Finite Group Databasebeta

← #11685730

Subgroups — #11685730

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#87048C211yesmaximal, characteristic, complemented
2#87018C211yesmaximal, characteristic, complemented
3C3×#3387C211yesmaximal, characteristic, complemented
4Q8×#215C211yesmaximal, characteristic, complemented
5#83689C211yesmaximal, characteristic, complemented
6#81989C212yesmaximal, complemented
7#81968C212yesmaximal, complemented
8#81905C211yesmaximal, characteristic, complemented
9#81896C211yesmaximal, characteristic, complemented
10#81265C212yesmaximal, complemented
11#81241C212yesmaximal, complemented
12#81136C211yesmaximal, characteristic, complemented
13#81095C211yesmaximal, characteristic, complemented
14#81043C212yesmaximal, complemented
15#81037C211yesmaximal, characteristic, complemented
16#81018C211yesmaximal, characteristic, complemented
17#81001C212yesmaximal
18#79970C211yesmaximal, characteristic, complemented
19#79965C211yesmaximal, characteristic, complemented
20#79849C212yesmaximal, complemented
21#79815C212yesmaximal, complemented
22#79746C211yesmaximal, characteristic
23#79702C211yesmaximal, characteristic, complemented
24#61858—31nomaximal, Sylow
25C3×Q82C2211yescharacteristic
26C3×#557C2211yescharacteristic
27#5735—22no—
28#5733C2212yes—
29#5732—21no—
30#5731—22no—
31#5730C2211yescharacteristic
32#5729—21no—
33#5728C2211yescharacteristic
34#5727—21no—
35#5727C2211yescharacteristic
36D3×C4⋊Q8—21no—
37D3×C4⋊Q8C2211yescharacteristic
38#5721C2212yes—
39#5690—22no—
40#5690C2212yes—
41#5689—22no—
42#5689C2212yes—
43#5584C2211yescharacteristic
44#5583—21no—
45#5583C2212yes—
46#5581—21no—
47#5580C2211yescharacteristic
48#5578—21no—
49#5578C2211yescharacteristic
50Q8×D12—21no—
51Q8×D12C2211yescharacteristic
52#5574C2212yes—
53C4×#239C2211yescharacteristic
54#5570C2211yescharacteristic
55#5568C2212yes—
56#5567C2211yescharacteristic
57Q8×Dic6C2212yes—
58C3×#501C2212yes—
59C3×#498C2211yescharacteristic
60C3×#479C2212yes—
61C3×#477C2211yescharacteristic
62C3×#475C2212yes—
63C3×#475C2211yescharacteristic
64C3×#446C2211yescharacteristic
65C3×#441C2212yes—
66C3×C4×Q16C2211yescharacteristic
67#5187C2211yescharacteristic
68#5185C2211yescharacteristic
69#5182C2212yes—
70#5093C2211yescharacteristic
71#5087C2211yescharacteristic
72#5084C2212yes—
73#5084C2211yescharacteristic
74#5080C2212yes—
75#5080C2211yescharacteristic
76#5068C2212yes—
77#5063C2212yes—
78#5031C2211yescharacteristic
79C4×#216C2212yes—
80#5028C2212yes—
81C4×#215C2212yes—
82C4×#215C2211yescharacteristic
83C4×#215C2211yescharacteristic
84Q8×C3⋊C8C2211yescharacteristic
85#5020C2211yescharacteristic
86#5020C2212yes—
87#4891C2211yescharacteristic
88#4891C2212yes—
89#4889C2212yes—
90#4888C2212yes—
91#4885C2211yescharacteristic
92#4878C2212yes—
93#4877C2212yes—
94#4871C2212yes—
95#4870C2212yes—
96#4869C2212yes—
97#4863C2212yes—
98#4862C2212yes—
99#4862C2212yes—
100#4856C2212yes—
101#4856C2212yes—
102#4854C2212yes—
103#4854C2212yes—
104#4854C2212yes—
105#4852C2212yes—
106#4850C2212yes—
107#4846C2211yescharacteristic
108#4844C2212yes—
109#4841C2211yescharacteristic
110#4840C2212yes—
111#4835C2211yescharacteristic
112#4831C2212yes—
113#4830C2211yescharacteristic
114#4819C2211yescharacteristic
115#4818C2212yes—
116#4814C2211yescharacteristic
117#4811C2212yes—
118#4810C2211yescharacteristic
119#4808C2212yes—
120#4797C2212yes—
121#4796C2211yescharacteristic
122#4796C2212yes—
123#4794C2212yes—
124#4792C2212yes—
125#4789C2212yes—
126#4789C2212yes—
127#4788C2212yes—
128#4714C2212yes—
129#4710C2212yes—
130#4709C2212yes—
131#4701C2212yes—
132C4×D24C2211yescharacteristic
133#4685C2211yescharacteristic
134#4681C2211yescharacteristic
135#4679C2211yescharacteristic
136#3555—31no—
137#3503—31no—
138#3388—32no—
139#3387—32no—
140#3387D311yescharacteristic, complemented
141#3384—31no—
142#3381—31no—
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×Q16C2311yescharacteristic
164C3×C4⋊Q8—21no—
165C3×C4⋊Q8—21no—
166C3×C4⋊Q8—22no—
167C3×C4⋊Q8C2312yes—
168C3×C4⋊Q8C2311yescharacteristic
169C3×C4⋊Q8C2311yescharacteristic
170C3×#125—22no—
171C3×#125C2312yes—
172C3×C4×Q8—21no—
173C3×C4×Q8—21no—
174C3×C4×Q8C2311yescharacteristic
175C3×C4×Q8C2312yes—
176C3×C4×Q8C2311yescharacteristic
177C3×C4×Q8C2312yes—
178C3×C4×Q8C2311yescharacteristic
179#947—22no—
180#947C2311yescharacteristic
181#946—21no—
182#946—21no—
183#946—21no—
184#946—22no—
185#946—22no—
186#946D411yescharacteristic
187#946C2311yescharacteristic
188Q8×Dic3—22no—
189Q8×Dic3—21no—
190Q8×Dic3C2312yes—
191Q8×Dic3C2311yescharacteristic
192#944—22no—
193#944—21no—
194#944D411yescharacteristic
195#944C2312yes—
196C2×#216C2312yes—
197C2×#215C2311yescharacteristic
198C2×#215C2311yescharacteristic
199C2×D24C2311yescharacteristic
200C2×#204C2312yes—
201#898—22no—
202#898—22no—
203#898—22no—
204#898—22no—
205#898—21no—
206#897—21no—
207#897—22no—
208#897—21no—
209#897—22no—
210#897—22no—
211#897D411yescharacteristic
212#897C2312yes—
213#896—22no—
214#896—22no—
215#896—22no—
216#896—22no—
217#896—22no—
218#896D412yes—
219#895C2311yescharacteristic
220#894—21no—
221#894—22no—
222#893—21no—
223#893—22no—
224#893C2312yes—
225#893C2312yes—
226#893C2311yescharacteristic
227#892—21no—
228#892—21no—
229#892—21no—
230#892C2311yescharacteristic
231D3×C4⋊C4—21no—
232D3×C4⋊C4—21no—
233D3×C4⋊C4—22no—
234D3×C4⋊C4—22no—
235D3×C4⋊C4C2312yes—
236#890—22no—
237#890—21no—
238#890C2312yes—
239#890C2312yes—
240#890C2311yescharacteristic
241#889—22no—
242#889—22no—
243#889—22no—
244#889—22no—
245#889—22no—
246#889D412yes—
247#888—22no—
248#888—22no—
249#888—22no—
250#888—21no—
251#888D411yescharacteristic
252#888C2312yes—
253#888C2312yes—
254#887C2312yes—
255#887C2312yes—
256#876—22no—
257#876—22no—
258#875C2312yes—
259C4×D12—21no—
260C4×D12—21no—
261C4×D12—22no—
262C4×D12C2312yes—
263C4×D12C2311yescharacteristic
264C4×D12C2311yescharacteristic
265#872—22no—
266#872—22no—
267#872—21no—
268#872C2312yes—
269C42×D3—21no—
270C42×D3C2311yescharacteristic
271#870—21no—
272#870—22no—
273#869—21no—
274#869—22no—
275#869C2311yescharacteristic
276#869C2312yes—
277#869C2311yescharacteristic
278C4×Dic6—22no—
279C4×Dic6—21no—
280C4×Dic6—21no—
281C4×Dic6C2312yes—
282C4×Dic6C2312yes—
283C4×Dic6C2311yescharacteristic
284C3×#107C2311yescharacteristic
285C3×#107C2312yes—
286C3×#106C2312yes—
287C3×#106C2312yes—
288C3×#106C2312yes—
289C3×C4⋊C8C2311yescharacteristic
290C3×C4⋊C8C2312yes—
291C3×#103C2312yes—
292C3×#103C2311yescharacteristic
293C3×#103C2312yes—
294C3×#103C2311yescharacteristic
295C3×#97C2312yes—
296C3×C4×C8C2311yescharacteristic
297#835C2312yes—
298#835C2311yescharacteristic
299#835C2311yescharacteristic
300#821C2311yescharacteristic
301#821C2311yescharacteristic
302#821C2312yes—
303(C2×D3)⋊C8C2311yescharacteristic
304(C2×D3)⋊C8C2312yes—
305(C2×D3)⋊C8C2311yescharacteristic
306#818C2312yes—
307#818C2311yescharacteristic
308#816C2312yes—
309#816C2312yes—
310#816C2312yes—
311#815C2312yes—
312#815C2312yes—
313Dic3⋊C8C2312yes—
314Dic3⋊C8C2311yescharacteristic
315Dic3⋊C8C2312yes—
316Dic3⋊C8C2311yescharacteristic
317C8×Dic3C2312yes—
318#810C2312yes—
319#810C2312yes—
320#810C2312yes—
321#809C2312yes—
322#809C2312yes—
323#809C2311yescharacteristic
324#809C2311yescharacteristic
325#808C2312yes—
326#808C2312yes—
327#808C2311yescharacteristic
328#808C2312yes—
329#808C2311yescharacteristic
330#808C2312yes—
331#807C2312yes—
332C4⋊(C3⋊C8)C2311yescharacteristic
333C4⋊(C3⋊C8)C2312yes—
334C4×C3⋊C8C2311yescharacteristic
335C4×C3⋊C8C2312yes—
336#563—62no—
337Q82—32no—
338Q82C2×D311yescharacteristic
339#557—32no—
340#557—31no—
341#557—31no—
342#557C2×D311yescharacteristic
343#556—32no—
344#556—31no—
345#556—61no—
346#554—31no—
347#554—32no—
348#554—62no—
349#552—61no—
350D4×Q8—31no—
351D4×Q8—31no—
352D4×Q8—61no—
353D4×Q8—61no—
354#544—32no—
355#544—62no—
356#544—61no—
357#542—32no—
358#541—32no—
359#541—61no—
360#541—62no—
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#501C2×D312yes—
372#499—32no—
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—32no—
382#487—31no—
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—31no—
393#479—32no—
394#479C2×D312yes—
395#478—31no—
396#478—32no—
397#478—32no—
398#477—32no—
399#477C2×D311yescharacteristic
400#476—31no—
401#476—32no—
402#476—32no—
403#475—32no—
404#475—31no—
405#475—32no—
406#475—32no—
407#475—32no—
408#475C2×D311yescharacteristic
409#475C2×D312yes—
410#474—31no—
411#474—31no—
412#464—31no—
413#464—32no—
414#463—32no—
415#463—31no—
416#462—32no—
417#462—31no—
418#461—31no—
419#461—32no—
420#452—31no—
421#452—32no—
422#449—31no—
423#446—32no—
424#446—32no—
425#446—31no—
426#446C2×D311yescharacteristic
427C8×Q8—31no—
428C8×Q8—31no—
429#442—32no—
430#441—32no—
431#441—32no—
432#441C2×D312yes—
433#440—32no—
434#440—32no—
435C4×Q16—32no—
436C4×Q16C2×D311yescharacteristic
437C4×SD16—31no—
438C4×SD16—31no—
439C4×SD16—32no—
440C4×SD16—32no—
441C4×SD16—32no—
442C4×D8—31no—
443#433—32no—
444#433—32no—
445#432—31no—
446#431—31no—
447C2×C3×Q8—21no—
448C2×C3×Q8—22no—
449C2×C3×Q8—21no—
450C2×C3×Q8C2×D411yescharacteristic
451C2×C3×Q8C2411yescharacteristic
452C2×C3×Q8C2411yescharacteristic
453#239—22no—
454#239—22no—
455D3×Q8—82no—
456D3×Q8—82no—
457D3×Q8—82no—
458C2×D12—21no—
459C2×D12—21no—
460C2×D12C2411yescharacteristic
461C2×D12C2411yescharacteristic
462C2×C4×D3—21no—
463C2×C4×D3—21no—
464C2×C4×D3—21no—
465C2×C4×D3—21no—
466C2×C4×D3—22no—
467C2×C4×D3—22no—
468C2×C4×D3—22no—
469C2×C4×D3—22no—
470C2×C4×D3C2×D411yescharacteristic
471C2×C4×D3C2×D411yescharacteristic
472C2×C4×D3C2411yescharacteristic
473C2×Dic6—21no—
474C2×Dic6—22no—
475C2×Dic6—22no—
476C2×Dic6—22no—
477C2×Dic6C2×D411yescharacteristic
478C2×Dic6C2×D412yes—
479C2×Dic6C2412yes—
480C3×Q16—22no—
481C2×C3×C8C2412yes—
482C2×C3×C8C2411yescharacteristic
483C2×C3×C8C2411yescharacteristic
484C3×C4⋊C4—22no—
485C3×C4⋊C4—21no—
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⋊C4—21no—
493C3×C4⋊C4C2×D411yescharacteristic
494C3×C4⋊C4C2×D412yes—
495C3×C4⋊C4C2412yes—
496C3×C4⋊C4C2411yescharacteristic
497C3×C4⋊C4C2412yes—
498C3×C4⋊C4C2411yescharacteristic
499C3×C42—21no—
500C3×C42—22no—
501C3×C42—21no—
502C3×C42—22no—
503C3×C42C2411yescharacteristic
504C3×C42C2412yes—
505#216—24no—
506#215—22no—
507#215—22no—
508(C2×D3)⋊C4—21no—
509(C2×D3)⋊C4—21no—
510(C2×D3)⋊C4—22no—
511(C2×D3)⋊C4—22no—
512(C2×D3)⋊C4—22no—
513(C2×D3)⋊C4—21no—
514(C2×D3)⋊C4—21no—
515(C2×D3)⋊C4—22no—
516(C2×D3)⋊C4—21no—
517(C2×D3)⋊C4—21no—
518(C2×D3)⋊C4—22no—
519(C2×D3)⋊C4—21no—
520(C2×D3)⋊C4—21no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4C2×D412yes—
523(C2×D3)⋊C4C2×D412yes—
524C4⋊Dic3—22no—
525C4⋊Dic3—21no—
526C4⋊Dic3—21no—
527C4⋊Dic3—21no—
528C4⋊Dic3—21no—
529C4⋊Dic3—22no—
530C4⋊Dic3—22no—
531C4⋊Dic3—22no—
532C4⋊Dic3—22no—
533C4⋊Dic3—21no—
534C4⋊Dic3C2×D411yescharacteristic
535C4⋊Dic3C2×D412yes—
536C4⋊Dic3C2411yescharacteristic
537C4⋊Dic3C2411yescharacteristic
538C4⋊Dic3C2412yes—
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—21no—
549Dic3⋊C4—22no—
550Dic3⋊C4—22no—
551Dic3⋊C4C2×D412yes—
552Dic3⋊C4C2×D412yes—
553Dic3⋊C4C2×D412yes—
554Dic3⋊C4C2×D412yes—
555Dic3⋊C4C2×D412yes—
556C4×Dic3—22no—
557C4×Dic3—21no—
558C4×Dic3—22no—
559C4×Dic3—22no—
560C4×Dic3—21no—
561C4×Dic3—22no—
562C4×Dic3C2×D411yescharacteristic
563C4×Dic3C2×D411yescharacteristic
564C4×Dic3C2412yes—
565C4×Dic3C2411yescharacteristic
566C2×C3⋊C8C2411yescharacteristic
567C2×C3⋊C8C2412yes—
568C2×C3⋊C8C2411yescharacteristic
569D24—22no—
570#204—24no—
571C2×#41—31no—
572C22×Q8—61no—
573C22×Q8—61no—
574C22×Q8—61no—
575C2×Q16—32no—
576C2×Q16C22×D311yescharacteristic
577C2×SD16—31no—
578C2×SD16—31no—
579C2×SD16—32no—
580C2×D8—31no—
581C4⋊Q8—21no—
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—31no—
585C4⋊Q8—31no—
586C4⋊Q8—32no—
587C4⋊Q8—32no—
588C4⋊Q8—32no—
589C4⋊Q8—31no—
590C4⋊Q8—32no—
591C4⋊Q8—31no—
592C4⋊Q8—62no—
593C4⋊Q8—61no—
594C4⋊Q8—61no—
595C4⋊Q8—61no—
596C4⋊Q8—62no—
597C4⋊Q8—62no—
598C4⋊Q8—62no—
599C4⋊Q8—62no—
600C4⋊Q8C22×D311yescharacteristic
601C4⋊Q8C22×D311yescharacteristic
602C4⋊Q8C22×D312yes—
603#126—62no—
604#126—62no—
605#126—61no—
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—32no—
615#125—62no—
616#125—61no—
617#125—61no—
618#125—62no—
619#125—62no—
620#125—62no—
621#125—62no—
622#125—62no—
623#125—62no—
624#125C22×D312yes—
625#124—31no—
626#124—32no—
627#124—62no—
628#123—62no—
629#123—61no—
630C22⋊Q8—31no—
631C22⋊Q8—31no—
632C22⋊Q8—32no—
633C22⋊Q8—31no—
634C22⋊Q8—32no—
635C22⋊Q8—62no—
636C22⋊Q8—62no—
637C22⋊Q8—62no—
638C22⋊Q8—62no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—61no—
642C22⋊Q8—62no—
643C22⋊Q8—61no—
644C22⋊Q8—62no—
645C22⋊Q8—62no—
646C22⋊Q8—61no—
647C22⋊Q8—61no—
648C22⋊Q8—61no—
649C22⋊Q8—62no—
650#121—31no—
651C4×Q8—21no—
652C4×Q8—21no—
653C4×Q8—31no—
654C4×Q8—32no—
655C4×Q8—31no—
656C4×Q8—32no—
657C4×Q8—32no—
658C4×Q8—32no—
659C4×Q8—32no—
660C4×Q8—61no—
661C4×Q8—62no—
662C4×Q8—61no—
663C4×Q8—61no—
664C4×Q8—62no—
665C4×Q8C22×D311yescharacteristic
666C4×Q8C22×D312yes—
667C4×Q8C22×D311yescharacteristic
668C4×Q8C22×D312yes—
669C4×Q8C22×D311yescharacteristic
670C4×D4—31no—
671C4×D4—32no—
672C4×D4—32no—
673C4×D4—31no—
674C4×D4—32no—
675C4×D4—31no—
676C4×D4—62no—
677C4×D4—61no—
678C4×D4—61no—
679C4×D4—62no—
680C4×D4—61no—
681#117—32no—
682#117—31no—
683#117—61no—
684#117—62no—
685#117—62no—
686#117—61no—
687#117—61no—
688#117—61no—
689C2×C4⋊C4—32no—
690C2×C4⋊C4—62no—
691C2×C4⋊C4—62no—
692C2×C4⋊C4—61no—
693C2×C4⋊C4—61no—
694C2×C42—31no—
695C2×C42—61no—
696#107—31no—
697#107—32no—
698#107—32no—
699#107C22×D311yescharacteristic
700#107C22×D312yes—
701#106—32no—
702#106—31no—
703#106—32no—
704#106—31no—
705#106—32no—
706#106—32no—
707#106C22×D312yes—
708#106C22×D312yes—
709#106C22×D312yes—
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—32no—
720#103—31no—
721#103—32no—
722#103—32no—
723#103—32no—
724#103—32no—
725#103—32no—
726#103—32no—
727#103C22×D312yes—
728#103C22×D311yescharacteristic
729#103C22×D311yescharacteristic
730#103C22×D312yes—
731#102—31no—
732#102—31no—
733#102—32no—
734#102—31no—
735#102—32no—
736#102—31no—
737#102—32no—
738C22⋊C8—31no—
739C22⋊C8—31no—
740C22⋊C8—32no—
741#97—32no—
742#97—32no—
743#97C22×D312yes—
744C4×C8—32no—
745C4×C8—31no—
746C4×C8—32no—
747C4×C8C22×D311yescharacteristic
748C22×D3—21no—
749C22×D3—21no—
750C22×D3C22×D411yescharacteristic
751C3×Q8—22no—
752C3×Q8—21no—
753C3×Q8—21no—
754C3×Q8—21no—
755C3×Q8—42no—
756C3×Q8—82no—
757C3×Q8—81no—
758C3×Q82−1+412yes—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—22no—
763C2×C3×C4—21no—
764C2×C3×C4—22no—
765C2×C3×C4C22×D412yes—
766C2×C3×C4C22×D411yescharacteristic
767C2×C3×C4C22×D412yes—
768C2×C3×C4C22×D411yescharacteristic
769C2×C3×C4C2511yescharacteristic
770C2×Dic3—22no—
771C2×Dic3—21no—
772C2×Dic3—21no—
773C2×Dic3—22no—
774C2×Dic3C22×D411yescharacteristic
775C2×Dic3C22×D411yescharacteristic
776C2×Dic3C22×D411yescharacteristic
777C2×Dic3C22×D412yes—
778C2×Dic3C22×D412yes—
779D12—24no—
780D12—21no—
781D12—21no—
782D12—21no—
783D12—81no—
784D122−1+412yes—
785C4×D3—24no—
786C4×D3—22no—
787C4×D3—21no—
788C4×D3—21no—
789C4×D3—41no—
790C4×D3—42no—
791C4×D3—42no—
792C4×D3—42no—
793C4×D3—82no—
794C4×D3—82no—
795C4×D3—82no—
796C4×D3—82no—
797Dic6—22no—
798Dic6—22no—
799Dic6—22no—
800Dic6—42no—
801Dic6—42no—
802Dic6—82no—
803Dic6—82no—
804Dic6—82no—
805C3×C8—22no—
806C3×C8—21no—
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—22no—
816C2×Q8—31no—
817C2×Q8—32no—
818C2×Q8—32no—
819C2×Q8—62no—
820C2×Q8—62no—
821C2×Q8—61no—
822C2×Q8—62no—
823C2×Q8—242no—
824C2×Q8—242no—
825C2×Q8—242no—
826C2×Q8D3×D411yescharacteristic
827C2×Q8C23×D311yescharacteristic
828C2×Q8C23×D311yescharacteristic
829C2×D4—31no—
830C2×D4—31no—
831C2×D4—61no—
832C2×D4—61no—
833C22×C4—31no—
834C22×C4—31no—
835C22×C4—31no—
836C22×C4—61no—
837C22×C4—61no—
838C22×C4—62no—
839C22×C4—62no—
840C22×C4—62no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—62no—
844Q16—22no—
845Q16—64no—
846SD16—64no—
847SD16—62no—
848SD16—62no—
849D8—62no—
850C2×C8—31no—
851C2×C8—31no—
852C2×C8—32no—
853C2×C8C23×D312yes—
854C2×C8C23×D311yescharacteristic
855C2×C8C23×D311yescharacteristic
856C4⋊C4—21no—
857C4⋊C4—22no—
858C4⋊C4—21no—
859C4⋊C4—22no—
860C4⋊C4—21no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—32no—
866C4⋊C4—31no—
867C4⋊C4—32no—
868C4⋊C4—32no—
869C4⋊C4—32no—
870C4⋊C4—32no—
871C4⋊C4—32no—
872C4⋊C4—32no—
873C4⋊C4—31no—
874C4⋊C4—31no—
875C4⋊C4—62no—
876C4⋊C4—62no—
877C4⋊C4—62no—
878C4⋊C4—62no—
879C4⋊C4—62no—
880C4⋊C4—61no—
881C4⋊C4—61no—
882C4⋊C4—62no—
883C4⋊C4—61no—
884C4⋊C4—61no—
885C4⋊C4—62no—
886C4⋊C4—62no—
887C4⋊C4—62no—
888C4⋊C4—62no—
889C4⋊C4—62no—
890C4⋊C4—62no—
891C4⋊C4—62no—
892C4⋊C4—61no—
893C4⋊C4—61no—
894C4⋊C4—62no—
895C4⋊C4—62no—
896C4⋊C4—61no—
897C4⋊C4D3×D411yescharacteristic
898C4⋊C4D3×D412yes—
899C4⋊C4C23×D311yescharacteristic
900C4⋊C4C23×D312yes—
901C4⋊C4C23×D312yes—
902C4⋊C4C23×D311yescharacteristic
903C22⋊C4—32no—
904C22⋊C4—32no—
905C22⋊C4—61no—
906C22⋊C4—61no—
907C22⋊C4—62no—
908C22⋊C4—61no—
909C22⋊C4—61no—
910C22⋊C4—62no—
911C22⋊C4—61no—
912C22⋊C4—62no—
913C22⋊C4—61no—
914C22⋊C4—61no—
915C22⋊C4—62no—
916C22⋊C4—62no—
917C22⋊C4—62no—
918C22⋊C4—61no—
919C42—21no—
920C42—22no—
921C42—21no—
922C42—22no—
923C42—31no—
924C42—31no—
925C42—32no—
926C42—31no—
927C42—61no—
928C42—61no—
929C42—62no—
930C42—62no—
931C42—62no—
932C42—62no—
933C42C23×D311yescharacteristic
934C42C23×D312yes—
935C22×C3C23×D411yescharacteristic
936C2×D3—21no—
937C2×D3—21no—
938C2×D3—22no—
939C2×D3—21no—
940C2×D3—41no—
941C2×D3—41no—
942C2×D3—41no—
943C2×D3—41no—
944C2×D3—41no—
945C3×C4—22no—
946C3×C4—21no—
947C3×C4—22no—
948C3×C4—22no—
949C3×C4—41no—
950C3×C4—42no—
951C3×C4—41no—
952C3×C4—41no—
953C3×C4—42no—
954C3×C4#57712yes—
955C3×C4C2×2−1+411yescharacteristic
956C3×C4C2×2−1+411yescharacteristic
957Dic3—21no—
958Dic3—22no—
959Dic3—21no—
960Dic3—22no—
961Dic3—21no—
962Dic3—42no—
963Dic3—42no—
964Dic3—41no—
965Dic3—41no—
966C23—31no—
967C23—61no—
968C23—61no—
969Q8—21no—
970Q8—22no—
971Q8—21no—
972Q8—21no—
973Q8—42no—
974Q8—62no—
975Q8—62no—
976Q8—62no—
977Q8—81no—
978Q8—82no—
979Q8—122no—
980Q8—122no—
981Q8—242no—
982Q8—242no—
983Q8—242no—
984Q8#100712yes—
985D4—32no—
986D4—64no—
987D4—61no—
988D4—61no—
989D4—61no—
990D4—241no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—31no—
998C2×C4—31no—
999C2×C4—31no—
1000C2×C4—32no—
1001C2×C4—32no—
1002C2×C4—64no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—62no—
1006C2×C4—62no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—62no—
1010C2×C4—121no—
1011C2×C4—122no—
1012C2×C4—122no—
1013C2×C4—122no—
1014C2×C4—242no—
1015C2×C4—242no—
1016C2×C4—242no—
1017C2×C4—242no—
1018C2×C4C2×D3×D412yes—
1019C2×C4C2×D3×D412yes—
1020C2×C4C2×D3×D411yescharacteristic
1021C2×C4C2×D3×D411yescharacteristic
1022C2×C4C24×D311yescharacteristic
1023C8—21no—
1024C8—21no—
1025C8—22no—
1026C8—61no—
1027C8—62no—
1028C8—61no—
1029C2×C3#348611yescharacteristic
1030C2×C3C2×#57711yescharacteristic
1031C2×C3#358611yescharacteristic
1032D3—41no—
1033D3—42no—
1034D3—81no—
1035C22—61no—
1036C22—61no—
1037C22—62no—
1038C22—61no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22—121no—
1044C22C22×D3×D411yescharacteristic
1045C4—22no—
1046C4—21no—
1047C4—22no—
1048C4—22no—
1049C4—42no—
1050C4—41no—
1051C4—42no—
1052C4—41no—
1053C4—41no—
1054C4—61no—
1055C4—62no—
1056C4—61no—
1057C4—62no—
1058C4—61no—
1059C4—121no—
1060C4—121no—
1061C4—122no—
1062C4—122no—
1063C4#577812yes—
1064C4C2×#100711yescharacteristic
1065C4D3×2−1+411yescharacteristic
1066C3#6185811yescharacteristic, complemented, Sylow
1067C2—121no—
1068C2—122no—
1069C2—241no—
1070C2#8675911yescharacteristic
1071C2C2×#577811yescharacteristic
1072C2#8720811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3387C2
socleC22×C3C23×D4
prime radical#4810C22
hypercenter#3387D3
hypocenterC3#61858
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3387

Complements

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

NH ≅ G/Ntype
1. #87048C2semidirect
2. #87018C2semidirect
3. C3×#3387C2semidirect
4. Q8×#215C2semidirect
5. #83689C2semidirect
6. #81989C2semidirect
7. #81968C2semidirect
8. #81905C2semidirect
9. #81896C2semidirect
10. #81265C2semidirect
11. #81241C2semidirect
12. #81136C2semidirect
13. #81095C2semidirect
14. #81043C2semidirect
15. #81037C2semidirect
16. #81018C2semidirect
18. #79970C2semidirect
19. #79965C2semidirect
20. #79849C2semidirect
21. #79815C2semidirect
23. #79702C2semidirect
140. #3387D3semidirect
1066. C3#61858semidirect

Maximal subgroups

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

subgroupindex
#870482
#870182
C3×#33872
Q8×#2152
#836892
#819892
#819682
#819052
#818962
#812652
#812412
#811362
#810952
#810432
#810372
#810182
#810012
#799702
#799652
#798492
#798152
#797462
#797022
#618583