Finite Group Databasebeta

← #11685732

Subgroups — #11685732

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#86956C211yesmaximal, characteristic, complemented
2#86747C211yesmaximal, characteristic, complemented
3C3×#3384C211yesmaximal, characteristic, complemented
4#83629C211yesmaximal, characteristic, complemented
5#83568C211yesmaximal, characteristic, complemented
6#81987C212yesmaximal, complemented
7#81967C212yesmaximal, complemented
8#81906C211yesmaximal, characteristic, complemented
9#81896C211yesmaximal, characteristic, complemented
10#81160C212yesmaximal, complemented
11#81145C212yesmaximal, complemented
12#81091C212yesmaximal, complemented
13#81069C212yesmaximal, complemented
14#81053C211yesmaximal, characteristic, complemented
15#81047C211yesmaximal, characteristic, complemented
16#80994C211yesmaximal, characteristic, complemented
17#80972C211yesmaximal, characteristic, complemented
18#79983C211yesmaximal, characteristic, complemented
19#79965C211yesmaximal, characteristic, complemented
20#79875C212yesmaximal
21#79854C212yesmaximal, complemented
22#79591C211yesmaximal, characteristic
23#79571C211yesmaximal, characteristic, complemented
24#61858—31nomaximal, Sylow
25C3×#554C2211yescharacteristic
26C3×D4×Q8C2211yescharacteristic
27Q8×#67—21no—
28C2×#944—21no—
29#5729C2212yes—
30#5728C2211yescharacteristic
31D3×C4⋊Q8C2211yescharacteristic
32#5722C2212yes—
33#5722C2211yescharacteristic
34#5721C2211yescharacteristic
35#5698C2212yes—
36#5685C2212yes—
37#5646—22no—
38#5641—21no—
39#5636—22no—
40#5632—21no—
41#5625—21no—
42#5625—22no—
43#5623—22no—
44#5622—21no—
45#5578C2211yescharacteristic
46#5570C2211yescharacteristic
47#5567C2211yescharacteristic
48#5561C2212yes—
49#5557C2211yescharacteristic
50#5546C2212yes—
51#5542C2211yescharacteristic
52#5542C2212yes—
53#5539C2212yes—
54D4×Dic6C2211yescharacteristic
55C4×#237C2211yescharacteristic
56#5513—21no—
57#5500—21no—
58C3×#501C2212yes—
59C3×#498C2211yescharacteristic
60C3×#478C2212yes—
61C3×#476C2211yescharacteristic
62C3×#476C2212yes—
63C3×#474C2211yescharacteristic
64C3×#446C2211yescharacteristic
65C3×#442C2212yes—
66C3×C4×D8C2211yescharacteristic
67#5158C2211yescharacteristic
68#5153C2212yes—
69#5153C2211yescharacteristic
70#5094C2212yes—
71#5094C2211yescharacteristic
72#5093C2212yes—
73#5093C2211yescharacteristic
74#5091C2211yescharacteristic
75#5080C2211yescharacteristic
76#5065C2212yes—
77#5063C2212yes—
78Q8×C3⋊C8C2211yescharacteristic
79#5019C2211yescharacteristic
80#5019C2212yes—
81C4×#214C2212yes—
82C4×#214C2212yes—
83C4×#214C2211yescharacteristic
84C4×#214C2211yescharacteristic
85#5009C2212yes—
86#5007C2211yescharacteristic
87#4888C2211yescharacteristic
88#4884C2212yes—
89#4877C2212yes—
90#4877C2211yescharacteristic
91#4876C2212yes—
92#4875C2212yes—
93#4873C2212yes—
94#4868C2212yes—
95#4862C2212yes—
96#4862C2212yes—
97#4857C2212yes—
98#4856C2212yes—
99#4855C2212yes—
100#4854C2212yes—
101#4854C2212yes—
102#4854C2212yes—
103#4854C2212yes—
104#4853C2212yes—
105#4853C2212yes—
106#4851C2211yescharacteristic
107#4849C2211yescharacteristic
108#4849C2212yes—
109#4840C2212yes—
110#4835C2211yescharacteristic
111#4831C2212yes—
112#4830C2211yescharacteristic
113#4829C2212yes—
114#4784C2211yescharacteristic
115#4783C2212yes—
116#4783C2211yescharacteristic
117#4777C2212yes—
118#4768C2212yes—
119#4767C2212yes—
120#4767C2211yescharacteristic
121#4766C2211yescharacteristic
122#4765C2212yes—
123#4765C2212yes—
124#4761C2212yes—
125#4758C2212yes—
126#4757C2212yes—
127#4757C2212yes—
128#4716C2212yes—
129#4709C2212yes—
130#4703C2212yes—
131#4701C2212yes—
132C4×Dic12C2211yescharacteristic
133#4685C2211yescharacteristic
134#4681C2211yescharacteristic
135#4679C2211yescharacteristic
136#3555—31no—
137#3503—31no—
138#3388—32no—
139#3387—32no—
140#3387—31no—
141#3384D311yescharacteristic, complemented
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—
159C22×C3×Q8—21no—
160C2×D3×Q8—21no—
161C2×#237C2311yescharacteristic
162C22×Dic6—21no—
163C2×C3×D8C2311yescharacteristic
164C3×C4⋊Q8C2311yescharacteristic
165C3×C4⋊Q8C2311yescharacteristic
166C3×C4⋊Q8C2312yes—
167C3×#125C2312yes—
168C3×C22⋊Q8—21no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8—22no—
171C3×C22⋊Q8—22no—
172C3×C4×Q8C2311yescharacteristic
173C3×C4×D4C2311yescharacteristic
174C3×C4×D4C2312yes—
175C3×C4×D4C2311yescharacteristic
176C3×C4×D4C2312yes—
177C2×C3×C4⋊C4—21no—
178#946—21no—
179#946—22no—
180#946D411yescharacteristic
181Q8×Dic3—21no—
182Q8×Dic3—21no—
183Q8×Dic3—21no—
184#944—21no—
185#944—21no—
186#944—22no—
187#944—22no—
188#944—22no—
189#944—22no—
190#944—21no—
191#944D411yescharacteristic
192#938C2311yescharacteristic
193#936C2311yescharacteristic
194#936C2312yes—
195D4×Dic3C2311yescharacteristic
196D4×Dic3C2312yes—
197C2×#214C2312yes—
198C2×#214C2311yescharacteristic
199C2×#214C2311yescharacteristic
200#929—22no—
201C4×#67—21no—
202C4×#67—21no—
203C4×#67—22no—
204#926—21no—
205#926—22no—
206#926—21no—
207#924—22no—
208#924—21no—
209#924—21no—
210#924—22no—
211#924—22no—
212C2×Dic3⋊C4—22no—
213C2×Dic3⋊C4—22no—
214C2×C4×Dic3—21no—
215C2×Dic12C2312yes—
216C2×Dic12C2311yescharacteristic
217#898—22no—
218#898—22no—
219#897D411yescharacteristic
220#897C2312yes—
221#897C2311yescharacteristic
222#896—22no—
223#896D412yes—
224#892—21no—
225#892C2311yescharacteristic
226D3×C4⋊C4—21no—
227D3×C4⋊C4C2312yes—
228#890—22no—
229#890—21no—
230#890—22no—
231#890—22no—
232#890—21no—
233#890C2311yescharacteristic
234#890C2312yes—
235#889—22no—
236#889—22no—
237#889—22no—
238#889—22no—
239#889—22no—
240#889D412yes—
241#888—22no—
242#888—22no—
243#888—21no—
244#888—21no—
245#888D411yescharacteristic
246#888C2312yes—
247#888C2312yes—
248#888C2312yes—
249#887—22no—
250#887—21no—
251#887—21no—
252#887—22no—
253#887C2312yes—
254#887C2312yes—
255#887C2311yescharacteristic
256#887C2312yes—
257#887C2312yes—
258#885—22no—
259#883—21no—
260#67⋊C4—21no—
261#67⋊C4—22no—
262#879—22no—
263#879—22no—
264#879—22no—
265#879—22no—
266#879—21no—
267#878—22no—
268#878—22no—
269#878—22no—
270#877—22no—
271#877—21no—
272#872C2312yes—
273C42×D3C2311yescharacteristic
274#870C2312yes—
275#869C2312yes—
276#869C2311yescharacteristic
277#869C2311yescharacteristic
278C4×Dic6C2312yes—
279C4×Dic6C2311yescharacteristic
280C4×Dic6C2311yescharacteristic
281C4×Dic6C2312yes—
282C4×Dic6C2312yes—
283C4×Dic6C2311yescharacteristic
284C3×#107C2312yes—
285C3×#107C2311yescharacteristic
286C3×#106C2312yes—
287C3×#106C2312yes—
288C3×#106C2312yes—
289C3×C4⋊C8C2312yes—
290C3×C4⋊C8C2311yescharacteristic
291C3×#102C2311yescharacteristic
292C3×#102C2312yes—
293C3×#102C2311yescharacteristic
294C3×#102C2312yes—
295C3×#97C2312yes—
296C3×C4×C8C2311yescharacteristic
297#832C2312yes—
298#832C2311yescharacteristic
299#832C2311yescharacteristic
300(C2×D3)⋊C8C2312yes—
301(C2×D3)⋊C8C2311yescharacteristic
302(C2×D3)⋊C8C2311yescharacteristic
303#818C2311yescharacteristic
304#817C2312yes—
305#816C2312yes—
306#816C2312yes—
307#816C2311yescharacteristic
308#816C2312yes—
309#816C2311yescharacteristic
310#816C2312yes—
311#815C2312yes—
312#815C2312yes—
313Dic3⋊C8C2312yes—
314Dic3⋊C8C2311yescharacteristic
315Dic3⋊C8C2312yes—
316Dic3⋊C8C2311yescharacteristic
317C8×Dic3C2312yes—
318#810C2312yes—
319#810C2311yescharacteristic
320#810C2312yes—
321#810C2312yes—
322#810C2312yes—
323#810C2311yescharacteristic
324#810C2312yes—
325#808C2312yes—
326#808C2311yescharacteristic
327#808C2311yescharacteristic
328#808C2312yes—
329#808C2312yes—
330#807C2312yes—
331#807C2312yes—
332C4⋊(C3⋊C8)C2311yescharacteristic
333C4⋊(C3⋊C8)C2312yes—
334C4×C3⋊C8C2311yescharacteristic
335C4×C3⋊C8C2312yes—
336#563—62no—
337Q82—32no—
338Q82—31no—
339#557—31no—
340#557—32no—
341#557—31no—
342#557—31no—
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—61no—
352D4×Q8—61no—
353D4×Q8C2×D311yescharacteristic
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#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—31no—
384#485—32no—
385#484—32no—
386#483—32no—
387#483—32no—
388#482—31no—
389#481—32no—
390#479—32no—
391#479—31no—
392#479—32no—
393#479—32no—
394#479—32no—
395#478—32no—
396#478—31no—
397#478C2×D312yes—
398#477—31no—
399#477—32no—
400#476—32no—
401#476C2×D312yes—
402#476C2×D311yescharacteristic
403#475—31no—
404#475—32no—
405#475—32no—
406#475—32no—
407#475—32no—
408#475—32no—
409#475—31no—
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—32no—
424#446—32no—
425#446—31no—
426#446C2×D311yescharacteristic
427C8×Q8—31no—
428C8×Q8—31no—
429#442C2×D312yes—
430#441—32no—
431#441—32no—
432#441—32no—
433#440—32no—
434#440—32no—
435C4×Q16—32no—
436C4×Q16—31no—
437C4×SD16—31no—
438C4×SD16—31no—
439C4×SD16—32no—
440C4×SD16—32no—
441C4×SD16—32no—
442C4×D8C2×D311yescharacteristic
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×Q8—82no—
451C2×C3×Q8C2×D411yescharacteristic
452C2×C3×D4C2411yescharacteristic
453C2×C3×D4C2411yescharacteristic
454C22×C3×C4—21no—
455C22×C3×C4—21no—
456C22×C3×C4—22no—
457C22×C3×C4—22no—
458C2×#67—21no—
459C2×#67—21no—
460C22×Dic3—21no—
461C22×Dic3—21no—
462C22×Dic3—22no—
463D3×Q8—82no—
464#237—22no—
465#237—22no—
466C2×C4×D3—22no—
467C2×C4×D3C2×D411yescharacteristic
468C2×C4×D3C2×D411yescharacteristic
469C2×C4×D3C2411yescharacteristic
470C2×Dic6—21no—
471C2×Dic6—22no—
472C2×Dic6—22no—
473C2×Dic6—22no—
474C2×Dic6—82no—
475C2×Dic6C2×D411yescharacteristic
476C2×Dic6C2×D412yes—
477C2×Dic6C2412yes—
478C2×Dic6C2411yescharacteristic
479C2×Dic6C2411yescharacteristic
480C3×D8—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—21no—
488C3×C4⋊C4—22no—
489C3×C4⋊C4C2×D411yescharacteristic
490C3×C4⋊C4C2×D412yes—
491C3×C4⋊C4C2411yescharacteristic
492C3×C4⋊C4C2412yes—
493C3×C4⋊C4C2411yescharacteristic
494C3×C4⋊C4C2412yes—
495C3×C22⋊C4—21no—
496C3×C22⋊C4—22no—
497C3×C22⋊C4—21no—
498C3×C22⋊C4—22no—
499C3×C42C2411yescharacteristic
500C3×C42C2412yes—
501#217—21no—
502#217—22no—
503#217—21no—
504#217—22no—
505#217—21no—
506#217—21no—
507#217—22no—
508#214—24no—
509#214—22no—
510#214—22no—
511(C2×D3)⋊C4—21no—
512(C2×D3)⋊C4—21no—
513(C2×D3)⋊C4—22no—
514(C2×D3)⋊C4C2×D412yes—
515(C2×D3)⋊C4C2×D412yes—
516C4⋊Dic3—21no—
517C4⋊Dic3—22no—
518C4⋊Dic3—21no—
519C4⋊Dic3—22no—
520C4⋊Dic3—21no—
521C4⋊Dic3—22no—
522C4⋊Dic3—21no—
523C4⋊Dic3—22no—
524C4⋊Dic3—21no—
525C4⋊Dic3C2×D412yes—
526C4⋊Dic3C2×D411yescharacteristic
527C4⋊Dic3C2411yescharacteristic
528C4⋊Dic3C2412yes—
529C4⋊Dic3C2411yescharacteristic
530Dic3⋊C4—21no—
531Dic3⋊C4—21no—
532Dic3⋊C4—22no—
533Dic3⋊C4—22no—
534Dic3⋊C4—22no—
535Dic3⋊C4—22no—
536Dic3⋊C4—21no—
537Dic3⋊C4—22no—
538Dic3⋊C4—22no—
539Dic3⋊C4—22no—
540Dic3⋊C4—22no—
541Dic3⋊C4—21no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4C2×D412yes—
548Dic3⋊C4C2×D412yes—
549Dic3⋊C4C2×D412yes—
550Dic3⋊C4C2×D412yes—
551Dic3⋊C4C2×D412yes—
552C4×Dic3—22no—
553C4×Dic3—22no—
554C4×Dic3—21no—
555C4×Dic3—21no—
556C4×Dic3—22no—
557C4×Dic3—21no—
558C4×Dic3—22no—
559C4×Dic3—22no—
560C4×Dic3—22no—
561C4×Dic3—21no—
562C4×Dic3C2×D411yescharacteristic
563C4×Dic3C2×D411yescharacteristic
564C4×Dic3C2412yes—
565C4×Dic3C2411yescharacteristic
566C2×C3⋊C8C2411yescharacteristic
567C2×C3⋊C8C2412yes—
568C2×C3⋊C8C2411yescharacteristic
569Dic12—24no—
570Dic12—22no—
571C2×#41—31no—
572C22×Q8—21no—
573C22×Q8—61no—
574C22×Q8—61no—
575C2×Q16—32no—
576C2×Q16—31no—
577C2×SD16—31no—
578C2×SD16—31no—
579C2×SD16—32no—
580C2×D8C22×D311yescharacteristic
581C4⋊Q8—31no—
582C4⋊Q8—31no—
583C4⋊Q8—32no—
584C4⋊Q8—32no—
585C4⋊Q8—32no—
586C4⋊Q8—31no—
587C4⋊Q8—31no—
588C4⋊Q8—32no—
589C4⋊Q8—61no—
590C4⋊Q8—61no—
591C4⋊Q8—62no—
592C4⋊Q8—61no—
593C4⋊Q8—62no—
594C4⋊Q8—62no—
595C4⋊Q8—62no—
596C4⋊Q8—62no—
597C4⋊Q8—62no—
598C4⋊Q8—61no—
599C4⋊Q8—61no—
600C4⋊Q8C22×D311yescharacteristic
601C4⋊Q8C22×D311yescharacteristic
602C4⋊Q8C22×D312yes—
603#126—61no—
604#126—62no—
605#126—62no—
606#126—62no—
607#126—62no—
608#126—62no—
609#126—62no—
610#125—32no—
611#125—31no—
612#125—32no—
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#125—62no—
624#125C22×D312yes—
625#124—31no—
626#124—32no—
627#124—62no—
628#123—61no—
629#123—62no—
630C22⋊Q8—21no—
631C22⋊Q8—21no—
632C22⋊Q8—22no—
633C22⋊Q8—22no—
634C22⋊Q8—31no—
635C22⋊Q8—31no—
636C22⋊Q8—32no—
637C22⋊Q8—31no—
638C22⋊Q8—32no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—62no—
643C22⋊Q8—62no—
644C22⋊Q8—61no—
645C22⋊Q8—62no—
646C22⋊Q8—62no—
647C22⋊Q8—61no—
648C22⋊Q8—62no—
649C22⋊Q8—61no—
650#121—31no—
651C4×Q8—31no—
652C4×Q8—32no—
653C4×Q8—31no—
654C4×Q8—32no—
655C4×Q8—32no—
656C4×Q8—32no—
657C4×Q8—32no—
658C4×Q8—31no—
659C4×Q8—32no—
660C4×Q8—31no—
661C4×Q8—32no—
662C4×Q8—61no—
663C4×Q8—62no—
664C4×Q8—62no—
665C4×Q8—61no—
666C4×Q8—61no—
667C4×Q8—61no—
668C4×Q8—61no—
669C4×Q8C22×D311yescharacteristic
670C4×D4—31no—
671C4×D4—32no—
672C4×D4—62no—
673C4×D4—61no—
674C4×D4—62no—
675C4×D4—61no—
676C4×D4—61no—
677C4×D4C22×D311yescharacteristic
678C4×D4C22×D312yes—
679C4×D4C22×D311yescharacteristic
680C4×D4C22×D312yes—
681#117—32no—
682#117—31no—
683#117—61no—
684#117—61no—
685#117—62no—
686#117—61no—
687#117—62no—
688#117—61no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—32no—
691C2×C4⋊C4—61no—
692C2×C4⋊C4—62no—
693C2×C4⋊C4—62no—
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—32no—
703#106—32no—
704#106—31no—
705#106—32no—
706#106—31no—
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—32no—
719#103—31no—
720#103—31no—
721#103—32no—
722#103—32no—
723#103—32no—
724#103—31no—
725#103—32no—
726#103—31no—
727#103—32no—
728#103—32no—
729#103—32no—
730#103—32no—
731#102—31no—
732#102—32no—
733#102—31no—
734#102C22×D311yescharacteristic
735#102C22×D311yescharacteristic
736#102C22×D312yes—
737#102C22×D312yes—
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
748C23×C3—21no—
749C23×C3—21no—
750C22×D3C22×D411yescharacteristic
751C3×Q8—22no—
752C3×Q8—42no—
753C3×Q8—81no—
754C3×Q8—82no—
755C3×D4—21no—
756C3×D4—21no—
757C3×D4—21no—
758C3×D42−1+412yes—
759C2×C3×C4—21no—
760C2×C3×C4—22no—
761C2×C3×C4—21no—
762C2×C3×C4—22no—
763C2×C3×C4—42no—
764C2×C3×C4—42no—
765C2×C3×C4—82no—
766C2×C3×C4—82no—
767C2×C3×C4C22×D412yes—
768C2×C3×C4C22×D412yes—
769C2×C3×C4C22×D411yescharacteristic
770C2×C3×C4C22×D411yescharacteristic
771C2×C3×C4C2511yescharacteristic
772#67—24no—
773#67—81no—
774C2×Dic3—24no—
775C2×Dic3—21no—
776C2×Dic3—21no—
777C2×Dic3—22no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—22no—
781C2×Dic3—42no—
782C2×Dic3—82no—
783C2×Dic3C22×D411yescharacteristic
784C2×Dic3C22×D412yes—
785C2×Dic3C22×D411yescharacteristic
786C2×Dic3C22×D411yescharacteristic
787C2×Dic3C22×D412yes—
788C4×D3—22no—
789C4×D3—21no—
790C4×D3—21no—
791C4×D3—41no—
792C4×D3—82no—
793Dic6—22no—
794Dic6—21no—
795Dic6—22no—
796Dic6—21no—
797Dic6—22no—
798Dic6—21no—
799Dic6—42no—
800Dic6—42no—
801Dic6—82no—
802Dic6—82no—
803Dic6—82no—
804Dic62−1+412yes—
805C3×C8—22no—
806C3×C8—21no—
807C3×C8—21no—
808C3⋊C8—22no—
809C3⋊C8—21no—
810C3⋊C8—21no—
811#41—62no—
812#41—62no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—22no—
816C2×Q8—31no—
817C2×Q8—32no—
818C2×Q8—31no—
819C2×Q8—31no—
820C2×Q8—32no—
821C2×Q8—62no—
822C2×Q8—62no—
823C2×Q8—62no—
824C2×Q8—61no—
825C2×Q8—82no—
826C2×Q8—242no—
827C2×Q8—242no—
828C2×Q8D3×D411yescharacteristic
829C2×D4—61no—
830C2×D4—61no—
831C2×D4C23×D311yescharacteristic
832C2×D4C23×D311yescharacteristic
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—31no—
838C22×C4—31no—
839C22×C4—31no—
840C22×C4—62no—
841C22×C4—61no—
842C22×C4—61no—
843C22×C4—62no—
844Q16—64no—
845Q16—62no—
846SD16—62no—
847SD16—62no—
848SD16—64no—
849D8—22no—
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—22no—
861C4⋊C4—32no—
862C4⋊C4—32no—
863C4⋊C4—32no—
864C4⋊C4—31no—
865C4⋊C4—32no—
866C4⋊C4—32no—
867C4⋊C4—32no—
868C4⋊C4—32no—
869C4⋊C4—31no—
870C4⋊C4—31no—
871C4⋊C4—62no—
872C4⋊C4—62no—
873C4⋊C4—62no—
874C4⋊C4—62no—
875C4⋊C4—61no—
876C4⋊C4—61no—
877C4⋊C4—61no—
878C4⋊C4—61no—
879C4⋊C4—62no—
880C4⋊C4—62no—
881C4⋊C4—62no—
882C4⋊C4—62no—
883C4⋊C4—62no—
884C4⋊C4—62no—
885C4⋊C4—62no—
886C4⋊C4—62no—
887C4⋊C4—62no—
888C4⋊C4—61no—
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—21no—
906C22⋊C4—22no—
907C22⋊C4—32no—
908C22⋊C4—32no—
909C22⋊C4—61no—
910C22⋊C4—62no—
911C22⋊C4—61no—
912C22⋊C4—61no—
913C22⋊C4—61no—
914C22⋊C4—62no—
915C22⋊C4—61no—
916C22⋊C4—61no—
917C22⋊C4—62no—
918C22⋊C4—62no—
919C42—31no—
920C42—31no—
921C42—32no—
922C42—31no—
923C42—61no—
924C42—61no—
925C42—62no—
926C42—62no—
927C42—62no—
928C42—62no—
929C42—61no—
930C42—62no—
931C42—61no—
932C42—62no—
933C42C23×D311yescharacteristic
934C42C23×D312yes—
935C22×C3—22no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3—41no—
939C22×C3—41no—
940C22×C3—41no—
941C22×C3C23×D411yescharacteristic
942C2×D3—21no—
943C2×D3—21no—
944C2×D3—21no—
945C3×C4—22no—
946C3×C4—21no—
947C3×C4—22no—
948C3×C4—42no—
949C3×C4—41no—
950C3×C4—42no—
951C3×C4—41no—
952C3×C4#57712yes—
953C3×C4C2×2−1+411yescharacteristic
954C3×C4C2×2−1+411yescharacteristic
955Dic3—21no—
956Dic3—22no—
957Dic3—22no—
958Dic3—21no—
959Dic3—22no—
960Dic3—21no—
961Dic3—41no—
962Dic3—41no—
963Dic3—42no—
964Dic3—41no—
965Dic3—42no—
966C23—21no—
967C23—21no—
968C23—31no—
969Q8—22no—
970Q8—32no—
971Q8—42no—
972Q8—61no—
973Q8—62no—
974Q8—61no—
975Q8—62no—
976Q8—61no—
977Q8—62no—
978Q8—82no—
979Q8—81no—
980Q8—122no—
981Q8—122no—
982Q8—242no—
983Q8—242no—
984Q8—242no—
985D4—21no—
986D4—21no—
987D4—21no—
988D4—64no—
989D4—241no—
990D4#100712yes—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—31no—
996C2×C4—31no—
997C2×C4—31no—
998C2×C4—32no—
999C2×C4—32no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—64no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—62no—
1012C2×C4—82no—
1013C2×C4—82no—
1014C2×C4—121no—
1015C2×C4—122no—
1016C2×C4—242no—
1017C2×C4—242no—
1018C2×C4C2×D3×D411yescharacteristic
1019C2×C4C2×D3×D412yes—
1020C2×C4C2×D3×D412yes—
1021C2×C4C2×D3×D411yescharacteristic
1022C2×C4C24×D311yescharacteristic
1023C8—21no—
1024C8—22no—
1025C8—21no—
1026C8—61no—
1027C8—62no—
1028C8—61no—
1029C2×C3—42no—
1030C2×C3—81no—
1031C2×C3#348611yescharacteristic
1032C2×C3C2×#57711yescharacteristic
1033C2×C3#358611yescharacteristic
1034D3—41no—
1035C22—22no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—61no—
1042C22—61no—
1043C22—61no—
1044C22C22×D3×D411yescharacteristic
1045C4—22no—
1046C4—22no—
1047C4—21no—
1048C4—41no—
1049C4—41no—
1050C4—42no—
1051C4—42no—
1052C4—61no—
1053C4—62no—
1054C4—61no—
1055C4—62no—
1056C4—61no—
1057C4—62no—
1058C4—122no—
1059C4—121no—
1060C4—121no—
1061C4—122no—
1062C4—121no—
1063C4#577512yes—
1064C4C2×#100711yescharacteristic
1065C4D3×2−1+411yescharacteristic
1066C3#6185811yescharacteristic, complemented, Sylow
1067C2—42no—
1068C2—81no—
1069C2—121no—
1070C2#8675911yescharacteristic
1071C2C2×#577511yescharacteristic
1072C2#8720811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3384C2
socleC22×C3C23×D4
prime radical#5158C22
hypercenter#3384D3
hypocenterC3#61858
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3384

Complements

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

NH ≅ G/Ntype
1. #86956C2semidirect
2. #86747C2semidirect
3. C3×#3384C2semidirect
4. #83629C2semidirect
5. #83568C2semidirect
6. #81987C2semidirect
7. #81967C2semidirect
8. #81906C2semidirect
9. #81896C2semidirect
10. #81160C2semidirect
11. #81145C2semidirect
12. #81091C2semidirect
13. #81069C2semidirect
14. #81053C2semidirect
15. #81047C2semidirect
16. #80994C2semidirect
17. #80972C2semidirect
18. #79983C2semidirect
19. #79965C2semidirect
21. #79854C2semidirect
23. #79571C2semidirect
141. #3384D3semidirect
1066. C3#61858semidirect

Maximal subgroups

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

subgroupindex
#869562
#867472
C3×#33842
#836292
#835682
#819872
#819672
#819062
#818962
#811602
#811452
#810912
#810692
#810532
#810472
#809942
#809722
#799832
#799652
#798752
#798542
#795912
#795712
#618583