Finite Group Databasebeta

← #11675595

Subgroups — #11675595

Order 768.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86224C211yesmaximal, characteristic, complemented
2#86098C211yesmaximal, characteristic, complemented
3C3×#3142C211yesmaximal, characteristic, complemented
4#83296C211yesmaximal, characteristic
5C2×#5063C211yesmaximal, characteristic, complemented
6#81733C212yesmaximal, complemented
7#81732C212yesmaximal, complemented
8#81711C212yesmaximal, complemented
9#81710C212yesmaximal, complemented
10#81663C212yesmaximal, complemented
11#81661C212yesmaximal, complemented
12#81634C212yesmaximal, complemented
13#81632C212yesmaximal, complemented
14#78912C211yesmaximal, characteristic, complemented
15#78912C211yesmaximal, characteristic, complemented
16#78877C211yesmaximal, characteristic, complemented
17#78877C211yesmaximal, characteristic, complemented
18#78873C211yesmaximal, characteristic, complemented
19#78872C211yesmaximal, characteristic, complemented
20#78869C211yesmaximal, characteristic, complemented
21#78868C211yesmaximal, characteristic, complemented
22C4×#909C211yesmaximal, characteristic, complemented
23#78508C211yesmaximal, characteristic, complemented
24#61350—31nomaximal, Sylow
25C3×#532C2211yescharacteristic
26C2×C3×#125C2211yescharacteristic
27#5827C2211yescharacteristic
28#5827C2211yescharacteristic
29#5825C2211yescharacteristic
30#5825C2211yescharacteristic
31C2×#950C2211yescharacteristic
32C2×#950C2211yescharacteristic
33C2×#909C2211yescharacteristic
34#5721C2212yes—
35#5713C2212yes—
36#5690C2212yes—
37#5690C2212yes—
38#5689—21no—
39#5689—21no—
40#5688—21no—
41D3×#125—21no—
42#5685C2212yes—
43#5685C2212yes—
44#5671C2212yes—
45#5671C2212yes—
46#5602—22no—
47#5600—22no—
48#5543—21no—
49#5542—21no—
50#5541—21no—
51#5541—21no—
52#5511—22no—
53#5511—22no—
54#5504C2211yescharacteristic
55#5504C2211yescharacteristic
56#5500C2211yescharacteristic
57#5500C2211yescharacteristic
58C4×#235C2211yescharacteristic
59#5470C2211yescharacteristic
60C2×C4×Dic6C2211yescharacteristic
61C3×#491C2212yes—
62C3×#490C2212yes—
63C3×#488C2212yes—
64C3×#488C2212yes—
65C3×#417C2211yescharacteristic
66C3×#417C2211yescharacteristic
67C3×#417C2211yescharacteristic
68C3×#417C2211yescharacteristic
69C3×C4×M16C2211yescharacteristic
70#5233C2211yescharacteristic
71#5233C2211yescharacteristic
72#5133C2211yescharacteristic
73#5122C2211yescharacteristic
74#5122C2211yescharacteristic
75#5121C2211yescharacteristic
76#5120C2211yescharacteristic
77#5119C2211yescharacteristic
78#5119C2211yescharacteristic
79#5090C2211yescharacteristic
80#5083C2211yescharacteristic
81#5075C2211yescharacteristic
82#5072C2211yescharacteristic
83#5063C2212yes—
84#5063C2212yes—
85#5063C2212yes—
86#5063C2212yes—
87#5057C2211yescharacteristic
88#5057C2211yescharacteristic
89#5054C2211yescharacteristic
90#5054C2211yescharacteristic
91C2×#810C2211yescharacteristic
92C2×#810C2211yescharacteristic
93C2×#808C2211yescharacteristic
94C2×#807C2211yescharacteristic
95C2×C4⋊(C3⋊C8)C2211yescharacteristic
96#4818C2212yes—
97#4818C2212yes—
98#4817C2212yes—
99#4799C2212yes—
100#4797C2212yes—
101#4797C2212yes—
102#4796C2212yes—
103#4795C2212yes—
104#4795C2212yes—
105#4793C2212yes—
106#4792C2212yes—
107#4792C2212yes—
108#4791C2212yes—
109#4790C2212yes—
110#4789C2212yes—
111#4788C2212yes—
112#4787C2212yes—
113#4787C2212yes—
114#4785C2212yes—
115#4768C2212yes—
116#4768C2212yes—
117#4767C2212yes—
118#4767C2212yes—
119#4766C2212yes—
120#4765C2212yes—
121#4765C2212yes—
122#4763C2212yes—
123#4761C2212yes—
124#4759C2212yes—
125#4758C2212yes—
126#4757C2212yes—
127#4756C2212yes—
128#4716C2212yes—
129#4710C2212yes—
130#4701C2212yes—
131#4701C2212yes—
132C4×Dic12C2212yes—
133C4×#204C2212yes—
134#4679C2212yes—
135C8×Dic6C2212yes—
136#3507—31no—
137#3504—31no—
138#3377—32no—
139#3376—32no—
140#3374—32no—
141#3372—32no—
142#3371—32no—
143#3370—32no—
144#3364—32no—
145#3360—32no—
146#3142D311yescharacteristic, complemented
147#3137—31no—
148#3137—31no—
149#3084—31no—
150#3083—31no—
151C2×#479—31no—
152#3046—31no—
153#3046—31no—
154#3035—31no—
155#2962—31no—
156#2952—31no—
157#2951—31no—
158C4×#137—31no—
159C2×C3×#41C2311yescharacteristic
160C2×C3×#41C2311yescharacteristic
161C2×#235C2311yescharacteristic
162C22×Dic6C2311yescharacteristic
163C2×C3×M16C2311yescharacteristic
164C2×C3×M16C2311yescharacteristic
165C3×C4⋊Q8C2311yescharacteristic
166C3×#127C2311yescharacteristic
167C3×#125—21no—
168C3×#125—21no—
169C3×#125C2312yes—
170C3×#125C2312yes—
171C3×#124C2311yescharacteristic
172C3×#124C2311yescharacteristic
173C3×#121—21no—
174C3×#121—21no—
175C3×C4×D4—21no—
176C3×C4×D4—21no—
177C2×C3×C4⋊C4—21no—
178C2×C3×C4⋊C4—21no—
179C2×C3×C4⋊C4C2311yescharacteristic
180C2×C3×C4⋊C4C2311yescharacteristic
181C2×C3×C42C2311yescharacteristic
182#950—24no—
183#950—24no—
184Q8×Dic3C2312yes—
185Q8×Dic3C2312yes—
186#944C2312yes—
187#944C2312yes—
188C2×#216C2311yescharacteristic
189C2×#216C2311yescharacteristic
190C2×#215C2311yescharacteristic
191C2×#215C2311yescharacteristic
192#936—22no—
193#936C2312yes—
194#936C2312yes—
195#935—22no—
196#935—22no—
197#935—22no—
198#935—22no—
199D4×Dic3—22no—
200D4×Dic3—22no—
201D4×Dic3—22no—
202D4×Dic3C2312yes—
203D4×Dic3C2312yes—
204C2×#214C2311yescharacteristic
205C2×#214C2311yescharacteristic
206C2×#213C2311yescharacteristic
207C2×#213C2311yescharacteristic
208C4×#67—21no—
209C4×#67—21no—
210C4×#67—22no—
211C4×#67—22no—
212#926—21no—
213#926—21no—
214#926C2311yescharacteristic
215#926C2311yescharacteristic
216#926C2311yescharacteristic
217C2×C4⋊Dic3—21no—
218C2×C4⋊Dic3—21no—
219C2×C4⋊Dic3C2311yescharacteristic
220#924—22no—
221#924—22no—
222#924—21no—
223#924—21no—
224#924—21no—
225#924—21no—
226#924D412yes—
227#924D412yes—
228C2×Dic3⋊C4—21no—
229C2×C4×Dic3—21no—
230C22×C3⋊C8C2311yescharacteristic
231C22×C3⋊C8C2311yescharacteristic
232#909—24no—
233C2×Dic12C2312yes—
234C2×#204C2312yes—
235#897—22no—
236#897—22no—
237#896—22no—
238#896—22no—
239#896—22no—
240#896—22no—
241#893C2312yes—
242#893C2312yes—
243#892—21no—
244#892—21no—
245D3×C4⋊C4—21no—
246D3×C4⋊C4—21no—
247D3×C4⋊C4—22no—
248D3×C4⋊C4—22no—
249#890—21no—
250#890—21no—
251#890—22no—
252#890C2312yes—
253#890C2312yes—
254#889—22no—
255#889—22no—
256#889—22no—
257#889—22no—
258#889—22no—
259#889—22no—
260#888—22no—
261#888—22no—
262#888—21no—
263#888—21no—
264#888C2312yes—
265#888C2312yes—
266#887—22no—
267#887—22no—
268#887—22no—
269#887C2312yes—
270#887C2312yes—
271#879—22no—
272#879—22no—
273#879—22no—
274#879—22no—
275#878—22no—
276#878—22no—
277#877—22no—
278#877—22no—
279C4×D12C2311yescharacteristic
280C4×D12C2311yescharacteristic
281#872—21no—
282C42×D3—21no—
283#870D411yescharacteristic
284#870D411yescharacteristic
285#869D411yescharacteristic
286#869D411yescharacteristic
287C4×Dic6—21no—
288C4×Dic6—21no—
289C4×Dic6C2312yes—
290C4×Dic6C2311yescharacteristic
291C4×Dic6C2311yescharacteristic
292C4×Dic6C2312yes—
293C4×Dic6C2312yes—
294C4×Dic6C2312yes—
295C3×#103C2312yes—
296C3×#103C2312yes—
297C3×#103C2312yes—
298C3×#103C2312yes—
299C3×#102C2312yes—
300C3×#102C2312yes—
301C3×#102C2312yes—
302C3×#102C2312yes—
303C3×#97C2312yes—
304C3×C4×C8C2312yes—
305#835C2311yescharacteristic
306#835C2311yescharacteristic
307#835C2311yescharacteristic
308#835C2311yescharacteristic
309#832C2311yescharacteristic
310#832C2311yescharacteristic
311#832C2311yescharacteristic
312#832C2311yescharacteristic
313#821C2312yes—
314#818C2312yes—
315#817C2312yes—
316#816C2312yes—
317#816C2312yes—
318#816C2312yes—
319#815C2312yes—
320#815C2312yes—
321Dic3⋊C8C2312yes—
322Dic3⋊C8C2312yes—
323Dic3⋊C8C2312yes—
324Dic3⋊C8C2312yes—
325C8×Dic3C2312yes—
326C8×Dic3C2312yes—
327#810C2312yes—
328#810C2312yes—
329#810C2312yes—
330#810C2312yes—
331#808C2312yes—
332#808C2312yes—
333#807C2312yes—
334#807C2312yes—
335C4⋊(C3⋊C8)C2311yescharacteristic
336C4⋊(C3⋊C8)C2311yescharacteristic
337C4⋊(C3⋊C8)C2311yescharacteristic
338C4⋊(C3⋊C8)C2311yescharacteristic
339C2×#137—31no—
340C2×#135—31no—
341C2×#135—31no—
342#559—32no—
343#557—32no—
344#557—32no—
345#557—32no—
346#556—32no—
347#556—32no—
348#556—61no—
349#554—32no—
350#554—32no—
351#554—62no—
352#554—62no—
353#554—61no—
354#552—61no—
355#552—61no—
356#544—31no—
357#544—31no—
358#544—61no—
359#544—61no—
360#539—62no—
361#536—31no—
362#536—31no—
363#533—31no—
364#533—61no—
365#532C2×D311yescharacteristic
366#529—62no—
367C2×#125—61no—
368C2×#125C2×D311yescharacteristic
369#520—31no—
370#520—31no—
371#520—31no—
372#520—31no—
373C4×#41—31no—
374C2×C4×Q8—31no—
375#491—32no—
376#491—32no—
377#491C2×D312yes—
378#490C2×D312yes—
379#489—32no—
380#489—32no—
381#488—32no—
382#488—32no—
383#488C2×D312yes—
384#488C2×D312yes—
385#487—32no—
386#487—32no—
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#476—32no—
397#475—32no—
398#474—32no—
399#464—31no—
400#464—31no—
401#464—32no—
402#464—32no—
403#463—31no—
404#463—31no—
405#463—32no—
406#463—32no—
407#462—31no—
408#462—32no—
409#462—32no—
410#461—31no—
411#461—32no—
412#461—32no—
413#460—31no—
414#459—31no—
415#446—32no—
416#446—32no—
417#446—32no—
418C8×Q8—32no—
419#442—32no—
420#441—32no—
421#441—32no—
422#440—32no—
423#440—32no—
424#440—32no—
425C4×Q16—32no—
426C4×Q16—32no—
427C4×SD16—32no—
428C4×SD16—32no—
429C4×SD16—32no—
430C4×D8—32no—
431#428—31no—
432C2×#107—31no—
433C2×#106—31no—
434#424—31no—
435#424—31no—
436C2×C4⋊C8—31no—
437#419—31no—
438#417—31no—
439#417C2×D311yescharacteristic
440#417C2×D311yescharacteristic
441#417C2×D311yescharacteristic
442#417C2×D311yescharacteristic
443#416—31no—
444#416—31no—
445C2×#103—31no—
446C2×#103—31no—
447#405—31no—
448#405—31no—
449C4×M16C2×D311yescharacteristic
450C3×#41—22no—
451C3×#41—22no—
452C3×#41—22no—
453C3×#41—22no—
454C2×C3×Q8C2411yescharacteristic
455C2×C3×Q8C2411yescharacteristic
456C2×C3×D4—21no—
457C2×C3×D4—21no—
458C2×C3×D4—21no—
459C2×C3×D4—21no—
460C2×C3×D4C2411yescharacteristic
461C2×C3×D4C2411yescharacteristic
462C22×C3×C4—21no—
463C22×C3×C4—21no—
464C22×C3×C4—21no—
465C22×C3×C4—21no—
466C22×C3×C4C2×D411yescharacteristic
467C22×C3×C4C2×D411yescharacteristic
468C22×C3×C4C2411yescharacteristic
469C2×#67—21no—
470C22×Dic3—21no—
471C22×Dic3—21no—
472C22×Dic3—22no—
473C22×Dic3—22no—
474#235—22no—
475#235#4114yes—
476C2×D12C2411yescharacteristic
477C2×C4×D3—21no—
478C2×C4×D3—21no—
479C2×C4×D3—21no—
480C2×C4×D3—22no—
481C2×C4×D3—22no—
482C2×Dic6—22no—
483C2×Dic6—22no—
484C2×Dic6—21no—
485C2×Dic6—22no—
486C2×Dic6—22no—
487C2×Dic6C2×D412yes—
488C2×Dic6C2×D412yes—
489C2×Dic6C2412yes—
490C2×Dic6C2411yescharacteristic
491C3×M16—22no—
492C3×M16—22no—
493C2×C3×C8C2412yes—
494C2×C3×C8C2412yes—
495C3×C4⋊C4—21no—
496C3×C4⋊C4—22no—
497C3×C4⋊C4—22no—
498C3×C4⋊C4—22no—
499C3×C4⋊C4—22no—
500C3×C4⋊C4—21no—
501C3×C4⋊C4—21no—
502C3×C4⋊C4—21no—
503C3×C4⋊C4C2412yes—
504C3×C4⋊C4C2412yes—
505C3×C22⋊C4—21no—
506C3×C22⋊C4—21no—
507C3×C22⋊C4—21no—
508C3×C22⋊C4—21no—
509C3×C42C2×D411yescharacteristic
510C3×C42C2×D411yescharacteristic
511C3×C42C2411yescharacteristic
512C3×C42C2411yescharacteristic
513#217—21no—
514#217—22no—
515#217—22no—
516#217—22no—
517#217—22no—
518#217—22no—
519#217—22no—
520#217C2×D412yes—
521#217C2×D412yes—
522#216—22no—
523#216—22no—
524#215—22no—
525#215—22no—
526#214—22no—
527#214—22no—
528#213—22no—
529#213—22no—
530(C2×D3)⋊C4—21no—
531(C2×D3)⋊C4—21no—
532(C2×D3)⋊C4—22no—
533(C2×D3)⋊C4—22no—
534C4⋊Dic3—21no—
535C4⋊Dic3—22no—
536C4⋊Dic3—22no—
537C4⋊Dic3—22no—
538C4⋊Dic3—22no—
539C4⋊Dic3C2×D412yes—
540C4⋊Dic3C2×D412yes—
541C4⋊Dic3C2×D411yescharacteristic
542C4⋊Dic3C2×D411yescharacteristic
543C4⋊Dic3C2×D411yescharacteristic
544C4⋊Dic3C2×D411yescharacteristic
545C4⋊Dic3C2412yes—
546C4⋊Dic3C2411yescharacteristic
547C4⋊Dic3C2411yescharacteristic
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—21no—
551Dic3⋊C4—21no—
552Dic3⋊C4—22no—
553Dic3⋊C4—22no—
554Dic3⋊C4—22no—
555Dic3⋊C4—22no—
556Dic3⋊C4—22no—
557Dic3⋊C4—22no—
558Dic3⋊C4—22no—
559Dic3⋊C4—22no—
560Dic3⋊C4—22no—
561Dic3⋊C4—22no—
562Dic3⋊C4C2×D412yes—
563Dic3⋊C4C2×D412yes—
564Dic3⋊C4C2×D412yes—
565Dic3⋊C4C2×D412yes—
566C4×Dic3—22no—
567C4×Dic3—22no—
568C4×Dic3—21no—
569C4×Dic3—21no—
570C4×Dic3—21no—
571C4×Dic3—22no—
572C4×Dic3—22no—
573C4×Dic3—22no—
574C4×Dic3—22no—
575C4×Dic3C2412yes—
576C4×Dic3C2412yes—
577C2×C3⋊C8—22no—
578C2×C3⋊C8—22no—
579C2×C3⋊C8C2411yescharacteristic
580C2×C3⋊C8C2411yescharacteristic
581C2×C3⋊C8C2411yescharacteristic
582C2×C3⋊C8C2411yescharacteristic
583Dic12—24no—
584#204—24no—
585C2×#41—31no—
586C2×#41C22×D311yescharacteristic
587C2×#41C22×D311yescharacteristic
588C22×Q8—31no—
589#137—64no—
590#135—64no—
591#135—64no—
592C2×Q16—31no—
593C2×Q16—31no—
594C2×Q16—32no—
595C2×SD16—31no—
596C2×SD16—31no—
597C2×SD16—31no—
598C2×SD16—31no—
599C2×SD16—32no—
600C2×D8—31no—
601C2×D8—31no—
602C2×M16C22×D311yescharacteristic
603C2×M16C22×D311yescharacteristic
604C22×C8—31no—
605C22×C8—31no—
606C4⋊Q8—32no—
607C4⋊Q8—32no—
608C4⋊Q8—32no—
609C4⋊Q8—32no—
610C4⋊Q8—31no—
611C4⋊Q8—31no—
612C4⋊Q8—61no—
613C4⋊Q8—61no—
614C4⋊Q8—62no—
615C4⋊Q8—62no—
616C4⋊Q8C22×D311yescharacteristic
617#127C22×D311yescharacteristic
618#126—62no—
619#126—62no—
620#126—62no—
621#126—62no—
622#125—21no—
623#125—21no—
624#125—32no—
625#125—32no—
626#125—31no—
627#125—31no—
628#125—61no—
629#125—61no—
630#125—62no—
631#125—62no—
632#125—62no—
633#125—62no—
634#125—62no—
635#125—62no—
636#125—62no—
637#125C22×D312yes—
638#125C22×D312yes—
639#124—32no—
640#124—32no—
641#124—62no—
642#124C22×D311yescharacteristic
643#124C22×D311yescharacteristic
644#123—62no—
645#123—62no—
646#123—62no—
647#123—62no—
648C22⋊Q8—32no—
649C22⋊Q8—32no—
650C22⋊Q8—62no—
651C22⋊Q8—62no—
652C22⋊Q8—62no—
653C22⋊Q8—62no—
654C22⋊Q8—62no—
655C22⋊Q8—62no—
656C22⋊Q8—62no—
657C22⋊Q8—62no—
658C22⋊Q8—62no—
659C22⋊Q8—62no—
660C22⋊Q8—61no—
661C22⋊Q8—61no—
662C22⋊Q8—61no—
663C22⋊Q8—61no—
664#121—21no—
665#121—21no—
666C4×Q8—32no—
667C4×Q8—32no—
668C4×Q8—32no—
669C4×Q8—32no—
670C4×Q8—32no—
671C4×Q8—32no—
672C4×Q8—32no—
673C4×Q8—32no—
674C4×Q8—31no—
675C4×Q8—31no—
676C4×Q8—62no—
677C4×Q8—62no—
678C4×Q8—62no—
679C4×Q8—61no—
680C4×Q8—61no—
681C4×D4—21no—
682C4×D4—21no—
683C4×D4—32no—
684C4×D4—32no—
685C4×D4—32no—
686C4×D4—32no—
687C4×D4—31no—
688C4×D4—31no—
689C4×D4—62no—
690C4×D4—62no—
691C4×D4—62no—
692C4×D4—62no—
693C4×D4—62no—
694C4×D4—61no—
695C4×D4—61no—
696#117—31no—
697#117—31no—
698#117—31no—
699#117—62no—
700#117—62no—
701#117—61no—
702#117—61no—
703#117—61no—
704#117—61no—
705#117—61no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—31no—
709C2×C4⋊C4—61no—
710C2×C4⋊C4—61no—
711C2×C4⋊C4—62no—
712C2×C4⋊C4—62no—
713C2×C4⋊C4—61no—
714C2×C4⋊C4—61no—
715C2×C4⋊C4—61no—
716C2×C4⋊C4C22×D311yescharacteristic
717C2×C4⋊C4C22×D311yescharacteristic
718C2×C42—61no—
719C2×C42—61no—
720C2×C42C22×D311yescharacteristic
721#107—32no—
722#107—32no—
723#107—32no—
724#106—32no—
725#106—32no—
726#106—32no—
727C4⋊C8—32no—
728C4⋊C8—32no—
729C4⋊C8—32no—
730C4⋊C8—32no—
731C4⋊C8—31no—
732C4⋊C8—31no—
733C4⋊C8—31no—
734C4⋊C8—31no—
735#103—31no—
736#103—31no—
737#103—31no—
738#103—31no—
739#103—32no—
740#103—32no—
741#103—32no—
742#103—32no—
743#103—32no—
744#103—32no—
745#103—32no—
746#103C22×D312yes—
747#103C22×D312yes—
748#103C22×D312yes—
749#103C22×D312yes—
750#102—31no—
751#102—31no—
752#102—31no—
753#102—31no—
754#102—32no—
755#102C22×D312yes—
756#102C22×D312yes—
757#102C22×D312yes—
758#102C22×D312yes—
759#97—32no—
760#97—32no—
761#97C22×D312yes—
762C4×C8—32no—
763C4×C8—32no—
764C4×C8C22×D312yes—
765C23×C3—21no—
766C23×C3—21no—
767C23×C3C22×D411yescharacteristic
768C22×D3—21no—
769C3×Q8—21no—
770C3×Q8—21no—
771C3×Q8—21no—
772C3×Q8—21no—
773C3×D4—21no—
774C3×D4—21no—
775C3×D4—21no—
776C3×D4—21no—
777C3×D4—42no—
778C3×D4—42no—
779C3×D4—42no—
780C3×D4—81no—
781C2×C3×C4—21no—
782C2×C3×C4—21no—
783C2×C3×C4—22no—
784C2×C3×C4—22no—
785C2×C3×C4—41no—
786C2×C3×C4—41no—
787C2×C3×C4—42no—
788C2×C3×C4—42no—
789C2×C3×C4—81no—
790C2×C3×C4—81no—
791C2×C3×C4C22×D411yescharacteristic
792C2×C3×C4C22×D411yescharacteristic
793C2×C3×C4C22×D411yescharacteristic
794C2×C3×C4C22×D411yescharacteristic
795C2×C3×C4C22×D411yescharacteristic
796C2×C3×C4C2×#4112yes—
797C2×C3×C42−1+412yes—
798C2×C3×C4C2511yescharacteristic
799#67—24no—
800C2×Dic3—21no—
801C2×Dic3—22no—
802C2×Dic3—22no—
803C2×Dic3—21no—
804C2×Dic3—21no—
805C2×Dic3—42no—
806C2×Dic3—82no—
807C2×Dic3—82no—
808C2×Dic3—81no—
809C2×Dic3C22×D412yes—
810C2×Dic3C22×D412yes—
811C2×Dic3C22×D412yes—
812C2×Dic3C22×D412yes—
813D12—21no—
814D12C2×#4112yes—
815C4×D3—24no—
816C4×D3—82no—
817C4×D3—82no—
818C4×D3—81no—
819C4×D3—81no—
820Dic6—21no—
821Dic6—22no—
822Dic6—22no—
823Dic6—42no—
824Dic6—42no—
825Dic6—42no—
826Dic6—82no—
827Dic6—82no—
828Dic6C2×#4112yes—
829C3×C8—22no—
830C3×C8—22no—
831C3⋊C8—21no—
832C3⋊C8—21no—
833C3⋊C8—21no—
834C3⋊C8—21no—
835#41—22no—
836#41—22no—
837#41—22no—
838#41—22no—
839#41—34no—
840#41—62no—
841C2×Q8—32no—
842C2×Q8—32no—
843C2×Q8—31no—
844C2×Q8—32no—
845C2×Q8—62no—
846C2×Q8—62no—
847C2×Q8—61no—
848C2×Q8—62no—
849C2×Q8—62no—
850C2×Q8C23×D311yescharacteristic
851C2×Q8C23×D311yescharacteristic
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—31no—
857C2×D4—61no—
858C2×D4C23×D311yescharacteristic
859C2×D4C23×D311yescharacteristic
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—62no—
865C22×C4—62no—
866C22×C4—62no—
867C22×C4—62no—
868C22×C4—61no—
869C22×C4—61no—
870C22×C4—61no—
871C22×C4—61no—
872C22×C4—61no—
873C22×C4D3×D411yescharacteristic
874C22×C4D3×D411yescharacteristic
875C22×C4C23×D311yescharacteristic
876Q16—64no—
877Q16—62no—
878Q16—62no—
879SD16—64no—
880SD16—62no—
881SD16—62no—
882SD16—62no—
883SD16—62no—
884D8—62no—
885D8—62no—
886M16—22no—
887M16—22no—
888C2×C8—31no—
889C2×C8—31no—
890C2×C8—31no—
891C2×C8—31no—
892C2×C8—62no—
893C2×C8—62no—
894C2×C8C23×D312yes—
895C2×C8C23×D312yes—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—31no—
905C4⋊C4—31no—
906C4⋊C4—31no—
907C4⋊C4—32no—
908C4⋊C4—32no—
909C4⋊C4—31no—
910C4⋊C4—32no—
911C4⋊C4—32no—
912C4⋊C4—32no—
913C4⋊C4—32no—
914C4⋊C4—31no—
915C4⋊C4—31no—
916C4⋊C4—32no—
917C4⋊C4—62no—
918C4⋊C4—62no—
919C4⋊C4—62no—
920C4⋊C4—62no—
921C4⋊C4—62no—
922C4⋊C4—62no—
923C4⋊C4—62no—
924C4⋊C4—62no—
925C4⋊C4—62no—
926C4⋊C4—62no—
927C4⋊C4—62no—
928C4⋊C4—62no—
929C4⋊C4—62no—
930C4⋊C4—62no—
931C4⋊C4—61no—
932C4⋊C4—62no—
933C4⋊C4—62no—
934C4⋊C4—61no—
935C4⋊C4—61no—
936C4⋊C4C23×D312yes—
937C4⋊C4C23×D312yes—
938C22⋊C4—21no—
939C22⋊C4—21no—
940C22⋊C4—21no—
941C22⋊C4—21no—
942C22⋊C4—32no—
943C22⋊C4—32no—
944C22⋊C4—62no—
945C22⋊C4—62no—
946C22⋊C4—62no—
947C22⋊C4—62no—
948C22⋊C4—62no—
949C22⋊C4—62no—
950C22⋊C4—62no—
951C22⋊C4—62no—
952C22⋊C4—61no—
953C22⋊C4—61no—
954C22⋊C4—61no—
955C42—32no—
956C42—32no—
957C42—62no—
958C42—62no—
959C42—62no—
960C42—62no—
961C42—61no—
962C42—62no—
963C42—62no—
964C42—61no—
965C42—61no—
966C42D3×D411yescharacteristic
967C42D3×D411yescharacteristic
968C42C23×D311yescharacteristic
969C42C23×D311yescharacteristic
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3#54812yes—
979C22×C3C23×D411yescharacteristic
980C2×D3—22no—
981C2×D3—41no—
982C2×D3—41no—
983C3×C4—21no—
984C3×C4—21no—
985C3×C4—21no—
986C3×C4—21no—
987C3×C4—42no—
988C3×C4—42no—
989C3×C4—41no—
990C3×C4—41no—
991C3×C4#54812yes—
992C3×C4C22×#4111yescharacteristic
993C3×C4C2×2−1+411yescharacteristic
994Dic3—22no—
995Dic3—22no—
996Dic3—22no—
997Dic3—22no—
998Dic3—22no—
999Dic3—41no—
1000Dic3—42no—
1001Dic3—41no—
1002Dic3—42no—
1003C23—21no—
1004C23—21no—
1005C23—61no—
1006C23C2×D3×D411yescharacteristic
1007Q8—21no—
1008Q8—21no—
1009Q8—21no—
1010Q8—21no—
1011Q8—32no—
1012Q8—61no—
1013Q8—62no—
1014Q8—62no—
1015Q8—122no—
1016Q8—122no—
1017Q8—122no—
1018Q8—242no—
1019Q8—242no—
1020D4—21no—
1021D4—21no—
1022D4—21no—
1023D4—21no—
1024D4—32no—
1025D4—42no—
1026D4—42no—
1027D4—42no—
1028D4—64no—
1029D4—61no—
1030D4—81no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—32no—
1036C2×C4—32no—
1037C2×C4—32no—
1038C2×C4—32no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—61no—
1044C2×C4—64no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—61no—
1048C2×C4—61no—
1049C2×C4—81no—
1050C2×C4—81no—
1051C2×C4—122no—
1052C2×C4—241no—
1053C2×C4—241no—
1054C2×C4—242no—
1055C2×C4—242no—
1056C2×C4—242no—
1057C2×C4—242no—
1058C2×C4—241no—
1059C2×C4C2×D3×D411yescharacteristic
1060C2×C4C2×D3×D411yescharacteristic
1061C2×C4C2×D3×D411yescharacteristic
1062C2×C4C2×D3×D411yescharacteristic
1063C2×C4C2×D3×D411yescharacteristic
1064C2×C4D3×#4112yes—
1065C2×C4#101012yes—
1066C2×C4C24×D311yescharacteristic
1067C8—22no—
1068C8—22no—
1069C8—61no—
1070C8—61no—
1071C8—61no—
1072C8—61no—
1073C2×C3—22no—
1074C2×C3—81no—
1075C2×C3—81no—
1076C2×C3C2×#54811yescharacteristic
1077C2×C3#358411yescharacteristic
1078C2×C3#358611yescharacteristic
1079D3—42no—
1080C22—21no—
1081C22—21no—
1082C22—41no—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22—41no—
1087C22—41no—
1088C22—62no—
1089C22—121no—
1090C22—121no—
1091C22#567712yes—
1092C22C22×D3×D411yescharacteristic
1093C4—21no—
1094C4—21no—
1095C4—21no—
1096C4—21no—
1097C4—41no—
1098C4—41no—
1099C4—42no—
1100C4—42no—
1101C4—62no—
1102C4—62no—
1103C4—62no—
1104C4—62no—
1105C4—62no—
1106C4—122no—
1107C4—122no—
1108C4—121no—
1109C4—121no—
1110C4#567712yes—
1111C4C2×D3×#4111yescharacteristic
1112C4C2×#101011yescharacteristic
1113C3#6135011yescharacteristic, complemented, Sylow
1114C2—22no—
1115C2—81no—
1116C2—81no—
1117C2—122no—
1118C2C2×#567711yescharacteristic
1119C2#8719911yescharacteristic
1120C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3142C2
socleC22×C3C23×D4
prime radical#83296C2
hypercenter#3142D3
hypocenterC3#61350
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. #86224C2semidirect
2. #86098C2semidirect
3. C3×#3142C2semidirect
5. C2×#5063C2semidirect
6. #81733C2semidirect
7. #81732C2semidirect
8. #81711C2semidirect
9. #81710C2semidirect
10. #81663C2semidirect
11. #81661C2semidirect
12. #81634C2semidirect
13. #81632C2semidirect
14. #78912C2semidirect
15. #78912C2semidirect
16. #78877C2semidirect
17. #78877C2semidirect
18. #78873C2semidirect
19. #78872C2semidirect
20. #78869C2semidirect
21. #78868C2semidirect
22. C4×#909C2semidirect
23. #78508C2semidirect
146. #3142D3semidirect
1113. C3#61350semidirect

Maximal subgroups

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

subgroupindex
#862242
#860982
C3×#31422
#832962
C2×#50632
#817332
#817322
#817112
#817102
#816632
#816612
#816342
#816322
#789122
#788772
#788732
#788722
#788692
#788682
C4×#9092
#785082
#613503