Finite Group Databasebeta

← #6520563

Subgroups — #6520563

Order 512.

2286 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3258C211yesmaximal, characteristic, complemented
2C2×#3224C211yesmaximal, characteristic
3C2×#3127C211yesmaximal, characteristic, complemented
4C2×#3043C211yesmaximal, characteristic, complemented
5#37424C211yesmaximal, characteristic, complemented
6#35669C211yesmaximal, characteristic, complemented
7#28481C211yesmaximal, characteristic, complemented
8#28481C211yesmaximal, characteristic, complemented
9#28469C211yesmaximal, characteristic, complemented
10#28466C211yesmaximal, characteristic, complemented
11#28456C211yesmaximal, characteristic, complemented
12#28453C211yesmaximal, characteristic, complemented
13#28451C211yesmaximal, characteristic, complemented
14#28439C211yesmaximal, characteristic, complemented
15#28432C211yesmaximal, characteristic, complemented
16#28424C211yesmaximal, characteristic, complemented
17#28418C211yesmaximal, characteristic, complemented
18#28402C211yesmaximal, characteristic, complemented
19#28392C211yesmaximal, characteristic, complemented
20#28389C211yesmaximal, characteristic, complemented
21#28379C211yesmaximal, characteristic, complemented
22#28377C211yesmaximal, characteristic, complemented
23#28361C211yesmaximal, characteristic, complemented
24#28357C211yesmaximal, characteristic, complemented
25#28351C211yesmaximal, characteristic, complemented
26#28338C211yesmaximal, characteristic, complemented
27#25795C211yesmaximal, characteristic, complemented
28#25792C211yesmaximal, characteristic, complemented
29#25784C211yesmaximal, characteristic, complemented
30#25776C211yesmaximal, characteristic, complemented
31#20553C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C23×SD16C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#541C2211yescharacteristic
36C2×#535C2211yescharacteristic
37C2×#519C2211yescharacteristic
38#3258—28no—
39#3224—28no—
40C2×#497C2211yescharacteristic
41C2×#497C2211yescharacteristic
42C2×#497C2211yescharacteristic, complemented
43C2×#497C2211yescharacteristic, complemented
44C2×#496C2211yescharacteristic
45C2×#495C2211yescharacteristic
46C2×#495C2211yescharacteristic
47C2×#495C2211yescharacteristic
48C2×#495C2211yescharacteristic, complemented
49C2×#494C2211yescharacteristic, complemented
50C2×#489C2211yescharacteristic
51C2×#486C2211yescharacteristic
52#3127—28no—
53C2×#485C2211yescharacteristic
54C2×#485C2211yescharacteristic
55C2×#479C2211yescharacteristic, complemented
56C2×#479C2211yescharacteristic, complemented
57C2×#479C2211yescharacteristic, complemented
58C2×#477C2211yescharacteristic, complemented
59C2×#475C2211yescharacteristic, complemented
60C2×#478C2211yescharacteristic, complemented
61C2×#470C2211yescharacteristic
62C2×#468C2211yescharacteristic
63C2×#467C2211yescharacteristic
64C2×#465C2211yescharacteristic
65#3043—28no—
66C2×#464C2211yescharacteristic
67C2×#464C2211yescharacteristic
68C2×#464C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#464C2211yescharacteristic
71C2×#464C2211yescharacteristic, complemented
72C2×#464C2211yescharacteristic, complemented
73C2×#462C2211yescharacteristic, complemented
74C2×#462C2211yescharacteristic, complemented
75C2×#462C2211yescharacteristic, complemented
76C2×#460C2211yescharacteristic
77C2×#460C2211yescharacteristic
78C2×#460C2211yescharacteristic
79C2×#460C2211yescharacteristic
80C2×#460C2211yescharacteristic
81C2×#463C2211yescharacteristic
82C2×#461C2211yescharacteristic, complemented
83C2×#459C2211yescharacteristic
84C2×#452C2211yescharacteristic
85C2×#449C2211yescharacteristic
86C2×#451C2211yescharacteristic
87C2×#451C2211yescharacteristic
88C2×#450C2211yescharacteristic
89C2×#447C2211yescharacteristic
90C2×#441C2211yescharacteristic, complemented
91C2×#441C2211yescharacteristic, complemented
92C2×C4×Q16C2211yescharacteristic, complemented
93C2×C4×Q16C2211yescharacteristic, complemented
94C2×#433C2211yescharacteristic
95C2×#424C2211yescharacteristic
96C2×#418C2211yescharacteristic
97C2×#416C2211yescharacteristic
98#2861C2211yescharacteristic
99#2858C2211yescharacteristic
100#2711—22no—
101#2711—22no—
102#2685—22no—
103#2685—22no—
104#2658C2211yescharacteristic
105#2641C2211yescharacteristic
106#2568C2211yescharacteristic, complemented
107#2567C2211yescharacteristic, complemented
108#2548C2211yescharacteristic
109#2548C2211yescharacteristic
110#2545C2211yescharacteristic
111#2545C2211yescharacteristic
112#2545C2211yescharacteristic, complemented
113#2545C2211yescharacteristic, complemented
114#2500C2211yescharacteristic
115#2499C2211yescharacteristic
116#2474—22no—
117#2470—22no—
118#2469—22no—
119#2465—22no—
120#2436C2211yescharacteristic
121#2435C2211yescharacteristic
122#2435C2211yescharacteristic
123#2434C2211yescharacteristic
124#2432C2211yescharacteristic
125#2432C2211yescharacteristic
126#2327C2211yescharacteristic, complemented
127#2326C2211yescharacteristic, complemented
128C4×C4⋊Q8C2211yescharacteristic, complemented
129C4×#124C2211yescharacteristic, complemented
130#2298C2211yescharacteristic
131#2097C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2094C2211yescharacteristic
134#2093C2211yescharacteristic
135#2093C2211yescharacteristic, complemented
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic, complemented
139#2016C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2016C2211yescharacteristic, complemented
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic
146#2015C2211yescharacteristic
147#2015C2211yescharacteristic
148#2015C2211yescharacteristic
149#2015C2211yescharacteristic, complemented
150#2015C2211yescharacteristic, complemented
151#2015C2211yescharacteristic, complemented
152#2015C2211yescharacteristic, complemented
153#2013C2211yescharacteristic
154#2013C2211yescharacteristic
155#2013C2211yescharacteristic, complemented
156#2013C2211yescharacteristic, complemented
157#2012C2211yescharacteristic
158#2012C2211yescharacteristic
159#2012C2211yescharacteristic
160#2012C2211yescharacteristic
161#2012C2211yescharacteristic, complemented
162#2012C2211yescharacteristic, complemented
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic
165#1973C2211yescharacteristic
166#1973C2211yescharacteristic, complemented
167#1973C2211yescharacteristic, complemented
168#1972C2211yescharacteristic
169#1972C2211yescharacteristic, complemented
170#1971C2211yescharacteristic, complemented
171#1970C2211yescharacteristic
172#1969C2211yescharacteristic, complemented
173#1969C2211yescharacteristic, complemented
174#1968C2211yescharacteristic
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1960C2211yescharacteristic, complemented
180#1959C2211yescharacteristic
181#1959C2211yescharacteristic
182#1959C2211yescharacteristic, complemented
183#1958C2211yescharacteristic
184#1958C2211yescharacteristic
185#1958C2211yescharacteristic, 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
200C23×Q8C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C2×#137—24no—
203C2×#137—42no—
204C2×#137—42no—
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×SD16—24no—
215C22×SD16—42no—
216C22×SD16—42no—
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×SD16C2311yescharacteristic
224C22×SD16C2311yescharacteristic
225C22×SD16C2311yescharacteristic
226C22×SD16C2311yescharacteristic
227C22×SD16C2311yescharacteristic
228C22×SD16C2311yescharacteristic
229C22×D8C2311yescharacteristic
230C22×D8C2311yescharacteristic
231C22×D8C2311yescharacteristic
232C22×M16C2311yescharacteristic
233C23×C8C2311yescharacteristic
234#542—24no—
235#542—24no—
236#541—24no—
237#541—24no—
238#535—24no—
239#535—24no—
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2311yescharacteristic
246C2×#127C2311yescharacteristic
247C2×#127C2311yescharacteristic
248C2×#126—21no—
249C2×#126—21no—
250C2×#126—21no—
251C2×#125—21no—
252C2×#125—21no—
253C2×#125C2311yescharacteristic
254C2×#124—21no—
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2311yescharacteristic
263C2×#124C2311yescharacteristic
264C2×#124C2311yescharacteristic
265C2×#124C2311yescharacteristic
266C2×#123—21no—
267C2×C22⋊Q8—21no—
268C2×C22⋊Q8C2311yescharacteristic
269C2×C22⋊Q8C2311yescharacteristic
270C2×C22⋊Q8C2311yescharacteristic
271C2×#121—21no—
272C2×#121—21no—
273C2×#121C2311yescharacteristic
274C2×#120—21no—
275C2×#120—21no—
276#519—24no—
277#519—24no—
278C2×C4×Q8—21no—
279C2×C4×Q8—21no—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×#117—21no—
289C2×#117—21no—
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292#497—42no—
293#497—42no—
294#497—42no—
295#497—42no—
296#496—24no—
297#495—24no—
298#495—42no—
299#495—42no—
300#495—42no—
301#494—42no—
302#489—24no—
303#486—24no—
304#485—24no—
305#485—24no—
306#479—24no—
307#479—24no—
308#479—24no—
309#478—24no—
310#477—24no—
311#475—24no—
312#470—24no—
313#468—24no—
314#467—24no—
315#465—24no—
316#464—24no—
317#464—24no—
318#464—24no—
319#464—24no—
320#464—24no—
321#464—24no—
322#464—24no—
323#463—24no—
324#462—24no—
325#462—24no—
326#462—24no—
327#461—24no—
328#460—24no—
329#460—24no—
330#460—24no—
331#460—24no—
332#460—24no—
333#459—24no—
334#452—24no—
335#451—24no—
336#451—24no—
337#450—24no—
338#449—24no—
339#447—24no—
340#441—24no—
341#441—24no—
342C4×Q16—24no—
343C4×Q16—24no—
344#433D418yes—
345C2×#107C2311yescharacteristic
346C2×#107C2311yescharacteristic
347C2×#107C2311yescharacteristic
348C2×#107C2311yescharacteristic
349C2×#106C2311yescharacteristic
350C2×#106C2311yescharacteristic
351C2×#106C2311yescharacteristic
352C2×#106C2311yescharacteristic
353#424D418yes—
354C2×C4⋊C8C2311yescharacteristic
355C2×C4⋊C8C2311yescharacteristic
356C2×C4⋊C8C2311yescharacteristic
357C2×C4⋊C8C2311yescharacteristic
358C2×C4⋊C8C2311yescharacteristic
359C2×C4⋊C8C2311yescharacteristic
360#418—24no—
361#416—24no—
362C2×#103C2311yescharacteristic
363C2×#103C2311yescharacteristic
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
395C2×C22⋊C8C2311yescharacteristic
396C2×#97C2311yescharacteristic
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406#400—22no—
407#399—22no—
408#399—22no—
409#397—22no—
410#396—22no—
411#396—22no—
412#396—22no—
413#396—22no—
414#395—22no—
415#395—22no—
416#394—22no—
417#394—22no—
418#394—22no—
419#394—22no—
420#394—22no—
421#394—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#393—22no—
426#391—22no—
427#391C2311yescharacteristic
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#390—22no—
436#390—22no—
437#390—22no—
438#390—22no—
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#389—22no—
448#389—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#388—22no—
453#388—22no—
454#388—22no—
455#388—22no—
456#388—22no—
457#388—22no—
458#388D412yes—
459#388D412yes—
460#387—22no—
461#387—22no—
462#387—22no—
463#387D412yes—
464#387D412yes—
465#386—22no—
466#385—22no—
467#385—22no—
468#385—22no—
469#385—22no—
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#379—22no—
475#379—22no—
476C4×C4⋊C4—22no—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4—22no—
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—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534#137—416no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
561C2×Q16—41no—
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—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—22no—
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×SD16—41no—
595C2×SD16—41no—
596C2×SD16—41no—
597C2×SD16—41no—
598C2×SD16—416no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×D8—41no—
605C2×D8—41no—
606C2×D8—41no—
607C2×D8—41no—
608C2×M16—41no—
609C2×M16—41no—
610C2×M16C2×D414yes—
611C22×C8—41no—
612C22×C8—41no—
613C22×C8C2×D414yes—
614C22×C8C2411yescharacteristic
615C22×C8C2411yescharacteristic
616C22×C8C2411yescharacteristic
617C22×C8C2411yescharacteristic
618C22×C8C2411yescharacteristic
619C22×C8C2411yescharacteristic
620C22×C8C2411yescharacteristic
621C22×C8C2411yescharacteristic
622C4⋊Q8—22no—
623C4⋊Q8—22no—
624C4⋊Q8—22no—
625C4⋊Q8—22no—
626C4⋊Q8—22no—
627C4⋊Q8—22no—
628C4⋊Q8—41no—
629C4⋊Q8—41no—
630C4⋊Q8—41no—
631C4⋊Q8—41no—
632C4⋊Q8—41no—
633C4⋊Q8—41no—
634#127—22no—
635#127—22no—
636#127—22no—
637#127—22no—
638#126—44no—
639#126—44no—
640#126—44no—
641#125—22no—
642#125—22no—
643#125—44no—
644#125—44no—
645#124—22no—
646#124—22no—
647#124—22no—
648#124—22no—
649#124—22no—
650#124—22no—
651#124—22no—
652#124—22no—
653#124—41no—
654#124—41no—
655#124—41no—
656#124—41no—
657#124—41no—
658#124—41no—
659#124—41no—
660#124—41no—
661#124—41no—
662#124—41no—
663#124—41no—
664#124—41no—
665#124—41no—
666#124—41no—
667#124—44no—
668#123—44no—
669C22⋊Q8—22no—
670C22⋊Q8—22no—
671C22⋊Q8—22no—
672C22⋊Q8—22no—
673C22⋊Q8—22no—
674C22⋊Q8—22no—
675C22⋊Q8—44no—
676#121—22no—
677#121—22no—
678#121—44no—
679#121—44no—
680#120—44no—
681#120—44no—
682C4×Q8—22no—
683C4×Q8—22no—
684C4×Q8—22no—
685C4×Q8—22no—
686C4×Q8—22no—
687C4×Q8—22no—
688C4×Q8—22no—
689C4×Q8—22no—
690C4×Q8—22no—
691C4×Q8—22no—
692C4×Q8—22no—
693C4×Q8—22no—
694C4×Q8—22no—
695C4×Q8—22no—
696C4×Q8—44no—
697C4×Q8—44no—
698C4×D4—22no—
699C4×D4—22no—
700#117—22no—
701#117—22no—
702#117—44no—
703#117—44no—
704#117C2×D414yes—
705#117C2×D414yes—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—21no—
709C2×C4⋊C4—21no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4—21no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4—22no—
726C2×C4⋊C4—22no—
727C2×C4⋊C4C2×D412yes—
728C2×C4⋊C4C2×D412yes—
729C2×C4⋊C4C2×D411yescharacteristic
730C2×C4⋊C4C2×D411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4C2×D412yes—
766C2×C22⋊C4C2×D412yes—
767C2×C22⋊C4C2×D411yescharacteristic
768C2×C22⋊C4C2×D411yescharacteristic
769C2×C42—21no—
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—21no—
773C2×C42—21no—
774C2×C42—21no—
775C2×C42—21no—
776C2×C42—21no—
777C2×C42C2×D412yes—
778C2×C42C2×D412yes—
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785#107—22no—
786#107—22no—
787#107—22no—
788#107—22no—
789#106—22no—
790#106—22no—
791#106—22no—
792#106—22no—
793C4⋊C8C2×D414yes—
794C4⋊C8C2×D414yes—
795C4⋊C8C2×D414yes—
796C4⋊C8C2×D414yes—
797C4⋊C8C2×D414yes—
798C4⋊C8C2×D414yes—
799#103—22no—
800#103—22no—
801#103—22no—
802#103—22no—
803#103—22no—
804#103—22no—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
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#102—22no—
818#102—22no—
819#102—22no—
820#102—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—
831C22⋊C8C2×D414yes—
832C22⋊C8C2×D414yes—
833#97—41no—
834#97—41no—
835#97—41no—
836#97—41no—
837#97C2×D414yes—
838C4×C8—41no—
839C4×C8—41no—
840C4×C8—41no—
841C4×C8—41no—
842C4×C8C2×D414yes—
843#95—22no—
844#95—22no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95C2×D412yes—
854#95C2×D412yes—
855#95C2×D412yes—
856#95C2×D412yes—
857#95C2×D412yes—
858#95C2×D412yes—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—42no—
864C24—81no—
865C24—81no—
866C24—82no—
867C24—82no—
868C24C22×D411yescharacteristic
869#41—44no—
870#41—44no—
871#41—82no—
872#41—82no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—28no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
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—44no—
911C2×Q8—44no—
912C2×Q8—44no—
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—82no—
916C2×Q8H(5,𝔽2)12yes—
917C2×Q8H(5,𝔽2)12yes—
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—44no—
943C2×D4—44no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—82no—
952C2×D4—82no—
953C2×D4—81no—
954C2×D4—81no—
955C2×D4—82no—
956C2×D4—82no—
957C2×D4—82no—
958C2×D4—82no—
959C2×D4—81no—
960C2×D4—81no—
961C2×D4—82no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—82no—
986C22×C4C22×D412yes—
987C22×C4C22×D412yes—
988C22×C4C22×D412yes—
989C22×C4C22×D412yes—
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D412yes—
996C22×C4C22×D412yes—
997C22×C4C2511yescharacteristic
998Q16—44no—
999Q16—44no—
1000Q16—44no—
1001Q16—44no—
1002Q16—44no—
1003Q16—44no—
1004Q16—82no—
1005Q16—82no—
1006Q16—82no—
1007SD16—44no—
1008SD16—44no—
1009SD16—44no—
1010SD16—44no—
1011SD16—44no—
1012SD16—44no—
1013SD16—82no—
1014SD16—82no—
1015SD16—82no—
1016SD16—82no—
1017SD16—82no—
1018SD16—82no—
1019D8—82no—
1020D8—82no—
1021D8—82no—
1022M16—44no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—44no—
1040C2×C8C22×D412yes—
1041C2×C8C22×D412yes—
1042C2×C8C22×D412yes—
1043C2×C8C22×D412yes—
1044C2×C8C22×D412yes—
1045C2×C8C22×D412yes—
1046C2×C8C22×D412yes—
1047C2×C8C22×D412yes—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—82no—
1080C4⋊C4—82no—
1081C4⋊C4—82no—
1082C4⋊C4—82no—
1083C4⋊C4#12714yes—
1084C4⋊C4#12714yes—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—82no—
1103C22⋊C4—82no—
1104C22⋊C4—82no—
1105C22⋊C4—82no—
1106C22⋊C4—82no—
1107C22⋊C4—82no—
1108C22⋊C4—82no—
1109C22⋊C4—82no—
1110C22⋊C4—82no—
1111C22⋊C4—82no—
1112C22⋊C4—82no—
1113C22⋊C4—82no—
1114C22⋊C4—82no—
1115C22⋊C4#12714yes—
1116C22⋊C4#12714yes—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42C22×D412yes—
1136C42C22×D412yes—
1137C42C22×D412yes—
1138C42C22×D412yes—
1139C23—22no—
1140C23—22no—
1141C23—21no—
1142C23—21no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—42no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—42no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—84no—
1164C23—162no—
1165C23—162no—
1166C23—164no—
1167C23—164no—
1168C23C2×#12712yes—
1169C23C23×D411yescharacteristic
1170Q8—22no—
1171Q8—22no—
1172Q8—22no—
1173Q8—22no—
1174Q8—48no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—162no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—84no—
1213D4—84no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
1218D4—162no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—48no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—84no—
1273C2×C4—162no—
1274C2×C4C2×#12712yes—
1275C2×C4C2×#12712yes—
1276C2×C4C2×#12712yes—
1277C2×C4C2×#12712yes—
1278C2×C4C2×#12712yes—
1279C2×C4C23×D411yescharacteristic
1280C2×C4C23×D411yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4#58511yescharacteristic
1284C2×C4#58511yescharacteristic
1285C8—22no—
1286C8—22no—
1287C8—22no—
1288C8—22no—
1289C8—22no—
1290C8—22no—
1291C8—22no—
1292C8—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—42no—
1297C22—42no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—82no—
1303C22—82no—
1304C22—82no—
1305C22—82no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—168no—
1319C22C22×#12711yescharacteristic
1320C22#348811yescharacteristic
1321C22#348811yescharacteristic
1322C22#358412yes—
1323C22#358612yes—
1324C4—22no—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4#348411yescharacteristic
1346C4#348711yescharacteristic
1347C4#348811yescharacteristic
1348C4#348811yescharacteristic
1349C2—42no—
1350C2—161no—
1351C2—161no—
1352C2—161no—
1353C2—161no—
1354C2#3556511yescharacteristic
1355C2#6064911yescharacteristic
1356C2#6065111yescharacteristic
1357C2#6201312yes—
1358C2#6203012yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3224C2
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×#3258C2semidirect
3. C2×#3127C2semidirect
4. C2×#3043C2semidirect
5. #37424C2semidirect
6. #35669C2semidirect
7. #28481C2semidirect
8. #28481C2semidirect
9. #28469C2semidirect
10. #28466C2semidirect
11. #28456C2semidirect
12. #28453C2semidirect
13. #28451C2semidirect
14. #28439C2semidirect
15. #28432C2semidirect
16. #28424C2semidirect
17. #28418C2semidirect
18. #28402C2semidirect
19. #28392C2semidirect
20. #28389C2semidirect
21. #28379C2semidirect
22. #28377C2semidirect
23. #28361C2semidirect
24. #28357C2semidirect
25. #28351C2semidirect
26. #28338C2semidirect
27. #25795C2semidirect
28. #25792C2semidirect
29. #25784C2semidirect
30. #25776C2semidirect
31. #20553C2semidirect
42. C2×#497C22semidirect
43. C2×#497C22semidirect
48. C2×#495C22semidirect
49. C2×#494C22semidirect
55. C2×#479C22semidirect
56. C2×#479C22semidirect
57. C2×#479C22semidirect
58. C2×#477C22semidirect
59. C2×#475C22semidirect
60. C2×#478C22semidirect
71. C2×#464C22semidirect
72. C2×#464C22semidirect
73. C2×#462C22semidirect
74. C2×#462C22semidirect
75. C2×#462C22semidirect
82. C2×#461C22semidirect
90. C2×#441C22semidirect
91. C2×#441C22semidirect
92. C2×C4×Q16C22semidirect
93. C2×C4×Q16C22semidirect
106. #2568C22semidirect
107. #2567C22semidirect
112. #2545C22semidirect
113. #2545C22semidirect
126. #2327C22semidirect
127. #2326C22semidirect
128. C4×C4⋊Q8C22semidirect
129. C4×#124C22semidirect
131. #2097C22semidirect
132. #2096C22semidirect
135. #2093C22semidirect
138. #2092C22semidirect
139. #2016C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
142. #2016C22semidirect
149. #2015C22semidirect
150. #2015C22semidirect
151. #2015C22semidirect
152. #2015C22semidirect
155. #2013C22semidirect
156. #2013C22semidirect
161. #2012C22semidirect
162. #2012C22semidirect
166. #1973C22semidirect
167. #1973C22semidirect
169. #1972C22semidirect
170. #1971C22semidirect
172. #1969C22semidirect
173. #1969C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1960C22semidirect
182. #1959C22semidirect
185. #1958C22semidirect
186. #1956C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. #1770C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
192. #1768C22semidirect
193. #1767C22semidirect
194. C4×C4⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
C2×#32582
C2×#32242
C2×#31272
C2×#30432
#374242
#356692
#284812
#284692
#284662
#284562
#284532
#284512
#284392
#284322
#284242
#284182
#284022
#283922
#283892
#283792
#283772
#283612
#283572
#283512
#283382
#257952
#257922
#257842
#257762
#205532