81224C2semidirect
11. #81209C2semidirect
12. #81179C2semidirect
13. #81154C2semidirect
14. #81104C2semidirect
15. #81095C2semidirect
16. #80993C2semidirect
17. #80972C2semidirect
18. #79925C2semidirect
19. #79922C2semidirect
22. #79626C2semidirect
23. #79623C2semidirect
142. #3381D3semidirect
1066. C3#61858semidirect

Maximal subgroups

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

subgroupindex
#870182
#869562
C3×#33812
#836982
#836302
#819302
#819232
#819032
#818962
#812242
#812092
#811792
#811542
#811042
#810952
#809932
#809722
#799252
#799222
#796982
#796942
#796262
#796232
#618583