Finite Group Databasebeta

← #11675358

Subgroups — #11675358

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#86343C211yesmaximal, characteristic, complemented
3C3×#3137C211yesmaximal, characteristic, complemented
4#83480C211yesmaximal, characteristic, complemented
5#83406C211yesmaximal, characteristic
6#81733C212yesmaximal, complemented
7#81732C212yesmaximal, complemented
8#81677C212yesmaximal, complemented
9#81676C212yesmaximal, complemented
10#81663C212yesmaximal, complemented
11#81661C212yesmaximal, complemented
12#81627C212yesmaximal, complemented
13#81623C212yesmaximal, complemented
14#78974C211yesmaximal, characteristic, complemented
15#78950C211yesmaximal, characteristic, complemented
16#78912C211yesmaximal, characteristic
17#78871C211yesmaximal, characteristic, complemented
18#78828C211yesmaximal, characteristic, complemented
19#78819C211yesmaximal, characteristic
20C2×#4797C211yesmaximal, characteristic, complemented
21#78774C211yesmaximal, characteristic, complemented
22#78571C211yesmaximal, characteristic, complemented
23#78543C211yesmaximal, characteristic, complemented
24#61338—31nomaximal, Sylow
25C3×#544C2211yescharacteristic
26C3×#536C2211yescharacteristic
27Dic3×#41C2211yescharacteristic
28#5825C2211yescharacteristic
29C2×#950C2211yescharacteristic
30#5812C2211yescharacteristic
31C2×#944C2211yescharacteristic
32C2×#942C2211yescharacteristic
33C2×#909C2211yescharacteristic
34#5730C2212yes—
35#5729—21no—
36#5728—21no—
37#5721C2212yes—
38#5721C2212yes—
39#5721C2212yes—
40#5690C2212yes—
41#5689—21no—
42D3×#125—21no—
43#5685C2212yes—
44#5671C2212yes—
45#5671C2212yes—
46#5650—22no—
47#5650—22no—
48#5636—22no—
49#5635—22no—
50#5625—21no—
51#5625—21no—
52#5622—21no—
53#5622—21no—
54#5523C2211yescharacteristic
55#5522C2211yescharacteristic
56#5519C2211yescharacteristic
57#5517C2211yescharacteristic
58#5516C2211yescharacteristic
59#5504C2211yescharacteristic
60C2×#890C2211yescharacteristic
61C3×#491C2212yes—
62C3×#489C2212yes—
63C3×#488C2212yes—
64C3×#487C2212yes—
65C3×#419C2211yescharacteristic
66C3×#417C2211yescharacteristic
67C3×#416C2211yescharacteristic
68C2×C3×#103C2211yescharacteristic
69C3×#405C2211yescharacteristic
70#5232C2211yescharacteristic
71C2×#835C2211yescharacteristic
72#5121C2211yescharacteristic
73#5119C2211yescharacteristic
74#5118C2211yescharacteristic
75#5113C2211yescharacteristic
76C2×#816C2211yescharacteristic
77#5101C2211yescharacteristic
78C2×#815C2211yescharacteristic
79#5094C2212yes—
80#5091C2212yes—
81#5090C2212yes—
82#5083C2212yes—
83#5063C2212yes—
84#5063C2212yes—
85#5057C2212yes—
86#5054C2212yes—
87#5004C2211yescharacteristic
88#4999C2211yescharacteristic
89#4998C2211yescharacteristic
90C2×#810C2211yescharacteristic
91#4964C2211yescharacteristic
92#4818C2212yes—
93#4818C2212yes—
94#4818C2212yes—
95#4817C2211yescharacteristic
96#4817C2212yes—
97#4817C2211yescharacteristic
98#4799C2212yes—
99#4799C2212yes—
100#4797C2212yes—
101#4797C2212yes—
102#4797C2212yes—
103#4797C2212yes—
104#4797C2212yes—
105#4796C2212yes—
106#4796C2212yes—
107#4795C2212yes—
108#4795C2212yes—
109#4795C2212yes—
110#4793C2212yes—
111#4792C2212yes—
112#4791C2212yes—
113#4790C2212yes—
114#4789C2211yescharacteristic
115#4789C2212yes—
116#4789C2211yescharacteristic
117#4788C2212yes—
118#4787C2212yes—
119#4785C2211yescharacteristic
120#4785C2211yescharacteristic
121#4768C2212yes—
122#4767C2212yes—
123#4766C2212yes—
124#4765C2212yes—
125#4763C2212yes—
126#4757C2211yescharacteristic
127#4757C2211yescharacteristic
128#4716C2212yes—
129#4710C2212yes—
130#4701C2212yes—
131#4701C2212yes—
132C4×Dic12C2212yes—
133C4×#204C2212yes—
134#4679C2212yes—
135#4679C2212yes—
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#3137D311yescharacteristic, complemented
148C2×#491—31no—
149#3082—31no—
150#3082—31no—
151#3080—31no—
152#3046—31no—
153#3046—31no—
154#3039—31no—
155#2961—31no—
156#2947—31no—
157#2947—31no—
158#2943—31no—
159C2×C3×#41C2311yescharacteristic
160C22×C3×Q8C2311yescharacteristic
161C2×#235C2311yescharacteristic
162C22×Dic6C2311yescharacteristic
163C2×C3×M16C2311yescharacteristic
164C22×C3×C8C2311yescharacteristic
165C3×C4⋊Q8—21no—
166C3×C4⋊Q8C2312yes—
167C3×C4⋊Q8C2312yes—
168C3×#125—21no—
169C3×#125C2312yes—
170C3×#124C2312yes—
171C3×#123—22no—
172C3×C22⋊Q8—21no—
173C3×C22⋊Q8—21no—
174C3×C22⋊Q8—22no—
175C3×#117C2311yescharacteristic
176C3×#117C2311yescharacteristic
177C2×C3×C4⋊C4C2311yescharacteristic
178#950—24no—
179#946—22no—
180#946—22no—
181Q8×Dic3—22no—
182Q8×Dic3—21no—
183Q8×Dic3—21no—
184Q8×Dic3C2312yes—
185Q8×Dic3C2312yes—
186Q8×Dic3C2311yescharacteristic
187Q8×Dic3C2311yescharacteristic
188#944—22no—
189#944—21no—
190#944—21no—
191#944C2312yes—
192#944C2312yes—
193#944C2312yes—
194C2×#216C2312yes—
195C2×#216C2311yescharacteristic
196#942—24no—
197C2×#215C2312yes—
198C2×#215C2311yescharacteristic
199#936C2312yes—
200#935—22no—
201D4×Dic3—21no—
202D4×Dic3—21no—
203D4×Dic3C2311yescharacteristic
204D4×Dic3C2311yescharacteristic
205C2×#214C2311yescharacteristic
206C2×#213C2311yescharacteristic
207C4×#67—22no—
208#926—22no—
209#926—21no—
210#926C2311yescharacteristic
211#926C2311yescharacteristic
212C2×C4⋊Dic3—21no—
213C2×C4⋊Dic3C2311yescharacteristic
214#924—21no—
215#924—21no—
216C2×Dic3⋊C4—21no—
217C2×Dic3⋊C4—21no—
218C2×Dic3⋊C4—21no—
219C2×C4×Dic3—21no—
220C2×C4×Dic3C2311yescharacteristic
221C2×#208C2311yescharacteristic
222C22×C3⋊C8C2311yescharacteristic
223#909—24no—
224C2×Dic12C2312yes—
225C2×#204C2312yes—
226#897—22no—
227#897—22no—
228#896—22no—
229#896—22no—
230#893C2311yescharacteristic
231#893C2312yes—
232#893C2311yescharacteristic
233#892—21no—
234#892—21no—
235D3×C4⋊C4—21no—
236D3×C4⋊C4—22no—
237D3×C4⋊C4—21no—
238D3×C4⋊C4—22no—
239#890—22no—
240#890—22no—
241#890—21no—
242#890—21no—
243#890D411yescharacteristic
244#890D411yescharacteristic
245#890C2312yes—
246#890C2312yes—
247#890C2312yes—
248#889—22no—
249#889—22no—
250#889—22no—
251#889—22no—
252#889—22no—
253#889—22no—
254#889—22no—
255#889—22no—
256#888—22no—
257#888D411yescharacteristic
258#888D411yescharacteristic
259#888C2312yes—
260#887—22no—
261#887—22no—
262#887—21no—
263#887—21no—
264#887—22no—
265#887C2311yescharacteristic
266#887C2312yes—
267#887C2311yescharacteristic
268#67⋊C4—21no—
269#67⋊C4—21no—
270#67⋊C4—22no—
271#879—22no—
272#879—22no—
273#879—22no—
274#879—22no—
275#878—22no—
276#878—22no—
277#878—22no—
278#878D412yes—
279#878D412yes—
280#877—22no—
281#877—22no—
282#877—22no—
283C4×D12C2312yes—
284#872—21no—
285C42×D3—21no—
286#870—21no—
287#869—21no—
288C4×Dic6C2312yes—
289C4×Dic6C2312yes—
290C4×Dic6C2312yes—
291C4×Dic6C2312yes—
292C4×Dic6C2312yes—
293C3×#103C2312yes—
294C3×#103C2312yes—
295C3×#103C2311yescharacteristic
296C3×#103C2311yescharacteristic
297C3×#103C2312yes—
298C3×#103C2312yes—
299C3×#103C2312yes—
300C3×#102C2311yescharacteristic
301C3×#102C2311yescharacteristic
302C3×#102C2312yes—
303C3×#97C2312yes—
304C3×C4×C8C2312yes—
305#835C2312yes—
306#835C2312yes—
307#835C2312yes—
308#832C2312yes—
309#821C2311yescharacteristic
310#821C2311yescharacteristic
311#818C2312yes—
312#817C2312yes—
313#816C2312yes—
314#816C2311yescharacteristic
315#816C2312yes—
316#816C2311yescharacteristic
317#815C2311yescharacteristic
318#815C2312yes—
319#815C2311yescharacteristic
320#815C2311yescharacteristic
321#815C2311yescharacteristic
322Dic3⋊C8C2312yes—
323Dic3⋊C8C2312yes—
324Dic3⋊C8C2312yes—
325Dic3⋊C8C2312yes—
326C8×Dic3C2312yes—
327#810C2312yes—
328#810C2312yes—
329#810C2312yes—
330#810C2312yes—
331#808C2312yes—
332#808C2311yescharacteristic
333#808C2311yescharacteristic
334#807C2312yes—
335#807C2311yescharacteristic
336#807C2311yescharacteristic
337C4⋊(C3⋊C8)C2312yes—
338C4⋊(C3⋊C8)C2312yes—
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#536C2×D311yescharacteristic
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#519—31no—
373C4×#41—31no—
374C4×#41—31no—
375#491—32no—
376#491—32no—
377#491—32no—
378#491—32no—
379#491—32no—
380#491C2×D312yes—
381#489—32no—
382#489C2×D312yes—
383#488—32no—
384#488C2×D312yes—
385#487—32no—
386#487C2×D312yes—
387#479—32no—
388#479—32no—
389#479—32no—
390#479—32no—
391#479—32no—
392#479—32no—
393#478—32no—
394#478—32no—
395#477—32no—
396#477—32no—
397#475—32no—
398#475—32no—
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—31no—
418#441—31no—
419#441—32no—
420#441—32no—
421#440—31no—
422#440—31no—
423#440—32no—
424#440—31no—
425#440—31no—
426#440—32no—
427C4×Q16—32no—
428C4×Q16—32no—
429C4×SD16—32no—
430C4×SD16—32no—
431#428—31no—
432#428—31no—
433#427—31no—
434#424—31no—
435#424—31no—
436#423—31no—
437#419—31no—
438#419C2×D311yescharacteristic
439#417—31no—
440#417C2×D311yescharacteristic
441#416—31no—
442#416C2×D311yescharacteristic
443C2×#103—31no—
444C2×#103—31no—
445C2×#103—31no—
446C2×#103C2×D311yescharacteristic
447#405—31no—
448#405C2×D311yescharacteristic
449C2×#97—31no—
450C3×#41—22no—
451C3×#41—22no—
452C2×C3×Q8—21no—
453C2×C3×Q8—22no—
454C2×C3×Q8—22no—
455C2×C3×Q8—22no—
456C2×C3×Q8C2412yes—
457C2×C3×Q8C2411yescharacteristic
458C2×C3×D4—21no—
459C2×C3×D4C2411yescharacteristic
460C22×C3×C4—21no—
461C22×C3×C4—21no—
462C22×C3×C4—21no—
463C22×C3×C4C2411yescharacteristic
464C2×#67—21no—
465C22×Dic3—21no—
466C22×Dic3—21no—
467C22×Dic3—21no—
468C22×Dic3—21no—
469C22×Dic3C2×D411yescharacteristic
470C22×Dic3C2×D411yescharacteristic
471#235—22no—
472#235#4114yes—
473C2×D12C2411yescharacteristic
474C2×C4×D3—21no—
475C2×C4×D3—22no—
476C2×C4×D3—21no—
477C2×C4×D3—21no—
478C2×C4×D3—22no—
479C2×Dic6—22no—
480C2×Dic6—22no—
481C2×Dic6—21no—
482C2×Dic6—22no—
483C2×Dic6C2×D412yes—
484C2×Dic6C2×D412yes—
485C2×Dic6C2412yes—
486C2×Dic6C2411yescharacteristic
487C3×M16—22no—
488C2×C3×C8—22no—
489C2×C3×C8C2411yescharacteristic
490C2×C3×C8C2412yes—
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⋊C4C2412yes—
502C3×C4⋊C4C2411yescharacteristic
503C3×C22⋊C4—21no—
504C3×C22⋊C4—22no—
505C3×C22⋊C4—22no—
506C3×C22⋊C4C2×D412yes—
507C3×C42—21no—
508C3×C42C2412yes—
509#217—21no—
510#217—22no—
511#217—22no—
512#217—21no—
513#217—21no—
514#217C2×D412yes—
515#216—24no—
516#216—22no—
517#215—24no—
518#215—22no—
519#214—22no—
520#213—22no—
521(C2×D3)⋊C4—22no—
522(C2×D3)⋊C4—21no—
523(C2×D3)⋊C4—21no—
524(C2×D3)⋊C4—22no—
525C4⋊Dic3—21no—
526C4⋊Dic3—22no—
527C4⋊Dic3—22no—
528C4⋊Dic3—22no—
529C4⋊Dic3—22no—
530C4⋊Dic3—21no—
531C4⋊Dic3—21no—
532C4⋊Dic3—22no—
533C4⋊Dic3C2×D412yes—
534C4⋊Dic3C2×D412yes—
535C4⋊Dic3C2×D411yescharacteristic
536C4⋊Dic3C2×D411yescharacteristic
537C4⋊Dic3C2411yescharacteristic
538C4⋊Dic3C2411yescharacteristic
539C4⋊Dic3C2412yes—
540Dic3⋊C4—22no—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—21no—
546Dic3⋊C4—21no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—22no—
551Dic3⋊C4—22no—
552Dic3⋊C4—22no—
553Dic3⋊C4—22no—
554Dic3⋊C4—22no—
555Dic3⋊C4—22no—
556Dic3⋊C4C2×D412yes—
557Dic3⋊C4C2×D412yes—
558Dic3⋊C4C2×D412yes—
559Dic3⋊C4C2×D412yes—
560C4×Dic3—22no—
561C4×Dic3—22no—
562C4×Dic3—22no—
563C4×Dic3—21no—
564C4×Dic3—21no—
565C4×Dic3—21no—
566C4×Dic3—22no—
567C4×Dic3—22no—
568C4×Dic3—21no—
569C4×Dic3—21no—
570C4×Dic3—22no—
571C4×Dic3C2×D411yescharacteristic
572C4×Dic3C2×D411yescharacteristic
573C4×Dic3C2412yes—
574C4×Dic3C2411yescharacteristic
575C4×Dic3C2411yescharacteristic
576#208—22no—
577C2×C3⋊C8—22no—
578C2×C3⋊C8C2411yescharacteristic
579C2×C3⋊C8C2412yes—
580C2×C3⋊C8C2411yescharacteristic
581Dic12—24no—
582#204—24no—
583C2×#41—31no—
584C2×#41C22×D311yescharacteristic
585C22×Q8—31no—
586C22×Q8C22×D311yescharacteristic
587#137—64no—
588#137—64no—
589#135—64no—
590C2×Q16—31no—
591C2×Q16—32no—
592C2×Q16—32no—
593C2×SD16—31no—
594C2×SD16—32no—
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—61no—
610C4⋊Q8—61no—
611C4⋊Q8—61no—
612C4⋊Q8—62no—
613C4⋊Q8—62no—
614C4⋊Q8C22×D312yes—
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—61no—
628#125—61no—
629#125—62no—
630#125—62no—
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#124C22×D312yes—
642#123—22no—
643#123—62no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8—22no—
647C22⋊Q8—32no—
648C22⋊Q8—32no—
649C22⋊Q8—62no—
650C22⋊Q8—62no—
651C22⋊Q8—62no—
652C22⋊Q8—62no—
653C22⋊Q8—62no—
654C22⋊Q8—62no—
655C22⋊Q8—62no—
656C22⋊Q8—61no—
657C22⋊Q8—61no—
658C22⋊Q8—62no—
659C22⋊Q8—62no—
660C4×Q8—32no—
661C4×Q8—32no—
662C4×Q8—31no—
663C4×Q8—31no—
664C4×Q8—32no—
665C4×Q8—32no—
666C4×Q8—31no—
667C4×Q8—31no—
668C4×Q8—32no—
669C4×Q8—32no—
670C4×Q8—32no—
671C4×Q8—32no—
672C4×Q8—62no—
673C4×Q8—62no—
674C4×Q8—62no—
675C4×Q8—61no—
676C4×Q8—61no—
677C4×Q8—62no—
678C4×Q8—61no—
679C4×Q8—61no—
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—62no—
689C4×D4—61no—
690C4×D4—61no—
691C4×D4—62no—
692#117—31no—
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#117—62no—
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#107—31no—
719#107—31no—
720#107—32no—
721#106—32no—
722#106—31no—
723#106—31no—
724#106—32no—
725C4⋊C8—32no—
726C4⋊C8—32no—
727C4⋊C8—32no—
728C4⋊C8—32no—
729C4⋊C8—32no—
730C4⋊C8—32no—
731#103—32no—
732#103—32no—
733#103—32no—
734#103—32no—
735#103—32no—
736#103—31no—
737#103—31no—
738#103—32no—
739#103—32no—
740#103—32no—
741#103—32no—
742#103C22×D312yes—
743#103C22×D312yes—
744#103C22×D311yescharacteristic
745#103C22×D311yescharacteristic
746#103C22×D312yes—
747#103C22×D312yes—
748#103C22×D312yes—
749#102—32no—
750#102—31no—
751#102—31no—
752#102C22×D311yescharacteristic
753#102C22×D311yescharacteristic
754#102C22×D312yes—
755#97—31no—
756#97—31no—
757#97—31no—
758#97—31no—
759#97—32no—
760#97C22×D312yes—
761C4×C8—32no—
762C4×C8C22×D312yes—
763C23×C3—21no—
764C23×C3C22×D411yescharacteristic
765C22×D3—21no—
766C3×Q8—22no—
767C3×Q8—21no—
768C3×Q8—22no—
769C3×Q8—21no—
770C3×Q8—42no—
771C3×Q8—82no—
772C3×D4—21no—
773C3×D4—21no—
774C3×D4—42no—
775C2×C3×C4—22no—
776C2×C3×C4—21no—
777C2×C3×C4—21no—
778C2×C3×C4—22no—
779C2×C3×C4—21no—
780C2×C3×C4—42no—
781C2×C3×C4—42no—
782C2×C3×C4—81no—
783C2×C3×C4C22×D412yes—
784C2×C3×C4C22×D412yes—
785C2×C3×C4C22×D411yescharacteristic
786C2×C3×C4C2×#4112yes—
787C2×C3×C42−1+412yes—
788C2×C3×C4C2511yescharacteristic
789#67—24no—
790C2×Dic3—21no—
791C2×Dic3—21no—
792C2×Dic3—21no—
793C2×Dic3—22no—
794C2×Dic3—22no—
795C2×Dic3—41no—
796C2×Dic3—41no—
797C2×Dic3—42no—
798C2×Dic3—42no—
799C2×Dic3—42no—
800C2×Dic3—81no—
801C2×Dic3C22×D412yes—
802C2×Dic3C22×D411yescharacteristic
803C2×Dic3C22×D411yescharacteristic
804C2×Dic3C22×D411yescharacteristic
805C2×Dic3C22×D411yescharacteristic
806C2×Dic3C22×D412yes—
807D12—21no—
808D12C2×#4112yes—
809C4×D3—24no—
810C4×D3—82no—
811C4×D3—81no—
812C4×D3—81no—
813C4×D3—82no—
814Dic6—21no—
815Dic6—22no—
816Dic6—22no—
817Dic6—42no—
818Dic6—42no—
819Dic6—42no—
820Dic6—82no—
821Dic6C2×#4112yes—
822C3×C8—22no—
823C3×C8—21no—
824C3×C8—21no—
825C3⋊C8—21no—
826C3⋊C8—21no—
827C3⋊C8—22no—
828#41—22no—
829#41—22no—
830#41—34no—
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—62no—
841C2×Q8—61no—
842C2×Q8—62no—
843C2×Q8—62no—
844C2×Q8C23×D312yes—
845C2×Q8C23×D311yescharacteristic
846C2×D4—21no—
847C2×D4—31no—
848C2×D4—61no—
849C2×D4C23×D311yescharacteristic
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—31no—
854C22×C4—31no—
855C22×C4—61no—
856C22×C4—61no—
857C22×C4—62no—
858C22×C4—61no—
859C22×C4—61no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—62no—
864C22×C4C23×D311yescharacteristic
865Q16—64no—
866Q16—62no—
867Q16—64no—
868SD16—64no—
869SD16—62no—
870SD16—62no—
871SD16—64no—
872D8—62no—
873M16—22no—
874M16—62no—
875C2×C8—22no—
876C2×C8—32no—
877C2×C8—31no—
878C2×C8—31no—
879C2×C8—62no—
880C2×C8C23×D311yescharacteristic
881C2×C8C23×D311yescharacteristic
882C2×C8C23×D312yes—
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—31no—
899C4⋊C4—31no—
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—62no—
910C4⋊C4—62no—
911C4⋊C4—61no—
912C4⋊C4—61no—
913C4⋊C4—61no—
914C4⋊C4—61no—
915C4⋊C4—62no—
916C4⋊C4—62no—
917C4⋊C4—62no—
918C4⋊C4—62no—
919C4⋊C4—62no—
920C4⋊C4—61no—
921C4⋊C4—62no—
922C4⋊C4—62no—
923C4⋊C4—62no—
924C4⋊C4D3×D411yescharacteristic
925C4⋊C4D3×D411yescharacteristic
926C4⋊C4C23×D312yes—
927C4⋊C4C23×D311yescharacteristic
928C4⋊C4C23×D311yescharacteristic
929C22⋊C4—21no—
930C22⋊C4—22no—
931C22⋊C4—22no—
932C22⋊C4—32no—
933C22⋊C4—61no—
934C22⋊C4—61no—
935C22⋊C4—62no—
936C22⋊C4—61no—
937C22⋊C4—61no—
938C22⋊C4—62no—
939C22⋊C4—62no—
940C22⋊C4—61no—
941C22⋊C4—62no—
942C22⋊C4D3×D412yes—
943C42—21no—
944C42—31no—
945C42—31no—
946C42—32no—
947C42—31no—
948C42—31no—
949C42—61no—
950C42—61no—
951C42—61no—
952C42—61no—
953C42—62no—
954C42—62no—
955C42—62no—
956C42—61no—
957C42—62no—
958C42—62no—
959C42—62no—
960C42C23×D312yes—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—41no—
964C22×C3—41no—
965C22×C3—41no—
966C22×C3#54812yes—
967C22×C3C23×D411yescharacteristic
968C2×D3—22no—
969C2×D3—41no—
970C2×D3—41no—
971C3×C4—22no—
972C3×C4—22no—
973C3×C4—41no—
974C3×C4—42no—
975C3×C4—41no—
976C3×C4—41no—
977C3×C4—42no—
978C3×C4#54812yes—
979C3×C4C22×#4111yescharacteristic
980C3×C4C2×2−1+411yescharacteristic
981Dic3—21no—
982Dic3—21no—
983Dic3—22no—
984Dic3—22no—
985Dic3—21no—
986Dic3—21no—
987Dic3—22no—
988Dic3—42no—
989Dic3—41no—
990Dic3—41no—
991Dic3—42no—
992C23—21no—
993C23—61no—
994C23C2×D3×D411yescharacteristic
995Q8—22no—
996Q8—21no—
997Q8—22no—
998Q8—21no—
999Q8—32no—
1000Q8—42no—
1001Q8—61no—
1002Q8—62no—
1003Q8—62no—
1004Q8—82no—
1005Q8—122no—
1006Q8—122no—
1007Q8—122no—
1008Q8—242no—
1009D4—21no—
1010D4—21no—
1011D4—32no—
1012D4—42no—
1013D4—64no—
1014D4—61no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—31no—
1021C2×C4—31no—
1022C2×C4—31no—
1023C2×C4—31no—
1024C2×C4—32no—
1025C2×C4—32no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—61no—
1029C2×C4—64no—
1030C2×C4—61no—
1031C2×C4—61no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—81no—
1035C2×C4—121no—
1036C2×C4—121no—
1037C2×C4—122no—
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×C4D3×#4112yes—
1049C2×C4#101012yes—
1050C2×C4C24×D311yescharacteristic
1051C8—22no—
1052C8—21no—
1053C8—21no—
1054C8—61no—
1055C8—61no—
1056C8—62no—
1057C2×C3—22no—
1058C2×C3—81no—
1059C2×C3C2×#54811yescharacteristic
1060C2×C3#358611yescharacteristic
1061C2×C3#358611yescharacteristic
1062D3—42no—
1063C22—21no—
1064C22—21no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—62no—
1069C22—121no—
1070C22—121no—
1071C22#567712yes—
1072C22C22×D3×D411yescharacteristic
1073C4—22no—
1074C4—22no—
1075C4—41no—
1076C4—42no—
1077C4—42no—
1078C4—41no—
1079C4—41no—
1080C4—62no—
1081C4—61no—
1082C4—61no—
1083C4—62no—
1084C4—61no—
1085C4—61no—
1086C4—62no—
1087C4—122no—
1088C4—121no—
1089C4—121no—
1090C4—122no—
1091C4#567712yes—
1092C4C2×D3×#4111yescharacteristic
1093C4C2×#101011yescharacteristic
1094C3#6133811yescharacteristic, complemented, Sylow
1095C2—22no—
1096C2—81no—
1097C2—122no—
1098C2C2×#567711yescharacteristic
1099C2#8720811yescharacteristic
1100C2#8721111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3137C2
socleC22×C3C23×D4
prime radicalC2×#950C22
hypercenter#3137D3
hypocenterC3#61338
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #3137

Complements

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

NH ≅ G/Ntype
1. #86587C2semidirect
2. #86343C2semidirect
3. C3×#3137C2semidirect
4. #83480C2semidirect
6. #81733C2semidirect
7. #81732C2semidirect
8. #81677C2semidirect
9. #81676C2semidirect
10. #81663C2semidirect
11. #81661C2semidirect
12. #81627C2semidirect
13. #81623C2semidirect
14. #78974C2semidirect
15. #78950C2semidirect
17. #78871C2semidirect
18. #78828C2semidirect
20. C2×#4797C2semidirect
21. #78774C2semidirect
22. #78571C2semidirect
23. #78543C2semidirect
147. #3137D3semidirect
1094. C3#61338semidirect

Maximal subgroups

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

subgroupindex
#865872
#863432
C3×#31372
#834802
#834062
#817332
#817322
#816772
#816762
#816632
#816612
#816272
#816232
#789742
#789502
#789122
#788712
#788282
#788192
C2×#47972
#787742
#785712
#785432
#613383