Finite Group Databasebeta

← #11692185

Subgroups — #11692185

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#86233C211yesmaximal, characteristic, complemented
2#85767C211yesmaximal, characteristic, complemented
3C3×#3109C211yesmaximal, characteristic, complemented
4#83320C211yesmaximal, characteristic, complemented
5C2×#5009C211yesmaximal, characteristic, complemented
6#81322C212yesmaximal, complemented
7#81320C212yesmaximal, complemented
8#81069C212yesmaximal, complemented
9#81063C212yesmaximal, complemented
10#80346C212yesmaximal, complemented
11#80316C212yesmaximal, complemented
12#80016C212yesmaximal, complemented
13#80015C212yesmaximal, complemented
14#79884C212yesmaximal, complemented
15#79881C212yesmaximal, complemented
16#79855C212yesmaximal, complemented
17#79854C212yesmaximal, complemented
18#79341C211yesmaximal, characteristic, complemented
19#79320C211yesmaximal, characteristic, complemented
20#62166—31nomaximal, Sylow
21C3×#532C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23#5824—22no—
24#5806C2212yes—
25#5791—21no—
26C2×#924—21no—
27#5729C2212yescomplemented
28#5719C2212yescomplemented
29#5684—21no—
30#5672—21no—
31#5618C2212yes—
32#5611C2212yes—
33#5602—21no—
34#5597—21no—
35#5564—22no—
36#5564—22no—
37#5561C2212yes—
38#5558C2212yescomplemented
39#5555C2211yescharacteristic
40#5552—21no—
41#5551C2211yescharacteristic
42#5546C2212yes—
43#5542C2211yescharacteristic
44#5541—21no—
45#5539C2212yescomplemented
46D4×Dic6C2211yescharacteristic
47#5511C2212yes—
48#5495—22no—
49#5479C2211yescharacteristic
50#5470C2211yescharacteristic
51C2×#870C2211yescharacteristic
52C3×#481C2212yes—
53C3×#476C2211yescharacteristic
54C3×#476C2211yescharacteristic
55C3×#459C2211yescharacteristic
56C3×#459C2211yescharacteristic
57C3×#447C2212yes—
58C3×#442C2212yes—
59C3×#442C2212yes—
60C3×#432C2211yescharacteristic
61C2×#832C2211yescharacteristic
62C2×#832C2211yescharacteristic
63#5159C2212yes—
64#5158C2212yes—
65#5158C2212yes—
66#5157C2212yes—
67#5153C2212yes—
68#5153C2212yes—
69#5152C2212yes—
70Dic3×D8C2212yes—
71#5094C2212yescomplemented
72#5075C2212yescomplemented
73#5041C2212yes—
74#5041C2212yes—
75#5019C2212yescomplemented
76#5009C2212yes—
77#5009C2212yes—
78#5009C2212yes—
79#5009C2212yes—
80#5008C2212yescomplemented
81C2×#808C2211yescharacteristic
82C2×#807C2211yescharacteristic
83C2×C4⋊(C3⋊C8)C2211yescharacteristic
84#4868C2212yescomplemented
85#4862C2212yescomplemented
86#4861C2212yescomplemented
87D3×#106C2212yescomplemented
88#4857C2212yescomplemented
89#4856C2212yescomplemented
90#4855C2212yescomplemented
91#4854C2212yescomplemented
92#4840C2212yescomplemented
93#4839C2212yescomplemented
94#4829C2212yescomplemented
95#4829C2212yescomplemented
96#4784C2212yes—
97#4780C2212yescomplemented
98#4778C2212yescomplemented
99#4777C2212yes—
100#4777C2212yescomplemented
101#4774C2212yescomplemented
102#4772C2212yes—
103#4771C2212yes—
104#4768C2212yes—
105#4766C2212yes—
106#4765C2212yes—
107#4761C2212yes—
108#4761C2212yescomplemented
109#4759C2212yescomplemented
110#4758C2212yescomplemented
111#4757C2212yescomplemented
112#4730C2212yes—
113#67⋊C8C2212yes—
114#4722C2212yes—
115#4721C2212yes—
116#4706C2212yescomplemented
117#4703C2212yescomplemented
118#4702C2212yescomplemented
119#4701C2212yescomplemented
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#3246—31no—
132#3244—32no—
133#3236—31no—
134#3119—32no—
135#3109D311yescharacteristic, complemented
136#3084—32no—
137C2×#478—31no—
138#2992—31no—
139C2×C3×#41—21no—
140C22×C3×D4C2311yescharacteristic
141C23×C3×C4—21no—
142C2×#237—22no—
143C2×#237C2312yes—
144C2×#235—21no—
145C22×Dic6—21no—
146C2×C3×D8C2312yes—
147C2×C3×D8C2312yes—
148C3×C4⋊Q8C2311yescharacteristic
149C3×#127C2311yescharacteristic
150C3×#124—21no—
151C3×#121—21no—
152C3×#121C2312yes—
153C3×C4×D4—21no—
154C3×C4×D4—21no—
155C3×C4×D4—21no—
156C3×C4×D4C2312yes—
157C3×C4×D4C2311yescharacteristic
158C3×C4×D4C2311yescharacteristic
159C3×C4×D4C2311yescharacteristic
160C3×C4×D4C2311yescharacteristic
161C2×C3×C4⋊C4C2311yescharacteristic
162C2×C3×C22⋊C4—21no—
163C2×C3×C42C2311yescharacteristic
164#953—22no—
165C2×#217—22no—
166#946—22no—
167#944—22no—
168#939—22no—
169#939—22no—
170#939—22no—
171#939—22no—
172#938C2312yes—
173#938C2312yes—
174#938C2312yes—
175#936C2312yes—
176#935—22no—
177#935—22no—
178#935—22no—
179#935—22no—
180D4×Dic3—22no—
181D4×Dic3C2312yes—
182D4×Dic3C2312yes—
183D4×Dic3C2312yes—
184C2×#214C2312yes—
185C2×#214C2312yes—
186#930—21no—
187#930D411yescharacteristic
188#929—22no—
189#929—22no—
190#929D412yes—
191C4×#67—22no—
192C4×#67—22no—
193C4×#67—22no—
194C4×#67C2312yes—
195#926—21no—
196#926—21no—
197C2×C4⋊Dic3—21no—
198C2×C4⋊Dic3C2311yescharacteristic
199C2×C4⋊Dic3C2311yescharacteristic
200#924—21no—
201#924—21no—
202#924—22no—
203#924—21no—
204#924—21no—
205#924—22no—
206#924—22no—
207#924D411yescharacteristic
208#924C2312yes—
209C2×Dic3⋊C4—21no—
210C2×Dic3⋊C4—21no—
211C2×Dic3⋊C4—22no—
212C2×Dic3⋊C4—22no—
213C22×C3⋊C8C2311yescharacteristic
214C22×C3⋊C8C2311yescharacteristic
215C2×ΓL(1,𝔽25)C2312yes—
216C2×D3×C8C2312yes—
217#897C2312yes—
218#896—22no—
219#896—22no—
220#892C2312yes—
221D3×C4⋊C4C2312yes—
222D3×C4⋊C4C2312yes—
223#890C2312yes—
224#889—22no—
225#889—22no—
226#888C2312yes—
227#888C2312yes—
228#887C2312yes—
229#886—22no—
230#886—22no—
231#885—22no—
232#884—22no—
233#883—22no—
234#883—22no—
235#67⋊C4—22no—
236#879—22no—
237#879—22no—
238#879—22no—
239#879—22no—
240#878—22no—
241#878—22no—
242#878—22no—
243#878—22no—
244#877—22no—
245#876D412yes—
246#875D411yescharacteristic
247C4×D12C2311yescharacteristic
248#872C2312yes—
249#870—21no—
250#870—21no—
251#870—21no—
252#870D411yescharacteristic
253#870C2312yes—
254#870C2312yes—
255#869C2311yescharacteristic
256#869C2311yescharacteristic
257C4×Dic6—21no—
258C4×Dic6C2312yes—
259C4×Dic6C2311yescharacteristic
260C3×#106C2312yes—
261C3×#106C2312yes—
262C3×C4⋊C8C2311yescharacteristic
263C3×C4⋊C8C2311yescharacteristic
264C3×#102C2312yes—
265C3×#102C2312yes—
266C3×#102C2312yes—
267C3×#102C2312yes—
268C3×C22⋊C8C2312yes—
269C3×#97C2312yes—
270#832C2312yes—
271#832C2312yes—
272#832C2312yes—
273#832C2312yes—
274#832C2312yes—
275#832C2312yes—
276(C2×D3)⋊C8C2312yes—
277(C2×D3)⋊C8C2312yes—
278#818C2312yes—
279#818C2312yes—
280#817C2312yes—
281#817C2312yes—
282#816C2312yes—
283#816C2312yes—
284#816C2312yes—
285#816C2312yes—
286#815C2312yes—
287Dic3⋊C8C2312yes—
288Dic3⋊C8C2312yes—
289C8×Dic3C2312yes—
290#810C2312yes—
291#810C2312yes—
292#808C2312yes—
293#808C2312yes—
294#808C2312yes—
295#808C2312yes—
296#807C2312yes—
297#807C2312yes—
298C4⋊(C3⋊C8)C2312yes—
299C4⋊(C3⋊C8)C2312yes—
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—32no—
312#547—31no—
313#547—31no—
314#547—62no—
315#546—32no—
316#544—32no—
317#542—32no—
318#540—32no—
319#539—62no—
320#539—62no—
321#539—61no—
322#537—61no—
323#533—31no—
324#532C2×D311yescharacteristic
325#529—31no—
326C2×#125—31no—
327#525—61no—
328C2×C22⋊Q8—61no—
329#520—32no—
330C2×C4×D4C2×D311yescharacteristic
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#481C2×D312yes—
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—32no—
355#476—32no—
356#476—32no—
357#476C2×D311yescharacteristic
358#476C2×D311yescharacteristic
359#475—32no—
360#475—32no—
361#474—32no—
362#469—32no—
363#468—32no—
364#466—32no—
365#465—32no—
366#465—32no—
367#465—32no—
368#463—32no—
369#463—32no—
370#461—32no—
371#460—32no—
372#459C2×D311yescharacteristic
373#459C2×D311yescharacteristic
374#449—32no—
375#449—32no—
376#447C2×D312yes—
377#446—32no—
378#442—32no—
379#442C2×D312yes—
380#442C2×D312yes—
381#440—32no—
382C4×SD16—32no—
383C4×D8—32no—
384#435—32no—
385#435—32no—
386C8×D4—32no—
387#433—32no—
388#432C2×D311yescharacteristic
389#428—32no—
390C2×#107—31no—
391C2×#106—31no—
392C2×#106—32no—
393#424—32no—
394C2×C4⋊C8—31no—
395#417—32no—
396#416—32no—
397C2×#102—31no—
398C2×#102—31no—
399C24×C3—21no—
400C3×#41—82no—
401C2×C3×Q8—21no—
402C2×C3×D4—22no—
403C2×C3×D4—22no—
404C2×C3×D4—21no—
405C2×C3×D4—21no—
406C2×C3×D4—21no—
407C2×C3×D4—41no—
408C2×C3×D4C2411yescharacteristic
409C2×C3×D4C2412yes—
410C2×C3×D4C2411yescharacteristic
411C22×C3×C4—21no—
412C22×C3×C4—21no—
413C22×C3×C4—21no—
414C22×C3×C4—21no—
415C22×C3×C4—22no—
416C22×C3×C4—21no—
417C22×C3×C4—82no—
418C22×C3×C4C2×D411yescharacteristic
419C22×C3×C4C2×D411yescharacteristic
420C22×C3×C4C2411yescharacteristic
421C2×#67—22no—
422C2×#67—22no—
423C2×#67—22no—
424C2×#67—22no—
425C2×#67C2×D412yes—
426C22×Dic3—21no—
427C22×Dic3—21no—
428C22×Dic3—22no—
429C22×Dic3—22no—
430C22×Dic3—22no—
431C22×Dic3—22no—
432#237—24no—
433#237—42no—
434#237—84no—
435#235—82no—
436C2×D12C2×D411yescharacteristic
437C2×C4×D3—22no—
438C2×C4×D3—22no—
439C2×C4×D3C2412yes—
440C2×Dic6—21no—
441C2×Dic6—22no—
442C2×Dic6—22no—
443C2×Dic6—82no—
444C2×Dic6C2×D411yescharacteristic
445C2×Dic6C2412yes—
446C3×D8—24no—
447C3×D8—42no—
448C2×C3×C8C2412yes—
449C2×C3×C8C2412yes—
450C3×C4⋊C4—21no—
451C3×C4⋊C4—21no—
452C3×C4⋊C4C2411yescharacteristic
453C3×C4⋊C4C2411yescharacteristic
454C3×C4⋊C4C2412yes—
455C3×C22⋊C4—21no—
456C3×C22⋊C4—22no—
457C3×C22⋊C4—21no—
458C3×C22⋊C4—22no—
459C3×C22⋊C4—21no—
460C3×C22⋊C4—21no—
461C3×C42C2×D411yescharacteristic
462C3×C42C2×D411yescharacteristic
463C3×C42C2411yescharacteristic
464C3×C42C2411yescharacteristic
465#217—22no—
466#217—22no—
467#217—22no—
468#217—22no—
469#217—22no—
470#217—22no—
471#217—22no—
472#217—22no—
473#217—22no—
474#217C2×D412yes—
475#214—42no—
476#214—42no—
477(C2×D3)⋊C4—22no—
478(C2×D3)⋊C4—22no—
479(C2×D3)⋊C4C2×D412yes—
480(C2×D3)⋊C4C2×D412yes—
481(C2×D3)⋊C4C2×D412yes—
482(C2×D3)⋊C4C2×D412yes—
483C4⋊Dic3—21no—
484C4⋊Dic3—21no—
485C4⋊Dic3—21no—
486C4⋊Dic3—21no—
487C4⋊Dic3—21no—
488C4⋊Dic3—22no—
489C4⋊Dic3—22no—
490C4⋊Dic3C2×D411yescharacteristic
491C4⋊Dic3C2×D411yescharacteristic
492C4⋊Dic3C2412yes—
493C4⋊Dic3C2412yes—
494C4⋊Dic3C2412yes—
495Dic3⋊C4—22no—
496Dic3⋊C4—22no—
497Dic3⋊C4—22no—
498Dic3⋊C4—22no—
499Dic3⋊C4—22no—
500Dic3⋊C4—22no—
501Dic3⋊C4—22no—
502Dic3⋊C4—22no—
503Dic3⋊C4—22no—
504Dic3⋊C4—22no—
505Dic3⋊C4—22no—
506Dic3⋊C4—22no—
507Dic3⋊C4C2×D412yes—
508Dic3⋊C4C2×D412yes—
509Dic3⋊C4C2×D412yes—
510Dic3⋊C4C2×D412yes—
511C4×Dic3—22no—
512C4×Dic3—22no—
513C4×Dic3—22no—
514C4×Dic3C2412yes—
515C2×C3⋊C8—41no—
516C2×C3⋊C8—41no—
517C2×C3⋊C8C2412yes—
518C2×C3⋊C8C2412yes—
519ΓL(1,𝔽25)—42no—
520D3×C8—42no—
521C2×#41—21no—
522C2×#41—32no—
523C2×#41—61no—
524C2×#41—62no—
525C22×Q8—61no—
526C22×D4C22×D311yescharacteristic
527C23×C4—21no—
528C2×SD16—32no—
529C2×SD16—32no—
530C2×D8C22×D312yes—
531C2×D8C22×D312yes—
532C2×M16—32no—
533C22×C8—31no—
534C22×C8—31no—
535C22×C8—32no—
536C4⋊Q8—32no—
537C4⋊Q8—32no—
538C4⋊Q8—31no—
539C4⋊Q8—31no—
540C4⋊Q8—62no—
541C4⋊Q8C22×D311yescharacteristic
542#127C22×D311yescharacteristic
543#126—32no—
544#126—62no—
545#126—62no—
546#126—62no—
547#126—62no—
548#125—32no—
549#125—31no—
550#125—32no—
551#125—32no—
552#125—62no—
553#125—62no—
554#125—61no—
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—31no—
573C22⋊Q8—32no—
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—61no—
586C22⋊Q8—62no—
587C22⋊Q8—61no—
588C22⋊Q8—61no—
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—31no—
603C4×Q8—32no—
604C4×Q8—32no—
605C4×Q8—61no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—32no—
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—32no—
613C4×D4—31no—
614C4×D4—62no—
615C4×D4—62no—
616C4×D4—62no—
617C4×D4—62no—
618C4×D4—62no—
619C4×D4C22×D311yescharacteristic
620C4×D4C22×D311yescharacteristic
621C4×D4C22×D311yescharacteristic
622C4×D4C22×D311yescharacteristic
623C4×D4C22×D312yes—
624#117—32no—
625#117—32no—
626#117—62no—
627#117—61no—
628#117—61no—
629C2×C4⋊C4—31no—
630C2×C4⋊C4—31no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—62no—
634C2×C4⋊C4—61no—
635C2×C4⋊C4—62no—
636C2×C4⋊C4—61no—
637C2×C4⋊C4—61no—
638C2×C4⋊C4C22×D311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—62no—
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—32no—
657C4⋊C8—32no—
658C4⋊C8C22×D311yescharacteristic
659C4⋊C8C22×D311yescharacteristic
660#103—32no—
661#103—32no—
662#103—32no—
663#103—32no—
664#103—32no—
665#103—32no—
666#102—32no—
667#102—32no—
668#102—32no—
669#102—32no—
670#102—32no—
671#102—32no—
672#102C22×D312yes—
673#102C22×D312yes—
674#102C22×D312yes—
675#102C22×D312yes—
676C22⋊C8—32no—
677C22⋊C8—32no—
678C22⋊C8C22×D312yes—
679#97—32no—
680#97C22×D312yes—
681C4×C8—32no—
682C23×C3—21no—
683C23×C3—21no—
684C23×C3—22no—
685C23×C3—42no—
686C23×C3—42no—
687C23×C3—81no—
688C23×C3C22×D411yescharacteristic
689C22×D3C22×D412yes—
690C3×Q8—81no—
691C3×D4—22no—
692C3×D4—21no—
693C3×D4—21no—
694C3×D4—22no—
695C3×D4—21no—
696C3×D4—42no—
697C3×D4—44no—
698C3×D4—81no—
699C3×D4—81no—
700C3×D42−1+412yes—
701C2×C3×C4—22no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—22no—
706C2×C3×C4—21no—
707C2×C3×C4—41no—
708C2×C3×C4—42no—
709C2×C3×C4—42no—
710C2×C3×C4—81no—
711C2×C3×C4—81no—
712C2×C3×C4—82no—
713C2×C3×C4—81no—
714C2×C3×C4C22×D411yescharacteristic
715C2×C3×C4C22×D411yescharacteristic
716C2×C3×C4C22×D411yescharacteristic
717C2×C3×C4C22×D411yescharacteristic
718C2×C3×C4C22×D411yescharacteristic
719C2×C3×C4C2511yescharacteristic
720#67—24no—
721#67—44no—
722#67—82no—
723#67—82no—
724#67—82no—
725C2×Dic3—22no—
726C2×Dic3—22no—
727C2×Dic3—22no—
728C2×Dic3—22no—
729C2×Dic3—44no—
730C2×Dic3—42no—
731C2×Dic3—82no—
732C2×Dic3—82no—
733C2×Dic3—82no—
734C2×Dic3—81no—
735C2×Dic3C22×D412yes—
736C2×Dic3C22×D412yes—
737C2×Dic3C22×D412yes—
738D12—41no—
739C4×D3—22no—
740C4×D3—22no—
741C4×D3—82no—
742C4×D3—82no—
743Dic6—22no—
744Dic6—22no—
745Dic6—41no—
746Dic6—42no—
747Dic6—82no—
748Dic6—82no—
749C3×C8—22no—
750C3×C8—22no—
751C3⋊C8—22no—
752C3⋊C8—22no—
753C24—21no—
754#41—64no—
755#41—82no—
756#41—122no—
757#41—242no—
758#41—244no—
759C2×Q8—21no—
760C2×Q8—31no—
761C2×Q8—32no—
762C2×Q8—62no—
763C2×Q8—62no—
764C2×Q8—61no—
765C2×Q8—242no—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—32no—
772C2×D4—31no—
773C2×D4—41no—
774C2×D4—62no—
775C2×D4—62no—
776C2×D4—62no—
777C2×D4—62no—
778C2×D4C23×D311yescharacteristic
779C2×D4C23×D312yes—
780C2×D4C23×D311yescharacteristic
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—32no—
788C22×C4—62no—
789C22×C4—62no—
790C22×C4—62no—
791C22×C4—62no—
792C22×C4—62no—
793C22×C4—62no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—82no—
797C22×C4D3×D411yescharacteristic
798C22×C4D3×D411yescharacteristic
799C22×C4C23×D311yescharacteristic
800SD16—122no—
801SD16—122no—
802D8—24no—
803D8—42no—
804M16—122no—
805C2×C8—32no—
806C2×C8—32no—
807C2×C8—122no—
808C2×C8—121no—
809C2×C8—121no—
810C2×C8C23×D312yes—
811C2×C8C23×D312yes—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—32no—
815C4⋊C4—31no—
816C4⋊C4—32no—
817C4⋊C4—32no—
818C4⋊C4—31no—
819C4⋊C4—32no—
820C4⋊C4—32no—
821C4⋊C4—32no—
822C4⋊C4—32no—
823C4⋊C4—62no—
824C4⋊C4—62no—
825C4⋊C4—62no—
826C4⋊C4—62no—
827C4⋊C4—62no—
828C4⋊C4—62no—
829C4⋊C4—62no—
830C4⋊C4—62no—
831C4⋊C4—61no—
832C4⋊C4—61no—
833C4⋊C4—62no—
834C4⋊C4—61no—
835C4⋊C4—62no—
836C4⋊C4—62no—
837C4⋊C4—62no—
838C4⋊C4—62no—
839C4⋊C4—61no—
840C4⋊C4—61no—
841C4⋊C4—62no—
842C4⋊C4C23×D312yes—
843C4⋊C4C23×D311yescharacteristic
844C4⋊C4C23×D311yescharacteristic
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—32no—
852C22⋊C4—32no—
853C22⋊C4—32no—
854C22⋊C4—32no—
855C22⋊C4—32no—
856C22⋊C4—62no—
857C22⋊C4—62no—
858C22⋊C4—62no—
859C22⋊C4—62no—
860C22⋊C4—62no—
861C22⋊C4—62no—
862C22⋊C4—62no—
863C22⋊C4—62no—
864C22⋊C4—62no—
865C22⋊C4—62no—
866C22⋊C4—62no—
867C42—32no—
868C42—62no—
869C42—62no—
870C42—62no—
871C42D3×D411yescharacteristic
872C42D3×D411yescharacteristic
873C42C23×D311yescharacteristic
874C42C23×D311yescharacteristic
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—22no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—42no—
881C22×C3—41no—
882C22×C3—41no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—41no—
886C22×C3—84no—
887C22×C3#57712yes—
888C22×C3C23×D411yescharacteristic
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—22no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—41no—
898C3×C4—41no—
899C3×C4—42no—
900C3×C4C2×2−1+411yescharacteristic
901C3×C4#58511yescharacteristic
902Dic3—22no—
903Dic3—22no—
904Dic3—22no—
905Dic3—42no—
906Dic3—42no—
907Dic3—42no—
908Dic3—42no—
909C23—21no—
910C23—21no—
911C23—22no—
912C23—32no—
913C23—42no—
914C23—42no—
915C23—81no—
916C23C2×D3×D411yescharacteristic
917Q8—62no—
918Q8—62no—
919Q8—81no—
920Q8—121no—
921Q8—122no—
922Q8—242no—
923Q8—242no—
924D4—22no—
925D4—21no—
926D4—21no—
927D4—21no—
928D4—22no—
929D4—42no—
930D4—44no—
931D4—64no—
932D4—81no—
933D4—81no—
934D4—121no—
935D4—124no—
936D4—242no—
937D4—242no—
938D4—242no—
939D4#101012yes—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—32no—
947C2×C4—32no—
948C2×C4—32no—
949C2×C4—41no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—62no—
953C2×C4—62no—
954C2×C4—62no—
955C2×C4—62no—
956C2×C4—62no—
957C2×C4—62no—
958C2×C4—81no—
959C2×C4—81no—
960C2×C4—82no—
961C2×C4—81no—
962C2×C4—124no—
963C2×C4—122no—
964C2×C4—242no—
965C2×C4—242no—
966C2×C4—242no—
967C2×C4—242no—
968C2×C4—242no—
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—42no—
982C2×C3—82no—
983C2×C3—81no—
984C2×C3#348911yescharacteristic
985C2×C3C2×#57711yescharacteristic
986C2×C3#358511yescharacteristic
987D3—42no—
988C22—21no—
989C22—21no—
990C22—22no—
991C22—41no—
992C22—41no—
993C22—41no—
994C22—42no—
995C22—42no—
996C22—41no—
997C22—41no—
998C22—42no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—84no—
1003C22#577512yes—
1004C22C22×D3×D411yescharacteristic
1005C4—21no—
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—21no—
1010C4—42no—
1011C4—41no—
1012C4—41no—
1013C4—62no—
1014C4—62no—
1015C4—62no—
1016C4—122no—
1017C4—122no—
1018C4—122no—
1019C4—122no—
1020C4C2×#101011yescharacteristic
1021C4#596411yescharacteristic
1022C3#6216611yescharacteristic, complemented, Sylow
1023C2—22no—
1024C2—42no—
1025C2—81no—
1026C2—82no—
1027C2—122no—
1028C2#8604211yescharacteristic
1029C2C2×#577511yescharacteristic
1030C2#8719211yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3109C2
socleC22×C3C23×D4
hypercenter#3109D3
hypocenterC3#62166
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. #86233C2semidirect
2. #85767C2semidirect
3. C3×#3109C2semidirect
4. #83320C2semidirect
5. C2×#5009C2semidirect
6. #81322C2semidirect
7. #81320C2semidirect
8. #81069C2semidirect
9. #81063C2semidirect
10. #80346C2semidirect
11. #80316C2semidirect
12. #80016C2semidirect
13. #80015C2semidirect
14. #79884C2semidirect
15. #79881C2semidirect
16. #79855C2semidirect
17. #79854C2semidirect
18. #79341C2semidirect
19. #79320C2semidirect
27. #5729C22semidirect
28. #5719C22semidirect
38. #5558C22semidirect
45. #5539C22semidirect
71. #5094C22semidirect
72. #5075C22semidirect
75. #5019C22semidirect
80. #5008C22semidirect
84. #4868C22semidirect
85. #4862C22semidirect
86. #4861C22semidirect
87. D3×#106C22semidirect
88. #4857C22semidirect
89. #4856C22semidirect
90. #4855C22semidirect
91. #4854C22semidirect
92. #4840C22semidirect
93. #4839C22semidirect
94. #4829C22semidirect
95. #4829C22semidirect
97. #4780C22semidirect
98. #4778C22semidirect
100. #4777C22semidirect
101. #4774C22semidirect
108. #4761C22semidirect
109. #4759C22semidirect
110. #4758C22semidirect
111. #4757C22semidirect
116. #4706C22semidirect
117. #4703C22semidirect
118. #4702C22semidirect
119. #4701C22semidirect
135. #3109D3semidirect
1022. C3#62166semidirect

Maximal subgroups

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

subgroupindex
#862332
#857672
C3×#31092
#833202
C2×#50092
#813222
#813202
#810692
#810632
#803462
#803162
#800162
#800152
#798842
#798812
#798552
#798542
#793412
#793202
#621663