Finite Group Databasebeta

← #11664212

Subgroups — #11664212

Order 768.

2110 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85848C211yesmaximal, characteristic, complemented
2C4×#1010C211yesmaximal, characteristic, complemented
3C3×#2925C211yesmaximal, characteristic, complemented
4#79395C214yesmaximal, complemented
5#79384C214yesmaximal, complemented
6#79355C212yesmaximal, complemented
7#79347C212yesmaximal, complemented
8#79309C212yesmaximal, complemented
9#79301C212yesmaximal, complemented
10#79068C211yesmaximal, characteristic, complemented
11#79056C211yesmaximal, characteristic, complemented
12C2×#4848C211yesmaximal, characteristic, complemented
13#79025C211yesmaximal, characteristic, complemented
14#78678C212yesmaximal, complemented
15#78651C212yesmaximal, complemented
16#78572C212yesmaximal, complemented
17#78560C212yesmaximal, complemented
18#60593—31nomaximal, Sylow
19C2×#1010C2211yescharacteristic
20C3×C4×#41C2211yescharacteristic
21#5830C2212yes—
22#5827C2211yescharacteristic
23C2×#908C2212yes—
24C22×#204C2212yes—
25#5585—21no—
26#5585—21no—
27#5572—21no—
28C4×D3×Q8—21no—
29#5553—21no—
30#5553—21no—
31#5550—22no—
32#5550—22no—
33#5546—21no—
34#5546—22no—
35C4×#237—21no—
36C4×#237—22no—
37#5535C2214yes—
38#5523C2211yescharacteristic
39#5523C2212yescomplemented
40#5521C2212yes—
41#5516C2211yescharacteristic
42#5516C2212yescomplemented
43#5477C2212yes—
44#5477C2212yes—
45C2×#874C2211yescharacteristic
46C4×#235C2211yescharacteristic
47C4×#235C2212yescomplemented
48#5470C2211yescharacteristic
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2212yescomplemented
51C3×#433C2214yescomplemented
52C3×#432C2212yescomplemented
53C3×#431C2212yescomplemented
54C3×#423C2211yescharacteristic
55C2×C3×C4⋊C8C2211yescharacteristic
56C3×#408C2212yes—
57C3×#405C2212yes—
58#5131C2212yes—
59#5121C2212yes—
60#5120C2212yes—
61#5113C2212yes—
62C2×#821C2212yes—
63#5106C2212yes—
64#4851C2211yescharacteristic, complemented
65#4851C2212yescomplemented
66#4850C2211yescharacteristic, complemented
67#4850C2212yescomplemented
68#4848C2214yes—
69#4848C2212yes—
70#4848C2212yes—
71#4848C2212yes—
72#4848C2212yes—
73#4847C2212yescomplemented
74#4846C2211yescharacteristic, complemented
75#4843C2212yes—
76#4843C2212yes—
77#4842C2211yescharacteristic, complemented
78#4829C2214yescomplemented
79#4829C2212yescomplemented
80#4738C2214yescomplemented
81#4738C2214yescomplemented
82#4737C2214yescomplemented
83#4737C2214yescomplemented
84#4736C2214yescomplemented
85#4735C2214yescomplemented
86#4734C2214yescomplemented
87#4734C2214yescomplemented
88#4711C2214yescomplemented
89#4710C2214yescomplemented
90#4710C2214yescomplemented
91#4710C2214yescomplemented
92C4×D24C2214yescomplemented
93C4×#204C2214yescomplemented
94C4×#204C2214yescomplemented
95C4×#204C2214yescomplemented
96#3508—31no—
97C4×2−1+4—31no—
98#3126—34no—
99#3119—34no—
100#3115—32no—
101#3112—32no—
102#3106—32no—
103#3103—32no—
104#3096—32no—
105#3078—31no—
106#3076—31no—
107#3038—31no—
108C2×#460—31no—
109#3010—32no—
110#2949—32no—
111#2946—32no—
112#2925D311yescharacteristic, complemented
113C2×C3×#41C2311yescharacteristic
114#1010—24no—
115#1010—24no—
116C2×D3×Q8—21no—
117C2×#237—22no—
118C2×#237—21no—
119C2×#235—22no—
120C2×#235—22no—
121C2×#235C2312yes—
122C2×#235C2311yescharacteristic
123C22×D12—21no—
124C22×D12—21no—
125C22×D12C2312yes—
126C22×Dic6C2312yes—
127C22×Dic6C2311yescharacteristic
128C2×C3×M16C2312yes—
129C22×C3×C8C2312yes—
130C3×C4×Q8D411yescharacteristic
131C3×C4×Q8D411yescharacteristic
132C3×C4×D4D412yes—
133C3×C4×D4D411yescharacteristic
134C3×C4×D4D412yes—
135C3×C4×D4D411yescharacteristic
136C3×#117C2311yescharacteristic
137C3×#117C2312yes—
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2312yes—
140#947—22no—
141Q8×Dic3—21no—
142#940—22no—
143#937—24no—
144D4×Dic3—22no—
145D4×Dic3—21no—
146#930—22no—
147#930—22no—
148#930C2314yes—
149#930C2314yes—
150C4×#67—21no—
151C4×#67—21no—
152C4×#67—22no—
153C4×#67—22no—
154#926C2312yes—
155#926C2311yescharacteristic
156#926C2312yes—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2312yes—
159#924—21no—
160#924—21no—
161C2×Dic3⋊C4—21no—
162C2×Dic3⋊C4—22no—
163C2×C4×Dic3—21no—
164C2×C4×Dic3—22no—
165#908—28no—
166C2×D24C2314yes—
167C2×#204—28no—
168C2×#204C2314yes—
169C2×#204C2314yes—
170C2×#204C2314yes—
171#894—24no—
172#894—24no—
173#893—22no—
174#893—22no—
175#892—21no—
176#892—22no—
177D3×C4⋊C4—21no—
178D3×C4⋊C4—22no—
179#887—21no—
180#887—21no—
181#887—22no—
182#887—22no—
183#884—24no—
184#884—24no—
185#67⋊C4—22no—
186#67⋊C4—22no—
187#67⋊C4—22no—
188D3×C22⋊C4—24no—
189#877—22no—
190#877—22no—
191#877—22no—
192#875—22no—
193#875—22no—
194#874—21no—
195#874—21no—
196#874C2312yes—
197#874C2312yes—
198C4×D12—22no—
199C4×D12—22no—
200C4×D12C2314yes—
201C4×D12C2314yes—
202C4×D12C2312yes—
203C4×D12C2311yescharacteristic
204C4×D12C2311yescharacteristic
205#872—21no—
206#872—22no—
207C42×D3—21no—
208C42×D3—22no—
209#870C2312yes—
210#869C2311yescharacteristic
211#869C2311yescharacteristic
212C4×Dic6—21no—
213C4×Dic6—21no—
214C4×Dic6—22no—
215C4×Dic6—22no—
216C4×Dic6—21no—
217C4×Dic6—21no—
218C4×Dic6C2312yes—
219C4×Dic6C2312yes—
220C4×Dic6C2312yes—
221C4×Dic6C2312yes—
222C4×Dic6C2312yes—
223C4×Dic6C2311yescharacteristic
224C4×Dic6C2311yescharacteristic
225C3×C4⋊C8C2311yescharacteristic
226C3×C4⋊C8C2311yescharacteristic
227C3×C4⋊C8C2312yes—
228C3×C4⋊C8C2312yes—
229C3×C4⋊C8C2312yes—
230C3×C22⋊C8C2314yes—
231C3×C22⋊C8C2314yes—
232C3×#97C2314yes—
233C3×C4×C8C2314yes—
234#821C2314yes—
235#821C2314yes—
236#821C2314yes—
237#821C2312yes—
238#821C2314yes—
239#821C2312yes—
240#818C2314yes—
241#818C2312yes—
242#818C2312yes—
243#817C2314yes—
244#817C2312yes—
245#817C2312yes—
246#816C2314yes—
247#816C2314yes—
248#816C2312yes—
249#816C2312yes—
250C2×2−1+4—31no—
251C2×AGL(1,ℤ/8)—32no—
252C22×SD16—32no—
253#559—61no—
254#559—61no—
255#550—61no—
256#550—61no—
257#546—62no—
258#546—62no—
259#540—34no—
260#535—32no—
261#533—31no—
262#532—32no—
263#532—32no—
264C2×#127—31no—
265#520—31no—
266#520—32no—
267#520—31no—
268#520—62no—
269#520—61no—
270#519—32no—
271#519—31no—
272#519—61no—
273#518—32no—
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—62no—
277C4×#41—61no—
278C4×#41C2×D311yescharacteristic
279C2×C4×Q8—31no—
280C2×C4×Q8—32no—
281C2×C4×Q8—61no—
282#482—34no—
283#482—34no—
284#481—34no—
285#480—34no—
286#479—32no—
287#479—34no—
288#478—32no—
289#477—31no—
290#477—32no—
291#476—31no—
292#475—31no—
293#475—32no—
294#474—31no—
295#460—32no—
296#460—32no—
297#460—32no—
298#460—34no—
299#460—32no—
300#459—32no—
301#459—32no—
302#449—34no—
303#449—34no—
304#448—34no—
305#448—34no—
306#442—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×SD16—34no—
311C4×SD16—34no—
312C4×SD16—34no—
313C4×D8—34no—
314#433C2×D314yescomplemented
315#432C2×D312yescomplemented
316#431C2×D312yescomplemented
317#428—32no—
318#427—32no—
319#423C2×D311yescharacteristic
320C2×C4⋊C8C2×D311yescharacteristic
321#419—32no—
322#418—32no—
323#416—32no—
324C2×#102—32no—
325#408C2×D312yes—
326#405C2×D312yes—
327C23×D3—22no—
328C3×#41—22no—
329C3×#41—22no—
330C2×C3×Q8C2×D411yescharacteristic
331C2×C3×D4C2×D412yes—
332C2×C3×D4C2×D411yescharacteristic
333C22×C3×C4C2×D411yescharacteristic
334C22×C3×C4C2×D412yes—
335C22×C3×C4C2×D411yescharacteristic
336C22×C3×C4C2×D412yes—
337C22×C3×C4C2412yes—
338C22×C3×C4C2411yescharacteristic
339C2×#67—22no—
340C2×#67—21no—
341C2×#67—24no—
342C2×#67—24no—
343C22×Dic3—22no—
344C22×Dic3—21no—
345C22×Dic3—22no—
346C22×Dic3—21no—
347D3×Q8—28no—
348#237—216no—
349#237—28no—
350#235—22no—
351#235—24no—
352#235—24no—
353#235—84no—
354#235—84no—
355#235#4114yescomplemented
356C2×D12—24no—
357C2×D12—24no—
358C2×D12—22no—
359C2×D12—22no—
360C2×D12—22no—
361C2×D12—22no—
362C2×D12—22no—
363C2×D12—82no—
364C2×D12—82no—
365C2×D12C2414yes—
366C2×D12C2411yescharacteristic
367C2×C4×D3—22no—
368C2×C4×D3—21no—
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—22no—
372C2×C4×D3—24no—
373C2×C4×D3—24no—
374C2×Dic6—22no—
375C2×Dic6—21no—
376C2×Dic6—22no—
377C2×Dic6—24no—
378C2×Dic6—24no—
379C2×Dic6—21no—
380C2×Dic6—21no—
381C2×Dic6#4114yescomplemented
382C2×Dic6C2411yescharacteristic
383C2×Dic6C2412yes—
384C3×M16—24no—
385C2×C3×C8—24no—
386C2×C3×C8C2414yes—
387C2×C3×C8C2412yes—
388C2×C3×C8C2412yes—
389C3×C4⋊C4C2×D411yescharacteristic
390C3×C4⋊C4C2×D412yes—
391C3×C4⋊C4C2×D411yescharacteristic
392C3×C4⋊C4C2×D412yes—
393C3×C22⋊C4C2×D412yes—
394C3×C22⋊C4C2×D412yes—
395C3×C22⋊C4C2×D412yes—
396C3×C42C2×D411yescharacteristic
397C3×C42C2×D411yescharacteristic
398C3×C42C2×D412yes—
399C3×C42C2×D412yes—
400C3×C42C2412yes—
401C3×C42C2411yescharacteristic
402C3×C42C2411yescharacteristic
403#217—22no—
404#217—21no—
405#217—22no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—24no—
410(C2×D3)⋊C4—24no—
411(C2×D3)⋊C4—24no—
412(C2×D3)⋊C4—24no—
413C4⋊Dic3—22no—
414C4⋊Dic3—21no—
415C4⋊Dic3—21no—
416C4⋊Dic3—21no—
417C4⋊Dic3C2412yes—
418C4⋊Dic3C2412yes—
419C4⋊Dic3C2412yes—
420C4⋊Dic3C2411yescharacteristic
421C4⋊Dic3C2411yescharacteristic
422Dic3⋊C4—22no—
423Dic3⋊C4—21no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—22no—
429Dic3⋊C4—21no—
430Dic3⋊C4—22no—
431C4×Dic3—22no—
432C4×Dic3—21no—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3—22no—
436C4×Dic3—22no—
437C4×Dic3—21no—
438C4×Dic3—22no—
439C4×Dic3—22no—
440C4×Dic3—21no—
441D24—28no—
442#204—28no—
443#204—28no—
444#204—28no—
4452−1+4—64no—
4462−1+4—64no—
447C2×#41—31no—
448C2×#41—32no—
449C2×#41—62no—
450C2×#41—61no—
451C2×#41—62no—
452C2×#41—62no—
453C2×#41C22×D311yescharacteristic
454C22×Q8—31no—
455C22×Q8—32no—
456C22×Q8—61no—
457C22×D4—32no—
458C22×D4—61no—
459C22×D4—61no—
460AGL(1,ℤ/8)—68no—
461C2×SD16—34no—
462C2×SD16—34no—
463C2×SD16—34no—
464C2×SD16—68no—
465C2×D8—34no—
466C2×M16C22×D312yes—
467C22×C8C22×D312yes—
468C4⋊Q8—31no—
469C4⋊Q8—31no—
470#127—32no—
471#127—32no—
472#127—62no—
473#127—61no—
474#127—61no—
475#125—32no—
476#124—62no—
477#124—62no—
478#124—62no—
479#123—64no—
480#123—64no—
481C22⋊Q8—61no—
482C22⋊Q8—61no—
483#121—34no—
484#121—34no—
485#121—62no—
486#121—62no—
487#121—64no—
488#121—64no—
489#120—64no—
490C4×Q8—32no—
491C4×Q8—31no—
492C4×Q8—32no—
493C4×Q8—32no—
494C4×Q8—32no—
495C4×Q8—32no—
496C4×Q8—31no—
497C4×Q8—61no—
498C4×Q8—61no—
499C4×Q8—62no—
500C4×Q8—61no—
501C4×Q8—62no—
502C4×Q8—62no—
503C4×Q8—61no—
504C4×Q8—62no—
505C4×Q8—61no—
506C4×Q8—61no—
507C4×Q8—61no—
508C4×Q8D1211yescharacteristic
509C4×Q8D1211yescharacteristic
510C4×D4—31no—
511C4×D4—32no—
512C4×D4—31no—
513C4×D4—34no—
514C4×D4—34no—
515C4×D4—62no—
516C4×D4—61no—
517C4×D4—62no—
518C4×D4—61no—
519C4×D4—62no—
520C4×D4—61no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—62no—
527C4×D4—62no—
528C4×D4D1212yes—
529C4×D4D1211yescharacteristic
530C4×D4D1212yes—
531C4×D4D1211yescharacteristic
532#117—31no—
533#117—32no—
534#117—32no—
535#117—61no—
536#117—62no—
537#117—62no—
538#117—62no—
539#117—62no—
540#117—62no—
541#117—61no—
542#117C22×D311yescharacteristic
543#117C22×D312yes—
544C2×C4⋊C4—31no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—62no—
547C2×C4⋊C4—61no—
548C2×C4⋊C4—61no—
549C2×C4⋊C4—62no—
550C2×C22⋊C4—64no—
551C2×C42—62no—
552C2×C42—61no—
553C2×C42—62no—
554C2×C42—61no—
555C2×C42C22×D311yescharacteristic
556C2×C42C22×D312yes—
557#107—32no—
558#107—32no—
559#107—34no—
560#106—32no—
561#106—32no—
562#106—34no—
563C4⋊C8C22×D311yescharacteristic
564C4⋊C8C22×D311yescharacteristic
565C4⋊C8C22×D312yes—
566C4⋊C8C22×D312yes—
567C4⋊C8C22×D312yes—
568#103—32no—
569#103—32no—
570#103—34no—
571#103—34no—
572#102—34no—
573#102—34no—
574#102—32no—
575#102—32no—
576#102—34no—
577#102—34no—
578C22⋊C8C22×D314yes—
579C22⋊C8C22×D314yes—
580#97C22×D314yes—
581C4×C8C22×D314yes—
582C23×C3C22×D412yes—
583C23×C3C22×D411yescharacteristic
584C22×D3—21no—
585C22×D3—24no—
586C22×D3—44no—
587C22×D3—82no—
588C22×D3—82no—
589C3×Q8—22no—
590C3×D4—24no—
591C3×D4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—24no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—41no—
597C2×C3×C4—42no—
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D412yes—
600C2×C3×C4C22×D411yescharacteristic
601C2×C3×C4C22×D412yes—
602C2×C3×C4C22×D412yes—
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C2×#4112yes—
607C2×C3×C4C2×#4112yes—
608C2×C3×C4C2511yescharacteristic
609#67—28no—
610#67—24no—
611#67—84no—
612#67—84no—
613C2×Dic3—28no—
614C2×Dic3—24no—
615C2×Dic3—21no—
616C2×Dic3—22no—
617C2×Dic3—21no—
618C2×Dic3—22no—
619C2×Dic3—21no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—81no—
623C2×Dic3—82no—
624D12—21no—
625D12—24no—
626D12—24no—
627D12—44no—
628D12—44no—
629D12—44no—
630D12—82no—
631D12—82no—
632D12C2×#4112yes—
633C4×D3—28no—
634C4×D3—24no—
635C4×D3—42no—
636C4×D3—82no—
637C4×D3—81no—
638C4×D3—84no—
639C4×D3—84no—
640Dic6—28no—
641Dic6—24no—
642Dic6—22no—
643Dic6—21no—
644Dic6—42no—
645Dic6—42no—
646Dic6C2×#4112yes—
647Dic6C2×#4114yes—
648C3×C8—22no—
649C3×C8—22no—
650C3×C8—24no—
651C24—62no—
652#41—22no—
653#41—22no—
654#41—34no—
655#41—64no—
656#41—64no—
657#41—616no—
658#41—68no—
659#41—62no—
660#41—244no—
661#41—244no—
662C2×Q8—34no—
663C2×Q8—32no—
664C2×Q8—31no—
665C2×Q8—64no—
666C2×Q8—64no—
667C2×Q8—68no—
668C2×Q8—62no—
669C2×Q8—61no—
670C2×Q8—61no—
671C2×Q8—61no—
672C2×Q8—62no—
673C2×Q8C2×D1211yescharacteristic
674C2×D4—31no—
675C2×D4—34no—
676C2×D4—62no—
677C2×D4—61no—
678C2×D4—64no—
679C2×D4—64no—
680C2×D4—62no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—62no—
685C2×D4—64no—
686C2×D4—64no—
687C2×D4—242no—
688C2×D4—242no—
689C2×D4C2×D1212yes—
690C2×D4C2×D1211yescharacteristic
691C22×C4—62no—
692C22×C4—61no—
693C22×C4—62no—
694C22×C4—61no—
695C22×C4—62no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—62no—
699C22×C4—61no—
700C22×C4—64no—
701C22×C4—64no—
702C22×C4C2×D1212yes—
703C22×C4C2×D1211yescharacteristic
704C22×C4C2×D1212yes—
705C22×C4C2×D1211yescharacteristic
706C22×C4C23×D312yes—
707C22×C4C23×D311yescharacteristic
708SD16—68no—
709SD16—68no—
710SD16—68no—
711D8—68no—
712M16—24no—
713C2×C8—24no—
714C2×C8C23×D312yes—
715C2×C8C23×D314yes—
716C2×C8C23×D312yes—
717C4⋊C4—32no—
718C4⋊C4—31no—
719C4⋊C4—31no—
720C4⋊C4—32no—
721C4⋊C4—32no—
722C4⋊C4—62no—
723C4⋊C4—61no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—61no—
728C4⋊C4—62no—
729C4⋊C4—62no—
730C4⋊C4—61no—
731C4⋊C4—61no—
732C4⋊C4—61no—
733C4⋊C4—62no—
734C4⋊C4—62no—
735C4⋊C4C2×D1211yescharacteristic
736C4⋊C4C2×D1212yes—
737C4⋊C4C2×D1211yescharacteristic
738C4⋊C4C2×D1212yes—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—61no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C22⋊C4—61no—
745C22⋊C4—62no—
746C22⋊C4—61no—
747C22⋊C4—64no—
748C22⋊C4—64no—
749C22⋊C4C2×D1212yes—
750C22⋊C4C2×D1212yes—
751C22⋊C4C2×D1212yes—
752C42—61no—
753C42—62no—
754C42—62no—
755C42—61no—
756C42—62no—
757C42—61no—
758C42—62no—
759C42—62no—
760C42—62no—
761C42—62no—
762C42C2×D1212yes—
763C42C2×D1211yescharacteristic
764C42C2×D1212yes—
765C42C2×D1211yescharacteristic
766C42C23×D312yes—
767C42C23×D311yescharacteristic
768C42C23×D311yescharacteristic
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3#52512yes—
775C22×C3C23×D411yescharacteristic
776C2×D3—22no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—44no—
780C2×D3—44no—
781C2×D3—44no—
782C2×D3—164no—
783C3×C4—21no—
784C3×C4—22no—
785C3×C4—21no—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—21no—
789C3×C4#52512yes—
790C3×C4#57712yes—
791C3×C4C22×#4111yescharacteristic
792C3×C4C22×#4111yescharacteristic
793Dic3—22no—
794Dic3—24no—
795Dic3—42no—
796Dic3—42no—
797Dic3—41no—
798Dic3—42no—
799Dic3—41no—
800C23—61no—
801C23—64no—
802C23—124no—
803C23—242no—
804C23—242no—
805C23C22×D1212yes—
806C23C22×D1211yescharacteristic
807Q8—22no—
808Q8—34no—
809Q8—32no—
810Q8—68no—
811Q8—62no—
812Q8—61no—
813Q8—64no—
814Q8—122no—
815Q8—122no—
816D4—24no—
817D4—22no—
818D4—32no—
819D4—68no—
820D4—64no—
821D4—61no—
822D4—64no—
823D4—64no—
824D4—124no—
825D4—124no—
826D4—124no—
827D4—242no—
828D4—242no—
829D4—244no—
830D4—244no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—68no—
838C2×C4—68no—
839C2×C4—62no—
840C2×C4—61no—
841C2×C4—64no—
842C2×C4—64no—
843C2×C4—61no—
844C2×C4—62no—
845C2×C4—61no—
846C2×C4—62no—
847C2×C4—62no—
848C2×C4—122no—
849C2×C4—244no—
850C2×C4—244no—
851C2×C4—242no—
852C2×C4—241no—
853C2×C4—241no—
854C2×C4—242no—
855C2×C4C22×D1212yes—
856C2×C4C22×D1211yescharacteristic
857C2×C4C22×D1212yes—
858C2×C4C22×D1212yes—
859C2×C4C22×D1211yescharacteristic
860C2×C4C22×D1211yescharacteristic
861C2×C4C22×D1211yescharacteristic
862C2×C4C22×D1211yescharacteristic
863C2×C4D3×#4112yes—
864C2×C4D3×#4112yes—
865C2×C4C24×D311yescharacteristic
866C8—22no—
867C8—22no—
868C8—24no—
869C2×C3—22no—
870C2×C3—42no—
871C2×C3C2×#52511yescharacteristic
872C2×C3C2×#57711yescharacteristic
873C2×C3#358511yescharacteristic
874D3—42no—
875D3—84no—
876C22—21no—
877C22—21no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—62no—
882C22—121no—
883C22—121no—
884C22—124no—
885C22—124no—
886C22—124no—
887C22—484no—
888C22#552412yes—
889C22C23×D1211yescharacteristic
890C4—22no—
891C4—21no—
892C4—21no—
893C4—22no—
894C4—21no—
895C4—22no—
896C4—64no—
897C4—62no—
898C4—121no—
899C4—122no—
900C4—122no—
901C4—121no—
902C4—122no—
903C4#552412yes—
904C4#575112yes—
905C4C2×D3×#4111yescharacteristic
906C4C2×D3×#4111yescharacteristic
907C3#6059311yescharacteristic, complemented, Sylow
908C2—22no—
909C2—42no—
910C2—122no—
911C2—244no—
912C2C2×#552411yescharacteristic
913C2C2×#575111yescharacteristic
914C2#8716711yescharacteristic
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2925C2
socleC22×C3C23×D4
hypercenter#2925D3
hypocenterC3#60593
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
1. #85848C2semidirect
2. C4×#1010C2semidirect
3. C3×#2925C2semidirect
4. #79395C2semidirect
5. #79384C2semidirect
6. #79355C2semidirect
7. #79347C2semidirect
8. #79309C2semidirect
9. #79301C2semidirect
10. #79068C2semidirect
11. #79056C2semidirect
12. C2×#4848C2semidirect
13. #79025C2semidirect
14. #78678C2semidirect
15. #78651C2semidirect
16. #78572C2semidirect
17. #78560C2semidirect
39. #5523C22semidirect
42. #5516C22semidirect
47. C4×#235C22semidirect
50. C2×C4×Dic6C22semidirect
51. C3×#433C22semidirect
52. C3×#432C22semidirect
53. C3×#431C22semidirect
64. #4851C22semidirect
65. #4851C22semidirect
66. #4850C22semidirect
67. #4850C22semidirect
73. #4847C22semidirect
74. #4846C22semidirect
77. #4842C22semidirect
78. #4829C22semidirect
79. #4829C22semidirect
80. #4738C22semidirect
81. #4738C22semidirect
82. #4737C22semidirect
83. #4737C22semidirect
84. #4736C22semidirect
85. #4735C22semidirect
86. #4734C22semidirect
87. #4734C22semidirect
88. #4711C22semidirect
89. #4710C22semidirect
90. #4710C22semidirect
91. #4710C22semidirect
92. C4×D24C22semidirect
93. C4×#204C22semidirect
94. C4×#204C22semidirect
95. C4×#204C22semidirect
112. #2925D3semidirect
314. #433C2×D3semidirect
315. #432C2×D3semidirect
316. #431C2×D3semidirect
355. #235#41semidirect
381. C2×Dic6#41semidirect
907. C3#60593semidirect

Maximal subgroups

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

subgroupindex
#858482
C4×#10102
C3×#29252
#793952
#793842
#793552
#793472
#793092
#793012
#790682
#790562
C2×#48482
#790252
#786782
#786512
#785722
#785602
#605933