Finite Group Databasebeta

← #8120089

Subgroups — #8120089

Order 512.

4540 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#55775C214yesmaximal, complemented
2#54999C214yesmaximal, complemented
3#53812C214yesmaximal, complemented
4#53670C214yesmaximal, complemented
5#52413C214yesmaximal, complemented
6#47728C214yesmaximal, complemented
7#47396C214yesmaximal, complemented
8#46821C214yesmaximal, complemented
9#46560C214yesmaximal, complemented
10#43196C214yesmaximal, complemented
11#39805C212yesmaximal, complemented
12#39796C212yesmaximal, complemented
13#39639C212yesmaximal, complemented
14#39632C212yesmaximal, complemented
15#38503C214yesmaximal, complemented
16#37721C214yesmaximal, complemented
17#36728C211yesmaximal, characteristic, complemented
18#36727C211yesmaximal, characteristic
19#35080C212yesmaximal, complemented
20#34997C212yesmaximal, complemented
21C2×#2549C211yesmaximal, characteristic, complemented
22C2×#539C2214yes—
23C22×C22⋊Q8C2212yes—
24#2857C2212yes—
25#2850C2212yes—
26#2849C2214yes—
27#2848C2212yes—
28#2847C2212yes—
29#2843C2214yescomplemented
30#2838C2214yescomplemented
31#2838C2214yescomplemented
32#2833C2214yescomplemented
33#2833C2214yescomplemented
34#2832C2214yescomplemented
35#2814C2214yescomplemented
36#2814C2214yescomplemented
37#2809C2214yescomplemented
38#2807C2214yescomplemented
39#2806C2214yescomplemented
40#2804C2214yescomplemented
41#2803C2214yescomplemented
42#2802C2214yescomplemented
43#2802C2214yescomplemented
44#2799C2214yescomplemented
45#2790C2214yes—
46#2788C2214yescomplemented
47#2788C2214yescomplemented
48#2776C2214yescomplemented
49#2773C2214yescomplemented
50#2768C2214yescomplemented
51#2765C2214yescomplemented
52#2764C2214yes—
53#2764C2214yescomplemented
54#2762C2214yescomplemented
55#2759C2214yescomplemented
56#2759C2214yescomplemented
57#2759C2214yescomplemented
58#2757C2214yes—
59#2751C2214yes—
60#2748C2214yes—
61#2747C2214yes—
62#2747C2214yescomplemented
63#2746C2214yes—
64#2741C2214yes—
65#2738C2214yescomplemented
66#2732C2214yes—
67#2728C2214yes—
68#2726C2214yescomplemented
69#2722C2214yes—
70#2721C2214yescomplemented
71#2720C2214yes—
72#2720C2214yescomplemented
73#2720C2214yescomplemented
74#2718C2214yes—
75#2712C2214yes—
76#2710C2214yescomplemented
77#2707C2214yescomplemented
78#2704C2214yes—
79#2703C2214yes—
80#2701C2214yes—
81#2700C2214yescomplemented
82#2696C2214yes—
83#2690C2214yes—
84#2690C2214yescomplemented
85#2690C2214yescomplemented
86#2689C2214yes—
87#2689C2214yescomplemented
88#2687C2214yes—
89#2681C2214yes—
90#2680C2214yes—
91#2680C2214yescomplemented
92#2671C2214yes—
93#2663C2214yes—
94#2659C2211yescharacteristic
95#2656C2211yescharacteristic
96#2653C2214yes—
97#2652C2214yes—
98#2649C2214yes—
99#2646C2211yescharacteristic
100#2646C2211yescharacteristic
101#2646C2212yes—
102#2643C2214yes—
103#2639C2212yes—
104#2638C2214yes—
105#2630C2214yes—
106#2606C2214yescomplemented
107#2605C2214yescomplemented
108#2602C2214yescomplemented
109#2596C2214yescomplemented
110#2591C2214yes—
111#2589C2214yescomplemented
112#2582C2214yescomplemented
113#2565C2214yescomplemented
114#2560C2214yes—
115#2560C2214yescomplemented
116#2556C2214yes—
117#2552C2214yescomplemented
118#2549C2214yes—
119#2549C2214yes—
120#2549C2214yes—
121#2549C2214yes—
122#2532C2214yescomplemented
123#2532C2214yescomplemented
124#2527C2214yes—
125#2524C2214yescomplemented
126#2511C2214yescomplemented
127#2511C2214yescomplemented
128#2510C2214yes—
129#2510C2214yes—
130#2510C2214yes—
131#2505C2214yes—
132#2502C2214yes—
133#2502C2214yescomplemented
134#2495C2212yes—
135#2494C2212yes—
136#2493C2214yes—
137#2492C2212yes—
138#2492C2214yescomplemented
139#2491C2212yes—
140#2488C2214yes—
141#2486C2214yescomplemented
142#2481C2214yes—
143#2480C2214yes—
144#2473C2214yes—
145#2473C2214yes—
146#2473C2214yes—
147#2473C2214yescomplemented
148#2472C2214yes—
149#2468C2214yes—
150#2468C2214yescomplemented
151#2465C2214yescomplemented
152#2463C2214yes—
153#2458C2214yes—
154#2458C2214yescomplemented
155#2455C2214yescomplemented
156#2450C2214yes—
157#2450C2214yes—
158#2450C2214yes—
159#2450C2214yes—
160#2449C2214yes—
161#2446C2214yescomplemented
162#2444C2214yes—
163#2443C2214yes—
164#2443C2214yes—
165#2443C2214yes—
166#2427C2212yes—
167#2426C2212yes—
168#2425C2214yes—
169#2424C2214yes—
170#2423C2212yes—
171#2422C2212yes—
172#2422C2214yes—
173#2419C2214yes—
174#2418C2214yes—
175#2417C2214yescomplemented
176#2409C2214yes—
177#2409C2214yes—
178C2×#398C2212yes—
179C2×#395C2212yes—
180#2361C2214yes—
181#2360C2214yes—
182#2353C2214yes—
183D4×C4⋊C4C2214yes—
184#2337C2214yes—
185#2337C2214yes—
186#2335C2214yes—
187#2332C2214yes—
188#2329C2212yes—
189#2329C2212yes—
190#2326C2214yes—
191#2325C2212yes—
192#2325C2212yes—
193#2318C2214yes—
194C4×C22⋊Q8C2212yes—
195C4×#121C2212yes—
196C4×#120C2214yes—
197C2×#391C2212yes—
198C2×#389C2212yes—
199C2×#385C2212yes—
200C2×#380C2211yescharacteristic
201C2×C4×C22⋊C4C2211yescharacteristic
202C22×#95C2211yescharacteristic
203C23×Q8C2312yes—
204C24×C4C2311yescharacteristic
205C24×C4C2312yes—
206#539—416no—
207C2×C4⋊Q8C2312yes—
208C2×#126C2314yes—
209C2×#126C2314yes—
210C2×#125C2314yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×#124C2314yes—
214C2×#124C2312yes—
215C2×#123C2314yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×C22⋊Q8—48no—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×#121C2312yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#120C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C22⋊C4C2311yescharacteristic
257C22×C22⋊C4C2311yescharacteristic
258C22×C22⋊C4C2312yes—
259C22×C42C2312yes—
260#401C2314yes—
261#401C2314yes—
262#401C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#399C2314yes—
284#399C2314yes—
285#399C2314yes—
286#399C2314yes—
287#399C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#397C2314yes—
317#397C2314yes—
318#397C2314yes—
319#397C2314yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#397C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2314yes—
331#397C2314yes—
332#397C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#395C2314yes—
341#395C2314yes—
342#395C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2314yes—
348#395C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#393C2314yes—
362#393C2314yes—
363#393C2314yes—
364#393C2314yes—
365#393C2314yes—
366#393C2314yes—
367#393C2314yes—
368#393C2314yes—
369#393C2314yes—
370#392C2314yes—
371#392C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#391C2314yes—
381#391C2314yes—
382#391C2314yes—
383#391C2312yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2312yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#390C2314yes—
392#390C2312yes—
393#390C2314yes—
394#390C2314yes—
395#390C2312yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2312yes—
407#389C2312yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2312yes—
414#389C2312yes—
415#389C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#386C2314yes—
477#386C2314yes—
478#386C2314yes—
479#386C2314yes—
480#386C2314yes—
481#386C2314yes—
482#386C2314yes—
483#386C2314yes—
484#386C2314yes—
485#386C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#385C2314yes—
495#385C2314yes—
496#385C2314yes—
497#385C2314yes—
498#385C2314yes—
499#385C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#384C2314yes—
525#384C2314yes—
526#384C2314yes—
527#384C2312yes—
528#383C2314yes—
529#383C2314yes—
530#383C2314yes—
531#383C2314yes—
532#382C2314yes—
533#382C2312yes—
534#381C2314yes—
535#381C2314yes—
536#381C2314yes—
537#381C2314yes—
538#380C2314yes—
539#380C2312yes—
540#380C2312yes—
541#380C2314yes—
542#380C2312yes—
543#380C2312yes—
544#380C2312yes—
545#380C2312yes—
546#380C2314yes—
547#380C2314yes—
548#380C2314yes—
549#380C2314yes—
550#380C2314yes—
551#380C2314yes—
552#380C2314yes—
553#379C2314yes—
554C4×C4⋊C4C2314yes—
555C4×C4⋊C4C2314yes—
556C4×C4⋊C4C2314yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2312yes—
559C4×C4⋊C4C2312yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2312yes—
567C4×C22⋊C4C2312yes—
568C4×C22⋊C4C2314yes—
569C4×C22⋊C4C2312yes—
570C4×C22⋊C4C2312yes—
571#376C2314yes—
572C2×#95C2311yescharacteristic
573C2×#95C2311yescharacteristic
574C2×#95C2312yes—
575C2×#95C2311yescharacteristic
576C2×#95C2312yes—
577C2×#95C2311yescharacteristic
578C2×#95C2312yes—
579C2×#95C2312yes—
580C2×#95C2314yes—
581C2×#95C2314yes—
582C25C2411yescharacteristic
583C22×Q8—44no—
584C22×Q8—44no—
585C22×Q8—82no—
586C22×Q8C2412yes—
587C22×Q8C2414yes—
588C22×Q8C2414yes—
589C22×Q8C2414yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2414yes—
593C22×D4C2412yes—
594C22×D4C2414yes—
595C23×C4—24no—
596C23×C4—44no—
597C23×C4—44no—
598C23×C4—82no—
599C23×C4—82no—
600C23×C4C2412yes—
601C23×C4C2412yes—
602C23×C4C2412yes—
603C23×C4C2412yes—
604C23×C4C2412yes—
605C23×C4C2412yes—
606C23×C4C2411yescharacteristic
607C23×C4C2414yes—
608C23×C4C2414yes—
609C23×C4C2412yes—
610C23×C4C2412yes—
611C23×C4C2414yes—
612C23×C4C2414yes—
613C23×C4C2414yes—
614C23×C4C2411yescharacteristic
615C4⋊Q8—82no—
616#126—48no—
617#126—48no—
618#125—48no—
619#125—48no—
620#125—84no—
621#124—216no—
622#124—82no—
623#123—216no—
624#123—48no—
625#123—48no—
626#123—84no—
627#123—84no—
628#123—84no—
629C22⋊Q8—28no—
630C22⋊Q8—216no—
631C22⋊Q8—48no—
632C22⋊Q8—48no—
633C22⋊Q8—48no—
634C22⋊Q8—48no—
635C22⋊Q8—48no—
636C22⋊Q8—48no—
637C22⋊Q8—82no—
638C22⋊Q8—84no—
639C22⋊Q8—84no—
640C22⋊Q8—82no—
641#121—28no—
642#121—48no—
643#121—48no—
644#121—82no—
645#121—82no—
646#120—48no—
647C4×Q8—82no—
648C4×Q8—84no—
649C4×D4—48no—
650C4×D4—48no—
651C4×D4—48no—
652C4×D4—48no—
653C4×D4—48no—
654C4×D4—82no—
655C4×D4—84no—
656C2×C4⋊C4—44no—
657C2×C4⋊C4—44no—
658C2×C4⋊C4—44no—
659C2×C4⋊C4—48no—
660C2×C4⋊C4—44no—
661C2×C4⋊C4—82no—
662C2×C4⋊C4—82no—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
711C2×C22⋊C4—44no—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2412yes—
714C2×C22⋊C4C2411yescharacteristic
715C2×C22⋊C4C2412yes—
716C2×C22⋊C4C2411yescharacteristic
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2411yescharacteristic
750C2×C22⋊C4C2411yescharacteristic
751C2×C42—82no—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2412yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2412yes—
763C2×C42C2412yes—
764C2×C42C2412yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2412yes—
771#95C2412yes—
772#95C2412yes—
773#95C2412yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823C24—22no—
824C24—22no—
825C24—22no—
826C24—24no—
827C24—42no—
828C24C2514yes—
829C24C2511yescharacteristic
830C24C2511yescharacteristic
831C24C2511yescharacteristic
832C2×Q8—28no—
833C2×Q8—24no—
834C2×Q8—28no—
835C2×Q8—42no—
836C2×Q8—44no—
837C2×Q8—44no—
838C2×Q8—44no—
839C2×Q8—42no—
840C2×Q8—44no—
841C2×Q8—44no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8—816no—
845C2×D4—28no—
846C2×D4—28no—
847C2×D4—28no—
848C2×D4—28no—
849C2×D4—28no—
850C2×D4—24no—
851C2×D4—44no—
852C2×D4—42no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—42no—
859C2×D4—44no—
860C22×C4—22no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—28no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—28no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—44no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—88no—
903C22×C4—816no—
904C22×C42−1+414yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2514yes—
910C22×C4C2512yes—
911C22×C4C2514yes—
912C22×C4C2514yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2512yes—
916C22×C4C2514yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2512yes—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—24no—
928C4⋊C4—24no—
929C4⋊C4—28no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—42no—
946C4⋊C4—44no—
947C4⋊C4—42no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—42no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—44no—
959C4⋊C4—44no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—42no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C22⋊C4—22no—
969C22⋊C4—28no—
970C22⋊C4—28no—
971C22⋊C4—22no—
972C22⋊C4—28no—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—24no—
977C22⋊C4—28no—
978C22⋊C4—24no—
979C22⋊C4—28no—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4H(5,𝔽2)14yes—
1006C22⋊C42−1+414yes—
1007C42—28no—
1008C42—42no—
1009C42—42no—
1010C42—42no—
1011C42—42no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42—44no—
1016C42—44no—
1017C42—44no—
1018C42—44no—
1019C42—44no—
1020C23—21no—
1021C23—21no—
1022C23—22no—
1023C23—28no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—48no—
1040C23—48no—
1041C23—44no—
1042C23—44no—
1043C23C2×H(5,𝔽2)12yes—
1044C23C2×2−1+412yes—
1045C23C2×2−1+412yes—
1046C23#58514yes—
1047C23C2611yescharacteristic
1048Q8—84no—
1049Q8—88no—
1050Q8—88no—
1051Q8—88no—
1052D4—416no—
1053D4—84no—
1054D4—88no—
1055D4—88no—
1056D4—88no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—44no—
1106C2×C4—48no—
1107C2×C4—48no—
1108C2×C4—44no—
1109C2×C4—48no—
1110C2×C4—88no—
1111C2×C4—84no—
1112C2×C4—84no—
1113C2×C4—84no—
1114C2×C4—88no—
1115C2×C4—84no—
1116C2×C4—84no—
1117C2×C4—88no—
1118C2×C4—164no—
1119C2×C4—164no—
1120C2×C4C2×H(5,𝔽2)14yes—
1121C2×C4C2×2−1+414yes—
1122C2×C4C2×2−1+414yes—
1123C22—22no—
1124C22—22no—
1125C22—24no—
1126C22—24no—
1127C22—22no—
1128C22—22no—
1129C22—24no—
1130C22—24no—
1131C22—416no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—42no—
1137C22—42no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—44no—
1144C22—44no—
1145C22#355714yes—
1146C22C22×H(5,𝔽2)11yescharacteristic
1147C22C22×2−1+411yescharacteristic
1148C22C22×2−1+411yescharacteristic
1149C22C2×#58512yes—
1150C22H(7,𝔽2)12yes—
1151C4—24no—
1152C4—24no—
1153C4—24no—
1154C4—44no—
1155C4—44no—
1156C4—42no—
1157C4—44no—
1158C4—44no—
1159C4—42no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4—44no—
1164C4—44no—
1165C4—42no—
1166C4—44no—
1167C4—44no—
1168C2—24no—
1169C2—42no—
1170C2—42no—
1171C2—84no—
1172C2C2×#355711yescharacteristic
1173C2#6283311yescharacteristic
1174C2#6286411yescharacteristic
1175C2#6289612yes—
1176C2#6294812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36727C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #55775C2semidirect
2. #54999C2semidirect
3. #53812C2semidirect
4. #53670C2semidirect
5. #52413C2semidirect
6. #47728C2semidirect
7. #47396C2semidirect
8. #46821C2semidirect
9. #46560C2semidirect
10. #43196C2semidirect
11. #39805C2semidirect
12. #39796C2semidirect
13. #39639C2semidirect
14. #39632C2semidirect
15. #38503C2semidirect
16. #37721C2semidirect
17. #36728C2semidirect
19. #35080C2semidirect
20. #34997C2semidirect
21. C2×#2549C2semidirect
29. #2843C22semidirect
30. #2838C22semidirect
31. #2838C22semidirect
32. #2833C22semidirect
33. #2833C22semidirect
34. #2832C22semidirect
35. #2814C22semidirect
36. #2814C22semidirect
37. #2809C22semidirect
38. #2807C22semidirect
39. #2806C22semidirect
40. #2804C22semidirect
41. #2803C22semidirect
42. #2802C22semidirect
43. #2802C22semidirect
44. #2799C22semidirect
46. #2788C22semidirect
47. #2788C22semidirect
48. #2776C22semidirect
49. #2773C22semidirect
50. #2768C22semidirect
51. #2765C22semidirect
53. #2764C22semidirect
54. #2762C22semidirect
55. #2759C22semidirect
56. #2759C22semidirect
57. #2759C22semidirect
62. #2747C22semidirect
65. #2738C22semidirect
68. #2726C22semidirect
70. #2721C22semidirect
72. #2720C22semidirect
73. #2720C22semidirect
76. #2710C22semidirect
77. #2707C22semidirect
81. #2700C22semidirect
84. #2690C22semidirect
85. #2690C22semidirect
87. #2689C22semidirect
91. #2680C22semidirect
106. #2606C22semidirect
107. #2605C22semidirect
108. #2602C22semidirect
109. #2596C22semidirect
111. #2589C22semidirect
112. #2582C22semidirect
113. #2565C22semidirect
115. #2560C22semidirect
117. #2552C22semidirect
122. #2532C22semidirect
123. #2532C22semidirect
125. #2524C22semidirect
126. #2511C22semidirect
127. #2511C22semidirect
133. #2502C22semidirect
138. #2492C22semidirect
141. #2486C22semidirect
147. #2473C22semidirect
150. #2468C22semidirect
151. #2465C22semidirect
154. #2458C22semidirect
155. #2455C22semidirect
161. #2446C22semidirect
175. #2417C22semidirect

Maximal subgroups

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

subgroupindex
#557752
#549992
#538122
#536702
#524132
#477282
#473962
#468212
#465602
#431962
#398052
#397962
#396392
#396322
#385032
#377212
#367282
#367272
#350802
#349972
C2×#25492