Finite Group Databasebeta

← #11673148

Subgroups — #11673148

Order 768.

2152 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86205C211yesmaximal, characteristic, complemented
2#85786C211yesmaximal, characteristic, complemented
3C2×C3×#476C211yesmaximal, characteristic, complemented
4#83199C211yesmaximal, characteristic, complemented
5C4×#932C211yesmaximal, characteristic, complemented
6#81080C212yesmaximal, complemented
7#81079C212yesmaximal, complemented
8#81078C214yesmaximal, complemented
9#81077C214yesmaximal, complemented
10#81076C212yesmaximal, complemented
11#81075C212yesmaximal, complemented
12#79120C212yesmaximal, complemented
13#79112C212yesmaximal, complemented
14#79021C211yesmaximal, characteristic, complemented
15#79004C211yesmaximal, characteristic, complemented
16#78747C212yesmaximal, complemented
17#78742C212yesmaximal, complemented
18#61200—31nomaximal, Sylow
19C2×#1004C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic, complemented
21C2×C3×C4×D4C2211yescharacteristic
22#5817—22no—
23C2×#932C2211yescharacteristic
24C2×#930—22no—
25C2×#904C2212yescomplemented
26C2×#901C2212yescomplemented
27#5734C2212yescomplemented
28#5733—22no—
29#5732C2212yescomplemented
30#5730C2212yescomplemented
31#5728—21no—
32#5726C2212yescomplemented
33#5725—21no—
34#5555—21no—
35#5555C2212yes—
36#5554—22no—
37#5554C2214yes—
38D4×D12—21no—
39D4×D12C2212yes—
40#5514—22no—
41#5510C2212yes—
42#5510C2212yescomplemented
43#5504C2212yescomplemented
44#5493—22no—
45#5477C2211yescharacteristic
46#5477C2211yescharacteristic
47C4×#235C2211yescharacteristic, complemented
48C3×#476C2212yescomplemented
49C3×#476C2214yescomplemented
50C3×#476C2212yescomplemented
51C2×C3×#106C2212yescomplemented
52C2×C3×C4⋊C8C2211yescharacteristic, complemented
53C2×C3×#102C2212yes—
54#5215C2211yescharacteristic
55#5113C2212yescomplemented
56#5110C2212yescomplemented
57#5093C2212yescomplemented
58#5089C2214yescomplemented
59#5088C2212yescomplemented
60#5018C2212yescomplemented
61C4×#214C2212yescomplemented
62#5014C2212yescomplemented
63C4×#213C2212yescomplemented
64#4966C2212yescomplemented
65#4966C2211yescharacteristic, complemented
66#4966C2212yescomplemented
67#4964C2211yescharacteristic, complemented
68C4×#208C2211yescharacteristic, complemented
69#4868C2214yescomplemented
70#4867C2214yescomplemented
71#4866C2214yescomplemented
72#4865C2214yescomplemented
73#4864C2214yescomplemented
74#4864C2214yescomplemented
75#4863C2214yescomplemented
76#4862C2214yescomplemented
77#4849C2211yescharacteristic, complemented
78#4848C2211yescharacteristic, complemented
79#4845C2212yescomplemented
80#4844C2212yescomplemented
81#4843C2211yescharacteristic, complemented
82#4841C2211yescharacteristic, complemented
83#4838C2212yescomplemented
84#4836C2214yescomplemented
85#4834C2212yescomplemented
86#4783C2214yescomplemented
87#4781C2214yescomplemented
88#4776C2214yescomplemented
89#4773C2214yescomplemented
90#4772C2214yescomplemented
91#4771C2214yescomplemented
92#4770C2214yescomplemented
93D3×#102C2214yescomplemented
94#3511—31no—
95#3496—31no—
96#3331—32no—
97#3325—32no—
98#3311—34no—
99#3306—34no—
100#3303—32no—
101#3295—32no—
102#3141—31no—
103#3099—32no—
104C2×#476D311yescharacteristic, complemented
105#3060—32no—
106#3035—31no—
107#3012—32no—
108C4×AGL(1,ℤ/8)—31no—
109#2935—31no—
110#2897—32no—
111C22×C3×Q8—21no—
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C22×#67—24no—
115C2×#239—22no—
116#1004—28no—
117#1004—44no—
118C2×#237—22no—
119C2×#237C2314yes—
120C2×D3×D4—22no—
121C2×D3×D4C2314yes—
122C2×#235C2312yes—
123C2×#235C2312yes—
124C2×#235C2311yescharacteristic
125C22×D12—22no—
126C22×C3×C8C2312yes—
127C3×C4⋊Q8—21no—
128C3×C4⋊Q8—21no—
129C3×C4⋊Q8C2312yes—
130C3×C4⋊Q8C2312yes—
131C3×C4×D4—21no—
132C3×C4×D4—21no—
133C3×C4×D4C2312yes—
134C3×C4×D4C2312yes—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2312yes—
138C2×C3×C22⋊C4—21no—
139C2×C3×C42C2311yescharacteristic
140#947—22no—
141#947—24no—
142#946—24no—
143#946—22no—
144Q8×Dic3—22no—
145C2×#214C2312yes—
146#932—24no—
147C2×#213C2312yes—
148#930—21no—
149#930—21no—
150#930—24no—
151#930—24no—
152#930—22no—
153#930—24no—
154#930—22no—
155#930D412yes—
156#930D412yes—
157C4×#67—21no—
158C4×#67—21no—
159C4×#67—24no—
160C2×(C2×D3)⋊C4—24no—
161#926C2311yescharacteristic
162C2×C4⋊Dic3—22no—
163C2×#208C2311yescharacteristic
164C2×#208C2311yescharacteristic
165C2×Dic12C2312yes—
166#904—44no—
167C2×D24C2312yes—
168C2×#204C2312yes—
169C2×#204C2312yes—
170#901—44no—
171C2×ΓL(1,𝔽25)C2314yes—
172C2×D3×C8C2314yes—
173#898—24no—
174#897—22no—
175#897—22no—
176#897C2314yes—
177#897C2314yes—
178#895—22no—
179#895—22no—
180#895—22no—
181#895C2314yes—
182#895C2314yes—
183#894—24no—
184#893—22no—
185#893—22no—
186#892—22no—
187#892C2314yes—
188D3×C4⋊C4C2314yes—
189#890—22no—
190#887—22no—
191#886—24no—
192#886—24no—
193#882—24no—
194#882—24no—
195#875D412yes—
196#875C2312yes—
197#874D411yescharacteristic
198#874C2311yescharacteristic
199C4×D12—21no—
200C4×D12—21no—
201C4×D12C2312yes—
202C4×D12C2312yes—
203C4×D12C2311yescharacteristic
204C4×D12C2311yescharacteristic
205#872—21no—
206C42×D3—21no—
207#869D411yescharacteristic
208#869C2311yescharacteristic
209C4×Dic6C2311yescharacteristic
210C4×Dic6C2311yescharacteristic
211C3×#106C2314yes—
212C3×#106C2314yes—
213C3×C4⋊C8C2311yescharacteristic
214C3×C4⋊C8C2312yes—
215C3×C4⋊C8C2311yescharacteristic
216C3×#102C2314yes—
217C3×#102C2314yes—
218#832C2312yes—
219#832C2312yes—
220#821C2312yes—
221#821C2312yes—
222(C2×D3)⋊C8C2314yes—
223(C2×D3)⋊C8C2314yes—
224#816C2312yes—
225#816C2312yes—
226#810C2312yes—
227#810C2314yes—
228#810C2314yes—
229#809C2312yes—
230#809C2314yes—
231#809C2314yes—
232#808C2312yes—
233#807C2312yes—
234#803C2312yes—
235C4×C3⋊C8C2312yes—
236C2×H(5,𝔽2)—32no—
237C2×AGL(1,ℤ/8)—31no—
238C2×#135—32no—
239C2×#131—32no—
240#556—32no—
241#555—32no—
242#554—32no—
243#553—62no—
244#548—62no—
245#547—32no—
246#547—32no—
247#547—61no—
248#546—34no—
249#546—62no—
250D42—32no—
251D42—61no—
252#542—62no—
253#537—32no—
254#537—32no—
255#534—62no—
256#533—61no—
257#532—31no—
258#532—31no—
259#532—61no—
260C2×C4⋊Q8C2×D311yescharacteristic, complemented
261C2×#121—62no—
262#520—32no—
263C4×#41—31no—
264C2×C4×D4C2×D311yescharacteristic
265#489—34no—
266#487—32no—
267#486—32no—
268#485—34no—
269#483—34no—
270#482—34no—
271#481—34no—
272#476C2×D312yescomplemented
273#476C2×D312yescomplemented
274#476C2×D314yescomplemented
275#470—34no—
276#469—34no—
277#465—34no—
278#465—34no—
279#464—32no—
280#463—32no—
281#462—31no—
282#461—31no—
283#460—31no—
284#459—31no—
285#452—34no—
286#450—34no—
287#449—34no—
288#447—34no—
289#442—32no—
290#440—32no—
291C4×SD16—32no—
292C4×D8—32no—
293#436—32no—
294#435—34no—
295C8×D4—32no—
296#428—31no—
297C2×#106C2×D312yescomplemented
298C2×C4⋊C8C2×D311yescharacteristic, complemented
299#418—31no—
300#418—34no—
301#417—32no—
302#417—32no—
303#417—31no—
304#417—34no—
305#416—32no—
306#416—34no—
307C2×#102—34no—
308C2×#102C2×D312yes—
309#408—32no—
310C4×M16—31no—
311C24×C3—21no—
312C23×D3—24no—
313C2×C3×Q8—22no—
314C2×C3×Q8—22no—
315C2×C3×Q8—82no—
316C2×C3×D4—21no—
317C2×C3×D4—22no—
318C2×C3×D4#4114yescomplemented
319C2×C3×D4C2412yes—
320C22×C3×C4—22no—
321C22×C3×C4—21no—
322C22×C3×C4—22no—
323C22×C3×C4—22no—
324C22×C3×C4—82no—
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2411yescharacteristic
328C2×#67—21no—
329C2×#67—22no—
330C2×#67—24no—
331C2×#67—24no—
332C2×#67—416no—
333C2×#67C2×D414yes—
334C22×Dic3—24no—
335#239—84no—
336#237—28no—
337#237—44no—
338#237—48no—
339D3×D4—28no—
340D3×D4—44no—
341D3×D4—48no—
342#235—24no—
343#235—24no—
344#235—22no—
345#235—24no—
346#235—22no—
347#235—24no—
348C2×D12—21no—
349C2×D12—24no—
350C2×D12—24no—
351C2×D12—21no—
352C2×D12—84no—
353C2×D12C2×D412yes—
354C2×D12C2×D412yes—
355C2×D12C2×D412yes—
356C2×D12C2412yes—
357C2×D12C2411yescharacteristic
358C2×C4×D3—21no—
359C2×C4×D3—21no—
360C2×C4×D3—21no—
361C2×C4×D3—22no—
362C2×C4×D3—24no—
363C2×C4×D3C2414yes—
364C2×Dic6C2×D412yes—
365C2×Dic6C2412yes—
366C2×Dic6C2411yescharacteristic
367C2×C3×C8—24no—
368C2×C3×C8C2412yes—
369C2×C3×C8C2412yes—
370C3×C4⋊C4—22no—
371C3×C4⋊C4—22no—
372C3×C4⋊C4—22no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4C2412yes—
375C3×C4⋊C4C2414yes—
376C3×C22⋊C4—22no—
377C3×C22⋊C4—22no—
378C3×C42C2×D411yescharacteristic
379C3×C42C2×D411yescharacteristic
380C3×C42C2411yescharacteristic
381C3×C42C2411yescharacteristic
382#217—21no—
383#214—24no—
384#213—24no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—24no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—22no—
391(C2×D3)⋊C4—22no—
392(C2×D3)⋊C4—24no—
393(C2×D3)⋊C4—24no—
394(C2×D3)⋊C4C2×D414yes—
395(C2×D3)⋊C4C2×D414yes—
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3—24no—
399C4⋊Dic3—24no—
400C4⋊Dic3C2×D412yes—
401C4⋊Dic3C2×D412yes—
402C4⋊Dic3C2411yescharacteristic
403C4⋊Dic3C2411yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4—24no—
407C4×Dic3—21no—
408C4×Dic3—21no—
409C4×Dic3—21no—
410C4×Dic3—24no—
411#208—22no—
412#208—22no—
413C2×C3⋊C8C2412yes—
414C2×C3⋊C8C2412yes—
415Dic12—42no—
416D24—42no—
417#204—42no—
418#204—42no—
419ΓL(1,𝔽25)—44no—
420D3×C8—44no—
421H(5,𝔽2)—68no—
422H(5,𝔽2)—124no—
423C2×#41—32no—
424C2×#41—34no—
425C2×#41—31no—
426C2×#41—32no—
427C2×#41—62no—
428C2×#41—62no—
429C22×Q8—21no—
430C22×D4—34no—
431C22×D4—62no—
432C22×D4—62no—
433C22×D4—64no—
434C22×D4C22×D311yescharacteristic
435C23×C4—21no—
436AGL(1,ℤ/8)—64no—
437#135—124no—
438C2×Q16—32no—
439C2×SD16—32no—
440C2×SD16—32no—
441C2×SD16—32no—
442C2×D8—32no—
443C2×D8—32no—
444#131—124no—
445C2×M16—31no—
446C2×M16—31no—
447C2×M16—34no—
448C22×C8—34no—
449C22×C8C22×D312yes—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—31no—
453C4⋊Q8—31no—
454C4⋊Q8C22×D312yes—
455C4⋊Q8C22×D312yes—
456#127—31no—
457#127—31no—
458#126—64no—
459#125—62no—
460#124—32no—
461#124—32no—
462#124—64no—
463#124—62no—
464#123—64no—
465#123—64no—
466#123—64no—
467C22⋊Q8—34no—
468C22⋊Q8—34no—
469C22⋊Q8—64no—
470C22⋊Q8—62no—
471C22⋊Q8—62no—
472C22⋊Q8—62no—
473#121—32no—
474#121—32no—
475#121—34no—
476#121—34no—
477#121—64no—
478#121—62no—
479#121—62no—
480#121—62no—
481#121—62no—
482#121—64no—
483#121—62no—
484#121—64no—
485#121—61no—
486#121—61no—
487#120—64no—
488#120—64no—
489C4×Q8—31no—
490C4×Q8—31no—
491C4×Q8—62no—
492C4×Q8—62no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—32no—
496C4×D4—32no—
497C4×D4—31no—
498C4×D4—31no—
499C4×D4—62no—
500C4×D4—62no—
501C4×D4—64no—
502C4×D4—61no—
503C4×D4—61no—
504C4×D4—61no—
505C4×D4—61no—
506C4×D4C22×D312yes—
507C4×D4C22×D312yes—
508#117—31no—
509#117—34no—
510#117—62no—
511#117—61no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—34no—
514C2×C4⋊C4—62no—
515C2×C4⋊C4C22×D311yescharacteristic
516C2×C4⋊C4C22×D312yes—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—64no—
519C2×C42—61no—
520C2×C42C22×D311yescharacteristic
521#107—32no—
522#106—32no—
523#106C22×D314yes—
524#106C22×D314yes—
525C4⋊C8C22×D311yescharacteristic
526C4⋊C8C22×D312yes—
527C4⋊C8C22×D311yescharacteristic
528#103—32no—
529#103—32no—
530#103—34no—
531#103—32no—
532#103—34no—
533#102—32no—
534#102—32no—
535#102—32no—
536#102—32no—
537#102—34no—
538#102—32no—
539#102—34no—
540#102C22×D314yes—
541#102C22×D314yes—
542C22⋊C8—34no—
543C22⋊C8—34no—
544#97—32no—
545C4×C8—32no—
546C23×C3—22no—
547C23×C3—24no—
548C23×C3—81no—
549C23×C3—81no—
550C23×C3C22×D411yescharacteristic
551C22×D3—21no—
552C22×D3—22no—
553C22×D3—48no—
554C22×D3—84no—
555C22×D3—84no—
556C22×D3C22×D414yes—
557C3×Q8—44no—
558C3×Q8—82no—
559C3×D4—24no—
560C3×D4—22no—
561C3×D4C2×#4114yes—
562C2×C3×C4—22no—
563C2×C3×C4—24no—
564C2×C3×C4—22no—
565C2×C3×C4—41no—
566C2×C3×C4—44no—
567C2×C3×C4—82no—
568C2×C3×C4—81no—
569C2×C3×C4—82no—
570C2×C3×C4C22×D411yescharacteristic
571C2×C3×C4C22×D411yescharacteristic
572C2×C3×C4C22×D411yescharacteristic
573C2×C3×C4C22×D411yescharacteristic
574C2×C3×C4C22×D411yescharacteristic
575C2×C3×C4C2×#4112yes—
576C2×C3×C4H(5,𝔽2)12yes—
577C2×C3×C4C2511yescharacteristic
578#67—28no—
579#67—48no—
580#67—48no—
581#67—42no—
582#67—44no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—22no—
587C2×Dic3—48no—
588C2×Dic3C22×D414yes—
589D12—24no—
590D12—24no—
591D12—21no—
592D12—22no—
593D12—21no—
594D12—22no—
595D12—42no—
596D12—42no—
597D12—81no—
598D12—84no—
599D12—84no—
600C4×D3—24no—
601C4×D3—24no—
602C4×D3—42no—
603C4×D3—42no—
604C4×D3—44no—
605C4×D3—42no—
606C4×D3—84no—
607Dic6—24no—
608Dic6—21no—
609Dic6—22no—
610Dic6—21no—
611Dic6—22no—
612C3×C8—22no—
613C3×C8—22no—
614C3⋊C8—22no—
615C3⋊C8—22no—
616C24—21no—
617C24—64no—
618#41—64no—
619#41—64no—
620#41—68no—
621#41—62no—
622#41—64no—
623#41—62no—
624#41—64no—
625#41—124no—
626#41—128no—
627#41—244no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—32no—
631C2×Q8—32no—
632C2×Q8—31no—
633C2×Q8—82no—
634C2×D4—21no—
635C2×D4—22no—
636C2×D4—34no—
637C2×D4—32no—
638C2×D4—32no—
639C2×D4—32no—
640C2×D4—32no—
641C2×D4—31no—
642C2×D4—64no—
643C2×D4—64no—
644C2×D4—64no—
645C2×D4—68no—
646C2×D4—64no—
647C2×D4—61no—
648C2×D4—62no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—124no—
652C2×D4—128no—
653C2×D4—1216no—
654C2×D4—244no—
655C2×D4#23914yescomplemented
656C2×D4C23×D312yes—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—34no—
662C22×C4—64no—
663C22×C4—64no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—62no—
668C22×C4—82no—
669C22×C4D3×D411yescharacteristic
670C22×C4D3×D411yescharacteristic
671C22×C4C23×D311yescharacteristic
672Q16—122no—
673SD16—64no—
674SD16—122no—
675SD16—122no—
676D8—64no—
677D8—122no—
678M16—62no—
679M16—62no—
680M16—124no—
681C2×C8—24no—
682C2×C8—32no—
683C2×C8—32no—
684C2×C8—124no—
685C2×C8C23×D312yes—
686C2×C8C23×D312yes—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—22no—
691C4⋊C4—32no—
692C4⋊C4—32no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—64no—
696C4⋊C4—64no—
697C4⋊C4—64no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4—61no—
701C4⋊C4—61no—
702C4⋊C4C23×D314yes—
703C4⋊C4C23×D312yes—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—64no—
709C22⋊C4—64no—
710C22⋊C4—64no—
711C22⋊C4—64no—
712C22⋊C4—64no—
713C22⋊C4—61no—
714C22⋊C4—62no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—62no—
718C42—64no—
719C42—61no—
720C42—61no—
721C42—61no—
722C42D3×D411yescharacteristic
723C42D3×D411yescharacteristic
724C42C23×D311yescharacteristic
725C42C23×D311yescharacteristic
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—24no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—84no—
732C22×C3#54612yes—
733C22×C3C23×D411yescharacteristic
734C2×D3—24no—
735C2×D3—24no—
736C2×D3—24no—
737C2×D3—41no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—42no—
743C2×D3—168no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—44no—
748C3×C4—42no—
749C3×C4#54612yes—
750C3×C4#57712yes—
751C3×C4C22×#4111yescharacteristic
752C3×C4C2×H(5,𝔽2)11yescharacteristic
753Dic3—24no—
754Dic3—41no—
755Dic3—42no—
756Dic3—41no—
757Dic3—41no—
758C23—22no—
759C23—24no—
760C23—34no—
761C23—61no—
762C23—62no—
763C23—81no—
764C23—81no—
765C23—128no—
766C23—244no—
767C23—244no—
768C23C2×D3×D411yescharacteristic
769Q8—44no—
770Q8—64no—
771Q8—61no—
772Q8—62no—
773Q8—61no—
774Q8—62no—
775Q8—82no—
776D4—22no—
777D4—24no—
778D4—68no—
779D4—61no—
780D4—62no—
781D4—61no—
782D4—62no—
783D4—64no—
784D4—64no—
785D4—122no—
786D4—128no—
787D4—128no—
788D4—124no—
789D4—122no—
790D4—122no—
791D4—241no—
792D4—244no—
793D4—244no—
794D4C2×#23914yes—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—34no—
799C2×C4—41no—
800C2×C4—44no—
801C2×C4—64no—
802C2×C4—64no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—62no—
807C2×C4—82no—
808C2×C4—81no—
809C2×C4—82no—
810C2×C4—122no—
811C2×C4—128no—
812C2×C4—122no—
813C2×C4—124no—
814C2×C4—122no—
815C2×C4—244no—
816C2×C4C2×D3×D411yescharacteristic
817C2×C4C2×D3×D411yescharacteristic
818C2×C4C2×D3×D411yescharacteristic
819C2×C4C2×D3×D411yescharacteristic
820C2×C4C2×D3×D411yescharacteristic
821C2×C4C2×#23912yes—
822C2×C4#100912yes—
823C2×C4C24×D311yescharacteristic
824C8—22no—
825C8—22no—
826C8—62no—
827C8—62no—
828C2×C3—22no—
829C2×C3—44no—
830C2×C3C2×#54611yescharacteristic
831C2×C3C2×#57711yescharacteristic
832C2×C3#358511yescharacteristic
833D3—44no—
834D3—81no—
835D3—82no—
836C22—21no—
837C22—21no—
838C22—24no—
839C22—42no—
840C22—42no—
841C22—64no—
842C22—64no—
843C22—64no—
844C22—84no—
845C22—121no—
846C22—122no—
847C22—121no—
848C22—122no—
849C22—122no—
850C22—121no—
851C22—488no—
852C22#563012yes—
853C22C22×D3×D411yescharacteristic
854C4—21no—
855C4—21no—
856C4—21no—
857C4—42no—
858C4—44no—
859C4—64no—
860C4—121no—
861C4—121no—
862C4—122no—
863C4—121no—
864C4#563012yes—
865C4#576212yes—
866C4C22×#23911yescharacteristic
867C4C2×#100911yescharacteristic
868C3#6120011yescharacteristic, complemented, Sylow
869C2—22no—
870C2—44no—
871C2—124no—
872C2—242no—
873C2—241no—
874C2C2×#563011yescharacteristic
875C2C2×#576211yescharacteristic
876C2#8719211yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#476C2
socleC22×C3C23×D4
hypercenterC2×#476D3
hypocenterC3#61200
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #86205C2semidirect
2. #85786C2semidirect
3. C2×C3×#476C2semidirect
4. #83199C2semidirect
5. C4×#932C2semidirect
6. #81080C2semidirect
7. #81079C2semidirect
8. #81078C2semidirect
9. #81077C2semidirect
10. #81076C2semidirect
11. #81075C2semidirect
12. #79120C2semidirect
13. #79112C2semidirect
14. #79021C2semidirect
15. #79004C2semidirect
16. #78747C2semidirect
17. #78742C2semidirect
20. C2×C3×C4⋊Q8C22semidirect
25. C2×#904C22semidirect
26. C2×#901C22semidirect
27. #5734C22semidirect
29. #5732C22semidirect
30. #5730C22semidirect
32. #5726C22semidirect
42. #5510C22semidirect
43. #5504C22semidirect
47. C4×#235C22semidirect
48. C3×#476C22semidirect
49. C3×#476C22semidirect
50. C3×#476C22semidirect
51. C2×C3×#106C22semidirect
52. C2×C3×C4⋊C8C22semidirect
55. #5113C22semidirect
56. #5110C22semidirect
57. #5093C22semidirect
58. #5089C22semidirect
59. #5088C22semidirect
60. #5018C22semidirect
61. C4×#214C22semidirect
62. #5014C22semidirect
63. C4×#213C22semidirect
64. #4966C22semidirect
65. #4966C22semidirect
66. #4966C22semidirect
67. #4964C22semidirect
68. C4×#208C22semidirect
69. #4868C22semidirect
70. #4867C22semidirect
71. #4866C22semidirect
72. #4865C22semidirect
73. #4864C22semidirect
74. #4864C22semidirect
75. #4863C22semidirect
76. #4862C22semidirect
77. #4849C22semidirect
78. #4848C22semidirect
79. #4845C22semidirect
80. #4844C22semidirect
81. #4843C22semidirect
82. #4841C22semidirect
83. #4838C22semidirect
84. #4836C22semidirect
85. #4834C22semidirect
86. #4783C22semidirect
87. #4781C22semidirect
88. #4776C22semidirect
89. #4773C22semidirect
90. #4772C22semidirect
91. #4771C22semidirect
92. #4770C22semidirect
93. D3×#102C22semidirect
104. C2×#476D3semidirect
260. C2×C4⋊Q8C2×D3semidirect
272. #476C2×D3semidirect
273. #476C2×D3semidirect
274. #476C2×D3semidirect
297. C2×#106C2×D3semidirect
298. C2×C4⋊C8C2×D3semidirect
318. C2×C3×D4#41semidirect
655. C2×D4#239semidirect
868. C3#61200semidirect

Maximal subgroups

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

subgroupindex
#862052
#857862
C2×C3×#4762
#831992
C4×#9322
#810802
#810792
#810782
#810772
#810762
#810752
#791202
#791122
#790212
#790042
#787472
#787422
#612003