Finite Group Databasebeta

← #11675420

Subgroups — #11675420

Order 768.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87046C211yesmaximal, characteristic, complemented
2#87020C211yesmaximal, characteristic
3C3×#3363C211yesmaximal, characteristic, complemented
4#83704C211yesmaximal, characteristic, complemented
5#83699C211yesmaximal, characteristic, complemented
6#81627C212yesmaximal, complemented
7#81626C211yesmaximal, characteristic, complemented
8#81600C211yesmaximal, characteristic, complemented
9#81599C212yesmaximal
10#81138C211yesmaximal, characteristic, complemented
11#81110C212yesmaximal, complemented
12#81107C211yesmaximal, characteristic
13#81101C212yesmaximal, complemented
14#80478C212yesmaximal
15D3×#462C211yesmaximal, characteristic, complemented
16#80466C212yesmaximal, complemented
17#80463C211yesmaximal, characteristic, complemented
18#79934C211yesmaximal, characteristic, complemented
19#79918C211yesmaximal, characteristic, complemented
20#79720C212yesmaximal, complemented
21C4×#918C211yesmaximal, characteristic
22#79704C212yesmaximal, complemented
23#79702C211yesmaximal, characteristic, complemented
24#61342—31nomaximal, Sylow
25C3×Q82C2211yescharacteristic
26C3×#557C2211yescharacteristic
27C2×#918C2211yescharacteristic
28C2×D3×Q16C2212yes—
29#5732C2211yescharacteristic
30#5729—22no—
31#5729C2212yes—
32#5728—21no—
33#5728C2211yescharacteristic
34#5724C2212yes—
35D3×C4⋊Q8C2211yescharacteristic
36#5722—21no—
37#5722C2211yescharacteristic
38#5721—22no—
39#5721C2212yes—
40#5721C2212yes—
41#5696—22no—
42#5694—21no—
43#5693—22no—
44#5688—21no—
45#5584C2211yescharacteristic
46#5581—21no—
47#5578—21no—
48#5578—21no—
49#5578C2211yescharacteristic
50C4×#239C2211yescharacteristic
51#5572C2212yes—
52#5572C2212yes—
53C4×D3×Q8C2211yescharacteristic
54#5570C2211yescharacteristic
55#5569C2212yes—
56#5568C2212yes—
57#5567—21no—
58#5567C2211yescharacteristic
59#5567C2211yescharacteristic
60C3×#487C2212yes—
61C3×#487C2211yescharacteristic
62C3×#477C2212yes—
63C3×#477C2211yescharacteristic
64C3×#462C2211yescharacteristic
65C3×#462C2212yes—
66C3×C8×Q8C2211yescharacteristic
67C3×C4×Q16C2211yescharacteristic
68C3×C4×Q16C2212yes—
69#5185C2212yes—
70#5184C2211yescharacteristic
71#5182C2212yes—
72#5182C2212yes—
73Dic3×Q16C2212yes—
74#5094C2212yes—
75#5093C2211yescharacteristic
76#5090C2211yescharacteristic
77#5090C2212yes—
78#5089C2212yes—
79#5084C2211yescharacteristic
80#5082C2212yes—
81#5079C2211yescharacteristic
82#5031C2211yescharacteristic
83#5030C2212yes—
84#5030C2212yes—
85C4×#216C2211yescharacteristic
86#5028C2212yes—
87C4×#215C2211yescharacteristic
88#5024C2211yescharacteristic
89#5022C2212yes—
90#5020C2211yescharacteristic
91#4891C2212yes—
92#4889C2211yescharacteristic
93#4881C2211yescharacteristic
94#4880C2212yes—
95#4877C2212yes—
96#4875C2212yes—
97#4873C2212yes—
98#4849C2211yescharacteristic
99#4846C2211yescharacteristic
100#4845C2212yes—
101#4839C2212yes—
102D3×C4⋊C8C2211yescharacteristic
103#4830C2211yescharacteristic
104#4829C2212yes—
105#4828C2212yes—
106#4817C2211yescharacteristic
107#4804C2212yes—
108#4803C2211yescharacteristic
109#4802C2212yes—
110#4802C2211yescharacteristic
111#4802C2212yes—
112D3×#103C2212yes—
113#4800C2212yes—
114#4798C2212yes—
115#4797C2212yes—
116#4797C2212yes—
117#4797C2212yes—
118#4796C2212yes—
119#4796C2212yes—
120#4795C2212yes—
121#4795C2212yes—
122#4794C2212yes—
123#4792C2212yes—
124#4791C2212yes—
125#4789C2212yes—
126#4789C2211yescharacteristic
127#4789C2212yes—
128C4×Dic12C2212yes—
129#4697C2212yes—
130C4×#204C2211yescharacteristic
131#4689C2212yes—
132C4×ΓL(1,𝔽25)C2211yescharacteristic
133#4681C2211yescharacteristic
134#4679C2211yescharacteristic
135#4679C2212yes—
136#3509—31no—
137#3502—31no—
138#3377—32no—
139#3377—32no—
140#3374—32no—
141#3374—32no—
142#3374—31no—
143#3374—31no—
144#3369—31no—
145#3369—31no—
146#3364—31no—
147#3364—31no—
148#3363—31no—
149#3363D311yescharacteristic, complemented
150#3139—31no—
151#3137—32no—
152#3082—32no—
153#3076—31no—
154#3044—32no—
155C2×#462—31no—
156#2962—31no—
157#2950—32no—
158C4×#137—31no—
159C2×#239C2311yescharacteristic
160C2×D3×Q8C2312yes—
161C2×D3×Q8C2311yescharacteristic
162C2×C3×Q16C2312yes—
163C2×C3×Q16C2311yescharacteristic
164C3×C4⋊Q8—22no—
165C3×C4⋊Q8—21no—
166C3×C4⋊Q8C2312yes—
167C3×C4⋊Q8C2311yescharacteristic
168C3×C4⋊Q8C2312yes—
169C3×C4⋊Q8C2311yescharacteristic
170C3×#125—21no—
171C3×#125—22no—
172C3×C4×Q8—21no—
173C3×C4×Q8—21no—
174C3×C4×Q8C2311yescharacteristic
175C3×C4×Q8C2312yes—
176C3×C4×Q8C2311yescharacteristic
177C3×C4×Q8C2312yes—
178C3×C4×Q8C2311yescharacteristic
179#947C2312yes—
180#946—21no—
181#946—21no—
182#946—22no—
183#946D411yescharacteristic
184Q8×Dic3—22no—
185Q8×Dic3—21no—
186Q8×Dic3C2312yes—
187Q8×Dic3C2312yes—
188Q8×Dic3C2311yescharacteristic
189Q8×Dic3C2311yescharacteristic
190#944—21no—
191#944—22no—
192#944—22no—
193#944—22no—
194#944D411yescharacteristic
195#944C2312yes—
196#944C2312yes—
197C2×#216C2312yes—
198C2×#216C2312yes—
199C2×#216C2311yescharacteristic
200C2×#215C2311yescharacteristic
201#918—24no—
202D3×Q16—28no—
203C2×Dic12C2312yes—
204C2×#204C2311yescharacteristic
205C2×ΓL(1,𝔽25)C2311yescharacteristic
206C2×ΓL(1,𝔽25)C2311yescharacteristic
207C2×D3×C8C2312yes—
208#898—22no—
209#898—22no—
210#898—22no—
211#897—21no—
212#897—21no—
213#897D411yescharacteristic
214#896—22no—
215#896—22no—
216#896—22no—
217#896—22no—
218#896D412yes—
219#894—22no—
220#894—22no—
221#893—21no—
222#893C2311yescharacteristic
223#892—21no—
224#892—22no—
225#892—22no—
226#892—21no—
227#892—21no—
228#892C2311yescharacteristic
229#892C2312yes—
230D3×C4⋊C4—21no—
231D3×C4⋊C4—21no—
232D3×C4⋊C4—21no—
233D3×C4⋊C4C2311yescharacteristic
234#890—22no—
235#890—22no—
236#890—22no—
237#890C2312yes—
238#890C2312yes—
239#889—22no—
240#889—22no—
241#889—22no—
242#889—22no—
243#889—22no—
244#889—22no—
245#889—22no—
246#889D412yes—
247#888—22no—
248#888—21no—
249#888—21no—
250#888—21no—
251#888D411yescharacteristic
252#888C2312yes—
253#887—22no—
254#887—21no—
255#887—21no—
256#887—22no—
257#887—22no—
258#887—21no—
259#887—21no—
260#887C2312yes—
261#887C2312yes—
262#887C2311yescharacteristic
263#876—22no—
264#875C2312yes—
265C4×D12—21no—
266C4×D12C2311yescharacteristic
267#872—22no—
268#872—22no—
269#872—22no—
270#872C2312yes—
271C42×D3—21no—
272C42×D3—21no—
273C42×D3C2311yescharacteristic
274#870—21no—
275#870—22no—
276#870C2312yes—
277#869—21no—
278#869C2311yescharacteristic
279#869C2311yescharacteristic
280C4×Dic6—21no—
281C4×Dic6—21no—
282C4×Dic6—22no—
283C4×Dic6—22no—
284C4×Dic6—22no—
285C4×Dic6—21no—
286C4×Dic6C2311yescharacteristic
287C4×Dic6C2312yes—
288C4×Dic6C2312yes—
289C4×Dic6C2312yes—
290C4×Dic6C2311yescharacteristic
291C3×#107C2312yes—
292C3×#107C2311yescharacteristic
293C3×C4⋊C8C2312yes—
294C3×C4⋊C8C2311yescharacteristic
295C3×#103C2311yescharacteristic
296C3×#103C2312yes—
297C3×#103C2311yescharacteristic
298C3×#103C2312yes—
299C3×#103C2312yes—
300C3×#103C2312yes—
301C3×C4×C8C2311yescharacteristic
302C3×C4×C8C2312yes—
303#835C2311yescharacteristic
304#835C2312yes—
305#835C2312yes—
306#835C2312yes—
307#835C2311yescharacteristic
308#835C2312yes—
309#821C2312yes—
310#821C2311yescharacteristic
311#818C2312yes—
312#817C2311yescharacteristic
313#816C2312yes—
314#816C2312yes—
315#816C2312yes—
316#816C2311yescharacteristic
317#815C2311yescharacteristic
318#815C2311yescharacteristic
319#815C2312yes—
320Dic3⋊C8C2312yes—
321Dic3⋊C8C2312yes—
322Dic3⋊C8C2312yes—
323C8×Dic3C2312yes—
324#810C2311yescharacteristic
325#810C2312yes—
326#810C2312yes—
327#810C2312yes—
328#809C2311yescharacteristic
329#809C2312yes—
330#808C2312yes—
331#808C2312yes—
332#808C2311yescharacteristic
333#807C2311yescharacteristic
334C4⋊(C3⋊C8)C2311yescharacteristic
335C4⋊(C3⋊C8)C2312yes—
336#803C2312yes—
337C4×C3⋊C8C2311yescharacteristic
338C2×#137—31no—
339C22×Q16—32no—
340Q82—31no—
341Q82—61no—
342Q82C2×D311yescharacteristic
343#557—32no—
344#557—32no—
345#557—31no—
346#557—32no—
347#557—31no—
348#557—31no—
349#557—61no—
350#557—62no—
351#557C2×D311yescharacteristic
352#556—31no—
353#556—32no—
354#556—31no—
355#552—61no—
356#552—62no—
357#552—61no—
358#544—32no—
359#544—62no—
360#541—62no—
361#536—32no—
362#533—31no—
363#533—31no—
364#533—61no—
365#533—61no—
366#533—61no—
367#533—61no—
368C2×C4⋊Q8—31no—
369#519—32no—
370#519—32no—
371C4×#41—31no—
372C2×C4×Q8—31no—
373#491—32no—
374#491—32no—
375#491—32no—
376#491—32no—
377#489—32no—
378#489—32no—
379#488—32no—
380#488—32no—
381#487—31no—
382#487—31no—
383#487—32no—
384#487—31no—
385#487C2×D311yescharacteristic
386#487C2×D312yes—
387#479—32no—
388#479—32no—
389#479—32no—
390#479—32no—
391#479—32no—
392#478—32no—
393#477—32no—
394#477C2×D311yescharacteristic
395#477C2×D312yes—
396#476—31no—
397#475—32no—
398#475—31no—
399#475—32no—
400#474—31no—
401#464—32no—
402#464—32no—
403#464—32no—
404#464—32no—
405#462—32no—
406#462—32no—
407#462—31no—
408#462—32no—
409#462—31no—
410#462—31no—
411#462—32no—
412#462—32no—
413#462C2×D311yescharacteristic
414#462C2×D312yes—
415#446—31no—
416#446—32no—
417#446—31no—
418#446—32no—
419C8×Q8—31no—
420C8×Q8C2×D311yescharacteristic
421#441—31no—
422#441—32no—
423#441—32no—
424#441—32no—
425#441—31no—
426#441—32no—
427#440—31no—
428#440—31no—
429C4×Q16—32no—
430C4×Q16—31no—
431C4×Q16—32no—
432C4×Q16—32no—
433C4×Q16C2×D311yescharacteristic
434C4×Q16C2×D312yes—
435C4×SD16—31no—
436C4×SD16—31no—
437#428—31no—
438#427—32no—
439#424—32no—
440C2×C4⋊C8—31no—
441#419—32no—
442#419—32no—
443#419—31no—
444#417—31no—
445#416—32no—
446C2×#103—32no—
447#405—32no—
448C4×M16—31no—
449C2×C3×Q8—21no—
450C2×C3×Q8—22no—
451C2×C3×Q8C2×D411yescharacteristic
452C2×C3×Q8C2411yescharacteristic
453C2×C3×Q8C2412yes—
454C2×C3×Q8C2411yescharacteristic
455#239—22no—
456#239—22no—
457D3×Q8—22no—
458D3×Q8—24no—
459D3×Q8—24no—
460D3×Q8#4114yes—
461C2×D12—21no—
462C2×D12C2411yescharacteristic
463C2×C4×D3—21no—
464C2×C4×D3—22no—
465C2×C4×D3—21no—
466C2×C4×D3—21no—
467C2×C4×D3—21no—
468C2×C4×D3—21no—
469C2×C4×D3C2×D411yescharacteristic
470C2×C4×D3C2×D411yescharacteristic
471C2×C4×D3C2411yescharacteristic
472C2×Dic6—21no—
473C2×Dic6—21no—
474C2×Dic6—22no—
475C2×Dic6—22no—
476C2×Dic6C2×D411yescharacteristic
477C2×Dic6C2×D412yes—
478C2×Dic6C2412yes—
479C2×Dic6C2411yescharacteristic
480C3×Q16—24no—
481C3×Q16—22no—
482C2×C3×C8C2412yes—
483C2×C3×C8C2411yescharacteristic
484C2×C3×C8C2411yescharacteristic
485C3×C4⋊C4—21no—
486C3×C4⋊C4—22no—
487C3×C4⋊C4—21no—
488C3×C4⋊C4—22no—
489C3×C4⋊C4—22no—
490C3×C4⋊C4—21no—
491C3×C4⋊C4—21no—
492C3×C4⋊C4—22no—
493C3×C4⋊C4—21no—
494C3×C4⋊C4—22no—
495C3×C4⋊C4C2×D411yescharacteristic
496C3×C4⋊C4C2×D412yes—
497C3×C4⋊C4C2411yescharacteristic
498C3×C4⋊C4C2412yes—
499C3×C4⋊C4C2411yescharacteristic
500C3×C42—21no—
501C3×C42—22no—
502C3×C42—21no—
503C3×C42—22no—
504C3×C42C2411yescharacteristic
505C3×C42C2412yes—
506#216—24no—
507#216—24no—
508#216—22no—
509#215—22no—
510(C2×D3)⋊C4—21no—
511(C2×D3)⋊C4—22no—
512(C2×D3)⋊C4—22no—
513(C2×D3)⋊C4—21no—
514(C2×D3)⋊C4—22no—
515(C2×D3)⋊C4—22no—
516(C2×D3)⋊C4—21no—
517(C2×D3)⋊C4—22no—
518(C2×D3)⋊C4C2×D412yes—
519(C2×D3)⋊C4C2×D412yes—
520C4⋊Dic3—21no—
521C4⋊Dic3—21no—
522C4⋊Dic3—21no—
523C4⋊Dic3—22no—
524C4⋊Dic3—21no—
525C4⋊Dic3—22no—
526C4⋊Dic3—22no—
527C4⋊Dic3—22no—
528C4⋊Dic3—21no—
529C4⋊Dic3C2×D411yescharacteristic
530C4⋊Dic3C2×D412yes—
531C4⋊Dic3C2411yescharacteristic
532C4⋊Dic3C2411yescharacteristic
533C4⋊Dic3C2412yes—
534Dic3⋊C4—22no—
535Dic3⋊C4—22no—
536Dic3⋊C4—22no—
537Dic3⋊C4—21no—
538Dic3⋊C4—22no—
539Dic3⋊C4—21no—
540Dic3⋊C4—21no—
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—
554Dic3⋊C4C2×D412yes—
555C4×Dic3—21no—
556C4×Dic3—22no—
557C4×Dic3—22no—
558C4×Dic3—21no—
559C4×Dic3—21no—
560C4×Dic3—22no—
561C4×Dic3—22no—
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
571C2×C3⋊C8C2411yescharacteristic
572C2×C3⋊C8C2411yescharacteristic
573C2×C3⋊C8C2412yes—
574Dic12—24no—
575#204—22no—
576ΓL(1,𝔽25)—22no—
577ΓL(1,𝔽25)—22no—
578D3×C8—24no—
579C2×#41—31no—
580C22×Q8—31no—
581C22×Q8—32no—
582#137—64no—
583C2×Q16—32no—
584C2×Q16—32no—
585C2×Q16—31no—
586C2×Q16—32no—
587C2×Q16—68no—
588C2×Q16C22×D312yes—
589C2×Q16C22×D311yescharacteristic
590C2×SD16—31no—
591C2×SD16—31no—
592C2×M16—31no—
593C2×M16—31no—
594C22×C8—32no—
595C4⋊Q8—21no—
596C4⋊Q8—22no—
597C4⋊Q8—31no—
598C4⋊Q8—31no—
599C4⋊Q8—32no—
600C4⋊Q8—32no—
601C4⋊Q8—32no—
602C4⋊Q8—31no—
603C4⋊Q8—31no—
604C4⋊Q8—61no—
605C4⋊Q8—61no—
606C4⋊Q8—61no—
607C4⋊Q8—61no—
608C4⋊Q8—62no—
609C4⋊Q8—62no—
610C4⋊Q8—62no—
611C4⋊Q8—62no—
612C4⋊Q8—61no—
613C4⋊Q8C22×D311yescharacteristic
614C4⋊Q8C22×D312yes—
615C4⋊Q8C22×D311yescharacteristic
616C4⋊Q8C22×D312yes—
617#126—62no—
618#126—62no—
619#126—62no—
620#126—62no—
621#125—21no—
622#125—22no—
623#125—32no—
624#125—32no—
625#125—32no—
626#125—32no—
627#125—61no—
628#125—62no—
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#124—32no—
640#124—32no—
641#123—62no—
642#123—62no—
643C22⋊Q8—31no—
644C22⋊Q8—31no—
645C22⋊Q8—32no—
646C22⋊Q8—62no—
647C22⋊Q8—62no—
648C22⋊Q8—62no—
649C22⋊Q8—62no—
650C22⋊Q8—61no—
651C22⋊Q8—62no—
652C22⋊Q8—61no—
653C22⋊Q8—61no—
654C22⋊Q8—61no—
655C4×Q8—21no—
656C4×Q8—21no—
657C4×Q8—32no—
658C4×Q8—31no—
659C4×Q8—31no—
660C4×Q8—31no—
661C4×Q8—32no—
662C4×Q8—32no—
663C4×Q8—31no—
664C4×Q8—32no—
665C4×Q8—32no—
666C4×Q8—31no—
667C4×Q8—32no—
668C4×Q8—32no—
669C4×Q8—61no—
670C4×Q8—62no—
671C4×Q8—62no—
672C4×Q8—62no—
673C4×Q8—61no—
674C4×Q8—61no—
675C4×Q8—61no—
676C4×Q8—61no—
677C4×Q8—61no—
678C4×Q8—62no—
679C4×Q8—62no—
680C4×Q8—62no—
681C4×Q8—61no—
682C4×Q8—62no—
683C4×Q8—61no—
684C4×Q8C22×D311yescharacteristic
685C4×Q8C22×D311yescharacteristic
686C4×Q8C22×D312yes—
687C4×Q8C22×D312yes—
688C4×Q8C22×D311yescharacteristic
689C4×D4—31no—
690C4×D4—31no—
691C4×D4—61no—
692C4×D4—61no—
693#117—32no—
694#117—31no—
695#117—32no—
696#117—62no—
697#117—62no—
698#117—62no—
699#117—61no—
700#117—62no—
701#117—62no—
702#117—61no—
703#117—61no—
704C2×C4⋊C4—31no—
705C2×C4⋊C4—61no—
706C2×C4⋊C4—61no—
707C2×C4⋊C4—61no—
708C2×C42—31no—
709C2×C42—61no—
710C2×C42—61no—
711#107—32no—
712#107—31no—
713#107C22×D312yes—
714#107C22×D311yescharacteristic
715#106—31no—
716#106—32no—
717#106—32no—
718#106—31no—
719C4⋊C8—32no—
720C4⋊C8—32no—
721C4⋊C8—32no—
722C4⋊C8—31no—
723C4⋊C8—32no—
724C4⋊C8C22×D311yescharacteristic
725C4⋊C8C22×D312yes—
726#103—32no—
727#103—32no—
728#103—31no—
729#103—31no—
730#103—32no—
731#103—32no—
732#103—32no—
733#103—31no—
734#103—32no—
735#103—32no—
736#103—32no—
737#103—31no—
738#103—32no—
739#103—32no—
740#103C22×D312yes—
741#103C22×D312yes—
742#103C22×D311yescharacteristic
743#103C22×D311yescharacteristic
744#103C22×D312yes—
745#103C22×D312yes—
746#102—32no—
747#102—31no—
748#102—32no—
749#102—31no—
750#97—31no—
751#97—31no—
752#97—32no—
753#97—32no—
754C4×C8—32no—
755C4×C8—31no—
756C4×C8C22×D311yescharacteristic
757C4×C8C22×D312yes—
758C22×D3—21no—
759C22×D3C22×D411yescharacteristic
760C3×Q8—22no—
761C3×Q8—21no—
762C3×Q8—22no—
763C3×Q8—21no—
764C3×Q8—22no—
765C3×Q8—21no—
766C3×Q8—82no—
767C3×Q8—81no—
768C3×Q8C2×#4112yes—
769C2×C3×C4—21no—
770C2×C3×C4—21no—
771C2×C3×C4—22no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—22no—
775C2×C3×C4C22×D412yes—
776C2×C3×C4C22×D411yescharacteristic
777C2×C3×C4C22×D412yes—
778C2×C3×C4C22×D411yescharacteristic
779C2×C3×C4C2511yescharacteristic
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—22no—
783C2×Dic3—21no—
784C2×Dic3—22no—
785C2×Dic3C22×D411yescharacteristic
786C2×Dic3C22×D412yes—
787C2×Dic3C22×D412yes—
788C2×Dic3C22×D411yescharacteristic
789C2×Dic3C22×D411yescharacteristic
790D12—21no—
791D12—21no—
792D12—42no—
793C4×D3—24no—
794C4×D3—22no—
795C4×D3—41no—
796C4×D3—42no—
797C4×D3—44no—
798C4×D3—42no—
799C4×D3—42no—
800C4×D3—81no—
801C4×D3C2×#4112yes—
802C4×D32−1+412yes—
803Dic6—22no—
804Dic6—21no—
805Dic6—24no—
806Dic6—22no—
807Dic6—22no—
808Dic6—42no—
809Dic6—42no—
810Dic6—44no—
811Dic6—82no—
812Dic6C2×#4112yes—
813C3×C8—22no—
814C3×C8—21no—
815C3×C8—21no—
816C3⋊C8—22no—
817C3⋊C8—21no—
818C3⋊C8—21no—
819#41—62no—
820#41—62no—
821C2×Q8—21no—
822C2×Q8—22no—
823C2×Q8—31no—
824C2×Q8—32no—
825C2×Q8—34no—
826C2×Q8—31no—
827C2×Q8—32no—
828C2×Q8—61no—
829C2×Q8—62no—
830C2×Q8—62no—
831C2×Q8—62no—
832C2×Q8—64no—
833C2×Q8—64no—
834C2×Q8—61no—
835C2×Q8D3×D411yescharacteristic
836C2×Q8C23×D312yes—
837C2×Q8C23×D311yescharacteristic
838C2×Q8C23×D311yescharacteristic
839C2×D4—31no—
840C2×D4—61no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—31no—
844C22×C4—61no—
845C22×C4—61no—
846C22×C4—61no—
847C22×C4—62no—
848C22×C4—61no—
849C22×C4—61no—
850Q16—24no—
851Q16—22no—
852Q16—64no—
853Q16—64no—
854Q16—62no—
855Q16—64no—
856SD16—62no—
857SD16—62no—
858M16—62no—
859M16—62no—
860C2×C8—31no—
861C2×C8—31no—
862C2×C8—32no—
863C2×C8—64no—
864C2×C8C23×D312yes—
865C2×C8C23×D311yescharacteristic
866C2×C8C23×D311yescharacteristic
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—21no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—32no—
878C4⋊C4—32no—
879C4⋊C4—31no—
880C4⋊C4—32no—
881C4⋊C4—32no—
882C4⋊C4—32no—
883C4⋊C4—32no—
884C4⋊C4—31no—
885C4⋊C4—32no—
886C4⋊C4—31no—
887C4⋊C4—61no—
888C4⋊C4—62no—
889C4⋊C4—61no—
890C4⋊C4—61no—
891C4⋊C4—62no—
892C4⋊C4—61no—
893C4⋊C4—62no—
894C4⋊C4—62no—
895C4⋊C4—62no—
896C4⋊C4—62no—
897C4⋊C4—62no—
898C4⋊C4—62no—
899C4⋊C4—62no—
900C4⋊C4—62no—
901C4⋊C4—62no—
902C4⋊C4—62no—
903C4⋊C4—62no—
904C4⋊C4—61no—
905C4⋊C4—61no—
906C4⋊C4—61no—
907C4⋊C4—62no—
908C4⋊C4—62no—
909C4⋊C4—62no—
910C4⋊C4—62no—
911C4⋊C4—61no—
912C4⋊C4D3×D411yescharacteristic
913C4⋊C4D3×D412yes—
914C4⋊C4C23×D311yescharacteristic
915C4⋊C4C23×D312yes—
916C4⋊C4C23×D311yescharacteristic
917C22⋊C4—32no—
918C22⋊C4—32no—
919C22⋊C4—61no—
920C22⋊C4—62no—
921C22⋊C4—62no—
922C22⋊C4—61no—
923C22⋊C4—62no—
924C22⋊C4—61no—
925C22⋊C4—62no—
926C22⋊C4—62no—
927C42—21no—
928C42—21no—
929C42—22no—
930C42—22no—
931C42—31no—
932C42—31no—
933C42—32no—
934C42—31no—
935C42—61no—
936C42—61no—
937C42—61no—
938C42—61no—
939C42—62no—
940C42—62no—
941C42—62no—
942C42—62no—
943C42—62no—
944C42—61no—
945C42—62no—
946C42—62no—
947C42C23×D311yescharacteristic
948C42C23×D312yes—
949C22×C3C23×D411yescharacteristic
950C2×D3—21no—
951C2×D3—21no—
952C2×D3—41no—
953C2×D3—41no—
954C2×D3—41no—
955C2×D3#54812yes—
956C3×C4—22no—
957C3×C4—21no—
958C3×C4—22no—
959C3×C4—22no—
960C3×C4—42no—
961C3×C4—41no—
962C3×C4—41no—
963C3×C4—42no—
964C3×C4—41no—
965C3×C4#57812yes—
966C3×C4C22×#4111yescharacteristic
967C3×C4C2×2−1+411yescharacteristic
968Dic3—21no—
969Dic3—22no—
970Dic3—22no—
971Dic3—22no—
972Dic3—21no—
973Dic3—41no—
974Dic3—42no—
975Dic3—42no—
976Dic3—41no—
977Dic3#54812yes—
978C23—31no—
979C23—61no—
980Q8—21no—
981Q8—22no—
982Q8—22no—
983Q8—21no—
984Q8—22no—
985Q8—21no—
986Q8—32no—
987Q8—64no—
988Q8—61no—
989Q8—62no—
990Q8—62no—
991Q8—62no—
992Q8—81no—
993Q8—82no—
994Q8—122no—
995Q8—124no—
996Q8—122no—
997Q8—242no—
998Q8D3×#4112yes—
999D4—61no—
1000D4—61no—
1001D4—122no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—31no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—31no—
1012C2×C4—31no—
1013C2×C4—32no—
1014C2×C4—32no—
1015C2×C4—64no—
1016C2×C4—61no—
1017C2×C4—62no—
1018C2×C4—61no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—61no—
1022C2×C4—121no—
1023C2×C4—122no—
1024C2×C4—122no—
1025C2×C4—124no—
1026C2×C4—122no—
1027C2×C4—241no—
1028C2×C4C2×D3×D412yes—
1029C2×C4C2×D3×D411yescharacteristic
1030C2×C4C2×D3×D412yes—
1031C2×C4C2×D3×D411yescharacteristic
1032C2×C4C24×D311yescharacteristic
1033C8—22no—
1034C8—21no—
1035C8—21no—
1036C8—62no—
1037C8—61no—
1038C8—61no—
1039C2×C3C2×#54811yescharacteristic
1040C2×C3C2×#57811yescharacteristic
1041C2×C3#358611yescharacteristic
1042D3—22no—
1043D3—81no—
1044C22—32no—
1045C22—61no—
1046C22—61no—
1047C22—121no—
1048C22—121no—
1049C22—121no—
1050C22C22×D3×D411yescharacteristic
1051C4—22no—
1052C4—21no—
1053C4—22no—
1054C4—22no—
1055C4—32no—
1056C4—41no—
1057C4—41no—
1058C4—42no—
1059C4—41no—
1060C4—42no—
1061C4—61no—
1062C4—62no—
1063C4—61no—
1064C4—62no—
1065C4—62no—
1066C4—121no—
1067C4—122no—
1068C4—121no—
1069C4—122no—
1070C4#576612yes—
1071C4C2×D3×#4111yescharacteristic
1072C4D3×2−1+411yescharacteristic
1073C3#6134211yescharacteristic, complemented, Sylow
1074C2—62no—
1075C2—241no—
1076C2D3×#54811yescharacteristic
1077C2C2×#576611yescharacteristic
1078C2#8720811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3363C2
socleC22×C3C23×D4
prime radicalC2×#239C23
hypercenter#3363D3
hypocenterC3#61342
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3363

Complements

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

NH ≅ G/Ntype
1. #87046C2semidirect
3. C3×#3363C2semidirect
4. #83704C2semidirect
5. #83699C2semidirect
6. #81627C2semidirect
7. #81626C2semidirect
8. #81600C2semidirect
10. #81138C2semidirect
11. #81110C2semidirect
13. #81101C2semidirect
15. D3×#462C2semidirect
16. #80466C2semidirect
17. #80463C2semidirect
18. #79934C2semidirect
19. #79918C2semidirect
20. #79720C2semidirect
22. #79704C2semidirect
23. #79702C2semidirect
149. #3363D3semidirect
1073. C3#61342semidirect

Maximal subgroups

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

subgroupindex
#870462
#870202
C3×#33632
#837042
#836992
#816272
#816262
#816002
#815992
#811382
#811102
#811072
#811012
#804782
D3×#4622
#804662
#804632
#799342
#799182
#797202
C4×#9182
#797042
#797022
#613423