Finite Group Databasebeta

← #8110561

Subgroups — #8110561

Order 512.

4624 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59924C211yesmaximal, characteristic, complemented
2#59871C211yesmaximal, characteristic, complemented
3#59864C211yesmaximal, characteristic, complemented
4#59863C211yesmaximal, characteristic, complemented
5#53366C214yesmaximal, complemented
6#53197C214yesmaximal, complemented
7#46343C214yesmaximal, complemented
8#46174C214yesmaximal, complemented
9#45633C214yesmaximal, complemented
10#39515C212yesmaximal, complemented
11#39514C212yesmaximal, complemented
12#39480C212yesmaximal, complemented
13#39479C212yesmaximal, complemented
14#39370C212yesmaximal, complemented
15#39369C212yesmaximal, complemented
16#39351C212yesmaximal
17#39350C212yesmaximal, complemented
18#39181C212yesmaximal, complemented
19#39158C212yesmaximal, complemented
20#38985C212yesmaximal, complemented
21#38932C212yesmaximal, complemented
22#37337C214yesmaximal, complemented
23#37281C214yesmaximal, complemented
24#37275C214yesmaximal, complemented
25#36645C211yesmaximal, characteristic, complemented
26#36635C211yesmaximal, characteristic, complemented
27#36631C211yesmaximal, characteristic
28C2×#544C2214yes—
29C2×#542C2214yes—
30C2×#533C2212yes—
31C2×#529C2212yes—
32#2868C2211yescharacteristic
33#2868C2211yescharacteristic
34#2864C2212yes—
35#2863C2212yes—
36#2863C2212yes—
37#2862C2211yescharacteristic
38#2862C2212yes—
39#2861C2212yes—
40#2860C2212yes—
41#2860C2212yes—
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2212yes—
45#2859C2212yes—
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2857C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2857C2211yescharacteristic
55#2856C2211yescharacteristic
56#2855C2212yes—
57#2855C2212yes—
58#2854C2212yes—
59#2854C2212yes—
60#2851C2212yes—
61#2850C2212yes—
62#2838C2218yes—
63#2811C2214yes—
64#2808C2214yes—
65#2806C2214yes—
66#2804C2214yes—
67#2798C2218yes—
68#2774C2218yes—
69#2764C2218yes—
70#2762C2218yes—
71#2759C2218yes—
72#2759C2218yes—
73#2754C2218yes—
74#2729C2218yes—
75#2723C2218yes—
76#2721C2218yes—
77#2721C2218yes—
78#2720C2218yes—
79#2717C2218yes—
80#2716C2218yes—
81#2716C2218yes—
82#2715C2218yes—
83#2713C2218yes—
84#2704C2218yes—
85#2702C2218yes—
86#2700C2218yes—
87#2700C2218yes—
88#2698C2218yes—
89#2690C2218yes—
90#2690C2218yes—
91#2689C2218yes—
92#2687C2218yes—
93#2680C2218yes—
94#2677C2218yes—
95#2674C2218yes—
96#2672C2218yes—
97#2647C2214yes—
98#2644C2214yes—
99#2629C2214yes—
100#2628C2214yes—
101#2625C2214yes—
102#2624C2214yes—
103#2592C2214yes—
104#2592C2214yes—
105#2584C2214yes—
106#2582C2214yes—
107#2581C2214yes—
108#2580C2214yes—
109#2580C2214yes—
110#2571C2212yes—
111#2570C2214yes—
112#2570C2214yes—
113#2567C2214yes—
114#2567C2214yes—
115#2567C2214yes—
116#2567C2212yes—
117#2563C2212yes—
118#2563C2212yes—
119#2563C2212yes—
120#2562C2214yes—
121#2552C2212yes—
122#2552C2212yes—
123#2551C2212yes—
124#2551C2214yes—
125#2551C2212yes—
126#2551C2212yes—
127#2548C2212yes—
128#2547C2212yes—
129#2547C2214yes—
130#2546C2214yes—
131#2542C2214yes—
132#2538C2214yes—
133#2514C2214yes—
134#2513C2214yes—
135#2512C2214yes—
136#2512C2214yes—
137#2512C2214yes—
138#2509C2214yes—
139#2507C2214yes—
140#2506C2214yes—
141#2506C2214yes—
142#2496C2214yes—
143#2496C2214yes—
144#2495C2214yes—
145#2495C2214yes—
146#2494C2214yes—
147#2494C2214yes—
148#2491C2214yes—
149#2487C2214yes—
150#2486C2214yes—
151#2485C2214yes—
152#2485C2214yes—
153#2452C2214yes—
154#2452C2214yes—
155#2451C2214yes—
156#2448C2214yes—
157#2447C2214yes—
158#2442C2214yes—
159#2441C2214yes—
160#2440C2214yes—
161#2439C2214yes—
162#2422C2214yes—
163#2383C2218yes—
164#2369C2212yes—
165#2369C2212yes—
166#2369C2212yes—
167#2369C2212yes—
168#2366C2212yes—
169#2365C2212yes—
170#2355C2212yes—
171#2354C2212yes—
172#2354C2212yes—
173Q8×C4⋊C4C2212yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176#2331C2214yes—
177#2319C2214yes—
178#2314C2214yes—
179#2314C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2211yescharacteristic
186C4×C4⋊Q8C2212yes—
187C4×C4⋊Q8C2211yescharacteristic
188C4×#127C2211yescharacteristic
189C4×#125C2212yes—
190C4×#124C2212yes—
191C4×C22⋊Q8C2212yes—
192C4×C22⋊Q8C2212yes—
193C4×#121C2212yes—
194C4×#121C2212yes—
195#2295C2212yes—
196#2295C2212yes—
197#2293C2212yes—
198#2293C2212yes—
199#2285C2212yes—
200#2285C2212yes—
201#2283C2212yes—
202C2×C43C2211yescharacteristic
203#544—416no—
204#542—416no—
205#533—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2318yes—
220C2×#127C2311yescharacteristic
221#529—48no—
222C2×#126C2314yes—
223C2×#126C2318yes—
224C2×#126C2318yes—
225C2×#125C2312yes—
226C2×#125C2314yes—
227C2×#125C2314yes—
228C2×#125C2312yes—
229C2×#125C2318yes—
230C2×#124C2314yes—
231C2×#124C2312yes—
232C2×#124C2312yes—
233C2×#124C2318yes—
234C2×#123C2314yes—
235C2×#123C2318yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2318yes—
243C2×C22⋊Q8C2318yes—
244C2×C22⋊Q8C2318yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×#121C2312yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×#117C2314yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2311yescharacteristic
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272#401C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#399C2318yes—
281#399C2318yes—
282#399C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#393C2318yes—
319#393C2318yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2318yes—
331#391C2318yes—
332#391C2318yes—
333#391C2312yes—
334#391C2314yes—
335#391C2318yes—
336#391C2318yes—
337#391C2318yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#391C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2312yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2312yes—
358#390C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2312yes—
388#389C2312yes—
389#389C2314yes—
390#389C2314yes—
391#389C2312yes—
392#389C2318yes—
393#389C2314yes—
394#389C2318yes—
395#389C2314yes—
396#389C2314yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2318yes—
415#388C2318yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2318yes—
424#388C2318yes—
425#387C2314yes—
426#387C2314yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2314yes—
434#387C2318yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#386C2314yes—
444#386C2314yes—
445#386C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2314yes—
450#385C2314yes—
451#385C2318yes—
452#385C2318yes—
453#384C2311yescharacteristic
454#384C2312yes—
455#384C2312yes—
456#384C2311yescharacteristic
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2311yescharacteristic
460#384C2311yescharacteristic
461#384C2312yes—
462#384C2318yes—
463#384C2314yes—
464#384C2312yes—
465#384C2312yes—
466#384C2312yes—
467#384C2312yes—
468#384C2314yes—
469#383C2314yes—
470#383C2318yes—
471#382C2312yes—
472#382C2314yes—
473#382C2314yes—
474#382C2314yes—
475#382C2312yes—
476#382C2314yes—
477#382C2314yes—
478#382C2312yes—
479#382C2312yes—
480#381C2318yes—
481#381C2314yes—
482#380C2312yes—
483#380C2312yes—
484#380C2314yes—
485#380C2314yes—
486#380C2314yes—
487#380C2314yes—
488#380C2314yes—
489#380C2312yes—
490#380C2312yes—
491#380C2318yes—
492#380C2312yes—
493#380C2312yes—
494#380C2312yes—
495#380C2314yes—
496#380C2312yes—
497#380C2314yes—
498#380C2312yes—
499#380C2312yes—
500#380C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2314yes—
511C4×C4⋊C4C2314yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2314yes—
521C4×C4⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2314yes—
525#376C2314yes—
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C22×Q8C2412yes—
535C22×Q8C2414yes—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2418yes—
541C22×D4C2412yes—
542C22×D4C2412yes—
543C22×D4C2414yes—
544C22×D4C2412yes—
545C23×C4C2414yes—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2418yes—
554C4⋊Q8—28no—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8—24no—
560C4⋊Q8—44no—
561C4⋊Q8—44no—
562C4⋊Q8—48no—
563C4⋊Q8—44no—
564C4⋊Q8—44no—
565C4⋊Q8—48no—
566C4⋊Q8—48no—
567C4⋊Q8—416no—
568#127—24no—
569#126—48no—
570#126—416no—
571#126—416no—
572#125—28no—
573#125—44no—
574#125—48no—
575#125—48no—
576#125—416no—
577#124—44no—
578#124—44no—
579#124—48no—
580#124—416no—
581#123—416no—
582#123—48no—
583C22⋊Q8—28no—
584C22⋊Q8—44no—
585C22⋊Q8—48no—
586C22⋊Q8—44no—
587C22⋊Q8—416no—
588C22⋊Q8—416no—
589C22⋊Q8—416no—
590C22⋊Q8—44no—
591C22⋊Q8—44no—
592#121—28no—
593#121—44no—
594#121—44no—
595C4×Q8—28no—
596C4×Q8—44no—
597C4×Q8—44no—
598C4×Q8—44no—
599C4×Q8—48no—
600C4×Q8—44no—
601C4×Q8—48no—
602C4×D4—28no—
603C4×D4—28no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—44no—
607C4×D4—48no—
608#117—216no—
609#117—216no—
610#117—48no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C42—24no—
692C2×C42—24no—
693C2×C42—24no—
694C2×C42—24no—
695C2×C42—24no—
696C2×C42—42no—
697C2×C42—42no—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2411yescharacteristic
702C2×C42C2414yes—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2418yes—
724C2×C42C2418yes—
725C2×C42C2418yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774C24C2514yes—
775C24C2511yescharacteristic
776C2×Q8—24no—
777C2×Q8—28no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8—44no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—44no—
794C2×Q8—48no—
795C2×Q8—48no—
796C2×Q8—48no—
797C2×D4—28no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—44no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—42no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—28no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—28no—
825C22×C4—28no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4H(5,𝔽2)14yes—
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2511yescharacteristic
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—48no—
895C4⋊C4—42no—
896C4⋊C4—44no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—42no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—44no—
909C4⋊C4—42no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C42—22no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—22no—
946C42—22no—
947C42—28no—
948C42—28no—
949C42—28no—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—22no—
955C42—22no—
956C42—22no—
957C42—22no—
958C42—22no—
959C42—28no—
960C42—22no—
961C42—22no—
962C42—22no—
963C42—22no—
964C42—28no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—41no—
969C42—48no—
970C42—48no—
971C42—48no—
972C42H(5,𝔽2)14yes—
973C422−1+414yes—
974C422−1+414yes—
975C422−1+414yes—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23C2×H(5,𝔽2)12yes—
990C23C2611yescharacteristic
991Q8—48no—
992Q8—84no—
993Q8—88no—
994Q8—84no—
995Q8—84no—
996Q8—84no—
997Q8—168no—
998D4—48no—
999D4—48no—
1000D4—84no—
1001D4—88no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—28no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—21no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—44no—
1063C2×C4—44no—
1064C2×C4—44no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—416no—
1068C2×C4—44no—
1069C2×C4—168no—
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×C4C2×2−1+412yes—
1079C2×C4C2×2−1+412yes—
1080C2×C4C2×2−1+412yes—
1081C2×C4C2×2−1+412yes—
1082C2×C4C2×2−1+412yes—
1083C2×C4C2×2−1+412yes—
1084C2×C4#58512yes—
1085C2×C4#58512yes—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—41no—
1090C22—41no—
1091C22—41no—
1092C22—41no—
1093C22—44no—
1094C22—44no—
1095C22—44no—
1096C22—44no—
1097C22—44no—
1098C22—44no—
1099C22—44no—
1100C22C22×H(5,𝔽2)11yescharacteristic
1101C22C22×H(5,𝔽2)11yescharacteristic
1102C22C22×2−1+411yescharacteristic
1103C22C22×2−1+411yescharacteristic
1104C22C22×2−1+411yescharacteristic
1105C22C2×#58511yescharacteristic
1106C22C2×#58511yescharacteristic
1107C4—22no—
1108C4—22no—
1109C4—22no—
1110C4—22no—
1111C4—22no—
1112C4—22no—
1113C4—22no—
1114C4—44no—
1115C4—41no—
1116C4—41no—
1117C4—44no—
1118C4—44no—
1119C4—41no—
1120C4—44no—
1121C4—44no—
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—41no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4#354414yes—
1130C4#355014yes—
1131C4#355514yes—
1132C2—42no—
1133C2—84no—
1134C2C2×#354411yescharacteristic
1135C2C2×#355511yescharacteristic
1136C2C2×#355011yescharacteristic
1137C2#6283111yescharacteristic
1138C2#6283411yescharacteristic
1139C2#6283511yescharacteristic
1140C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59924C2semidirect
2. #59871C2semidirect
3. #59864C2semidirect
4. #59863C2semidirect
5. #53366C2semidirect
6. #53197C2semidirect
7. #46343C2semidirect
8. #46174C2semidirect
9. #45633C2semidirect
10. #39515C2semidirect
11. #39514C2semidirect
12. #39480C2semidirect
13. #39479C2semidirect
14. #39370C2semidirect
15. #39369C2semidirect
17. #39350C2semidirect
18. #39181C2semidirect
19. #39158C2semidirect
20. #38985C2semidirect
21. #38932C2semidirect
22. #37337C2semidirect
23. #37281C2semidirect
24. #37275C2semidirect
25. #36645C2semidirect
26. #36635C2semidirect

Maximal subgroups

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

subgroupindex
#599242
#598712
#598642
#598632
#533662
#531972
#463432
#461742
#456332
#395152
#395142
#394802
#394792
#393702
#393692
#393512
#393502
#391812
#391582
#389852
#389322
#373372
#372812
#372752
#366452
#366352
#366312