Finite Group Databasebeta

← #8358720

Subgroups — #8358720

Order 512.

5344 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59189C212yesmaximal
2#58057C214yesmaximal, complemented
3#55532C214yesmaximal, complemented
4#55526C214yesmaximal, complemented
5#54913C214yesmaximal, complemented
6#52413C212yesmaximal, complemented
7#49602C214yesmaximal, complemented
8#47945C214yesmaximal, complemented
9#45456C212yesmaximal, complemented
10#43965C212yesmaximal, complemented
11#43553C212yesmaximal, complemented
12#43003C212yesmaximal, complemented
13#42481C214yesmaximal, complemented
14#41055C214yesmaximal, complemented
15#40843C214yesmaximal, complemented
16#40495C212yesmaximal, complemented
17#39150C212yesmaximal, complemented
18#37902C214yesmaximal, complemented
19#36720C211yesmaximal, characteristic, complemented
20Q8×#120C212yesmaximal, complemented
21#35743C212yesmaximal, complemented
22#35396C211yesmaximal, characteristic
23C2×#2614C211yesmaximal, characteristic, complemented
24C24×Q8C2211yescharacteristic
25C2×#563C2212yes—
26C2×#559C2212yes—
27C2×D4×Q8C2212yes—
28C2×D4×Q8C2214yescomplemented
29C2×#543C2211yescharacteristic
30C2×#539C2211yescharacteristic
31C22×#123C2212yes—
32C22×#123C2211yescharacteristic
33#2848C2214yes—
34#2848C2212yes—
35#2843C2212yescomplemented
36#2838C2214yescomplemented
37#2838C2214yescomplemented
38#2833C2214yescomplemented
39#2832C2212yescomplemented
40#2830C2214yescomplemented
41#2821C2212yescomplemented
42#2817C2212yescomplemented
43#2814C2214yes—
44#2814C2214yescomplemented
45#2811C2212yescomplemented
46#2808C2214yescomplemented
47#2806C2214yescomplemented
48#2799C2212yescomplemented
49#2792C2214yescomplemented
50#2792C2212yescomplemented
51#2775C2214yescomplemented
52#2765C2214yescomplemented
53#2764C2214yescomplemented
54#2763C2214yescomplemented
55#2761C2214yescomplemented
56#2759C2214yescomplemented
57#2759C2214yescomplemented
58#2759C2214yescomplemented
59#2751C2214yescomplemented
60#2751C2214yescomplemented
61#2745C2214yescomplemented
62#2740C2214yescomplemented
63#2739C2214yescomplemented
64#2737C2214yescomplemented
65#2737C2214yescomplemented
66#2734C2214yescomplemented
67#2729C2214yescomplemented
68#2729C2214yescomplemented
69#2724C2212yes—
70#2724C2212yes—
71#2723C2214yescomplemented
72#2720C2214yescomplemented
73#2718C2214yes—
74#2717C2212yes—
75#2716C2214yescomplemented
76#2713C2214yescomplemented
77#2710C2214yes—
78#2709C2212yes—
79#2707C2214yes—
80#2700C2214yescomplemented
81#2700C2214yescomplemented
82#2700C2214yescomplemented
83#2700C2214yescomplemented
84#2698C2214yescomplemented
85#2698C2214yescomplemented
86#2695C2214yes—
87#2692C2214yescomplemented
88#2692C2214yescomplemented
89#2690C2214yescomplemented
90#2689C2214yescomplemented
91#2687C2214yes—
92#2687C2214yes—
93#2680C2214yes—
94#2680C2214yes—
95#2680C2214yes—
96#2680C2214yescomplemented
97#2680C2212yescomplemented
98#2677C2214yescomplemented
99#2677C2214yescomplemented
100#2674C2214yes—
101#2666C2214yescomplemented
102#2665C2214yescomplemented
103#2665C2214yescomplemented
104#2663C2212yescomplemented
105#2660C2212yescomplemented
106#2650C2214yescomplemented
107#2643C2214yes—
108#2640C2214yescomplemented
109#2638C2214yescomplemented
110#2638C2214yescomplemented
111#2634C2212yescomplemented
112#2627C2212yes—
113#2614C2214yes—
114#2614C2214yes—
115#2614C2214yes—
116#2614C2214yes—
117#2614C2212yescomplemented
118#2605C2214yescomplemented
119#2604C2212yescomplemented
120#2602C2214yes—
121#2592C2214yescomplemented
122#2591C2211yescharacteristic
123#2588C2214yescomplemented
124#2586C2214yescomplemented
125#2586C2212yescomplemented
126#2586C2214yescomplemented
127#2583C2211yescharacteristic
128#2573C2214yescomplemented
129#2567C2214yescomplemented
130#2564C2212yes—
131#2561C2212yes—
132#2560C2214yescomplemented
133#2558C2214yes—
134#2557C2214yes—
135#2554C2214yes—
136#2551C2212yescomplemented
137#2550C2214yescomplemented
138#2549C2214yes—
139#2549C2212yes—
140#2532C2214yescomplemented
141#2527C2214yescomplemented
142#2527C2214yescomplemented
143#2527C2214yescomplemented
144#2515C2214yescomplemented
145#2510C2214yes—
146#2502C2212yes—
147#2492C2214yescomplemented
148#2488C2214yes—
149#2483C2212yes—
150#2480C2214yes—
151#2480C2214yes—
152#2473C2214yes—
153#2472C2214yes—
154#2472C2214yes—
155#2469C2214yescomplemented
156#2468C2214yescomplemented
157#2466C2214yescomplemented
158#2465C2214yescomplemented
159#2462C2214yescomplemented
160#2461C2214yes—
161#2458C2214yes—
162#2455C2214yes—
163#2452C2214yescomplemented
164#2452C2214yescomplemented
165#2451C2214yescomplemented
166#2451C2214yescomplemented
167#2450C2214yes—
168#2447C2214yescomplemented
169#2447C2214yescomplemented
170#2445C2214yes—
171#2445C2214yes—
172#2443C2214yes—
173#2440C2214yes—
174#2438C2214yes—
175#2437C2214yes—
176#2435C2211yescharacteristic
177#2434C2214yes—
178#2434C2212yes—
179#2434C2212yescomplemented
180#2434C2214yescomplemented
181#2434C2214yescomplemented
182#2434C2214yescomplemented
183#2433C2211yescharacteristic
184#2419C2214yes—
185#2411C2212yes—
186#2411C2212yes—
187#2409C2212yes—
188#2409C2214yes—
189#2409C2214yescomplemented
190#2409C2214yescomplemented
191#2409C2214yescomplemented
192#2409C2214yescomplemented
193#2405C2212yes—
194#2399C2214yescomplemented
195C2×#395C2212yes—
196C2×#395C2212yes—
197C2×#393C2212yes—
198C2×#393C2212yes—
199#2376C2212yes—
200#2374C2212yes—
201#2368C2214yes—
202#2368C2212yes—
203#2360C2214yes—
204#2358C2214yes—
205#2353C2212yes—
206#2343C2214yes—
207Q8×C22⋊C4C2212yes—
208Q8×C22⋊C4C2214yescomplemented
209#2332C2214yescomplemented
210#2329C2214yes—
211#2321C2212yes—
212#2319C2214yescomplemented
213#2312C2211yescharacteristic
214C4×#120C2214yes—
215C4×#120C2212yes—
216C2×#381C2212yes—
217C2×#381C2211yescharacteristic
218#2274C2211yescharacteristic
219C23×Q8—44no—
220C23×Q8—48no—
221C23×Q8C2312yes—
222C23×Q8C2314yes—
223C23×Q8C2314yes—
224C23×Q8C2312yes—
225C23×Q8C2312yes—
226C23×D4C2311yescharacteristic
227C24×C4C2312yes—
228C24×C4C2311yescharacteristic
229#563—48no—
230#559—48no—
231D4×Q8—48no—
232D4×Q8—416no—
233#543—44no—
234#539—44no—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2314yes—
241C2×#127C2312yes—
242C2×#126C2314yes—
243C2×#126C2312yes—
244C2×#126C2314yes—
245C2×#125C2312yes—
246C2×#125C2314yes—
247C2×#124C2314yes—
248C2×#124C2312yes—
249C2×#124C2314yes—
250C2×#123—44no—
251C2×#123—48no—
252C2×#123C2312yes—
253C2×#123C2312yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×#123C2312yes—
259C2×#123C2312yes—
260C2×#123C2312yes—
261C2×#123C2314yes—
262C2×#123C2312yes—
263C2×#123C2312yes—
264C2×#123C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2311yescharacteristic
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×#121C2311yescharacteristic
283C2×#120C2312yes—
284C2×#120C2312yes—
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2314yes—
294C2×#117C2312yes—
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2314yes—
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2314yes—
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2312yes—
304#401C2314yes—
305#401C2314yes—
306#400C2312yes—
307#400C2314yes—
308#400C2312yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2312yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2312yes—
319#400C2314yes—
320#399C2312yes—
321#399C2314yes—
322#399C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2312yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#395C2312yes—
370#395C2312yes—
371#395C2314yes—
372#395C2312yes—
373#395C2312yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2312yes—
380#395C2314yes—
381#395C2314yes—
382#395C2312yes—
383#395C2314yes—
384#395C2312yes—
385#395C2314yes—
386#395C2312yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2312yes—
392#395C2314yes—
393#395C2314yes—
394#395C2312yes—
395#395C2312yes—
396#395C2312yes—
397#395C2314yes—
398#395C2312yes—
399#395C2312yes—
400#395C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2312yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2312yes—
415#393C2312yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2312yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#392C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#390C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2312yes—
533#386C2312yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2312yes—
538#386C2312yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2312yes—
546#385C2312yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#384C2312yes—
570#384C2314yes—
571#384C2312yes—
572#383C2312yes—
573#383C2314yes—
574#383C2314yes—
575#382C2314yes—
576#382C2314yes—
577#381C2314yes—
578#381C2312yes—
579#381C2314yes—
580#381C2314yes—
581#381C2314yes—
582#381C2314yes—
583#381C2314yes—
584#381C2314yes—
585#381C2314yes—
586#381C2314yes—
587#380C2314yes—
588#380C2312yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2314yes—
595#379C2314yes—
596#379C2312yes—
597#379C2312yes—
598#379C2312yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C22⋊C4C2312yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2311yescharacteristic
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2311yescharacteristic
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618#376C2314yes—
619#376C2312yes—
620C2×#95C2312yes—
621C2×#95C2312yes—
622C2×#95C2314yes—
623C2×#95C2314yes—
624C25C2411yescharacteristic
625C25C2411yescharacteristic
626C22×Q8—28no—
627C22×Q8—216no—
628C22×Q8—44no—
629C22×Q8—48no—
630C22×Q8—48no—
631C22×Q8—48no—
632C22×Q8—48no—
633C22×Q8—48no—
634C22×Q8—48no—
635C22×Q8—48no—
636C22×Q8—48no—
637C22×Q8—44no—
638C22×Q8—464no—
639C22×Q8C2412yes—
640C22×Q8C2414yes—
641C22×Q8C2412yes—
642C22×Q8C2414yes—
643C22×Q8C2412yes—
644C22×Q8C2414yes—
645C22×Q8C2412yes—
646C22×Q8C2414yes—
647C22×Q8C2411yescharacteristic
648C22×Q8C2412yes—
649C22×Q8C2412yes—
650C22×D4—42no—
651C22×D4—44no—
652C22×D4C2412yes—
653C22×D4C2414yes—
654C22×D4C2414yes—
655C22×D4C2412yes—
656C22×D4C2412yes—
657C22×D4C2411yescharacteristic
658C23×C4—24no—
659C23×C4—28no—
660C23×C4—44no—
661C23×C4—44no—
662C23×C4—44no—
663C23×C4C2411yescharacteristic
664C23×C4C2414yes—
665C23×C4C2414yes—
666C23×C4C2414yes—
667C23×C4C2411yescharacteristic
668C23×C4C2414yes—
669C23×C4C2411yescharacteristic
670C23×C4C2411yescharacteristic
671C23×C4C2414yes—
672C23×C4C2412yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2412yes—
676C23×C4C2411yescharacteristic
677C23×C4C2412yes—
678C4⋊Q8—48no—
679C4⋊Q8—44no—
680C4⋊Q8—48no—
681C4⋊Q8—48no—
682C4⋊Q8—48no—
683C4⋊Q8—48no—
684#127—44no—
685#126—44no—
686#126—48no—
687#126—48no—
688#125—44no—
689#125—48no—
690#124—48no—
691#124—48no—
692#124—44no—
693#123—28no—
694#123—28no—
695#123—44no—
696#123—44no—
697#123—48no—
698#123—48no—
699#123—48no—
700#123—48no—
701#123—44no—
702#123—48no—
703#123—44no—
704#123—44no—
705#123—44no—
706C22⋊Q8—28no—
707C22⋊Q8—216no—
708C22⋊Q8—216no—
709C22⋊Q8—42no—
710C22⋊Q8—44no—
711C22⋊Q8—48no—
712C22⋊Q8—48no—
713C22⋊Q8—48no—
714C22⋊Q8—48no—
715C22⋊Q8—48no—
716C22⋊Q8—48no—
717C22⋊Q8—48no—
718C22⋊Q8—48no—
719C22⋊Q8—48no—
720C22⋊Q8—44no—
721C22⋊Q8—44no—
722C22⋊Q8—48no—
723#121—42no—
724#120—28no—
725#120—28no—
726C4×Q8—48no—
727C4×Q8—48no—
728C4×Q8—44no—
729C4×D4—28no—
730C4×D4—216no—
731C4×D4—48no—
732C4×D4—48no—
733C4×D4—48no—
734C4×D4—48no—
735#117—28no—
736C2×C4⋊C4—24no—
737C2×C4⋊C4—48no—
738C2×C4⋊C4—42no—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C22⋊C4—24no—
787C2×C22⋊C4—48no—
788C2×C22⋊C4—44no—
789C2×C22⋊C4—44no—
790C2×C22⋊C4—42no—
791C2×C22⋊C4—42no—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2412yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C42C2414yes—
835C2×C42C2414yes—
836C2×C42C2412yes—
837C2×C42C2414yes—
838C2×C42C2414yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2414yes—
844C2×C42C2414yes—
845C2×C42C2414yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848#95C2412yes—
849#95C2414yes—
850#95C2414yes—
851#95C2412yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2412yes—
859#95C2414yes—
860#95C2412yes—
861#95C2414yes—
862#95C2414yes—
863#95C2412yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2412yes—
870#95C2412yes—
871#95C2412yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906C24—24no—
907C24—22no—
908C24—24no—
909C24—22no—
910C24—24no—
911C24—42no—
912C24—42no—
913C24—42no—
914C24C2512yes—
915C24C2512yes—
916C24C2512yes—
917C24C2511yescharacteristic
918C2×Q8—24no—
919C2×Q8—28no—
920C2×Q8—28no—
921C2×Q8—28no—
922C2×Q8—28no—
923C2×Q8—24no—
924C2×Q8—28no—
925C2×Q8—24no—
926C2×Q8—28no—
927C2×Q8—28no—
928C2×Q8—42no—
929C2×Q8—44no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8—44no—
933C2×Q8—42no—
934C2×Q8—44no—
935C2×Q8—44no—
936C2×Q8—44no—
937C2×Q8—44no—
938C2×Q8—44no—
939C2×Q8—44no—
940C2×Q8—42no—
941C2×Q8—41no—
942C2×Q8—42no—
943C2×Q8—42no—
944C2×Q8—42no—
945C2×Q8—432no—
946C2×Q8—464no—
947C2×Q8—432no—
948C2×Q8—464no—
949C2×Q8—816no—
950C2×D4—24no—
951C2×D4—28no—
952C2×D4—24no—
953C2×D4—24no—
954C2×D4—24no—
955C2×D4—24no—
956C2×D4—28no—
957C2×D4—28no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—44no—
965C2×D4—41no—
966C2×D4—42no—
967C2×D4—88no—
968C22×C4—22no—
969C22×C4—22no—
970C22×C4—28no—
971C22×C4—28no—
972C22×C4—28no—
973C22×C4—24no—
974C22×C4—24no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—28no—
980C22×C4—28no—
981C22×C4—28no—
982C22×C4—24no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—44no—
993C22×C4—42no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—42no—
1000C22×C4—42no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—44no—
1004C22×C4—416no—
1005C22×C4—432no—
1006C22×C4H(5,𝔽2)14yes—
1007C22×C4H(5,𝔽2)18yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2514yes—
1013C22×C4C2514yes—
1014C22×C4C2512yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2511yescharacteristic
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—24no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—41no—
1058C4⋊C4—44no—
1059C4⋊C4—42no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—41no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C22⋊C4—28no—
1075C22⋊C4—24no—
1076C22⋊C4—24no—
1077C22⋊C4—24no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—24no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—24no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—44no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—44no—
1114C22⋊C4—42no—
1115C22⋊C42−1+418yes—
1116C42—28no—
1117C42—24no—
1118C42—28no—
1119C42—44no—
1120C42—42no—
1121C42—44no—
1122C42—42no—
1123C42—44no—
1124C42—44no—
1125C42—44no—
1126C42—44no—
1127C42—42no—
1128C42—42no—
1129C42—44no—
1130C23—22no—
1131C23—22no—
1132C23—28no—
1133C23—22no—
1134C23—22no—
1135C23—24no—
1136C23—24no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—24no—
1142C23—24no—
1143C23—22no—
1144C23—22no—
1145C23—24no—
1146C23—24no—
1147C23—416no—
1148C23—44no—
1149C23—44no—
1150C23—44no—
1151C23—82no—
1152C23—82no—
1153C23—88no—
1154C23C2×H(5,𝔽2)14yes—
1155C23C2×H(5,𝔽2)12yes—
1156C23C2×2−1+414yes—
1157C23C2611yescharacteristic
1158Q8—216no—
1159Q8—48no—
1160Q8—416no—
1161Q8—416no—
1162Q8—48no—
1163Q8—48no—
1164Q8—88no—
1165Q8—84no—
1166Q8—88no—
1167Q8—161no—
1168Q8—162no—
1169D4—416no—
1170D4—48no—
1171D4—88no—
1172D4—84no—
1173D4—84no—
1174D4—161no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—22no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—44no—
1224C2×C4—48no—
1225C2×C4—416no—
1226C2×C4—416no—
1227C2×C4—416no—
1228C2×C4—44no—
1229C2×C4—48no—
1230C2×C4—44no—
1231C2×C4—88no—
1232C2×C4—84no—
1233C2×C4—82no—
1234C2×C4—88no—
1235C2×C4—82no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4C2×H(5,𝔽2)14yes—
1239C2×C4C2×H(5,𝔽2)18yes—
1240C2×C4C2×2−1+418yes—
1241C22—22no—
1242C22—22no—
1243C22—28no—
1244C22—24no—
1245C22—28no—
1246C22—416no—
1247C22—42no—
1248C22—42no—
1249C22—44no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—164no—
1261C22#355014yes—
1262C22C22×H(5,𝔽2)11yescharacteristic
1263C22C22×H(5,𝔽2)12yes—
1264C22C22×2−1+412yes—
1265C222−1+612yes—
1266C4—28no—
1267C4—24no—
1268C4—28no—
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—44no—
1273C4—44no—
1274C4—41no—
1275C4—41no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—44no—
1280C4—44no—
1281C4—44no—
1282C4—44no—
1283C4—44no—
1284C4—44no—
1285C2—24no—
1286C2—44no—
1287C2—82no—
1288C2—82no—
1289C2C2×#355011yescharacteristic
1290C2#6281711yescharacteristic
1291C2#6288711yescharacteristic
1292C2#6294214yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2433C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #58057C2semidirect
3. #55532C2semidirect
4. #55526C2semidirect
5. #54913C2semidirect
6. #52413C2semidirect
7. #49602C2semidirect
8. #47945C2semidirect
9. #45456C2semidirect
10. #43965C2semidirect
11. #43553C2semidirect
12. #43003C2semidirect
13. #42481C2semidirect
14. #41055C2semidirect
15. #40843C2semidirect
16. #40495C2semidirect
17. #39150C2semidirect
18. #37902C2semidirect
19. #36720C2semidirect
20. Q8×#120C2semidirect
21. #35743C2semidirect
23. C2×#2614C2semidirect
28. C2×D4×Q8C22semidirect
35. #2843C22semidirect
36. #2838C22semidirect
37. #2838C22semidirect
38. #2833C22semidirect
39. #2832C22semidirect
40. #2830C22semidirect
41. #2821C22semidirect
42. #2817C22semidirect
44. #2814C22semidirect
45. #2811C22semidirect
46. #2808C22semidirect
47. #2806C22semidirect
48. #2799C22semidirect
49. #2792C22semidirect
50. #2792C22semidirect
51. #2775C22semidirect
52. #2765C22semidirect
53. #2764C22semidirect
54. #2763C22semidirect
55. #2761C22semidirect
56. #2759C22semidirect
57. #2759C22semidirect
58. #2759C22semidirect
59. #2751C22semidirect
60. #2751C22semidirect
61. #2745C22semidirect
62. #2740C22semidirect
63. #2739C22semidirect
64. #2737C22semidirect
65. #2737C22semidirect
66. #2734C22semidirect
67. #2729C22semidirect
68. #2729C22semidirect
71. #2723C22semidirect
72. #2720C22semidirect
75. #2716C22semidirect
76. #2713C22semidirect
80. #2700C22semidirect
81. #2700C22semidirect
82. #2700C22semidirect
83. #2700C22semidirect
84. #2698C22semidirect
85. #2698C22semidirect
87. #2692C22semidirect
88. #2692C22semidirect
89. #2690C22semidirect
90. #2689C22semidirect
96. #2680C22semidirect
97. #2680C22semidirect
98. #2677C22semidirect
99. #2677C22semidirect
101. #2666C22semidirect
102. #2665C22semidirect
103. #2665C22semidirect
104. #2663C22semidirect
105. #2660C22semidirect
106. #2650C22semidirect
108. #2640C22semidirect
109. #2638C22semidirect
110. #2638C22semidirect
111. #2634C22semidirect
117. #2614C22semidirect
118. #2605C22semidirect
119. #2604C22semidirect
121. #2592C22semidirect
123. #2588C22semidirect
124. #2586C22semidirect
125. #2586C22semidirect
126. #2586C22semidirect
128. #2573C22semidirect
129. #2567C22semidirect
132. #2560C22semidirect
136. #2551C22semidirect
137. #2550C22semidirect
140. #2532C22semidirect
141. #2527C22semidirect
142. #2527C22semidirect
143. #2527C22semidirect
144. #2515C22semidirect
147. #2492C22semidirect
155. #2469C22semidirect
156. #2468C22semidirect
157. #2466C22semidirect
158. #2465C22semidirect
159. #2462C22semidirect
163. #2452C22semidirect
164. #2452C22semidirect
165. #2451C22semidirect
166. #2451C22semidirect
168. #2447C22semidirect
169. #2447C22semidirect
179. #2434C22semidirect
180. #2434C22semidirect
181. #2434C22semidirect
182. #2434C22semidirect
189. #2409C22semidirect
190. #2409C22semidirect
191. #2409C22semidirect
192. #2409C22semidirect
194. #2399C22semidirect
208. Q8×C22⋊C4C22semidirect
209. #2332C22semidirect
212. #2319C22semidirect

Maximal subgroups

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

subgroupindex
#591892
#580572
#555322
#555262
#549132
#524132
#496022
#479452
#454562
#439652
#435532
#430032
#424812
#410552
#408432
#404952
#391502
#379022
#367202
Q8×#1202
#357432
#353962
C2×#26142