Finite Group Databasebeta

← #8429555

Subgroups — #8429555

Order 512.

4857 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59457C212yesmaximal, complemented
3#59411C212yesmaximal, complemented
4#59064C212yesmaximal, complemented
5#53787C218yesmaximal, complemented
6#53087C214yesmaximal, complemented
7#52995C214yesmaximal, complemented
8#52979C214yesmaximal, complemented
9#42605C214yesmaximal, complemented
10#42560C214yesmaximal, complemented
11#42536C214yesmaximal, complemented
12#39771C212yesmaximal, complemented
13#39746C212yesmaximal, complemented
14#39726C212yesmaximal, complemented
15#39202C212yesmaximal, complemented
16#39174C212yesmaximal, complemented
17#39147C212yesmaximal, complemented
18#37629C212yesmaximal, complemented
19#37625C212yesmaximal, complemented
20#37619C212yesmaximal, complemented
21#36595C211yesmaximal, characteristic, complemented
22#36595C211yesmaximal, characteristic, complemented
23#36128C211yesmaximal, characteristic
24#34951C211yesmaximal, characteristic, complemented
25#34945C211yesmaximal, characteristic, complemented
26#34929C211yesmaximal, characteristic, complemented
27C2×#559C2212yes—
28C2×#559C2212yes—
29C2×#557C2212yes—
30C2×#550C2212yes—
31C2×#533C2212yes—
32C2×#532C2212yes—
33#2867C2211yescharacteristic
34#2858C2212yes—
35#2858C2212yes—
36#2856C2212yes—
37#2830C2218yes—
38#2829C2218yes—
39#2829C2218yes—
40#2827C2218yes—
41#2826C2218yes—
42#2824C2218yes—
43#2816C2218yes—
44#2797C2218yes—
45#2796C2218yes—
46#2780C2218yes—
47#2757C2218yes—
48#2752C2218yes—
49#2751C2218yes—
50#2750C2218yes—
51#2746C2218yes—
52#2726C2214yes—
53#2711C2218yes—
54#2711C2218yes—
55#2708C2218yes—
56#2707C2218yes—
57#2701C2218yes—
58#2701C2218yes—
59#2696C2218yes—
60#2694C2218yes—
61#2694C2218yes—
62#2681C2218yes—
63#2658C2214yes—
64#2644C2214yes—
65#2644C2214yes—
66#2643C2218yes—
67#2641C2214yes—
68#2640C2214yes—
69#2640C2214yes—
70#2638C2218yes—
71#2633C2218yes—
72#2630C2218yes—
73#2624C2214yes—
74#2624C2214yes—
75#2620C2214yes—
76#2592C2214yes—
77#2585C2214yes—
78#2582C2212yes—
79#2582C2211yescharacteristic
80#2580C2214yes—
81#2580C2214yes—
82#2573C2214yes—
83#2571C2211yescharacteristic
84#2568C2211yescharacteristic
85#2568C2211yescharacteristic
86#2566C2214yes—
87#2566C2214yes—
88#2556C2214yes—
89#2552C2212yes—
90#2552C2211yescharacteristic
91#2551C2211yescharacteristic
92#2548C2214yes—
93#2548C2212yes—
94#2548C2212yes—
95#2548C2212yes—
96#2548C2212yes—
97#2548C2212yes—
98#2548C2212yes—
99#2548C2212yes—
100#2547C2211yescharacteristic
101#2547C2214yes—
102#2546C2211yescharacteristic
103#2546C2211yescharacteristic
104#2546C2212yes—
105#2545C2214yes—
106#2544C2214yes—
107#2544C2214yes—
108#2544C2214yes—
109#2542C2211yescharacteristic
110#2541C2212yes—
111#2541C2212yes—
112#2538C2211yescharacteristic
113#2538C2214yes—
114#2538C2211yescharacteristic
115#2514C2212yes—
116#2513C2214yes—
117#2511C2212yes—
118#2509C2212yes—
119#2506C2212yes—
120#2506C2214yes—
121#2494C2212yes—
122#2492C2212yes—
123#2490C2214yes—
124#2454C2214yes—
125#2454C2214yes—
126#2453C2214yes—
127#2453C2212yes—
128#2452C2212yes—
129#2452C2214yes—
130#2452C2214yes—
131#2450C2218yes—
132#2448C2214yes—
133#2448C2214yes—
134#2447C2212yes—
135#2447C2214yes—
136#2447C2214yes—
137#2447C2214yes—
138#2447C2214yes—
139#2446C2214yes—
140#2446C2212yes—
141#2445C2214yes—
142#2445C2214yes—
143#2445C2214yes—
144#2445C2214yes—
145#2445C2214yes—
146#2432C2214yes—
147#2432C2214yes—
148#2432C2214yes—
149#2431C2214yes—
150#2429C2212yes—
151#2428C2214yes—
152#2428C2214yes—
153#2427C2214yes—
154#2427C2214yes—
155#2426C2214yes—
156#2426C2214yes—
157#2425C2218yes—
158#2422C2214yes—
159#2422C2214yes—
160#2421C2212yes—
161#2420C2214yes—
162#2419C2218yes—
163#2402C2214yes—
164#2401C2214yes—
165#2396C2214yes—
166#2366C2212yes—
167#2366C2212yes—
168#2366C2212yes—
169#2366C2212yes—
170#2366C2212yes—
171#2366C2212yes—
172#2365C2212yes—
173Q8×C4⋊C4C2212yes—
174#2349C2214yes—
175#2349C2214yes—
176#2339C2214yes—
177#2326C2214yes—
178#2326C2214yes—
179#2324C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×#127C2212yes—
186C4×#127C2212yes—
187C4×#125C2212yes—
188C4×#124C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2295C2212yes—
194#2293C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C22×#41C2314yes—
200#559—48no—
201#559—48no—
202#557—48no—
203#550—48no—
204#533—48no—
205#532—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×#127C2312yes—
215C2×#127C2312yes—
216C2×#127C2312yes—
217C2×#127C2312yes—
218C2×#127C2312yes—
219C2×#127C2312yes—
220C2×#127C2314yes—
221C2×#127C2312yes—
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2318yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2314yes—
233C2×#124C2312yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2318yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#121C2318yes—
248C2×#121C2314yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×#117C2314yes—
276C22×C42C2312yes—
277#401C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2318yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#399C2318yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2314yes—
292#398C2314yes—
293#398C2318yes—
294#398C2314yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#397C2314yes—
302#397C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2314yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2314yes—
319#396C2318yes—
320#396C2318yes—
321#396C2314yes—
322#396C2318yes—
323#396C2314yes—
324#395C2314yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#393C2318yes—
343#393C2318yes—
344#393C2314yes—
345#393C2318yes—
346#392C2318yes—
347#392C2318yes—
348#391C2312yes—
349#391C2312yes—
350#391C2312yes—
351#391C2312yes—
352#391C2312yes—
353#391C2314yes—
354#391C2312yes—
355#391C2312yes—
356#391C2312yes—
357#391C2312yes—
358#391C2312yes—
359#391C2312yes—
360#391C2312yes—
361#391C2314yes—
362#391C2314yes—
363#391C2312yes—
364#391C2312yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2318yes—
375#390C2314yes—
376#390C2318yes—
377#390C2314yes—
378#390C2314yes—
379#390C2314yes—
380#390C2314yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2314yes—
385#390C2314yes—
386#390C2314yes—
387#390C2314yes—
388#390C2314yes—
389#390C2314yes—
390#390C2312yes—
391#390C2312yes—
392#390C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2314yes—
398#389C2314yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2314yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2312yes—
414#389C2318yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#389C2312yes—
419#389C2312yes—
420#389C2312yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2318yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2318yes—
442#387C2314yes—
443#386C2318yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#386C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2314yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2314yes—
465#384C2311yescharacteristic
466#384C2311yescharacteristic
467#384C2312yes—
468#384C2312yes—
469#384C2311yescharacteristic
470#384C2314yes—
471#383C2314yes—
472#382C2312yes—
473#382C2312yes—
474#382C2312yes—
475#382C2312yes—
476#381C2314yes—
477#381C2318yes—
478#381C2318yes—
479#380C2312yes—
480#380C2312yes—
481#380C2318yes—
482#380C2318yes—
483#380C2312yes—
484#380C2312yes—
485#380C2318yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2311yescharacteristic
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519#376C2314yes—
520#376C2314yes—
521C2×#95C2318yes—
522C43C2312yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C2×#41—48no—
526C2×#41—48no—
527C2×#41—48no—
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×D4C2414yes—
535C22×D4C2411yescharacteristic
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2414yes—
540C22×D4C2414yes—
541C22×D4C2418yes—
542C22×D4C2418yes—
543C22×D4C2414yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2418yes—
548C23×C4C2418yes—
549C23×C4C2418yes—
550C4⋊Q8—24no—
551C4⋊Q8—24no—
552C4⋊Q8—24no—
553C4⋊Q8—44no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557C4⋊Q8—48no—
558#127—28no—
559#127—28no—
560#127—28no—
561#127—44no—
562#127—44no—
563#127—44no—
564#127—48no—
565#127—82no—
566#125—44no—
567#125—48no—
568#125—48no—
569#125—416no—
570#124—44no—
571#124—48no—
572#124—48no—
573#124—48no—
574#124—48no—
575#124—48no—
576#124—48no—
577#124—48no—
578#123—416no—
579#123—416no—
580#123—88no—
581C22⋊Q8—48no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—44no—
585C22⋊Q8—44no—
586C22⋊Q8—88no—
587#121—416no—
588#121—48no—
589#121—48no—
590#121—48no—
591#121—48no—
592#121—84no—
593C4×Q8—24no—
594C4×Q8—28no—
595C4×Q8—28no—
596C4×Q8—28no—
597C4×Q8—24no—
598C4×Q8—24no—
599C4×Q8—24no—
600C4×Q8—48no—
601C4×Q8—42no—
602C4×Q8—42no—
603C4×Q8—48no—
604C4×Q8—48no—
605C4×D4—24no—
606C4×D4—24no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—42no—
610C4×D4—48no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—48no—
616C4×D4—48no—
617C4×D4—84no—
618C4×D4—84no—
619#117—48no—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C42—28no—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2418yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771C24C2512yes—
772C24C2518yes—
773#41—832no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×D4—22no—
793C2×D4—28no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—22no—
800C2×D4—28no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—22no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—48no—
810C2×D4—48no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—48no—
816C2×D4—48no—
817C2×D4—48no—
818C2×D4—48no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—44no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4C2511yescharacteristic
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—24no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—42no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—42no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—28no—
951C42—24no—
952C42—24no—
953C42—28no—
954C42—28no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—24no—
962C42—24no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—48no—
968C42—41no—
969C42H(5,𝔽2)14yes—
970C42H(5,𝔽2)14yes—
971C422−1+414yes—
972C23—22no—
973C23—28no—
974C23—22no—
975C23—28no—
976C23—22no—
977C23—28no—
978C23—22no—
979C23—28no—
980C23—22no—
981C23—22no—
982C23—28no—
983C23—28no—
984C23—22no—
985C23—28no—
986C23C2611yescharacteristic
987Q8—44no—
988Q8—48no—
989Q8—48no—
990Q8—44no—
991Q8—48no—
992Q8—88no—
993D4—416no—
994D4—416no—
995D4—44no—
996D4—416no—
997D4—88no—
998D4—88no—
999D4—88no—
1000D4—816no—
1001D4—164no—
1002D4—168no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—84no—
1066C2×C4—816no—
1067C2×C4—168no—
1068C2×C4—168no—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C2×C4C2×H(5,𝔽2)12yes—
1072C2×C4C2×H(5,𝔽2)12yes—
1073C2×C4C2×H(5,𝔽2)12yes—
1074C2×C4C2×H(5,𝔽2)12yes—
1075C2×C4C2×2−1+412yes—
1076C2×C4C2×2−1+412yes—
1077C2×C4C2×2−1+412yes—
1078C2×C4#58512yes—
1079C2×C4#58512yes—
1080C2×C4#58512yes—
1081C22—42no—
1082C22—42no—
1083C22—48no—
1084C22—48no—
1085C22—42no—
1086C22—48no—
1087C22—48no—
1088C22—42no—
1089C22—42no—
1090C22—48no—
1091C22—48no—
1092C22—42no—
1093C22—48no—
1094C22—42no—
1095C22C22×H(5,𝔽2)11yescharacteristic
1096C22C22×H(5,𝔽2)11yescharacteristic
1097C22C22×2−1+411yescharacteristic
1098C22C2×#58511yescharacteristic
1099C22C2×#58511yescharacteristic
1100C22C2×#58511yescharacteristic
1101C22H(7,𝔽2)11yescharacteristic
1102C4—22no—
1103C4—22no—
1104C4—22no—
1105C4—42no—
1106C4—44no—
1107C4—42no—
1108C4—42no—
1109C4—44no—
1110C4—42no—
1111C4—44no—
1112C4—42no—
1113C4—42no—
1114C4—41no—
1115C4—42no—
1116C4—42no—
1117C4—44no—
1118C4—42no—
1119C4—44no—
1120C4—42no—
1121C4—44no—
1122C4—42no—
1123C4#354614yes—
1124C4#355414yes—
1125C4#355414yes—
1126C2—82no—
1127C2—88no—
1128C2C2×#355411yescharacteristic
1129C2C2×#355411yescharacteristic
1130C2C2×#354611yescharacteristic
1131C2#6295511yescharacteristic
1132C2#6296111yescharacteristic
1133C2#6296211yescharacteristic
1134C2#6303611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36128C2
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. #59457C2semidirect
3. #59411C2semidirect
4. #59064C2semidirect
5. #53787C2semidirect
6. #53087C2semidirect
7. #52995C2semidirect
8. #52979C2semidirect
9. #42605C2semidirect
10. #42560C2semidirect
11. #42536C2semidirect
12. #39771C2semidirect
13. #39746C2semidirect
14. #39726C2semidirect
15. #39202C2semidirect
16. #39174C2semidirect
17. #39147C2semidirect
18. #37629C2semidirect
19. #37625C2semidirect
20. #37619C2semidirect
21. #36595C2semidirect
22. #36595C2semidirect
24. #34951C2semidirect
25. #34945C2semidirect
26. #34929C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#594572
#594112
#590642
#537872
#530872
#529952
#529792
#426052
#425602
#425362
#397712
#397462
#397262
#392022
#391742
#391472
#376292
#376252
#376192
#365952
#361282
#349512
#349452
#349292