Finite Group Databasebeta

← #6520544

Subgroups — #6520544

Order 512.

2425 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3263C211yesmaximal, characteristic, complemented
2C2×#3224C211yesmaximal, characteristic, complemented
3C2×#3125C211yesmaximal, characteristic, complemented
4C2×#3045C211yesmaximal, characteristic, complemented
5#37305C211yesmaximal, characteristic, complemented
6#35535C211yesmaximal, characteristic, complemented
7#28481C211yesmaximal, characteristic, complemented
8#28475C211yesmaximal, characteristic, complemented
9#28468C211yesmaximal, characteristic, complemented
10#28464C211yesmaximal, characteristic, complemented
11#28452C211yesmaximal, characteristic, complemented
12#28452C211yesmaximal, characteristic, complemented
13#28447C211yesmaximal, characteristic, complemented
14#28443C211yesmaximal, characteristic, complemented
15#28432C211yesmaximal, characteristic, complemented
16#28430C211yesmaximal, characteristic, complemented
17#28415C211yesmaximal, characteristic, complemented
18#28404C211yesmaximal, characteristic, complemented
19#28395C211yesmaximal, characteristic, complemented
20#28395C211yesmaximal, characteristic, complemented
21#28381C211yesmaximal, characteristic, complemented
22#28374C211yesmaximal, characteristic, complemented
23#28364C211yesmaximal, characteristic, complemented
24#28362C211yesmaximal, characteristic, complemented
25#28343C211yesmaximal, characteristic, complemented
26#28332C211yesmaximal, characteristic, complemented
27#25796C211yesmaximal, characteristic, complemented
28#25794C211yesmaximal, characteristic, complemented
29#25787C211yesmaximal, characteristic, complemented
30#25775C211yesmaximal, characteristic, complemented
31#20553C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C22×#135C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#542C2211yescharacteristic
36C2×#535C2211yescharacteristic
37C2×#520C2211yescharacteristic
38#3263—28no—
39#3224—28no—
40C2×#497C2211yescharacteristic
41C2×#497C2211yescharacteristic, complemented
42C2×#496C2211yescharacteristic
43C2×#496C2211yescharacteristic
44C2×#496C2211yescharacteristic, complemented
45C2×#495C2211yescharacteristic
46C2×#495C2211yescharacteristic
47C2×#495C2211yescharacteristic, complemented
48C2×#493C2211yescharacteristic
49C2×#492C2211yescharacteristic, complemented
50C2×#489C2211yescharacteristic
51C2×#486C2211yescharacteristic
52#3125—28no—
53C2×#481C2211yescharacteristic
54C2×#483C2211yescharacteristic
55C2×#475C2211yescharacteristic, complemented
56C2×#475C2211yescharacteristic, complemented
57C2×#475C2211yescharacteristic, complemented
58C2×#476C2211yescharacteristic, complemented
59C2×#476C2211yescharacteristic, complemented
60C2×#476C2211yescharacteristic, complemented
61C2×#470C2211yescharacteristic
62C2×#469C2211yescharacteristic
63C2×#465C2211yescharacteristic
64C2×#465C2211yescharacteristic
65#3045—28no—
66C2×#464C2211yescharacteristic
67C2×#464C2211yescharacteristic
68C2×#464C2211yescharacteristic
69C2×#464C2211yescharacteristic, complemented
70C2×#464C2211yescharacteristic, complemented
71C2×#464C2211yescharacteristic, complemented
72C2×#460C2211yescharacteristic
73C2×#460C2211yescharacteristic
74C2×#460C2211yescharacteristic
75C2×#463C2211yescharacteristic
76C2×#463C2211yescharacteristic
77C2×#463C2211yescharacteristic
78C2×#463C2211yescharacteristic, complemented
79C2×#463C2211yescharacteristic, complemented
80C2×#463C2211yescharacteristic, complemented
81C2×#459C2211yescharacteristic
82C2×#459C2211yescharacteristic
83C2×#459C2211yescharacteristic
84C2×#452C2211yescharacteristic
85C2×#452C2211yescharacteristic
86C2×#449C2211yescharacteristic
87C2×#449C2211yescharacteristic
88C2×#450C2211yescharacteristic
89C2×#447C2211yescharacteristic
90C2×#442C2211yescharacteristic, complemented
91C2×#441C2211yescharacteristic, complemented
92C2×C4×SD16C2211yescharacteristic, complemented
93C2×C4×SD16C2211yescharacteristic, complemented
94C2×#433C2211yescharacteristic
95C2×#424C2211yescharacteristic
96C2×#417C2211yescharacteristic
97C22×#102C2211yescharacteristic
98#2858C2211yescharacteristic
99#2858C2211yescharacteristic
100#2714—22no—
101#2678—22no—
102#2676—22no—
103#2670—22no—
104#2657C2211yescharacteristic
105#2640C2211yescharacteristic
106#2567C2211yescharacteristic, complemented
107#2548C2211yescharacteristic
108#2545C2211yescharacteristic
109#2545C2211yescharacteristic, complemented
110#2544C2211yescharacteristic
111#2544C2211yescharacteristic, complemented
112#2542C2211yescharacteristic, complemented
113#2541C2211yescharacteristic
114#2502C2211yescharacteristic
115#2501C2211yescharacteristic
116#2479—22no—
117#2461—22no—
118#2455—22no—
119#2449—22no—
120#2435C2211yescharacteristic
121#2433C2211yescharacteristic
122#2432C2211yescharacteristic
123#2432C2211yescharacteristic
124#2431C2211yescharacteristic
125#2431C2211yescharacteristic
126#2326C2211yescharacteristic, complemented
127#2326C2211yescharacteristic, complemented
128C4×C4⋊Q8C2211yescharacteristic, complemented
129C4×#127C2211yescharacteristic, complemented
130#2298C2211yescharacteristic
131#2096C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2094C2211yescharacteristic
134#2094C2211yescharacteristic
135#2094C2211yescharacteristic
136#2094C2211yescharacteristic
137#2094C2211yescharacteristic, complemented
138#2094C2211yescharacteristic, complemented
139#2016C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic, complemented
143#2015C2211yescharacteristic, complemented
144#2015C2211yescharacteristic, complemented
145#2014C2211yescharacteristic
146#2014C2211yescharacteristic
147#2014C2211yescharacteristic
148#2014C2211yescharacteristic, complemented
149#2013C2211yescharacteristic
150#2013C2211yescharacteristic, complemented
151#2012C2211yescharacteristic
152#2012C2211yescharacteristic
153#2012C2211yescharacteristic
154#2012C2211yescharacteristic
155#2012C2211yescharacteristic
156#2012C2211yescharacteristic, complemented
157#2012C2211yescharacteristic, complemented
158#2012C2211yescharacteristic, complemented
159#2011C2211yescharacteristic
160#2011C2211yescharacteristic
161#2011C2211yescharacteristic, complemented
162#2011C2211yescharacteristic, complemented
163#1972C2211yescharacteristic
164#1972C2211yescharacteristic
165#1972C2211yescharacteristic
166#1972C2211yescharacteristic
167#1972C2211yescharacteristic, complemented
168#1972C2211yescharacteristic, complemented
169#1971C2211yescharacteristic, complemented
170#1971C2211yescharacteristic, complemented
171#1968C2211yescharacteristic
172#1968C2211yescharacteristic
173#1968C2211yescharacteristic
174#1968C2211yescharacteristic
175#1968C2211yescharacteristic, complemented
176#1968C2211yescharacteristic, complemented
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1959C2211yescharacteristic
180#1959C2211yescharacteristic
181#1959C2211yescharacteristic, complemented
182#1959C2211yescharacteristic, complemented
183#1957C2211yescharacteristic
184#1957C2211yescharacteristic
185#1957C2211yescharacteristic, complemented
186#1956C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189#1770C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1768C2211yescharacteristic, complemented
193#1767C2211yescharacteristic, complemented
194C4×C4⋊C8C2211yescharacteristic, complemented
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C2×AGL(1,ℤ/8)—24no—
203C2×AGL(1,ℤ/8)—42no—
204C2×AGL(1,ℤ/8)—42no—
205C2×#135—24no—
206C2×#135—42no—
207C2×#135—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×SD16C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226C22×D8C2311yescharacteristic
227C22×D8C2311yescharacteristic
228C22×D8C2311yescharacteristic
229C22×D8C2311yescharacteristic
230C22×D8C2311yescharacteristic
231C22×D8C2311yescharacteristic
232C22×M16C2311yescharacteristic
233C23×C8C2311yescharacteristic
234#542—24no—
235#542—24no—
236#542—24no—
237#542—24no—
238#535—24no—
239#535—24no—
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×#127C2311yescharacteristic
245C2×#127C2311yescharacteristic
246C2×#127C2311yescharacteristic
247C2×#127C2311yescharacteristic
248C2×#127C2311yescharacteristic
249C2×#127C2311yescharacteristic
250C2×#126—21no—
251C2×#126—21no—
252C2×#124—21no—
253C2×#124—21no—
254C2×#124—22no—
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2311yescharacteristic
263C2×#124C2311yescharacteristic
264C2×#124C2311yescharacteristic
265C2×#123—21no—
266C2×#123—21no—
267C2×#123—22no—
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8—22no—
271C2×C22⋊Q8C2311yescharacteristic
272C2×C22⋊Q8C2311yescharacteristic
273C2×#121—21no—
274C2×#121—21no—
275C2×#121—22no—
276C2×#121C2311yescharacteristic
277C2×#121C2311yescharacteristic
278C2×#120—21no—
279C2×#120—21no—
280C2×#120—22no—
281#520—24no—
282#520—24no—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4—21no—
288C2×C4×D4—21no—
289C2×C4×D4—22no—
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×#117—21no—
295C2×#117C2311yescharacteristic
296C22×C4⋊C4—21no—
297C22×C4⋊C4C2311yescharacteristic
298#497—42no—
299#497—42no—
300#496—24no—
301#496—42no—
302#496—42no—
303#495—24no—
304#495—42no—
305#495—42no—
306#493—42no—
307#492—42no—
308#489—24no—
309#486—24no—
310#483—24no—
311#481—24no—
312#476—24no—
313#476—24no—
314#476—24no—
315#475—24no—
316#475—24no—
317#475—24no—
318#470—24no—
319#469—24no—
320#465—24no—
321#465—24no—
322#464—24no—
323#464—24no—
324#464—24no—
325#464—24no—
326#464—24no—
327#464—24no—
328#463—24no—
329#463—24no—
330#463—24no—
331#463—24no—
332#463—24no—
333#463—24no—
334#460—24no—
335#460—24no—
336#460—24no—
337#459—24no—
338#459—24no—
339#459—24no—
340#452—24no—
341#452—24no—
342#450—24no—
343#449—24no—
344#449—24no—
345#447—24no—
346#442—24no—
347#441—24no—
348C4×SD16—24no—
349C4×SD16—24no—
350#433D418yescomplemented
351C2×#106C2311yescharacteristic
352C2×#106C2311yescharacteristic
353C2×#106C2311yescharacteristic
354C2×#106C2311yescharacteristic
355C2×#106C2311yescharacteristic
356C2×#106C2311yescharacteristic
357C2×#106C2311yescharacteristic
358C2×#106C2311yescharacteristic
359#424D418yescomplemented
360C2×C4⋊C8C2311yescharacteristic
361C2×C4⋊C8C2311yescharacteristic
362C2×C4⋊C8C2311yescharacteristic
363C2×C4⋊C8C2311yescharacteristic
364C2×C4⋊C8C2311yescharacteristic
365C2×C4⋊C8C2311yescharacteristic
366#417—24no—
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#103C2311yescharacteristic
378C2×#103C2311yescharacteristic
379C2×#102—24no—
380C2×#102C2311yescharacteristic
381C2×#102C2311yescharacteristic
382C2×#102C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×#102C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×#102C2311yescharacteristic
390C2×#102C2311yescharacteristic
391C2×#102C2311yescharacteristic
392C2×#102C2311yescharacteristic
393C2×#102C2311yescharacteristic
394C2×#102C2311yescharacteristic
395C2×#102C2311yescharacteristic
396C2×#102C2311yescharacteristic
397C2×#102C2311yescharacteristic
398C2×#102C2311yescharacteristic
399C2×#102C2311yescharacteristic
400C2×C22⋊C8C2311yescharacteristic
401C2×C22⋊C8C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×#97C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411C2×C4×C8C2311yescharacteristic
412#399—22no—
413#399—22no—
414#398—22no—
415#397—22no—
416#396—22no—
417#396—22no—
418#395—22no—
419#394—22no—
420#394—22no—
421#394—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#393—22no—
426#392—22no—
427#392—22no—
428#392—22no—
429#392—22no—
430#392—22no—
431#392—22no—
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#390—22no—
439#390—22no—
440#390—22no—
441#390—22no—
442#390—22no—
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#390C2311yescharacteristic
450#390C2311yescharacteristic
451#390C2311yescharacteristic
452#390C2311yescharacteristic
453#389—22no—
454#389—22no—
455#388—22no—
456#388—22no—
457#388—22no—
458#388—22no—
459#388D412yes—
460#388D412yes—
461#387D412yes—
462#387D412yes—
463#386—22no—
464#386—22no—
465#386—22no—
466#386—22no—
467#385—22no—
468#385—22no—
469#385—22no—
470#385—22no—
471#385—22no—
472#384C2311yescharacteristic
473#384C2311yescharacteristic
474#384C2311yescharacteristic
475#384C2311yescharacteristic
476#379—22no—
477C4×C4⋊C4—22no—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
483C43C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492C25—21no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2411yescharacteristic
544AGL(1,ℤ/8)—416no—
545#135—416no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×SD16—41no—
584C2×SD16—41no—
585C2×SD16—41no—
586C2×SD16—41no—
587C2×SD16—41no—
588C2×SD16—41no—
589C2×SD16—41no—
590C2×SD16—41no—
591C2×SD16—41no—
592C2×SD16—41no—
593C2×SD16—41no—
594C2×D8—22no—
595C2×D8—22no—
596C2×D8—22no—
597C2×D8—22no—
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—22no—
605C2×D8—22no—
606C2×D8—41no—
607C2×D8—41no—
608C2×D8—41no—
609C2×D8—41no—
610C2×D8—41no—
611C2×D8—41no—
612C2×D8—41no—
613C2×D8—41no—
614C2×D8—41no—
615C2×D8—41no—
616C2×D8—41no—
617C2×D8—41no—
618C2×M16—41no—
619C2×M16—41no—
620C2×M16C2×D414yes—
621C22×C8—41no—
622C22×C8—41no—
623C22×C8C2×D414yes—
624C22×C8C2411yescharacteristic
625C22×C8C2411yescharacteristic
626C22×C8C2411yescharacteristic
627C22×C8C2411yescharacteristic
628C22×C8C2411yescharacteristic
629C22×C8C2411yescharacteristic
630C22×C8C2411yescharacteristic
631C22×C8C2411yescharacteristic
632C4⋊Q8—22no—
633C4⋊Q8—22no—
634C4⋊Q8—22no—
635C4⋊Q8—22no—
636C4⋊Q8—22no—
637C4⋊Q8—41no—
638C4⋊Q8—41no—
639C4⋊Q8—41no—
640#127—22no—
641#127—22no—
642#127—22no—
643#127—22no—
644#127—22no—
645#127—41no—
646#127—41no—
647#127—41no—
648#127—41no—
649#127—41no—
650#127—41no—
651#127—41no—
652#126—44no—
653#126—44no—
654#124—22no—
655#124—22no—
656#124—22no—
657#124—22no—
658#124—22no—
659#124—22no—
660#124—22no—
661#124—22no—
662#124—22no—
663#124—22no—
664#124—41no—
665#124—41no—
666#124—41no—
667#124—41no—
668#124—41no—
669#124—41no—
670#124—41no—
671#124—41no—
672#124—41no—
673#124—41no—
674#124—44no—
675#124—44no—
676#124—84no—
677#123—44no—
678#123—44no—
679#123—84no—
680C22⋊Q8—22no—
681C22⋊Q8—22no—
682C22⋊Q8—22no—
683C22⋊Q8—22no—
684C22⋊Q8—44no—
685C22⋊Q8—44no—
686C22⋊Q8—84no—
687#121—22no—
688#121—22no—
689#121—22no—
690#121—22no—
691#121—44no—
692#121—44no—
693#121—84no—
694#120—44no—
695#120—44no—
696#120—84no—
697C4×Q8—22no—
698C4×Q8—22no—
699C4×Q8—22no—
700C4×Q8—22no—
701C4×Q8—22no—
702C4×Q8—22no—
703C4×Q8—22no—
704C4×Q8—22no—
705C4×D4—22no—
706C4×D4—22no—
707C4×D4—22no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—22no—
711C4×D4—22no—
712C4×D4—22no—
713C4×D4—44no—
714C4×D4—44no—
715C4×D4—84no—
716#117—44no—
717#117C2×D414yes—
718#117C2×D414yes—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4—21no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—21no—
725C2×C4⋊C4—21no—
726C2×C4⋊C4—21no—
727C2×C4⋊C4—21no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—21no—
730C2×C4⋊C4—21no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—22no—
733C2×C4⋊C4—22no—
734C2×C4⋊C4—22no—
735C2×C4⋊C4—22no—
736C2×C4⋊C4—44no—
737C2×C4⋊C4C2×D412yes—
738C2×C4⋊C4C2×D412yes—
739C2×C4⋊C4C2×D411yescharacteristic
740C2×C4⋊C4C2×D411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4—21no—
757C2×C22⋊C4—21no—
758C2×C22⋊C4—21no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—21no—
762C2×C22⋊C4—21no—
763C2×C22⋊C4—21no—
764C2×C22⋊C4—21no—
765C2×C22⋊C4—21no—
766C2×C22⋊C4—21no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4C2×D412yes—
780C2×C22⋊C4C2×D412yes—
781C2×C22⋊C4C2×D411yescharacteristic
782C2×C22⋊C4C2×D411yescharacteristic
783C2×C42—21no—
784C2×C42—21no—
785C2×C42—21no—
786C2×C42—21no—
787C2×C42C2×D412yes—
788C2×C42C2×D412yes—
789C2×C42C2411yescharacteristic
790C2×C42C2411yescharacteristic
791C2×C42C2411yescharacteristic
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
794C2×C42C2411yescharacteristic
795#106—22no—
796#106—22no—
797#106—22no—
798#106—22no—
799#106—22no—
800#106—22no—
801#106—22no—
802#106—22no—
803C4⋊C8C2×D414yes—
804C4⋊C8C2×D414yes—
805C4⋊C8C2×D414yes—
806C4⋊C8C2×D414yes—
807C4⋊C8C2×D414yes—
808C4⋊C8C2×D414yes—
809#103—22no—
810#103—22no—
811#103—22no—
812#103—22no—
813#103—22no—
814#103—22no—
815#103—22no—
816#103—22no—
817#103—22no—
818#103—22no—
819#103—22no—
820#103—22no—
821#102—22no—
822#102—22no—
823#102—22no—
824#102—22no—
825#102—22no—
826#102—22no—
827#102—22no—
828#102—22no—
829#102—22no—
830#102—22no—
831#102—22no—
832#102—22no—
833#102—22no—
834#102—22no—
835#102—22no—
836#102—22no—
837#102—22no—
838#102—22no—
839#102—22no—
840#102—22no—
841C22⋊C8C2×D414yes—
842C22⋊C8C2×D414yes—
843#97—41no—
844#97—41no—
845#97—41no—
846#97—41no—
847#97C2×D414yes—
848C4×C8—41no—
849C4×C8—41no—
850C4×C8—41no—
851C4×C8—41no—
852C4×C8C2×D414yes—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—22no—
857#95—22no—
858#95—22no—
859#95C2×D412yes—
860#95C2×D412yes—
861#95C2×D412yes—
862#95C2×D412yes—
863#95C2×D412yes—
864#95C2×D412yes—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—42no—
872C24—81no—
873C24—81no—
874C24—82no—
875C24—82no—
876C24C22×D411yescharacteristic
877#41—28no—
878#41—44no—
879#41—44no—
880#41—44no—
881#41—44no—
882#41—44no—
883#41—82no—
884#41—82no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—21no—
908C2×Q8—42no—
909C2×Q8—42no—
910C2×Q8—82no—
911C2×Q8—82no—
912C2×Q8H(5,𝔽2)12yes—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—21no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4—21no—
937C2×D4—21no—
938C2×D4—21no—
939C2×D4—21no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—21no—
945C2×D4—21no—
946C2×D4—21no—
947C2×D4—21no—
948C2×D4—42no—
949C2×D4—44no—
950C2×D4—44no—
951C2×D4—44no—
952C2×D4—42no—
953C2×D4—42no—
954C2×D4—42no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—82no—
965C2×D4—82no—
966C2×D4—82no—
967C2×D4—81no—
968C2×D4—81no—
969C2×D4—82no—
970C2×D4—82no—
971C2×D4—82no—
972C2×D4—82no—
973C2×D4—82no—
974C2×D4—82no—
975C2×D4—82no—
976C2×D4—82no—
977C2×D4—82no—
978C2×D4—82no—
979C2×D4—82no—
980C2×D4—82no—
981C2×D4—81no—
982C2×D4—81no—
983C2×D4—82no—
984C2×D4—82no—
985C2×D4H(5,𝔽2)12yes—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—42no—
1006C22×C4—42no—
1007C22×C4—42no—
1008C22×C4—42no—
1009C22×C4—81no—
1010C22×C4—81no—
1011C22×C4—82no—
1012C22×C4—82no—
1013C22×C4—82no—
1014C22×C4—82no—
1015C22×C4—82no—
1016C22×C4C22×D412yes—
1017C22×C4C22×D412yes—
1018C22×C4C22×D412yes—
1019C22×C4C22×D411yescharacteristic
1020C22×C4C22×D411yescharacteristic
1021C22×C4C22×D411yescharacteristic
1022C22×C4C22×D411yescharacteristic
1023C22×C4C22×D411yescharacteristic
1024C22×C4C22×D412yes—
1025C22×C4C22×D412yes—
1026C22×C4C22×D412yes—
1027C22×C4C2511yescharacteristic
1028Q16—44no—
1029Q16—44no—
1030Q16—82no—
1031Q16—82no—
1032SD16—44no—
1033SD16—44no—
1034SD16—44no—
1035SD16—44no—
1036SD16—44no—
1037SD16—44no—
1038SD16—82no—
1039SD16—82no—
1040SD16—82no—
1041SD16—82no—
1042SD16—82no—
1043SD16—82no—
1044D8—44no—
1045D8—44no—
1046D8—44no—
1047D8—44no—
1048D8—82no—
1049D8—82no—
1050D8—82no—
1051D8—82no—
1052M16—44no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8—21no—
1057C2×C8—21no—
1058C2×C8—21no—
1059C2×C8—21no—
1060C2×C8—21no—
1061C2×C8—21no—
1062C2×C8—21no—
1063C2×C8—21no—
1064C2×C8—21no—
1065C2×C8—21no—
1066C2×C8—21no—
1067C2×C8—21no—
1068C2×C8—21no—
1069C2×C8—44no—
1070C2×C8C22×D412yes—
1071C2×C8C22×D412yes—
1072C2×C8C22×D412yes—
1073C2×C8C22×D412yes—
1074C2×C8C22×D412yes—
1075C2×C8C22×D412yes—
1076C2×C8C22×D412yes—
1077C2×C8C22×D412yes—
1078C4⋊C4—24no—
1079C4⋊C4—21no—
1080C4⋊C4—21no—
1081C4⋊C4—21no—
1082C4⋊C4—21no—
1083C4⋊C4—21no—
1084C4⋊C4—21no—
1085C4⋊C4—21no—
1086C4⋊C4—21no—
1087C4⋊C4—21no—
1088C4⋊C4—21no—
1089C4⋊C4—21no—
1090C4⋊C4—21no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—82no—
1104C4⋊C4—82no—
1105C4⋊C4—82no—
1106C4⋊C4—82no—
1107C4⋊C4#12714yes—
1108C4⋊C4#12714yes—
1109C22⋊C4—24no—
1110C22⋊C4—42no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—42no—
1121C22⋊C4—42no—
1122C22⋊C4—42no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—82no—
1134C22⋊C4—82no—
1135C22⋊C4—82no—
1136C22⋊C4—82no—
1137C22⋊C4—82no—
1138C22⋊C4—82no—
1139C22⋊C4—82no—
1140C22⋊C4—82no—
1141C22⋊C4—82no—
1142C22⋊C4—82no—
1143C22⋊C4#12714yes—
1144C22⋊C4#12714yes—
1145C42—24no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—42no—
1155C42—42no—
1156C42—42no—
1157C42—42no—
1158C42—42no—
1159C42C22×D412yes—
1160C42C22×D412yes—
1161C42C22×D412yes—
1162C42C22×D412yes—
1163C23—22no—
1164C23—21no—
1165C23—21no—
1166C23—22no—
1167C23—22no—
1168C23—42no—
1169C23—41no—
1170C23—41no—
1171C23—42no—
1172C23—42no—
1173C23—42no—
1174C23—42no—
1175C23—42no—
1176C23—42no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—42no—
1193C23—42no—
1194C23—42no—
1195C23—42no—
1196C23—42no—
1197C23—84no—
1198C23—162no—
1199C23—162no—
1200C23—164no—
1201C23—164no—
1202C23C2×#12712yes—
1203C23C23×D411yescharacteristic
1204Q8—22no—
1205Q8—22no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—162no—
1221Q8—162no—
1222D4—22no—
1223D4—22no—
1224D4—48no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—41no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—41no—
1240D4—41no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—41no—
1245D4—41no—
1246D4—41no—
1247D4—88no—
1248D4—84no—
1249D4—84no—
1250D4—164no—
1251D4—162no—
1252D4—162no—
1253D4—162no—
1254D4—162no—
1255D4—164no—
1256D4—164no—
1257D4—162no—
1258D4—162no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—48no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—42no—
1304C2×C4—42no—
1305C2×C4—84no—
1306C2×C4—162no—
1307C2×C4—162no—
1308C2×C4—162no—
1309C2×C4—162no—
1310C2×C4—162no—
1311C2×C4C2×#12712yes—
1312C2×C4C2×#12712yes—
1313C2×C4C2×#12712yes—
1314C2×C4C2×#12712yes—
1315C2×C4C2×#12712yes—
1316C2×C4#57714yes—
1317C2×C4C23×D411yescharacteristic
1318C2×C4C23×D411yescharacteristic
1319C2×C4C2×H(5,𝔽2)11yescharacteristic
1320C2×C4C2×H(5,𝔽2)11yescharacteristic
1321C2×C4#58511yescharacteristic
1322C2×C4#58511yescharacteristic
1323C8—22no—
1324C8—22no—
1325C8—22no—
1326C8—22no—
1327C8—22no—
1328C8—22no—
1329C8—22no—
1330C8—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—42no—
1335C22—42no—
1336C22—44no—
1337C22—42no—
1338C22—82no—
1339C22—81no—
1340C22—81no—
1341C22—82no—
1342C22—82no—
1343C22—82no—
1344C22—82no—
1345C22—82no—
1346C22—82no—
1347C22—82no—
1348C22—82no—
1349C22—82no—
1350C22—82no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—168no—
1367C22C22×#12711yescharacteristic
1368C22#348811yescharacteristic
1369C22#348811yescharacteristic
1370C22C2×#57712yes—
1371C22#358512yes—
1372C4—24no—
1373C4—22no—
1374C4—22no—
1375C4—22no—
1376C4—22no—
1377C4—22no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4#348411yescharacteristic
1392C4#348711yescharacteristic
1393C4#348811yescharacteristic
1394C4#348811yescharacteristic
1395C2—42no—
1396C2—82no—
1397C2—161no—
1398C2—161no—
1399C2—161no—
1400C2—161no—
1401C2—161no—
1402C2#3556511yescharacteristic
1403C2#6064611yescharacteristic
1404C2#6065011yescharacteristic
1405C2#6201812yes—
1406C2#6204512yes—
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×#3263C2semidirect
2. C2×#3224C2semidirect
3. C2×#3125C2semidirect
4. C2×#3045C2semidirect
5. #37305C2semidirect
6. #35535C2semidirect
7. #28481C2semidirect
8. #28475C2semidirect
9. #28468C2semidirect
10. #28464C2semidirect
11. #28452C2semidirect
12. #28452C2semidirect
13. #28447C2semidirect
14. #28443C2semidirect
15. #28432C2semidirect
16. #28430C2semidirect
17. #28415C2semidirect
18. #28404C2semidirect
19. #28395C2semidirect
20. #28395C2semidirect
21. #28381C2semidirect
22. #28374C2semidirect
23. #28364C2semidirect
24. #28362C2semidirect
25. #28343C2semidirect
26. #28332C2semidirect
27. #25796C2semidirect
28. #25794C2semidirect
29. #25787C2semidirect
30. #25775C2semidirect
31. #20553C2semidirect
41. C2×#497C22semidirect
44. C2×#496C22semidirect
47. C2×#495C22semidirect
49. C2×#492C22semidirect
55. C2×#475C22semidirect
56. C2×#475C22semidirect
57. C2×#475C22semidirect
58. C2×#476C22semidirect
59. C2×#476C22semidirect
60. C2×#476C22semidirect
69. C2×#464C22semidirect
70. C2×#464C22semidirect
71. C2×#464C22semidirect
78. C2×#463C22semidirect
79. C2×#463C22semidirect
80. C2×#463C22semidirect
90. C2×#442C22semidirect
91. C2×#441C22semidirect
92. C2×C4×SD16C22semidirect
93. C2×C4×SD16C22semidirect
106. #2567C22semidirect
109. #2545C22semidirect
111. #2544C22semidirect
112. #2542C22semidirect
126. #2326C22semidirect
127. #2326C22semidirect
128. C4×C4⋊Q8C22semidirect
129. C4×#127C22semidirect
131. #2096C22semidirect
132. #2096C22semidirect
137. #2094C22semidirect
138. #2094C22semidirect
139. #2016C22semidirect
140. #2016C22semidirect
142. #2015C22semidirect
143. #2015C22semidirect
144. #2015C22semidirect
148. #2014C22semidirect
150. #2013C22semidirect
156. #2012C22semidirect
157. #2012C22semidirect
158. #2012C22semidirect
161. #2011C22semidirect
162. #2011C22semidirect
167. #1972C22semidirect
168. #1972C22semidirect
169. #1971C22semidirect
170. #1971C22semidirect
175. #1968C22semidirect
176. #1968C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
181. #1959C22semidirect
182. #1959C22semidirect
185. #1957C22semidirect
186. #1956C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. #1770C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
192. #1768C22semidirect
193. #1767C22semidirect
194. C4×C4⋊C8C22semidirect
350. #433D4semidirect
359. #424D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32632
C2×#32242
C2×#31252
C2×#30452
#373052
#355352
#284812
#284752
#284682
#284642
#284522
#284472
#284432
#284322
#284302
#284152
#284042
#283952
#283812
#283742
#283642
#283622
#283432
#283322
#257962
#257942
#257872
#257752
#205532