Finite Group Databasebeta

← #6498917

Subgroups — #6498917

Order 512.

2167 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3244C211yesmaximal, characteristic, complemented
2C2×#3224C211yesmaximal, characteristic, complemented
3C2×#3173C211yesmaximal, characteristic, complemented
4C2×#3136C211yesmaximal, characteristic, complemented
5#37305C211yesmaximal, characteristic, complemented
6#37303C211yesmaximal, characteristic, complemented
7#33251C211yesmaximal, characteristic, complemented
8#33245C211yesmaximal, characteristic, complemented
9#33230C211yesmaximal, characteristic, complemented
10#33228C211yesmaximal, characteristic, complemented
11#30290C211yesmaximal, characteristic, complemented
12#30277C211yesmaximal, characteristic, complemented
13#30274C211yesmaximal, characteristic, complemented
14#30264C211yesmaximal, characteristic, complemented
15#28432C211yesmaximal, characteristic, complemented
16#28431C211yesmaximal, characteristic, complemented
17#28430C211yesmaximal, characteristic, complemented
18#28421C211yesmaximal, characteristic, complemented
19#28415C211yesmaximal, characteristic, complemented
20#28412C211yesmaximal, characteristic, complemented
21#28406C211yesmaximal, characteristic, complemented
22#28404C211yesmaximal, characteristic, complemented
23#28364C211yesmaximal, characteristic, complemented
24#28362C211yesmaximal, characteristic, complemented
25#28361C211yesmaximal, characteristic, complemented
26#28353C211yesmaximal, characteristic, complemented
27#28352C211yesmaximal, characteristic, complemented
28#28343C211yesmaximal, characteristic, complemented
29#28339C211yesmaximal, characteristic, complemented
30#28332C211yesmaximal, characteristic, complemented
31#20478C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#535C2211yescharacteristic
36#3244—28no—
37#3224—28no—
38#3173—28no—
39C2×#501C2211yescharacteristic, complemented
40C2×#498C2211yescharacteristic, complemented
41C2×#498C2211yescharacteristic, complemented
42C2×#496C2211yescharacteristic
43C2×#495C2211yescharacteristic
44C2×#495C2211yescharacteristic, complemented
45#3136—28no—
46C2×#490C2211yescharacteristic
47C2×#490C2211yescharacteristic
48C2×#489C2211yescharacteristic
49C2×#489C2211yescharacteristic
50C2×#489C2211yescharacteristic
51C2×#489C2211yescharacteristic, complemented
52C2×#489C2211yescharacteristic, complemented
53C2×#489C2211yescharacteristic, complemented
54C2×#488C2211yescharacteristic
55C2×#488C2211yescharacteristic
56C2×#488C2211yescharacteristic, complemented
57C2×#486C2211yescharacteristic
58C2×#486C2211yescharacteristic
59C2×#486C2211yescharacteristic
60C2×#481C2211yescharacteristic
61C2×#485C2211yescharacteristic
62C2×#482C2211yescharacteristic
63C2×#483C2211yescharacteristic
64C2×#479C2211yescharacteristic, complemented
65C2×#475C2211yescharacteristic, complemented
66C2×#478C2211yescharacteristic, complemented
67C2×#476C2211yescharacteristic, complemented
68C2×#470C2211yescharacteristic
69C2×#469C2211yescharacteristic
70C2×#465C2211yescharacteristic
71C2×#465C2211yescharacteristic
72C2×#464C2211yescharacteristic
73C2×#460C2211yescharacteristic
74C2×#463C2211yescharacteristic
75C2×#459C2211yescharacteristic
76C2×#452C2211yescharacteristic
77C2×#449C2211yescharacteristic
78C2×#450C2211yescharacteristic
79C2×#447C2211yescharacteristic
80C2×#442C2211yescharacteristic, complemented
81C2×#441C2211yescharacteristic, complemented
82C2×C4×SD16C2211yescharacteristic, complemented
83C2×C4×SD16C2211yescharacteristic, complemented
84C2×#433C2211yescharacteristic
85C2×#417C2211yescharacteristic
86C2×#418C2211yescharacteristic
87C2×#416C2211yescharacteristic
88C22×#102C2211yescharacteristic
89C2×#405C2211yescharacteristic
90#2868C2211yescharacteristic, complemented
91#2861C2211yescharacteristic, complemented
92#2858C2211yescharacteristic
93#2858C2211yescharacteristic
94#2721—22no—
95#2714—22no—
96#2680—22no—
97#2678—22no—
98#2677—22no—
99#2676—22no—
100#2674—22no—
101#2670—22no—
102#2660C2211yescharacteristic, complemented
103#2657C2211yescharacteristic
104#2640C2211yescharacteristic
105#2640C2211yescharacteristic, complemented
106#2567C2211yescharacteristic, complemented
107#2566C2211yescharacteristic, complemented
108#2565C2211yescharacteristic, complemented
109#2548C2211yescharacteristic
110#2545C2211yescharacteristic
111#2544C2211yescharacteristic
112#2542C2211yescharacteristic, complemented
113#2541C2211yescharacteristic
114#2502C2211yescharacteristic
115#2501C2211yescharacteristic
116#2500C2211yescharacteristic
117#2499C2211yescharacteristic
118#2435C2211yescharacteristic
119#2433C2211yescharacteristic
120#2432C2211yescharacteristic
121#2431C2211yescharacteristic
122#2298C2211yescharacteristic
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2096C2211yescharacteristic, complemented
126#2096C2211yescharacteristic, complemented
127#2094C2211yescharacteristic
128#2094C2211yescharacteristic
129#2094C2211yescharacteristic
130#2094C2211yescharacteristic
131#2094C2211yescharacteristic
132#2094C2211yescharacteristic
133#2094C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2094C2211yescharacteristic, complemented
136#2094C2211yescharacteristic, complemented
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic
139#2016C2211yescharacteristic, complemented
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic, complemented
143#2015C2211yescharacteristic, complemented
144#2014C2211yescharacteristic
145#2014C2211yescharacteristic
146#2014C2211yescharacteristic, complemented
147#2013C2211yescharacteristic, complemented
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic, complemented
151#2012C2211yescharacteristic, complemented
152#2011C2211yescharacteristic
153#2011C2211yescharacteristic
154#2011C2211yescharacteristic, complemented
155#1973C2211yescharacteristic
156#1973C2211yescharacteristic, complemented
157#1972C2211yescharacteristic
158#1972C2211yescharacteristic
159#1972C2211yescharacteristic
160#1972C2211yescharacteristic, complemented
161#1971C2211yescharacteristic, complemented
162#1971C2211yescharacteristic, complemented
163#1970C2211yescharacteristic
164#1970C2211yescharacteristic, complemented
165#1968C2211yescharacteristic
166#1968C2211yescharacteristic
167#1968C2211yescharacteristic
168#1968C2211yescharacteristic, complemented
169#1968C2211yescharacteristic, complemented
170#1968C2211yescharacteristic, complemented
171#1961C2211yescharacteristic
172#1961C2211yescharacteristic, complemented
173#1959C2211yescharacteristic
174#1959C2211yescharacteristic
175#1959C2211yescharacteristic
176#1959C2211yescharacteristic, complemented
177#1959C2211yescharacteristic, complemented
178#1959C2211yescharacteristic, complemented
179#1958C2211yescharacteristic
180#1958C2211yescharacteristic, complemented
181#1957C2211yescharacteristic
182#1957C2211yescharacteristic
183#1957C2211yescharacteristic
184#1957C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1956C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1770C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1753C2211yescharacteristic
192#1753C2211yescharacteristic
193#1752C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195#1746C2211yescharacteristic, complemented
196#1744C2211yescharacteristic, complemented
197#1726C2211yescharacteristic, complemented
198C4×#97C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×D4C2311yescharacteristic
201C22×Q16C2311yescharacteristic
202C22×Q16C2311yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
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#542—24no—
220#542—24no—
221#535—24no—
222#535—24no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8—22no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×#127C2311yescharacteristic
231C2×#127C2311yescharacteristic
232C2×#127C2311yescharacteristic
233C2×#127C2311yescharacteristic
234C2×#127C2311yescharacteristic
235C2×#126—21no—
236C2×#126—21no—
237C2×#125—21no—
238C2×#125C2311yescharacteristic
239C2×#125C2311yescharacteristic
240C2×#124—21no—
241C2×#124—21no—
242C2×#124—22no—
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251C2×#123—21no—
252C2×#123—21no—
253C2×#123—22no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8—22no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—21no—
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×#121—21no—
262C2×#121—21no—
263C2×#121—22no—
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#120—21no—
267C2×#120—21no—
268C2×#120—22no—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276#501—24no—
277#498—24no—
278#498—24no—
279#496—24no—
280#495—24no—
281#495—24no—
282#490—24no—
283#490—24no—
284#489—24no—
285#489—24no—
286#489—24no—
287#489—24no—
288#489—24no—
289#489—24no—
290#488—24no—
291#488—24no—
292#488—24no—
293#486—24no—
294#486—24no—
295#486—24no—
296#485—24no—
297#483—24no—
298#482—24no—
299#481—24no—
300#479—24no—
301#478—24no—
302#476—24no—
303#475—24no—
304#470—24no—
305#469—24no—
306#465—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#441—24no—
318C4×SD16—24no—
319C4×SD16—24no—
320#433D418yescomplemented
321C2×#107C2311yescharacteristic
322C2×#107C2311yescharacteristic
323C2×#106C2311yescharacteristic
324C2×#106C2311yescharacteristic
325C2×#106C2311yescharacteristic
326C2×#106C2311yescharacteristic
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×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
352C2×#102—24no—
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×C4×C8C2311yescharacteristic
390C2×C4×C8C2311yescharacteristic
391C2×C4×C8C2311yescharacteristic
392C2×C4×C8C2311yescharacteristic
393C2×C4×C8C2311yescharacteristic
394C2×C4×C8C2311yescharacteristic
395C2×C4×C8C2311yescharacteristic
396#399—22no—
397#399—22no—
398#398—22no—
399#398—22no—
400#398—22no—
401#397—22no—
402#397—22no—
403#397—22no—
404#396—22no—
405#396—22no—
406#395—22no—
407#395—22no—
408#394—22no—
409#394—22no—
410#394—22no—
411#394—22no—
412#394—22no—
413#393—22no—
414#393—22no—
415#392—22no—
416#392—22no—
417#392—22no—
418#392—22no—
419#392—22no—
420#391C2311yescharacteristic
421#391C2311yescharacteristic
422#391C2311yescharacteristic
423#391C2311yescharacteristic
424#391C2311yescharacteristic
425#391C2311yescharacteristic
426#390—22no—
427#390—22no—
428#390—22no—
429#390—22no—
430#390C2311yescharacteristic
431#390C2311yescharacteristic
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#389—22no—
441#388—22no—
442#388—22no—
443#388—22no—
444#388—22no—
445#388D412yes—
446#388D412yes—
447#387—22no—
448#387—22no—
449#387D412yes—
450#387D412yes—
451#386—22no—
452#386—22no—
453#385—22no—
454#385—22no—
455#385—22no—
456#384—22no—
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#382C2311yescharacteristic
464#382C2311yescharacteristic
465#379—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×Q8—21no—
491C22×Q8C2411yescharacteristic
492C22×Q8C2411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2411yescharacteristic
521C2×Q16—22no—
522C2×Q16—22no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
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×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16C2×D414yes—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8C2×D414yes—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—22no—
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575C4⋊Q8—22no—
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—41no—
580C4⋊Q8—41no—
581C4⋊Q8—44no—
582C4⋊Q8—84no—
583#127—22no—
584#127—22no—
585#127—22no—
586#127—22no—
587#127—41no—
588#127—41no—
589#127—41no—
590#127—41no—
591#127—41no—
592#127—41no—
593#126—44no—
594#126—44no—
595#125—22no—
596#125—22no—
597#125—22no—
598#125—22no—
599#125—44no—
600#124—22no—
601#124—22no—
602#124—22no—
603#124—22no—
604#124—22no—
605#124—22no—
606#124—22no—
607#124—22no—
608#124—41no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124—41no—
613#124—41no—
614#124—41no—
615#124—41no—
616#124—44no—
617#124—44no—
618#124—84no—
619#123—44no—
620#123—44no—
621#123—84no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—22no—
626C22⋊Q8—44no—
627C22⋊Q8—44no—
628C22⋊Q8—44no—
629C22⋊Q8—44no—
630C22⋊Q8—84no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—44no—
636#121—44no—
637#121—84no—
638#120—44no—
639#120—44no—
640#120—84no—
641C4×Q8—22no—
642C4×Q8—22no—
643C4×Q8—22no—
644C4×Q8—22no—
645C4×D4—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—22no—
649#117—22no—
650#117—22no—
651#117C2×D414yes—
652#117C2×D414yes—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
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—22no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
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⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4C2×D412yes—
717C2×C22⋊C4C2×D412yes—
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42C2×D412yes—
724C2×C42C2×D412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—22no—
733#106—22no—
734#106—22no—
735#106—22no—
736#106—22no—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743C4⋊C8C2×D414yes—
744C4⋊C8C2×D414yes—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—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—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785C22⋊C8C2×D414yes—
786C22⋊C8C2×D414yes—
787#97—41no—
788#97—41no—
789#97—41no—
790#97—41no—
791#97C2×D414yes—
792#97C2×D414yes—
793#97C2×D414yes—
794C4×C8—41no—
795C4×C8—41no—
796C4×C8—41no—
797C4×C8—41no—
798C4×C8C2×D414yes—
799C4×C8C2×D414yes—
800C4×C8C2×D414yes—
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—42no—
821C24—81no—
822C24—81no—
823C24—82no—
824C24—82no—
825C24C22×D411yescharacteristic
826#41—44no—
827#41—44no—
828#41—82no—
829#41—82no—
830C2×Q8—21no—
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—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—42no—
851C2×Q8—42no—
852C2×Q8—82no—
853C2×Q8—82no—
854C2×Q8—82no—
855C2×Q8—82no—
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—21no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—44no—
897C2×D4—82no—
898C2×D4—82no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—82no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—82no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—82no—
916C2×D4—82no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—82no—
939C22×C4—82no—
940C22×C4—82no—
941C22×C4C22×D412yes—
942C22×C4C22×D412yes—
943C22×C4C22×D412yes—
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D412yes—
950C22×C4C22×D412yes—
951C22×C4C22×D412yes—
952C22×C4C2511yescharacteristic
953Q16—44no—
954Q16—82no—
955SD16—44no—
956SD16—44no—
957SD16—82no—
958SD16—82no—
959SD16—82no—
960SD16—82no—
961D8—44no—
962D8—82no—
963D8—82no—
964D8—82no—
965M16—44no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—44no—
983C2×C8C22×D412yes—
984C2×C8C22×D412yes—
985C2×C8C22×D412yes—
986C2×C8C22×D412yes—
987C2×C8C22×D412yes—
988C2×C8C22×D412yes—
989C2×C8C22×D412yes—
990C2×C8C22×D412yes—
991C4⋊C4—24no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—42no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—82no—
1025C4⋊C4—82no—
1026C4⋊C4—82no—
1027C4⋊C4—82no—
1028C4⋊C4—82no—
1029C4⋊C4#12714yes—
1030C4⋊C4#12714yes—
1031C22⋊C4—24no—
1032C22⋊C4—42no—
1033C22⋊C4—44no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—82no—
1053C22⋊C4—82no—
1054C22⋊C4—82no—
1055C22⋊C4—82no—
1056C22⋊C4—82no—
1057C22⋊C4—82no—
1058C22⋊C4—82no—
1059C22⋊C4—82no—
1060C22⋊C4—82no—
1061C22⋊C4—82no—
1062C22⋊C4#12714yes—
1063C22⋊C4#12714yes—
1064C42—24no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42C22×D412yes—
1078C42C22×D412yes—
1079C42C22×D412yes—
1080C42C22×D412yes—
1081C23—22no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—84no—
1111C23—162no—
1112C23—162no—
1113C23—164no—
1114C23—164no—
1115C23C2×#12712yes—
1116C23C23×D411yescharacteristic
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—162no—
1130Q8—162no—
1131Q8—162no—
1132Q8—162no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
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—84no—
1154D4—84no—
1155D4—164no—
1156D4—162no—
1157D4—162no—
1158D4—162no—
1159D4—162no—
1160D4—164no—
1161D4—164no—
1162D4—162no—
1163D4—162no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—84no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4—162no—
1214C2×C4C2×#12712yes—
1215C2×C4C2×#12712yes—
1216C2×C4C2×#12712yes—
1217C2×C4C2×#12712yes—
1218C2×C4C2×#12712yes—
1219C2×C4#57714yes—
1220C2×C4C23×D411yescharacteristic
1221C2×C4C23×D411yescharacteristic
1222C2×C4#58511yescharacteristic
1223C2×C4#58511yescharacteristic
1224C2×C4#58511yescharacteristic
1225C2×C4#58511yescharacteristic
1226C8—22no—
1227C8—22no—
1228C8—22no—
1229C8—22no—
1230C8—22no—
1231C8—22no—
1232C8—22no—
1233C8—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—42no—
1238C22—42no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—168no—
1265C22C22×#12711yescharacteristic
1266C22#350011yescharacteristic
1267C22#350011yescharacteristic
1268C22C2×#57712yes—
1269C22#358512yes—
1270C4—22no—
1271C4—24no—
1272C4—22no—
1273C4—22no—
1274C4—22no—
1275C4—22no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4#344911yescharacteristic
1291C4#344911yescharacteristic
1292C4#350011yescharacteristic
1293C4#350011yescharacteristic
1294C2—42no—
1295C2—161no—
1296C2—161no—
1297C2—161no—
1298C2—161no—
1299C2—161no—
1300C2#3532911yescharacteristic
1301C2#6064611yescharacteristic
1302C2#6065011yescharacteristic
1303C2#6260212yes—
1304C2#6261712yes—
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×#3244C2semidirect
2. C2×#3224C2semidirect
3. C2×#3173C2semidirect
4. C2×#3136C2semidirect
5. #37305C2semidirect
6. #37303C2semidirect
7. #33251C2semidirect
8. #33245C2semidirect
9. #33230C2semidirect
10. #33228C2semidirect
11. #30290C2semidirect
12. #30277C2semidirect
13. #30274C2semidirect
14. #30264C2semidirect
15. #28432C2semidirect
16. #28431C2semidirect
17. #28430C2semidirect
18. #28421C2semidirect
19. #28415C2semidirect
20. #28412C2semidirect
21. #28406C2semidirect
22. #28404C2semidirect
23. #28364C2semidirect
24. #28362C2semidirect
25. #28361C2semidirect
26. #28353C2semidirect
27. #28352C2semidirect
28. #28343C2semidirect
29. #28339C2semidirect
30. #28332C2semidirect
31. #20478C2semidirect
39. C2×#501C22semidirect
40. C2×#498C22semidirect
41. C2×#498C22semidirect
44. C2×#495C22semidirect
51. C2×#489C22semidirect
52. C2×#489C22semidirect
53. C2×#489C22semidirect
56. C2×#488C22semidirect
64. C2×#479C22semidirect
65. C2×#475C22semidirect
66. C2×#478C22semidirect
67. C2×#476C22semidirect
80. C2×#442C22semidirect
81. C2×#441C22semidirect
82. C2×C4×SD16C22semidirect
83. C2×C4×SD16C22semidirect
90. #2868C22semidirect
91. #2861C22semidirect
102. #2660C22semidirect
105. #2640C22semidirect
106. #2567C22semidirect
107. #2566C22semidirect
108. #2565C22semidirect
112. #2542C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2096C22semidirect
126. #2096C22semidirect
133. #2094C22semidirect
134. #2094C22semidirect
135. #2094C22semidirect
136. #2094C22semidirect
139. #2016C22semidirect
142. #2015C22semidirect
143. #2015C22semidirect
146. #2014C22semidirect
147. #2013C22semidirect
150. #2012C22semidirect
151. #2012C22semidirect
154. #2011C22semidirect
156. #1973C22semidirect
160. #1972C22semidirect
161. #1971C22semidirect
162. #1971C22semidirect
164. #1970C22semidirect
168. #1968C22semidirect
169. #1968C22semidirect
170. #1968C22semidirect
172. #1961C22semidirect
176. #1959C22semidirect
177. #1959C22semidirect
178. #1959C22semidirect
180. #1958C22semidirect
184. #1957C22semidirect
185. #1956C22semidirect
186. #1956C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. #1770C22semidirect
190. C8×C4⋊C4C22semidirect
195. #1746C22semidirect
196. #1744C22semidirect
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×#32442
C2×#32242
C2×#31732
C2×#31362
#373052
#373032
#332512
#332452
#332302
#332282
#302902
#302772
#302742
#302642
#284322
#284312
#284302
#284212
#284152
#284122
#284062
#284042
#283642
#283622
#283612
#283532
#283522
#283432
#283392
#283322
#204782