Finite Group Databasebeta

← #6498927

Subgroups — #6498927

Order 512.

2192 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3243C211yesmaximal, characteristic, complemented
2C2×#3220C211yesmaximal, characteristic, complemented
3C2×#3179C211yesmaximal, characteristic, complemented
4C2×#3136C211yesmaximal, characteristic, complemented
5#37305C211yesmaximal, characteristic, complemented
6#37304C211yesmaximal, characteristic, complemented
7#33243C211yesmaximal, characteristic, complemented
8#33241C211yesmaximal, characteristic, complemented
9#33228C211yesmaximal, characteristic, complemented
10#33226C211yesmaximal, characteristic, complemented
11#30289C211yesmaximal, characteristic, complemented
12#30283C211yesmaximal, characteristic, complemented
13#30270C211yesmaximal, characteristic, complemented
14#30268C211yesmaximal, characteristic, complemented
15#28426C211yesmaximal, characteristic, complemented
16#28425C211yesmaximal, characteristic, complemented
17#28422C211yesmaximal, characteristic, complemented
18#28421C211yesmaximal, characteristic, complemented
19#28406C211yesmaximal, characteristic, complemented
20#28405C211yesmaximal, characteristic, complemented
21#28399C211yesmaximal, characteristic, complemented
22#28397C211yesmaximal, characteristic, complemented
23#28358C211yesmaximal, characteristic, complemented
24#28357C211yesmaximal, characteristic, complemented
25#28354C211yesmaximal, characteristic, complemented
26#28353C211yesmaximal, characteristic, complemented
27#28339C211yesmaximal, characteristic, complemented
28#28337C211yesmaximal, characteristic, complemented
29#28331C211yesmaximal, characteristic, complemented
30#28329C211yesmaximal, characteristic, complemented
31#20474C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#540C2211yescharacteristic
35C2×#535C2211yescharacteristic
36#3243—28no—
37#3220—28no—
38#3179—28no—
39C2×#501C2211yescharacteristic, complemented
40C2×#501C2211yescharacteristic, complemented
41C2×#500C2211yescharacteristic, complemented
42C2×#496C2211yescharacteristic
43C2×#496C2211yescharacteristic, complemented
44C2×#493C2211yescharacteristic
45#3136—28no—
46C2×#490C2211yescharacteristic
47C2×#490C2211yescharacteristic
48C2×#490C2211yescharacteristic
49C2×#489C2211yescharacteristic
50C2×#489C2211yescharacteristic
51C2×#489C2211yescharacteristic, complemented
52C2×#488C2211yescharacteristic
53C2×#488C2211yescharacteristic
54C2×#488C2211yescharacteristic
55C2×#488C2211yescharacteristic, complemented
56C2×#488C2211yescharacteristic, complemented
57C2×#486C2211yescharacteristic
58C2×#486C2211yescharacteristic
59C2×#486C2211yescharacteristic, complemented
60C2×#484C2211yescharacteristic
61C2×#485C2211yescharacteristic
62C2×#482C2211yescharacteristic
63C2×#480C2211yescharacteristic
64C2×#479C2211yescharacteristic, complemented
65C2×#477C2211yescharacteristic, complemented
66C2×#478C2211yescharacteristic, complemented
67C2×#474C2211yescharacteristic, complemented
68C2×#469C2211yescharacteristic
69C2×#468C2211yescharacteristic
70C2×#466C2211yescharacteristic
71C2×#465C2211yescharacteristic
72C2×#463C2211yescharacteristic
73C2×#463C2211yescharacteristic
74C2×#459C2211yescharacteristic
75C2×#459C2211yescharacteristic
76C2×#449C2211yescharacteristic
77C2×#449C2211yescharacteristic
78C2×#447C2211yescharacteristic
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#2859C2211yescharacteristic, complemented
91#2858C2211yescharacteristic
92#2858C2211yescharacteristic
93#2858C2211yescharacteristic, complemented
94#2714—22no—
95#2694—22no—
96#2681—22no—
97#2678—22no—
98#2676—22no—
99#2674—22no—
100#2672—22no—
101#2670—22no—
102#2660C2211yescharacteristic, complemented
103#2657C2211yescharacteristic
104#2641C2211yescharacteristic, complemented
105#2640C2211yescharacteristic
106#2566C2211yescharacteristic, complemented
107#2566C2211yescharacteristic, complemented
108#2563C2211yescharacteristic, complemented
109#2548C2211yescharacteristic
110#2545C2211yescharacteristic
111#2544C2211yescharacteristic
112#2542C2211yescharacteristic, complemented
113#2541C2211yescharacteristic
114#2504C2211yescharacteristic
115#2501C2211yescharacteristic
116#2500C2211yescharacteristic
117#2500C2211yescharacteristic
118#2435C2211yescharacteristic
119#2433C2211yescharacteristic
120#2432C2211yescharacteristic
121#2431C2211yescharacteristic
122#2298C2211yescharacteristic
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2095C2211yescharacteristic, complemented
126#2095C2211yescharacteristic, complemented
127#2094C2211yescharacteristic
128#2094C2211yescharacteristic, complemented
129#2093C2211yescharacteristic
130#2093C2211yescharacteristic
131#2093C2211yescharacteristic
132#2093C2211yescharacteristic, complemented
133#2092C2211yescharacteristic
134#2092C2211yescharacteristic
135#2092C2211yescharacteristic
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2013C2211yescharacteristic, complemented
140#2013C2211yescharacteristic, complemented
141#2012C2211yescharacteristic
142#2012C2211yescharacteristic
143#2012C2211yescharacteristic
144#2012C2211yescharacteristic
145#2012C2211yescharacteristic, complemented
146#2012C2211yescharacteristic, complemented
147#2012C2211yescharacteristic, complemented
148#2012C2211yescharacteristic, complemented
149#2011C2211yescharacteristic
150#2011C2211yescharacteristic
151#2011C2211yescharacteristic
152#2011C2211yescharacteristic
153#2011C2211yescharacteristic, complemented
154#2011C2211yescharacteristic, complemented
155#1973C2211yescharacteristic, complemented
156#1973C2211yescharacteristic, complemented
157#1972C2211yescharacteristic
158#1972C2211yescharacteristic
159#1970C2211yescharacteristic
160#1970C2211yescharacteristic
161#1970C2211yescharacteristic
162#1970C2211yescharacteristic
163#1970C2211yescharacteristic
164#1970C2211yescharacteristic
165#1970C2211yescharacteristic, complemented
166#1970C2211yescharacteristic, complemented
167#1970C2211yescharacteristic, complemented
168#1970C2211yescharacteristic, complemented
169#1968C2211yescharacteristic, complemented
170#1968C2211yescharacteristic, complemented
171#1961C2211yescharacteristic
172#1961C2211yescharacteristic, complemented
173#1959C2211yescharacteristic
174#1959C2211yescharacteristic, complemented
175#1958C2211yescharacteristic
176#1958C2211yescharacteristic
177#1958C2211yescharacteristic
178#1958C2211yescharacteristic, complemented
179#1958C2211yescharacteristic, complemented
180#1958C2211yescharacteristic, complemented
181#1957C2211yescharacteristic
182#1957C2211yescharacteristic
183#1957C2211yescharacteristic
184#1957C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1956C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189C8×C4⋊C4C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1753C2211yescharacteristic
192#1753C2211yescharacteristic
193C8×C22⋊C4C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195#1746C2211yescharacteristic, complemented
196#1745C2211yescharacteristic, complemented
197#1726C2211yescharacteristic, complemented
198C42×C8C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×D4C2311yescharacteristic
201C22×SD16C2311yescharacteristic
202C22×SD16C2311yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
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×C4⋊Q8C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#127C2311yescharacteristic
230C2×#127C2311yescharacteristic
231C2×#127C2311yescharacteristic
232C2×#127C2311yescharacteristic
233C2×#127C2311yescharacteristic
234C2×#126—21no—
235C2×#125—21no—
236C2×#125C2311yescharacteristic
237C2×#125C2311yescharacteristic
238C2×#125C2311yescharacteristic
239C2×#124—21no—
240C2×#124—22no—
241C2×#124—22no—
242C2×#124C2311yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#123—21no—
250C2×#123—21no—
251C2×#123—21no—
252C2×#123—22no—
253C2×C22⋊Q8—21no—
254C2×C22⋊Q8—22no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8C2311yescharacteristic
258C2×#121—21no—
259C2×#121—21no—
260C2×#121—22no—
261C2×#121—21no—
262C2×#121—21no—
263C2×#121C2311yescharacteristic
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#120—21no—
267C2×#120—21no—
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#500—24no—
279#496—24no—
280#496—24no—
281#493—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#488—24no—
292#488—24no—
293#486—24no—
294#486—24no—
295#486—24no—
296#485—24no—
297#484—24no—
298#482—24no—
299#480—24no—
300#479—24no—
301#478—24no—
302#477—24no—
303#474—24no—
304#469—24no—
305#468—24no—
306#466—24no—
307#465—24no—
308#463—24no—
309#463—24no—
310#459—24no—
311#459—24no—
312#449—24no—
313#449—24no—
314#447—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×#107C2311yescharacteristic
328C2×#107C2311yescharacteristic
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×#102—24no—
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×C4×C8C2311yescharacteristic
388C2×C4×C8C2311yescharacteristic
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#397—22no—
400#397—22no—
401#396—22no—
402#396—22no—
403#396—22no—
404#395—22no—
405#394—22no—
406#394—22no—
407#394—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#390—22no—
423#390—22no—
424#390—22no—
425#390—22no—
426#390—22no—
427#390C2311yescharacteristic
428#390C2311yescharacteristic
429#390C2311yescharacteristic
430#390C2311yescharacteristic
431#390C2311yescharacteristic
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#389—22no—
442#389—22no—
443#388—22no—
444#388—22no—
445#388—22no—
446#388D412yes—
447#388D412yes—
448#387D412yes—
449#387D412yes—
450#386—22no—
451#386—22no—
452#386—22no—
453#385—22no—
454#385—22no—
455#385—22no—
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#382C2311yescharacteristic
461#382C2311yescharacteristic
462#382C2311yescharacteristic
463#382C2311yescharacteristic
464#380—22no—
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×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—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C2411yescharacteristic
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
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×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×M16—41no—
561C2×M16—41no—
562C2×M16C2×D414yes—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8C2×D414yes—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C4⋊Q8—22no—
575C4⋊Q8—22no—
576C4⋊Q8—22no—
577C4⋊Q8—22no—
578C4⋊Q8—22no—
579C4⋊Q8—22no—
580C4⋊Q8—41no—
581C4⋊Q8—41no—
582C4⋊Q8—44no—
583#127—22no—
584#127—22no—
585#127—22no—
586#127—22no—
587#127—22no—
588#127—22no—
589#127—41no—
590#127—41no—
591#127—41no—
592#127—41no—
593#127—41no—
594#127—41no—
595#126—44no—
596#125—22no—
597#125—22no—
598#125—22no—
599#125—22no—
600#125—22no—
601#125—22no—
602#125—44no—
603#124—22no—
604#124—22no—
605#124—22no—
606#124—22no—
607#124—22no—
608#124—22no—
609#124—41no—
610#124—41no—
611#124—41no—
612#124—41no—
613#124—41no—
614#124—41no—
615#124—41no—
616#124—41no—
617#124—44no—
618#124—84no—
619#124—84no—
620#123—44no—
621#123—44no—
622#123—44no—
623#123—84no—
624C22⋊Q8—22no—
625C22⋊Q8—22no—
626C22⋊Q8—44no—
627C22⋊Q8—44no—
628C22⋊Q8—44no—
629C22⋊Q8—84no—
630#121—22no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—44no—
637#121—44no—
638#121—44no—
639#121—44no—
640#121—84no—
641#120—44no—
642#120—44no—
643#120—84no—
644C4×Q8—22no—
645C4×Q8—22no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C4×D4—22no—
652#117—22no—
653#117—22no—
654#117C2×D414yes—
655#117C2×D414yes—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—22no—
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—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—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
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⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4C2×D412yes—
720C2×C22⋊C4C2×D412yes—
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C42—21no—
724C2×C42—21no—
725C2×C42C2×D412yes—
726C2×C42C2×D412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#107—22no—
734#107—22no—
735#107—22no—
736#107—22no—
737#107—22no—
738#107—22no—
739#107—22no—
740#107—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—22no—
745C4⋊C8C2×D414yes—
746C4⋊C8C2×D414yes—
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—
785#102—22no—
786#102—22no—
787C22⋊C8C2×D414yes—
788C22⋊C8C2×D414yes—
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×C8—41no—
799C4×C8—41no—
800C4×C8C2×D414yes—
801C4×C8C2×D414yes—
802C4×C8C2×D414yes—
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—42no—
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—42no—
897C2×D4—42no—
898C2×D4—44no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—81no—
902C2×D4—81no—
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—82no—
914C2×D4—82no—
915C2×D4—82no—
916C2×D4—82no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—82no—
920C2×D4—82no—
921C2×D4—82no—
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—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—82no—
944C22×C4—82no—
945C22×C4—82no—
946C22×C4—82no—
947C22×C4C22×D412yes—
948C22×C4C22×D412yes—
949C22×C4C22×D412yes—
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D412yes—
956C22×C4C22×D412yes—
957C22×C4C22×D412yes—
958C22×C4C2511yescharacteristic
959SD16—44no—
960SD16—44no—
961SD16—82no—
962SD16—82no—
963D8—44no—
964D8—44no—
965D8—82no—
966D8—82no—
967D8—82no—
968D8—82no—
969D8—82no—
970D8—82no—
971M16—44no—
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—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—44no—
989C2×C8C22×D412yes—
990C2×C8C22×D412yes—
991C2×C8C22×D412yes—
992C2×C8C22×D412yes—
993C2×C8C22×D412yes—
994C2×C8C22×D412yes—
995C2×C8C22×D412yes—
996C2×C8C22×D412yes—
997C4⋊C4—24no—
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—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
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—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—44no—
1028C4⋊C4—82no—
1029C4⋊C4—82no—
1030C4⋊C4—82no—
1031C4⋊C4—82no—
1032C4⋊C4#12714yes—
1033C4⋊C4#12714yes—
1034C22⋊C4—24no—
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—42no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
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—82no—
1063C22⋊C4—82no—
1064C22⋊C4—82no—
1065C22⋊C4—82no—
1066C22⋊C4—82no—
1067C22⋊C4—82no—
1068C22⋊C4#12714yes—
1069C22⋊C4#12714yes—
1070C42—24no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—42no—
1080C42—42no—
1081C42—42no—
1082C42C22×D412yes—
1083C42C22×D412yes—
1084C42C22×D412yes—
1085C42C22×D412yes—
1086C23—22no—
1087C23—21no—
1088C23—21no—
1089C23—22no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
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—42no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—42no—
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—164no—
1165D4—162no—
1166D4—162no—
1167D4—162no—
1168D4—162no—
1169D4—162no—
1170D4—162no—
1171D4—164no—
1172D4—164no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
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—42no—
1198C2×C4—42no—
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—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—84no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4C2×#12712yes—
1225C2×C4C2×#12712yes—
1226C2×C4C2×#12712yes—
1227C2×C4C2×#12712yes—
1228C2×C4C2×#12712yes—
1229C2×C4#57614yes—
1230C2×C4C23×D411yescharacteristic
1231C2×C4C23×D411yescharacteristic
1232C2×C4#58511yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C8—22no—
1237C8—22no—
1238C8—22no—
1239C8—22no—
1240C8—22no—
1241C8—22no—
1242C8—22no—
1243C8—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—42no—
1248C22—42no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—168no—
1280C22C22×#12711yescharacteristic
1281C22#350011yescharacteristic
1282C22#350011yescharacteristic
1283C22C2×#57612yes—
1284C22#358412yes—
1285C4—22no—
1286C4—24no—
1287C4—22no—
1288C4—22no—
1289C4—22no—
1290C4—22no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4#344911yescharacteristic
1305C4#344911yescharacteristic
1306C4#350011yescharacteristic
1307C4#350011yescharacteristic
1308C2—42no—
1309C2—161no—
1310C2—161no—
1311C2—161no—
1312C2—161no—
1313C2—161no—
1314C2—161no—
1315C2#3532911yescharacteristic
1316C2#6064711yescharacteristic
1317C2#6064911yescharacteristic
1318C2#6255812yes—
1319C2#6256112yes—
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×#3243C2semidirect
2. C2×#3220C2semidirect
3. C2×#3179C2semidirect
4. C2×#3136C2semidirect
5. #37305C2semidirect
6. #37304C2semidirect
7. #33243C2semidirect
8. #33241C2semidirect
9. #33228C2semidirect
10. #33226C2semidirect
11. #30289C2semidirect
12. #30283C2semidirect
13. #30270C2semidirect
14. #30268C2semidirect
15. #28426C2semidirect
16. #28425C2semidirect
17. #28422C2semidirect
18. #28421C2semidirect
19. #28406C2semidirect
20. #28405C2semidirect
21. #28399C2semidirect
22. #28397C2semidirect
23. #28358C2semidirect
24. #28357C2semidirect
25. #28354C2semidirect
26. #28353C2semidirect
27. #28339C2semidirect
28. #28337C2semidirect
29. #28331C2semidirect
30. #28329C2semidirect
31. #20474C2semidirect
39. C2×#501C22semidirect
40. C2×#501C22semidirect
41. C2×#500C22semidirect
43. C2×#496C22semidirect
51. C2×#489C22semidirect
55. C2×#488C22semidirect
56. C2×#488C22semidirect
59. C2×#486C22semidirect
64. C2×#479C22semidirect
65. C2×#477C22semidirect
66. C2×#478C22semidirect
67. C2×#474C22semidirect
80. C2×#442C22semidirect
81. C2×#440C22semidirect
82. C2×C4×SD16C22semidirect
83. C2×C4×D8C22semidirect
90. #2859C22semidirect
93. #2858C22semidirect
102. #2660C22semidirect
104. #2641C22semidirect
106. #2566C22semidirect
107. #2566C22semidirect
108. #2563C22semidirect
112. #2542C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2095C22semidirect
126. #2095C22semidirect
128. #2094C22semidirect
132. #2093C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2013C22semidirect
140. #2013C22semidirect
145. #2012C22semidirect
146. #2012C22semidirect
147. #2012C22semidirect
148. #2012C22semidirect
153. #2011C22semidirect
154. #2011C22semidirect
155. #1973C22semidirect
156. #1973C22semidirect
165. #1970C22semidirect
166. #1970C22semidirect
167. #1970C22semidirect
168. #1970C22semidirect
169. #1968C22semidirect
170. #1968C22semidirect
172. #1961C22semidirect
174. #1959C22semidirect
178. #1958C22semidirect
179. #1958C22semidirect
180. #1958C22semidirect
184. #1957C22semidirect
185. #1956C22semidirect
186. #1956C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. C8×C4⋊C4C22semidirect
190. C8×C4⋊C4C22semidirect
195. #1746C22semidirect
196. #1745C22semidirect
197. #1726C22semidirect
198. C42×C8C22semidirect
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×#32432
C2×#32202
C2×#31792
C2×#31362
#373052
#373042
#332432
#332412
#332282
#332262
#302892
#302832
#302702
#302682
#284262
#284252
#284222
#284212
#284062
#284052
#283992
#283972
#283582
#283572
#283542
#283532
#283392
#283372
#283312
#283292
#204742