Finite Group Databasebeta

← #11685729

Subgroups — #11685729

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#86215C211yesmaximal, characteristic, complemented
2#86138C211yesmaximal, characteristic, complemented
3C3×#3239C211yesmaximal, characteristic, complemented
4#83223C211yesmaximal, characteristic, complemented
5#83140C211yesmaximal, characteristic
6#81969C212yesmaximal, complemented
7#81967C212yesmaximal, complemented
8#81676C212yesmaximal, complemented
9#81671C212yesmaximal, complemented
10#81460C212yesmaximal, complemented
11#81456C212yesmaximal, complemented
12#81317C212yesmaximal, complemented
13#81313C212yesmaximal
14#81043C211yesmaximal, characteristic, complemented
15#81042C211yesmaximal, characteristic, complemented
16#81039C211yesmaximal, characteristic, complemented
17#81037C211yesmaximal, characteristic, complemented
18#80994C211yesmaximal, characteristic, complemented
19#80993C211yesmaximal, characteristic, complemented
20#80959C211yesmaximal, characteristic, complemented
21#80958C211yesmaximal, characteristic, complemented
22#79348C211yesmaximal, characteristic, complemented
23#79316C211yesmaximal, characteristic, complemented
24#61858—31nomaximal, Sylow
25C2×C3×C4⋊Q8C2211yescharacteristic
26C3×#529C2211yescharacteristic
27Q8×#67—21no—
28Q8×#67—21no—
29#5730C2212yes—
30#5729—22no—
31#5728—21no—
32#5727C2211yescharacteristic
33#5727C2211yescharacteristic
34D3×C4⋊Q8—21no—
35#5722C2212yes—
36#5721C2211yescharacteristic
37#5721C2211yescharacteristic
38#5701—22no—
39#5685C2212yes—
40#5671C2212yes—
41#5651—22no—
42#5625C2212yes—
43#5603C2212yes—
44#5567C2211yescharacteristic
45Q8×Dic6C2211yescharacteristic
46#5543C2211yescharacteristic
47#5542—21no—
48#5542C2211yescharacteristic
49#5541—21no—
50#5519—21no—
51#5518—21no—
52#5511—22no—
53#5504C2212yes—
54#5500C2212yes—
55C4×#235C2211yescharacteristic
56#5470C2211yescharacteristic
57#5470C2211yescharacteristic
58C3×#501C2212yes—
59C3×#489C2212yes—
60C3×#484C2212yes—
61C3×#481C2212yes—
62C3×#475C2211yescharacteristic
63C3×#475C2211yescharacteristic
64C3×#474C2211yescharacteristic
65C3×#474C2211yescharacteristic
66C3×#432C2211yescharacteristic
67#5094C2212yes—
68#5094C2212yes—
69#5093C2211yescharacteristic
70#5093C2211yescharacteristic
71#5080C2211yescharacteristic
72#5080C2211yescharacteristic
73#5066C2211yescharacteristic
74#5063C2211yescharacteristic
75#5057C2211yescharacteristic
76#5054C2211yescharacteristic
77#5047C2211yescharacteristic
78#5045C2211yescharacteristic
79#5037C2211yescharacteristic
80#5035C2211yescharacteristic
81C4×#216C2211yescharacteristic
82C4×#215C2211yescharacteristic
83C4×#214C2211yescharacteristic
84C4×#213C2211yescharacteristic
85#4971C2212yes—
86#4971C2212yes—
87#4925C2211yescharacteristic
88#4891C2212yes—
89#4889C2212yes—
90#4878C2212yes—
91#4877C2212yes—
92#4877C2212yes—
93#4876C2212yes—
94#4875C2212yes—
95#4873C2212yes—
96#4870C2212yes—
97#4857C2212yes—
98#4856C2212yes—
99#4855C2212yes—
100#4854C2212yes—
101#4854C2212yes—
102#4853C2212yes—
103#4852C2212yes—
104#4850C2211yescharacteristic
105#4849C2211yescharacteristic
106#4842C2211yescharacteristic
107#4841C2211yescharacteristic
108#4831C2211yescharacteristic
109#4831C2211yescharacteristic
110#4830C2211yescharacteristic
111#4830C2211yescharacteristic
112#4818C2212yes—
113#4797C2212yes—
114#4796C2212yes—
115#4795C2212yes—
116#4792C2212yes—
117#4791C2212yes—
118#4789C2212yes—
119#4788C2212yes—
120#4787C2212yes—
121#4785C2212yes—
122#4768C2212yes—
123#4767C2212yes—
124#4766C2212yes—
125#4765C2212yes—
126#4761C2212yes—
127#4758C2212yes—
128#4733C2212yes—
129#4723C2212yes—
130#4720C2212yes—
131#4720C2212yes—
132#4716C2212yes—
133#4710C2212yes—
134#4701C2212yes—
135#4701C2212yes—
136#3555—31no—
137#3503—31no—
138#3388—32no—
139#3387—32no—
140#3387—31no—
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#3239D311yescharacteristic, complemented
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×D3×Q8—21no—
162C2×#235C2311yescharacteristic
163C3×C4⋊Q8—21no—
164C3×C4⋊Q8—21no—
165C3×C4⋊Q8C2311yescharacteristic
166C3×C4⋊Q8C2311yescharacteristic
167C3×C4⋊Q8C2312yes—
168C3×#126—21no—
169C3×#125C2311yescharacteristic
170C3×#124C2311yescharacteristic
171C3×#123—21no—
172C3×C22⋊Q8C2311yescharacteristic
173C3×#121C2311yescharacteristic
174C3×C4×Q8C2311yescharacteristic
175C3×C4×D4—21no—
176C3×C4×D4C2311yescharacteristic
177C3×#117—21no—
178C2×C3×C4⋊C4—21no—
179C2×C3×C4⋊C4C2312yes—
180C2×C3×C42C2311yescharacteristic
181#946—21no—
182#946—21no—
183#946—22no—
184#946—22no—
185Q8×Dic3—21no—
186Q8×Dic3—21no—
187Q8×Dic3C2312yes—
188#944—21no—
189#944—21no—
190#944—22no—
191#944—22no—
192#944C2312yes—
193C2×#216C2311yescharacteristic
194C2×#215C2311yescharacteristic
195#936—22no—
196#936C2312yes—
197#935—22no—
198D4×Dic3C2312yes—
199C2×#214C2311yescharacteristic
200C2×#213C2311yescharacteristic
201C4×#67—21no—
202C4×#67—21no—
203C4×#67—22no—
204C4×#67—22no—
205#926—21no—
206#926—21no—
207#926C2311yescharacteristic
208#926C2312yes—
209C2×C4⋊Dic3—21no—
210#924—21no—
211#924—21no—
212#924—21no—
213#924—22no—
214#924—22no—
215#924D412yes—
216#924D411yescharacteristic
217#924D411yescharacteristic
218#924C2312yes—
219C2×Dic12C2312yes—
220C2×#204C2312yes—
221#897—22no—
222#896—22no—
223#896—22no—
224#893C2312yes—
225#893C2312yes—
226#892—22no—
227D3×C4⋊C4—22no—
228D3×C4⋊C4—22no—
229#890—22no—
230#890—22no—
231#890C2312yes—
232#890C2312yes—
233#890C2312yes—
234#889—22no—
235#889—22no—
236#889—22no—
237#889—22no—
238#889—22no—
239#889—22no—
240#888—22no—
241#888—22no—
242#888—22no—
243#888—22no—
244#888C2312yes—
245#888C2312yes—
246#888C2312yes—
247#887—22no—
248#887—22no—
249#887C2312yes—
250#887C2312yes—
251#887C2312yes—
252#887C2312yes—
253#879—22no—
254#879—22no—
255#879—22no—
256#879—22no—
257#879—22no—
258#879—22no—
259#878—22no—
260#878—22no—
261#878—22no—
262#877—22no—
263C4×D12C2311yescharacteristic
264C4×D12C2311yescharacteristic
265#872—21no—
266C42×D3—21no—
267#870—21no—
268#870—21no—
269#870D412yes—
270#869—21no—
271#869D411yescharacteristic
272#869D411yescharacteristic
273#869C2311yescharacteristic
274#869C2311yescharacteristic
275C4×Dic6—21no—
276C4×Dic6—21no—
277C4×Dic6—21no—
278C4×Dic6C2312yes—
279C4×Dic6C2311yescharacteristic
280C4×Dic6C2311yescharacteristic
281C4×Dic6C2312yes—
282C4×Dic6C2311yescharacteristic
283C4×Dic6C2311yescharacteristic
284C3×#107C2312yes—
285C3×#107C2312yes—
286C3×#106C2312yes—
287C3×#106C2312yes—
288C3×C4⋊C8C2311yescharacteristic
289C3×C4⋊C8C2311yescharacteristic
290C3×#103C2312yes—
291C3×#103C2312yes—
292C3×#102C2312yes—
293C3×#102C2312yes—
294C3×C22⋊C8C2312yes—
295C3×#97C2312yes—
296#835C2311yescharacteristic
297#835C2311yescharacteristic
298#832C2311yescharacteristic
299#832C2311yescharacteristic
300#830C2311yescharacteristic
301#830C2311yescharacteristic
302#821C2312yes—
303#818C2312yes—
304#817C2312yes—
305#816C2312yes—
306#816C2312yes—
307#816C2312yes—
308#815C2312yes—
309#815C2312yes—
310Dic3⋊C8C2312yes—
311Dic3⋊C8C2312yes—
312Dic3⋊C8C2312yes—
313Dic3⋊C8C2312yes—
314C8×Dic3C2312yes—
315C8×Dic3C2312yes—
316#810C2311yescharacteristic
317#810C2312yes—
318#810C2312yes—
319#810C2312yes—
320#810C2312yes—
321#810C2311yescharacteristic
322#809C2311yescharacteristic
323#809C2311yescharacteristic
324#808C2312yes—
325#808C2312yes—
326#808C2311yescharacteristic
327#808C2312yes—
328#808C2312yes—
329#808C2311yescharacteristic
330#807C2311yescharacteristic
331#807C2311yescharacteristic
332C4⋊(C3⋊C8)C2311yescharacteristic
333C4⋊(C3⋊C8)C2311yescharacteristic
334C4×C3⋊C8C2311yescharacteristic
335C4×C3⋊C8C2311yescharacteristic
336#563—62no—
337Q82—32no—
338Q82—31no—
339#557—31no—
340#557—31no—
341#557—32no—
342#557—31no—
343#556—32no—
344#556—31no—
345#556—61no—
346#554—32no—
347#554—31no—
348#554—62no—
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—61no—
360#541—62no—
361#533—31no—
362#533—31no—
363#533—61no—
364C2×C4⋊Q8—61no—
365C2×C4⋊Q8C2×D311yescharacteristic
366#529C2×D311yescharacteristic
367#520—32no—
368C4×#41—31no—
369#501—32no—
370#501—32no—
371#501C2×D312yes—
372#499—32no—
373#498—31no—
374#498—31no—
375#498—32no—
376#491—32no—
377#489—32no—
378#489C2×D312yes—
379#488—32no—
380#487—31no—
381#487—31no—
382#487—32no—
383#485—31no—
384#485—32no—
385#484C2×D312yes—
386#483—32no—
387#483—32no—
388#482—31no—
389#481C2×D312yes—
390#479—31no—
391#479—32no—
392#479—32no—
393#479—32no—
394#479—32no—
395#478—31no—
396#478—32no—
397#478—32no—
398#477—32no—
399#477—31no—
400#476—32no—
401#476—31no—
402#476—32no—
403#475—32no—
404#475—32no—
405#475—32no—
406#475—32no—
407#475—32no—
408#475C2×D311yescharacteristic
409#475C2×D311yescharacteristic
410#474C2×D311yescharacteristic
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×Q8—31no—
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—31no—
438C4×SD16—31no—
439C4×SD16—32no—
440C4×SD16—32no—
441C4×SD16—32no—
442C4×D8—31no—
443#433—32no—
444#433—32no—
445#432C2×D311yescharacteristic
446#431—31no—
447C2×C3×Q8—21no—
448C2×C3×Q8—21no—
449C2×C3×Q8—22no—
450C2×C3×Q8—82no—
451C2×C3×Q8C2411yescharacteristic
452C2×C3×D4—21no—
453C2×C3×D4C2411yescharacteristic
454C22×C3×C4—22no—
455C22×C3×C4—21no—
456C22×C3×C4C2×D411yescharacteristic
457C22×C3×C4C2×D411yescharacteristic
458C22×C3×C4C2411yescharacteristic
459C2×#67—21no—
460C22×Dic3—22no—
461D3×Q8—82no—
462D3×Q8—82no—
463#235—22no—
464#235—22no—
465C2×D12C2411yescharacteristic
466C2×C4×D3—21no—
467C2×C4×D3—21no—
468C2×C4×D3—21no—
469C2×C4×D3—22no—
470C2×C4×D3—22no—
471C2×Dic6—21no—
472C2×Dic6—22no—
473C2×Dic6—22no—
474C2×Dic6—22no—
475C2×Dic6C2×D411yescharacteristic
476C2×Dic6C2×D411yescharacteristic
477C2×Dic6C2×D412yes—
478C2×Dic6C2412yes—
479C2×Dic6C2411yescharacteristic
480C2×C3×C8C2412yes—
481C2×C3×C8C2412yes—
482C3×C4⋊C4—21no—
483C3×C4⋊C4—22no—
484C3×C4⋊C4—21no—
485C3×C4⋊C4—21no—
486C3×C4⋊C4—22no—
487C3×C4⋊C4—21no—
488C3×C4⋊C4—21no—
489C3×C4⋊C4—21no—
490C3×C4⋊C4C2411yescharacteristic
491C3×C4⋊C4C2411yescharacteristic
492C3×C4⋊C4C2412yes—
493C3×C4⋊C4C2412yes—
494C3×C22⋊C4—21no—
495C3×C22⋊C4—21no—
496C3×C22⋊C4—21no—
497C3×C22⋊C4—21no—
498C3×C22⋊C4—21no—
499C3×C42—21no—
500C3×C42C2×D411yescharacteristic
501C3×C42C2×D411yescharacteristic
502C3×C42C2411yescharacteristic
503C3×C42C2411yescharacteristic
504#217—22no—
505#217—21no—
506#217—22no—
507#217—22no—
508#217—22no—
509#217C2×D412yes—
510#217C2×D412yes—
511#216—22no—
512#215—22no—
513#214—22no—
514#213—22no—
515(C2×D3)⋊C4—21no—
516(C2×D3)⋊C4—21no—
517(C2×D3)⋊C4—22no—
518(C2×D3)⋊C4—22no—
519C4⋊Dic3—21no—
520C4⋊Dic3—21no—
521C4⋊Dic3—21no—
522C4⋊Dic3—22no—
523C4⋊Dic3—22no—
524C4⋊Dic3—22no—
525C4⋊Dic3—22no—
526C4⋊Dic3C2×D411yescharacteristic
527C4⋊Dic3C2×D411yescharacteristic
528C4⋊Dic3C2×D412yes—
529C4⋊Dic3C2×D412yes—
530C4⋊Dic3C2×D412yes—
531C4⋊Dic3C2411yescharacteristic
532C4⋊Dic3C2411yescharacteristic
533C4⋊Dic3C2412yes—
534Dic3⋊C4—22no—
535Dic3⋊C4—22no—
536Dic3⋊C4—21no—
537Dic3⋊C4—21no—
538Dic3⋊C4—22no—
539Dic3⋊C4—22no—
540Dic3⋊C4—22no—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4C2×D412yes—
551Dic3⋊C4C2×D412yes—
552Dic3⋊C4C2×D412yes—
553Dic3⋊C4C2×D412yes—
554C4×Dic3—22no—
555C4×Dic3—21no—
556C4×Dic3—21no—
557C4×Dic3—21no—
558C4×Dic3—22no—
559C4×Dic3—22no—
560C4×Dic3—22no—
561C4×Dic3—22no—
562C4×Dic3—22no—
563C4×Dic3C2412yes—
564C4×Dic3C2412yes—
565C2×C3⋊C8C2411yescharacteristic
566C2×C3⋊C8C2411yescharacteristic
567C2×C3⋊C8C2411yescharacteristic
568C2×C3⋊C8C2411yescharacteristic
569Dic12—24no—
570#204—24no—
571C2×#41—31no—
572C22×Q8—21no—
573C22×Q8—61no—
574C22×Q8—61no—
575C2×Q16—31no—
576C2×Q16—32no—
577C2×SD16—31no—
578C2×SD16—31no—
579C2×SD16—32no—
580C2×D8—31no—
581C4⋊Q8—21no—
582C4⋊Q8—21no—
583C4⋊Q8—32no—
584C4⋊Q8—32no—
585C4⋊Q8—32no—
586C4⋊Q8—32no—
587C4⋊Q8—31no—
588C4⋊Q8—31no—
589C4⋊Q8—31no—
590C4⋊Q8—31no—
591C4⋊Q8—61no—
592C4⋊Q8—62no—
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—21no—
604#126—62no—
605#126—62no—
606#126—62no—
607#126—62no—
608#126—62no—
609#126—62no—
610#125—32no—
611#125—32no—
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—62no—
623#125—61no—
624#125C22×D311yescharacteristic
625#124—32no—
626#124—62no—
627#124C22×D311yescharacteristic
628#123—21no—
629#123—62no—
630C22⋊Q8—31no—
631C22⋊Q8—31no—
632C22⋊Q8—32no—
633C22⋊Q8—32no—
634C22⋊Q8—62no—
635C22⋊Q8—62no—
636C22⋊Q8—62no—
637C22⋊Q8—62no—
638C22⋊Q8—62no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—61no—
643C22⋊Q8—61no—
644C22⋊Q8—62no—
645C22⋊Q8—62no—
646C22⋊Q8—61no—
647C22⋊Q8—61no—
648C22⋊Q8—61no—
649C22⋊Q8C22×D311yescharacteristic
650#121C22×D311yescharacteristic
651C4×Q8—31no—
652C4×Q8—31no—
653C4×Q8—32no—
654C4×Q8—32no—
655C4×Q8—32no—
656C4×Q8—32no—
657C4×Q8—32no—
658C4×Q8—32no—
659C4×Q8—31no—
660C4×Q8—31no—
661C4×Q8—32no—
662C4×Q8—61no—
663C4×Q8—61no—
664C4×Q8—62no—
665C4×Q8—62no—
666C4×Q8—61no—
667C4×Q8—61no—
668C4×Q8—61no—
669C4×Q8C22×D311yescharacteristic
670C4×D4—21no—
671C4×D4—32no—
672C4×D4—32no—
673C4×D4—32no—
674C4×D4—31no—
675C4×D4—31no—
676C4×D4—62no—
677C4×D4—62no—
678C4×D4—61no—
679C4×D4—61no—
680C4×D4C22×D311yescharacteristic
681#117—21no—
682#117—32no—
683#117—31no—
684#117—62no—
685#117—62no—
686#117—61no—
687#117—61no—
688#117—61no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—62no—
691C2×C4⋊C4—62no—
692C2×C4⋊C4—61no—
693C2×C4⋊C4C22×D312yes—
694C2×C42—61no—
695C2×C42C22×D311yescharacteristic
696#107—32no—
697#107—31no—
698#107—31no—
699#107C22×D312yes—
700#107C22×D312yes—
701#106—32no—
702#106—32no—
703#106—31no—
704#106—32no—
705#106—31no—
706#106—32no—
707#106—32no—
708#106C22×D312yes—
709#106C22×D312yes—
710C4⋊C8—32no—
711C4⋊C8—32no—
712C4⋊C8—32no—
713C4⋊C8—32no—
714C4⋊C8—31no—
715C4⋊C8—31no—
716C4⋊C8C22×D311yescharacteristic
717C4⋊C8C22×D311yescharacteristic
718#103—31no—
719#103—31no—
720#103—32no—
721#103—32no—
722#103—32no—
723#103—31no—
724#103—32no—
725#103—31no—
726#103—32no—
727#103—32no—
728#103—32no—
729#103C22×D312yes—
730#103C22×D312yes—
731#102—31no—
732#102—31no—
733#102—32no—
734#102—31no—
735#102—31no—
736#102C22×D312yes—
737#102C22×D312yes—
738C22⋊C8—31no—
739C22⋊C8—31no—
740C22⋊C8C22×D312yes—
741#97—32no—
742#97—32no—
743#97C22×D312yes—
744C4×C8—32no—
745C4×C8—32no—
746C4×C8—31no—
747C4×C8—31no—
748C23×C3—21no—
749C23×C3C22×D411yescharacteristic
750C22×D3—21no—
751C3×Q8—21no—
752C3×Q8—21no—
753C3×Q8—42no—
754C3×Q8—42no—
755C3×Q8—82no—
756C3×D4—21no—
757C3×D4—21no—
758C3×D4—81no—
759C2×C3×C4—22no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—22no—
766C2×C3×C4—22no—
767C2×C3×C4—41no—
768C2×C3×C4—42no—
769C2×C3×C4—82no—
770C2×C3×C4C22×D411yescharacteristic
771C2×C3×C4C22×D411yescharacteristic
772C2×C3×C4C22×D411yescharacteristic
773C2×C3×C4C22×D411yescharacteristic
774C2×C3×C4C22×D411yescharacteristic
775C2×C3×C4C2511yescharacteristic
776#67—24no—
777C2×Dic3—21no—
778C2×Dic3—22no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—22no—
782C2×Dic3—82no—
783C2×Dic3C22×D412yes—
784C2×Dic3C22×D412yes—
785C2×Dic3C22×D412yes—
786C2×Dic3C22×D412yes—
787D12—21no—
788D122−1+412yes—
789C4×D3—24no—
790C4×D3—42no—
791C4×D3—42no—
792C4×D3—82no—
793C4×D3—82no—
794Dic6—22no—
795Dic6—22no—
796Dic6—21no—
797Dic6—22no—
798Dic6—22no—
799Dic6—42no—
800Dic6—82no—
801Dic6—82no—
802Dic6—82no—
803Dic6—81no—
804Dic62−1+412yes—
805C3×C8—22no—
806C3×C8—22no—
807C3⋊C8—21no—
808C3⋊C8—21no—
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—31no—
818C2×Q8—32no—
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×Q8C23×D311yescharacteristic
829C2×D4—21no—
830C2×D4—31no—
831C2×D4—61no—
832C2×D4C23×D311yescharacteristic
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—62no—
836C22×C4—62no—
837C22×C4—62no—
838C22×C4—61no—
839C22×C4—61no—
840C22×C4—61no—
841C22×C4D3×D411yescharacteristic
842C22×C4D3×D411yescharacteristic
843C22×C4C23×D311yescharacteristic
844Q16—64no—
845Q16—62no—
846SD16—64no—
847SD16—62no—
848SD16—62no—
849D8—62no—
850C2×C8—31no—
851C2×C8—31no—
852C2×C8—31no—
853C2×C8—31no—
854C2×C8C23×D312yes—
855C2×C8C23×D312yes—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—22no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—32no—
865C4⋊C4—31no—
866C4⋊C4—32no—
867C4⋊C4—32no—
868C4⋊C4—31no—
869C4⋊C4—32no—
870C4⋊C4—32no—
871C4⋊C4—32no—
872C4⋊C4—32no—
873C4⋊C4—31no—
874C4⋊C4—31no—
875C4⋊C4—32no—
876C4⋊C4—62no—
877C4⋊C4—62no—
878C4⋊C4—62no—
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—62no—
889C4⋊C4—62no—
890C4⋊C4—62no—
891C4⋊C4—62no—
892C4⋊C4—61no—
893C4⋊C4—61no—
894C4⋊C4—61no—
895C4⋊C4—61no—
896C4⋊C4—62no—
897C4⋊C4—62no—
898C4⋊C4—61no—
899C4⋊C4C23×D311yescharacteristic
900C4⋊C4C23×D311yescharacteristic
901C4⋊C4C23×D312yes—
902C4⋊C4C23×D312yes—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—21no—
908C22⋊C4—32no—
909C22⋊C4—32no—
910C22⋊C4—62no—
911C22⋊C4—62no—
912C22⋊C4—62no—
913C22⋊C4—62no—
914C22⋊C4—62no—
915C22⋊C4—61no—
916C22⋊C4—62no—
917C22⋊C4—61no—
918C22⋊C4—61no—
919C42—21no—
920C42—32no—
921C42—32no—
922C42—62no—
923C42—62no—
924C42—62no—
925C42—62no—
926C42—62no—
927C42—61no—
928C42—61no—
929C42—61no—
930C42—62no—
931C42D3×D411yescharacteristic
932C42D3×D411yescharacteristic
933C42C23×D311yescharacteristic
934C42C23×D311yescharacteristic
935C22×C3—21no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—41no—
939C22×C3—41no—
940C22×C3—41no—
941C22×C3C23×D411yescharacteristic
942C2×D3—22no—
943C2×D3—41no—
944C2×D3—41no—
945C3×C4—21no—
946C3×C4—21no—
947C3×C4—21no—
948C3×C4—21no—
949C3×C4—41no—
950C3×C4—41no—
951C3×C4—42no—
952C3×C4—42no—
953C3×C4—41no—
954C3×C4#57712yes—
955C3×C4C2×2−1+411yescharacteristic
956C3×C4C2×2−1+411yescharacteristic
957Dic3—22no—
958Dic3—22no—
959Dic3—22no—
960Dic3—22no—
961Dic3—22no—
962Dic3—42no—
963Dic3—41no—
964Dic3—42no—
965Dic3—41no—
966C23—21no—
967C23—61no—
968C23C2×D3×D411yescharacteristic
969Q8—21no—
970Q8—21no—
971Q8—32no—
972Q8—42no—
973Q8—42no—
974Q8—61no—
975Q8—62no—
976Q8—62no—
977Q8—62no—
978Q8—62no—
979Q8—82no—
980Q8—122no—
981Q8—241no—
982Q8—242no—
983Q8—242no—
984Q8—242no—
985D4—21no—
986D4—21no—
987D4—32no—
988D4—64no—
989D4—61no—
990D4—81no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—32no—
1000C2×C4—32no—
1001C2×C4—32no—
1002C2×C4—32no—
1003C2×C4—41no—
1004C2×C4—42no—
1005C2×C4—64no—
1006C2×C4—61no—
1007C2×C4—62no—
1008C2×C4—61no—
1009C2×C4—62no—
1010C2×C4—61no—
1011C2×C4—82no—
1012C2×C4—122no—
1013C2×C4—122no—
1014C2×C4—242no—
1015C2×C4—242no—
1016C2×C4—242no—
1017C2×C4C2×D3×D411yescharacteristic
1018C2×C4C2×D3×D411yescharacteristic
1019C2×C4C2×D3×D411yescharacteristic
1020C2×C4C2×D3×D411yescharacteristic
1021C2×C4C2×D3×D411yescharacteristic
1022C2×C4C24×D311yescharacteristic
1023C8—22no—
1024C8—22no—
1025C8—61no—
1026C8—61no—
1027C8—61no—
1028C8—61no—
1029C2×C3—41no—
1030C2×C3—81no—
1031C2×C3#348611yescharacteristic
1032C2×C3C2×#57711yescharacteristic
1033C2×C3#358611yescharacteristic
1034D3—42no—
1035C22—21no—
1036C22—21no—
1037C22—21no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—62no—
1042C22—121no—
1043C22—121no—
1044C22C22×D3×D411yescharacteristic
1045C4—21no—
1046C4—21no—
1047C4—21no—
1048C4—21no—
1049C4—41no—
1050C4—41no—
1051C4—42no—
1052C4—42no—
1053C4—41no—
1054C4—62no—
1055C4—62no—
1056C4—62no—
1057C4—62no—
1058C4—62no—
1059C4—122no—
1060C4—121no—
1061C4—121no—
1062C4—122no—
1063C4#577512yes—
1064C4D3×2−1+411yescharacteristic
1065C4D3×2−1+411yescharacteristic
1066C3#6185811yescharacteristic, complemented, Sylow
1067C2—41no—
1068C2—81no—
1069C2—122no—
1070C2#8635511yescharacteristic
1071C2C2×#577511yescharacteristic
1072C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3239C2
socleC22×C3C23×D4
prime radical#5037C22
hypercenter#3239D3
hypocenterC3#61858
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3239

Complements

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

NH ≅ G/Ntype
1. #86215C2semidirect
2. #86138C2semidirect
3. C3×#3239C2semidirect
4. #83223C2semidirect
6. #81969C2semidirect
7. #81967C2semidirect
8. #81676C2semidirect
9. #81671C2semidirect
10. #81460C2semidirect
11. #81456C2semidirect
12. #81317C2semidirect
14. #81043C2semidirect
15. #81042C2semidirect
16. #81039C2semidirect
17. #81037C2semidirect
18. #80994C2semidirect
19. #80993C2semidirect
20. #80959C2semidirect
21. #80958C2semidirect
22. #79348C2semidirect
23. #79316C2semidirect
152. #3239D3semidirect
1066. C3#61858semidirect

Maximal subgroups

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

subgroupindex
#862152
#861382
C3×#32392
#832232
#831402
#819692
#819672
#816762
#816712
#814602
#814562
#813172
#813132
#810432
#810422
#810392
#810372
#809942
#809932
#809592
#809582
#793482
#793162
#618583