Finite Group Databasebeta

← #11685751

Subgroups — #11685751

Order 768.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86956C211yesmaximal, characteristic, complemented
2#86926C211yesmaximal, characteristic, complemented
3C3×#3380C211yesmaximal, characteristic, complemented
4#83644C211yesmaximal, characteristic, complemented
5#83631C211yesmaximal, characteristic, complemented
6#81956C211yesmaximal, characteristic, complemented
7#81943C211yesmaximal, characteristic, complemented
8#81932C212yesmaximal, complemented
9#81923C212yesmaximal, complemented
10#81178C212yesmaximal, complemented
11#81159C212yesmaximal, complemented
12#81155C212yesmaximal, complemented
13#81145C212yesmaximal, complemented
14#81091C211yesmaximal, characteristic, complemented
15#81067C211yesmaximal, characteristic, complemented
16#81056C211yesmaximal, characteristic, complemented
17#81047C211yesmaximal, characteristic, complemented
18#79933C211yesmaximal, characteristic, complemented
19#79922C211yesmaximal, characteristic, complemented
20#79597C212yesmaximal
21#79591C211yesmaximal, characteristic
22#79571C212yesmaximal, complemented
23#79568C211yesmaximal, characteristic, complemented
24#61859—31nomaximal, Sylow
25C3×#554C2211yescharacteristic
26C3×#554C2211yescharacteristic
27#5728C2211yescharacteristic
28D3×C4⋊Q8C2211yescharacteristic
29#5722C2211yescharacteristic
30#5722C2211yescharacteristic
31#5698C2212yes—
32#5689C2212yes—
33#5685C2212yes—
34#5685C2212yes—
35#5646—22no—
36#5641—21no—
37#5635—21no—
38#5632—22no—
39#5625—21no—
40#5625—22no—
41#5623—22no—
42#5622—21no—
43#5578C2211yescharacteristic
44#5570C2211yescharacteristic
45Q8×Dic6C2211yescharacteristic
46#5561C2212yes—
47#5557C2211yescharacteristic
48#5546C2212yes—
49#5543C2211yescharacteristic
50#5542C2212yes—
51#5542C2211yescharacteristic
52D4×Dic6C2212yes—
53C4×#237C2211yescharacteristic
54#5513—21no—
55#5511—21no—
56#5500—21no—
57C2×#888—21no—
58C3×#500C2211yescharacteristic
59C3×#499C2212yes—
60C3×#478C2212yes—
61C3×#478C2212yes—
62C3×#476C2211yescharacteristic
63C3×#476C2211yescharacteristic
64C3×C8×Q8C2211yescharacteristic
65C3×C4×D8C2211yescharacteristic
66C3×C4×D8C2212yes—
67#5158C2211yescharacteristic
68#5153C2212yes—
69#5153C2211yescharacteristic
70#5093C2211yescharacteristic
71#5091C2211yescharacteristic
72#5091C2211yescharacteristic
73#5078C2211yescharacteristic
74#5069C2212yes—
75#5064C2212yes—
76#5063C2212yes—
77#5063C2212yes—
78#5024C2211yescharacteristic
79#5019C2211yescharacteristic
80#5019C2212yes—
81#5018C2212yes—
82#5018C2212yes—
83C4×#214C2211yescharacteristic
84C4×#214C2211yescharacteristic
85#5008C2211yescharacteristic
86#5007C2212yes—
87#4888C2211yescharacteristic
88#4884C2212yes—
89#4884C2212yes—
90#4877C2212yes—
91#4877C2211yescharacteristic
92#4875C2212yes—
93#4875C2212yes—
94#4875C2212yes—
95#4875C2212yes—
96#4874C2212yes—
97#4873C2212yes—
98#4868C2212yes—
99#4862C2212yes—
100#4857C2212yes—
101#4856C2212yes—
102#4856C2212yes—
103#4854C2212yes—
104#4853C2212yes—
105#4853C2212yes—
106#4850C2212yes—
107#4850C2211yescharacteristic
108#4849C2212yes—
109#4849C2211yescharacteristic
110#4840C2212yes—
111#4835C2211yescharacteristic
112#4831C2211yescharacteristic
113#4828C2212yes—
114#4784C2211yescharacteristic
115#4783C2212yes—
116#4783C2211yescharacteristic
117#4774C2212yes—
118#4768C2212yes—
119#4767C2211yescharacteristic
120#4767C2212yes—
121#4766C2211yescharacteristic
122#4765C2212yes—
123#4765C2212yes—
124#4759C2212yes—
125#4758C2212yes—
126#4757C2212yes—
127#4757C2212yes—
128C4×Dic12C2212yes—
129C4×Dic12C2211yescharacteristic
130#4690C2212yes—
131#4685C2211yescharacteristic
132#4681C2212yes—
133#4681C2211yescharacteristic
134#4679C2212yes—
135C8×Dic6C2211yescharacteristic
136#3555—31no—
137#3503—31no—
138#3390—32no—
139#3386—32no—
140#3385—31no—
141#3385—31no—
142Q8×Q16—31no—
143#3380D311yescharacteristic, complemented
144#3377—32no—
145#3372—31no—
146#3369—31no—
147#3367—32no—
148#3363—31no—
149#3360—31no—
150#3243—32no—
151#3242—32no—
152#3238—31no—
153#3230—31no—
154#3124—32no—
155#3120—32no—
156#3116—31no—
157#3102—31no—
158#2985—31no—
159C2×D3×Q8—21no—
160C2×#237C2311yescharacteristic
161C22×Dic6—22no—
162C2×C3×D8C2311yescharacteristic
163C3×C4⋊Q8C2311yescharacteristic
164C3×C4⋊Q8C2311yescharacteristic
165C3×#125C2312yes—
166C3×#125C2312yes—
167C3×C22⋊Q8—21no—
168C3×C22⋊Q8—21no—
169C3×C22⋊Q8—22no—
170C3×C22⋊Q8—22no—
171C3×C4×Q8C2311yescharacteristic
172C3×C4×D4C2312yes—
173C3×C4×D4C2311yescharacteristic
174C3×C4×D4C2311yescharacteristic
175C3×C4×D4C2312yes—
176C2×C3×C4⋊C4—21no—
177C2×C3×C4⋊C4—21no—
178#946—21no—
179#946D411yescharacteristic
180Q8×Dic3—21no—
181Q8×Dic3—21no—
182Q8×Dic3—21no—
183#944—22no—
184#944—22no—
185#944—21no—
186#944D411yescharacteristic
187#938C2311yescharacteristic
188#936C2311yescharacteristic
189#936C2312yes—
190D4×Dic3C2311yescharacteristic
191D4×Dic3C2312yes—
192C2×#214C2311yescharacteristic
193C2×#214C2312yes—
194C2×#214C2311yescharacteristic
195#929—22no—
196C4×#67—21no—
197C4×#67—21no—
198C4×#67—22no—
199#926—21no—
200#926—22no—
201#926—21no—
202C2×C4⋊Dic3—21no—
203#924—22no—
204#924—21no—
205#924—21no—
206#924—22no—
207#924—22no—
208C2×Dic3⋊C4—22no—
209C2×C4×Dic3—21no—
210C2×Dic12C2311yescharacteristic
211C2×Dic12C2312yes—
212#898—22no—
213#898—22no—
214#897—22no—
215#897D411yescharacteristic
216#897C2312yes—
217#897C2311yescharacteristic
218#896—22no—
219#896D412yes—
220#892—21no—
221#892C2311yescharacteristic
222D3×C4⋊C4—21no—
223D3×C4⋊C4C2312yes—
224#890—22no—
225#890—21no—
226#890—22no—
227#890—22no—
228#890—21no—
229#890C2311yescharacteristic
230#890C2312yes—
231#889—22no—
232#889—22no—
233#889—22no—
234#889—22no—
235#889—22no—
236#889D412yes—
237#888—22no—
238#888—22no—
239#888—22no—
240#888—21no—
241#888—21no—
242#888—21no—
243#888—22no—
244#888—21no—
245#888D411yescharacteristic
246#888C2312yes—
247#888C2312yes—
248#888C2312yes—
249#887—21no—
250#887—21no—
251#887—22no—
252#887—22no—
253#887C2312yes—
254#887C2312yes—
255#887C2312yes—
256#887C2311yescharacteristic
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#869C2312yes—
275#869C2311yescharacteristic
276#869C2312yes—
277#869C2311yescharacteristic
278C4×Dic6C2312yes—
279C4×Dic6C2312yes—
280C4×Dic6C2311yescharacteristic
281C4×Dic6C2311yescharacteristic
282C4×Dic6C2312yes—
283C4×Dic6C2311yescharacteristic
284C3×#107C2312yes—
285C3×#107C2312yes—
286C3×#107C2311yescharacteristic
287C3×#106C2312yes—
288C3×#106C2312yes—
289C3×C4⋊C8C2312yes—
290C3×C4⋊C8C2311yescharacteristic
291C3×#102C2312yes—
292C3×#102C2311yescharacteristic
293C3×#102C2312yes—
294C3×#102C2311yescharacteristic
295C3×C4×C8C2311yescharacteristic
296C3×C4×C8C2312yes—
297#832C2311yescharacteristic
298#832C2312yes—
299#832C2311yescharacteristic
300(C2×D3)⋊C8C2312yes—
301(C2×D3)⋊C8C2311yescharacteristic
302(C2×D3)⋊C8C2311yescharacteristic
303#818C2311yescharacteristic
304#818C2312yes—
305#816C2312yes—
306#816C2311yescharacteristic
307#816C2311yescharacteristic
308#816C2312yes—
309#816C2312yes—
310#816C2312yes—
311#815C2312yes—
312#815C2312yes—
313Dic3⋊C8C2312yes—
314Dic3⋊C8C2311yescharacteristic
315Dic3⋊C8C2311yescharacteristic
316Dic3⋊C8C2312yes—
317C8×Dic3C2312yes—
318#810C2312yes—
319#810C2312yes—
320#810C2312yes—
321#810C2312yes—
322#810C2312yes—
323#810C2311yescharacteristic
324#810C2311yescharacteristic
325#808C2312yes—
326#808C2311yescharacteristic
327#808C2311yescharacteristic
328#807C2312yes—
329#807C2312yes—
330#807C2312yes—
331#807C2312yes—
332C4⋊(C3⋊C8)C2311yescharacteristic
333C4⋊(C3⋊C8)C2312yes—
334#803C2312yes—
335C4×C3⋊C8C2311yescharacteristic
336#563—62no—
337Q82—31no—
338Q82—31no—
339Q82—31no—
340#557—32no—
341#557—32no—
342#557—31no—
343#556—31no—
344#556—32no—
345#556—61no—
346#554—31no—
347#554—61no—
348#554—61no—
349#554C2×D311yescharacteristic
350#554C2×D311yescharacteristic
351#552—61no—
352D4×Q8—32no—
353D4×Q8—62no—
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#500—31no—
373#500—32no—
374#500C2×D311yescharacteristic
375#499C2×D312yes—
376#491—32no—
377#489—32no—
378#489—32no—
379#488—32no—
380#487—31no—
381#487—31no—
382#487—32no—
383#485—31no—
384#485—32no—
385#484—32no—
386#484—32no—
387#483—32no—
388#482—31no—
389#480—32no—
390#479—32no—
391#479—32no—
392#479—31no—
393#479—32no—
394#479—32no—
395#478—31no—
396#478C2×D312yes—
397#478C2×D312yes—
398#477—31no—
399#477—31no—
400#477—32no—
401#477—32no—
402#477—32no—
403#477—32no—
404#477—31no—
405#477—32no—
406#476—31no—
407#476C2×D311yescharacteristic
408#476C2×D311yescharacteristic
409#475—32no—
410#474—32no—
411#474—32no—
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#441—32no—
430#441—32no—
431#440—32no—
432#440—32no—
433#440—32no—
434#440—32no—
435C4×Q16—32no—
436C4×Q16—31no—
437C4×Q16—32no—
438C4×SD16—31no—
439C4×SD16—31no—
440C4×SD16—32no—
441C4×D8C2×D311yescharacteristic
442C4×D8C2×D312yes—
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×D4C2411yescharacteristic
451C2×C3×D4C2411yescharacteristic
452C22×C3×C4—21no—
453C22×C3×C4—21no—
454C22×C3×C4—22no—
455C22×C3×C4—22no—
456C2×#67—21no—
457C2×#67—21no—
458C22×Dic3—21no—
459C22×Dic3—21no—
460C22×Dic3—22no—
461D3×Q8—82no—
462#237—22no—
463#237—22no—
464C2×C4×D3—22no—
465C2×C4×D3C2×D411yescharacteristic
466C2×C4×D3C2×D411yescharacteristic
467C2×C4×D3C2411yescharacteristic
468C2×Dic6—22no—
469C2×Dic6—21no—
470C2×Dic6—22no—
471C2×Dic6—22no—
472C2×Dic6—22no—
473C2×Dic6—84no—
474C2×Dic6C2×D411yescharacteristic
475C2×Dic6C2×D412yes—
476C2×Dic6C2412yes—
477C2×Dic6C2411yescharacteristic
478C2×Dic6C2411yescharacteristic
479C3×D8—22no—
480C2×C3×C8C2411yescharacteristic
481C2×C3×C8C2411yescharacteristic
482C2×C3×C8C2412yes—
483C3×C4⋊C4—21no—
484C3×C4⋊C4—21no—
485C3×C4⋊C4—22no—
486C3×C4⋊C4—22no—
487C3×C4⋊C4—22no—
488C3×C4⋊C4—22no—
489C3×C4⋊C4C2×D411yescharacteristic
490C3×C4⋊C4C2×D412yes—
491C3×C4⋊C4C2412yes—
492C3×C4⋊C4C2412yes—
493C3×C4⋊C4C2411yescharacteristic
494C3×C4⋊C4C2411yescharacteristic
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—22no—
509#214—24no—
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—22no—
517C4⋊Dic3—22no—
518C4⋊Dic3—21no—
519C4⋊Dic3—21no—
520C4⋊Dic3—22no—
521C4⋊Dic3—21no—
522C4⋊Dic3—22no—
523C4⋊Dic3—21no—
524C4⋊Dic3—22no—
525C4⋊Dic3—21no—
526C4⋊Dic3C2×D411yescharacteristic
527C4⋊Dic3C2×D412yes—
528C4⋊Dic3C2411yescharacteristic
529C4⋊Dic3C2412yes—
530C4⋊Dic3C2411yescharacteristic
531Dic3⋊C4—21no—
532Dic3⋊C4—21no—
533Dic3⋊C4—22no—
534Dic3⋊C4—22no—
535Dic3⋊C4—21no—
536Dic3⋊C4—22no—
537Dic3⋊C4—22no—
538Dic3⋊C4—22no—
539Dic3⋊C4—22no—
540Dic3⋊C4—21no—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4C2×D412yes—
547Dic3⋊C4C2×D412yes—
548Dic3⋊C4C2×D412yes—
549Dic3⋊C4C2×D412yes—
550Dic3⋊C4C2×D412yes—
551C4×Dic3—22no—
552C4×Dic3—22no—
553C4×Dic3—21no—
554C4×Dic3—21no—
555C4×Dic3—22no—
556C4×Dic3—21no—
557C4×Dic3—22no—
558C4×Dic3—22no—
559C4×Dic3—22no—
560C4×Dic3—21no—
561C4×Dic3C2×D411yescharacteristic
562C4×Dic3C2×D411yescharacteristic
563C4×Dic3C2412yes—
564C4×Dic3C2411yescharacteristic
565C2×C3⋊C8C2411yescharacteristic
566C2×C3⋊C8C2411yescharacteristic
567C2×C3⋊C8C2412yes—
568Dic12—22no—
569Dic12—24no—
570C2×#41—31no—
571C22×Q8—62no—
572C22×Q8—61no—
573C2×Q16—31no—
574C2×Q16—32no—
575C2×SD16—31no—
576C2×SD16—31no—
577C2×SD16—32no—
578C2×D8C22×D311yescharacteristic
579C4⋊Q8—31no—
580C4⋊Q8—31no—
581C4⋊Q8—32no—
582C4⋊Q8—32no—
583C4⋊Q8—32no—
584C4⋊Q8—31no—
585C4⋊Q8—32no—
586C4⋊Q8—31no—
587C4⋊Q8—32no—
588C4⋊Q8—61no—
589C4⋊Q8—61no—
590C4⋊Q8—62no—
591C4⋊Q8—61no—
592C4⋊Q8—61no—
593C4⋊Q8—62no—
594C4⋊Q8—62no—
595C4⋊Q8—62no—
596C4⋊Q8—62no—
597C4⋊Q8—61no—
598C4⋊Q8—62no—
599C4⋊Q8C22×D311yescharacteristic
600C4⋊Q8C22×D311yescharacteristic
601#126—61no—
602#126—62no—
603#126—62no—
604#126—62no—
605#126—62no—
606#126—62no—
607#126—62no—
608#125—32no—
609#125—31no—
610#125—32no—
611#125—61no—
612#125—62no—
613#125—62no—
614#125—62no—
615#125—62no—
616#125—62no—
617#125—62no—
618#125—62no—
619#125—62no—
620#125—61no—
621#125C22×D312yes—
622#125C22×D312yes—
623#124—31no—
624#124—32no—
625#124—62no—
626#123—61no—
627#123—62no—
628C22⋊Q8—21no—
629C22⋊Q8—21no—
630C22⋊Q8—22no—
631C22⋊Q8—22no—
632C22⋊Q8—31no—
633C22⋊Q8—32no—
634C22⋊Q8—31no—
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—
648#121—31no—
649C4×Q8—32no—
650C4×Q8—31no—
651C4×Q8—31no—
652C4×Q8—32no—
653C4×Q8—32no—
654C4×Q8—32no—
655C4×Q8—32no—
656C4×Q8—31no—
657C4×Q8—32no—
658C4×Q8—31no—
659C4×Q8—32no—
660C4×Q8—61no—
661C4×Q8—62no—
662C4×Q8—62no—
663C4×Q8—61no—
664C4×Q8—61no—
665C4×Q8—61no—
666C4×Q8—61no—
667C4×Q8C22×D311yescharacteristic
668C4×D4—31no—
669C4×D4—32no—
670C4×D4—62no—
671C4×D4—61no—
672C4×D4—62no—
673C4×D4—61no—
674C4×D4—61no—
675C4×D4C22×D311yescharacteristic
676C4×D4C22×D312yes—
677C4×D4C22×D311yescharacteristic
678C4×D4C22×D312yes—
679#117—32no—
680#117—31no—
681#117—61no—
682#117—61no—
683#117—62no—
684#117—61no—
685#117—62no—
686#117—61no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—32no—
690C2×C4⋊C4—61no—
691C2×C4⋊C4—62no—
692C2×C4⋊C4—61no—
693C2×C42—31no—
694C2×C42—61no—
695#107—32no—
696#107—31no—
697#107—32no—
698#107—32no—
699#107—32no—
700#107—32no—
701#107C22×D312yes—
702#107C22×D311yescharacteristic
703#107C22×D312yes—
704#106—31no—
705#106—32no—
706#106—31no—
707#106C22×D312yes—
708#106C22×D312yes—
709C4⋊C8—31no—
710C4⋊C8—31no—
711C4⋊C8—32no—
712C4⋊C8—32no—
713C4⋊C8—31no—
714C4⋊C8—32no—
715C4⋊C8C22×D311yescharacteristic
716C4⋊C8C22×D312yes—
717#103—32no—
718#103—31no—
719#103—31no—
720#103—32no—
721#103—32no—
722#103—32no—
723#103—31no—
724#103—31no—
725#103—32no—
726#103—32no—
727#103—32no—
728#103—32no—
729#103—32no—
730#102—31no—
731#102—31no—
732#102—32no—
733#102C22×D311yescharacteristic
734#102C22×D312yes—
735#102C22×D312yes—
736#102C22×D311yescharacteristic
737C22⋊C8—31no—
738C22⋊C8—31no—
739C22⋊C8—32no—
740#97—32no—
741#97—32no—
742#97—32no—
743C4×C8—32no—
744C4×C8—31no—
745C4×C8C22×D311yescharacteristic
746C4×C8C22×D312yes—
747C23×C3—21no—
748C23×C3—21no—
749C22×D3C22×D411yescharacteristic
750C3×Q8—22no—
751C3×Q8—81no—
752C3×Q8—81no—
753C3×D4—21no—
754C3×D4—21no—
755C3×D4—21no—
756C3×D42−1+412yes—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—42no—
762C2×C3×C4—42no—
763C2×C3×C4—82no—
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—24no—
771#67—81no—
772C2×Dic3—24no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—22no—
776C2×Dic3—21no—
777C2×Dic3—21no—
778C2×Dic3—22no—
779C2×Dic3—42no—
780C2×Dic3—82no—
781C2×Dic3C22×D411yescharacteristic
782C2×Dic3C22×D412yes—
783C2×Dic3C22×D411yescharacteristic
784C2×Dic3C22×D411yescharacteristic
785C2×Dic3C22×D412yes—
786C4×D3—22no—
787C4×D3—21no—
788C4×D3—21no—
789C4×D3—41no—
790C4×D3—82no—
791Dic6—22no—
792Dic6—21no—
793Dic6—21no—
794Dic6—22no—
795Dic6—21no—
796Dic6—22no—
797Dic6—42no—
798Dic6—44no—
799Dic6—82no—
800Dic6—82no—
801Dic6—82no—
802Dic6—81no—
803Dic62−1+412yes—
804C3×C8—21no—
805C3×C8—22no—
806C3×C8—21no—
807C3⋊C8—21no—
808C3⋊C8—22no—
809C3⋊C8—21no—
810#41—62no—
811#41—62no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—31no—
815C2×Q8—32no—
816C2×Q8—31no—
817C2×Q8—32no—
818C2×Q8—31no—
819C2×Q8—62no—
820C2×Q8—62no—
821C2×Q8—62no—
822C2×Q8—62no—
823C2×Q8—61no—
824C2×Q8—244no—
825C2×Q8—242no—
826C2×Q8D3×D411yescharacteristic
827C2×D4—61no—
828C2×D4—61no—
829C2×D4C23×D311yescharacteristic
830C2×D4C23×D311yescharacteristic
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—31no—
836C22×C4—31no—
837C22×C4—31no—
838C22×C4—62no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4—62no—
842Q16—62no—
843Q16—64no—
844SD16—62no—
845SD16—62no—
846SD16—64no—
847D8—22no—
848C2×C8—32no—
849C2×C8—31no—
850C2×C8—31no—
851C2×C8C23×D311yescharacteristic
852C2×C8C23×D311yescharacteristic
853C2×C8C23×D312yes—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—32no—
861C4⋊C4—31no—
862C4⋊C4—32no—
863C4⋊C4—32no—
864C4⋊C4—32no—
865C4⋊C4—32no—
866C4⋊C4—32no—
867C4⋊C4—32no—
868C4⋊C4—31no—
869C4⋊C4—31no—
870C4⋊C4—62no—
871C4⋊C4—62no—
872C4⋊C4—62no—
873C4⋊C4—62no—
874C4⋊C4—61no—
875C4⋊C4—61no—
876C4⋊C4—61no—
877C4⋊C4—61no—
878C4⋊C4—62no—
879C4⋊C4—62no—
880C4⋊C4—62no—
881C4⋊C4—62no—
882C4⋊C4—62no—
883C4⋊C4—62no—
884C4⋊C4—62no—
885C4⋊C4—61no—
886C4⋊C4—62no—
887C4⋊C4—61no—
888C4⋊C4—61no—
889C4⋊C4—62no—
890C4⋊C4—62no—
891C4⋊C4—61no—
892C4⋊C4—62no—
893C4⋊C4—61no—
894C4⋊C4—62no—
895C4⋊C4D3×D411yescharacteristic
896C4⋊C4D3×D412yes—
897C4⋊C4C23×D311yescharacteristic
898C4⋊C4C23×D312yes—
899C4⋊C4C23×D311yescharacteristic
900C4⋊C4C23×D312yes—
901C22⋊C4—21no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—22no—
905C22⋊C4—32no—
906C22⋊C4—32no—
907C22⋊C4—61no—
908C22⋊C4—62no—
909C22⋊C4—61no—
910C22⋊C4—61no—
911C22⋊C4—61no—
912C22⋊C4—62no—
913C22⋊C4—61no—
914C22⋊C4—61no—
915C22⋊C4—62no—
916C22⋊C4—62no—
917C42—31no—
918C42—31no—
919C42—32no—
920C42—31no—
921C42—61no—
922C42—61no—
923C42—62no—
924C42—62no—
925C42—62no—
926C42—62no—
927C42—61no—
928C42—62no—
929C42—61no—
930C42—62no—
931C42C23×D311yescharacteristic
932C42C23×D312yes—
933C22×C3—22no—
934C22×C3—41no—
935C22×C3—41no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3—41no—
939C22×C3C23×D411yescharacteristic
940C2×D3—21no—
941C2×D3—21no—
942C2×D3—21no—
943C3×C4—22no—
944C3×C4—21no—
945C3×C4—22no—
946C3×C4—42no—
947C3×C4—42no—
948C3×C4—41no—
949C3×C4—41no—
950C3×C4#57812yes—
951C3×C4C2×2−1+411yescharacteristic
952C3×C4C2×2−1+411yescharacteristic
953Dic3—21no—
954Dic3—22no—
955Dic3—22no—
956Dic3—21no—
957Dic3—22no—
958Dic3—21no—
959Dic3—42no—
960Dic3—41no—
961Dic3—41no—
962Dic3—42no—
963Dic3—41no—
964C23—21no—
965C23—21no—
966C23—31no—
967Q8—22no—
968Q8—32no—
969Q8—61no—
970Q8—62no—
971Q8—62no—
972Q8—61no—
973Q8—61no—
974Q8—62no—
975Q8—81no—
976Q8—81no—
977Q8—122no—
978Q8—124no—
979Q8—242no—
980Q8—241no—
981Q8—242no—
982Q8—242no—
983D4—21no—
984D4—21no—
985D4—21no—
986D4—64no—
987D4—241no—
988D4#100712yes—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—31no—
994C2×C4—31no—
995C2×C4—31no—
996C2×C4—32no—
997C2×C4—32no—
998C2×C4—42no—
999C2×C4—42no—
1000C2×C4—64no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—62no—
1005C2×C4—62no—
1006C2×C4—61no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—62no—
1010C2×C4—82no—
1011C2×C4—82no—
1012C2×C4—121no—
1013C2×C4—122no—
1014C2×C4—242no—
1015C2×C4—242no—
1016C2×C4C2×D3×D411yescharacteristic
1017C2×C4C2×D3×D412yes—
1018C2×C4C2×D3×D412yes—
1019C2×C4C2×D3×D411yescharacteristic
1020C2×C4C24×D311yescharacteristic
1021C8—21no—
1022C8—21no—
1023C8—22no—
1024C8—62no—
1025C8—61no—
1026C8—61no—
1027C2×C3—42no—
1028C2×C3—81no—
1029C2×C3#348611yescharacteristic
1030C2×C3C2×#57811yescharacteristic
1031C2×C3#358511yescharacteristic
1032D3—41no—
1033C22—22no—
1034C22—41no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—61no—
1040C22—61no—
1041C22—61no—
1042C22C22×D3×D411yescharacteristic
1043C4—22no—
1044C4—22no—
1045C4—21no—
1046C4—41no—
1047C4—41no—
1048C4—42no—
1049C4—42no—
1050C4—61no—
1051C4—62no—
1052C4—61no—
1053C4—62no—
1054C4—61no—
1055C4—62no—
1056C4—121no—
1057C4—122no—
1058C4—121no—
1059C4—122no—
1060C4—121no—
1061C4#577112yes—
1062C4C2×#100711yescharacteristic
1063C4D3×2−1+411yescharacteristic
1064C3#6185911yescharacteristic, complemented, Sylow
1065C2—42no—
1066C2—81no—
1067C2—121no—
1068C2#8675911yescharacteristic
1069C2C2×#577111yescharacteristic
1070C2#8720411yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3380C2
socleC22×C3C23×D4
prime radical#5158C22
hypercenter#3380D3
hypocenterC3#61859
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3380

Complements

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

NH ≅ G/Ntype
1. #86956C2semidirect
2. #86926C2semidirect
3. C3×#3380C2semidirect
4. #83644C2semidirect
5. #83631C2semidirect
6. #81956C2semidirect
7. #81943C2semidirect
8. #81932C2semidirect
9. #81923C2semidirect
10. #81178C2semidirect
11. #81159C2semidirect
12. #81155C2semidirect
13. #81145C2semidirect
14. #81091C2semidirect
15. #81067C2semidirect
16. #81056C2semidirect
17. #81047C2semidirect
18. #79933C2semidirect
19. #79922C2semidirect
22. #79571C2semidirect
23. #79568C2semidirect
143. #3380D3semidirect
1064. C3#61859semidirect

Maximal subgroups

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

subgroupindex
#869562
#869262
C3×#33802
#836442
#836312
#819562
#819432
#819322
#819232
#811782
#811592
#811552
#811452
#810912
#810672
#810562
#810472
#799332
#799222
#795972
#795912
#795712
#795682
#618593