Finite Group Databasebeta

← #7642080

Subgroups — #7642080

Order 512.

6832 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3460C211yesmaximal, characteristic, complemented
2C22×#539C211yesmaximal, characteristic, complemented
3#37234C218yesmaximal, complemented
4#37121C218yesmaximal, complemented
5#36960C212yesmaximal, complemented
6#36959C211yesmaximal, characteristic, complemented
7#36958C211yesmaximal, characteristic, complemented
8#36956C212yesmaximal, complemented
9#36955C212yesmaximal, complemented
10#36746C218yesmaximal, complemented
11#36743C218yesmaximal, complemented
12#36709C212yesmaximal, complemented
13#36708C211yesmaximal, characteristic, complemented
14#36707C211yesmaximal, characteristic, complemented
15#36705C212yesmaximal, complemented
16#36704C212yesmaximal, complemented
17#35143C212yesmaximal, complemented
18#35138C212yesmaximal, complemented
19#35085C212yesmaximal, complemented
20#35064C212yesmaximal, complemented
21#35057C212yesmaximal, complemented
22#35031C212yesmaximal, complemented
23#34057C211yesmaximal, characteristic, complemented
24#3460—216no—
25C2×#544C2211yescharacteristic
26C2×#542C2214yescomplemented
27C2×#540C2214yescomplemented
28C2×#539—216no—
29C2×#539C2218yes—
30C2×#539C2218yes—
31C2×#538C2212yes—
32C2×#538C2212yes—
33C2×#537C2211yescharacteristic
34C2×#535C2212yes—
35C2×#532C2214yescomplemented
36C2×#529C2214yescomplemented
37C22×#126C2211yescharacteristic
38C22×#126C2211yescharacteristic
39C22×#125C2211yescharacteristic
40C22×#125C2211yescharacteristic
41C2×#525C2212yes—
42C2×#525C2212yes—
43C22×#123C2211yescharacteristic
44C22×#123C2211yescharacteristic
45C22×#123C2211yescharacteristic
46C22×#123C2211yescharacteristic
47C22×C22⋊Q8C2211yescharacteristic
48C22×C22⋊Q8C2211yescharacteristic
49C22×C22⋊Q8C2211yescharacteristic
50C22×#121C2211yescharacteristic
51C2×C4×#41C2212yes—
52C22×C4×D4C2211yescharacteristic
53C22×C4×D4C2211yescharacteristic
54C23×C4⋊C4C2211yescharacteristic
55#2857C2214yescomplemented
56#2855C2212yes—
57#2854C2212yes—
58#2854C2218yescomplemented
59#2852C2218yescomplemented
60#2851C2218yescomplemented
61#2850C2214yescomplemented
62#2849C2214yes—
63#2849C2214yes—
64#2848C2212yes—
65#2847C2212yes—
66#2722C2218yescomplemented
67#2720C2218yescomplemented
68#2719C2218yescomplemented
69#2718C2218yescomplemented
70#2717C2218yescomplemented
71#2715C2218yescomplemented
72#2713C2218yescomplemented
73#2711C2218yescomplemented
74#2710C2218yescomplemented
75#2709C2218yescomplemented
76#2708C2218yescomplemented
77#2708C2218yescomplemented
78#2706C2218yescomplemented
79#2703C2218yescomplemented
80#2695C2218yescomplemented
81#2695C2218yescomplemented
82#2693C2218yescomplemented
83#2692C2218yescomplemented
84#2691C2218yescomplemented
85#2690C2218yescomplemented
86#2689C2218yescomplemented
87#2688C2218yes—
88#2687C2218yescomplemented
89#2686C2218yes—
90#2677C2218yescomplemented
91#2676C2218yescomplemented
92#2674C2218yescomplemented
93#2673C2218yes—
94#2672C2218yescomplemented
95#2672C2218yescomplemented
96#2671C2218yes—
97#2671C2218yescomplemented
98#2663C2218yescomplemented
99#2663C2214yescomplemented
100#2661C2214yescomplemented
101#2637C2214yescomplemented
102#2636C2214yescomplemented
103#2634C2214yescomplemented
104#2633C2214yescomplemented
105#2627C2212yes—
106#2627C2212yes—
107#2622C2214yes—
108#2618C2212yes—
109#2618C2212yes—
110#2613C2214yes—
111#2611C2218yescomplemented
112#2604C2214yescomplemented
113#2603C2214yescomplemented
114#2602C2218yescomplemented
115#2602C2218yescomplemented
116#2601C2218yescomplemented
117#2600C2218yescomplemented
118#2591C2212yes—
119#2591C2214yescomplemented
120#2584C2214yescomplemented
121#2583C2212yes—
122#2583C2214yescomplemented
123#2579C2214yes—
124#2579C2218yescomplemented
125#2564C2218yescomplemented
126#2562C2214yescomplemented
127#2561C2212yes—
128#2539C2212yes—
129#2534C2214yes—
130#2503C2212yes—
131#2501C2212yes—
132#2499C2214yescomplemented
133#2498C2214yescomplemented
134#2487C2214yes—
135#2486C2214yes—
136#2485C2214yescomplemented
137#2484C2212yes—
138#2484C2212yes—
139#2484C2212yes—
140#2484C2214yescomplemented
141#2482C2212yes—
142#2436C2212yes—
143#2434C2212yes—
144#2432C2214yescomplemented
145#2430C2214yescomplemented
146#2415C2214yescomplemented
147#2414C2214yescomplemented
148#2413C2218yescomplemented
149#2412C2214yes—
150#2412C2214yes—
151#2412C2214yes—
152#2410C2214yes—
153#2407C2214yescomplemented
154#2406C2212yes—
155#2406C2212yes—
156#2406C2212yes—
157#2406C2214yescomplemented
158#2404C2212yes—
159#2322C2214yes—
160#2322C2214yes—
161#2322C2214yes—
162#2321C2214yes—
163#2318C2218yescomplemented
164#2315C2212yes—
165#2313C2211yescharacteristic
166#2313C2211yescharacteristic
167#2312C2212yes—
168#2308C2212yes—
169#2290C2218yescomplemented
170#2283C2212yes—
171#2280C2212yes—
172C2×C4×C22⋊C4C2212yes—
173C22×#41C2312yes—
174C22×#41C2312yes—
175C22×#41C2312yes—
176C23×Q8C2311yescharacteristic
177C23×D4C2311yescharacteristic
178C23×D4C2311yescharacteristic
179C23×D4C2311yescharacteristic
180C24×C4C2311yescharacteristic
181C24×C4C2311yescharacteristic
182C24×C4C2311yescharacteristic
183C24×C4C2311yescharacteristic
184C24×C4C2311yescharacteristic
185#544—28no—
186#542—232no—
187#540—232no—
188#539—264no—
189#539—264no—
190#538—216no—
191#538—216no—
192#537—28no—
193#535—216no—
194#532—232no—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2314yes—
197C2×#127C2314yes—
198#529—232no—
199C2×#126—28no—
200C2×#126—28no—
201C2×#126C2314yes—
202C2×#126C2314yes—
203C2×#126C2318yes—
204C2×#126C2314yes—
205C2×#126C2314yes—
206C2×#125—28no—
207C2×#125—28no—
208C2×#125C2314yes—
209C2×#125C2314yes—
210C2×#125C2318yes—
211C2×#125C2314yes—
212C2×#124C2314yes—
213C2×#124C2314yes—
214C2×#124C2314yes—
215C2×#124C2314yes—
216#525—216no—
217#525—216no—
218C2×#123—28no—
219C2×#123—28no—
220C2×#123—28no—
221C2×#123—28no—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×#123C2318yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×#123C2314yes—
230C2×#123C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×#123C2318yes—
235C2×C22⋊Q8—28no—
236C2×C22⋊Q8—28no—
237C2×C22⋊Q8—28no—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2318yes—
245C2×C22⋊Q8C2318yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×#121—28no—
249C2×#121C2312yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2312yes—
253C2×#121C2318yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2314yes—
258C2×#121C2314yes—
259C2×#121C2314yes—
260C2×#121C2318yes—
261C2×#120C2314yes—
262C2×#120C2314yes—
263C2×#120C2314yes—
264C4×#41—216no—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×D4—28no—
268C2×C4×D4D4116yescomplemented
269C2×C4×D4C2312yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×#117C2314yes—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2314yes—
284C22×C4⋊C4—28no—
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2314yes—
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2314yes—
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2314yes—
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2311yescharacteristic
312C22×C42C2314yes—
313C22×C42C2311yescharacteristic
314C22×C42C2314yes—
315C22×C42C2311yescharacteristic
316#400C2314yes—
317#400C2314yes—
318#400C2318yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2318yes—
324#399C2318yes—
325#399C2314yes—
326#399C2318yes—
327#399C2314yes—
328#398C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2318yes—
338#397C2314yes—
339#397C2318yes—
340#397C2318yes—
341#397C2318yes—
342#397C2314yes—
343#397C2318yes—
344#397C2318yes—
345#397C2318yes—
346#396C2318yes—
347#396C2318yes—
348#396C2318yes—
349#396C2318yes—
350#395C2318yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#395C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2318yes—
363#394C2318yes—
364#394C2318yes—
365#394C2318yes—
366#394C2318yes—
367#394C2318yes—
368#394C2318yes—
369#394C2314yes—
370#394C2318yes—
371#394C2318yes—
372#393C2314yes—
373#393C2318yes—
374#393C2314yes—
375#392C2318yes—
376#392C2318yes—
377#392C2318yes—
378#392C2314yes—
379#392C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2314yes—
384#390C2318yes—
385#390C2314yes—
386#390C2314yes—
387#390C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2318yes—
393#389C2318yes—
394#389C2314yes—
395#389C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2318yes—
424#386C2314yes—
425#386C2314yes—
426#386C2314yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2314yes—
440#385C2314yes—
441#385C2318yes—
442#385C2314yes—
443#385C2314yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#384C2314yes—
453#383C2314yes—
454#382C2314yes—
455#382C2314yes—
456#381C2314yes—
457#381C2312yes—
458#381C2312yes—
459#381C2314yes—
460#381C2314yes—
461#381C2314yes—
462#381C2318yes—
463#380C2318yes—
464#380C2318yes—
465#380C2318yes—
466#380C2318yes—
467#380C2314yes—
468#380C2312yes—
469#380C2312yes—
470#380C2314yes—
471#380C2314yes—
472#380C2314yes—
473#380C2318yes—
474#379C2314yes—
475#379C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483#376C2314yes—
484C2×#95C2314yes—
485C25C2411yescharacteristic
486C25C2411yescharacteristic
487C25C2411yescharacteristic
488C2×#41—28no—
489C2×#41—28no—
490C2×#41—28no—
491C2×#41—48no—
492C2×#41—84no—
493C2×#41—84no—
494C22×Q8—24no—
495C22×Q8—82no—
496C22×Q8C2412yes—
497C22×Q8C2414yes—
498C22×Q8C2412yes—
499C22×Q8C2412yes—
500C22×D4—24no—
501C22×D4—24no—
502C22×D4—44no—
503C22×D4—44no—
504C22×D4—82no—
505C22×D4C2×D418yes—
506C22×D4C2414yes—
507C22×D4C2414yes—
508C22×D4C2412yes—
509C22×D4C2414yes—
510C22×D4C2414yes—
511C22×D4C2414yes—
512C22×D4C2414yes—
513C22×D4C2412yes—
514C22×D4C2412yes—
515C22×D4C2414yes—
516C22×D4C2418yes—
517C22×D4C2414yes—
518C23×C4—24no—
519C23×C4—24no—
520C23×C4—24no—
521C23×C4—44no—
522C23×C4—82no—
523C23×C4—82no—
524C23×C4—82no—
525C23×C4—82no—
526C23×C4C2×D418yes—
527C23×C4C2×D418yes—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2414yes—
537C23×C4C2414yes—
538C23×C4C2414yes—
539C23×C4C2414yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2418yes—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C4⋊Q8—216no—
552C4⋊Q8—84no—
553#127—216no—
554#126—232no—
555#126—216no—
556#126—216no—
557#126—216no—
558#126—216no—
559#125—232no—
560#125—216no—
561#125—216no—
562#125—216no—
563#124—216no—
564#124—216no—
565#124—216no—
566#124—84no—
567#123—232no—
568#123—216no—
569#123—216no—
570#123—216no—
571#123—216no—
572#123—232no—
573#123—232no—
574#123—216no—
575#123—216no—
576#123—48no—
577#123—48no—
578#123—48no—
579#123—88no—
580C22⋊Q8—216no—
581C22⋊Q8—216no—
582C22⋊Q8—28no—
583C22⋊Q8—28no—
584C22⋊Q8—28no—
585C22⋊Q8—28no—
586C22⋊Q8—232no—
587C22⋊Q8—216no—
588C22⋊Q8—232no—
589C22⋊Q8—84no—
590#121—232no—
591#121—216no—
592#121—216no—
593#121—28no—
594#121—28no—
595#121—28no—
596#121—28no—
597#121—216no—
598#121—216no—
599#121—216no—
600#121—88no—
601#121—84no—
602#120—216no—
603#120—216no—
604#120—48no—
605C4×Q8—28no—
606C4×Q8—28no—
607C4×D4—216no—
608C4×D4—216no—
609C4×D4—216no—
610C4×D4—216no—
611C4×D4—216no—
612C4×D4—216no—
613C4×D4—28no—
614C4×D4—28no—
615C4×D4C2×D4132yes—
616C4×D4C2×D4132yes—
617#117—28no—
618#117—28no—
619#117—28no—
620#117—216no—
621#117—84no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—216no—
627C2×C4⋊C4—216no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4C2×D418yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C22⋊C4—24no—
676C2×C22⋊C4—24no—
677C2×C22⋊C4—24no—
678C2×C22⋊C4—24no—
679C2×C22⋊C4—24no—
680C2×C22⋊C4—24no—
681C2×C22⋊C4—24no—
682C2×C22⋊C4—24no—
683C2×C22⋊C4—48no—
684C2×C22⋊C4C2×D418yes—
685C2×C22⋊C4C2×D418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C42—24no—
722C2×C42—216no—
723C2×C42—84no—
724C2×C42C2×D418yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2414yes—
729C2×C42C2418yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758C24—24no—
759C24—24no—
760C24—22no—
761C24—24no—
762C24—42no—
763C24—42no—
764C24—42no—
765C24—42no—
766C24—42no—
767C24—42no—
768C24C22×D414yes—
769C24C22×D414yes—
770C24C2512yes—
771C24C2514yes—
772C24C2512yes—
773C24C2512yes—
774C24C2511yescharacteristic
775#41—432no—
776#41—816no—
777#41—816no—
778C2×Q8—24no—
779C2×Q8—28no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—88no—
788C2×D4—28no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—416no—
801C2×D4—48no—
802C2×D4—48no—
803C2×D4—44no—
804C2×D4—48no—
805C2×D4—44no—
806C2×D4—48no—
807C2×D4—48no—
808C2×D4—44no—
809C2×D4—48no—
810C2×D4—48no—
811C2×D4—48no—
812C2×D4—48no—
813C2×D4—48no—
814C2×D4—416no—
815C2×D4—88no—
816C2×D4C22×D4116yes—
817C22×C4—24no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—28no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—28no—
833C22×C4—28no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—48no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—416no—
858C22×C4—88no—
859C22×C4—88no—
860C22×C4—88no—
861C22×C4—88no—
862C22×C4C22×D414yes—
863C22×C4C22×D414yes—
864C22×C4C22×D414yes—
865C22×C4C22×D414yes—
866C22×C4C22×D414yes—
867C22×C4C22×D418yes—
868C22×C4C22×D418yes—
869C22×C4C22×D418yes—
870C22×C4C22×D418yes—
871C22×C4C2518yes—
872C22×C4C2518yes—
873C22×C4C2514yes—
874C22×C4C2512yes—
875C22×C4C2514yes—
876C22×C4C2512yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2512yes—
883C22×C4C2511yescharacteristic
884C22×C4C2512yes—
885C22×C4C2512yes—
886C22×C4C2512yes—
887C22×C4C2512yes—
888C22×C4C2511yescharacteristic
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—28no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—28no—
914C4⋊C4—28no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4C22×D4116yes—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4C22×D4116yes—
960C22⋊C4C22×D4116yes—
961C42—28no—
962C42—28no—
963C42—28no—
964C42—28no—
965C42—48no—
966C42—44no—
967C42—44no—
968C42C22×D418yes—
969C42C22×D418yes—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—28no—
979C23—28no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—28no—
986C23—24no—
987C23—22no—
988C23—28no—
989C23—22no—
990C23—44no—
991C23—44no—
992C23—44no—
993C23—44no—
994C23—416no—
995C23—44no—
996C23—44no—
997C23—44no—
998C23—88no—
999C23—88no—
1000C23C23×D414yes—
1001C23C23×D414yes—
1002C23C23×D412yes—
1003C23#58514yes—
1004C23C2611yescharacteristic
1005Q8—48no—
1006Q8—88no—
1007Q8—84no—
1008Q8—84no—
1009D4—416no—
1010D4—48no—
1011D4—416no—
1012D4—416no—
1013D4—84no—
1014D4—84no—
1015D4—88no—
1016D4—88no—
1017D4—88no—
1018D4—88no—
1019D4—88no—
1020D4—168no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—28no—
1039C2×C4—28no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—28no—
1046C2×C4—28no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—28no—
1054C2×C4—28no—
1055C2×C4—28no—
1056C2×C4—22no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—44no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—44no—
1065C2×C4—416no—
1066C2×C4—416no—
1067C2×C4—44no—
1068C2×C4—416no—
1069C2×C4—44no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—88no—
1076C2×C4—88no—
1077C2×C4—88no—
1078C2×C4—816no—
1079C2×C4C23×D412yes—
1080C2×C4C23×D414yes—
1081C2×C4C23×D414yes—
1082C2×C4C23×D414yes—
1083C2×C4C23×D412yes—
1084C2×C4C23×D414yes—
1085C22—22no—
1086C22—22no—
1087C22—28no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—416no—
1095C22—48no—
1096C22—48no—
1097C22—44no—
1098C22—42no—
1099C22—44no—
1100C22—42no—
1101C22—44no—
1102C22—48no—
1103C22—48no—
1104C22—44no—
1105C22—44no—
1106C22—42no—
1107C22—88no—
1108C22—88no—
1109C22#344914yes—
1110C22C24×D411yescharacteristic
1111C22C2×#58512yes—
1112C22H(7,𝔽2)12yes—
1113C222−1+612yes—
1114C4—22no—
1115C4—22no—
1116C4—24no—
1117C4—24no—
1118C4—24no—
1119C4—24no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—44no—
1124C4—42no—
1125C4—44no—
1126C4—48no—
1127C4—48no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—44no—
1132C2—24no—
1133C2—44no—
1134C2—44no—
1135C2—84no—
1136C2—82no—
1137C2C2×#344911yescharacteristic
1138C2#6284211yescharacteristic
1139C2#6285911yescharacteristic
1140C2#6286814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3460C2semidirect
2. C22×#539C2semidirect
3. #37234C2semidirect
4. #37121C2semidirect
5. #36960C2semidirect
6. #36959C2semidirect
7. #36958C2semidirect
8. #36956C2semidirect
9. #36955C2semidirect
10. #36746C2semidirect
11. #36743C2semidirect
12. #36709C2semidirect
13. #36708C2semidirect
14. #36707C2semidirect
15. #36705C2semidirect
16. #36704C2semidirect
17. #35143C2semidirect
18. #35138C2semidirect
19. #35085C2semidirect
20. #35064C2semidirect
21. #35057C2semidirect
22. #35031C2semidirect
23. #34057C2semidirect
26. C2×#542C22semidirect
27. C2×#540C22semidirect
35. C2×#532C22semidirect
36. C2×#529C22semidirect
55. #2857C22semidirect
58. #2854C22semidirect
59. #2852C22semidirect
60. #2851C22semidirect
61. #2850C22semidirect
66. #2722C22semidirect
67. #2720C22semidirect
68. #2719C22semidirect
69. #2718C22semidirect
70. #2717C22semidirect
71. #2715C22semidirect
72. #2713C22semidirect
73. #2711C22semidirect
74. #2710C22semidirect
75. #2709C22semidirect
76. #2708C22semidirect
77. #2708C22semidirect
78. #2706C22semidirect
79. #2703C22semidirect
80. #2695C22semidirect
81. #2695C22semidirect
82. #2693C22semidirect
83. #2692C22semidirect
84. #2691C22semidirect
85. #2690C22semidirect
86. #2689C22semidirect
88. #2687C22semidirect
90. #2677C22semidirect
91. #2676C22semidirect
92. #2674C22semidirect
94. #2672C22semidirect
95. #2672C22semidirect
97. #2671C22semidirect
98. #2663C22semidirect
99. #2663C22semidirect
100. #2661C22semidirect
101. #2637C22semidirect
102. #2636C22semidirect
103. #2634C22semidirect
104. #2633C22semidirect
111. #2611C22semidirect
112. #2604C22semidirect
113. #2603C22semidirect
114. #2602C22semidirect
115. #2602C22semidirect
116. #2601C22semidirect
117. #2600C22semidirect
119. #2591C22semidirect
120. #2584C22semidirect
122. #2583C22semidirect
124. #2579C22semidirect
125. #2564C22semidirect
126. #2562C22semidirect
132. #2499C22semidirect
133. #2498C22semidirect
136. #2485C22semidirect
140. #2484C22semidirect
144. #2432C22semidirect
145. #2430C22semidirect
146. #2415C22semidirect
147. #2414C22semidirect
148. #2413C22semidirect
153. #2407C22semidirect
157. #2406C22semidirect
163. #2318C22semidirect
169. #2290C22semidirect
268. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34602
C22×#5392
#372342
#371212
#369602
#369592
#369582
#369562
#369552
#367462
#367432
#367092
#367082
#367072
#367052
#367042
#351432
#351382
#350852
#350642
#350572
#350312
#340572