Finite Group Databasebeta

← #7701477

Subgroups — #7701477

Order 512.

5885 conjugacy classes of subgroups.

The subgroup lattice has 1001 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52294C213yesmaximal, complemented
2#52164C216yesmaximal, complemented
3#52096C213yesmaximal, complemented
4#47621C213yesmaximal, complemented
5#47604C213yesmaximal, complemented
6#47603C216yesmaximal, complemented
7#47586C213yesmaximal, complemented
8#47569C216yesmaximal, complemented
9#47568C213yesmaximal, complemented
10#47563C211yesmaximal, characteristic, complemented
11#47026C213yesmaximal, complemented
12#46842C211yesmaximal, characteristic, complemented
13#46414C213yesmaximal, complemented
14#36675C211yesmaximal, characteristic, complemented
15#34977C213yesmaximal, complemented
16#34876C213yesmaximal, complemented
17#34874C216yesmaximal, complemented
18#34655C213yesmaximal, complemented
19C4×#535C213yesmaximal, complemented
20C2×#535C2213yes—
21C2×#532C2213yescomplemented
22C2×#529C2213yescomplemented
23C2×#525C2216yescomplemented
24C2×C4×#41C2213yescomplemented
25C22×C4×D4C2213yes—
26#2840C2211yescharacteristic
27#2835C2213yescomplemented
28#2824C2213yescomplemented
29#2824C2216yescomplemented
30#2812C2213yes—
31#2763C2213yescomplemented
32#2763C2216yescomplemented
33#2753C2216yescomplemented
34#2753C2216yescomplemented
35#2753C2216yescomplemented
36#2736C2213yescomplemented
37#2723C2216yescomplemented
38#2720C2216yescomplemented
39#2718C2216yescomplemented
40#2714C2216yescomplemented
41#2712C2213yes—
42#2712C2216yescomplemented
43#2711C2216yescomplemented
44#2710C2216yescomplemented
45#2706C2216yescomplemented
46#2703C2216yescomplemented
47#2696C2216yescomplemented
48#2692C2216yescomplemented
49#2685C2216yescomplemented
50#2678C2216yescomplemented
51#2677C2213yescomplemented
52#2676C2216yescomplemented
53#2676C2216yescomplemented
54#2675C2213yes—
55#2674C2216yescomplemented
56#2673C2216yes—
57#2673C2216yescomplemented
58#2672C2216yescomplemented
59#2671C2216yescomplemented
60#2670C2213yes—
61#2670C2213yes—
62#2670C2216yes—
63#2670C2216yescomplemented
64#2669C2216yescomplemented
65#2669C2216yescomplemented
66#2668C2213yescomplemented
67#2612C2216yescomplemented
68#2611C2213yescomplemented
69#2611C2213yescomplemented
70#2610C2216yes—
71#2610C2213yes—
72#2610C2213yes—
73#2610C2216yescomplemented
74#2610C2213yescomplemented
75#2610C2213yescomplemented
76#2610C2213yescomplemented
77#2610C2213yescomplemented
78#2609C2216yescomplemented
79#2604C2216yescomplemented
80#2603C2216yescomplemented
81#2593C2216yescomplemented
82#2574C2216yescomplemented
83#2574C2216yescomplemented
84#2567C2213yescomplemented
85#2564C2213yescomplemented
86#2564C2213yescomplemented
87#2563C2213yescomplemented
88#2555C2216yes—
89#2548C2213yescomplemented
90#2543C2213yes—
91#2543C2213yescomplemented
92#2541C2213yes—
93#2531C2216yescomplemented
94#2531C2216yescomplemented
95#2529C2216yescomplemented
96#2529C2216yescomplemented
97#2500C2216yescomplemented
98#2498C2216yescomplemented
99#2476C2216yescomplemented
100#2476C2216yescomplemented
101#2474C2216yescomplemented
102#2474C2216yescomplemented
103#2463C2213yes—
104#2456C2216yes—
105#2455C2213yes—
106#2449C2216yescomplemented
107#2443C2216yescomplemented
108#2437C2213yes—
109#2431C2216yescomplemented
110#2430C2216yescomplemented
111#2424C2216yescomplemented
112#2418C2216yescomplemented
113#2414C2216yescomplemented
114#2414C2216yescomplemented
115#2410C2216yes—
116#2403C2213yes—
117#2399C2213yescomplemented
118#2398C2216yescomplemented
119#2398C2213yescomplemented
120#2398C2213yescomplemented
121#2397C2213yes—
122#2397C2212yescomplemented
123#2392C2216yes—
124#2392C2216yescomplemented
125#2388C2213yes—
126#2388C2213yescomplemented
127#2388C2216yescomplemented
128#2388C2211yescharacteristic, complemented
129#2388C2213yescomplemented
130#2328C2216yescomplemented
131#2326C2216yescomplemented
132#2324C2216yescomplemented
133#2324C2216yescomplemented
134#2321C2213yes—
135#2321C2213yes—
136#2321C2213yescomplemented
137#2321C2213yescomplemented
138#2317C2213yescomplemented
139#2311C2213yescomplemented
140#2309C2213yes—
141C4×#127C2216yescomplemented
142C4×#124C2216yescomplemented
143C4×#124C2216yescomplemented
144C4×#124C2216yescomplemented
145C4×#121C2216yescomplemented
146C4×#121C2216yescomplemented
147C4×#121C2216yescomplemented
148C4×#121C2216yescomplemented
149C4×#120C2211yescharacteristic
150C4×#120C2213yes—
151C4×#120C2213yescomplemented
152C4×#120C2213yescomplemented
153C4×#120C2216yescomplemented
154#2298C2216yescomplemented
155#2290C2216yescomplemented
156#2290C2216yescomplemented
157C4×#117C2213yescomplemented
158C4×#117C2213yescomplemented
159C2×#376C2211yescharacteristic, complemented
160C22×#41C2313yes—
161C22×#41C2313yes—
162C22×#41C2311yescharacteristic
163C23×D4C2313yes—
164C24×C4C2311yescharacteristic
165C24×C4C2313yes—
166#535—224no—
167#532—412no—
168C2×C4⋊Q8C2313yes—
169C2×#127C2316yes—
170C2×#127C2313yes—
171#529—412no—
172C2×#126C2316yes—
173C2×#125C2313yes—
174C2×#124C2316yes—
175C2×#124C2313yes—
176C2×#124C2313yes—
177C2×#124C2316yes—
178C2×#124C2313yes—
179C2×#124C2316yes—
180#525—424no—
181C2×#123C2316yes—
182C2×#123C2316yes—
183C2×#123C2316yes—
184C2×C22⋊Q8C2313yes—
185C2×C22⋊Q8C2316yes—
186C2×C22⋊Q8C2316yes—
187C2×#121C2316yes—
188C2×#121C2316yes—
189C2×#121C2316yes—
190C2×#121C2316yes—
191C2×#121C2316yes—
192C2×#121C2316yes—
193C2×#121C2313yes—
194C2×#121C2316yes—
195C2×#121C2316yes—
196C2×#120C2313yes—
197C2×#120C2313yes—
198C2×#120C2313yes—
199C2×#120C2316yes—
200C2×#120C2316yes—
201C2×#120C2316yes—
202C2×#120C2311yescharacteristic
203C4×#41—412no—
204C2×C4×Q8C2313yes—
205C2×C4×Q8C2313yes—
206C2×C4×Q8C2313yes—
207C2×C4×D4—412no—
208C2×C4×D4C2316yes—
209C2×C4×D4C2316yes—
210C2×C4×D4C2313yes—
211C2×C4×D4C2313yes—
212C2×C4×D4C2316yes—
213C2×C4×D4C2316yes—
214C2×C4×D4C2316yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C2313yes—
217C2×C4×D4C2313yes—
218C2×C4×D4C2313yes—
219C2×C4×D4C2316yes—
220C2×C4×D4C2316yes—
221C2×C4×D4C2313yes—
222C2×C4×D4C2313yes—
223C2×C4×D4C2316yes—
224C2×#117C2313yes—
225C2×#117C2316yes—
226C2×#117C2313yes—
227C2×#117C2313yes—
228C2×#117C2313yes—
229C2×#117C2313yes—
230C2×#117C2316yes—
231C22×C4⋊C4C2313yes—
232C22×C22⋊C4C2313yes—
233C22×C22⋊C4C2313yes—
234C22×C42C2313yes—
235C22×C42C2313yes—
236C22×C42C2313yes—
237#400C2313yes—
238#400C2313yes—
239#400C2316yes—
240#400C2316yes—
241#400C2316yes—
242#399C2313yes—
243#399C2313yes—
244#399C2316yes—
245#399C2316yes—
246#399C2312yes—
247#398C2316yes—
248#398C2316yes—
249#398C2316yes—
250#398C2313yes—
251#398C2313yes—
252#397C2313yes—
253#397C2316yes—
254#397C2313yes—
255#397C2316yes—
256#397C2316yes—
257#397C2316yes—
258#397C2316yes—
259#396C2316yes—
260#396C2316yes—
261#396C2316yes—
262#396C2316yes—
263#395C2313yes—
264#395C2313yes—
265#395C2311yescharacteristic
266#395C2313yes—
267#395C2313yes—
268#395C2313yes—
269#395C2316yes—
270#395C2316yes—
271#394C2313yes—
272#394C2316yes—
273#394C2316yes—
274#394C2316yes—
275#394C2316yes—
276#394C2316yes—
277#394C2316yes—
278#394C2313yes—
279#394C2313yes—
280#394C2313yes—
281#394C2313yes—
282#394C2313yes—
283#394C2316yes—
284#394C2316yes—
285#394C2316yes—
286#394C2316yes—
287#394C2316yes—
288#394C2316yes—
289#394C2316yes—
290#394C2316yes—
291#394C2316yes—
292#393C2311yescharacteristic
293#393C2313yes—
294#393C2313yes—
295#393C2313yes—
296#393C2313yes—
297#393C2313yes—
298#393C2316yes—
299#393C2316yes—
300#393C2316yes—
301#393C2316yes—
302#392C2313yes—
303#392C2316yes—
304#392C2316yes—
305#392C2313yes—
306#392C2316yes—
307#392C2313yes—
308#392C2313yes—
309#392C2313yes—
310#392C2316yes—
311#392C2313yes—
312#392C2316yes—
313#392C2316yes—
314#392C2316yes—
315#392C2316yes—
316#392C2316yes—
317#392C2316yes—
318#392C2312yes—
319#391C2316yes—
320#391C2316yes—
321#391C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2316yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C2316yes—
334#390C2316yes—
335#389C2316yes—
336#389C2316yes—
337#389C2316yes—
338#389C2316yes—
339#388C2316yes—
340#388C2316yes—
341#388C2316yes—
342#388C2316yes—
343#388C2316yes—
344#388C2316yes—
345#388C2316yes—
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#388C2316yes—
351#388C2316yes—
352#388C2316yes—
353#388C2316yes—
354#388C2316yes—
355#388C2316yes—
356#388C2316yes—
357#388C2316yes—
358#388C2316yes—
359#388C2316yes—
360#388C2316yes—
361#388C2316yes—
362#388C2316yes—
363#388C2316yes—
364#388C2316yes—
365#388C2316yes—
366#388C2316yes—
367#387C2316yes—
368#387C2316yes—
369#387C2316yes—
370#387C2316yes—
371#387C2316yes—
372#387C2316yes—
373#387C2316yes—
374#387C2316yes—
375#386C2316yes—
376#386C2316yes—
377#386C2313yes—
378#386C2313yes—
379#386C2313yes—
380#386C2313yes—
381#386C2316yes—
382#386C2316yes—
383#386C2316yes—
384#386C2316yes—
385#386C2316yes—
386#386C2316yes—
387#386C2316yes—
388#386C2316yes—
389#386C2316yes—
390#386C2316yes—
391#386C2316yes—
392#386C2316yes—
393#386C2316yes—
394#386C2316yes—
395#386C2316yes—
396#386C2316yes—
397#385C2316yes—
398#385C2316yes—
399#385C2313yes—
400#385C2316yes—
401#385C2313yes—
402#385C2313yes—
403#385C2313yes—
404#385C2316yes—
405#385C2316yes—
406#385C2316yes—
407#385C2316yes—
408#385C2316yes—
409#385C2316yes—
410#385C2316yes—
411#384C2316yes—
412#382C2316yes—
413#382C2316yes—
414#382C2316yes—
415#380C2316yes—
416#380C2316yes—
417#380C2316yes—
418#380C2316yes—
419#379C2311yescharacteristic
420#379C2313yes—
421#379C2313yes—
422#379C2313yes—
423#379C2316yes—
424C4×C4⋊C4C2313yes—
425C4×C4⋊C4C2313yes—
426C4×C4⋊C4C2316yes—
427C4×C4⋊C4C2316yes—
428C4×C4⋊C4C2316yes—
429C4×C22⋊C4C2313yes—
430C4×C22⋊C4C2316yes—
431C4×C22⋊C4C2313yes—
432C4×C22⋊C4C2313yes—
433C4×C22⋊C4C2316yes—
434C4×C22⋊C4C2313yes—
435C4×C22⋊C4C2316yes—
436C4×C22⋊C4C2316yes—
437C4×C22⋊C4C2316yes—
438C4×C22⋊C4C2316yes—
439C4×C22⋊C4C2313yes—
440C4×C22⋊C4C2316yes—
441C4×C22⋊C4C2313yes—
442#376C2316yes—
443#376C2313yes—
444#376C2313yes—
445#376C2311yescharacteristic
446#376C2313yes—
447#376C2313yes—
448#376C2312yes—
449#376C2311yescharacteristic
450C2×#95C2311yescharacteristic
451C2×#95C2313yes—
452C43C2316yes—
453C25C2413yes—
454C25C2411yescharacteristic
455C2×#41—212no—
456C2×#41—46no—
457C2×#41—412no—
458C2×#41—46no—
459C2×#41—46no—
460C2×#41—46no—
461C22×Q8C2413yes—
462C22×Q8C2413yes—
463C22×Q8C2413yes—
464C22×Q8C2411yescharacteristic
465C22×D4—212no—
466C22×D4—46no—
467C22×D4—46no—
468C22×D4C2416yes—
469C22×D4C2416yes—
470C22×D4C2413yes—
471C22×D4C2413yes—
472C22×D4C2416yes—
473C22×D4C2416yes—
474C22×D4C2416yes—
475C22×D4C2416yes—
476C22×D4C2413yes—
477C22×D4C2416yes—
478C22×D4C2413yes—
479C22×D4C2416yes—
480C22×D4C2413yes—
481C22×D4C2413yes—
482C23×C4—46no—
483C23×C4—46no—
484C23×C4—412no—
485C23×C4C2413yes—
486C23×C4C2416yes—
487C23×C4C2411yescharacteristic
488C23×C4C2413yes—
489C23×C4C2413yes—
490C23×C4C2413yes—
491C23×C4C2413yes—
492C23×C4C2413yes—
493C23×C4C2413yes—
494C23×C4C2413yes—
495C23×C4C2413yes—
496C23×C4C2413yes—
497C23×C4C2416yes—
498C4⋊Q8—46no—
499#127—224no—
500#127—46no—
501#126—412no—
502#125—46no—
503#124—224no—
504#124—412no—
505#124—46no—
506#124—46no—
507#124—46no—
508#124—412no—
509#123—412no—
510#123—412no—
511#123—412no—
512C22⋊Q8—412no—
513C22⋊Q8—412no—
514C22⋊Q8—46no—
515#121—224no—
516#121—224no—
517#121—46no—
518#121—412no—
519#121—412no—
520#121—412no—
521#121—412no—
522#121—412no—
523#121—412no—
524#120—212no—
525#120—212no—
526#120—212no—
527#120—412no—
528#120—412no—
529#120—412no—
530#120#4118yescomplemented
531C4×Q8—46no—
532C4×Q8—46no—
533C4×Q8—46no—
534C4×D4—224no—
535C4×D4—224no—
536C4×D4—412no—
537C4×D4—412no—
538C4×D4—412no—
539C4×D4—46no—
540C4×D4—46no—
541C4×D4—46no—
542C4×D4—46no—
543C4×D4—46no—
544C4×D4—46no—
545C4×D4—412no—
546C4×D4—412no—
547C4×D4—46no—
548C4×D4—412no—
549C4×D4—412no—
550#117—212no—
551#117—224no—
552#117—46no—
553#117—46no—
554#117—46no—
555#117—46no—
556#117—412no—
557C2×C4⋊C4—46no—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C2413yes—
566C2×C4⋊C4C2413yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2413yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2413yes—
579C2×C4⋊C4C2416yes—
580C2×C22⋊C4—46no—
581C2×C22⋊C4—46no—
582C2×C22⋊C4C2416yes—
583C2×C22⋊C4C2416yes—
584C2×C22⋊C4C2413yes—
585C2×C22⋊C4C2416yes—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C2416yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2413yes—
598C2×C22⋊C4C2413yes—
599C2×C22⋊C4C2413yes—
600C2×C22⋊C4C2413yes—
601C2×C22⋊C4C2413yes—
602C2×C22⋊C4C2413yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2416yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2413yes—
623C2×C42—212no—
624C2×C42—212no—
625C2×C42—212no—
626C2×C42C2413yes—
627C2×C42C2413yes—
628C2×C42C2413yes—
629C2×C42C2416yes—
630C2×C42C2416yes—
631C2×C42C2413yes—
632C2×C42C2413yes—
633C2×C42C2413yes—
634C2×C42C2416yes—
635C2×C42C2413yes—
636C2×C42C2413yes—
637C2×C42C2413yes—
638C2×C42C2416yes—
639C2×C42C2416yes—
640C2×C42C2413yes—
641#95C2413yes—
642#95C2416yes—
643#95C2413yes—
644#95C2411yescharacteristic
645#95C2413yes—
646#95C2413yes—
647#95C2416yes—
648#95C2416yes—
649#95C2416yes—
650#95C2416yes—
651#95C2416yes—
652#95C2416yes—
653#95C2413yes—
654#95C2413yes—
655#95C2413yes—
656#95C2412yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C2416yes—
669#95C2416yes—
670C24—26no—
671C24—43no—
672C24—43no—
673C24—43no—
674C24—43no—
675C24—46no—
676C24—46no—
677C24C2×#4114yes—
678C24C2516yes—
679C24C2513yes—
680C24C2513yes—
681C24C2511yescharacteristic
682#41—448no—
683#41—824no—
684#41—88no—
685C2×Q8—26no—
686C2×Q8—26no—
687C2×Q8—43no—
688C2×Q8—43no—
689C2×Q8—46no—
690C2×Q8—43no—
691C2×Q8—43no—
692C2×Q8—46no—
693C2×D4—26no—
694C2×D4—212no—
695C2×D4—212no—
696C2×D4—26no—
697C2×D4—212no—
698C2×D4—212no—
699C2×D4—212no—
700C2×D4—212no—
701C2×D4—212no—
702C2×D4—212no—
703C2×D4—26no—
704C2×D4—46no—
705C2×D4—43no—
706C2×D4—43no—
707C2×D4—43no—
708C2×D4—46no—
709C2×D4—43no—
710C2×D4—43no—
711C2×D4—448no—
712C2×D4—46no—
713C2×D4—46no—
714C2×D4—46no—
715C2×D4—43no—
716C2×D4—46no—
717C2×D4—46no—
718C2×D4—46no—
719C2×D4—46no—
720C2×D4—46no—
721C2×D4—46no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—43no—
729C2×D4—43no—
730C2×D4—46no—
731C2×D4—46no—
732C2×D4C2×#41112yes—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—26no—
738C22×C4—26no—
739C22×C4—26no—
740C22×C4—26no—
741C22×C4—26no—
742C22×C4—26no—
743C22×C4—26no—
744C22×C4—212no—
745C22×C4—212no—
746C22×C4—212no—
747C22×C4—212no—
748C22×C4—212no—
749C22×C4—26no—
750C22×C4—26no—
751C22×C4—46no—
752C22×C4—43no—
753C22×C4—43no—
754C22×C4—43no—
755C22×C4—43no—
756C22×C4—46no—
757C22×C4—46no—
758C22×C4—46no—
759C22×C4—46no—
760C22×C4—46no—
761C22×C4—46no—
762C22×C4—46no—
763C22×C4—88no—
764C22×C4—824no—
765C22×C4C2513yes—
766C22×C4C2513yes—
767C22×C4C2516yes—
768C22×C4C2516yes—
769C22×C4C2513yes—
770C22×C4C2513yes—
771C22×C4C2513yes—
772C22×C4C2513yes—
773C22×C4C2516yes—
774C22×C4C2511yescharacteristic
775C22×C4C2513yes—
776C22×C4C2513yes—
777C22×C4C2513yes—
778C22×C4C2513yes—
779C22×C4C2511yescharacteristic
780C4⋊C4—212no—
781C4⋊C4—212no—
782C4⋊C4—212no—
783C4⋊C4—212no—
784C4⋊C4—212no—
785C4⋊C4—212no—
786C4⋊C4—46no—
787C4⋊C4—46no—
788C4⋊C4—46no—
789C4⋊C4—43no—
790C4⋊C4—43no—
791C4⋊C4—43no—
792C4⋊C4—43no—
793C4⋊C4—43no—
794C4⋊C4—43no—
795C4⋊C4—46no—
796C4⋊C4—46no—
797C4⋊C4—46no—
798C4⋊C4—43no—
799C4⋊C4—46no—
800C4⋊C4—43no—
801C4⋊C4—46no—
802C22⋊C4—26no—
803C22⋊C4—212no—
804C22⋊C4—212no—
805C22⋊C4—212no—
806C22⋊C4—212no—
807C22⋊C4—212no—
808C22⋊C4—212no—
809C22⋊C4—212no—
810C22⋊C4—212no—
811C22⋊C4—212no—
812C22⋊C4—212no—
813C22⋊C4—212no—
814C22⋊C4—212no—
815C22⋊C4—46no—
816C22⋊C4—46no—
817C22⋊C4—43no—
818C22⋊C4—43no—
819C22⋊C4—46no—
820C22⋊C4—43no—
821C22⋊C4—43no—
822C22⋊C4—43no—
823C22⋊C4—43no—
824C22⋊C4—43no—
825C22⋊C4—43no—
826C22⋊C4—46no—
827C22⋊C4—46no—
828C22⋊C4—46no—
829C22⋊C4—46no—
830C22⋊C4—46no—
831C22⋊C4—46no—
832C22⋊C4—46no—
833C22⋊C4—46no—
834C22⋊C4—46no—
835C22⋊C4—46no—
836C22⋊C4—46no—
837C22⋊C4—46no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—46no—
841C22⋊C4—46no—
842C22⋊C4C2×#41112yes—
843C42—212no—
844C42—26no—
845C42—26no—
846C42—26no—
847C42—26no—
848C42—26no—
849C42—26no—
850C42—26no—
851C42—26no—
852C42—26no—
853C42—212no—
854C42—212no—
855C42—46no—
856C42—46no—
857C42H(5,𝔽2)112yes—
858C23—26no—
859C23—23no—
860C23—23no—
861C23—23no—
862C23—26no—
863C23—23no—
864C23—26no—
865C23—23no—
866C23—26no—
867C23—26no—
868C23—26no—
869C23—26no—
870C23—23no—
871C23—26no—
872C23—26no—
873C23—26no—
874C23—23no—
875C23—26no—
876C23—412no—
877C23—412no—
878C23—812no—
879C23—82no—
880C23—86no—
881C23—86no—
882C23—86no—
883C23—812no—
884C23C22×#4116yes—
885C23C22×#4112yes—
886C23C2611yescharacteristic
887Q8—412no—
888Q8—86no—
889Q8—86no—
890Q8—82no—
891D4—412no—
892D4—424no—
893D4—424no—
894D4—412no—
895D4—412no—
896D4—812no—
897D4—812no—
898D4—812no—
899D4—812no—
900D4—86no—
901D4—812no—
902D4—812no—
903D4—86no—
904D4—86no—
905C2×C4—224no—
906C2×C4—23no—
907C2×C4—23no—
908C2×C4—23no—
909C2×C4—23no—
910C2×C4—23no—
911C2×C4—26no—
912C2×C4—23no—
913C2×C4—26no—
914C2×C4—23no—
915C2×C4—23no—
916C2×C4—23no—
917C2×C4—23no—
918C2×C4—23no—
919C2×C4—23no—
920C2×C4—23no—
921C2×C4—23no—
922C2×C4—26no—
923C2×C4—26no—
924C2×C4—26no—
925C2×C4—26no—
926C2×C4—26no—
927C2×C4—26no—
928C2×C4—26no—
929C2×C4—26no—
930C2×C4—26no—
931C2×C4—26no—
932C2×C4—26no—
933C2×C4—26no—
934C2×C4—26no—
935C2×C4—23no—
936C2×C4—412no—
937C2×C4—412no—
938C2×C4—412no—
939C2×C4—44no—
940C2×C4—412no—
941C2×C4—424no—
942C2×C4—412no—
943C2×C4—86no—
944C2×C4—86no—
945C2×C4—86no—
946C2×C4—812no—
947C2×C4—86no—
948C2×C4C22×#4116yes—
949C2×C4C2×H(5,𝔽2)16yes—
950C2×C4C2×H(5,𝔽2)16yes—
951C2×C4C2×H(5,𝔽2)16yes—
952C2×C4#58516yes—
953C22—26no—
954C22—26no—
955C22—212no—
956C22—43no—
957C22—41no—
958C22—43no—
959C22—43no—
960C22—46no—
961C22—46no—
962C22—43no—
963C22—43no—
964C22—46no—
965C22—46no—
966C22—46no—
967C22—46no—
968C22—43no—
969C22—46no—
970C22—46no—
971C22—46no—
972C22—46no—
973C22—88no—
974C22—824no—
975C22C23×#4111yescharacteristic
976C22C22×H(5,𝔽2)13yes—
977C22C2×#58513yes—
978C4—26no—
979C4—26no—
980C4—26no—
981C4—26no—
982C4—41no—
983C4—43no—
984C4—46no—
985C4—43no—
986C4—43no—
987C4—43no—
988C4—43no—
989C4—46no—
990C4—43no—
991C4—46no—
992C4#354914yes—
993C2—42no—
994C2—46no—
995C2—83no—
996C2—86no—
997C2C2×#354911yescharacteristic
998C2#6275913yes—
999C2#6277313yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52294C2semidirect
2. #52164C2semidirect
3. #52096C2semidirect
4. #47621C2semidirect
5. #47604C2semidirect
6. #47603C2semidirect
7. #47586C2semidirect
8. #47569C2semidirect
9. #47568C2semidirect
10. #47563C2semidirect
11. #47026C2semidirect
12. #46842C2semidirect
13. #46414C2semidirect
14. #36675C2semidirect
15. #34977C2semidirect
16. #34876C2semidirect
17. #34874C2semidirect
18. #34655C2semidirect
19. C4×#535C2semidirect
21. C2×#532C22semidirect
22. C2×#529C22semidirect
23. C2×#525C22semidirect
24. C2×C4×#41C22semidirect
27. #2835C22semidirect
28. #2824C22semidirect
29. #2824C22semidirect
31. #2763C22semidirect
32. #2763C22semidirect
33. #2753C22semidirect
34. #2753C22semidirect
35. #2753C22semidirect
36. #2736C22semidirect
37. #2723C22semidirect
38. #2720C22semidirect
39. #2718C22semidirect
40. #2714C22semidirect
42. #2712C22semidirect
43. #2711C22semidirect
44. #2710C22semidirect
45. #2706C22semidirect
46. #2703C22semidirect
47. #2696C22semidirect
48. #2692C22semidirect
49. #2685C22semidirect
50. #2678C22semidirect
51. #2677C22semidirect
52. #2676C22semidirect
53. #2676C22semidirect
55. #2674C22semidirect
57. #2673C22semidirect
58. #2672C22semidirect
59. #2671C22semidirect
63. #2670C22semidirect
64. #2669C22semidirect
65. #2669C22semidirect
66. #2668C22semidirect
67. #2612C22semidirect
68. #2611C22semidirect
69. #2611C22semidirect
73. #2610C22semidirect
74. #2610C22semidirect
75. #2610C22semidirect
76. #2610C22semidirect
77. #2610C22semidirect
78. #2609C22semidirect
79. #2604C22semidirect
80. #2603C22semidirect
81. #2593C22semidirect
82. #2574C22semidirect
83. #2574C22semidirect
84. #2567C22semidirect
85. #2564C22semidirect
86. #2564C22semidirect
87. #2563C22semidirect
89. #2548C22semidirect
91. #2543C22semidirect
93. #2531C22semidirect
94. #2531C22semidirect
95. #2529C22semidirect
96. #2529C22semidirect
97. #2500C22semidirect
98. #2498C22semidirect
99. #2476C22semidirect
100. #2476C22semidirect
101. #2474C22semidirect
102. #2474C22semidirect
106. #2449C22semidirect
107. #2443C22semidirect
109. #2431C22semidirect
110. #2430C22semidirect
111. #2424C22semidirect
112. #2418C22semidirect
113. #2414C22semidirect
114. #2414C22semidirect
117. #2399C22semidirect
118. #2398C22semidirect
119. #2398C22semidirect
120. #2398C22semidirect
122. #2397C22semidirect
124. #2392C22semidirect
126. #2388C22semidirect
127. #2388C22semidirect
128. #2388C22semidirect
129. #2388C22semidirect
130. #2328C22semidirect
131. #2326C22semidirect
132. #2324C22semidirect
133. #2324C22semidirect
136. #2321C22semidirect
137. #2321C22semidirect
138. #2317C22semidirect
139. #2311C22semidirect
141. C4×#127C22semidirect
142. C4×#124C22semidirect
143. C4×#124C22semidirect
144. C4×#124C22semidirect
145. C4×#121C22semidirect
146. C4×#121C22semidirect
147. C4×#121C22semidirect
148. C4×#121C22semidirect
151. C4×#120C22semidirect
152. C4×#120C22semidirect
153. C4×#120C22semidirect
154. #2298C22semidirect
155. #2290C22semidirect
156. #2290C22semidirect
157. C4×#117C22semidirect
158. C4×#117C22semidirect
159. C2×#376C22semidirect
530. #120#41semidirect

Maximal subgroups

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

subgroupindex
#522942
#521642
#520962
#476212
#476042
#476032
#475862
#475692
#475682
#475632
#470262
#468422
#464142
#366752
#349772
#348762
#348742
#346552
C4×#5352