Finite Group Databasebeta

← #8105566

Subgroups — #8105566

Order 512.

5857 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58944C211yesmaximal, characteristic, complemented
2#58889C213yesmaximal, complemented
3#58802C213yesmaximal, complemented
4#58750C211yesmaximal, characteristic, complemented
5#58588C213yesmaximal, complemented
6#58267C213yesmaximal, complemented
7#56609C216yesmaximal, complemented
8#56317C213yesmaximal, complemented
9#53907C216yesmaximal, complemented
10#53422C213yesmaximal, complemented
11#52307C211yesmaximal, characteristic, complemented
12#52245C216yesmaximal, complemented
13#52129C216yesmaximal, complemented
14#52103C213yesmaximal, complemented
15#36696C213yesmaximal, complemented
16#34965C213yesmaximal, complemented
17#34871C213yesmaximal, complemented
18#34736C213yesmaximal, complemented
19#34562C213yesmaximal, complemented
20C23×#41C2211yescharacteristic
21C2×#529C2213yescomplemented
22C2×#525C2213yescomplemented
23C2×#525C2216yescomplemented
24C22×C4×D4C2213yescomplemented
25#2843C2213yescomplemented
26#2830C2216yescomplemented
27#2830C2213yescomplemented
28#2829C2216yescomplemented
29#2829C2216yescomplemented
30#2829C2216yescomplemented
31#2828C2216yescomplemented
32#2828C2213yescomplemented
33#2823C2213yescomplemented
34#2818C2216yescomplemented
35#2811C2211yescharacteristic, complemented
36#2785C2213yescomplemented
37#2785C2213yescomplemented
38#2779C2216yescomplemented
39#2779C2216yescomplemented
40#2768C2216yescomplemented
41#2768C2216yescomplemented
42#2764C2216yescomplemented
43#2761C2216yescomplemented
44#2761C2216yescomplemented
45#2756C2216yescomplemented
46#2756C2216yescomplemented
47#2752C2216yescomplemented
48#2735C2216yescomplemented
49#2733C2216yescomplemented
50#2733C2213yescomplemented
51#2715C2216yescomplemented
52#2715C2216yescomplemented
53#2707C2216yescomplemented
54#2706C2216yescomplemented
55#2705C2216yescomplemented
56#2704C2216yescomplemented
57#2703C2216yescomplemented
58#2702C2216yescomplemented
59#2701C2216yescomplemented
60#2700C2216yescomplemented
61#2699C2216yescomplemented
62#2698C2216yescomplemented
63#2697C2216yescomplemented
64#2687C2216yescomplemented
65#2685C2216yescomplemented
66#2685C2216yescomplemented
67#2685C2216yescomplemented
68#2683C2213yescomplemented
69#2682C2216yescomplemented
70#2681C2216yescomplemented
71#2681C2216yescomplemented
72#2680C2213yescomplemented
73#2680C2213yescomplemented
74#2679C2213yescomplemented
75#2678C2216yescomplemented
76#2678C2216yescomplemented
77#2678C2216yescomplemented
78#2672C2216yescomplemented
79#2670C2216yes—
80#2670C2216yescomplemented
81#2669C2216yescomplemented
82#2638C2213yescomplemented
83#2638C2213yescomplemented
84#2635C2213yes—
85#2635C2213yescomplemented
86#2630C2216yescomplemented
87#2630C2216yescomplemented
88#2627C2213yescomplemented
89#2626C2213yescomplemented
90#2622C2216yescomplemented
91#2618C2213yescomplemented
92#2617C2213yes—
93#2613C2216yescomplemented
94#2612C2213yescomplemented
95#2610C2216yescomplemented
96#2609C2213yescomplemented
97#2603C2216yescomplemented
98#2603C2216yescomplemented
99#2586C2213yescomplemented
100#2572C2213yescomplemented
101#2566C2213yescomplemented
102#2566C2213yescomplemented
103#2554C2216yescomplemented
104#2544C2213yes—
105#2544C2213yescomplemented
106#2532C2216yescomplemented
107#2526C2216yescomplemented
108#2504C2213yescomplemented
109#2502C2213yescomplemented
110#2479C2216yescomplemented
111#2471C2216yescomplemented
112#2435C2213yescomplemented
113#2433C2213yes—
114#2411C2216yescomplemented
115#2411C2216yescomplemented
116#2409C2213yescomplemented
117#2409C2213yescomplemented
118#2408C2213yes—
119#2408C2213yes—
120#2407C2216yescomplemented
121#2407C2216yescomplemented
122#2406C2213yes—
123#2406C2213yescomplemented
124#2405C2216yescomplemented
125#2404C2213yes—
126#2404C2213yescomplemented
127#2403C2216yescomplemented
128#2396C2216yescomplemented
129#2395C2213yescomplemented
130#2395C2213yescomplemented
131#2395C2216yescomplemented
132#2392C2216yescomplemented
133#2392C2216yescomplemented
134#2392C2216yescomplemented
135#2392C2216yescomplemented
136#2392C2216yescomplemented
137#2388C2211yescharacteristic
138#2388C2213yes—
139#2388C2213yes—
140#2388C2213yescomplemented
141#2388C2213yescomplemented
142#2388C2213yescomplemented
143C4×#127C2211yescharacteristic
144C4×#127C2213yescomplemented
145C4×#126C2212yescomplemented
146C4×#126C2216yescomplemented
147C4×#124C2213yescomplemented
148C4×#124C2216yescomplemented
149C4×#124C2213yescomplemented
150C4×#123C2216yescomplemented
151C4×#120C2216yescomplemented
152C4×#120C2216yescomplemented
153C4×#120C2216yescomplemented
154#2297C2216yescomplemented
155#2293C2216yescomplemented
156#2293C2216yescomplemented
157#2280C2213yescomplemented
158#2280C2213yescomplemented
159C4×#117C2213yescomplemented
160C22×#41—412no—
161C22×#41C2313yes—
162C22×#41C2311yescharacteristic
163C22×#41C2311yescharacteristic
164C22×#41C2313yes—
165C22×#41C2311yescharacteristic
166C23×Q8C2311yescharacteristic
167C23×D4C2313yes—
168C23×D4C2313yes—
169C24×C4C2313yes—
170C24×C4C2313yes—
171C2×#127C2311yescharacteristic
172C2×#127C2313yes—
173#529—412no—
174C2×#126C2316yes—
175C2×#126C2312yes—
176C2×#126C2316yes—
177C2×#125C2313yes—
178C2×#124C2313yes—
179C2×#124C2313yes—
180C2×#124C2316yes—
181C2×#124C2313yes—
182#525—412no—
183#525—424no—
184C2×#123C2316yes—
185C2×#123C2316yes—
186C2×#123C2316yes—
187C2×#123C2316yes—
188C2×#123C2316yes—
189C2×C22⋊Q8C2313yes—
190C2×C22⋊Q8C2313yes—
191C2×C22⋊Q8C2316yes—
192C2×C22⋊Q8C2316yes—
193C2×C22⋊Q8C2313yes—
194C2×#121C2313yes—
195C2×#121C2313yes—
196C2×#121C2316yes—
197C2×#121C2316yes—
198C2×#121C2313yes—
199C2×#120C2316yes—
200C2×#120C2316yes—
201C2×#120C2316yes—
202C2×#120C2316yes—
203C2×#120C2316yes—
204C2×#120C2316yes—
205C2×C4×Q8C2313yes—
206C2×C4×D4—412no—
207C2×C4×D4C2316yes—
208C2×C4×D4C2316yes—
209C2×C4×D4C2313yes—
210C2×C4×D4C2313yes—
211C2×C4×D4C2313yes—
212C2×C4×D4C2316yes—
213C2×C4×D4C2316yes—
214C2×C4×D4C2313yes—
215C2×C4×D4C2313yes—
216C2×C4×D4C2313yes—
217C2×C4×D4C2313yes—
218C2×C4×D4C2313yes—
219C2×C4×D4C2313yes—
220C2×C4×D4C2316yes—
221C2×#117C2316yes—
222C2×#117C2316yes—
223C2×#117C2313yes—
224C2×#117C2316yes—
225C22×C4⋊C4C2313yes—
226C22×C22⋊C4C2313yes—
227C22×C22⋊C4C2313yes—
228C22×C42C2313yes—
229#400C2313yes—
230#400C2316yes—
231#400C2313yes—
232#400C2316yes—
233#399C2313yes—
234#399C2316yes—
235#399C2313yes—
236#399C2316yes—
237#398C2313yes—
238#398C2316yes—
239#398C2316yes—
240#398C2316yes—
241#398C2316yes—
242#398C2316yes—
243#398C2316yes—
244#398C2313yes—
245#398C2316yes—
246#398C2316yes—
247#397C2316yes—
248#397C2316yes—
249#397C2316yes—
250#397C2313yes—
251#397C2316yes—
252#397C2316yes—
253#397C2316yes—
254#397C2316yes—
255#397C2316yes—
256#397C2313yes—
257#397C2316yes—
258#397C2316yes—
259#396C2316yes—
260#396C2316yes—
261#396C2316yes—
262#396C2316yes—
263#396C2316yes—
264#396C2316yes—
265#396C2316yes—
266#396C2316yes—
267#396C2316yes—
268#396C2316yes—
269#396C2316yes—
270#396C2316yes—
271#395C2313yes—
272#395C2313yes—
273#395C2316yes—
274#395C2313yes—
275#395C2311yescharacteristic
276#395C2313yes—
277#395C2313yes—
278#394C2316yes—
279#394C2316yes—
280#394C2316yes—
281#394C2316yes—
282#394C2316yes—
283#394C2316yes—
284#394C2316yes—
285#394C2313yes—
286#394C2313yes—
287#394C2316yes—
288#394C2316yes—
289#394C2316yes—
290#394C2316yes—
291#394C2316yes—
292#394C2316yes—
293#394C2313yes—
294#394C2316yes—
295#394C2316yes—
296#394C2316yes—
297#394C2316yes—
298#394C2313yes—
299#394C2313yes—
300#394C2316yes—
301#394C2316yes—
302#394C2316yes—
303#394C2316yes—
304#394C2313yes—
305#394C2316yes—
306#394C2316yes—
307#394C2316yes—
308#393C2316yes—
309#393C2313yes—
310#393C2313yes—
311#393C2311yescharacteristic
312#393C2313yes—
313#393C2313yes—
314#393C2313yes—
315#392C2313yes—
316#392C2316yes—
317#392C2316yes—
318#392C2316yes—
319#392C2316yes—
320#392C2316yes—
321#392C2313yes—
322#392C2316yes—
323#392C2316yes—
324#392C2313yes—
325#392C2316yes—
326#392C2313yes—
327#392C2316yes—
328#392C2313yes—
329#392C2313yes—
330#392C2316yes—
331#391C2313yes—
332#391C2316yes—
333#391C2316yes—
334#391C2316yes—
335#391C2313yes—
336#390C2313yes—
337#390C2313yes—
338#390C2313yes—
339#390C2316yes—
340#390C2313yes—
341#390C2316yes—
342#390C2313yes—
343#390C2313yes—
344#390C2316yes—
345#390C2316yes—
346#390C2316yes—
347#390C2316yes—
348#390C2316yes—
349#390C2316yes—
350#390C2316yes—
351#389C2316yes—
352#389C2316yes—
353#389C2316yes—
354#389C2316yes—
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#388C2316yes—
368#388C2316yes—
369#388C2316yes—
370#388C2316yes—
371#388C2316yes—
372#388C2316yes—
373#388C2316yes—
374#388C2316yes—
375#388C2316yes—
376#388C2316yes—
377#387C2316yes—
378#387C2316yes—
379#387C2316yes—
380#387C2316yes—
381#387C2316yes—
382#387C2316yes—
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#385C2316yes—
400#385C2316yes—
401#385C2316yes—
402#385C2316yes—
403#385C2316yes—
404#385C2316yes—
405#385C2316yes—
406#385C2316yes—
407#384C2311yescharacteristic
408#384C2313yes—
409#383C2316yes—
410#383C2312yes—
411#382C2313yes—
412#382C2313yes—
413#382C2316yes—
414#381C2316yes—
415#381C2313yes—
416#381C2313yes—
417#381C2313yes—
418#381C2313yes—
419#380C2313yes—
420#380C2313yes—
421#380C2316yes—
422#380C2316yes—
423#380C2313yes—
424#380C2313yes—
425#379C2316yes—
426#379C2316yes—
427#379C2316yes—
428#379C2316yes—
429#379C2316yes—
430C4×C4⋊C4C2316yes—
431C4×C4⋊C4C2316yes—
432C4×C4⋊C4C2316yes—
433C4×C4⋊C4C2313yes—
434C4×C4⋊C4C2313yes—
435C4×C22⋊C4C2313yes—
436C4×C22⋊C4C2316yes—
437C4×C22⋊C4C2316yes—
438C4×C22⋊C4C2316yes—
439C4×C22⋊C4C2313yes—
440C4×C22⋊C4C2313yes—
441C4×C22⋊C4C2313yes—
442C4×C22⋊C4C2316yes—
443C4×C22⋊C4C2316yes—
444C4×C22⋊C4C2313yes—
445C4×C22⋊C4C2316yes—
446C4×C22⋊C4C2316yes—
447C4×C22⋊C4C2313yes—
448#376C2316yes—
449C43C2313yes—
450C43C2312yes—
451C43C2311yescharacteristic
452C25C2413yes—
453C25C2413yes—
454C2×#41—224no—
455C2×#41—46no—
456C2×#41—46no—
457C2×#41—46no—
458C2×#41—46no—
459C2×#41—46no—
460C2×#41—412no—
461C2×#41—464no—
462C22×Q8—46no—
463C22×Q8C2413yes—
464C22×Q8C2413yes—
465C22×Q8C2411yescharacteristic
466C22×Q8C2411yescharacteristic
467C22×D4—46no—
468C22×D4—46no—
469C22×D4—46no—
470C22×D4—46no—
471C22×D4—412no—
472C22×D4C2413yes—
473C22×D4C2413yes—
474C22×D4C2416yes—
475C22×D4C2413yes—
476C22×D4C2413yes—
477C22×D4C2416yes—
478C22×D4C2416yes—
479C22×D4C2413yes—
480C22×D4C2413yes—
481C22×D4C2416yes—
482C22×D4C2416yes—
483C22×D4C2416yes—
484C22×D4C2413yes—
485C22×D4C2413yes—
486C23×C4—212no—
487C23×C4—212no—
488C23×C4—412no—
489C23×C4—412no—
490C23×C4C2413yes—
491C23×C4C2413yes—
492C23×C4C2411yescharacteristic
493C23×C4C2413yes—
494C23×C4C2413yes—
495C23×C4C2413yes—
496C23×C4C2413yes—
497C23×C4C2413yes—
498C23×C4C2413yes—
499C23×C4C2413yes—
500C23×C4C2413yes—
501C23×C4C2413yes—
502C23×C4C2413yes—
503#127—46no—
504#127—42no—
505#126—412no—
506#126—412no—
507#126—44no—
508#125—46no—
509#124—46no—
510#124—46no—
511#124—46no—
512#124—412no—
513#123—412no—
514#123—412no—
515#123—412no—
516#123—412no—
517#123—412no—
518C22⋊Q8—46no—
519C22⋊Q8—46no—
520C22⋊Q8—412no—
521C22⋊Q8—412no—
522C22⋊Q8—46no—
523#121—46no—
524#121—412no—
525#121—412no—
526#121—46no—
527#121—46no—
528#120—412no—
529#120—412no—
530#120—412no—
531#120—412no—
532#120—412no—
533#120—412no—
534C4×Q8—46no—
535C4×D4—224no—
536C4×D4—224no—
537C4×D4—46no—
538C4×D4—46no—
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—412no—
548C4×D4—46no—
549#117—46no—
550#117—412no—
551#117—412no—
552#117—412no—
553C2×C4⋊C4—46no—
554C2×C4⋊C4C2416yes—
555C2×C4⋊C4C2416yes—
556C2×C4⋊C4C2416yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2413yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2416yes—
568C2×C4⋊C4C2416yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2413yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2416yes—
577C2×C4⋊C4C2416yes—
578C2×C22⋊C4—46no—
579C2×C22⋊C4—46no—
580C2×C22⋊C4C2416yes—
581C2×C22⋊C4C2416yes—
582C2×C22⋊C4C2416yes—
583C2×C22⋊C4C2416yes—
584C2×C22⋊C4C2416yes—
585C2×C22⋊C4C2416yes—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2413yes—
589C2×C22⋊C4C2413yes—
590C2×C22⋊C4C2413yes—
591C2×C22⋊C4C2413yes—
592C2×C22⋊C4C2413yes—
593C2×C22⋊C4C2413yes—
594C2×C22⋊C4C2413yes—
595C2×C22⋊C4C2413yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C2416yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C2416yes—
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×C42—212no—
623C2×C42C2413yes—
624C2×C42C2413yes—
625C2×C42C2413yes—
626C2×C42C2413yes—
627C2×C42C2416yes—
628C2×C42C2416yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2416yes—
632C2×C42C2413yes—
633C2×C42C2416yes—
634C2×C42C2412yes—
635C2×C42C2411yescharacteristic
636#95C2416yes—
637#95C2416yes—
638#95C2416yes—
639#95C2416yes—
640#95C2413yes—
641#95C2413yes—
642#95C2413yes—
643#95C2416yes—
644#95C2413yes—
645#95C2416yes—
646#95C2413yes—
647#95C2416yes—
648#95C2416yes—
649#95C2413yes—
650#95C2413yes—
651#95C2413yes—
652#95C2416yes—
653#95C2416yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664C24—26no—
665C24—26no—
666C24—26no—
667C24—46no—
668C24—43no—
669C24—43no—
670C24—43no—
671C24—46no—
672C24—46no—
673C24—46no—
674C24C2513yes—
675C24C2513yes—
676C24C2513yes—
677C24C2513yes—
678C24C2511yescharacteristic
679#41—448no—
680#41—448no—
681#41—416no—
682#41—416no—
683#41—88no—
684C2×Q8—212no—
685C2×Q8—26no—
686C2×Q8—43no—
687C2×Q8—43no—
688C2×Q8—43no—
689C2×Q8—43no—
690C2×Q8—43no—
691C2×Q8—416no—
692C2×D4—212no—
693C2×D4—212no—
694C2×D4—26no—
695C2×D4—26no—
696C2×D4—212no—
697C2×D4—212no—
698C2×D4—212no—
699C2×D4—26no—
700C2×D4—26no—
701C2×D4—26no—
702C2×D4—43no—
703C2×D4—43no—
704C2×D4—43no—
705C2×D4—43no—
706C2×D4—43no—
707C2×D4—43no—
708C2×D4—43no—
709C2×D4—43no—
710C2×D4—46no—
711C2×D4—43no—
712C2×D4—43no—
713C2×D4—46no—
714C2×D4—46no—
715C2×D4—46no—
716C2×D4—46no—
717C2×D4—43no—
718C2×D4—46no—
719C2×D4—46no—
720C2×D4—46no—
721C2×D4—46no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—43no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—43no—
729C2×D4—46no—
730C2×D4—46no—
731C2×D4—448no—
732C2×D4—448no—
733C22×C4—212no—
734C22×C4—26no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—26no—
738C22×C4—212no—
739C22×C4—26no—
740C22×C4—212no—
741C22×C4—26no—
742C22×C4—26no—
743C22×C4—26no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—212no—
747C22×C4—26no—
748C22×C4—26no—
749C22×C4—26no—
750C22×C4—46no—
751C22×C4—46no—
752C22×C4—46no—
753C22×C4—46no—
754C22×C4—43no—
755C22×C4—46no—
756C22×C4—46no—
757C22×C4—46no—
758C22×C4—448no—
759C22×C4—824no—
760C22×C4H(5,𝔽2)112yes—
761C22×C4C2513yes—
762C22×C4C2511yescharacteristic
763C22×C4C2513yes—
764C22×C4C2516yes—
765C22×C4C2516yes—
766C22×C4C2513yes—
767C22×C4C2516yes—
768C22×C4C2516yes—
769C22×C4C2513yes—
770C22×C4C2513yes—
771C22×C4C2513yes—
772C22×C4C2513yes—
773C22×C4C2513yes—
774C22×C4C2511yescharacteristic
775C4⋊C4—212no—
776C4⋊C4—212no—
777C4⋊C4—212no—
778C4⋊C4—43no—
779C4⋊C4—43no—
780C4⋊C4—43no—
781C4⋊C4—43no—
782C4⋊C4—46no—
783C4⋊C4—46no—
784C4⋊C4—46no—
785C4⋊C4—43no—
786C4⋊C4—43no—
787C4⋊C4—46no—
788C4⋊C4—46no—
789C4⋊C4—46no—
790C4⋊C4—46no—
791C4⋊C4—46no—
792C4⋊C4—43no—
793C4⋊C4—43no—
794C4⋊C4—46no—
795C4⋊C4—46no—
796C4⋊C4—46no—
797C4⋊C4—46no—
798C4⋊C4—46no—
799C22⋊C4—212no—
800C22⋊C4—212no—
801C22⋊C4—212no—
802C22⋊C4—212no—
803C22⋊C4—212no—
804C22⋊C4—212no—
805C22⋊C4—212no—
806C22⋊C4—212no—
807C22⋊C4—43no—
808C22⋊C4—43no—
809C22⋊C4—43no—
810C22⋊C4—43no—
811C22⋊C4—43no—
812C22⋊C4—43no—
813C22⋊C4—43no—
814C22⋊C4—43no—
815C22⋊C4—46no—
816C22⋊C4—46no—
817C22⋊C4—46no—
818C22⋊C4—46no—
819C22⋊C4—46no—
820C22⋊C4—46no—
821C22⋊C4—46no—
822C22⋊C4—46no—
823C22⋊C4—46no—
824C22⋊C4—46no—
825C22⋊C4—46no—
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—
841C42—26no—
842C42—26no—
843C42—26no—
844C42—26no—
845C42—212no—
846C42—212no—
847C42—26no—
848C42—26no—
849C42—46no—
850C42—43no—
851C42—46no—
852C42—42no—
853C42—41no—
854C23—23no—
855C23—26no—
856C23—26no—
857C23—23no—
858C23—23no—
859C23—23no—
860C23—26no—
861C23—26no—
862C23—23no—
863C23—23no—
864C23—23no—
865C23—26no—
866C23—26no—
867C23—26no—
868C23—23no—
869C23—23no—
870C23—23no—
871C23—23no—
872C23—26no—
873C23—23no—
874C23—23no—
875C23—412no—
876C23—412no—
877C23—412no—
878C23—86no—
879C23—812no—
880C23—86no—
881C23—86no—
882C23—812no—
883C23—812no—
884C23—812no—
885C23C2×H(5,𝔽2)16yes—
886C23#58512yes—
887C23C2611yescharacteristic
888Q8—412no—
889Q8—44no—
890Q8—86no—
891Q8—82no—
892D4—412no—
893D4—424no—
894D4—412no—
895D4—412no—
896D4—412no—
897D4—412no—
898D4—412no—
899D4—86no—
900D4—812no—
901D4—812no—
902D4—812no—
903D4—812no—
904D4—812no—
905D4—86no—
906C2×C4—23no—
907C2×C4—26no—
908C2×C4—23no—
909C2×C4—224no—
910C2×C4—23no—
911C2×C4—23no—
912C2×C4—23no—
913C2×C4—26no—
914C2×C4—26no—
915C2×C4—26no—
916C2×C4—26no—
917C2×C4—26no—
918C2×C4—26no—
919C2×C4—23no—
920C2×C4—23no—
921C2×C4—23no—
922C2×C4—23no—
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—23no—
934C2×C4—26no—
935C2×C4—23no—
936C2×C4—412no—
937C2×C4—412no—
938C2×C4—412no—
939C2×C4—412no—
940C2×C4—412no—
941C2×C4—44no—
942C2×C4—412no—
943C2×C4—412no—
944C2×C4—412no—
945C2×C4—86no—
946C2×C4—86no—
947C2×C4—86no—
948C2×C4C2×H(5,𝔽2)16yes—
949C2×C4C2×H(5,𝔽2)16yes—
950C2×C4#58516yes—
951C22—26no—
952C22—26no—
953C22—26no—
954C22—26no—
955C22—46no—
956C22—46no—
957C22—43no—
958C22—41no—
959C22—43no—
960C22—43no—
961C22—43no—
962C22—46no—
963C22—46no—
964C22—46no—
965C22—46no—
966C22—43no—
967C22—46no—
968C22—46no—
969C22—43no—
970C22—43no—
971C22—43no—
972C22—43no—
973C22—43no—
974C22—824no—
975C22—824no—
976C22C22×H(5,𝔽2)13yes—
977C22C2×#58511yescharacteristic
978C22C2×#58513yes—
979C4—26no—
980C4—26no—
981C4—43no—
982C4—46no—
983C4—46no—
984C4—43no—
985C4—43no—
986C4—46no—
987C4—46no—
988C4—41no—
989C4—43no—
990C4—43no—
991C4—43no—
992C4#353214yes—
993C2—46no—
994C2—42no—
995C2—83no—
996C2—83no—
997C2—83no—
998C2C2×#353211yescharacteristic
999C2#6272913yes—
1000C2#6275913yes—
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. #58944C2semidirect
2. #58889C2semidirect
3. #58802C2semidirect
4. #58750C2semidirect
5. #58588C2semidirect
6. #58267C2semidirect
7. #56609C2semidirect
8. #56317C2semidirect
9. #53907C2semidirect
10. #53422C2semidirect
11. #52307C2semidirect
12. #52245C2semidirect
13. #52129C2semidirect
14. #52103C2semidirect
15. #36696C2semidirect
16. #34965C2semidirect
17. #34871C2semidirect
18. #34736C2semidirect
19. #34562C2semidirect
21. C2×#529C22semidirect
22. C2×#525C22semidirect
23. C2×#525C22semidirect
24. C22×C4×D4C22semidirect
25. #2843C22semidirect
26. #2830C22semidirect
27. #2830C22semidirect
28. #2829C22semidirect
29. #2829C22semidirect
30. #2829C22semidirect
31. #2828C22semidirect
32. #2828C22semidirect
33. #2823C22semidirect
34. #2818C22semidirect
35. #2811C22semidirect
36. #2785C22semidirect
37. #2785C22semidirect
38. #2779C22semidirect
39. #2779C22semidirect
40. #2768C22semidirect
41. #2768C22semidirect
42. #2764C22semidirect
43. #2761C22semidirect
44. #2761C22semidirect
45. #2756C22semidirect
46. #2756C22semidirect
47. #2752C22semidirect
48. #2735C22semidirect
49. #2733C22semidirect
50. #2733C22semidirect
51. #2715C22semidirect
52. #2715C22semidirect
53. #2707C22semidirect
54. #2706C22semidirect
55. #2705C22semidirect
56. #2704C22semidirect
57. #2703C22semidirect
58. #2702C22semidirect
59. #2701C22semidirect
60. #2700C22semidirect
61. #2699C22semidirect
62. #2698C22semidirect
63. #2697C22semidirect
64. #2687C22semidirect
65. #2685C22semidirect
66. #2685C22semidirect
67. #2685C22semidirect
68. #2683C22semidirect
69. #2682C22semidirect
70. #2681C22semidirect
71. #2681C22semidirect
72. #2680C22semidirect
73. #2680C22semidirect
74. #2679C22semidirect
75. #2678C22semidirect
76. #2678C22semidirect
77. #2678C22semidirect
78. #2672C22semidirect
80. #2670C22semidirect
81. #2669C22semidirect
82. #2638C22semidirect
83. #2638C22semidirect
85. #2635C22semidirect
86. #2630C22semidirect
87. #2630C22semidirect
88. #2627C22semidirect
89. #2626C22semidirect
90. #2622C22semidirect
91. #2618C22semidirect
93. #2613C22semidirect
94. #2612C22semidirect
95. #2610C22semidirect
96. #2609C22semidirect
97. #2603C22semidirect
98. #2603C22semidirect
99. #2586C22semidirect
100. #2572C22semidirect
101. #2566C22semidirect
102. #2566C22semidirect
103. #2554C22semidirect
105. #2544C22semidirect
106. #2532C22semidirect
107. #2526C22semidirect
108. #2504C22semidirect
109. #2502C22semidirect
110. #2479C22semidirect
111. #2471C22semidirect
112. #2435C22semidirect
114. #2411C22semidirect
115. #2411C22semidirect
116. #2409C22semidirect
117. #2409C22semidirect
120. #2407C22semidirect
121. #2407C22semidirect
123. #2406C22semidirect
124. #2405C22semidirect
126. #2404C22semidirect
127. #2403C22semidirect
128. #2396C22semidirect
129. #2395C22semidirect
130. #2395C22semidirect
131. #2395C22semidirect
132. #2392C22semidirect
133. #2392C22semidirect
134. #2392C22semidirect
135. #2392C22semidirect
136. #2392C22semidirect
140. #2388C22semidirect
141. #2388C22semidirect
142. #2388C22semidirect
144. C4×#127C22semidirect
145. C4×#126C22semidirect
146. C4×#126C22semidirect
147. C4×#124C22semidirect
148. C4×#124C22semidirect
149. C4×#124C22semidirect
150. C4×#123C22semidirect
151. C4×#120C22semidirect
152. C4×#120C22semidirect
153. C4×#120C22semidirect
154. #2297C22semidirect
155. #2293C22semidirect
156. #2293C22semidirect
157. #2280C22semidirect
158. #2280C22semidirect
159. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#589442
#588892
#588022
#587502
#585882
#582672
#566092
#563172
#539072
#534222
#523072
#522452
#521292
#521032
#366962
#349652
#348712
#347362
#345622