Finite Group Databasebeta

← #11675548

Subgroups — #11675548

Order 768.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86586C211yesmaximal, characteristic, complemented
2#85892C211yesmaximal, characteristic, complemented
3C3×#3083C211yesmaximal, characteristic, complemented
4#83471C211yesmaximal, characteristic, complemented
5#82557C211yesmaximal, characteristic, complemented
6#81267C212yesmaximal, complemented
7#81219C212yesmaximal, complemented
8#81155C212yesmaximal, complemented
9#81150C212yesmaximal, complemented
10#81138C212yesmaximal, complemented
11#81100C212yesmaximal, complemented
12#80993C212yesmaximal, complemented
13#80956C212yesmaximal, complemented
14#79243C211yesmaximal, characteristic, complemented
15#79200C211yesmaximal, characteristic, complemented
16C2×#4875C211yesmaximal, characteristic, complemented
17#79136C211yesmaximal, characteristic, complemented
18#79089C211yesmaximal, characteristic, complemented
19#79078C211yesmaximal, characteristic, complemented
20#78912C211yesmaximal, characteristic, complemented
21#78878C211yesmaximal, characteristic, complemented
22#78861C211yesmaximal, characteristic
23#78828C211yesmaximal, characteristic, complemented
24#61348—31nomaximal, Sylow
25C3×#544C2211yescharacteristic
26C3×#520C2211yescharacteristic
27#5832C2211yescharacteristic
28#5825C2211yescharacteristic
29C2×#950C2211yescharacteristic
30C2×#909C2211yescharacteristic
31C2×#904C2211yescharacteristic
32#5729—21no—
33#5727C2212yes—
34D3×C4⋊Q8—21no—
35#5722C2212yes—
36#5690C2212yes—
37#5689—21no—
38#5688—21no—
39#5685C2212yes—
40#5636—22no—
41#5632—22no—
42#5568C2212yes—
43#5567C2212yes—
44#5564—22no—
45#5559C2212yes—
46#5542C2212yes—
47#5538—22no—
48#5533—21no—
49#5529—21no—
50#5526C2211yescharacteristic
51#5523C2211yescharacteristic
52#5522C2211yescharacteristic
53#5519C2211yescharacteristic
54#5517C2211yescharacteristic
55#5513—21no—
56#5511—21no—
57#5504C2211yescharacteristic
58#5504C2211yescharacteristic
59C2×#888C2211yescharacteristic
60C2×#887C2211yescharacteristic
61C3×#479C2212yes—
62C3×#478C2212yes—
63C3×#477C2212yes—
64C3×#474C2212yes—
65C3×#428C2211yescharacteristic
66C2×C3×#107C2211yescharacteristic
67C3×#424C2211yescharacteristic
68C3×#417C2211yescharacteristic
69C3×#416C2211yescharacteristic
70#5232C2211yescharacteristic
71#5133C2211yescharacteristic
72#5119C2211yescharacteristic
73Dic3×M16C2211yescharacteristic
74C2×#816C2211yescharacteristic
75#5101C2211yescharacteristic
76C2×Dic3⋊C8C2211yescharacteristic
77#5093C2212yes—
78#5089C2212yes—
79#5069C2212yes—
80#5068C2212yes—
81C4×#216C2212yes—
82#5026C2212yes—
83#5018C2212yes—
84C4×#213C2212yes—
85#5004C2211yescharacteristic
86#5002C2211yescharacteristic
87#4997C2211yescharacteristic
88C2×#810C2211yescharacteristic
89#4966C2211yescharacteristic
90#4966C2211yescharacteristic
91C2×#807C2211yescharacteristic
92#4890C2212yes—
93#4889C2212yes—
94#4889C2212yes—
95#4889C2212yes—
96#4875C2212yes—
97#4875C2212yes—
98#4875C2212yes—
99#4875C2212yes—
100#4875C2212yes—
101#4873C2212yes—
102#4873C2212yes—
103#4872C2212yes—
104#4871C2212yes—
105#4857C2212yes—
106#4853C2212yes—
107#4852C2212yes—
108#4849C2212yes—
109#4845C2212yes—
110#4844C2212yes—
111#4841C2212yes—
112#4831C2212yes—
113#4830C2212yes—
114#4828C2212yes—
115#4828C2212yes—
116#4819C2211yescharacteristic
117#4818C2211yescharacteristic
118#4818C2212yes—
119#4798C2211yescharacteristic
120#4797C2212yes—
121#4795C2211yescharacteristic
122#4795C2212yes—
123#4794C2212yes—
124#4792C2212yes—
125#4792C2212yes—
126#4787C2211yescharacteristic
127#4787C2212yes—
128#4786C2211yescharacteristic
129#4768C2212yes—
130#4767C2211yescharacteristic
131#4767C2212yes—
132#4765C2212yes—
133#4765C2212yes—
134#4762C2211yescharacteristic
135#4760C2212yes—
136#3507—31no—
137#3503—31no—
138#3377—32no—
139#3377—32no—
140#3375—32no—
141#3372—32no—
142#3367—32no—
143#3367—32no—
144#3363—32no—
145#3361—32no—
146#3141—31no—
147#3137—31no—
148#3137—31no—
149#3083—31no—
150#3083D311yescharacteristic, complemented
151C2×#477—31no—
152#3046—31no—
153#3046—31no—
154#3035—31no—
155#2962—31no—
156#2951—31no—
157#2951—31no—
158C4×#137—31no—
159C2×C3×#41C2311yescharacteristic
160C2×D3×Q8—22no—
161C2×#235C2311yescharacteristic
162C2×#235C2311yescharacteristic
163C22×Dic6—21no—
164C22×Dic6C2311yescharacteristic
165C2×C3×M16C2311yescharacteristic
166C22×C3×C8C2311yescharacteristic
167C3×C4⋊Q8—21no—
168C3×C4⋊Q8C2312yes—
169C3×#125—21no—
170C3×#125C2312yes—
171C3×C22⋊Q8—22no—
172C3×C4×Q8C2312yes—
173C3×C4×D4—22no—
174C3×C4×D4C2312yes—
175C3×#117—21no—
176C3×#117C2311yescharacteristic
177C3×#117C2311yescharacteristic
178C2×C3×C4⋊C4—21no—
179C2×C3×C4⋊C4C2311yescharacteristic
180C2×C3×C4⋊C4C2311yescharacteristic
181#950—24no—
182#947C2311yescharacteristic
183#946—22no—
184#944—22no—
185#944—22no—
186#944C2311yescharacteristic
187#944C2312yes—
188C2×#216C2311yescharacteristic
189C2×#215C2311yescharacteristic
190#940C2311yescharacteristic
191#939—21no—
192#939—21no—
193#936C2311yescharacteristic
194#936C2312yes—
195#935—22no—
196C2×#214C2311yescharacteristic
197C2×#213C2311yescharacteristic
198#929—22no—
199C4×#67—22no—
200C4×#67—22no—
201C4×#67—22no—
202C4×#67—21no—
203C4×#67—21no—
204#926—22no—
205#926C2311yescharacteristic
206C2×C4⋊Dic3C2311yescharacteristic
207#924—22no—
208#924—21no—
209#924—21no—
210C2×Dic3⋊C4—21no—
211C2×Dic3⋊C4—21no—
212C2×C4×Dic3—21no—
213C2×C4×Dic3C2311yescharacteristic
214C2×#208C2311yescharacteristic
215C22×C3⋊C8C2311yescharacteristic
216#909—24no—
217C2×Dic12C2311yescharacteristic
218C2×Dic12C2312yes—
219#904—24no—
220C2×D24C2311yescharacteristic
221C2×#204C2311yescharacteristic
222C2×#204C2311yescharacteristic
223C2×#204C2312yes—
224#898—22no—
225#897—21no—
226#897—21no—
227#897—22no—
228#896—22no—
229#896—22no—
230#896—22no—
231#896—22no—
232#896—22no—
233#893C2312yes—
234#893C2312yes—
235#893C2311yescharacteristic
236#893C2311yescharacteristic
237#892—21no—
238#892—21no—
239#892—21no—
240D3×C4⋊C4—21no—
241D3×C4⋊C4—21no—
242D3×C4⋊C4—21no—
243D3×C4⋊C4—22no—
244#890D411yescharacteristic
245#890D411yescharacteristic
246#890C2312yes—
247#889—22no—
248#889—22no—
249#889—22no—
250#889—22no—
251#888—22no—
252#888—22no—
253#888—21no—
254#888—21no—
255#888D411yescharacteristic
256#888D411yescharacteristic
257#888C2312yes—
258#888C2312yes—
259#888C2312yes—
260#887—22no—
261#887—22no—
262#887—21no—
263#887—21no—
264#887C2311yescharacteristic
265#887C2312yes—
266#887C2312yes—
267#887C2312yes—
268#887C2312yes—
269#887C2311yescharacteristic
270#886—22no—
271#885—22no—
272#883—22no—
273#67⋊C4—21no—
274#67⋊C4—21no—
275#67⋊C4—22no—
276#879—22no—
277#879—22no—
278#878—22no—
279#878D412yes—
280#878D412yes—
281#876—22no—
282#875C2312yes—
283C4×D12C2312yes—
284#872—22no—
285#872—21no—
286C42×D3—21no—
287#870—21no—
288#870—22no—
289#869—21no—
290#869C2312yes—
291C4×Dic6—22no—
292C4×Dic6C2312yes—
293C4×Dic6C2312yes—
294C4×Dic6C2312yes—
295C3×#107C2312yes—
296C3×#107C2312yes—
297C3×#107C2312yes—
298C3×#106C2312yes—
299C3×C4⋊C8C2312yes—
300C3×C4⋊C8C2312yes—
301C3×#103C2311yescharacteristic
302C3×#103C2311yescharacteristic
303C3×#103C2312yes—
304C3×#102C2312yes—
305C3×#102C2311yescharacteristic
306C3×#102C2311yescharacteristic
307#835C2312yes—
308#832C2312yes—
309#821C2312yes—
310#816C2312yes—
311#816C2312yes—
312#816C2312yes—
313#815C2312yes—
314#815C2312yes—
315Dic3⋊C8C2312yes—
316Dic3⋊C8C2311yescharacteristic
317Dic3⋊C8C2311yescharacteristic
318Dic3⋊C8C2311yescharacteristic
319Dic3⋊C8C2311yescharacteristic
320Dic3⋊C8C2312yes—
321C8×Dic3C2312yes—
322C8×Dic3C2312yes—
323#810C2312yes—
324#810C2312yes—
325#810C2312yes—
326#810C2312yes—
327#810C2312yes—
328#810C2311yescharacteristic
329#810C2311yescharacteristic
330#810C2312yes—
331#809C2311yescharacteristic
332#809C2312yes—
333#809C2312yes—
334#809C2311yescharacteristic
335#807C2312yes—
336#807C2312yes—
337#803C2312yes—
338C4×C3⋊C8C2312yes—
339C2×#137—31no—
340C2×#135—31no—
341C2×#135—31no—
342#559—32no—
343Q82—32no—
344#557—32no—
345#557—32no—
346#556—32no—
347#556—32no—
348#556—61no—
349#554—32no—
350#554—61no—
351#554—62no—
352#552—61no—
353#552—61no—
354D4×Q8—32no—
355D4×Q8—62no—
356#544—31no—
357#544—61no—
358#544—61no—
359#544C2×D311yescharacteristic
360#539—62no—
361#536—31no—
362#536—31no—
363#533—31no—
364#533—61no—
365#532—31no—
366C2×C4⋊Q8—31no—
367C2×C4⋊Q8—61no—
368#529—62no—
369#520—31no—
370#520—31no—
371#520—31no—
372#520C2×D311yescharacteristic
373C4×#41—31no—
374C2×C4×Q8—31no—
375#491—32no—
376#491—32no—
377#489—32no—
378#489—32no—
379#489—32no—
380#489—32no—
381#488—32no—
382#488—32no—
383#487—32no—
384#487—32no—
385#487—32no—
386#486—32no—
387#479—32no—
388#479C2×D312yes—
389#478—32no—
390#478C2×D312yes—
391#477—32no—
392#477—32no—
393#477—32no—
394#477—32no—
395#477—32no—
396#477C2×D312yes—
397#474—32no—
398#474C2×D312yes—
399#464—32no—
400#464—31no—
401#464—32no—
402#464—31no—
403#463—32no—
404#463—31no—
405#463—32no—
406#463—31no—
407#462—32no—
408#462—31no—
409#462—32no—
410#461—32no—
411#461—32no—
412#461—31no—
413#460—31no—
414#459—31no—
415#446—32no—
416#446—32no—
417#446—32no—
418C8×Q8—32no—
419#441—32no—
420#440—32no—
421#440—32no—
422#440—32no—
423#440—32no—
424#440—32no—
425C4×Q16—32no—
426C4×Q16—32no—
427C4×Q16—32no—
428C4×SD16—32no—
429C4×D8—32no—
430C4×D8—32no—
431#428C2×D311yescharacteristic
432C2×#107—31no—
433C2×#107C2×D311yescharacteristic
434#424—31no—
435#424C2×D311yescharacteristic
436C2×C4⋊C8—31no—
437#419—31no—
438#417—31no—
439#417—31no—
440#417—31no—
441#417—31no—
442#417C2×D311yescharacteristic
443#416—31no—
444#416C2×D311yescharacteristic
445C2×#103—31no—
446C2×#103—31no—
447#405—31no—
448#405—31no—
449C4×M16—31no—
450C3×#41—22no—
451C3×#41—22no—
452C2×C3×Q8—22no—
453C2×C3×Q8C2411yescharacteristic
454C2×C3×D4—21no—
455C2×C3×D4C2411yescharacteristic
456C22×C3×C4—21no—
457C22×C3×C4—21no—
458C22×C3×C4—21no—
459C22×C3×C4—22no—
460C22×C3×C4C2411yescharacteristic
461C2×#67—21no—
462C2×#67—21no—
463C2×#67—21no—
464C2×#67—21no—
465C22×Dic3—21no—
466C22×Dic3—21no—
467C22×Dic3C2×D411yescharacteristic
468C22×Dic3C2×D411yescharacteristic
469D3×Q8—84no—
470#235—22no—
471#235—22no—
472#235—22no—
473#235#4114yes—
474C2×D12C2411yescharacteristic
475C2×D12C2411yescharacteristic
476C2×C4×D3—21no—
477C2×C4×D3—21no—
478C2×C4×D3—21no—
479C2×C4×D3—21no—
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×C4×D3—22no—
483C2×Dic6—22no—
484C2×Dic6—22no—
485C2×Dic6—21no—
486C2×Dic6—22no—
487C2×Dic6—22no—
488C2×Dic6—22no—
489C2×Dic6—82no—
490C2×Dic6C2×D412yes—
491C2×Dic6C2×D412yes—
492C2×Dic6C2411yescharacteristic
493C2×Dic6C2412yes—
494C2×Dic6C2411yescharacteristic
495C3×M16—22no—
496C2×C3×C8—22no—
497C2×C3×C8C2411yescharacteristic
498C2×C3×C8C2412yes—
499C2×C3×C8C2411yescharacteristic
500C3×C4⋊C4—21no—
501C3×C4⋊C4—22no—
502C3×C4⋊C4—22no—
503C3×C4⋊C4—21no—
504C3×C4⋊C4—22no—
505C3×C4⋊C4—22no—
506C3×C4⋊C4C2×D411yescharacteristic
507C3×C4⋊C4C2×D411yescharacteristic
508C3×C4⋊C4C2412yes—
509C3×C4⋊C4C2411yescharacteristic
510C3×C4⋊C4C2412yes—
511C3×C4⋊C4C2411yescharacteristic
512C3×C22⋊C4—21no—
513C3×C22⋊C4—22no—
514C3×C22⋊C4C2×D412yes—
515C3×C42—22no—
516C3×C42—21no—
517C3×C42C2412yes—
518#217—21no—
519#217—21no—
520#217—22no—
521#217—22no—
522#217C2×D412yes—
523#216—22no—
524#215—22no—
525#214—22no—
526#213—22no—
527(C2×D3)⋊C4—22no—
528(C2×D3)⋊C4—22no—
529(C2×D3)⋊C4—22no—
530(C2×D3)⋊C4—21no—
531(C2×D3)⋊C4—21no—
532(C2×D3)⋊C4—21no—
533(C2×D3)⋊C4—21no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4—22no—
536C4⋊Dic3—22no—
537C4⋊Dic3—21no—
538C4⋊Dic3—22no—
539C4⋊Dic3—22no—
540C4⋊Dic3C2×D412yes—
541C4⋊Dic3C2×D412yes—
542C4⋊Dic3C2×D411yescharacteristic
543C4⋊Dic3C2×D411yescharacteristic
544C4⋊Dic3C2412yes—
545Dic3⋊C4—22no—
546Dic3⋊C4—21no—
547Dic3⋊C4—22no—
548Dic3⋊C4—21no—
549Dic3⋊C4—22no—
550Dic3⋊C4—22no—
551Dic3⋊C4—22no—
552Dic3⋊C4—22no—
553Dic3⋊C4—22no—
554Dic3⋊C4—21no—
555Dic3⋊C4—21no—
556Dic3⋊C4—22no—
557Dic3⋊C4—22no—
558Dic3⋊C4—22no—
559Dic3⋊C4—22no—
560Dic3⋊C4C2×D412yes—
561Dic3⋊C4C2×D412yes—
562Dic3⋊C4C2×D412yes—
563Dic3⋊C4C2×D412yes—
564C4×Dic3—22no—
565C4×Dic3—22no—
566C4×Dic3—22no—
567C4×Dic3—21no—
568C4×Dic3—21no—
569C4×Dic3—22no—
570C4×Dic3—22no—
571C4×Dic3C2×D411yescharacteristic
572C4×Dic3C2×D411yescharacteristic
573C4×Dic3C2411yescharacteristic
574C4×Dic3C2412yes—
575C4×Dic3C2411yescharacteristic
576#208—22no—
577C2×C3⋊C8—22no—
578C2×C3⋊C8C2411yescharacteristic
579C2×C3⋊C8C2412yes—
580C2×C3⋊C8C2411yescharacteristic
581Dic12—22no—
582Dic12—24no—
583D24—22no—
584#204—22no—
585#204—24no—
586#204—22no—
587C2×#41—31no—
588C2×#41—31no—
589C2×#41C22×D311yescharacteristic
590C22×Q8—31no—
591C22×Q8—61no—
592C22×Q8—62no—
593#137—64no—
594#135—64no—
595#135—64no—
596C2×Q16—31no—
597C2×Q16—31no—
598C2×Q16—32no—
599C2×SD16—31no—
600C2×SD16—31no—
601C2×SD16—31no—
602C2×SD16—31no—
603C2×SD16—32no—
604C2×D8—31no—
605C2×D8—31no—
606C2×M16—31no—
607C2×M16C22×D311yescharacteristic
608C22×C8—31no—
609C22×C8C22×D311yescharacteristic
610C4⋊Q8—21no—
611C4⋊Q8—31no—
612C4⋊Q8—31no—
613C4⋊Q8—32no—
614C4⋊Q8—32no—
615C4⋊Q8—32no—
616C4⋊Q8—31no—
617C4⋊Q8—32no—
618C4⋊Q8—32no—
619C4⋊Q8—61no—
620C4⋊Q8—61no—
621C4⋊Q8—61no—
622C4⋊Q8—62no—
623C4⋊Q8—62no—
624C4⋊Q8—62no—
625C4⋊Q8—62no—
626C4⋊Q8C22×D312yes—
627#127—31no—
628#126—62no—
629#126—62no—
630#126—62no—
631#126—62no—
632#125—21no—
633#125—31no—
634#125—31no—
635#125—32no—
636#125—61no—
637#125—62no—
638#125—62no—
639#125—62no—
640#125—62no—
641#125—62no—
642#125C22×D312yes—
643#124—31no—
644#124—31no—
645#124—32no—
646#124—32no—
647#124—62no—
648#123—62no—
649#123—62no—
650#123—62no—
651#123—62no—
652C22⋊Q8—22no—
653C22⋊Q8—32no—
654C22⋊Q8—32no—
655C22⋊Q8—62no—
656C22⋊Q8—62no—
657C22⋊Q8—62no—
658C22⋊Q8—62no—
659C22⋊Q8—62no—
660C22⋊Q8—62no—
661C22⋊Q8—62no—
662C22⋊Q8—61no—
663C22⋊Q8—61no—
664C22⋊Q8—62no—
665C22⋊Q8—62no—
666C22⋊Q8—61no—
667C22⋊Q8—61no—
668#121—61no—
669#121—61no—
670C4×Q8—32no—
671C4×Q8—32no—
672C4×Q8—32no—
673C4×Q8—32no—
674C4×Q8—31no—
675C4×Q8—31no—
676C4×Q8—32no—
677C4×Q8—32no—
678C4×Q8—32no—
679C4×Q8—62no—
680C4×Q8—61no—
681C4×Q8—61no—
682C4×Q8—62no—
683C4×Q8—62no—
684C4×Q8C22×D312yes—
685C4×D4—22no—
686C4×D4—31no—
687C4×D4—31no—
688C4×D4—32no—
689C4×D4—32no—
690C4×D4—32no—
691C4×D4—61no—
692C4×D4—61no—
693C4×D4—61no—
694C4×D4—61no—
695C4×D4—62no—
696C4×D4—62no—
697C4×D4—62no—
698C4×D4—62no—
699C4×D4C22×D312yes—
700#117—21no—
701#117—31no—
702#117—61no—
703#117—62no—
704#117—61no—
705#117—61no—
706#117—62no—
707#117—61no—
708#117C22×D311yescharacteristic
709#117C22×D311yescharacteristic
710C2×C4⋊C4—21no—
711C2×C4⋊C4—31no—
712C2×C4⋊C4—61no—
713C2×C4⋊C4—61no—
714C2×C4⋊C4—62no—
715C2×C4⋊C4—61no—
716C2×C4⋊C4—61no—
717C2×C4⋊C4—61no—
718C2×C4⋊C4C22×D311yescharacteristic
719C2×C4⋊C4C22×D311yescharacteristic
720C2×C42—31no—
721C2×C42—61no—
722C2×C42—61no—
723#107—32no—
724#107—32no—
725#107C22×D312yes—
726#107C22×D312yes—
727#107C22×D312yes—
728#106C22×D312yes—
729C4⋊C8—31no—
730C4⋊C8—31no—
731C4⋊C8—31no—
732C4⋊C8—31no—
733C4⋊C8—32no—
734C4⋊C8—32no—
735C4⋊C8C22×D312yes—
736C4⋊C8C22×D312yes—
737#103—32no—
738#103—32no—
739#103—32no—
740#103—32no—
741#103—32no—
742#103—32no—
743#103—31no—
744#103—31no—
745#103—32no—
746#103—32no—
747#103—32no—
748#103—32no—
749#103C22×D311yescharacteristic
750#103C22×D311yescharacteristic
751#103C22×D312yes—
752#102—32no—
753#102—32no—
754#102—31no—
755#102—31no—
756#102—32no—
757#102—32no—
758#102C22×D311yescharacteristic
759#102C22×D311yescharacteristic
760#102C22×D312yes—
761#97—32no—
762#97—32no—
763#97—32no—
764C4×C8—32no—
765C4×C8—32no—
766C4×C8—32no—
767C23×C3—21no—
768C23×C3C22×D411yescharacteristic
769C22×D3—21no—
770C22×D3—21no—
771C3×Q8—21no—
772C3×Q8—21no—
773C3×Q8—82no—
774C3×D4—21no—
775C3×D4—21no—
776C3×D4—42no—
777C2×C3×C4—22no—
778C2×C3×C4—21no—
779C2×C3×C4—21no—
780C2×C3×C4—22no—
781C2×C3×C4—21no—
782C2×C3×C4—42no—
783C2×C3×C4—82no—
784C2×C3×C4—81no—
785C2×C3×C4—81no—
786C2×C3×C4C22×D412yes—
787C2×C3×C4C22×D412yes—
788C2×C3×C4C22×D411yescharacteristic
789C2×C3×C4C2×#4112yes—
790C2×C3×C42−1+412yes—
791C2×C3×C4C2511yescharacteristic
792#67—24no—
793#67—42no—
794#67—42no—
795#67—81no—
796C2×Dic3—21no—
797C2×Dic3—22no—
798C2×Dic3—21no—
799C2×Dic3—22no—
800C2×Dic3—22no—
801C2×Dic3—41no—
802C2×Dic3—42no—
803C2×Dic3—81no—
804C2×Dic3C22×D411yescharacteristic
805C2×Dic3C22×D412yes—
806C2×Dic3C22×D411yescharacteristic
807C2×Dic3C22×D411yescharacteristic
808C2×Dic3C22×D412yes—
809C2×Dic3C22×D411yescharacteristic
810D12—21no—
811D12—21no—
812D12—21no—
813D12C2×#4112yes—
814C4×D3—24no—
815C4×D3—42no—
816C4×D3—42no—
817C4×D3—42no—
818C4×D3—82no—
819C4×D3—82no—
820C4×D3—82no—
821Dic6—21no—
822Dic6—24no—
823Dic6—22no—
824Dic6—21no—
825Dic6—22no—
826Dic6—21no—
827Dic6—42no—
828Dic6—44no—
829Dic6—42no—
830Dic6—82no—
831Dic6—82no—
832Dic6C2×#4112yes—
833C3×C8—21no—
834C3×C8—22no—
835C3×C8—21no—
836C3⋊C8—21no—
837C3⋊C8—21no—
838C3⋊C8—22no—
839#41—22no—
840#41—22no—
841#41—34no—
842#41—62no—
843#41—62no—
844#41—62no—
845C2×Q8—22no—
846C2×Q8—32no—
847C2×Q8—32no—
848C2×Q8—31no—
849C2×Q8—32no—
850C2×Q8—31no—
851C2×Q8—62no—
852C2×Q8—62no—
853C2×Q8—62no—
854C2×Q8—61no—
855C2×Q8—62no—
856C2×Q8—62no—
857C2×Q8—242no—
858C2×Q8—244no—
859C2×Q8C23×D311yescharacteristic
860C2×D4—21no—
861C2×D4—31no—
862C2×D4—31no—
863C2×D4—61no—
864C2×D4—61no—
865C2×D4—61no—
866C2×D4—61no—
867C2×D4C23×D311yescharacteristic
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—31no—
873C22×C4—31no—
874C22×C4—61no—
875C22×C4—61no—
876C22×C4—62no—
877C22×C4—62no—
878C22×C4—61no—
879C22×C4—61no—
880C22×C4—61no—
881C22×C4—61no—
882C22×C4—62no—
883C22×C4C23×D311yescharacteristic
884Q16—62no—
885Q16—64no—
886Q16—62no—
887SD16—62no—
888SD16—64no—
889SD16—62no—
890SD16—62no—
891SD16—62no—
892D8—62no—
893D8—62no—
894M16—22no—
895M16—62no—
896C2×C8—22no—
897C2×C8—32no—
898C2×C8—31no—
899C2×C8—31no—
900C2×C8—62no—
901C2×C8C23×D311yescharacteristic
902C2×C8C23×D312yes—
903C2×C8C23×D311yescharacteristic
904C4⋊C4—21no—
905C4⋊C4—22no—
906C4⋊C4—21no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—31no—
911C4⋊C4—32no—
912C4⋊C4—31no—
913C4⋊C4—32no—
914C4⋊C4—32no—
915C4⋊C4—32no—
916C4⋊C4—32no—
917C4⋊C4—32no—
918C4⋊C4—32no—
919C4⋊C4—62no—
920C4⋊C4—62no—
921C4⋊C4—62no—
922C4⋊C4—62no—
923C4⋊C4—62no—
924C4⋊C4—62no—
925C4⋊C4—62no—
926C4⋊C4—61no—
927C4⋊C4—61no—
928C4⋊C4—62no—
929C4⋊C4—61no—
930C4⋊C4—61no—
931C4⋊C4—62no—
932C4⋊C4—62no—
933C4⋊C4—62no—
934C4⋊C4—61no—
935C4⋊C4—62no—
936C4⋊C4—62no—
937C4⋊C4—62no—
938C4⋊C4D3×D411yescharacteristic
939C4⋊C4D3×D411yescharacteristic
940C4⋊C4C23×D311yescharacteristic
941C4⋊C4C23×D312yes—
942C4⋊C4C23×D311yescharacteristic
943C4⋊C4C23×D312yes—
944C22⋊C4—21no—
945C22⋊C4—22no—
946C22⋊C4—32no—
947C22⋊C4—61no—
948C22⋊C4—61no—
949C22⋊C4—61no—
950C22⋊C4—62no—
951C22⋊C4—62no—
952C22⋊C4—61no—
953C22⋊C4—61no—
954C22⋊C4—62no—
955C22⋊C4—61no—
956C22⋊C4—62no—
957C22⋊C4—62no—
958C22⋊C4—62no—
959C22⋊C4—62no—
960C22⋊C4D3×D412yes—
961C42—21no—
962C42—22no—
963C42—31no—
964C42—31no—
965C42—31no—
966C42—32no—
967C42—31no—
968C42—62no—
969C42—62no—
970C42—61no—
971C42—61no—
972C42—62no—
973C42—62no—
974C42—62no—
975C42C23×D312yes—
976C22×C3—21no—
977C22×C3—21no—
978C22×C3—41no—
979C22×C3—41no—
980C22×C3—41no—
981C22×C3#54812yes—
982C22×C3C23×D411yescharacteristic
983C2×D3—22no—
984C2×D3—41no—
985C2×D3—41no—
986C2×D3—41no—
987C2×D3—41no—
988C2×D3—41no—
989C3×C4—22no—
990C3×C4—22no—
991C3×C4—42no—
992C3×C4—41no—
993C3×C4—42no—
994C3×C4—41no—
995C3×C4—41no—
996C3×C4#54812yes—
997C3×C4C22×#4111yescharacteristic
998C3×C4C2×2−1+411yescharacteristic
999Dic3—21no—
1000Dic3—22no—
1001Dic3—21no—
1002Dic3—22no—
1003Dic3—22no—
1004Dic3—21no—
1005Dic3—42no—
1006Dic3—42no—
1007Dic3—41no—
1008Dic3#57812yes—
1009C23—21no—
1010C23—61no—
1011C23—61no—
1012C23C2×D3×D411yescharacteristic
1013Q8—21no—
1014Q8—21no—
1015Q8—32no—
1016Q8—64no—
1017Q8—61no—
1018Q8—62no—
1019Q8—61no—
1020Q8—62no—
1021Q8—61no—
1022Q8—82no—
1023Q8—122no—
1024Q8—124no—
1025Q8—122no—
1026Q8—242no—
1027Q8—242no—
1028D4—21no—
1029D4—21no—
1030D4—32no—
1031D4—42no—
1032D4—64no—
1033D4—61no—
1034D4—61no—
1035D4—61no—
1036D4—122no—
1037D4—122no—
1038D4—241no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—31no—
1045C2×C4—31no—
1046C2×C4—31no—
1047C2×C4—31no—
1048C2×C4—32no—
1049C2×C4—32no—
1050C2×C4—42no—
1051C2×C4—62no—
1052C2×C4—61no—
1053C2×C4—64no—
1054C2×C4—62no—
1055C2×C4—61no—
1056C2×C4—62no—
1057C2×C4—82no—
1058C2×C4—81no—
1059C2×C4—81no—
1060C2×C4—122no—
1061C2×C4—122no—
1062C2×C4—121no—
1063C2×C4—122no—
1064C2×C4—122no—
1065C2×C4—242no—
1066C2×C4—242no—
1067C2×C4—242no—
1068C2×C4—241no—
1069C2×C4C2×D3×D412yes—
1070C2×C4C2×D3×D412yes—
1071C2×C4C2×D3×D411yescharacteristic
1072C2×C4#100712yes—
1073C2×C4D3×#4112yes—
1074C2×C4C24×D311yescharacteristic
1075C8—21no—
1076C8—21no—
1077C8—22no—
1078C8—62no—
1079C8—61no—
1080C8—61no—
1081C2×C3—22no—
1082C2×C3—81no—
1083C2×C3C2×#54811yescharacteristic
1084C2×C3C2×#57811yescharacteristic
1085C2×C3#358511yescharacteristic
1086D3—42no—
1087D3—81no—
1088C22—21no—
1089C22—21no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—62no—
1094C22—121no—
1095C22—121no—
1096C22—121no—
1097C22—121no—
1098C22—121no—
1099C22#563312yes—
1100C22C22×D3×D411yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—32no—
1104C4—42no—
1105C4—42no—
1106C4—41no—
1107C4—41no—
1108C4—41no—
1109C4—61no—
1110C4—61no—
1111C4—62no—
1112C4—61no—
1113C4—62no—
1114C4—62no—
1115C4—122no—
1116C4—121no—
1117C4—122no—
1118C4#563312yes—
1119C4C2×#100711yescharacteristic
1120C4C2×D3×#4111yescharacteristic
1121C3#6134811yescharacteristic, complemented, Sylow
1122C2—22no—
1123C2—81no—
1124C2—122no—
1125C2—241no—
1126C2C2×#563311yescharacteristic
1127C2#8720411yescharacteristic
1128C2D3×#57811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3083C2
socleC22×C3C23×D4
prime radical#78861C2
hypercenter#3083D3
hypocenterC3#61348
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #3083

Complements

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

NH ≅ G/Ntype
1. #86586C2semidirect
2. #85892C2semidirect
3. C3×#3083C2semidirect
4. #83471C2semidirect
5. #82557C2semidirect
6. #81267C2semidirect
7. #81219C2semidirect
8. #81155C2semidirect
9. #81150C2semidirect
10. #81138C2semidirect
11. #81100C2semidirect
12. #80993C2semidirect
13. #80956C2semidirect
14. #79243C2semidirect
15. #79200C2semidirect
16. C2×#4875C2semidirect
17. #79136C2semidirect
18. #79089C2semidirect
19. #79078C2semidirect
20. #78912C2semidirect
21. #78878C2semidirect
23. #78828C2semidirect
150. #3083D3semidirect
1121. C3#61348semidirect

Maximal subgroups

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

subgroupindex
#865862
#858922
C3×#30832
#834712
#825572
#812672
#812192
#811552
#811502
#811382
#811002
#809932
#809562
#792432
#792002
C2×#48752
#791362
#790892
#790782
#789122
#788782
#788612
#788282
#613483