Finite Group Databasebeta

← #11692186

Subgroups — #11692186

Order 768.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86285C211yesmaximal, characteristic, complemented
2#86233C211yesmaximal, characteristic, complemented
3C3×#3246C211yesmaximal, characteristic, complemented
4#83326C211yesmaximal, characteristic, complemented
5#83300C211yesmaximal, characteristic, complemented
6#81083C212yesmaximal, complemented
7#81055C212yesmaximal, complemented
8#81020C212yesmaximal, complemented
9#81014C212yesmaximal, complemented
10#80683C212yesmaximal, complemented
11#80681C212yesmaximal, complemented
12#80652C212yesmaximal, complemented
13#80648C212yesmaximal, complemented
14#80452C212yesmaximal, complemented
15#80419C212yesmaximal, complemented
16#80403C212yesmaximal, complemented
17#80364C212yesmaximal, complemented
18C2×#4847C211yesmaximal, characteristic, complemented
19#79016C211yesmaximal, characteristic, complemented
20#62166—31nomaximal, Sylow
21C3×#533C2211yescharacteristic
22C3×#532C2211yescharacteristic
23#5824—22no—
24#5732C2211yescharacteristic
25#5729C2212yescomplemented
26#5727C2211yescharacteristic
27#5726C2211yescharacteristic
28#5726C2211yescharacteristic
29#5719C2212yescomplemented
30#5692—22no—
31#5684—21no—
32#5672—21no—
33#5635C2212yes—
34#5630C2212yes—
35#5627—21no—
36D3×C22⋊Q8—21no—
37#5618C2212yes—
38#5611C2212yes—
39#5602—21no—
40#5597—21no—
41#5582C2212yes—
42#5581—21no—
43#5576—21no—
44#5574C2212yes—
45#5564—22no—
46#5558C2212yescomplemented
47#5539C2212yescomplemented
48#5527—22no—
49#5479C2211yescharacteristic
50C2×C4×D12C2211yescharacteristic
51C2×#870C2211yescharacteristic
52C3×#476C2212yescomplemented
53C3×#475C2212yescomplemented
54C3×#465C2212yes—
55C3×#465C2212yes—
56C3×#461C2212yescomplemented
57C3×#460C2212yescomplemented
58C2×C3×C4⋊C8C2211yescharacteristic
59#5174C2212yescomplemented
60#5172C2212yes—
61#5172C2212yes—
62#5171C2212yescomplemented
63#5165C2212yes—
64#5165C2212yes—
65#5164C2212yescomplemented
66Dic3×SD16C2212yescomplemented
67C2×#821C2211yescharacteristic
68C2×#821C2211yescharacteristic
69#5111C2212yes—
70C8×#67C2212yes—
71C2×#818C2211yescharacteristic
72C2×#817C2211yescharacteristic
73#5084C2211yescharacteristic
74#5084C2211yescharacteristic
75#5082C2212yescomplemented
76#5081C2212yescomplemented
77#5072C2211yescharacteristic
78#5072C2211yescharacteristic
79#5044C2212yes—
80#5043C2212yes—
81#5036C2212yes—
82#5034C2212yes—
83#5022C2212yescomplemented
84#5022C2212yescomplemented
85#5014C2212yes—
86#5014C2212yes—
87#4926C2211yescharacteristic
88#4871C2212yes—
89#4870C2212yes—
90#4866C2212yes—
91#4863C2212yes—
92#4861C2212yescomplemented
93D3×#106C2212yescomplemented
94#4856C2212yescomplemented
95#4855C2212yescomplemented
96#4847C2212yes—
97#4847C2212yes—
98#4847C2212yes—
99#4847C2212yes—
100#4840C2212yescomplemented
101#4839C2212yescomplemented
102#4836C2212yescomplemented
103#4828C2212yescomplemented
104#4814C2212yescomplemented
105#4805C2212yescomplemented
106#4804C2212yes—
107#4803C2212yes—
108#4800C2212yes—
109#4796C2212yescomplemented
110#4794C2212yes—
111#4791C2212yescomplemented
112#4785C2212yes—
113#4782C2212yes—
114#4777C2212yescomplemented
115#4775C2212yes—
116#4774C2212yescomplemented
117#4761C2212yescomplemented
118#4759C2212yescomplemented
119#4756C2212yes—
120#3559—31no—
121#3520—31no—
122#3384—32no—
123#3376—32no—
124#3346—32no—
125#3345—32no—
126#3335—32no—
127#3307—32no—
128#3306—32no—
129#3297—32no—
130#3257—32no—
131#3246D311yescharacteristic, complemented
132#3244—32no—
133#3236—31no—
134#3119—32no—
135#3109—31no—
136#3084—32no—
137C2×#478—31no—
138#2992—31no—
139C2×C3×#41—21no—
140C2×#239—21no—
141C2×#239C2312yes—
142C2×D3×Q8—21no—
143C2×#237—22no—
144C22×D12C2311yescharacteristic
145C22×C4×D3—21no—
146C2×C3×SD16C2312yes—
147C2×C3×SD16C2312yes—
148C22×C3×C8C2311yescharacteristic
149C22×C3×C8C2311yescharacteristic
150C3×C4⋊Q8C2311yescharacteristic
151C3×C4⋊Q8C2311yescharacteristic
152C3×C4⋊Q8C2311yescharacteristic
153C3×#127C2311yescharacteristic
154C3×#125—21no—
155C3×#124—21no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8C2312yes—
158C3×#121—21no—
159C3×#121C2312yes—
160C3×C4×Q8—21no—
161C3×C4×Q8C2312yes—
162C3×C4×D4—21no—
163C3×C4×D4C2312yes—
164C3×#117—21no—
165C2×C3×C42C2311yescharacteristic
166#947C2312yes—
167#946—22no—
168#946—21no—
169#946—21no—
170#946C2312yes—
171Q8×Dic3C2312yes—
172#944—22no—
173#939—22no—
174#939—22no—
175#939—22no—
176#938C2312yes—
177#938C2312yes—
178#935—22no—
179#935—22no—
180#935—22no—
181D4×Dic3—22no—
182D4×Dic3C2312yes—
183D4×Dic3C2312yes—
184C2×#213C2312yes—
185C2×#213C2312yes—
186#930D411yescharacteristic
187#929—22no—
188#929D412yes—
189C4×#67—22no—
190C4×#67C2312yes—
191C2×(C2×D3)⋊C4—21no—
192C2×C4⋊Dic3C2311yescharacteristic
193C2×C4⋊Dic3C2311yescharacteristic
194C2×C4⋊Dic3C2311yescharacteristic
195#924—22no—
196#924D411yescharacteristic
197C2×Dic3⋊C4—21no—
198C2×Dic3⋊C4—21no—
199C2×Dic3⋊C4—22no—
200C2×ΓL(1,𝔽25)C2312yes—
201C2×D3×C8C2312yes—
202#898—22no—
203#897—21no—
204#897—22no—
205#896—22no—
206#896—22no—
207#896—22no—
208#895—21no—
209#895—22no—
210#895C2312yes—
211#894—22no—
212#894—22no—
213#894—22no—
214#894—22no—
215#893—22no—
216#893C2312yes—
217#892—21no—
218#892C2312yes—
219D3×C4⋊C4—21no—
220D3×C4⋊C4—22no—
221D3×C4⋊C4C2312yes—
222D3×C4⋊C4C2312yes—
223#890C2312yes—
224#889—22no—
225#889—22no—
226#888C2312yes—
227#888C2312yes—
228#886—22no—
229#884—22no—
230#883—22no—
231#882—22no—
232#67⋊C4—22no—
233D3×C22⋊C4—22no—
234#879—22no—
235#879—22no—
236#878—22no—
237#878—22no—
238#878—22no—
239#878—22no—
240#876—22no—
241#876D412yes—
242#875—22no—
243#875D411yescharacteristic
244C4×D12—21no—
245C4×D12—21no—
246C4×D12—22no—
247C4×D12C2311yescharacteristic
248C4×D12C2311yescharacteristic
249C4×D12C2311yescharacteristic
250C4×D12C2311yescharacteristic
251C4×D12C2311yescharacteristic
252#872—22no—
253#872C2312yes—
254#870—21no—
255#870—21no—
256#870D411yescharacteristic
257#870C2312yes—
258#870C2312yes—
259C4×Dic6C2311yescharacteristic
260C3×#106C2312yes—
261C3×#106C2312yes—
262C3×C4⋊C8C2312yes—
263C3×C4⋊C8C2312yes—
264C3×#103C2312yes—
265C3×#103C2312yes—
266C3×#102C2312yes—
267C3×#102C2312yes—
268#835C2312yes—
269#835C2312yes—
270#835C2312yes—
271#835C2312yes—
272#832C2312yes—
273#832C2312yes—
274#830C2312yes—
275#821C2312yes—
276#821C2312yes—
277#821C2312yes—
278#821C2312yes—
279(C2×D3)⋊C8C2312yes—
280(C2×D3)⋊C8C2312yes—
281#818C2312yes—
282#818C2312yes—
283#817C2312yes—
284#817C2312yes—
285#815C2312yes—
286Dic3⋊C8C2312yes—
287Dic3⋊C8C2312yes—
288C8×Dic3C2312yes—
289#809C2312yes—
290#809C2312yes—
291#808C2312yes—
292#808C2312yes—
293#808C2312yes—
294#808C2312yes—
295#807C2312yes—
296#807C2312yes—
297C4⋊(C3⋊C8)C2311yescharacteristic
298C4⋊(C3⋊C8)C2311yescharacteristic
299#803C2312yes—
300#563—61no—
301#562—61no—
302#556—31no—
303#554—32no—
304#554—32no—
305#553—32no—
306#553—32no—
307#552—61no—
308#551—62no—
309D4×Q8—31no—
310#548—61no—
311#547—31no—
312#547—32no—
313#547—31no—
314#547—62no—
315#546—32no—
316#544—32no—
317#542—32no—
318#540—32no—
319#539—62no—
320#539—61no—
321#539—62no—
322#537—61no—
323#533C2×D311yescharacteristic
324#532C2×D311yescharacteristic
325#529—31no—
326C2×#125—31no—
327#525—61no—
328C2×C22⋊Q8—61no—
329#520—32no—
330C2×C4×D4—31no—
331#501—32no—
332#501—32no—
333#498—32no—
334#491—32no—
335#489—32no—
336#488—32no—
337#485—32no—
338#484—32no—
339#483—32no—
340#483—32no—
341#482—32no—
342#481—32no—
343#481—32no—
344#481—32no—
345#480—32no—
346#479—32no—
347#479—32no—
348#479—32no—
349#478—32no—
350#478—32no—
351#478—32no—
352#478—32no—
353#478—32no—
354#476—31no—
355#476—31no—
356#476—32no—
357#476—32no—
358#476C2×D312yescomplemented
359#475—32no—
360#475C2×D312yescomplemented
361#474—32no—
362#469—32no—
363#468—32no—
364#466—32no—
365#465—32no—
366#465C2×D312yes—
367#465C2×D312yes—
368#463—32no—
369#463—32no—
370#461C2×D312yescomplemented
371#460C2×D312yescomplemented
372#459—31no—
373#459—31no—
374#449—32no—
375#449—32no—
376#447—32no—
377#446—32no—
378#442—32no—
379#442—32no—
380#442—32no—
381#440—32no—
382C4×SD16—32no—
383C4×D8—32no—
384#435—32no—
385#435—32no—
386C8×D4—32no—
387#433—32no—
388#432—31no—
389#428—32no—
390C2×#107—31no—
391C2×#106—31no—
392C2×#106—32no—
393#424—32no—
394C2×C4⋊C8C2×D311yescharacteristic
395#417—32no—
396#416—32no—
397C2×#102—31no—
398C2×#102—31no—
399C23×D3—21no—
400C3×#41—82no—
401C2×C3×Q8—21no—
402C2×C3×Q8—21no—
403C2×C3×Q8C2412yes—
404C2×C3×D4—22no—
405C2×C3×D4—21no—
406C2×C3×D4—21no—
407C2×C3×D4C2412yes—
408C22×C3×C4—22no—
409C22×C3×C4C2×D411yescharacteristic
410C22×C3×C4C2×D411yescharacteristic
411C22×C3×C4C2411yescharacteristic
412C2×#67—22no—
413C2×#67—22no—
414C2×#67C2×D412yes—
415C22×Dic3—21no—
416C22×Dic3—21no—
417C22×Dic3—21no—
418C22×Dic3—22no—
419C22×Dic3—22no—
420#239—24no—
421#239—42no—
422#239—82no—
423D3×Q8—82no—
424#237—84no—
425C2×D12—22no—
426C2×D12—22no—
427C2×D12—21no—
428C2×D12—22no—
429C2×D12—41no—
430C2×D12C2×D411yescharacteristic
431C2×D12C2411yescharacteristic
432C2×D12C2411yescharacteristic
433C2×C4×D3—21no—
434C2×C4×D3—21no—
435C2×C4×D3—22no—
436C2×C4×D3—22no—
437C2×C4×D3—22no—
438C2×C4×D3—21no—
439C2×C4×D3—21no—
440C2×C4×D3—22no—
441C2×C4×D3—82no—
442C2×C4×D3C2412yes—
443C2×Dic6—22no—
444C2×Dic6—22no—
445C2×Dic6C2×D411yescharacteristic
446C3×SD16—42no—
447C3×SD16—42no—
448C2×C3×C8—41no—
449C2×C3×C8—41no—
450C2×C3×C8C2412yes—
451C2×C3×C8C2412yes—
452C3×C4⋊C4—21no—
453C3×C4⋊C4—22no—
454C3×C4⋊C4—21no—
455C3×C4⋊C4—22no—
456C3×C4⋊C4—21no—
457C3×C4⋊C4—21no—
458C3×C4⋊C4C2412yes—
459C3×C4⋊C4C2412yes—
460C3×C22⋊C4—22no—
461C3×C22⋊C4—22no—
462C3×C22⋊C4—22no—
463C3×C42—22no—
464C3×C42C2×D411yescharacteristic
465C3×C42C2×D411yescharacteristic
466C3×C42C2411yescharacteristic
467C3×C42C2411yescharacteristic
468#217—22no—
469#217—22no—
470#217—22no—
471#217—22no—
472#217C2×D412yes—
473#213—24no—
474#213—42no—
475(C2×D3)⋊C4—22no—
476(C2×D3)⋊C4—22no—
477(C2×D3)⋊C4—21no—
478(C2×D3)⋊C4—21no—
479(C2×D3)⋊C4—21no—
480(C2×D3)⋊C4—21no—
481(C2×D3)⋊C4—22no—
482(C2×D3)⋊C4—22no—
483(C2×D3)⋊C4—22no—
484(C2×D3)⋊C4—22no—
485(C2×D3)⋊C4C2×D412yes—
486(C2×D3)⋊C4C2×D412yes—
487(C2×D3)⋊C4C2×D412yes—
488(C2×D3)⋊C4C2×D412yes—
489C4⋊Dic3—21no—
490C4⋊Dic3—21no—
491C4⋊Dic3—21no—
492C4⋊Dic3—22no—
493C4⋊Dic3—22no—
494C4⋊Dic3C2×D411yescharacteristic
495C4⋊Dic3C2×D411yescharacteristic
496C4⋊Dic3C2412yes—
497C4⋊Dic3C2411yescharacteristic
498C4⋊Dic3C2411yescharacteristic
499C4⋊Dic3C2412yes—
500Dic3⋊C4—22no—
501Dic3⋊C4—22no—
502Dic3⋊C4—22no—
503Dic3⋊C4—22no—
504Dic3⋊C4—22no—
505Dic3⋊C4—22no—
506Dic3⋊C4—22no—
507Dic3⋊C4—22no—
508Dic3⋊C4—22no—
509Dic3⋊C4—22no—
510Dic3⋊C4C2×D412yes—
511Dic3⋊C4C2×D412yes—
512Dic3⋊C4C2×D412yes—
513Dic3⋊C4C2×D412yes—
514C4×Dic3—22no—
515C4×Dic3—22no—
516C4×Dic3C2412yes—
517C2×C3⋊C8C2412yes—
518C2×C3⋊C8C2412yes—
519ΓL(1,𝔽25)—42no—
520D3×C8—42no—
521C2×#41—21no—
522C2×#41—32no—
523C2×#41—62no—
524C2×#41—61no—
525C22×Q8—61no—
526C22×D4—31no—
527C23×C4—61no—
528C2×SD16C22×D312yes—
529C2×SD16C22×D312yes—
530C2×D8—32no—
531C2×D8—32no—
532C2×M16—32no—
533C22×C8—32no—
534C22×C8C22×D311yescharacteristic
535C22×C8C22×D311yescharacteristic
536C4⋊Q8—32no—
537C4⋊Q8—32no—
538C4⋊Q8—62no—
539C4⋊Q8C22×D311yescharacteristic
540C4⋊Q8C22×D311yescharacteristic
541C4⋊Q8C22×D311yescharacteristic
542#127C22×D311yescharacteristic
543#126—32no—
544#126—62no—
545#126—62no—
546#126—62no—
547#126—62no—
548#125—21no—
549#125—32no—
550#125—31no—
551#125—32no—
552#125—32no—
553#125—62no—
554#125—62no—
555#125—61no—
556#125—61no—
557#124—21no—
558#124—32no—
559#124—31no—
560#124—62no—
561#123—32no—
562#123—62no—
563#123—62no—
564#123—62no—
565#123—62no—
566#123—62no—
567#123—62no—
568#123—62no—
569#123—62no—
570#123—62no—
571#123—62no—
572C22⋊Q8—21no—
573C22⋊Q8—31no—
574C22⋊Q8—32no—
575C22⋊Q8—62no—
576C22⋊Q8—62no—
577C22⋊Q8—62no—
578C22⋊Q8—62no—
579C22⋊Q8—62no—
580C22⋊Q8—62no—
581C22⋊Q8—62no—
582C22⋊Q8—62no—
583C22⋊Q8—62no—
584C22⋊Q8—61no—
585C22⋊Q8—62no—
586C22⋊Q8—61no—
587C22⋊Q8—61no—
588C22⋊Q8C22×D312yes—
589#121—21no—
590#121—31no—
591#121—32no—
592#121—32no—
593#121—32no—
594#121—62no—
595#121—62no—
596#121—62no—
597#121—62no—
598#121—61no—
599#121—62no—
600#121C22×D312yes—
601#120—62no—
602C4×Q8—21no—
603C4×Q8—31no—
604C4×Q8—32no—
605C4×Q8C22×D312yes—
606C4×D4—21no—
607C4×D4—32no—
608C4×D4—32no—
609C4×D4—32no—
610C4×D4—32no—
611C4×D4—31no—
612C4×D4—31no—
613C4×D4—31no—
614C4×D4—31no—
615C4×D4—31no—
616C4×D4—62no—
617C4×D4—62no—
618C4×D4—62no—
619C4×D4—62no—
620C4×D4—62no—
621C4×D4—61no—
622C4×D4—61no—
623C4×D4C22×D312yes—
624#117—21no—
625#117—32no—
626#117—32no—
627#117—62no—
628#117—61no—
629C2×C4⋊C4—31no—
630C2×C4⋊C4—31no—
631C2×C4⋊C4—31no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—32no—
634C2×C4⋊C4—62no—
635C2×C4⋊C4—61no—
636C2×C4⋊C4—62no—
637C2×C4⋊C4—61no—
638C2×C4⋊C4—61no—
639C2×C22⋊C4—62no—
640C2×C22⋊C4—61no—
641C2×C42C22×D311yescharacteristic
642#107—32no—
643#107—32no—
644#107—32no—
645#107—32no—
646#106—32no—
647#106—32no—
648#106—32no—
649#106—32no—
650#106—32no—
651#106—32no—
652#106C22×D312yes—
653#106C22×D312yes—
654C4⋊C8—32no—
655C4⋊C8—32no—
656C4⋊C8—31no—
657C4⋊C8—31no—
658C4⋊C8C22×D312yes—
659C4⋊C8C22×D312yes—
660#103—32no—
661#103—32no—
662#103—32no—
663#103—32no—
664#103C22×D312yes—
665#103C22×D312yes—
666#102—32no—
667#102—32no—
668#102—32no—
669#102—32no—
670#102—32no—
671#102—32no—
672#102—32no—
673#102—32no—
674#102C22×D312yes—
675#102C22×D312yes—
676C22⋊C8—32no—
677C22⋊C8—32no—
678C22⋊C8—32no—
679#97—32no—
680#97—32no—
681C4×C8—32no—
682C23×C3—22no—
683C23×C3C22×D411yescharacteristic
684C22×D3—21no—
685C22×D3—21no—
686C22×D3—42no—
687C22×D3—42no—
688C22×D3—81no—
689C22×D3C22×D412yes—
690C3×Q8—22no—
691C3×Q8—22no—
692C3×Q8—42no—
693C3×Q8—81no—
694C3×D4—22no—
695C3×D4—22no—
696C3×D4—44no—
697C3×D4—81no—
698C3×D4—81no—
699C2×C3×C4—22no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—22no—
703C2×C3×C4—22no—
704C2×C3×C4—22no—
705C2×C3×C4—41no—
706C2×C3×C4—82no—
707C2×C3×C4C22×D411yescharacteristic
708C2×C3×C4C22×D411yescharacteristic
709C2×C3×C4C22×D411yescharacteristic
710C2×C3×C4C22×D411yescharacteristic
711C2×C3×C4C22×D411yescharacteristic
712C2×C3×C4C2511yescharacteristic
713#67—24no—
714#67—82no—
715#67—82no—
716C2×Dic3—21no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—21no—
720C2×Dic3—42no—
721C2×Dic3—82no—
722C2×Dic3—82no—
723C2×Dic3—81no—
724C2×Dic3—81no—
725C2×Dic3C22×D412yes—
726C2×Dic3C22×D412yes—
727C2×Dic3C22×D412yes—
728D12—21no—
729D12—21no—
730D12—21no—
731D12—41no—
732D12—42no—
733D12—44no—
734D12—82no—
735D122−1+412yes—
736C4×D3—22no—
737C4×D3—22no—
738C4×D3—44no—
739C4×D3—42no—
740C4×D3—42no—
741C4×D3—82no—
742C4×D3—81no—
743C4×D3—81no—
744C4×D3—82no—
745C4×D3—82no—
746Dic6—41no—
747Dic6—82no—
748Dic6—82no—
749C3×C8—22no—
750C3×C8—22no—
751C3⋊C8—22no—
752C3⋊C8—22no—
753C24—61no—
754#41—64no—
755#41—82no—
756#41—122no—
757#41—244no—
758#41—242no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—31no—
762C2×Q8—62no—
763C2×Q8—62no—
764C2×Q8—242no—
765C2×Q8C23×D312yes—
766C2×D4—22no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—32no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—31no—
773C2×D4—62no—
774C2×D4—62no—
775C2×D4—62no—
776C2×D4—62no—
777C2×D4—62no—
778C2×D4—61no—
779C2×D4—121no—
780C2×D4C23×D312yes—
781C22×C4—22no—
782C22×C4—32no—
783C22×C4—62no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—62no—
788C22×C4—62no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—242no—
797C22×C4D3×D411yescharacteristic
798C22×C4D3×D411yescharacteristic
799C22×C4C23×D311yescharacteristic
800SD16—42no—
801SD16—42no—
802D8—64no—
803D8—122no—
804M16—122no—
805C2×C8—32no—
806C2×C8—32no—
807C2×C8—41no—
808C2×C8—41no—
809C2×C8—122no—
810C2×C8C23×D312yes—
811C2×C8C23×D312yes—
812C4⋊C4—21no—
813C4⋊C4—22no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—22no—
818C4⋊C4—32no—
819C4⋊C4—31no—
820C4⋊C4—32no—
821C4⋊C4—32no—
822C4⋊C4—31no—
823C4⋊C4—32no—
824C4⋊C4—32no—
825C4⋊C4—32no—
826C4⋊C4—31no—
827C4⋊C4—31no—
828C4⋊C4—62no—
829C4⋊C4—62no—
830C4⋊C4—62no—
831C4⋊C4—62no—
832C4⋊C4—62no—
833C4⋊C4—62no—
834C4⋊C4—62no—
835C4⋊C4—62no—
836C4⋊C4—61no—
837C4⋊C4—61no—
838C4⋊C4—61no—
839C4⋊C4—62no—
840C4⋊C4—62no—
841C4⋊C4—62no—
842C4⋊C4—62no—
843C4⋊C4C23×D312yes—
844C4⋊C4C23×D312yes—
845C22⋊C4—22no—
846C22⋊C4—22no—
847C22⋊C4—22no—
848C22⋊C4—32no—
849C22⋊C4—32no—
850C22⋊C4—32no—
851C22⋊C4—32no—
852C22⋊C4—32no—
853C22⋊C4—62no—
854C22⋊C4—62no—
855C22⋊C4—62no—
856C22⋊C4—62no—
857C22⋊C4—62no—
858C22⋊C4—62no—
859C22⋊C4—62no—
860C22⋊C4—62no—
861C22⋊C4—62no—
862C22⋊C4—62no—
863C22⋊C4—61no—
864C22⋊C4—61no—
865C22⋊C4—61no—
866C22⋊C4—61no—
867C42—22no—
868C42—32no—
869C42—62no—
870C42—62no—
871C42D3×D411yescharacteristic
872C42D3×D411yescharacteristic
873C42C23×D311yescharacteristic
874C42C23×D311yescharacteristic
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—42no—
878C22×C3—42no—
879C22×C3—42no—
880C22×C3#57712yes—
881C22×C3C23×D411yescharacteristic
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—41no—
887C2×D3—41no—
888C2×D3—41no—
889C2×D3—41no—
890C2×D3—41no—
891C2×D3—84no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—42no—
898C3×C4—42no—
899C3×C4—42no—
900C3×C4C2×2−1+411yescharacteristic
901C3×C4#58511yescharacteristic
902Dic3—22no—
903Dic3—22no—
904Dic3—22no—
905Dic3—41no—
906Dic3—41no—
907Dic3—42no—
908Dic3—42no—
909C23—22no—
910C23—32no—
911C23—61no—
912C23—61no—
913C23—122no—
914C23—122no—
915C23—241no—
916C23C2×D3×D411yescharacteristic
917Q8—22no—
918Q8—22no—
919Q8—42no—
920Q8—81no—
921Q8—121no—
922Q8—242no—
923Q8—242no—
924D4—22no—
925D4—22no—
926D4—32no—
927D4—44no—
928D4—64no—
929D4—61no—
930D4—61no—
931D4—61no—
932D4—81no—
933D4—81no—
934D4—121no—
935D4—122no—
936D4—124no—
937D4—242no—
938D4—242no—
939D4—242no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—32no—
947C2×C4—32no—
948C2×C4—32no—
949C2×C4—41no—
950C2×C4—62no—
951C2×C4—62no—
952C2×C4—61no—
953C2×C4—62no—
954C2×C4—61no—
955C2×C4—62no—
956C2×C4—82no—
957C2×C4—122no—
958C2×C4—122no—
959C2×C4—124no—
960C2×C4—122no—
961C2×C4—241no—
962C2×C4—241no—
963C2×C4—242no—
964C2×C4—242no—
965C2×C4—242no—
966C2×C4—242no—
967C2×C4—242no—
968C2×C4—241no—
969C2×C4—241no—
970C2×C4C2×D3×D411yescharacteristic
971C2×C4C2×D3×D411yescharacteristic
972C2×C4C2×D3×D411yescharacteristic
973C2×C4C2×D3×D411yescharacteristic
974C2×C4C2×D3×D411yescharacteristic
975C2×C4C24×D311yescharacteristic
976C8—22no—
977C8—22no—
978C8—62no—
979C8—62no—
980C2×C3—22no—
981C2×C3—82no—
982C2×C3#348911yescharacteristic
983C2×C3C2×#57711yescharacteristic
984C2×C3#358511yescharacteristic
985D3—42no—
986D3—42no—
987D3—81no—
988C22—21no—
989C22—21no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—121no—
998C22—121no—
999C22—121no—
1000C22—121no—
1001C22—121no—
1002C22—244no—
1003C22#576212yes—
1004C22C22×D3×D411yescharacteristic
1005C4—21no—
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—21no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—62no—
1014C4—62no—
1015C4—62no—
1016C4—122no—
1017C4—121no—
1018C4—121no—
1019C4—122no—
1020C4#596611yescharacteristic
1021C4D3×2−1+411yescharacteristic
1022C3#6216611yescharacteristic, complemented, Sylow
1023C2—22no—
1024C2—82no—
1025C2—122no—
1026C2—122no—
1027C2—241no—
1028C2#8638011yescharacteristic
1029C2C2×#576211yescharacteristic
1030C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3246C2
socleC22×C3C23×D4
hypercenter#3246D3
hypocenterC3#62166
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3246

Complements

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

NH ≅ G/Ntype
1. #86285C2semidirect
2. #86233C2semidirect
3. C3×#3246C2semidirect
4. #83326C2semidirect
5. #83300C2semidirect
6. #81083C2semidirect
7. #81055C2semidirect
8. #81020C2semidirect
9. #81014C2semidirect
10. #80683C2semidirect
11. #80681C2semidirect
12. #80652C2semidirect
13. #80648C2semidirect
14. #80452C2semidirect
15. #80419C2semidirect
16. #80403C2semidirect
17. #80364C2semidirect
18. C2×#4847C2semidirect
19. #79016C2semidirect
25. #5729C22semidirect
29. #5719C22semidirect
46. #5558C22semidirect
47. #5539C22semidirect
52. C3×#476C22semidirect
53. C3×#475C22semidirect
56. C3×#461C22semidirect
57. C3×#460C22semidirect
59. #5174C22semidirect
62. #5171C22semidirect
65. #5164C22semidirect
66. Dic3×SD16C22semidirect
75. #5082C22semidirect
76. #5081C22semidirect
83. #5022C22semidirect
84. #5022C22semidirect
92. #4861C22semidirect
93. D3×#106C22semidirect
94. #4856C22semidirect
95. #4855C22semidirect
100. #4840C22semidirect
101. #4839C22semidirect
102. #4836C22semidirect
103. #4828C22semidirect
104. #4814C22semidirect
105. #4805C22semidirect
109. #4796C22semidirect
111. #4791C22semidirect
114. #4777C22semidirect
116. #4774C22semidirect
117. #4761C22semidirect
118. #4759C22semidirect
131. #3246D3semidirect
358. #476C2×D3semidirect
360. #475C2×D3semidirect
370. #461C2×D3semidirect
371. #460C2×D3semidirect
1022. C3#62166semidirect

Maximal subgroups

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

subgroupindex
#862852
#862332
C3×#32462
#833262
#833002
#810832
#810552
#810202
#810142
#806832
#806812
#806522
#806482
#804522
#804192
#804032
#803642
C2×#48472
#790162
#621663