Finite Group Databasebeta

← #11675366

Subgroups — #11675366

Order 768.

1732 conjugacy classes of subgroups.

The subgroup lattice has 1102 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86587C211yesmaximal, characteristic, complemented
2#85876C211yesmaximal, characteristic, complemented
3C3×#3082C211yesmaximal, characteristic, complemented
4#83471C211yesmaximal, characteristic, complemented
5#82547C211yesmaximal, characteristic, complemented
6#81267C212yesmaximal, complemented
7#81265C212yesmaximal, complemented
8#81220C212yesmaximal, complemented
9#81219C212yesmaximal, complemented
10#81135C212yesmaximal, complemented
11#81101C212yesmaximal, complemented
12#81042C212yesmaximal, complemented
13#81005C212yesmaximal, complemented
14#79241C211yesmaximal, characteristic, complemented
15#79202C211yesmaximal, characteristic, complemented
16#79198C211yesmaximal, characteristic, complemented
17#79166C211yesmaximal, characteristic
18#79089C211yesmaximal, characteristic
19#79077C211yesmaximal, characteristic, complemented
20#78974C211yesmaximal, characteristic, complemented
21#78952C211yesmaximal, characteristic, complemented
22#78815C211yesmaximal, characteristic
23C2×#4797C211yesmaximal, characteristic, complemented
24#61338—31nomaximal, Sylow
25C3×#544C2211yescharacteristic
26C3×#519C2211yescharacteristic
27#5816C2211yescharacteristic
28C2×#944C2211yescharacteristic
29C2×#942C2211yescharacteristic
30C2×#909C2211yescharacteristic
31C2×#904C2211yescharacteristic
32#5730C2212yes—
33#5729—21no—
34#5728—21no—
35#5721C2212yes—
36#5690C2212yes—
37#5689—21no—
38D3×#125—21no—
39#5685C2212yes—
40#5636—22no—
41#5635—22no—
42#5583—21no—
43#5583—21no—
44#5578—21no—
45#5578—21no—
46#5568C2212yes—
47#5568C2212yes—
48#5567C2212yes—
49#5567C2212yes—
50#5531—22no—
51#5531—22no—
52#5526C2211yescharacteristic
53#5523C2211yescharacteristic
54#5522C2211yescharacteristic
55#5522C2211yescharacteristic
56#5519C2211yescharacteristic
57#5517C2211yescharacteristic
58#5516C2211yescharacteristic
59#5504C2211yescharacteristic
60C2×#890C2211yescharacteristic
61C3×#479C2212yes—
62C3×#479C2212yes—
63C3×#477C2212yes—
64C3×#475C2212yes—
65C3×#428C2211yescharacteristic
66C3×#427C2211yescharacteristic
67C3×#424C2211yescharacteristic
68C3×#419C2211yescharacteristic
69C2×C3×#103C2211yescharacteristic
70C2×#835C2211yescharacteristic
71#5133C2211yescharacteristic
72#5122C2211yescharacteristic
73#5118C2211yescharacteristic
74C2×#816C2211yescharacteristic
75#5102C2211yescharacteristic
76C2×#815C2211yescharacteristic
77#5093C2212yes—
78#5089C2212yes—
79#5069C2212yes—
80#5068C2212yes—
81#5030C2212yes—
82C4×#216C2212yes—
83#5026C2212yes—
84C4×#215C2212yes—
85#5004C2211yescharacteristic
86#5002C2211yescharacteristic
87#5002C2211yescharacteristic
88#4997C2211yescharacteristic
89#4995C2211yescharacteristic
90C2×#810C2211yescharacteristic
91#4966C2211yescharacteristic
92#4891C2212yes—
93#4889C2211yescharacteristic
94#4889C2211yescharacteristic
95#4889C2211yescharacteristic
96#4889C2211yescharacteristic
97#4889C2212yes—
98#4877C2212yes—
99#4877C2212yes—
100#4875C2212yes—
101#4873C2212yes—
102#4871C2212yes—
103#4869C2211yescharacteristic
104#4869C2211yescharacteristic
105#4857C2212yes—
106#4857C2212yes—
107#4854C2212yes—
108#4853C2211yescharacteristic
109#4853C2211yescharacteristic
110#4853C2212yes—
111#4852C2212yes—
112#4849C2212yes—
113#4845C2212yes—
114#4844C2212yes—
115#4841C2212yes—
116#4831C2212yes—
117#4831C2212yes—
118#4828C2212yes—
119#4828C2212yes—
120#4819C2212yes—
121#4818C2212yes—
122#4818C2212yes—
123#4818C2212yes—
124#4800C2212yes—
125#4798C2212yes—
126#4797C2212yes—
127#4797C2212yes—
128#4797C2212yes—
129#4797C2212yes—
130#4797C2212yes—
131#4795C2212yes—
132#4795C2212yes—
133#4795C2212yes—
134#4794C2212yes—
135#4792C2212yes—
136#3509—31no—
137#3504—31no—
138#3377—32no—
139#3377—32no—
140#3376—32no—
141#3376—32no—
142#3374—32no—
143#3374—32no—
144#3372—32no—
145#3372—32no—
146#3137—31no—
147#3137—31no—
148C2×#491—31no—
149#3082—31no—
150#3082D311yescharacteristic, complemented
151#3080—31no—
152#3046—31no—
153#3046—31no—
154#3039—31no—
155#2961—31no—
156#2947—31no—
157#2947—31no—
158#2943—31no—
159C22×C3×Q8C2311yescharacteristic
160C2×#235C2311yescharacteristic
161C2×#235C2311yescharacteristic
162C22×Dic6C2311yescharacteristic
163C2×C3×M16C2311yescharacteristic
164C22×C3×C8C2311yescharacteristic
165C3×C4⋊Q8—21no—
166C3×C4⋊Q8C2312yes—
167C3×#125—21no—
168C3×#125C2312yes—
169C3×C22⋊Q8—22no—
170C3×C4×Q8—21no—
171C3×C4×Q8—21no—
172C3×C4×Q8C2312yes—
173C3×C4×Q8C2312yes—
174C3×#117—22no—
175C3×#117C2311yescharacteristic
176C3×#117C2311yescharacteristic
177C3×#117C2311yescharacteristic
178C2×C3×C4⋊C4C2311yescharacteristic
179#947C2312yes—
180#946—21no—
181#946—21no—
182#946—22no—
183#946—22no—
184Q8×Dic3—22no—
185#944—22no—
186#944—21no—
187#944—21no—
188#944C2312yes—
189#944C2312yes—
190#944C2312yes—
191C2×#216C2312yes—
192#942—24no—
193C2×#215C2312yes—
194#929—22no—
195C4×#67—22no—
196#926C2311yescharacteristic
197C2×C4⋊Dic3—21no—
198C2×C4⋊Dic3C2311yescharacteristic
199C2×Dic3⋊C4—21no—
200C2×Dic3⋊C4—21no—
201C2×Dic3⋊C4—21no—
202C2×C4×Dic3C2311yescharacteristic
203C2×#208C2311yescharacteristic
204C22×C3⋊C8C2311yescharacteristic
205#909—24no—
206C2×Dic12C2312yes—
207C2×Dic12C2311yescharacteristic
208#904—24no—
209C2×D24C2311yescharacteristic
210C2×#204C2311yescharacteristic
211C2×#204C2311yescharacteristic
212C2×#204C2312yes—
213#898—22no—
214#898—22no—
215#897—22no—
216#897—21no—
217#897—21no—
218#897—22no—
219#896—22no—
220#896—22no—
221#896—22no—
222#896—22no—
223#893C2311yescharacteristic
224#893C2311yescharacteristic
225#893C2311yescharacteristic
226#893C2311yescharacteristic
227#893C2312yes—
228#892—21no—
229#892—21no—
230D3×C4⋊C4—21no—
231D3×C4⋊C4—22no—
232D3×C4⋊C4—21no—
233D3×C4⋊C4—22no—
234#890—21no—
235#890—21no—
236#890D411yescharacteristic
237#890D411yescharacteristic
238#890C2312yes—
239#890C2312yes—
240#890C2312yes—
241#889—22no—
242#889—22no—
243#889—22no—
244#889—22no—
245#889—22no—
246#889—22no—
247#889—22no—
248#889—22no—
249#888—22no—
250#888D411yescharacteristic
251#888D411yescharacteristic
252#888C2312yes—
253#887—22no—
254#887C2312yes—
255#887C2312yes—
256#887C2312yes—
257#887C2311yescharacteristic
258#887C2311yescharacteristic
259#887C2311yescharacteristic
260#887C2311yescharacteristic
261#886—22no—
262#67⋊C4—21no—
263#67⋊C4—21no—
264#67⋊C4—21no—
265#67⋊C4—21no—
266#67⋊C4—22no—
267#878—22no—
268#878D412yes—
269#878D412yes—
270#877—22no—
271#876—22no—
272#876—22no—
273#875C2312yes—
274C4×D12C2312yes—
275#872—22no—
276#872—22no—
277#872—21no—
278#872—21no—
279C42×D3—21no—
280C42×D3—21no—
281#870—21no—
282#870—22no—
283#870—22no—
284#869—21no—
285#869C2312yes—
286C4×Dic6—22no—
287C4×Dic6—22no—
288C4×Dic6—21no—
289C4×Dic6—21no—
290C4×Dic6C2312yes—
291C4×Dic6C2312yes—
292C4×Dic6C2312yes—
293C3×#107C2312yes—
294C3×#107C2311yescharacteristic
295C3×#107C2311yescharacteristic
296C3×#106C2311yescharacteristic
297C3×#106C2311yescharacteristic
298C3×#106C2312yes—
299C3×C4⋊C8C2312yes—
300C3×C4⋊C8C2312yes—
301C3×#103C2312yes—
302C3×#103C2312yes—
303C3×#103C2312yes—
304C3×#103C2312yes—
305#835C2312yes—
306#835C2312yes—
307#821C2312yes—
308#816C2312yes—
309#816C2312yes—
310#816C2312yes—
311#815C2312yes—
312#815C2311yescharacteristic
313#815C2311yescharacteristic
314#815C2311yescharacteristic
315#815C2311yescharacteristic
316Dic3⋊C8C2312yes—
317Dic3⋊C8C2312yes—
318Dic3⋊C8C2312yes—
319Dic3⋊C8C2312yes—
320C8×Dic3C2312yes—
321#810C2311yescharacteristic
322#810C2312yes—
323#810C2312yes—
324#810C2312yes—
325#810C2312yes—
326#810C2312yes—
327#810C2311yescharacteristic
328#810C2311yescharacteristic
329#810C2311yescharacteristic
330#809C2311yescharacteristic
331#809C2311yescharacteristic
332#809C2311yescharacteristic
333#809C2311yescharacteristic
334#809C2312yes—
335#808C2312yes—
336#807C2312yes—
337#803C2312yes—
338C4×C3⋊C8C2312yes—
339C2×#137—31no—
340C2×#137—31no—
341C2×#135—31no—
342#557—32no—
343#557—32no—
344#557—32no—
345#557—32no—
346#556—32no—
347#556—32no—
348#554—32no—
349#554—32no—
350#554—62no—
351#554—62no—
352#552—62no—
353#552—62no—
354#544—31no—
355#544—61no—
356#544—61no—
357#544C2×D311yescharacteristic
358#541—61no—
359#541—61no—
360#536—31no—
361#536—31no—
362#533—31no—
363#533—61no—
364#533—61no—
365#533—61no—
366C2×C4⋊Q8—31no—
367C2×#125—31no—
368C2×#125—61no—
369#520—31no—
370#520—31no—
371#519—31no—
372#519C2×D311yescharacteristic
373C4×#41—31no—
374C4×#41—31no—
375#491—32no—
376#491—32no—
377#491—32no—
378#491—32no—
379#491—32no—
380#491—32no—
381#489—32no—
382#489—32no—
383#488—32no—
384#488—32no—
385#487—32no—
386#487—32no—
387#479—32no—
388#479—32no—
389#479—32no—
390#479—32no—
391#479C2×D312yes—
392#479C2×D312yes—
393#478—32no—
394#478—32no—
395#477—32no—
396#477C2×D312yes—
397#475—32no—
398#475C2×D312yes—
399#464—32no—
400#464—32no—
401#463—32no—
402#463—32no—
403#462—32no—
404#462—32no—
405#462—32no—
406#462—32no—
407#461—32no—
408#461—32no—
409#461—32no—
410#461—32no—
411#446—32no—
412#446—32no—
413#446—32no—
414#446—32no—
415#442—31no—
416#442—31no—
417#441—32no—
418#441—31no—
419#441—31no—
420#441—32no—
421#440—32no—
422#440—31no—
423#440—31no—
424#440—32no—
425#440—31no—
426#440—31no—
427C4×Q16—32no—
428C4×Q16—32no—
429C4×SD16—32no—
430C4×SD16—32no—
431#428—31no—
432#428C2×D311yescharacteristic
433#427C2×D311yescharacteristic
434#424—31no—
435#424C2×D311yescharacteristic
436#423—31no—
437#419—31no—
438#419C2×D311yescharacteristic
439#417—31no—
440#417—31no—
441#416—31no—
442#416—31no—
443C2×#103—31no—
444C2×#103—31no—
445C2×#103—31no—
446C2×#103C2×D311yescharacteristic
447#405—31no—
448#405—31no—
449C2×#97—31no—
450C2×C3×Q8—21no—
451C2×C3×Q8—22no—
452C2×C3×Q8—22no—
453C2×C3×Q8—22no—
454C2×C3×Q8C2412yes—
455C22×C3×C4—21no—
456C22×C3×C4—21no—
457C22×C3×C4C2411yescharacteristic
458C2×#67—21no—
459C2×#67—21no—
460C22×Dic3—21no—
461C22×Dic3—21no—
462C22×Dic3C2×D411yescharacteristic
463C22×Dic3C2×D411yescharacteristic
464#235—22no—
465#235—22no—
466#235—22no—
467#235#4114yes—
468C2×D12C2411yescharacteristic
469C2×D12C2411yescharacteristic
470C2×C4×D3—21no—
471C2×C4×D3—21no—
472C2×C4×D3—21no—
473C2×C4×D3—21no—
474C2×C4×D3—22no—
475C2×C4×D3—21no—
476C2×C4×D3—21no—
477C2×C4×D3—22no—
478C2×Dic6—22no—
479C2×Dic6—22no—
480C2×Dic6—21no—
481C2×Dic6—22no—
482C2×Dic6C2×D412yes—
483C2×Dic6C2×D412yes—
484C2×Dic6C2411yescharacteristic
485C2×Dic6C2412yes—
486C2×Dic6C2411yescharacteristic
487C3×M16—22no—
488C2×C3×C8—22no—
489C2×C3×C8C2412yes—
490C2×C3×C8C2411yescharacteristic
491C2×C3×C8C2411yescharacteristic
492C3×C4⋊C4—22no—
493C3×C4⋊C4—22no—
494C3×C4⋊C4—22no—
495C3×C4⋊C4—22no—
496C3×C4⋊C4—22no—
497C3×C4⋊C4—21no—
498C3×C4⋊C4C2×D411yescharacteristic
499C3×C4⋊C4C2×D411yescharacteristic
500C3×C4⋊C4C2411yescharacteristic
501C3×C4⋊C4C2411yescharacteristic
502C3×C4⋊C4C2411yescharacteristic
503C3×C4⋊C4C2412yes—
504C3×C4⋊C4C2411yescharacteristic
505C3×C22⋊C4—21no—
506C3×C22⋊C4—21no—
507C3×C22⋊C4C2×D412yes—
508C3×C42—21no—
509C3×C42—22no—
510C3×C42—22no—
511C3×C42—21no—
512C3×C42C2412yes—
513#217C2×D412yes—
514#216—24no—
515#215—24no—
516(C2×D3)⋊C4—22no—
517(C2×D3)⋊C4—22no—
518(C2×D3)⋊C4—22no—
519(C2×D3)⋊C4—21no—
520(C2×D3)⋊C4—21no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4—22no—
523(C2×D3)⋊C4—21no—
524(C2×D3)⋊C4—21no—
525(C2×D3)⋊C4—22no—
526C4⋊Dic3—22no—
527C4⋊Dic3—22no—
528C4⋊Dic3—21no—
529C4⋊Dic3—22no—
530C4⋊Dic3—22no—
531C4⋊Dic3—22no—
532C4⋊Dic3C2×D411yescharacteristic
533C4⋊Dic3C2×D411yescharacteristic
534C4⋊Dic3C2×D412yes—
535C4⋊Dic3C2×D412yes—
536C4⋊Dic3C2412yes—
537Dic3⋊C4—22no—
538Dic3⋊C4—22no—
539Dic3⋊C4—22no—
540Dic3⋊C4—22no—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—21no—
545Dic3⋊C4—21no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—21no—
551Dic3⋊C4—21no—
552Dic3⋊C4—22no—
553Dic3⋊C4—22no—
554Dic3⋊C4—22no—
555Dic3⋊C4C2×D412yes—
556Dic3⋊C4C2×D412yes—
557Dic3⋊C4C2×D412yes—
558Dic3⋊C4C2×D412yes—
559C4×Dic3—22no—
560C4×Dic3—21no—
561C4×Dic3—21no—
562C4×Dic3—22no—
563C4×Dic3—22no—
564C4×Dic3—21no—
565C4×Dic3—21no—
566C4×Dic3—22no—
567C4×Dic3C2×D411yescharacteristic
568C4×Dic3C2×D411yescharacteristic
569C4×Dic3C2412yes—
570C4×Dic3C2411yescharacteristic
571C4×Dic3C2411yescharacteristic
572#208—22no—
573C2×C3⋊C8—22no—
574C2×C3⋊C8C2411yescharacteristic
575C2×C3⋊C8C2412yes—
576C2×C3⋊C8C2411yescharacteristic
577Dic12—22no—
578Dic12—24no—
579D24—22no—
580#204—22no—
581#204—24no—
582#204—22no—
583C2×#41—31no—
584C2×#41—31no—
585C22×Q8—31no—
586C22×Q8C22×D311yescharacteristic
587#137—64no—
588#137—64no—
589#135—64no—
590C2×Q16—32no—
591C2×Q16—31no—
592C2×Q16—32no—
593C2×SD16—32no—
594C2×SD16—31no—
595C2×SD16—31no—
596C2×SD16—32no—
597C2×D8—31no—
598C2×M16—31no—
599C2×M16C22×D311yescharacteristic
600C22×C8—31no—
601C22×C8C22×D311yescharacteristic
602C4⋊Q8—21no—
603C4⋊Q8—31no—
604C4⋊Q8—31no—
605C4⋊Q8—32no—
606C4⋊Q8—32no—
607C4⋊Q8—32no—
608C4⋊Q8—32no—
609C4⋊Q8—32no—
610C4⋊Q8—61no—
611C4⋊Q8—61no—
612C4⋊Q8—61no—
613C4⋊Q8—62no—
614C4⋊Q8—62no—
615C4⋊Q8C22×D312yes—
616#126—62no—
617#126—62no—
618#126—62no—
619#126—62no—
620#125—21no—
621#125—31no—
622#125—31no—
623#125—32no—
624#125—32no—
625#125—32no—
626#125—61no—
627#125—62no—
628#125—62no—
629#125—61no—
630#125—61no—
631#125—62no—
632#125—62no—
633#125—62no—
634#125—62no—
635#125—62no—
636#125—62no—
637#125—62no—
638#125—62no—
639#125C22×D312yes—
640#124—32no—
641#124—32no—
642#123—62no—
643#123—62no—
644C22⋊Q8—22no—
645C22⋊Q8—32no—
646C22⋊Q8—32no—
647C22⋊Q8—62no—
648C22⋊Q8—62no—
649C22⋊Q8—62no—
650C22⋊Q8—62no—
651C22⋊Q8—62no—
652C22⋊Q8—62no—
653C22⋊Q8—62no—
654C22⋊Q8—61no—
655C22⋊Q8—61no—
656C22⋊Q8—62no—
657C22⋊Q8—62no—
658C22⋊Q8—61no—
659C22⋊Q8—61no—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8—32no—
663C4×Q8—32no—
664C4×Q8—31no—
665C4×Q8—31no—
666C4×Q8—31no—
667C4×Q8—31no—
668C4×Q8—32no—
669C4×Q8—32no—
670C4×Q8—32no—
671C4×Q8—32no—
672C4×Q8—61no—
673C4×Q8—61no—
674C4×Q8—62no—
675C4×Q8—62no—
676C4×Q8—62no—
677C4×Q8—62no—
678C4×Q8C22×D312yes—
679C4×Q8C22×D312yes—
680C4×D4—31no—
681C4×D4—31no—
682C4×D4—31no—
683C4×D4—31no—
684C4×D4—32no—
685C4×D4—32no—
686C4×D4—61no—
687C4×D4—61no—
688C4×D4—61no—
689C4×D4—61no—
690C4×D4—62no—
691C4×D4—62no—
692#117—22no—
693#117—31no—
694#117—61no—
695#117—61no—
696#117—62no—
697#117—62no—
698#117—62no—
699#117—61no—
700#117—61no—
701#117C22×D311yescharacteristic
702#117C22×D311yescharacteristic
703#117C22×D311yescharacteristic
704C2×C4⋊C4—31no—
705C2×C4⋊C4—61no—
706C2×C4⋊C4—62no—
707C2×C4⋊C4—62no—
708C2×C4⋊C4—61no—
709C2×C4⋊C4—61no—
710C2×C4⋊C4—61no—
711C2×C4⋊C4—61no—
712C2×C4⋊C4—61no—
713C2×C4⋊C4C22×D311yescharacteristic
714C2×C42—31no—
715C2×C42—61no—
716C2×C42—61no—
717#107—32no—
718#107C22×D311yescharacteristic
719#107C22×D311yescharacteristic
720#107C22×D312yes—
721#106—32no—
722#106C22×D311yescharacteristic
723#106C22×D311yescharacteristic
724#106C22×D312yes—
725C4⋊C8—32no—
726C4⋊C8—32no—
727C4⋊C8—32no—
728C4⋊C8—32no—
729C4⋊C8C22×D312yes—
730C4⋊C8C22×D312yes—
731#103—32no—
732#103—32no—
733#103—32no—
734#103—32no—
735#103—32no—
736#103—32no—
737#103—32no—
738#103—31no—
739#103—31no—
740#103—31no—
741#103—31no—
742#103—32no—
743#103—32no—
744#103—32no—
745#103C22×D312yes—
746#103C22×D312yes—
747#103C22×D312yes—
748#103C22×D312yes—
749#102—32no—
750#102—31no—
751#102—31no—
752#102—31no—
753#102—31no—
754#102—32no—
755#97—31no—
756#97—31no—
757#97—31no—
758#97—31no—
759#97—32no—
760#97—32no—
761C4×C8—32no—
762C4×C8—32no—
763C23×C3C22×D411yescharacteristic
764C22×D3—21no—
765C22×D3—21no—
766C3×Q8—22no—
767C3×Q8—22no—
768C3×Q8—42no—
769C3×Q8—82no—
770C2×C3×C4—21no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—22no—
774C2×C3×C4—21no—
775C2×C3×C4—22no—
776C2×C3×C4—42no—
777C2×C3×C4—81no—
778C2×C3×C4C22×D412yes—
779C2×C3×C4C22×D412yes—
780C2×C3×C4C22×D411yescharacteristic
781C2×C3×C4C2×#4112yes—
782C2×C3×C42−1+412yes—
783C2×C3×C4C2511yescharacteristic
784#67—24no—
785#67—42no—
786C2×Dic3—21no—
787C2×Dic3—21no—
788C2×Dic3—22no—
789C2×Dic3—22no—
790C2×Dic3—41no—
791C2×Dic3—41no—
792C2×Dic3—42no—
793C2×Dic3—81no—
794C2×Dic3C22×D412yes—
795C2×Dic3C22×D411yescharacteristic
796C2×Dic3C22×D411yescharacteristic
797C2×Dic3C22×D411yescharacteristic
798C2×Dic3C22×D411yescharacteristic
799C2×Dic3C22×D412yes—
800D12—21no—
801D12—21no—
802D12—21no—
803D12C2×#4112yes—
804C4×D3—24no—
805C4×D3—42no—
806C4×D3—42no—
807C4×D3—42no—
808C4×D3—82no—
809C4×D3—81no—
810C4×D3—81no—
811C4×D3—82no—
812Dic6—21no—
813Dic6—22no—
814Dic6—21no—
815Dic6—22no—
816Dic6—21no—
817Dic6—42no—
818Dic6—42no—
819Dic6—42no—
820Dic6—82no—
821Dic6C2×#4112yes—
822C3×C8—21no—
823C3×C8—22no—
824C3×C8—21no—
825C3⋊C8—22no—
826C3⋊C8—21no—
827C3⋊C8—21no—
828#41—34no—
829#41—62no—
830#41—62no—
831#41—62no—
832C2×Q8—21no—
833C2×Q8—22no—
834C2×Q8—22no—
835C2×Q8—22no—
836C2×Q8—32no—
837C2×Q8—32no—
838C2×Q8—31no—
839C2×Q8—32no—
840C2×Q8—31no—
841C2×Q8—62no—
842C2×Q8—61no—
843C2×Q8—62no—
844C2×Q8—62no—
845C2×Q8C23×D312yes—
846C2×D4—31no—
847C2×D4—31no—
848C2×D4—61no—
849C2×D4—61no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—31no—
853C22×C4—31no—
854C22×C4—61no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—61no—
858C22×C4—62no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—62no—
864C22×C4C23×D311yescharacteristic
865Q16—62no—
866Q16—64no—
867Q16—64no—
868SD16—62no—
869SD16—64no—
870SD16—62no—
871SD16—64no—
872D8—62no—
873M16—22no—
874M16—62no—
875C2×C8—22no—
876C2×C8—31no—
877C2×C8—31no—
878C2×C8—32no—
879C2×C8—62no—
880C2×C8C23×D312yes—
881C2×C8C23×D311yescharacteristic
882C2×C8C23×D311yescharacteristic
883C4⋊C4—21no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—31no—
890C4⋊C4—32no—
891C4⋊C4—32no—
892C4⋊C4—31no—
893C4⋊C4—32no—
894C4⋊C4—32no—
895C4⋊C4—32no—
896C4⋊C4—32no—
897C4⋊C4—32no—
898C4⋊C4—62no—
899C4⋊C4—62no—
900C4⋊C4—62no—
901C4⋊C4—62no—
902C4⋊C4—62no—
903C4⋊C4—62no—
904C4⋊C4—62no—
905C4⋊C4—62no—
906C4⋊C4—62no—
907C4⋊C4—62no—
908C4⋊C4—62no—
909C4⋊C4—61no—
910C4⋊C4—61no—
911C4⋊C4—61no—
912C4⋊C4—61no—
913C4⋊C4—62no—
914C4⋊C4—62no—
915C4⋊C4—62no—
916C4⋊C4—62no—
917C4⋊C4—62no—
918C4⋊C4—61no—
919C4⋊C4—62no—
920C4⋊C4—62no—
921C4⋊C4—62no—
922C4⋊C4D3×D411yescharacteristic
923C4⋊C4D3×D411yescharacteristic
924C4⋊C4C23×D312yes—
925C4⋊C4C23×D311yescharacteristic
926C4⋊C4C23×D311yescharacteristic
927C4⋊C4C23×D311yescharacteristic
928C4⋊C4C23×D311yescharacteristic
929C22⋊C4—21no—
930C22⋊C4—21no—
931C22⋊C4—32no—
932C22⋊C4—61no—
933C22⋊C4—61no—
934C22⋊C4—62no—
935C22⋊C4—61no—
936C22⋊C4—61no—
937C22⋊C4—62no—
938C22⋊C4—62no—
939C22⋊C4—62no—
940C22⋊C4—62no—
941C22⋊C4—62no—
942C22⋊C4D3×D412yes—
943C42—21no—
944C42—21no—
945C42—22no—
946C42—22no—
947C42—31no—
948C42—31no—
949C42—32no—
950C42—31no—
951C42—31no—
952C42—61no—
953C42—61no—
954C42—61no—
955C42—61no—
956C42—62no—
957C42—62no—
958C42—62no—
959C42—62no—
960C42C23×D312yes—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3#54812yes—
964C22×C3C23×D411yescharacteristic
965C2×D3—22no—
966C2×D3—41no—
967C2×D3—41no—
968C2×D3—41no—
969C2×D3—41no—
970C2×D3—41no—
971C3×C4—22no—
972C3×C4—22no—
973C3×C4—41no—
974C3×C4—41no—
975C3×C4—41no—
976C3×C4—42no—
977C3×C4—41no—
978C3×C4—42no—
979C3×C4#54812yes—
980C3×C4C22×#4111yescharacteristic
981C3×C4C2×2−1+411yescharacteristic
982Dic3—21no—
983Dic3—21no—
984Dic3—22no—
985Dic3—22no—
986Dic3—21no—
987Dic3—21no—
988Dic3—22no—
989Dic3—42no—
990Dic3—42no—
991Dic3—41no—
992C23—61no—
993C23—61no—
994C23C2×D3×D411yescharacteristic
995Q8—22no—
996Q8—22no—
997Q8—32no—
998Q8—42no—
999Q8—61no—
1000Q8—62no—
1001Q8—61no—
1002Q8—62no—
1003Q8—61no—
1004Q8—82no—
1005Q8—122no—
1006Q8—122no—
1007Q8—122no—
1008Q8—242no—
1009D4—32no—
1010D4—64no—
1011D4—61no—
1012D4—61no—
1013D4—61no—
1014D4—122no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—31no—
1022C2×C4—31no—
1023C2×C4—31no—
1024C2×C4—31no—
1025C2×C4—32no—
1026C2×C4—32no—
1027C2×C4—42no—
1028C2×C4—61no—
1029C2×C4—64no—
1030C2×C4—62no—
1031C2×C4—61no—
1032C2×C4—62no—
1033C2×C4—81no—
1034C2×C4—122no—
1035C2×C4—122no—
1036C2×C4—121no—
1037C2×C4—121no—
1038C2×C4—122no—
1039C2×C4—122no—
1040C2×C4—242no—
1041C2×C4—242no—
1042C2×C4—241no—
1043C2×C4—241no—
1044C2×C4—241no—
1045C2×C4C2×D3×D412yes—
1046C2×C4C2×D3×D412yes—
1047C2×C4C2×D3×D411yescharacteristic
1048C2×C4#100712yes—
1049C2×C4D3×#4112yes—
1050C2×C4C24×D311yescharacteristic
1051C8—21no—
1052C8—21no—
1053C8—22no—
1054C8—61no—
1055C8—61no—
1056C8—62no—
1057C2×C3—22no—
1058C2×C3C2×#54811yescharacteristic
1059C2×C3#358611yescharacteristic
1060C2×C3#358611yescharacteristic
1061D3—42no—
1062D3—81no—
1063C22—21no—
1064C22—21no—
1065C22—62no—
1066C22—121no—
1067C22—121no—
1068C22—121no—
1069C22—121no—
1070C22—121no—
1071C22#563312yes—
1072C22C22×D3×D411yescharacteristic
1073C4—22no—
1074C4—22no—
1075C4—42no—
1076C4—41no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—42no—
1081C4—61no—
1082C4—61no—
1083C4—62no—
1084C4—61no—
1085C4—61no—
1086C4—62no—
1087C4—62no—
1088C4—122no—
1089C4—121no—
1090C4—122no—
1091C4#563312yes—
1092C4C2×#100711yescharacteristic
1093C4C2×D3×#4111yescharacteristic
1094C3#6133811yescharacteristic, complemented, Sylow
1095C2—22no—
1096C2—122no—
1097C2—241no—
1098C2C2×#563311yescharacteristic
1099C2#8720811yescharacteristic
1100C2#8721111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3082C2
socleC22×C3C23×D4
prime radicalC2×#904C22
hypercenter#3082D3
hypocenterC3#61338
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #3082

Complements

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

NH ≅ G/Ntype
1. #86587C2semidirect
2. #85876C2semidirect
3. C3×#3082C2semidirect
4. #83471C2semidirect
5. #82547C2semidirect
6. #81267C2semidirect
7. #81265C2semidirect
8. #81220C2semidirect
9. #81219C2semidirect
10. #81135C2semidirect
11. #81101C2semidirect
12. #81042C2semidirect
13. #81005C2semidirect
14. #79241C2semidirect
15. #79202C2semidirect
16. #79198C2semidirect
19. #79077C2semidirect
20. #78974C2semidirect
21. #78952C2semidirect
23. C2×#4797C2semidirect
150. #3082D3semidirect
1094. C3#61338semidirect

Maximal subgroups

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

subgroupindex
#865872
#858762
C3×#30822
#834712
#825472
#812672
#812652
#812202
#812192
#811352
#811012
#810422
#810052
#792412
#792022
#791982
#791662
#790892
#790772
#789742
#789522
#788152
C2×#47972
#613383