Finite Group Databasebeta

← #11692183

Subgroups — #11692183

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#86167C211yesmaximal, characteristic, complemented
2#86140C211yesmaximal, characteristic, complemented
3C3×#2992C211yesmaximal, characteristic, complemented
4#79975C212yesmaximal, complemented
5#79974C212yesmaximal, complemented
6#79500C212yesmaximal, complemented
7#79499C212yesmaximal, complemented
8#79472C212yesmaximal, complemented
9#79471C212yesmaximal, complemented
10#79441C212yesmaximal, complemented
11#79412C212yesmaximal, complemented
12#79384C212yesmaximal, complemented
13#79365C212yesmaximal, complemented
14#79343C211yesmaximal, characteristic, complemented
15#79320C211yesmaximal, characteristic, complemented
16#79093C212yesmaximal, complemented
17#79092C212yesmaximal, complemented
18#79027C211yesmaximal, characteristic, complemented
19C2×#4847C211yesmaximal, characteristic, complemented
20#62166—31nomaximal, Sylow
21C3×#529C2211yescharacteristic
22#5707—22no—
23#5707—22no—
24#5699—21no—
25#5694—21no—
26#5684—21no—
27#5677—21no—
28#5658—22no—
29#5655—22no—
30#5645—21no—
31D3×C22⋊Q8—21no—
32#5606—21no—
33#5597—21no—
34#5584C2211yescharacteristic
35#5579C2212yescomplemented
36Q8×D12C2211yescharacteristic
37#5565C2212yes—
38#5565C2212yescomplemented
39#5555C2212yes—
40#5555C2211yescharacteristic
41#5551C2211yescharacteristic
42#5550C2212yes—
43#5543C2212yes—
44#5535C2212yescomplemented
45#5534C2212yes—
46#5523C2212yes—
47#5519C2212yescomplemented
48#5477C2211yescharacteristic
49C2×C4×D12C2211yescharacteristic
50#5470C2211yescharacteristic
51C2×#870C2211yescharacteristic
52C3×#446C2212yescomplemented
53C3×#435C2212yes—
54C3×#435C2212yescomplemented
55C3×C8×D4C2212yes—
56C3×#433C2212yescomplemented
57C3×#432C2211yescharacteristic
58C3×#424C2212yescomplemented
59C2×C3×C4⋊C8C2211yescharacteristic
60#5135C2212yes—
61#5134C2212yescomplemented
62#5133C2212yes—
63#5121C2212yescomplemented
64#5115C2212yes—
65#5114C2212yes—
66#5114C2212yes—
67#5114C2212yescomplemented
68#5113C2212yes—
69C2×#821C2211yescharacteristic
70C2×#821C2211yescharacteristic
71C2×#818C2211yescharacteristic
72C2×#817C2211yescharacteristic
73C2×#817C2212yescomplemented
74#4851C2212yescomplemented
75#4851C2212yescomplemented
76#4848C2212yescomplemented
77#4847C2212yes—
78#4847C2212yes—
79#4847C2212yes—
80#4847C2212yes—
81#4847C2212yes—
82#4846C2212yescomplemented
83#4844C2212yes—
84#4844C2212yes—
85#4843C2211yescharacteristic
86#4843C2211yescharacteristic
87#4842C2211yescharacteristic
88#4842C2212yes—
89#4842C2211yescharacteristic
90#4842C2212yescomplemented
91#4842C2212yescomplemented
92#4841C2212yescomplemented
93#4829C2212yescomplemented
94#4829C2212yescomplemented
95#4829C2212yescomplemented
96#4737C2212yes—
97#4736C2212yescomplemented
98#4735C2212yes—
99#4735C2212yes—
100#4735C2212yescomplemented
101#4734C2212yes—
102#4734C2212yes—
103#4732C2212yes—
104#4723C2212yescomplemented
105#4722C2212yes—
106#4721C2212yes—
107#4721C2212yescomplemented
108#4714C2212yes—
109#4711C2212yes—
110#4711C2212yes—
111#4711C2212yes—
112#4710C2212yescomplemented
113#4703C2212yescomplemented
114#4702C2212yescomplemented
115#4702C2212yescomplemented
116#4697C2212yes—
117C4×D24C2212yes—
118C4×#204C2212yescomplemented
119#4680C2212yescomplemented
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#3109—31no—
136#3084—32no—
137C2×#478—31no—
138#2992D311yescharacteristic, complemented
139C2×D3×Q8—21no—
140C2×#237—22no—
141C2×#237—21no—
142C2×#235—21no—
143C2×#235C2312yes—
144C22×D12C2311yescharacteristic
145C22×C4×D3—21no—
146C2×C3×M16C2312yes—
147C22×C3×C8C2311yescharacteristic
148C22×C3×C8C2311yescharacteristic
149C22×C3×C8C2312yes—
150C3×#126D412yes—
151C3×#125D411yescharacteristic
152C3×#124D411yescharacteristic
153C3×#123D412yes—
154C3×C22⋊Q8D411yescharacteristic
155C3×#121D411yescharacteristic
156C3×C4×Q8C2311yescharacteristic
157C3×C4×D4C2312yes—
158C3×C4×D4C2311yescharacteristic
159C3×#117C2312yes—
160C2×C3×C42C2311yescharacteristic
161#946—22no—
162#946—21no—
163#939—22no—
164#939—22no—
165#938—21no—
166#937—22no—
167D4×Dic3—22no—
168#930—21no—
169#930C2312yes—
170#930C2312yes—
171#930C2312yes—
172#930C2312yes—
173C2×(C2×D3)⋊C4—21no—
174#926—21no—
175#926C2312yes—
176C2×C4⋊Dic3C2312yes—
177C2×C4⋊Dic3C2312yes—
178C2×C4⋊Dic3C2311yescharacteristic
179C2×C4⋊Dic3C2311yescharacteristic
180C2×C4⋊Dic3C2311yescharacteristic
181#924—21no—
182#924C2312yes—
183#924C2312yes—
184C2×Dic3⋊C4—21no—
185C2×Dic3⋊C4—21no—
186C2×D24C2312yes—
187C2×D24C2312yes—
188C2×#204C2312yes—
189C2×#204C2312yes—
190#898—22no—
191#898—22no—
192#898—22no—
193#898—22no—
194#897—22no—
195#897—21no—
196#897—21no—
197#897—22no—
198#896—22no—
199#896—22no—
200#896—22no—
201#894—22no—
202#894—22no—
203#894—22no—
204#892—22no—
205#892—21no—
206D3×C4⋊C4—22no—
207D3×C4⋊C4—21no—
208D3×C4⋊C4—22no—
209#890—22no—
210#890—22no—
211#888—22no—
212#886—22no—
213#886—22no—
214#886—22no—
215#885—22no—
216#884—22no—
217#884—22no—
218#884—22no—
219#883—22no—
220#883—22no—
221#883—22no—
222#883—22no—
223#67⋊C4—22no—
224#67⋊C4—22no—
225#67⋊C4—22no—
226#67⋊C4—22no—
227D3×C22⋊C4—22no—
228#878—22no—
229#878—22no—
230#878—22no—
231#878—22no—
232#875—21no—
233#875C2312yes—
234#874C2311yescharacteristic
235C4×D12—21no—
236C4×D12—21no—
237C4×D12—21no—
238C4×D12C2312yes—
239C4×D12C2312yes—
240C4×D12C2312yes—
241C4×D12C2311yescharacteristic
242C4×D12C2311yescharacteristic
243C4×D12C2311yescharacteristic
244C4×D12C2311yescharacteristic
245C4×D12C2312yes—
246#870—21no—
247#870—21no—
248#870—21no—
249#870C2312yes—
250#870C2312yes—
251#870C2312yes—
252#869C2311yescharacteristic
253#869C2312yes—
254#869C2312yes—
255#869C2311yescharacteristic
256#869C2311yescharacteristic
257C4×Dic6—21no—
258C4×Dic6C2312yes—
259C4×Dic6C2312yes—
260C3×C4⋊C8C2312yes—
261C3×C4⋊C8C2312yes—
262C3×C4⋊C8C2311yescharacteristic
263C3×C4⋊C8C2312yes—
264C3×C4⋊C8C2312yes—
265C3×C4⋊C8C2311yescharacteristic
266C3×C22⋊C8C2312yes—
267C3×C22⋊C8C2312yes—
268C3×C22⋊C8C2312yes—
269C3×#97C2312yes—
270C3×#97C2312yes—
271C3×C4×C8C2312yes—
272#821C2312yes—
273#821C2312yes—
274#821C2312yes—
275#821C2312yes—
276#821C2312yes—
277#821C2312yes—
278#821C2312yes—
279#821C2312yes—
280#821C2312yes—
281#821C2312yes—
282#818C2312yes—
283#818C2312yes—
284#818C2312yes—
285#818C2312yes—
286#817C2312yes—
287#817C2312yes—
288#817C2312yes—
289#817C2312yes—
290#817C2312yes—
291#817C2312yes—
292#817C2312yes—
293#817C2312yes—
294#816C2312yes—
295#816C2312yes—
296#816C2312yes—
297#816C2312yes—
298#816C2312yes—
299#816C2312yes—
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#532—31no—
325#529C2×D311yescharacteristic
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—32no—
355#476—31no—
356#476—32no—
357#476—32no—
358#476—31no—
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#459—31no—
373#459—31no—
374#449—32no—
375#449—32no—
376#447—32no—
377#446C2×D312yescomplemented
378#442—32no—
379#442—32no—
380#442—32no—
381#440—32no—
382C4×SD16—32no—
383C4×D8—32no—
384#435C2×D312yes—
385#435C2×D312yescomplemented
386C8×D4C2×D312yes—
387#433C2×D312yescomplemented
388#432C2×D311yescharacteristic
389#428—32no—
390C2×#107—31no—
391C2×#106—31no—
392C2×#106—32no—
393#424C2×D312yescomplemented
394C2×C4⋊C8C2×D311yescharacteristic
395#417—32no—
396#416—32no—
397C2×#102—31no—
398C2×#102—31no—
399C23×D3—21no—
400C2×C3×Q8C2×D411yescharacteristic
401C2×C3×D4C2×D412yes—
402C2×C3×D4C2×D411yescharacteristic
403C22×C3×C4C2×D411yescharacteristic
404C22×C3×C4C2×D411yescharacteristic
405C22×C3×C4C2411yescharacteristic
406C22×C3×C4C2412yes—
407C2×#67—22no—
408C2×#67—22no—
409C2×#67—22no—
410C2×#67—22no—
411C2×#67—22no—
412C22×Dic3—21no—
413C22×Dic3—22no—
414C22×Dic3—21no—
415C22×Dic3—22no—
416C22×Dic3—21no—
417D3×Q8—82no—
418#237—82no—
419#237—84no—
420#235—24no—
421#235—42no—
422#235—82no—
423C2×D12—22no—
424C2×D12—21no—
425C2×D12—21no—
426C2×D12—21no—
427C2×D12—41no—
428C2×D12C2411yescharacteristic
429C2×D12C2412yes—
430C2×D12C2411yescharacteristic
431C2×C4×D3—21no—
432C2×C4×D3—21no—
433C2×C4×D3—22no—
434C2×C4×D3—21no—
435C2×C4×D3—22no—
436C2×C4×D3—21no—
437C2×C4×D3—22no—
438C2×C4×D3—22no—
439C2×C4×D3—22no—
440C2×C4×D3—82no—
441C2×Dic6—21no—
442C2×Dic6—21no—
443C2×Dic6—22no—
444C2×Dic6—22no—
445C2×Dic6C2412yes—
446C3×M16—42no—
447C2×C3×C8—41no—
448C2×C3×C8—42no—
449C2×C3×C8—41no—
450C2×C3×C8C2412yes—
451C2×C3×C8C2412yes—
452C2×C3×C8C2412yes—
453C2×C3×C8C2412yes—
454C3×C4⋊C4C2×D412yes—
455C3×C4⋊C4C2×D412yes—
456C3×C4⋊C4C2×D412yes—
457C3×C4⋊C4C2×D412yes—
458C3×C4⋊C4C2×D411yescharacteristic
459C3×C4⋊C4C2×D411yescharacteristic
460C3×C22⋊C4C2×D412yes—
461C3×C22⋊C4C2×D412yes—
462C3×C22⋊C4C2×D412yes—
463C3×C22⋊C4C2×D412yes—
464C3×C22⋊C4C2×D412yes—
465C3×C42C2×D411yescharacteristic
466C3×C42C2×D411yescharacteristic
467C3×C42C2412yes—
468C3×C42C2411yescharacteristic
469C3×C42C2411yescharacteristic
470#217—22no—
471#217—22no—
472#217—22no—
473(C2×D3)⋊C4—21no—
474(C2×D3)⋊C4—21no—
475(C2×D3)⋊C4—21no—
476(C2×D3)⋊C4—21no—
477(C2×D3)⋊C4—22no—
478(C2×D3)⋊C4—22no—
479(C2×D3)⋊C4—22no—
480(C2×D3)⋊C4—22no—
481(C2×D3)⋊C4—22no—
482(C2×D3)⋊C4—22no—
483(C2×D3)⋊C4—22no—
484(C2×D3)⋊C4—22no—
485(C2×D3)⋊C4—22no—
486(C2×D3)⋊C4—22no—
487C4⋊Dic3—21no—
488C4⋊Dic3—21no—
489C4⋊Dic3—21no—
490C4⋊Dic3—21no—
491C4⋊Dic3—22no—
492C4⋊Dic3—22no—
493C4⋊Dic3—21no—
494C4⋊Dic3—21no—
495C4⋊Dic3—21no—
496C4⋊Dic3—22no—
497C4⋊Dic3—22no—
498C4⋊Dic3C2412yes—
499C4⋊Dic3C2412yes—
500C4⋊Dic3C2412yes—
501C4⋊Dic3C2411yescharacteristic
502C4⋊Dic3C2412yes—
503C4⋊Dic3C2411yescharacteristic
504Dic3⋊C4—22no—
505Dic3⋊C4—22no—
506Dic3⋊C4—22no—
507Dic3⋊C4—22no—
508Dic3⋊C4—22no—
509Dic3⋊C4—22no—
510Dic3⋊C4—22no—
511Dic3⋊C4—22no—
512Dic3⋊C4—22no—
513Dic3⋊C4—22no—
514C4×Dic3—22no—
515C4×Dic3—22no—
516C4×Dic3—22no—
517D24—24no—
518D24—42no—
519#204—42no—
520#204—42no—
521C2×#41—32no—
522C2×#41—61no—
523C2×#41—62no—
524C2×#41—61no—
525C22×Q8—61no—
526C22×D4—31no—
527C23×C4—61no—
528C2×SD16—32no—
529C2×SD16—32no—
530C2×D8—32no—
531C2×D8—32no—
532C2×M16C22×D312yes—
533C22×C8C22×D311yescharacteristic
534C22×C8C22×D311yescharacteristic
535C22×C8C22×D312yes—
536C4⋊Q8—31no—
537C4⋊Q8—31no—
538C4⋊Q8—32no—
539C4⋊Q8—32no—
540C4⋊Q8—31no—
541C4⋊Q8—62no—
542#127—31no—
543#126—62no—
544#126—62no—
545#126—62no—
546#126—62no—
547#126D1212yes—
548#125—32no—
549#125—32no—
550#125—32no—
551#125—62no—
552#125—62no—
553#125—61no—
554#125—61no—
555#125—61no—
556#125D1211yescharacteristic
557#124—32no—
558#124—62no—
559#124—61no—
560#124D1211yescharacteristic
561#123—62no—
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#123D1212yes—
572C22⋊Q8—32no—
573C22⋊Q8—32no—
574C22⋊Q8—61no—
575C22⋊Q8—62no—
576C22⋊Q8—61no—
577C22⋊Q8—62no—
578C22⋊Q8—61no—
579C22⋊Q8—61no—
580C22⋊Q8—62no—
581C22⋊Q8—62no—
582C22⋊Q8—62no—
583C22⋊Q8—62no—
584C22⋊Q8—62no—
585C22⋊Q8—62no—
586C22⋊Q8—62no—
587C22⋊Q8—62no—
588C22⋊Q8D1211yescharacteristic
589#121—32no—
590#121—32no—
591#121—32no—
592#121—32no—
593#121—61no—
594#121—62no—
595#121—62no—
596#121—61no—
597#121—62no—
598#121—62no—
599#121—62no—
600#121D1211yescharacteristic
601#120—62no—
602C4×Q8—32no—
603C4×Q8—32no—
604C4×Q8—61no—
605C4×Q8C22×D311yescharacteristic
606C4×D4—31no—
607C4×D4—31no—
608C4×D4—31no—
609C4×D4—31no—
610C4×D4—32no—
611C4×D4—32no—
612C4×D4—32no—
613C4×D4—32no—
614C4×D4—62no—
615C4×D4—62no—
616C4×D4—62no—
617C4×D4—62no—
618C4×D4—62no—
619C4×D4—61no—
620C4×D4—61no—
621C4×D4—61no—
622C4×D4C22×D312yes—
623C4×D4C22×D311yescharacteristic
624#117—32no—
625#117—61no—
626#117—62no—
627#117—61no—
628#117C22×D312yes—
629C2×C4⋊C4—31no—
630C2×C4⋊C4—32no—
631C2×C4⋊C4—31no—
632C2×C4⋊C4—31no—
633C2×C4⋊C4—32no—
634C2×C4⋊C4—61no—
635C2×C4⋊C4—61no—
636C2×C4⋊C4—62no—
637C2×C4⋊C4—61no—
638C2×C4⋊C4—62no—
639C2×C22⋊C4—61no—
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#106—32no—
653#106—32no—
654C4⋊C8C22×D312yes—
655C4⋊C8C22×D312yes—
656C4⋊C8C22×D311yescharacteristic
657C4⋊C8C22×D312yes—
658C4⋊C8C22×D312yes—
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#102—32no—
673#102—32no—
674#102—32no—
675#102—32no—
676C22⋊C8C22×D312yes—
677C22⋊C8C22×D312yes—
678C22⋊C8C22×D312yes—
679#97C22×D312yes—
680#97C22×D312yes—
681C4×C8C22×D312yes—
682C23×C3C22×D412yes—
683C23×C3C22×D411yescharacteristic
684C22×D3—21no—
685C22×D3—21no—
686C22×D3—22no—
687C22×D3—42no—
688C22×D3—42no—
689C22×D3—81no—
690C3×Q8—41no—
691C3×D4—24no—
692C3×D4—41no—
693C2×C3×C4—22no—
694C2×C3×C4—21no—
695C2×C3×C4—22no—
696C2×C3×C4—21no—
697C2×C3×C4—22no—
698C2×C3×C4—41no—
699C2×C3×C4C22×D411yescharacteristic
700C2×C3×C4C22×D412yes—
701C2×C3×C4C22×D412yes—
702C2×C3×C4C22×D411yescharacteristic
703C2×C3×C4C22×D411yescharacteristic
704C2×C3×C4C22×D411yescharacteristic
705C2×C3×C4C22×D411yescharacteristic
706C2×C3×C4C22×D412yes—
707C2×C3×C4C2511yescharacteristic
708#67—44no—
709#67—44no—
710#67—82no—
711#67—82no—
712#67—82no—
713C2×Dic3—22no—
714C2×Dic3—21no—
715C2×Dic3—22no—
716C2×Dic3—22no—
717C2×Dic3—22no—
718C2×Dic3—22no—
719C2×Dic3—21no—
720C2×Dic3—42no—
721C2×Dic3—81no—
722C2×Dic3—82no—
723C2×Dic3—82no—
724C2×Dic3—81no—
725D12—22no—
726D12—21no—
727D12—21no—
728D12—22no—
729D12—21no—
730D12—42no—
731D12—81no—
732D12—81no—
733D122−1+412yes—
734C4×D3—44no—
735C4×D3—42no—
736C4×D3—42no—
737C4×D3—82no—
738C4×D3—81no—
739C4×D3—81no—
740C4×D3—82no—
741C4×D3—82no—
742C4×D3—82no—
743Dic6—22no—
744Dic6—22no—
745Dic6—42no—
746Dic6—81no—
747Dic6—82no—
748Dic6—82no—
749C3×C8—22no—
750C3×C8—22no—
751C3×C8—22no—
752C3×C8—22no—
753C24—61no—
754#41—64no—
755#41—122no—
756#41—242no—
757#41—244no—
758#41—242no—
759C2×Q8—32no—
760C2×Q8—61no—
761C2×Q8—62no—
762C2×Q8—62no—
763C2×Q8—61no—
764C2×Q8—242no—
765C2×Q8C2×D1211yescharacteristic
766C2×D4—31no—
767C2×D4—31no—
768C2×D4—32no—
769C2×D4—62no—
770C2×D4—62no—
771C2×D4—62no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—62no—
775C2×D4—61no—
776C2×D4—61no—
777C2×D4—61no—
778C2×D4—121no—
779C2×D4C2×D1212yes—
780C2×D4C2×D1211yescharacteristic
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—62no—
785C22×C4—62no—
786C22×C4—62no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—62no—
790C22×C4—61no—
791C22×C4—62no—
792C22×C4—62no—
793C22×C4—62no—
794C22×C4—61no—
795C22×C4—242no—
796C22×C4C2×D1211yescharacteristic
797C22×C4C2×D1211yescharacteristic
798C22×C4C23×D311yescharacteristic
799C22×C4C23×D312yes—
800SD16—122no—
801SD16—122no—
802D8—64no—
803D8—122no—
804M16—42no—
805C2×C8—41no—
806C2×C8—42no—
807C2×C8—41no—
808C2×C8C23×D312yes—
809C2×C8C23×D312yes—
810C2×C8C23×D312yes—
811C2×C8C23×D312yes—
812C4⋊C4—32no—
813C4⋊C4—32no—
814C4⋊C4—32no—
815C4⋊C4—31no—
816C4⋊C4—31no—
817C4⋊C4—32no—
818C4⋊C4—62no—
819C4⋊C4—61no—
820C4⋊C4—61no—
821C4⋊C4—62no—
822C4⋊C4—61no—
823C4⋊C4—62no—
824C4⋊C4—61no—
825C4⋊C4—62no—
826C4⋊C4—62no—
827C4⋊C4—62no—
828C4⋊C4—62no—
829C4⋊C4—62no—
830C4⋊C4—62no—
831C4⋊C4—62no—
832C4⋊C4—62no—
833C4⋊C4—61no—
834C4⋊C4—61no—
835C4⋊C4—61no—
836C4⋊C4—62no—
837C4⋊C4—62no—
838C4⋊C4—62no—
839C4⋊C4C2×D1212yes—
840C4⋊C4C2×D1211yescharacteristic
841C4⋊C4C2×D1212yes—
842C4⋊C4C2×D1212yes—
843C4⋊C4C2×D1211yescharacteristic
844C4⋊C4C2×D1212yes—
845C22⋊C4—62no—
846C22⋊C4—62no—
847C22⋊C4—62no—
848C22⋊C4—61no—
849C22⋊C4—61no—
850C22⋊C4—61no—
851C22⋊C4—61no—
852C22⋊C4—62no—
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⋊C4C2×D1212yes—
863C22⋊C4C2×D1212yes—
864C22⋊C4C2×D1212yes—
865C22⋊C4C2×D1212yes—
866C22⋊C4C2×D1212yes—
867C42—62no—
868C42—62no—
869C42—62no—
870C42C2×D1211yescharacteristic
871C42C2×D1211yescharacteristic
872C42C23×D312yes—
873C42C23×D311yescharacteristic
874C42C23×D311yescharacteristic
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3#57712yes—
881C22×C3C23×D411yescharacteristic
882C2×D3—22no—
883C2×D3—41no—
884C2×D3—41no—
885C2×D3—41no—
886C2×D3—42no—
887C2×D3—41no—
888C2×D3—42no—
889C2×D3—42no—
890C2×D3—41no—
891C2×D3—84no—
892C3×C4—21no—
893C3×C4—22no—
894C3×C4—21no—
895C3×C4—22no—
896C3×C4—21no—
897C3×C4—22no—
898C3×C4—21no—
899C3×C4—21no—
900C3×C4C2×2−1+411yescharacteristic
901C3×C4#58511yescharacteristic
902Dic3—42no—
903Dic3—41no—
904Dic3—41no—
905Dic3—42no—
906Dic3—42no—
907Dic3—42no—
908Dic3—42no—
909C23—61no—
910C23—61no—
911C23—62no—
912C23—122no—
913C23—122no—
914C23—241no—
915C23C22×D1212yes—
916C23C22×D1211yescharacteristic
917Q8—41no—
918Q8—62no—
919Q8—62no—
920Q8—122no—
921Q8—242no—
922Q8—241no—
923Q8—242no—
924D4—24no—
925D4—32no—
926D4—41no—
927D4—61no—
928D4—61no—
929D4—62no—
930D4—62no—
931D4—61no—
932D4—122no—
933D4—124no—
934D4—124no—
935D4—241no—
936D4—241no—
937D4—242no—
938D4—242no—
939D4—242no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—41no—
946C2×C4—62no—
947C2×C4—61no—
948C2×C4—62no—
949C2×C4—62no—
950C2×C4—62no—
951C2×C4—61no—
952C2×C4—62no—
953C2×C4—124no—
954C2×C4—122no—
955C2×C4—122no—
956C2×C4—122no—
957C2×C4—241no—
958C2×C4—241no—
959C2×C4—242no—
960C2×C4—242no—
961C2×C4—242no—
962C2×C4—242no—
963C2×C4—241no—
964C2×C4—242no—
965C2×C4—242no—
966C2×C4—241no—
967C2×C4C22×D1211yescharacteristic
968C2×C4C22×D1212yes—
969C2×C4C22×D1212yes—
970C2×C4C22×D1211yescharacteristic
971C2×C4C22×D1211yescharacteristic
972C2×C4C22×D1211yescharacteristic
973C2×C4C22×D1211yescharacteristic
974C2×C4C22×D1212yes—
975C2×C4C24×D311yescharacteristic
976C8—22no—
977C8—22no—
978C8—22no—
979C8—22no—
980C2×C3—22no—
981C2×C3—42no—
982C2×C3#348911yescharacteristic
983C2×C3C2×#57711yescharacteristic
984C2×C3#358511yescharacteristic
985D3—42no—
986D3—82no—
987D3—81no—
988C22—21no—
989C22—21no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—62no—
994C22—121no—
995C22—121no—
996C22—122no—
997C22—121no—
998C22—121no—
999C22—122no—
1000C22—121no—
1001C22—122no—
1002C22—244no—
1003C22#575112yes—
1004C22C23×D1211yescharacteristic
1005C4—21no—
1006C4—21no—
1007C4—22no—
1008C4—21no—
1009C4—21no—
1010C4—22no—
1011C4—22no—
1012C4—21no—
1013C4—122no—
1014C4—122no—
1015C4—121no—
1016C4—121no—
1017C4—122no—
1018C4—122no—
1019C4—122no—
1020C4#596611yescharacteristic
1021C4D3×2−1+411yescharacteristic
1022C3#6216611yescharacteristic, complemented, Sylow
1023C2—22no—
1024C2—42no—
1025C2—122no—
1026C2—241no—
1027C2—242no—
1028C2#8590111yescharacteristic
1029C2C2×#575111yescharacteristic
1030C2#8716711yescharacteristic
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2992C2
socleC22×C3C23×D4
hypercenter#2992D3
hypocenterC3#62166
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #529 ◁ #2992

Complements

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

NH ≅ G/Ntype
1. #86167C2semidirect
2. #86140C2semidirect
3. C3×#2992C2semidirect
4. #79975C2semidirect
5. #79974C2semidirect
6. #79500C2semidirect
7. #79499C2semidirect
8. #79472C2semidirect
9. #79471C2semidirect
10. #79441C2semidirect
11. #79412C2semidirect
12. #79384C2semidirect
13. #79365C2semidirect
14. #79343C2semidirect
15. #79320C2semidirect
16. #79093C2semidirect
17. #79092C2semidirect
18. #79027C2semidirect
19. C2×#4847C2semidirect
35. #5579C22semidirect
38. #5565C22semidirect
44. #5535C22semidirect
47. #5519C22semidirect
52. C3×#446C22semidirect
54. C3×#435C22semidirect
56. C3×#433C22semidirect
58. C3×#424C22semidirect
61. #5134C22semidirect
63. #5121C22semidirect
67. #5114C22semidirect
73. C2×#817C22semidirect
74. #4851C22semidirect
75. #4851C22semidirect
76. #4848C22semidirect
82. #4846C22semidirect
90. #4842C22semidirect
91. #4842C22semidirect
92. #4841C22semidirect
93. #4829C22semidirect
94. #4829C22semidirect
95. #4829C22semidirect
97. #4736C22semidirect
100. #4735C22semidirect
104. #4723C22semidirect
107. #4721C22semidirect
112. #4710C22semidirect
113. #4703C22semidirect
114. #4702C22semidirect
115. #4702C22semidirect
118. C4×#204C22semidirect
119. #4680C22semidirect
138. #2992D3semidirect
377. #446C2×D3semidirect
385. #435C2×D3semidirect
387. #433C2×D3semidirect
393. #424C2×D3semidirect
1022. C3#62166semidirect

Maximal subgroups

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

subgroupindex
#861672
#861402
C3×#29922
#799752
#799742
#795002
#794992
#794722
#794712
#794412
#794122
#793842
#793652
#793432
#793202
#790932
#790922
#790272
C2×#48472
#621663