Finite Group Databasebeta

← #7986696

Subgroups — #7986696

Order 512.

5291 conjugacy classes of subgroups.

The subgroup lattice has 1181 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59419C212yesmaximal, complemented
3#59064C212yesmaximal, complemented
4#59049C212yesmaximal, complemented
5#48988C218yesmaximal, complemented
6#46050C214yesmaximal, complemented
7#45045C214yesmaximal, complemented
8#45026C214yesmaximal, complemented
9#42895C214yesmaximal, complemented
10#42759C214yesmaximal, complemented
11#39736C212yesmaximal, complemented
12#39174C212yesmaximal, complemented
13#39137C212yesmaximal, complemented
14#39009C214yesmaximal, complemented
15#38942C212yesmaximal, complemented
16#36595C211yesmaximal, characteristic, complemented
17#36583C212yesmaximal, complemented
18#36460C212yesmaximal, complemented
19#36128C211yesmaximal, characteristic, complemented
20#36128C211yesmaximal, characteristic, complemented
21#35191C212yesmaximal, complemented
22#35186C212yesmaximal, complemented
23#34945C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic, complemented
25#34393C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#559C2212yes—
28C2×#557C2212yes—
29C2×#556C2211yescharacteristic
30C2×#550C2212yes—
31C2×#550C2212yes—
32C2×#532C2212yes—
33C2×#532C2212yes—
34C2×#529C2212yes—
35#2867C2211yescharacteristic
36#2861C2214yes—
37#2860C2214yes—
38#2858C2212yes—
39#2858C2214yes—
40#2856C2212yes—
41#2856C2212yes—
42#2828C2218yes—
43#2797C2218yes—
44#2778C2218yes—
45#2761C2218yes—
46#2756C2218yes—
47#2749C2218yes—
48#2743C2218yes—
49#2726C2214yes—
50#2714C2218yes—
51#2714C2218yes—
52#2711C2218yes—
53#2711C2218yes—
54#2708C2218yes—
55#2705C2218yes—
56#2699C2218yes—
57#2699C2218yes—
58#2691C2218yes—
59#2682C2218yes—
60#2661C2218yes—
61#2651C2218yes—
62#2648C2218yes—
63#2641C2214yes—
64#2620C2214yes—
65#2603C2218yes—
66#2582C2212yes—
67#2573C2214yes—
68#2571C2211yescharacteristic
69#2568C2211yescharacteristic
70#2566C2214yes—
71#2559C2218yes—
72#2553C2214yes—
73#2552C2212yes—
74#2552C2211yescharacteristic
75#2548C2212yes—
76#2548C2214yes—
77#2548C2212yes—
78#2548C2212yes—
79#2548C2212yes—
80#2548C2212yes—
81#2548C2214yes—
82#2547C2214yes—
83#2547C2211yescharacteristic
84#2547C2211yescharacteristic
85#2546C2212yes—
86#2544C2214yes—
87#2543C2218yes—
88#2542C2211yescharacteristic
89#2541C2212yes—
90#2541C2212yes—
91#2541C2212yes—
92#2541C2212yes—
93#2540C2214yes—
94#2538C2211yescharacteristic
95#2537C2211yescharacteristic
96#2537C2214yes—
97#2526C2218yes—
98#2514C2212yes—
99#2512C2214yes—
100#2512C2214yes—
101#2510C2218yes—
102#2506C2214yes—
103#2500C2214yes—
104#2496C2212yes—
105#2494C2212yes—
106#2490C2218yes—
107#2490C2214yes—
108#2490C2214yes—
109#2490C2218yes—
110#2489C2212yes—
111#2468C2218yes—
112#2467C2218yes—
113#2454C2214yes—
114#2453C2214yes—
115#2448C2214yes—
116#2447C2214yes—
117#2447C2214yes—
118#2447C2212yes—
119#2446C2214yes—
120#2445C2214yes—
121#2445C2214yes—
122#2432C2214yes—
123#2432C2214yes—
124#2431C2214yes—
125#2431C2214yes—
126#2431C2214yes—
127#2431C2214yes—
128#2428C2214yes—
129#2428C2214yes—
130#2428C2214yes—
131#2428C2214yes—
132#2428C2214yes—
133#2428C2214yes—
134#2427C2214yes—
135#2427C2212yes—
136#2426C2214yes—
137#2426C2214yes—
138#2422C2212yes—
139#2421C2212yes—
140#2420C2214yes—
141#2420C2214yes—
142#2420C2214yes—
143#2419C2218yes—
144#2414C2214yes—
145#2414C2214yes—
146#2401C2214yes—
147#2395C2214yes—
148#2377C2218yes—
149#2373C2214yes—
150#2367C2212yes—
151#2366C2212yes—
152#2366C2212yes—
153#2366C2212yes—
154#2366C2212yes—
155#2366C2212yes—
156#2366C2212yes—
157#2365C2211yescharacteristic
158#2365C2212yes—
159#2363C2214yes—
160#2362C2212yes—
161#2357C2214yes—
162#2356C2212yes—
163#2355C2211yescharacteristic
164#2354C2211yescharacteristic
165Q8×C4⋊C4C2212yes—
166#2349C2214yes—
167#2347C2212yes—
168#2341C2214yes—
169#2341C2214yes—
170#2339C2214yes—
171#2339C2214yes—
172#2326C2214yes—
173#2326C2214yes—
174#2324C2214yes—
175#2324C2214yes—
176#2324C2214yes—
177#2319C2214yes—
178#2318C2218yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×#127C2212yes—
183C4×#126C2214yes—
184C4×#124C2212yes—
185C4×#124C2212yes—
186C4×#124C2214yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191#2295C2212yes—
192#2285C2212yes—
193#2283C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C22×#41C2314yes—
200C22×#41C2314yes—
201#559—48no—
202#557—48no—
203#556—28no—
204#550—48no—
205#550—48no—
206#532—216no—
207#532—48no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2312yes—
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#127C2314yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2314yes—
220C2×#127C2312yes—
221#529—48no—
222C2×#126C2314yes—
223C2×#126C2314yes—
224C2×#126C2318yes—
225C2×#125C2314yes—
226C2×#125C2312yes—
227C2×#125C2318yes—
228C2×#124C2314yes—
229C2×#124C2312yes—
230C2×#124C2312yes—
231C2×#124C2314yes—
232C2×#124C2312yes—
233C2×#124C2314yes—
234C2×#124C2314yes—
235C2×#124C2314yes—
236C2×#123C2314yes—
237C2×#123C2318yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2312yes—
251C2×#121C2312yes—
252C2×#121C2318yes—
253C2×#121C2318yes—
254C2×#121C2314yes—
255C2×#121C2314yes—
256C2×#121C2318yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2314yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2311yescharacteristic
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2314yes—
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2314yes—
284C2×#117C2312yes—
285C2×#117C2314yes—
286C2×#117C2312yes—
287C22×C42C2312yes—
288C22×C42C2312yes—
289#401C2314yes—
290#400C2314yes—
291#400C2314yes—
292#400C2318yes—
293#400C2314yes—
294#400C2314yes—
295#399C2314yes—
296#399C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2314yes—
304#397C2314yes—
305#397C2318yes—
306#397C2314yes—
307#397C2314yes—
308#397C2318yes—
309#397C2314yes—
310#397C2318yes—
311#397C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2314yes—
315#396C2318yes—
316#394C2314yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2314yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#392C2318yes—
334#392C2318yes—
335#392C2318yes—
336#392C2318yes—
337#392C2318yes—
338#392C2318yes—
339#392C2318yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2314yes—
348#391C2314yes—
349#391C2312yes—
350#391C2312yes—
351#391C2312yes—
352#390C2314yes—
353#390C2314yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2318yes—
358#390C2314yes—
359#390C2318yes—
360#390C2314yes—
361#390C2318yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2318yes—
367#390C2318yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2318yes—
373#390C2314yes—
374#390C2314yes—
375#390C2314yes—
376#390C2314yes—
377#390C2312yes—
378#390C2318yes—
379#390C2312yes—
380#390C2318yes—
381#390C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2314yes—
392#389C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2312yes—
397#389C2318yes—
398#389C2312yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#388C2314yes—
415#388C2314yes—
416#388C2318yes—
417#388C2318yes—
418#387C2314yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2318yes—
425#387C2314yes—
426#387C2318yes—
427#387C2314yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2314yes—
441#385C2318yes—
442#385C2318yes—
443#385C2314yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2314yes—
449#385C2314yes—
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2312yes—
454#384C2312yes—
455#384C2314yes—
456#383C2314yes—
457#383C2314yes—
458#382C2312yes—
459#382C2312yes—
460#382C2312yes—
461#382C2312yes—
462#382C2314yes—
463#381C2314yes—
464#381C2318yes—
465#381C2318yes—
466#381C2318yes—
467#380C2318yes—
468#380C2318yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476#380C2318yes—
477#380C2312yes—
478#380C2314yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521#376C2314yes—
522#376C2314yes—
523C2×#95C2318yes—
524C43C2314yes—
525C43C2312yes—
526C43C2311yescharacteristic
527C2×#41—216no—
528C2×#41—48no—
529C2×#41—48no—
530C2×#41—48no—
531C2×#41—48no—
532C2×#41—48no—
533C22×Q8C2411yescharacteristic
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×D4C2414yes—
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2414yes—
541C22×D4C2414yes—
542C22×D4C2414yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C22×D4C2418yes—
546C22×D4C2414yes—
547C22×D4C2418yes—
548C22×D4C2418yes—
549C22×D4C2418yes—
550C22×D4C2414yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2418yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2418yes—
559C23×C4C2418yes—
560C4⋊Q8—24no—
561C4⋊Q8—24no—
562C4⋊Q8—48no—
563C4⋊Q8#4118yescomplemented
564#127—28no—
565#127—28no—
566#127—28no—
567#127—44no—
568#127—44no—
569#127—44no—
570#127—48no—
571#127—48no—
572#127—82no—
573#126—216no—
574#126—48no—
575#126—88no—
576#125—44no—
577#125—48no—
578#125—416no—
579#124—216no—
580#124—28no—
581#124—44no—
582#124—48no—
583#124—44no—
584#124—48no—
585#124—48no—
586#124—48no—
587#123—48no—
588#123—416no—
589C22⋊Q8—28no—
590C22⋊Q8—44no—
591C22⋊Q8—44no—
592C22⋊Q8—44no—
593#121—216no—
594#121—216no—
595#121—416no—
596#121—416no—
597#121—48no—
598#121—44no—
599#121—48no—
600#121—44no—
601#121—48no—
602#121—48no—
603#121—48no—
604#121—48no—
605#121—88no—
606#121—84no—
607#121—84no—
608C4×Q8—28no—
609C4×Q8—24no—
610C4×Q8—28no—
611C4×Q8—28no—
612C4×Q8—28no—
613C4×Q8—24no—
614C4×Q8—44no—
615C4×Q8—42no—
616C4×Q8—48no—
617C4×Q8—48no—
618C4×D4—216no—
619C4×D4—216no—
620C4×D4—24no—
621C4×D4—24no—
622C4×D4—24no—
623C4×D4—24no—
624C4×D4—48no—
625C4×D4—42no—
626C4×D4—42no—
627C4×D4—48no—
628C4×D4—48no—
629C4×D4—48no—
630C4×D4—48no—
631C4×D4—48no—
632C4×D4—48no—
633C4×D4—48no—
634C4×D4—84no—
635#117—28no—
636#117—48no—
637#117—44no—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2418yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2418yes—
718C2×C42—28no—
719C2×C42—28no—
720C2×C42C2412yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2412yes—
733C2×C42C2411yescharacteristic
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2412yes—
737C2×C42C2414yes—
738C2×C42C2412yes—
739C2×C42C2418yes—
740C2×C42C2414yes—
741C2×C42C2412yes—
742C2×C42C2414yes—
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2412yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2412yes—
763#95C2414yes—
764#95C2412yes—
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2412yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2412yes—
774#95C2412yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2418yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2418yes—
785C24C2512yes—
786C24C2518yes—
787C24C2512yes—
788#41—832no—
789#41—832no—
790C2×Q8—22no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—22no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—24no—
798C2×Q8—22no—
799C2×Q8—24no—
800C2×Q8—24no—
801C2×Q8C2×#4118yes—
802C2×D4—28no—
803C2×D4—22no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—216no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—28no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—44no—
822C2×D4—44no—
823C2×D4—48no—
824C2×D4—48no—
825C2×D4—48no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—48no—
834C2×D4—48no—
835C2×D4—48no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D4—48no—
839C2×D4—48no—
840C2×D4—48no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—44no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—216no—
858C22×C4—24no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4C2511yescharacteristic
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2514yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2514yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2512yes—
885C22×C4C2512yes—
886C22×C4C2514yes—
887C22×C4C2511yescharacteristic
888C22×C4C2514yes—
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—22no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—28no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—22no—
914C4⋊C4—24no—
915C4⋊C4—24no—
916C4⋊C4—22no—
917C4⋊C4—22no—
918C4⋊C4—24no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—42no—
923C4⋊C4—44no—
924C4⋊C4—42no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—48no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4C2×#4118yes—
936C4⋊C4C2×#4118yes—
937C22⋊C4—28no—
938C22⋊C4—216no—
939C22⋊C4—216no—
940C22⋊C4—24no—
941C22⋊C4—28no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C42—24no—
975C42—24no—
976C42—24no—
977C42—28no—
978C42—24no—
979C42—24no—
980C42—24no—
981C42—24no—
982C42—28no—
983C42—24no—
984C42—28no—
985C42—28no—
986C42—24no—
987C42—22no—
988C42—22no—
989C42—22no—
990C42—24no—
991C42—44no—
992C42—42no—
993C42—42no—
994C42—44no—
995C42—48no—
996C42—44no—
997C42—41no—
998C42C2×#4114yes—
999C42H(5,𝔽2)14yes—
1000C42H(5,𝔽2)14yes—
1001C23—22no—
1002C23—28no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—28no—
1008C23—22no—
1009C23—28no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—28no—
1016C23—28no—
1017C23—28no—
1018C23—22no—
1019C23—28no—
1020C23—22no—
1021C23—22no—
1022C23C2611yescharacteristic
1023Q8—216no—
1024Q8—44no—
1025Q8—48no—
1026Q8—48no—
1027D4—44no—
1028D4—416no—
1029D4—416no—
1030D4—44no—
1031D4—416no—
1032D4—88no—
1033D4—88no—
1034D4—88no—
1035D4—816no—
1036D4—88no—
1037D4—816no—
1038D4—164no—
1039D4—168no—
1040D4—168no—
1041C2×C4—24no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—24no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—48no—
1098C2×C4—48no—
1099C2×C4—48no—
1100C2×C4—48no—
1101C2×C4—84no—
1102C2×C4—84no—
1103C2×C4—816no—
1104C2×C4—816no—
1105C2×C4—168no—
1106C2×C4C22×#4112yes—
1107C2×C4C22×#4118yes—
1108C2×C4C22×#4112yes—
1109C2×C4C22×#4112yes—
1110C2×C4C2×H(5,𝔽2)12yes—
1111C2×C4C2×H(5,𝔽2)12yes—
1112C2×C4C2×H(5,𝔽2)12yes—
1113C2×C4C2×H(5,𝔽2)12yes—
1114C2×C4C2×H(5,𝔽2)12yes—
1115C2×C4C2×H(5,𝔽2)12yes—
1116C2×C4#58512yes—
1117C2×C4#58512yes—
1118C2×C4#58512yes—
1119C22—42no—
1120C22—48no—
1121C22—42no—
1122C22—42no—
1123C22—48no—
1124C22—42no—
1125C22—42no—
1126C22—48no—
1127C22—42no—
1128C22—48no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—48no—
1134C22—42no—
1135C22—48no—
1136C22—42no—
1137C22—48no—
1138C22—42no—
1139C22—42no—
1140C22C23×#4111yescharacteristic
1141C22C22×H(5,𝔽2)11yescharacteristic
1142C22C22×H(5,𝔽2)11yescharacteristic
1143C22C2×#58511yescharacteristic
1144C22C2×#58511yescharacteristic
1145C22C2×#58511yescharacteristic
1146C22H(7,𝔽2)11yescharacteristic
1147C4—22no—
1148C4—28no—
1149C4—22no—
1150C4—22no—
1151C4—42no—
1152C4—44no—
1153C4—44no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—41no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—44no—
1165C4—44no—
1166C4—44no—
1167C4#351414yes—
1168C4#351714yes—
1169C4#354614yes—
1170C2—82no—
1171C2—88no—
1172C2—82no—
1173C2C2×#354611yescharacteristic
1174C2C2×#351411yescharacteristic
1175C2C2×#351711yescharacteristic
1176C2#6295511yescharacteristic
1177C2#6296111yescharacteristic
1178C2#6300611yescharacteristic
1179C2#6303611yescharacteristic
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. #59828C2semidirect
2. #59419C2semidirect
3. #59064C2semidirect
4. #59049C2semidirect
5. #48988C2semidirect
6. #46050C2semidirect
7. #45045C2semidirect
8. #45026C2semidirect
9. #42895C2semidirect
10. #42759C2semidirect
11. #39736C2semidirect
12. #39174C2semidirect
13. #39137C2semidirect
14. #39009C2semidirect
15. #38942C2semidirect
16. #36595C2semidirect
17. #36583C2semidirect
18. #36460C2semidirect
19. #36128C2semidirect
20. #36128C2semidirect
21. #35191C2semidirect
22. #35186C2semidirect
23. #34945C2semidirect
24. #34932C2semidirect
25. #34393C2semidirect
26. C4×#556C2semidirect
563. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598282
#594192
#590642
#590492
#489882
#460502
#450452
#450262
#428952
#427592
#397362
#391742
#391372
#390092
#389422
#365952
#365832
#364602
#361282
#351912
#351862
#349452
#349322
#343932
C4×#5562