Finite Group Databasebeta

← #8925462

Subgroups — #8925462

Order 512.

5798 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#56353C216yesmaximal, complemented
2#55105C216yesmaximal, complemented
3#53941C216yesmaximal, complemented
4#53396C216yesmaximal, complemented
5#47213C213yesmaximal, complemented
6#47031C213yesmaximal, complemented
7#46813C213yesmaximal, complemented
8#46452C213yesmaximal, complemented
9#46425C213yesmaximal, complemented
10#46354C213yesmaximal, complemented
11#37302C213yesmaximal, complemented
12#37300C213yesmaximal, complemented
13#37010C213yesmaximal, complemented
14#36818C213yesmaximal, complemented
15#36703C213yesmaximal, complemented
16#36702C213yesmaximal, complemented
17#35504C211yesmaximal, characteristic, complemented
18#35438C211yesmaximal, characteristic, complemented
19#35390C211yesmaximal, characteristic, complemented
20C2×#540C2213yescomplemented
21C2×#538C2213yescomplemented
22C2×#537C2213yescomplemented
23C2×#535C2213yescomplemented
24C2×#534C2213yes—
25C22×#120C2213yes—
26#2867C2211yescharacteristic, complemented
27#2861C2213yescomplemented
28#2856C2211yescharacteristic, complemented
29#2850C2213yescomplemented
30#2846C2211yescharacteristic
31#2846C2213yes—
32#2828C2216yescomplemented
33#2827C2216yescomplemented
34#2825C2216yescomplemented
35#2816C2213yescomplemented
36#2815C2213yescomplemented
37#2813C2216yescomplemented
38#2801C2212yescomplemented
39#2786C2216yescomplemented
40#2754C2216yescomplemented
41#2752C2216yescomplemented
42#2752C2216yescomplemented
43#2730C2216yescomplemented
44#2730C2216yescomplemented
45#2730C2216yescomplemented
46#2721C2216yescomplemented
47#2714C2216yescomplemented
48#2712C2216yescomplemented
49#2710C2216yescomplemented
50#2709C2216yescomplemented
51#2706C2216yescomplemented
52#2706C2216yescomplemented
53#2699C2216yescomplemented
54#2696C2216yescomplemented
55#2694C2216yescomplemented
56#2688C2216yescomplemented
57#2688C2216yescomplemented
58#2687C2216yescomplemented
59#2685C2216yescomplemented
60#2685C2216yescomplemented
61#2684C2216yescomplemented
62#2684C2216yescomplemented
63#2682C2216yescomplemented
64#2678C2216yescomplemented
65#2678C2216yescomplemented
66#2678C2216yescomplemented
67#2676C2216yescomplemented
68#2673C2216yescomplemented
69#2673C2216yescomplemented
70#2673C2216yescomplemented
71#2673C2216yescomplemented
72#2673C2216yescomplemented
73#2673C2216yescomplemented
74#2671C2216yescomplemented
75#2670C2216yescomplemented
76#2670C2216yescomplemented
77#2669C2216yescomplemented
78#2669C2216yescomplemented
79#2669C2216yescomplemented
80#2669C2216yescomplemented
81#2669C2216yescomplemented
82#2669C2216yescomplemented
83#2668C2216yescomplemented
84#2668C2216yescomplemented
85#2668C2216yescomplemented
86#2668C2216yescomplemented
87#2668C2216yescomplemented
88#2657C2213yescomplemented
89#2651C2216yescomplemented
90#2648C2216yescomplemented
91#2641C2213yescomplemented
92#2622C2213yescomplemented
93#2622C2213yescomplemented
94#2620C2213yescomplemented
95#2619C2213yescomplemented
96#2613C2216yescomplemented
97#2607C2213yescomplemented
98#2607C2213yescomplemented
99#2575C2216yescomplemented
100#2561C2213yes—
101#2560C2216yescomplemented
102#2557C2216yescomplemented
103#2557C2216yescomplemented
104#2557C2216yescomplemented
105#2544C2213yescomplemented
106#2544C2213yescomplemented
107#2541C2213yescomplemented
108#2541C2213yescomplemented
109#2539C2213yes—
110#2539C2213yes—
111#2539C2216yes—
112#2539C2213yes—
113#2539C2216yescomplemented
114#2534C2216yescomplemented
115#2527C2216yescomplemented
116#2526C2216yescomplemented
117#2504C2213yescomplemented
118#2501C2213yescomplemented
119#2500C2213yescomplemented
120#2499C2213yescomplemented
121#2482C2213yes—
122#2482C2213yescomplemented
123#2476C2216yescomplemented
124#2472C2216yescomplemented
125#2471C2216yescomplemented
126#2467C2216yescomplemented
127#2464C2216yescomplemented
128#2456C2216yescomplemented
129#2443C2216yescomplemented
130#2443C2216yescomplemented
131#2435C2213yescomplemented
132#2433C2216yes—
133#2433C2213yes—
134#2433C2213yes—
135#2433C2213yescomplemented
136#2431C2213yescomplemented
137#2431C2216yescomplemented
138#2431C2213yescomplemented
139#2431C2213yescomplemented
140#2431C2213yescomplemented
141#2422C2216yescomplemented
142#2418C2216yescomplemented
143#2410C2213yes—
144#2410C2213yes—
145#2410C2213yescomplemented
146#2410C2213yescomplemented
147#2408C2216yes—
148#2404C2213yes—
149#2404C2213yescomplemented
150#2404C2216yescomplemented
151#2333C2213yescomplemented
152#2333C2213yescomplemented
153#2333C2213yescomplemented
154#2332C2213yescomplemented
155#2312C2213yescomplemented
156#2308C2213yescomplemented
157#2298C2213yescomplemented
158#2297C2213yescomplemented
159#2273C2211yescharacteristic
160C26C2311yescharacteristic
161C22×#41C2313yes—
162C22×#41C2313yescomplemented
163C23×D4C2313yes—
164C23×D4C2313yes—
165C23×D4C2313yes—
166#540—412no—
167#538—412no—
168#537—412no—
169#535—412no—
170#534—412no—
171C2×#127C2313yes—
172C2×#127C2313yes—
173C2×#127C2311yescharacteristic
174C2×#127C2313yes—
175C2×#127C2311yescharacteristic
176C2×#127C2313yes—
177C2×#127C2313yes—
178C2×#127C2313yes—
179C2×#127C2313yescomplemented
180C2×#127C2313yescomplemented
181C2×#127C2311yescharacteristic, complemented
182C2×#126C2316yes—
183C2×#125C2313yescomplemented
184C2×#124C2313yes—
185C2×#124C2316yes—
186C2×#124C2313yes—
187C2×#124C2313yes—
188C2×#124C2313yes—
189C2×#124C2313yescomplemented
190C2×#124C2313yescomplemented
191C2×#123C2316yes—
192C2×#123C2316yes—
193C2×#123C2316yes—
194C2×#123C2316yes—
195C2×#123C2316yescomplemented
196C2×#123C2316yescomplemented
197C2×#123C2316yescomplemented
198C2×C22⋊Q8C2313yes—
199C2×C22⋊Q8C2316yescomplemented
200C2×C22⋊Q8C2313yescomplemented
201C2×#121C2313yes—
202C2×#121C2313yes—
203C2×#121C2313yes—
204C2×#121C2313yes—
205C2×#121C2313yes—
206C2×#121C2316yes—
207C2×#121C2316yes—
208C2×#121C2316yes—
209C2×#121C2316yes—
210C2×#121C2313yes—
211C2×#121C2313yes—
212C2×#121C2316yes—
213C2×#121C2316yes—
214C2×#121C2316yes—
215C2×#121C2316yes—
216C2×#121C2313yescomplemented
217C2×#121C2316yescomplemented
218C2×#121C2316yescomplemented
219C2×#120—412no—
220C2×#120C2316yes—
221C2×#120C2313yes—
222C2×#120C2313yes—
223C2×#120C2316yes—
224C2×#120C2316yes—
225C2×#120C2316yes—
226C2×#120C2316yes—
227C2×#120C2316yes—
228C2×#120C2313yes—
229C2×#120C2313yes—
230C2×#120C2316yes—
231C2×#120C2311yescharacteristic
232C2×#120C2313yes—
233C2×#120C2313yes—
234C2×#120C2313yes—
235C2×#120C2316yes—
236C2×#120C2316yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2313yescomplemented
239C2×C4×D4C2313yescomplemented
240C2×#117C2313yes—
241C2×#117C2313yescomplemented
242C22×C4⋊C4C2313yescomplemented
243C22×C22⋊C4C2313yes—
244C22×C22⋊C4C2313yes—
245C22×C22⋊C4C2313yes—
246C22×C22⋊C4C2313yes—
247C22×C22⋊C4C2313yes—
248C22×C42C2311yescharacteristic, complemented
249#401C2312yescomplemented
250#400C2316yescomplemented
251#400C2316yescomplemented
252#399C2312yes—
253#399C2316yes—
254#399C2316yes—
255#399C2316yes—
256#399C2316yes—
257#399C2316yescomplemented
258#399C2316yescomplemented
259#398C2316yescomplemented
260#398C2316yescomplemented
261#398C2316yescomplemented
262#397C2316yes—
263#397C2316yes—
264#397C2316yes—
265#397C2316yes—
266#397C2316yes—
267#397C2316yes—
268#397C2316yes—
269#397C2316yescomplemented
270#397C2316yescomplemented
271#397C2316yescomplemented
272#397C2316yescomplemented
273#397C2316yescomplemented
274#396C2316yes—
275#396C2316yes—
276#396C2316yescomplemented
277#396C2316yescomplemented
278#396C2312yescomplemented
279#394C2316yes—
280#394C2316yes—
281#394C2316yes—
282#394C2316yes—
283#394C2316yes—
284#394C2316yes—
285#394C2316yes—
286#394C2316yes—
287#394C2316yes—
288#394C2316yes—
289#394C2316yes—
290#394C2316yes—
291#394C2316yes—
292#394C2316yes—
293#394C2316yes—
294#394C2316yes—
295#394C2316yes—
296#394C2316yes—
297#394C2316yescomplemented
298#394C2316yescomplemented
299#394C2316yescomplemented
300#394C2316yescomplemented
301#394C2316yescomplemented
302#394C2316yescomplemented
303#393C2316yes—
304#393C2316yes—
305#393C2316yes—
306#393C2316yescomplemented
307#392C2316yes—
308#392C2316yes—
309#392C2316yes—
310#392C2316yes—
311#392C2316yes—
312#392C2316yes—
313#392C2316yes—
314#392C2316yes—
315#392C2316yes—
316#392C2316yes—
317#392C2316yes—
318#392C2316yes—
319#392C2316yes—
320#392C2316yes—
321#392C2316yes—
322#392C2316yes—
323#392C2316yes—
324#392C2316yes—
325#392C2316yes—
326#392C2316yescomplemented
327#392C2316yescomplemented
328#392C2316yescomplemented
329#392C2316yescomplemented
330#392C2316yescomplemented
331#391C2313yescomplemented
332#391C2316yescomplemented
333#391C2313yescomplemented
334#391C2313yescomplemented
335#391C2316yescomplemented
336#391C2313yescomplemented
337#390C2313yes—
338#390C2316yes—
339#390C2316yes—
340#390C2316yes—
341#390C2313yes—
342#390C2313yes—
343#390C2313yes—
344#390C2313yes—
345#390C2313yes—
346#390C2313yes—
347#390C2313yes—
348#390C2316yes—
349#390C2316yes—
350#390C2316yes—
351#390C2316yescomplemented
352#390C2313yescomplemented
353#390C2313yescomplemented
354#390C2313yescomplemented
355#390C2313yescomplemented
356#389C2316yescomplemented
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C2316yes—
361#388C2316yes—
362#388C2316yes—
363#388C2316yes—
364#388C2316yes—
365#388C2316yes—
366#388C2316yes—
367#388C2316yes—
368#388C2316yes—
369#388C2316yescomplemented
370#388C2316yescomplemented
371#388C2316yescomplemented
372#388C2316yescomplemented
373#388C2316yescomplemented
374#388C2316yescomplemented
375#388C2316yescomplemented
376#387C2316yescomplemented
377#387C2316yescomplemented
378#387C2316yescomplemented
379#387C2316yescomplemented
380#387C2316yescomplemented
381#387C2316yescomplemented
382#387C2316yescomplemented
383#387C2316yescomplemented
384#387C2316yescomplemented
385#386C2316yes—
386#386C2316yes—
387#386C2316yes—
388#386C2316yes—
389#386C2316yes—
390#386C2316yes—
391#386C2316yes—
392#386C2316yes—
393#386C2316yes—
394#386C2316yes—
395#386C2313yes—
396#386C2313yes—
397#386C2313yes—
398#386C2313yes—
399#386C2316yes—
400#386C2316yes—
401#386C2316yes—
402#386C2316yes—
403#386C2316yescomplemented
404#386C2316yescomplemented
405#386C2316yescomplemented
406#386C2316yescomplemented
407#386C2316yescomplemented
408#386C2316yescomplemented
409#386C2316yescomplemented
410#386C2316yescomplemented
411#386C2316yescomplemented
412#386C2316yescomplemented
413#386C2316yescomplemented
414#385C2313yes—
415#385C2313yes—
416#385C2313yes—
417#385C2313yes—
418#385C2316yescomplemented
419#385C2316yescomplemented
420#385C2316yescomplemented
421#384C2311yescharacteristic, complemented
422#384C2313yescomplemented
423#382C2313yescomplemented
424#382C2313yescomplemented
425#381C2313yes—
426#381C2316yes—
427#381C2313yes—
428#381C2316yescomplemented
429#380C2316yes—
430#380C2316yescomplemented
431#379C2313yes—
432#379C2313yes—
433#379C2313yes—
434#379C2316yes—
435#379C2311yescharacteristic
436#379C2313yes—
437#379C2313yes—
438#379C2316yes—
439#379C2316yes—
440C4×C4⋊C4C2313yescomplemented
441C4×C4⋊C4C2313yescomplemented
442C4×C22⋊C4C2313yes—
443C4×C22⋊C4C2313yes—
444C4×C22⋊C4C2316yes—
445C4×C22⋊C4C2313yes—
446C4×C22⋊C4C2313yes—
447C4×C22⋊C4C2316yescomplemented
448C4×C22⋊C4C2313yescomplemented
449C4×C22⋊C4C2316yescomplemented
450C4×C22⋊C4C2313yescomplemented
451#376C2313yescomplemented
452C43C2311yescharacteristic, complemented
453C25—46no—
454C25—81no—
455C25—83no—
456C25C2411yescharacteristic
457C25C2413yes—
458C25C2413yes—
459C25C2413yes—
460C2×#41—212no—
461C2×#41—46no—
462C2×#41—83no—
463C2×#41—83no—
464C2×#41—83no—
465C2×#41—83no—
466C22×Q8C2413yes—
467C22×Q8C2413yes—
468C22×D4—212no—
469C22×D4—46no—
470C22×D4—46no—
471C22×D4—412no—
472C22×D4—83no—
473C22×D4—83no—
474C22×D4—86no—
475C22×D4C2416yes—
476C22×D4C2413yes—
477C22×D4C2413yes—
478C22×D4C2413yes—
479C22×D4C2413yes—
480C22×D4C2416yes—
481C22×D4C2416yes—
482C22×D4C2413yes—
483C22×D4C2413yes—
484C22×D4C2413yes—
485C22×D4C2413yes—
486C22×D4C2413yes—
487C22×D4C2413yes—
488C22×D4C2413yes—
489C22×D4C2411yescharacteristic
490C22×D4C2413yes—
491C22×D4C2416yes—
492C22×D4C2413yes—
493C22×D4C2416yes—
494C22×D4C2416yes—
495C22×D4C2416yes—
496C22×D4C2413yes—
497C22×D4C2413yes—
498C22×D4C2413yes—
499C22×D4C2413yes—
500C22×D4C2416yes—
501C22×D4C2416yes—
502C23×C4C2413yes—
503C23×C4C2413yes—
504C23×C4C2413yes—
505C23×C4C2413yes—
506C23×C4C2416yes—
507C23×C4C2416yes—
508C23×C4C2416yes—
509C23×C4C2413yes—
510#127—46no—
511#127—46no—
512#127—46no—
513#127—81no—
514#127—83no—
515#127—83no—
516#127—83no—
517#127—81no—
518#127—83no—
519#127—81no—
520#127—83no—
521#126—412no—
522#125—46no—
523#124—46no—
524#124—46no—
525#124—412no—
526#124—83no—
527#124—83no—
528#124—83no—
529#124—83no—
530#123—412no—
531#123—412no—
532#123—412no—
533#123—412no—
534#123—412no—
535#123—86no—
536#123—86no—
537C22⋊Q8—212no—
538C22⋊Q8—412no—
539C22⋊Q8—46no—
540#121—212no—
541#121—212no—
542#121—212no—
543#121—412no—
544#121—412no—
545#121—412no—
546#121—412no—
547#121—412no—
548#121—412no—
549#121—46no—
550#121—46no—
551#121—46no—
552#121—46no—
553#121—46no—
554#121—412no—
555#121—86no—
556#121—86no—
557#121—86no—
558#120—412no—
559#120—412no—
560#120—412no—
561#120—412no—
562#120—412no—
563#120—412no—
564#120—46no—
565#120—46no—
566#120—46no—
567#120—46no—
568#120—412no—
569#120—81no—
570#120—83no—
571#120—83no—
572#120—83no—
573#120—86no—
574#120—86no—
575C4×D4—46no—
576C4×D4—46no—
577C4×D4—412no—
578#117—212no—
579#117—83no—
580C2×C4⋊C4—46no—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2413yes—
583C2×C4⋊C4C2413yes—
584C2×C4⋊C4C2413yes—
585C2×C4⋊C4C2413yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2416yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2416yes—
594C2×C4⋊C4C2416yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C2416yes—
598C2×C22⋊C4—212no—
599C2×C22⋊C4—212no—
600C2×C22⋊C4—46no—
601C2×C22⋊C4—83no—
602C2×C22⋊C4—83no—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2413yes—
608C2×C22⋊C4C2413yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2413yes—
616C2×C22⋊C4C2413yes—
617C2×C22⋊C4C2413yes—
618C2×C22⋊C4C2413yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2416yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2413yes—
629C2×C22⋊C4C2413yes—
630C2×C22⋊C4C2413yes—
631C2×C22⋊C4C2413yes—
632C2×C22⋊C4C2413yes—
633C2×C22⋊C4C2413yes—
634C2×C22⋊C4C2413yes—
635C2×C22⋊C4C2413yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C2416yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C2416yes—
646C2×C22⋊C4C2416yes—
647C2×C22⋊C4C2416yes—
648C2×C22⋊C4C2416yes—
649C2×C22⋊C4C2416yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C2416yes—
652C2×C42—81no—
653C2×C42C2413yes—
654C2×C42C2413yes—
655C2×C42C2413yes—
656C2×C42C2413yes—
657C2×C42C2416yes—
658C2×C42C2413yes—
659C2×C42C2413yes—
660C2×C42C2413yes—
661C2×C42C2411yescharacteristic
662C2×C42C2413yes—
663C2×C42C2411yescharacteristic
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2412yes—
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C2416yes—
676#95C2416yes—
677#95C2416yes—
678#95C2416yes—
679#95C2416yes—
680#95C2416yes—
681#95C2416yes—
682#95C2416yes—
683#95C2416yes—
684#95C2416yes—
685#95C2416yes—
686C24—26no—
687C24—26no—
688C24—26no—
689C24—26no—
690C24—43no—
691C24—43no—
692C24—46no—
693C24—43no—
694C24—43no—
695C24—46no—
696C24—46no—
697C24—41no—
698C24—43no—
699C24—43no—
700C24—43no—
701C24—46no—
702C24—46no—
703C24—46no—
704C24—88no—
705C24—824no—
706C24—824no—
707C24C2513yes—
708C24C2511yescharacteristic
709C24C2513yes—
710C24C2513yes—
711C24C2513yes—
712C24C2511yescharacteristic
713C24C2513yes—
714#41—824no—
715#41—824no—
716C2×Q8—26no—
717C2×Q8—26no—
718C2×Q8—43no—
719C2×Q8—43no—
720C2×Q8—43no—
721C2×Q8—43no—
722C2×D4—212no—
723C2×D4—26no—
724C2×D4—26no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—26no—
728C2×D4—26no—
729C2×D4—26no—
730C2×D4—26no—
731C2×D4—26no—
732C2×D4—26no—
733C2×D4—26no—
734C2×D4—26no—
735C2×D4—46no—
736C2×D4—46no—
737C2×D4—46no—
738C2×D4—46no—
739C2×D4—46no—
740C2×D4—46no—
741C2×D4—46no—
742C2×D4—46no—
743C2×D4—43no—
744C2×D4—43no—
745C2×D4—46no—
746C2×D4—43no—
747C2×D4—43no—
748C2×D4—46no—
749C2×D4—46no—
750C2×D4—46no—
751C2×D4—43no—
752C2×D4—43no—
753C2×D4—43no—
754C2×D4—43no—
755C2×D4—43no—
756C2×D4—43no—
757C2×D4—43no—
758C2×D4—43no—
759C2×D4—43no—
760C2×D4—43no—
761C2×D4—43no—
762C2×D4—43no—
763C2×D4—46no—
764C2×D4—46no—
765C2×D4—43no—
766C2×D4—43no—
767C2×D4—43no—
768C2×D4—43no—
769C2×D4—46no—
770C2×D4—46no—
771C2×D4—46no—
772C2×D4—46no—
773C2×D4—43no—
774C2×D4—43no—
775C2×D4—43no—
776C2×D4—43no—
777C2×D4—43no—
778C2×D4—43no—
779C2×D4—43no—
780C2×D4—43no—
781C2×D4—46no—
782C2×D4—46no—
783C2×D4—46no—
784C2×D4—46no—
785C2×D4—46no—
786C2×D4—46no—
787C2×D4—46no—
788C2×D4—46no—
789C2×D4—46no—
790C2×D4—46no—
791C2×D4—46no—
792C2×D4—46no—
793C2×D4—46no—
794C2×D4—824no—
795C2×D4—824no—
796C2×D4—824no—
797C22×C4—26no—
798C22×C4—26no—
799C22×C4—26no—
800C22×C4—26no—
801C22×C4—43no—
802C22×C4—43no—
803C22×C4—43no—
804C22×C4—43no—
805C22×C4—43no—
806C22×C4—43no—
807C22×C4—46no—
808C22×C4—46no—
809C22×C4—46no—
810C22×C4—46no—
811C22×C4—46no—
812C22×C4—46no—
813C22×C4—46no—
814C22×C4—46no—
815C22×C4—46no—
816C22×C4—46no—
817C22×C4—46no—
818C22×C4H(5,𝔽2)112yes—
819C22×C4C2513yes—
820C22×C4C2513yes—
821C22×C4C2516yes—
822C22×C4C2516yes—
823C22×C4C2513yes—
824C22×C4C2513yes—
825C22×C4C2511yescharacteristic
826C22×C4C2516yes—
827C22×C4C2513yes—
828C22×C4C2516yes—
829C22×C4C2513yes—
830C22×C4C2513yes—
831C4⋊C4—26no—
832C4⋊C4—26no—
833C4⋊C4—26no—
834C4⋊C4—26no—
835C4⋊C4—26no—
836C4⋊C4—26no—
837C4⋊C4—212no—
838C4⋊C4—46no—
839C4⋊C4—46no—
840C4⋊C4—46no—
841C4⋊C4—46no—
842C4⋊C4—46no—
843C4⋊C4—46no—
844C4⋊C4—46no—
845C4⋊C4—46no—
846C4⋊C4—46no—
847C4⋊C4—46no—
848C22⋊C4—26no—
849C22⋊C4—26no—
850C22⋊C4—212no—
851C22⋊C4—212no—
852C22⋊C4—212no—
853C22⋊C4—212no—
854C22⋊C4—212no—
855C22⋊C4—212no—
856C22⋊C4—212no—
857C22⋊C4—212no—
858C22⋊C4—46no—
859C22⋊C4—46no—
860C22⋊C4—43no—
861C22⋊C4—43no—
862C22⋊C4—43no—
863C22⋊C4—43no—
864C22⋊C4—46no—
865C22⋊C4—46no—
866C22⋊C4—46no—
867C22⋊C4—46no—
868C22⋊C4—46no—
869C22⋊C4—46no—
870C22⋊C4—46no—
871C22⋊C4—46no—
872C22⋊C4—43no—
873C22⋊C4—43no—
874C22⋊C4—43no—
875C22⋊C4—43no—
876C22⋊C4—43no—
877C22⋊C4—43no—
878C22⋊C4—43no—
879C22⋊C4—43no—
880C22⋊C4—46no—
881C22⋊C4—46no—
882C22⋊C4—46no—
883C22⋊C4—46no—
884C22⋊C4—46no—
885C22⋊C4—46no—
886C22⋊C4—46no—
887C22⋊C4—46no—
888C22⋊C4—46no—
889C22⋊C4—46no—
890C22⋊C4—46no—
891C22⋊C4—46no—
892C22⋊C4—46no—
893C22⋊C4—46no—
894C22⋊C4—46no—
895C22⋊C4—46no—
896C22⋊C4—46no—
897C42—26no—
898C42—26no—
899C42—43no—
900C42—41no—
901C42—43no—
902C42—43no—
903C42—46no—
904C42—43no—
905C42—43no—
906C42—41no—
907C42—43no—
908C23—28no—
909C23—26no—
910C23—23no—
911C23—23no—
912C23—26no—
913C23—26no—
914C23—26no—
915C23—26no—
916C23—26no—
917C23—23no—
918C23—23no—
919C23—23no—
920C23—23no—
921C23—23no—
922C23—23no—
923C23—23no—
924C23—23no—
925C23—26no—
926C23—23no—
927C23—23no—
928C23—23no—
929C23—26no—
930C23—26no—
931C23—26no—
932C23—21no—
933C23—23no—
934C23—23no—
935C23—23no—
936C23—23no—
937C23—21no—
938C23—23no—
939C23—412no—
940C23—412no—
941C23—412no—
942C23—86no—
943C23—86no—
944C23—86no—
945C23—86no—
946C23—86no—
947C23—86no—
948C23—86no—
949C23—86no—
950C23—812no—
951C23—812no—
952C23—812no—
953C23—812no—
954C23—864no—
955C23—166no—
956C23—166no—
957C23C2×H(5,𝔽2)16yes—
958C23C2611yescharacteristic
959Q8—86no—
960Q8—86no—
961D4—86no—
962D4—86no—
963D4—86no—
964D4—86no—
965D4—86no—
966D4—86no—
967D4—86no—
968D4—86no—
969D4—812no—
970D4—812no—
971D4—812no—
972D4—86no—
973D4—86no—
974D4—812no—
975D4—812no—
976D4—812no—
977D4—163no—
978D4—163no—
979D4—163no—
980D4—161no—
981D4—166no—
982D4—166no—
983D4—163no—
984D4—163no—
985D4—166no—
986D4—163no—
987D4—163no—
988C2×C4—23no—
989C2×C4—23no—
990C2×C4—23no—
991C2×C4—23no—
992C2×C4—23no—
993C2×C4—23no—
994C2×C4—23no—
995C2×C4—23no—
996C2×C4—26no—
997C2×C4—26no—
998C2×C4—26no—
999C2×C4—26no—
1000C2×C4—26no—
1001C2×C4—26no—
1002C2×C4—26no—
1003C2×C4—23no—
1004C2×C4—23no—
1005C2×C4—23no—
1006C2×C4—26no—
1007C2×C4—26no—
1008C2×C4—26no—
1009C2×C4—26no—
1010C2×C4—26no—
1011C2×C4—26no—
1012C2×C4—23no—
1013C2×C4—26no—
1014C2×C4—23no—
1015C2×C4—23no—
1016C2×C4—26no—
1017C2×C4—412no—
1018C2×C4—412no—
1019C2×C4—412no—
1020C2×C4—86no—
1021C2×C4—86no—
1022C2×C4—812no—
1023C2×C4—166no—
1024C2×C4—166no—
1025C2×C4C2×H(5,𝔽2)16yes—
1026C2×C4C2×H(5,𝔽2)16yes—
1027C22—26no—
1028C22—26no—
1029C22—26no—
1030C22—46no—
1031C22—46no—
1032C22—43no—
1033C22—43no—
1034C22—43no—
1035C22—41no—
1036C22—43no—
1037C22—41no—
1038C22—43no—
1039C22—43no—
1040C22—46no—
1041C22—43no—
1042C22—43no—
1043C22—43no—
1044C22—43no—
1045C22—46no—
1046C22—46no—
1047C22—46no—
1048C22—46no—
1049C22—43no—
1050C22—43no—
1051C22—46no—
1052C22—46no—
1053C22—43no—
1054C22—43no—
1055C22—43no—
1056C22—43no—
1057C22—46no—
1058C22—88no—
1059C22—824no—
1060C22—824no—
1061C22—1612no—
1062C22C22×H(5,𝔽2)13yes—
1063C22H(7,𝔽2)11yescharacteristic
1064C22H(7,𝔽2)13yes—
1065C4—26no—
1066C4—26no—
1067C4—46no—
1068C4—43no—
1069C4—41no—
1070C4—43no—
1071C4—43no—
1072C4—46no—
1073C4—46no—
1074C4—43no—
1075C4—46no—
1076C4—43no—
1077C2—46no—
1078C2—83no—
1079C2—81no—
1080C2—81no—
1081C2—83no—
1082C2—83no—
1083C2—83no—
1084C2#6283211yescharacteristic
1085C2#6286213yes—
1086C2#6287613yes—
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. #56353C2semidirect
2. #55105C2semidirect
3. #53941C2semidirect
4. #53396C2semidirect
5. #47213C2semidirect
6. #47031C2semidirect
7. #46813C2semidirect
8. #46452C2semidirect
9. #46425C2semidirect
10. #46354C2semidirect
11. #37302C2semidirect
12. #37300C2semidirect
13. #37010C2semidirect
14. #36818C2semidirect
15. #36703C2semidirect
16. #36702C2semidirect
17. #35504C2semidirect
18. #35438C2semidirect
19. #35390C2semidirect
20. C2×#540C22semidirect
21. C2×#538C22semidirect
22. C2×#537C22semidirect
23. C2×#535C22semidirect
26. #2867C22semidirect
27. #2861C22semidirect
28. #2856C22semidirect
29. #2850C22semidirect
32. #2828C22semidirect
33. #2827C22semidirect
34. #2825C22semidirect
35. #2816C22semidirect
36. #2815C22semidirect
37. #2813C22semidirect
38. #2801C22semidirect
39. #2786C22semidirect
40. #2754C22semidirect
41. #2752C22semidirect
42. #2752C22semidirect
43. #2730C22semidirect
44. #2730C22semidirect
45. #2730C22semidirect
46. #2721C22semidirect
47. #2714C22semidirect
48. #2712C22semidirect
49. #2710C22semidirect
50. #2709C22semidirect
51. #2706C22semidirect
52. #2706C22semidirect
53. #2699C22semidirect
54. #2696C22semidirect
55. #2694C22semidirect
56. #2688C22semidirect
57. #2688C22semidirect
58. #2687C22semidirect
59. #2685C22semidirect
60. #2685C22semidirect
61. #2684C22semidirect
62. #2684C22semidirect
63. #2682C22semidirect
64. #2678C22semidirect
65. #2678C22semidirect
66. #2678C22semidirect
67. #2676C22semidirect
68. #2673C22semidirect
69. #2673C22semidirect
70. #2673C22semidirect
71. #2673C22semidirect
72. #2673C22semidirect
73. #2673C22semidirect
74. #2671C22semidirect
75. #2670C22semidirect
76. #2670C22semidirect
77. #2669C22semidirect
78. #2669C22semidirect
79. #2669C22semidirect
80. #2669C22semidirect
81. #2669C22semidirect
82. #2669C22semidirect
83. #2668C22semidirect
84. #2668C22semidirect
85. #2668C22semidirect
86. #2668C22semidirect
87. #2668C22semidirect
88. #2657C22semidirect
89. #2651C22semidirect
90. #2648C22semidirect
91. #2641C22semidirect
92. #2622C22semidirect
93. #2622C22semidirect
94. #2620C22semidirect
95. #2619C22semidirect
96. #2613C22semidirect
97. #2607C22semidirect
98. #2607C22semidirect
99. #2575C22semidirect
101. #2560C22semidirect
102. #2557C22semidirect
103. #2557C22semidirect
104. #2557C22semidirect
105. #2544C22semidirect
106. #2544C22semidirect
107. #2541C22semidirect
108. #2541C22semidirect
113. #2539C22semidirect
114. #2534C22semidirect
115. #2527C22semidirect
116. #2526C22semidirect
117. #2504C22semidirect
118. #2501C22semidirect
119. #2500C22semidirect
120. #2499C22semidirect
122. #2482C22semidirect
123. #2476C22semidirect
124. #2472C22semidirect
125. #2471C22semidirect
126. #2467C22semidirect
127. #2464C22semidirect
128. #2456C22semidirect
129. #2443C22semidirect
130. #2443C22semidirect
131. #2435C22semidirect
135. #2433C22semidirect
136. #2431C22semidirect
137. #2431C22semidirect
138. #2431C22semidirect
139. #2431C22semidirect
140. #2431C22semidirect
141. #2422C22semidirect
142. #2418C22semidirect
145. #2410C22semidirect
146. #2410C22semidirect
149. #2404C22semidirect
150. #2404C22semidirect
151. #2333C22semidirect
152. #2333C22semidirect
153. #2333C22semidirect
154. #2332C22semidirect
155. #2312C22semidirect
156. #2308C22semidirect
157. #2298C22semidirect
158. #2297C22semidirect
162. C22×#41C23semidirect
179. C2×#127C23semidirect
180. C2×#127C23semidirect
181. C2×#127C23semidirect
183. C2×#125C23semidirect
189. C2×#124C23semidirect
190. C2×#124C23semidirect
195. C2×#123C23semidirect
196. C2×#123C23semidirect
197. C2×#123C23semidirect
199. C2×C22⋊Q8C23semidirect
200. C2×C22⋊Q8C23semidirect
216. C2×#121C23semidirect
217. C2×#121C23semidirect
218. C2×#121C23semidirect
238. C2×C4×D4C23semidirect
239. C2×C4×D4C23semidirect
241. C2×#117C23semidirect
242. C22×C4⋊C4C23semidirect
248. C22×C42C23semidirect
249. #401C23semidirect
250. #400C23semidirect
251. #400C23semidirect
257. #399C23semidirect
258. #399C23semidirect
259. #398C23semidirect
260. #398C23semidirect
261. #398C23semidirect
269. #397C23semidirect
270. #397C23semidirect
271. #397C23semidirect
272. #397C23semidirect
273. #397C23semidirect
276. #396C23semidirect
277. #396C23semidirect
278. #396C23semidirect
297. #394C23semidirect
298. #394C23semidirect
299. #394C23semidirect
300. #394C23semidirect
301. #394C23semidirect
302. #394C23semidirect
306. #393C23semidirect
326. #392C23semidirect
327. #392C23semidirect
328. #392C23semidirect
329. #392C23semidirect
330. #392C23semidirect
331. #391C23semidirect
332. #391C23semidirect
333. #391C23semidirect
334. #391C23semidirect
335. #391C23semidirect
336. #391C23semidirect
351. #390C23semidirect
352. #390C23semidirect
353. #390C23semidirect
354. #390C23semidirect
355. #390C23semidirect
356. #389C23semidirect
369. #388C23semidirect
370. #388C23semidirect
371. #388C23semidirect
372. #388C23semidirect
373. #388C23semidirect
374. #388C23semidirect
375. #388C23semidirect
376. #387C23semidirect
377. #387C23semidirect
378. #387C23semidirect
379. #387C23semidirect
380. #387C23semidirect
381. #387C23semidirect
382. #387C23semidirect
383. #387C23semidirect
384. #387C23semidirect
403. #386C23semidirect
404. #386C23semidirect
405. #386C23semidirect
406. #386C23semidirect
407. #386C23semidirect
408. #386C23semidirect
409. #386C23semidirect
410. #386C23semidirect
411. #386C23semidirect
412. #386C23semidirect
413. #386C23semidirect
418. #385C23semidirect
419. #385C23semidirect
420. #385C23semidirect
421. #384C23semidirect
422. #384C23semidirect
423. #382C23semidirect
424. #382C23semidirect
428. #381C23semidirect
430. #380C23semidirect
440. C4×C4⋊C4C23semidirect
441. C4×C4⋊C4C23semidirect
447. C4×C22⋊C4C23semidirect
448. C4×C22⋊C4C23semidirect
449. C4×C22⋊C4C23semidirect
450. C4×C22⋊C4C23semidirect
451. #376C23semidirect
452. C43C23semidirect

Maximal subgroups

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

subgroupindex
#563532
#551052
#539412
#533962
#472132
#470312
#468132
#464522
#464252
#463542
#373022
#373002
#370102
#368182
#367032
#367022
#355042
#354382
#353902