Finite Group Databasebeta

← #6510834

Subgroups — #6510834

Order 512.

2268 conjugacy classes of subgroups.

The subgroup lattice has 1335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3197C211yesmaximal, characteristic, complemented
2C2×#3188C211yesmaximal, characteristic, complemented
3C2×#3094C211yesmaximal, characteristic, complemented
4C2×#3091C211yesmaximal, characteristic, complemented
5#37448C211yesmaximal, characteristic, complemented
6#35157C211yesmaximal, characteristic, complemented
7#28365C211yesmaximal, characteristic, complemented
8#28361C211yesmaximal, characteristic, complemented
9#28357C211yesmaximal, characteristic, complemented
10#28353C211yesmaximal, characteristic, complemented
11#28352C211yesmaximal, characteristic, complemented
12#28349C211yesmaximal, characteristic, complemented
13#28340C211yesmaximal, characteristic, complemented
14#28337C211yesmaximal, characteristic, complemented
15#28328C211yesmaximal, characteristic, complemented
16#28327C211yesmaximal, characteristic, complemented
17#28325C211yesmaximal, characteristic, complemented
18#28325C211yesmaximal, characteristic, complemented
19#27946C211yesmaximal, characteristic, complemented
20#27944C211yesmaximal, characteristic, complemented
21#27943C211yesmaximal, characteristic, complemented
22#27941C211yesmaximal, characteristic, complemented
23#27937C211yesmaximal, characteristic, complemented
24#27935C211yesmaximal, characteristic, complemented
25#27928C211yesmaximal, characteristic, complemented
26#27925C211yesmaximal, characteristic, complemented
27#27923C211yesmaximal, characteristic, complemented
28#27923C211yesmaximal, characteristic, complemented
29#27921C211yesmaximal, characteristic, complemented
30#27920C211yesmaximal, characteristic, complemented
31#20527C211yesmaximal, characteristic, complemented
32C2×#525C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C22×#117C2211yescharacteristic
36#3197—28no—
37#3188—28no—
38#3094—28no—
39#3091—28no—
40C2×#484C2211yescharacteristic
41C2×#484C2211yescharacteristic, complemented
42C2×#481C2211yescharacteristic
43C2×#481C2211yescharacteristic
44C2×#481C2211yescharacteristic
45C2×#481C2211yescharacteristic, complemented
46C2×#485C2211yescharacteristic
47C2×#485C2211yescharacteristic
48C2×#485C2211yescharacteristic, complemented
49C2×#485C2211yescharacteristic, complemented
50C2×#482C2211yescharacteristic
51C2×#482C2211yescharacteristic
52C2×#482C2211yescharacteristic
53C2×#482C2211yescharacteristic
54C2×#482C2211yescharacteristic
55C2×#482C2211yescharacteristic
56C2×#482C2211yescharacteristic
57C2×#482C2211yescharacteristic
58C2×#482C2211yescharacteristic, complemented
59C2×#482C2211yescharacteristic, complemented
60C2×#483C2211yescharacteristic, complemented
61C2×#480C2211yescharacteristic
62C2×#480C2211yescharacteristic
63C2×#480C2211yescharacteristic, complemented
64C2×#470C2211yescharacteristic
65C2×#469C2211yescharacteristic
66C2×#468C2211yescharacteristic
67C2×#468C2211yescharacteristic
68C2×#466C2211yescharacteristic
69C2×#466C2211yescharacteristic
70C2×#465C2211yescharacteristic
71C2×#465C2211yescharacteristic
72C2×#452C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic, complemented
74C2×#449C2211yescharacteristic
75C2×#449C2211yescharacteristic
76C2×#449C2211yescharacteristic, complemented
77C2×#449C2211yescharacteristic, complemented
78C2×#450C2211yescharacteristic
79C2×#447C2211yescharacteristic
80C2×#428C2211yescharacteristic
81C2×#428C2211yescharacteristic
82C2×#427C2211yescharacteristic, complemented
83C2×#427C2211yescharacteristic, complemented
84C2×#418C2211yescharacteristic
85C2×#418C2211yescharacteristic
86C2×#416C2211yescharacteristic, complemented
87C2×#416C2211yescharacteristic, complemented
88C2×#407C2211yescharacteristic
89C22×C22⋊C8C2211yescharacteristic
90#2853—22no—
91#2813—22no—
92#2635—22no—
93#2622—22no—
94#2620C2211yescharacteristic
95#2620C2211yescharacteristic
96#2619C2211yescharacteristic
97#2619C2211yescharacteristic
98#2613—22no—
99#2534—22no—
100#2503C2211yescharacteristic
101#2501C2211yescharacteristic
102#2500C2211yescharacteristic
103#2500C2211yescharacteristic
104#2500C2211yescharacteristic
105#2500C2211yescharacteristic
106#2500C2211yescharacteristic, complemented
107#2500C2211yescharacteristic, complemented
108#2499C2211yescharacteristic
109#2499C2211yescharacteristic
110#2499C2211yescharacteristic, complemented
111#2499C2211yescharacteristic, complemented
112#2485—22no—
113#2485—22no—
114#2435C2211yescharacteristic
115#2433C2211yescharacteristic
116#2431C2211yescharacteristic
117#2431C2211yescharacteristic
118#2317C2211yescharacteristic, complemented
119#2317C2211yescharacteristic, complemented
120#2311C2211yescharacteristic, complemented
121#2311C2211yescharacteristic, complemented
122#2280C2211yescharacteristic
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2097C2211yescharacteristic, complemented
126#2097C2211yescharacteristic, complemented
127#2096C2211yescharacteristic, complemented
128#2096C2211yescharacteristic, complemented
129#2095C2211yescharacteristic, complemented
130#2095C2211yescharacteristic, complemented
131#2094C2211yescharacteristic, complemented
132#2094C2211yescharacteristic, complemented
133#2094C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2093C2211yescharacteristic, complemented
136#2093C2211yescharacteristic, complemented
137#2093C2211yescharacteristic, complemented
138#2093C2211yescharacteristic, complemented
139#2092C2211yescharacteristic, complemented
140#2092C2211yescharacteristic, complemented
141#2092C2211yescharacteristic, complemented
142#2092C2211yescharacteristic, complemented
143#2092C2211yescharacteristic, complemented
144#2092C2211yescharacteristic, complemented
145#2092C2211yescharacteristic, complemented
146#2092C2211yescharacteristic, complemented
147#2015C2211yescharacteristic, complemented
148#2015C2211yescharacteristic, complemented
149#2014C2211yescharacteristic, complemented
150#2014C2211yescharacteristic, complemented
151#2012C2211yescharacteristic, complemented
152#2012C2211yescharacteristic, complemented
153#2011C2211yescharacteristic, complemented
154#2011C2211yescharacteristic, complemented
155#1973C2211yescharacteristic, complemented
156#1973C2211yescharacteristic, complemented
157#1973C2211yescharacteristic, complemented
158#1973C2211yescharacteristic, complemented
159#1972C2211yescharacteristic, complemented
160#1972C2211yescharacteristic, complemented
161#1972C2211yescharacteristic, complemented
162#1971C2211yescharacteristic, complemented
163#1970C2211yescharacteristic, complemented
164#1970C2211yescharacteristic, complemented
165#1970C2211yescharacteristic, complemented
166#1969C2211yescharacteristic, complemented
167#1968C2211yescharacteristic, complemented
168#1968C2211yescharacteristic, complemented
169#1968C2211yescharacteristic, complemented
170#1968C2211yescharacteristic, complemented
171#1961C2211yescharacteristic, complemented
172#1961C2211yescharacteristic, complemented
173#1959C2211yescharacteristic, complemented
174#1959C2211yescharacteristic, complemented
175#1958C2211yescharacteristic, complemented
176#1958C2211yescharacteristic, complemented
177#1957C2211yescharacteristic, complemented
178#1957C2211yescharacteristic, complemented
179#1847C2211yescharacteristic, complemented
180#1847C2211yescharacteristic, complemented
181#1847C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1846C2211yescharacteristic, complemented
184#1846C2211yescharacteristic, complemented
185#1845C2211yescharacteristic, complemented
186#1844C2211yescharacteristic, complemented
187#1753C2211yescharacteristic
188#1753C2211yescharacteristic
189#1753C2211yescharacteristic
190#1753C2211yescharacteristic
191#1752C2211yescharacteristic, complemented
192#1752C2211yescharacteristic, complemented
193C8×C22⋊C4C2211yescharacteristic, complemented
194C8×C22⋊C4C2211yescharacteristic, complemented
195#1750C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197#1750C2211yescharacteristic, complemented
198#1750C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×D4—21no—
202C23×D4C2311yescharacteristic
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220#525—24no—
221#525—24no—
222#525—24no—
223#525—24no—
224C2×#123—21no—
225C2×#123—21no—
226C2×#123—22no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—24no—
234C2×#121—24no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×#120—21no—
245C2×#120—22no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×#117—21no—
251C2×#117—21no—
252C2×#117—24no—
253C2×#117—24no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267C22×C42—21no—
268#485—24no—
269#485—24no—
270#485—24no—
271#485—24no—
272#484—24no—
273#484—24no—
274#483—24no—
275#482—24no—
276#482—24no—
277#482—24no—
278#482—24no—
279#482—24no—
280#482—24no—
281#482—24no—
282#482—24no—
283#482—24no—
284#482—24no—
285#481—24no—
286#481—24no—
287#481—24no—
288#481—24no—
289#480—24no—
290#480—24no—
291#480—24no—
292#470—24no—
293#469—24no—
294#468—24no—
295#468—24no—
296#466—24no—
297#466—24no—
298#465—24no—
299#465—24no—
300#452—24no—
301#452—24no—
302#450—24no—
303#449—24no—
304#449—24no—
305#449—24no—
306#449—24no—
307#447—24no—
308#428—24no—
309#428—24no—
310#427—24no—
311#427—24no—
312C2×#107C2311yescharacteristic
313C2×#107C2311yescharacteristic
314C2×#107C2311yescharacteristic
315C2×#107C2311yescharacteristic
316C2×#107C2311yescharacteristic
317C2×#107C2311yescharacteristic
318C2×#107C2311yescharacteristic
319C2×#107C2311yescharacteristic
320C2×#107C2311yescharacteristic
321C2×#107C2311yescharacteristic
322C2×#107C2311yescharacteristic
323C2×#107C2311yescharacteristic
324C2×#106C2311yescharacteristic
325C2×#106C2311yescharacteristic
326C2×#106C2311yescharacteristic
327C2×#106C2311yescharacteristic
328C2×#106C2311yescharacteristic
329C2×#106C2311yescharacteristic
330C2×#106C2311yescharacteristic
331C2×#106C2311yescharacteristic
332C2×#106C2311yescharacteristic
333C2×#106C2311yescharacteristic
334C2×#106C2311yescharacteristic
335C2×#106C2311yescharacteristic
336#418—24no—
337#418—24no—
338#416—24no—
339#416—24no—
340C2×#103C2311yescharacteristic
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
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
372#407D418yescomplemented
373C2×C22⋊C8D418yescomplemented
374C2×C22⋊C8C2311yescharacteristic
375C2×C22⋊C8C2311yescharacteristic
376C2×C22⋊C8C2311yescharacteristic
377C2×C22⋊C8C2311yescharacteristic
378C2×C22⋊C8C2311yescharacteristic
379C2×C22⋊C8C2311yescharacteristic
380C2×C22⋊C8C2311yescharacteristic
381C2×C22⋊C8C2311yescharacteristic
382C2×#97C2311yescharacteristic
383C2×#97C2311yescharacteristic
384C2×#97C2311yescharacteristic
385C2×#97C2311yescharacteristic
386C2×C4×C8C2311yescharacteristic
387C2×C4×C8C2311yescharacteristic
388C2×C4×C8C2311yescharacteristic
389C2×C4×C8C2311yescharacteristic
390#400—22no—
391#399—22no—
392#397—22no—
393#397—22no—
394#397—22no—
395#397—22no—
396#396—22no—
397#396—22no—
398#394—22no—
399#394—22no—
400#394—22no—
401#394—22no—
402#394—22no—
403#394—22no—
404#394—22no—
405#394—22no—
406#394—22no—
407#394—22no—
408#394—22no—
409#392—22no—
410#392—22no—
411#392—22no—
412#392—22no—
413#392—22no—
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#391C2311yescharacteristic
417#391C2311yescharacteristic
418#391C2311yescharacteristic
419#391C2311yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#390C2311yescharacteristic
426#390C2311yescharacteristic
427#390C2311yescharacteristic
428#390C2311yescharacteristic
429#390C2311yescharacteristic
430#389—22no—
431#389—22no—
432#388—22no—
433#388—22no—
434#388—22no—
435#388—22no—
436#388—22no—
437#388—22no—
438#387—22no—
439#387—22no—
440#387—22no—
441#387—22no—
442#386—22no—
443#386—22no—
444#386—22no—
445#386—22no—
446#385—22no—
447#385—22no—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#381—22no—
461#381D412yes—
462#380—22no—
463#380—22no—
464#380D412yes—
465#380D412yes—
466#379—22no—
467#379D412yes—
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C25—21no—
481C25C2×D411yescharacteristic
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—44no—
516C22×D4—84no—
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—41no—
527C23×C4—41no—
528C23×C4—41no—
529C23×C4—41no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D414yes—
534C23×C4C2×D414yes—
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C2×Q16—22no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×M16—41no—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16—41no—
566C2×M16C2×D414yes—
567C2×M16C2×D414yes—
568C22×C8—41no—
569C22×C8—41no—
570C22×C8—41no—
571C22×C8—41no—
572C22×C8C2×D414yes—
573C22×C8C2×D414yes—
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582#127—41no—
583#127—41no—
584#127—41no—
585#127—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#123—44no—
591#123—44no—
592#123—84no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—22no—
613#121—22no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121—44no—
618#121—44no—
619#120—44no—
620#120—44no—
621#120—84no—
622C4×D4—44no—
623C4×D4—44no—
624C4×D4—44no—
625C4×D4—44no—
626#117—22no—
627#117—22no—
628#117—22no—
629#117—22no—
630#117—22no—
631#117—22no—
632#117—22no—
633#117—22no—
634#117—22no—
635#117—22no—
636#117—22no—
637#117—22no—
638#117—41no—
639#117—41no—
640#117—41no—
641#117—41no—
642#117—44no—
643#117—44no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—22no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4C2×D412yes—
664C2×C4⋊C4C2×D412yes—
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
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—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—44no—
706C2×C22⋊C4—44no—
707C2×C22⋊C4C2×D412yes—
708C2×C22⋊C4C2×D412yes—
709C2×C22⋊C4C2×D412yes—
710C2×C22⋊C4C2×D412yes—
711C2×C22⋊C4C2×D412yes—
712C2×C22⋊C4C2×D412yes—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—44no—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—22no—
725#107—22no—
726#107—22no—
727#107—22no—
728#107—22no—
729#107—22no—
730#107—22no—
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—22no—
736#106—22no—
737#106—22no—
738#106—22no—
739#106—22no—
740#106—22no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—22no—
746#106—22no—
747#106—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#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—
780C22⋊C8C2×D414yes—
781C22⋊C8C2×D414yes—
782C22⋊C8C2×D414yes—
783C22⋊C8C2×D414yes—
784C22⋊C8C2×D414yes—
785C22⋊C8C2×D414yes—
786C22⋊C8C2×D414yes—
787C22⋊C8C2×D414yes—
788#97—41no—
789#97—41no—
790#97—41no—
791#97—41no—
792C4×C8—41no—
793C4×C8—41no—
794C4×C8—41no—
795C4×C8—41no—
796#95—22no—
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#95C2×D412yes—
809#95C2×D412yes—
810#95C2×D412yes—
811#95C2×D412yes—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—41no—
817C24—41no—
818C24—42no—
819C24—42no—
820C24—44no—
821C24—42no—
822C24—81no—
823C24—81no—
824C24—82no—
825C24#12714yes—
826C24C22×D411yescharacteristic
827C24C22×D411yescharacteristic
828C24C22×D411yescharacteristic
829#41—44no—
830#41—44no—
831#41—82no—
832#41—82no—
833#41—82no—
834#41—82no—
835#41—82no—
836#41—82no—
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—21no—
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—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—82no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—816no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
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—21no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—44no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—82no—
954C22×C4—82no—
955C22×C4#12714yes—
956C22×C4#12714yes—
957C22×C4#12714yes—
958C22×C4C22×D412yes—
959C22×C4C22×D412yes—
960C22×C4C22×D412yes—
961C22×C4C22×D412yes—
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D412yes—
966C22×C4C22×D412yes—
967C22×C4C22×D412yes—
968C22×C4C22×D412yes—
969C22×C4C22×D412yes—
970C22×C4C22×D412yes—
971C22×C4C2511yescharacteristic
972Q16—82no—
973SD16—82no—
974SD16—82no—
975SD16—82no—
976SD16—82no—
977D8—82no—
978D8—82no—
979D8—82no—
980M16—44no—
981M16—44no—
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—21no—
998C2×C8—44no—
999C2×C8—44no—
1000C2×C8C22×D412yes—
1001C2×C8C22×D412yes—
1002C2×C8C22×D412yes—
1003C2×C8C22×D412yes—
1004C2×C8C22×D412yes—
1005C2×C8C22×D412yes—
1006C2×C8C22×D412yes—
1007C2×C8C22×D412yes—
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—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
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—42no—
1037C4⋊C4—82no—
1038C4⋊C4—82no—
1039C4⋊C4—82no—
1040C4⋊C4—82no—
1041C4⋊C4—82no—
1042C4⋊C4—82no—
1043C22⋊C4—42no—
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—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—82no—
1068C22⋊C4—82no—
1069C22⋊C4—82no—
1070C22⋊C4—82no—
1071C22⋊C4—82no—
1072C22⋊C4—82no—
1073C22⋊C4—82no—
1074C22⋊C4—82no—
1075C22⋊C4—82no—
1076C22⋊C4—82no—
1077C22⋊C4—82no—
1078C22⋊C4—82no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—42no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—44no—
1106C23—44no—
1107C23—44no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—84no—
1129C23—84no—
1130C23—84no—
1131C23—84no—
1132C23—84no—
1133C23—164no—
1134C23—164no—
1135C23C2×#12712yes—
1136C23C2×#12712yes—
1137C23C2×#12712yes—
1138C23C23×D411yescharacteristic
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—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—41no—
1163D4—84no—
1164D4—84no—
1165D4—84no—
1166D4—84no—
1167D4—84no—
1168D4—84no—
1169D4—84no—
1170D4—84no—
1171D4—84no—
1172D4—84no—
1173D4—84no—
1174D4—164no—
1175D4—164no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
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—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—44no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—84no—
1236C2×C4—84no—
1237C2×C4—84no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4C2×#12712yes—
1241C2×C4C2×#12712yes—
1242C2×C4C2×#12712yes—
1243C2×C4C23×D411yescharacteristic
1244C2×C4C23×D411yescharacteristic
1245C2×C4#58511yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—22no—
1250C8—22no—
1251C8—22no—
1252C8—22no—
1253C8—22no—
1254C8—22no—
1255C8—22no—
1256C8—22no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—88no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—168no—
1294C22C22×#12711yescharacteristic
1295C22#348511yescharacteristic
1296C22#348511yescharacteristic
1297C22#358412yes—
1298C22#358512yes—
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4#348511yescharacteristic
1319C4#348511yescharacteristic
1320C4#348511yescharacteristic
1321C4#348511yescharacteristic
1322C2—42no—
1323C2—42no—
1324C2—42no—
1325C2—161no—
1326C2—161no—
1327C2—161no—
1328C2—161no—
1329C2#3546311yescharacteristic
1330C2#6064311yescharacteristic
1331C2#6064411yescharacteristic
1332C2#6174912yes—
1333C2#6175112yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3197C2semidirect
2. C2×#3188C2semidirect
3. C2×#3094C2semidirect
4. C2×#3091C2semidirect
5. #37448C2semidirect
6. #35157C2semidirect
7. #28365C2semidirect
8. #28361C2semidirect
9. #28357C2semidirect
10. #28353C2semidirect
11. #28352C2semidirect
12. #28349C2semidirect
13. #28340C2semidirect
14. #28337C2semidirect
15. #28328C2semidirect
16. #28327C2semidirect
17. #28325C2semidirect
18. #28325C2semidirect
19. #27946C2semidirect
20. #27944C2semidirect
21. #27943C2semidirect
22. #27941C2semidirect
23. #27937C2semidirect
24. #27935C2semidirect
25. #27928C2semidirect
26. #27925C2semidirect
27. #27923C2semidirect
28. #27923C2semidirect
29. #27921C2semidirect
30. #27920C2semidirect
31. #20527C2semidirect
41. C2×#484C22semidirect
45. C2×#481C22semidirect
48. C2×#485C22semidirect
49. C2×#485C22semidirect
58. C2×#482C22semidirect
59. C2×#482C22semidirect
60. C2×#483C22semidirect
63. C2×#480C22semidirect
72. C2×#452C22semidirect
73. C2×#452C22semidirect
76. C2×#449C22semidirect
77. C2×#449C22semidirect
82. C2×#427C22semidirect
83. C2×#427C22semidirect
86. C2×#416C22semidirect
87. C2×#416C22semidirect
106. #2500C22semidirect
107. #2500C22semidirect
110. #2499C22semidirect
111. #2499C22semidirect
118. #2317C22semidirect
119. #2317C22semidirect
120. #2311C22semidirect
121. #2311C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2097C22semidirect
126. #2097C22semidirect
127. #2096C22semidirect
128. #2096C22semidirect
129. #2095C22semidirect
130. #2095C22semidirect
131. #2094C22semidirect
132. #2094C22semidirect
133. #2094C22semidirect
134. #2094C22semidirect
135. #2093C22semidirect
136. #2093C22semidirect
137. #2093C22semidirect
138. #2093C22semidirect
139. #2092C22semidirect
140. #2092C22semidirect
141. #2092C22semidirect
142. #2092C22semidirect
143. #2092C22semidirect
144. #2092C22semidirect
145. #2092C22semidirect
146. #2092C22semidirect
147. #2015C22semidirect
148. #2015C22semidirect
149. #2014C22semidirect
150. #2014C22semidirect
151. #2012C22semidirect
152. #2012C22semidirect
153. #2011C22semidirect
154. #2011C22semidirect
155. #1973C22semidirect
156. #1973C22semidirect
157. #1973C22semidirect
158. #1973C22semidirect
159. #1972C22semidirect
160. #1972C22semidirect
161. #1972C22semidirect
162. #1971C22semidirect
163. #1970C22semidirect
164. #1970C22semidirect
165. #1970C22semidirect
166. #1969C22semidirect
167. #1968C22semidirect
168. #1968C22semidirect
169. #1968C22semidirect
170. #1968C22semidirect
171. #1961C22semidirect
172. #1961C22semidirect
173. #1959C22semidirect
174. #1959C22semidirect
175. #1958C22semidirect
176. #1958C22semidirect
177. #1957C22semidirect
178. #1957C22semidirect
179. #1847C22semidirect
180. #1847C22semidirect
181. #1847C22semidirect
182. #1847C22semidirect
183. #1846C22semidirect
184. #1846C22semidirect
185. #1845C22semidirect
186. #1844C22semidirect
191. #1752C22semidirect
192. #1752C22semidirect
193. C8×C22⋊C4C22semidirect
194. C8×C22⋊C4C22semidirect
195. #1750C22semidirect
196. #1750C22semidirect
197. #1750C22semidirect
198. #1750C22semidirect
372. #407D4semidirect
373. C2×C22⋊C8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#31972
C2×#31882
C2×#30942
C2×#30912
#374482
#351572
#283652
#283612
#283572
#283532
#283522
#283492
#283402
#283372
#283282
#283272
#283252
#279462
#279442
#279432
#279412
#279372
#279352
#279282
#279252
#279232
#279212
#279202
#205272