Finite Group Databasebeta

← #6498937

Subgroups — #6498937

Order 512.

2194 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3241C211yesmaximal, characteristic, complemented
2C2×#3224C211yesmaximal, characteristic, complemented
3C2×#3179C211yesmaximal, characteristic, complemented
4C2×#3136C211yesmaximal, characteristic, complemented
5#37423C211yesmaximal, characteristic, complemented
6#37302C211yesmaximal, characteristic, complemented
7#33253C211yesmaximal, characteristic, complemented
8#33243C211yesmaximal, characteristic, complemented
9#33235C211yesmaximal, characteristic, complemented
10#33228C211yesmaximal, characteristic, complemented
11#30287C211yesmaximal, characteristic, complemented
12#30286C211yesmaximal, characteristic, complemented
13#30274C211yesmaximal, characteristic, complemented
14#30265C211yesmaximal, characteristic, complemented
15#28436C211yesmaximal, characteristic, complemented
16#28435C211yesmaximal, characteristic, complemented
17#28422C211yesmaximal, characteristic, complemented
18#28421C211yesmaximal, characteristic, complemented
19#28420C211yesmaximal, characteristic, complemented
20#28413C211yesmaximal, characteristic, complemented
21#28412C211yesmaximal, characteristic, complemented
22#28409C211yesmaximal, characteristic, complemented
23#28366C211yesmaximal, characteristic, complemented
24#28365C211yesmaximal, characteristic, complemented
25#28354C211yesmaximal, characteristic, complemented
26#28353C211yesmaximal, characteristic, complemented
27#28352C211yesmaximal, characteristic, complemented
28#28349C211yesmaximal, characteristic, complemented
29#28344C211yesmaximal, characteristic, complemented
30#28341C211yesmaximal, characteristic, complemented
31#20475C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#540C2211yescharacteristic
35C2×#535C2211yescharacteristic
36#3241—28no—
37#3224—28no—
38#3179—28no—
39C2×#501C2211yescharacteristic, complemented
40C2×#501C2211yescharacteristic, complemented
41C2×#499C2211yescharacteristic, complemented
42C2×#496C2211yescharacteristic
43C2×#496C2211yescharacteristic, complemented
44C2×#495C2211yescharacteristic
45#3136—28no—
46C2×#490C2211yescharacteristic
47C2×#490C2211yescharacteristic
48C2×#490C2211yescharacteristic, complemented
49C2×#489C2211yescharacteristic
50C2×#489C2211yescharacteristic
51C2×#489C2211yescharacteristic
52C2×#488C2211yescharacteristic
53C2×#488C2211yescharacteristic
54C2×#488C2211yescharacteristic, complemented
55C2×#486C2211yescharacteristic
56C2×#486C2211yescharacteristic
57C2×#486C2211yescharacteristic
58C2×#486C2211yescharacteristic, complemented
59C2×#486C2211yescharacteristic, complemented
60C2×#481C2211yescharacteristic
61C2×#482C2211yescharacteristic
62C2×#482C2211yescharacteristic
63C2×#480C2211yescharacteristic
64C2×#478C2211yescharacteristic, complemented
65C2×#478C2211yescharacteristic, complemented
66C2×#476C2211yescharacteristic, complemented
67C2×#474C2211yescharacteristic, complemented
68C2×#469C2211yescharacteristic
69C2×#468C2211yescharacteristic
70C2×#466C2211yescharacteristic
71C2×#465C2211yescharacteristic
72C2×#464C2211yescharacteristic
73C2×#460C2211yescharacteristic
74C2×#463C2211yescharacteristic
75C2×#459C2211yescharacteristic
76C2×#452C2211yescharacteristic
77C2×#449C2211yescharacteristic
78C2×#450C2211yescharacteristic
79C2×#447C2211yescharacteristic
80C2×#442C2211yescharacteristic, complemented
81C2×#440C2211yescharacteristic, complemented
82C2×C4×SD16C2211yescharacteristic, complemented
83C2×C4×D8C2211yescharacteristic, complemented
84C2×#433C2211yescharacteristic
85C2×#417C2211yescharacteristic
86C2×#418C2211yescharacteristic
87C2×#416C2211yescharacteristic
88C22×#102C2211yescharacteristic
89C2×#405C2211yescharacteristic
90#2867C2211yescharacteristic
91#2862C2211yescharacteristic, complemented
92#2861C2211yescharacteristic
93#2861C2211yescharacteristic, complemented
94#2716—22no—
95#2700—22no—
96#2690—22no—
97#2687—22no—
98#2673—22no—
99#2673—22no—
100#2669—22no—
101#2669—22no—
102#2660C2211yescharacteristic, complemented
103#2657C2211yescharacteristic
104#2641C2211yescharacteristic
105#2640C2211yescharacteristic, complemented
106#2568C2211yescharacteristic, complemented
107#2566C2211yescharacteristic, complemented
108#2565C2211yescharacteristic, complemented
109#2563C2211yescharacteristic, complemented
110#2544C2211yescharacteristic
111#2544C2211yescharacteristic
112#2541C2211yescharacteristic
113#2541C2211yescharacteristic
114#2504C2211yescharacteristic
115#2503C2211yescharacteristic
116#2500C2211yescharacteristic
117#2499C2211yescharacteristic
118#2433C2211yescharacteristic
119#2433C2211yescharacteristic
120#2431C2211yescharacteristic
121#2431C2211yescharacteristic
122#2298C2211yescharacteristic
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2097C2211yescharacteristic, complemented
126#2097C2211yescharacteristic, complemented
127#2094C2211yescharacteristic
128#2094C2211yescharacteristic, complemented
129#2093C2211yescharacteristic
130#2093C2211yescharacteristic, complemented
131#2092C2211yescharacteristic
132#2092C2211yescharacteristic
133#2092C2211yescharacteristic
134#2092C2211yescharacteristic
135#2092C2211yescharacteristic
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2015C2211yescharacteristic, complemented
140#2015C2211yescharacteristic, complemented
141#2014C2211yescharacteristic
142#2014C2211yescharacteristic
143#2014C2211yescharacteristic
144#2014C2211yescharacteristic
145#2014C2211yescharacteristic, complemented
146#2014C2211yescharacteristic, complemented
147#2012C2211yescharacteristic, complemented
148#2012C2211yescharacteristic, complemented
149#2011C2211yescharacteristic
150#2011C2211yescharacteristic
151#2011C2211yescharacteristic
152#2011C2211yescharacteristic
153#2011C2211yescharacteristic, complemented
154#2011C2211yescharacteristic, complemented
155#1973C2211yescharacteristic
156#1973C2211yescharacteristic
157#1973C2211yescharacteristic
158#1973C2211yescharacteristic, complemented
159#1973C2211yescharacteristic, complemented
160#1973C2211yescharacteristic, complemented
161#1972C2211yescharacteristic
162#1972C2211yescharacteristic
163#1972C2211yescharacteristic
164#1972C2211yescharacteristic, complemented
165#1971C2211yescharacteristic, complemented
166#1971C2211yescharacteristic, complemented
167#1970C2211yescharacteristic
168#1970C2211yescharacteristic, complemented
169#1968C2211yescharacteristic
170#1968C2211yescharacteristic, complemented
171#1961C2211yescharacteristic
172#1961C2211yescharacteristic
173#1961C2211yescharacteristic
174#1961C2211yescharacteristic
175#1961C2211yescharacteristic
176#1961C2211yescharacteristic
177#1961C2211yescharacteristic, complemented
178#1961C2211yescharacteristic, complemented
179#1961C2211yescharacteristic, complemented
180#1961C2211yescharacteristic, complemented
181#1959C2211yescharacteristic, complemented
182#1959C2211yescharacteristic, complemented
183#1958C2211yescharacteristic, complemented
184#1958C2211yescharacteristic, complemented
185#1957C2211yescharacteristic
186#1957C2211yescharacteristic
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1770C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191#1753C2211yescharacteristic
192#1753C2211yescharacteristic
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic
195#1746C2211yescharacteristic, complemented
196#1745C2211yescharacteristic, complemented
197#1726C2211yescharacteristic, complemented
198C4×#97C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×D4C2311yescharacteristic
201C22×Q16C2311yescharacteristic
202C22×SD16C2311yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#544—24no—
216#544—24no—
217#542—24no—
218#542—24no—
219#540—24no—
220#540—24no—
221#535—24no—
222#535—24no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#127—22no—
228C2×#127—22no—
229C2×#127C2311yescharacteristic
230C2×#127C2311yescharacteristic
231C2×#127C2311yescharacteristic
232C2×#127C2311yescharacteristic
233C2×#127C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#127C2311yescharacteristic
236C2×#127C2311yescharacteristic
237C2×#127C2311yescharacteristic
238C2×#126—21no—
239C2×#125—21no—
240C2×#125C2311yescharacteristic
241C2×#125C2311yescharacteristic
242C2×#125C2311yescharacteristic
243C2×#124—21no—
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#123—21no—
250C2×#123—21no—
251C2×#123—21no—
252C2×C22⋊Q8—21no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8C2311yescharacteristic
256C2×#121—21no—
257C2×#121—21no—
258C2×#121—22no—
259C2×#121—22no—
260C2×#121—21no—
261C2×#121—21no—
262C2×#121C2311yescharacteristic
263C2×#121C2311yescharacteristic
264C2×#121C2311yescharacteristic
265C2×#120—21no—
266C2×#120—21no—
267C2×#120—22no—
268C2×#120—22no—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276#501—24no—
277#501—24no—
278#499—24no—
279#496—24no—
280#496—24no—
281#495—24no—
282#490—24no—
283#490—24no—
284#490—24no—
285#489—24no—
286#489—24no—
287#489—24no—
288#488—24no—
289#488—24no—
290#488—24no—
291#486—24no—
292#486—24no—
293#486—24no—
294#486—24no—
295#486—24no—
296#482—24no—
297#482—24no—
298#481—24no—
299#480—24no—
300#478—24no—
301#478—24no—
302#476—24no—
303#474—24no—
304#469—24no—
305#468—24no—
306#466—24no—
307#465—24no—
308#464—24no—
309#463—24no—
310#460—24no—
311#459—24no—
312#452—24no—
313#450—24no—
314#449—24no—
315#447—24no—
316#442—24no—
317#440—24no—
318C4×SD16—24no—
319C4×D8—24no—
320#433D418yescomplemented
321C2×#107C2311yescharacteristic
322C2×#107C2311yescharacteristic
323C2×#107C2311yescharacteristic
324C2×#107C2311yescharacteristic
325C2×#107C2311yescharacteristic
326C2×#107C2311yescharacteristic
327C2×#106C2311yescharacteristic
328C2×#106C2311yescharacteristic
329C2×#106C2311yescharacteristic
330C2×#106C2311yescharacteristic
331C2×#106C2311yescharacteristic
332C2×#106C2311yescharacteristic
333C2×C4⋊C8C2311yescharacteristic
334C2×C4⋊C8C2311yescharacteristic
335#418—24no—
336#417—24no—
337#416—24no—
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#102—24no—
347C2×#102C2311yescharacteristic
348C2×#102C2311yescharacteristic
349C2×#102C2311yescharacteristic
350C2×#102C2311yescharacteristic
351C2×#102C2311yescharacteristic
352C2×#102C2311yescharacteristic
353C2×#102C2311yescharacteristic
354C2×#102C2311yescharacteristic
355C2×#102C2311yescharacteristic
356C2×#102C2311yescharacteristic
357C2×#102C2311yescharacteristic
358C2×#102C2311yescharacteristic
359C2×#102C2311yescharacteristic
360C2×#102C2311yescharacteristic
361C2×#102C2311yescharacteristic
362C2×#102C2311yescharacteristic
363C2×#102C2311yescharacteristic
364C2×#102C2311yescharacteristic
365C2×#102C2311yescharacteristic
366C2×#102C2311yescharacteristic
367C2×#102C2311yescharacteristic
368C2×#102C2311yescharacteristic
369C2×#102C2311yescharacteristic
370C2×#102C2311yescharacteristic
371C2×#102C2311yescharacteristic
372C2×#102C2311yescharacteristic
373C2×#102C2311yescharacteristic
374C2×#102C2311yescharacteristic
375C2×#102C2311yescharacteristic
376C2×#102C2311yescharacteristic
377C2×#102C2311yescharacteristic
378C2×#102C2311yescharacteristic
379C2×C22⋊C8C2311yescharacteristic
380C2×C22⋊C8C2311yescharacteristic
381#405D418yescomplemented
382C2×#97C2311yescharacteristic
383C2×#97C2311yescharacteristic
384C2×#97C2311yescharacteristic
385C2×#97C2311yescharacteristic
386C2×#97C2311yescharacteristic
387C2×#97C2311yescharacteristic
388C2×#97C2311yescharacteristic
389C2×#97C2311yescharacteristic
390C2×#97C2311yescharacteristic
391C2×C4×C8C2311yescharacteristic
392C2×C4×C8C2311yescharacteristic
393C2×C4×C8C2311yescharacteristic
394C2×C4×C8C2311yescharacteristic
395C2×C4×C8C2311yescharacteristic
396#400—22no—
397#400—22no—
398#398—22no—
399#398—22no—
400#397—22no—
401#397—22no—
402#397—22no—
403#396—22no—
404#395—22no—
405#394—22no—
406#394—22no—
407#394—22no—
408#394—22no—
409#394—22no—
410#393—22no—
411#393—22no—
412#392—22no—
413#392—22no—
414#392—22no—
415#392—22no—
416#392—22no—
417#392—22no—
418#392—22no—
419#392—22no—
420#391—22no—
421#391—22no—
422#391—22no—
423#391C2311yescharacteristic
424#391C2311yescharacteristic
425#391C2311yescharacteristic
426#391C2311yescharacteristic
427#391C2311yescharacteristic
428#391C2311yescharacteristic
429#390C2311yescharacteristic
430#390C2311yescharacteristic
431#390C2311yescharacteristic
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#388—22no—
440#388—22no—
441#388—22no—
442#388—22no—
443#388—22no—
444#388D412yes—
445#388D412yes—
446#387—22no—
447#387—22no—
448#387D412yes—
449#387D412yes—
450#386—22no—
451#386—22no—
452#386—22no—
453#386—22no—
454#386—22no—
455#385—22no—
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#382C2311yescharacteristic
464#381—22no—
465#380—22no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470#376C2311yescharacteristic
471C43C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C25—21no—
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2411yescharacteristic
527C2×Q16—22no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16C2×D414yes—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8C2×D414yes—
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—22no—
580C4⋊Q8—22no—
581C4⋊Q8—22no—
582C4⋊Q8—22no—
583C4⋊Q8—44no—
584#127—22no—
585#127—22no—
586#127—22no—
587#127—22no—
588#127—22no—
589#127—22no—
590#127—41no—
591#127—41no—
592#127—41no—
593#127—41no—
594#127—41no—
595#127—41no—
596#127—41no—
597#127—41no—
598#127—41no—
599#127—41no—
600#127—41no—
601#127—41no—
602#127—84no—
603#127—84no—
604#126—44no—
605#125—22no—
606#125—22no—
607#125—22no—
608#125—22no—
609#125—22no—
610#125—22no—
611#125—44no—
612#124—22no—
613#124—22no—
614#124—22no—
615#124—22no—
616#124—22no—
617#124—22no—
618#124—41no—
619#124—41no—
620#124—41no—
621#124—41no—
622#124—44no—
623#123—44no—
624#123—44no—
625#123—44no—
626C22⋊Q8—22no—
627C22⋊Q8—22no—
628C22⋊Q8—44no—
629C22⋊Q8—44no—
630C22⋊Q8—44no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—44no—
638#121—44no—
639#121—44no—
640#121—44no—
641#121—84no—
642#121—84no—
643#120—44no—
644#120—44no—
645#120—84no—
646#120—84no—
647C4×Q8—22no—
648C4×Q8—22no—
649C4×D4—22no—
650C4×D4—22no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655#117—22no—
656#117—22no—
657#117C2×D414yes—
658#117C2×D414yes—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4C2×D412yes—
676C2×C4⋊C4C2×D412yes—
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4C2×D412yes—
714C2×C22⋊C4C2×D412yes—
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C42—21no—
718C2×C42—21no—
719C2×C42C2×D412yes—
720C2×C42C2×D412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#107—22no—
728#107—22no—
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#106—22no—
734#106—22no—
735#106—22no—
736#106—22no—
737#106—22no—
738#106—22no—
739C4⋊C8C2×D414yes—
740C4⋊C8C2×D414yes—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781C22⋊C8C2×D414yes—
782C22⋊C8C2×D414yes—
783#97—41no—
784#97—41no—
785#97—41no—
786#97—41no—
787#97—41no—
788#97—41no—
789#97C2×D414yes—
790#97C2×D414yes—
791#97C2×D414yes—
792C4×C8—41no—
793C4×C8—41no—
794C4×C8C2×D414yes—
795C4×C8C2×D414yes—
796C4×C8C2×D414yes—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—22no—
802#95—22no—
803#95—22no—
804#95—22no—
805#95—22no—
806#95—22no—
807#95—22no—
808#95—22no—
809#95C2×D412yes—
810#95C2×D412yes—
811#95C2×D412yes—
812#95C2×D412yes—
813#95C2×D412yes—
814#95C2×D412yes—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—42no—
822C24—81no—
823C24—81no—
824C24—82no—
825C24—82no—
826C24C22×D411yescharacteristic
827#41—44no—
828#41—44no—
829#41—82no—
830#41—82no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—82no—
847C2×Q8—82no—
848C2×Q8—82no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—82no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—82no—
914C2×D4—82no—
915C2×D4—82no—
916C2×D4—82no—
917C2×D4—82no—
918C2×D4—82no—
919C2×D4—82no—
920C2×D4—82no—
921C2×D4—82no—
922C2×D4—82no—
923C2×D4—82no—
924C2×D4—82no—
925C2×D4—82no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—82no—
929C2×D4—82no—
930C2×D4—82no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—82no—
953C22×C4—82no—
954C22×C4—82no—
955C22×C4—82no—
956C22×C4C22×D412yes—
957C22×C4C22×D412yes—
958C22×C4C22×D412yes—
959C22×C4C22×D412yes—
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D412yes—
966C22×C4C22×D412yes—
967C22×C4C2511yescharacteristic
968Q16—82no—
969SD16—44no—
970SD16—44no—
971SD16—82no—
972SD16—82no—
973SD16—82no—
974SD16—82no—
975D8—44no—
976D8—44no—
977D8—82no—
978D8—82no—
979D8—82no—
980M16—44no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—44no—
998C2×C8C22×D412yes—
999C2×C8C22×D412yes—
1000C2×C8C22×D412yes—
1001C2×C8C22×D412yes—
1002C2×C8C22×D412yes—
1003C2×C8C22×D412yes—
1004C2×C8C22×D412yes—
1005C2×C8C22×D412yes—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—82no—
1037C4⋊C4—82no—
1038C4⋊C4#12714yes—
1039C4⋊C4#12714yes—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—82no—
1059C22⋊C4—82no—
1060C22⋊C4—82no—
1061C22⋊C4—82no—
1062C22⋊C4—82no—
1063C22⋊C4—82no—
1064C22⋊C4—82no—
1065C22⋊C4—82no—
1066C22⋊C4—82no—
1067C22⋊C4—82no—
1068C22⋊C4#12714yes—
1069C22⋊C4#12714yes—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—42no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42C22×D412yes—
1083C42C22×D412yes—
1084C42C22×D412yes—
1085C42C22×D412yes—
1086C23—22no—
1087C23—22no—
1088C23—21no—
1089C23—21no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—84no—
1121C23—162no—
1122C23—162no—
1123C23—164no—
1124C23—164no—
1125C23C2×#12712yes—
1126C23C23×D411yescharacteristic
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—162no—
1136Q8—162no—
1137Q8—162no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—84no—
1163D4—84no—
1164D4—162no—
1165D4—162no—
1166D4—162no—
1167D4—162no—
1168D4—162no—
1169D4—162no—
1170D4—164no—
1171D4—164no—
1172D4—164no—
1173D4—164no—
1174D4—164no—
1175D4—164no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—84no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4C2×#12712yes—
1229C2×C4C2×#12712yes—
1230C2×C4C2×#12712yes—
1231C2×C4C2×#12712yes—
1232C2×C4C2×#12712yes—
1233C2×C4C23×D411yescharacteristic
1234C2×C4C23×D411yescharacteristic
1235C2×C4#58511yescharacteristic
1236C2×C4#58511yescharacteristic
1237C2×C4#58511yescharacteristic
1238C2×C4#58511yescharacteristic
1239C8—22no—
1240C8—22no—
1241C8—22no—
1242C8—22no—
1243C8—22no—
1244C8—22no—
1245C8—22no—
1246C8—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—42no—
1251C22—42no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—168no—
1283C22C22×#12711yescharacteristic
1284C22#350011yescharacteristic
1285C22#350011yescharacteristic
1286C22#358512yes—
1287C22#358512yes—
1288C4—22no—
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4#344911yescharacteristic
1308C4#344911yescharacteristic
1309C4#350011yescharacteristic
1310C4#350011yescharacteristic
1311C2—42no—
1312C2—161no—
1313C2—161no—
1314C2—161no—
1315C2—161no—
1316C2—161no—
1317C2—161no—
1318C2#3532911yescharacteristic
1319C2#6065011yescharacteristic
1320C2#6065011yescharacteristic
1321C2#6256412yes—
1322C2#6256412yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3241C2semidirect
2. C2×#3224C2semidirect
3. C2×#3179C2semidirect
4. C2×#3136C2semidirect
5. #37423C2semidirect
6. #37302C2semidirect
7. #33253C2semidirect
8. #33243C2semidirect
9. #33235C2semidirect
10. #33228C2semidirect
11. #30287C2semidirect
12. #30286C2semidirect
13. #30274C2semidirect
14. #30265C2semidirect
15. #28436C2semidirect
16. #28435C2semidirect
17. #28422C2semidirect
18. #28421C2semidirect
19. #28420C2semidirect
20. #28413C2semidirect
21. #28412C2semidirect
22. #28409C2semidirect
23. #28366C2semidirect
24. #28365C2semidirect
25. #28354C2semidirect
26. #28353C2semidirect
27. #28352C2semidirect
28. #28349C2semidirect
29. #28344C2semidirect
30. #28341C2semidirect
31. #20475C2semidirect
39. C2×#501C22semidirect
40. C2×#501C22semidirect
41. C2×#499C22semidirect
43. C2×#496C22semidirect
48. C2×#490C22semidirect
54. C2×#488C22semidirect
58. C2×#486C22semidirect
59. C2×#486C22semidirect
64. C2×#478C22semidirect
65. C2×#478C22semidirect
66. C2×#476C22semidirect
67. C2×#474C22semidirect
80. C2×#442C22semidirect
81. C2×#440C22semidirect
82. C2×C4×SD16C22semidirect
83. C2×C4×D8C22semidirect
91. #2862C22semidirect
93. #2861C22semidirect
102. #2660C22semidirect
105. #2640C22semidirect
106. #2568C22semidirect
107. #2566C22semidirect
108. #2565C22semidirect
109. #2563C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2097C22semidirect
126. #2097C22semidirect
128. #2094C22semidirect
130. #2093C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2015C22semidirect
140. #2015C22semidirect
145. #2014C22semidirect
146. #2014C22semidirect
147. #2012C22semidirect
148. #2012C22semidirect
153. #2011C22semidirect
154. #2011C22semidirect
158. #1973C22semidirect
159. #1973C22semidirect
160. #1973C22semidirect
164. #1972C22semidirect
165. #1971C22semidirect
166. #1971C22semidirect
168. #1970C22semidirect
170. #1968C22semidirect
177. #1961C22semidirect
178. #1961C22semidirect
179. #1961C22semidirect
180. #1961C22semidirect
181. #1959C22semidirect
182. #1959C22semidirect
183. #1958C22semidirect
184. #1958C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. #1770C22semidirect
190. #1770C22semidirect
195. #1746C22semidirect
196. #1745C22semidirect
197. #1726C22semidirect
198. C4×#97C22semidirect
320. #433D4semidirect
381. #405D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32412
C2×#32242
C2×#31792
C2×#31362
#374232
#373022
#332532
#332432
#332352
#332282
#302872
#302862
#302742
#302652
#284362
#284352
#284222
#284212
#284202
#284132
#284122
#284092
#283662
#283652
#283542
#283532
#283522
#283492
#283442
#283412
#204752