Finite Group Databasebeta

← #9062269

Subgroups — #9062269

Order 512.

5250 conjugacy classes of subgroups.

The subgroup lattice has 1323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60048C211yesmaximal, characteristic, complemented
2#60046C211yesmaximal, characteristic, complemented
3#60044C212yesmaximal, complemented
4#58588C212yesmaximal, complemented
5#54859C214yesmaximal, complemented
6#54850C212yesmaximal, complemented
7#49703C212yesmaximal, complemented
8#49635C214yesmaximal, complemented
9#47795C214yesmaximal, complemented
10#47752C212yesmaximal, complemented
11#46620C214yesmaximal, complemented
12#46423C212yesmaximal, complemented
13#45091C214yesmaximal, complemented
14#44758C212yesmaximal, complemented
15#44441C214yesmaximal, complemented
16#44435C214yesmaximal, complemented
17#44181C214yesmaximal, complemented
18#43779C214yesmaximal, complemented
19#43553C212yesmaximal, complemented
20#35740C212yesmaximal, complemented
21#35715C214yesmaximal, complemented
22#35532C212yesmaximal, complemented
23#35530C211yesmaximal, characteristic, complemented
24C2×#548C2212yes—
25C2×#547C2214yes—
26C2×#544C2212yes—
27C2×#537C2212yes—
28C2×#537C2211yescharacteristic
29C2×#536C2214yes—
30C2×#520C2212yes—
31C2×#520C2211yescharacteristic
32#2829C2214yes—
33#2823C2212yes—
34#2820C2214yes—
35#2816C2212yes—
36#2811C2211yescharacteristic
37#2808C2212yes—
38#2806C2214yes—
39#2806C2212yes—
40#2805C2212yes—
41#2803C2214yes—
42#2795C2214yes—
43#2792C2212yes—
44#2792C2214yes—
45#2777C2214yes—
46#2775C2214yes—
47#2773C2214yes—
48#2768C2214yes—
49#2768C2214yes—
50#2761C2214yes—
51#2757C2214yes—
52#2748C2214yes—
53#2741C2214yes—
54#2740C2214yes—
55#2734C2214yes—
56#2733C2212yes—
57#2733C2211yescharacteristic
58#2732C2212yes—
59#2731C2214yes—
60#2730C2214yes—
61#2730C2214yes—
62#2729C2214yes—
63#2724C2211yescharacteristic
64#2715C2214yes—
65#2709C2212yes—
66#2707C2214yes—
67#2705C2214yes—
68#2704C2214yes—
69#2694C2214yes—
70#2692C2214yes—
71#2690C2214yes—
72#2683C2212yes—
73#2683C2211yescharacteristic
74#2682C2214yes—
75#2682C2212yes—
76#2682C2214yes—
77#2681C2214yes—
78#2680C2212yes—
79#2677C2214yes—
80#2674C2214yes—
81#2674C2214yes—
82#2674C2214yes—
83#2672C2214yes—
84#2672C2214yes—
85#2672C2214yes—
86#2672C2214yes—
87#2671C2214yes—
88#2671C2214yes—
89#2671C2214yes—
90#2638C2212yes—
91#2632C2212yes—
92#2630C2214yes—
93#2630C2214yes—
94#2624C2214yes—
95#2618C2212yes—
96#2611C2214yes—
97#2610C2212yes—
98#2610C2214yes—
99#2609C2214yes—
100#2606C2214yes—
101#2606C2214yes—
102#2602C2214yes—
103#2602C2214yes—
104#2601C2214yes—
105#2599C2212yes—
106#2586C2214yes—
107#2586C2212yes—
108#2583C2212yes—
109#2583C2212yes—
110#2578C2214yes—
111#2574C2214yes—
112#2574C2214yes—
113#2573C2214yes—
114#2567C2214yes—
115#2566C2214yes—
116#2565C2214yes—
117#2558C2214yes—
118#2556C2214yes—
119#2555C2214yes—
120#2555C2214yes—
121#2555C2212yes—
122#2554C2214yes—
123#2553C2214yes—
124#2551C2212yes—
125#2549C2214yes—
126#2543C2212yes—
127#2542C2214yes—
128#2530C2214yes—
129#2522C2214yes—
130#2522C2214yes—
131#2518C2214yes—
132#2502C2212yes—
133#2501C2212yes—
134#2500C2212yes—
135#2499C2212yes—
136#2477C2214yes—
137#2477C2214yes—
138#2476C2214yes—
139#2474C2214yes—
140#2471C2214yes—
141#2471C2214yes—
142#2470C2214yes—
143#2465C2214yes—
144#2461C2214yes—
145#2461C2214yes—
146#2452C2214yes—
147#2451C2214yes—
148#2449C2214yes—
149#2449C2214yes—
150#2449C2214yes—
151#2449C2214yes—
152#2449C2214yes—
153#2443C2214yes—
154#2443C2214yes—
155#2443C2214yes—
156#2443C2214yes—
157#2441C2214yes—
158#2441C2214yes—
159#2440C2214yes—
160#2440C2214yes—
161#2440C2214yes—
162#2434C2214yes—
163#2432C2214yes—
164#2431C2214yes—
165#2431C2212yes—
166#2430C2214yes—
167#2430C2214yes—
168#2429C2214yes—
169#2428C2214yes—
170#2427C2214yes—
171#2426C2214yes—
172#2425C2214yes—
173#2423C2214yes—
174#2422C2214yes—
175#2422C2214yes—
176#2417C2214yes—
177#2415C2214yes—
178#2413C2214yes—
179#2409C2212yes—
180#2407C2214yes—
181#2407C2214yes—
182#2407C2214yes—
183#2406C2212yes—
184#2406C2212yes—
185#2399C2212yes—
186#2395C2214yes—
187#2388C2214yes—
188#2388C2212yes—
189C2×#395C2212yes—
190#2376C2212yes—
191#2374C2212yes—
192#2372C2214yes—
193#2372C2212yes—
194#2368C2214yes—
195#2367C2214yes—
196#2366C2212yes—
197#2363C2214yes—
198#2361C2214yes—
199#2360C2214yes—
200#2360C2214yes—
201#2359C2214yes—
202#2359C2214yes—
203#2353C2212yes—
204#2345C2214yes—
205#2337C2214yes—
206#2334C2214yes—
207#2333C2212yes—
208#2331C2214yes—
209#2329C2214yes—
210#2317C2211yescharacteristic
211#2317C2212yes—
212#2311C2212yes—
213#2311C2211yescharacteristic
214#2297C2211yescharacteristic
215#2297C2212yes—
216#2297C2211yescharacteristic
217#2296C2212yes—
218C2×#384C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2311yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C22×#41C2314yes—
224C23×Q8C2312yes—
225#548—48no—
226#547—416no—
227#544—48no—
228#537—48no—
229#537—44no—
230#536—416no—
231C2×C4⋊Q8C2314yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2314yes—
235C2×#127C2312yes—
236C2×#126C2314yes—
237C2×#125C2314yes—
238C2×#125C2314yes—
239C2×#124C2314yes—
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2312yes—
250C2×#123C2312yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×#121C2312yes—
270C2×#121C2314yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2312yes—
280#520—48no—
281#520—44no—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2312yes—
294C2×#117C2312yes—
295C2×#117C2311yescharacteristic
296C2×#117C2312yes—
297C2×#117C2311yescharacteristic
298C2×#117C2312yes—
299C2×#117C2314yes—
300C2×#117C2312yes—
301C2×#117C2314yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2312yes—
309C22×C4⋊C4C2314yes—
310C22×C42C2311yescharacteristic
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#399C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2312yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
339#398C2314yes—
340#398C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2312yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#397C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#395C2312yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2312yes—
375#395C2314yes—
376#395C2312yes—
377#395C2314yes—
378#395C2314yes—
379#395C2312yes—
380#395C2312yes—
381#395C2314yes—
382#395C2312yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2312yes—
389#394C2312yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2312yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2312yes—
409#393C2312yes—
410#393C2314yes—
411#392C2314yes—
412#392C2312yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2312yes—
427#391C2311yescharacteristic
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2311yescharacteristic
434#390C2312yes—
435#390C2314yes—
436#390C2312yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#390C2312yes—
443#390C2314yes—
444#390C2314yes—
445#390C2314yes—
446#390C2311yescharacteristic
447#390C2312yes—
448#390C2311yescharacteristic
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
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#387C2314yes—
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#386C2314yes—
528#386C2312yes—
529#386C2312yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2312yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2312yes—
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#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#384C2314yes—
575#384C2312yes—
576#384C2314yes—
577#384C2312yes—
578#384C2312yes—
579#383C2312yes—
580#383C2314yes—
581#382C2314yes—
582#382C2314yes—
583#382C2312yes—
584#381C2312yes—
585#381C2312yes—
586#380C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2314yes—
592#380C2314yes—
593#380C2314yes—
594#380C2312yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2312yes—
618#376C2314yes—
619#376C2312yes—
620C2×#95C2312yes—
621C2×#95C2314yes—
622C2×#41—28no—
623C2×#41—24no—
624C2×#41—44no—
625C2×#41—42no—
626C2×#41—42no—
627C2×#41—48no—
628C2×#41—44no—
629C2×#41—42no—
630C2×#41—48no—
631C2×#41—44no—
632C2×#41—42no—
633C2×#41—48no—
634C2×#41—48no—
635C2×#41—42no—
636C22×Q8—44no—
637C22×Q8—48no—
638C22×Q8C2412yes—
639C22×Q8C2411yescharacteristic
640C22×Q8C2414yes—
641C22×Q8C2414yes—
642C22×Q8C2411yescharacteristic
643C22×Q8C2412yes—
644C22×Q8C2412yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2414yes—
648C22×D4C2412yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2411yescharacteristic
653C22×D4C2412yes—
654C22×D4C2412yes—
655C22×D4C2414yes—
656C22×D4C2412yes—
657C22×D4C2411yescharacteristic
658C23×C4C2412yes—
659C23×C4C2411yescharacteristic
660C23×C4C2414yes—
661C23×C4C2414yes—
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2412yes—
665C23×C4C2414yes—
666C23×C4C2414yes—
667C23×C4C2412yes—
668C23×C4C2414yes—
669C23×C4C2412yes—
670C23×C4C2411yescharacteristic
671C23×C4C2412yes—
672C23×C4C2411yescharacteristic
673C23×C4C2412yes—
674C4⋊Q8—216no—
675C4⋊Q8—48no—
676C4⋊Q8—48no—
677C4⋊Q8—48no—
678#127—44no—
679#126—48no—
680#125—48no—
681#125—48no—
682#124—216no—
683#124—48no—
684#124—44no—
685#124—48no—
686#124—44no—
687#124—48no—
688#123—216no—
689#123—48no—
690#123—48no—
691#123—44no—
692#123—48no—
693#123—48no—
694#123—48no—
695#123—48no—
696#123—44no—
697#123—48no—
698C22⋊Q8—216no—
699C22⋊Q8—216no—
700C22⋊Q8—44no—
701C22⋊Q8—48no—
702C22⋊Q8—44no—
703C22⋊Q8—48no—
704C22⋊Q8—48no—
705C22⋊Q8—48no—
706C22⋊Q8—48no—
707C22⋊Q8—48no—
708C22⋊Q8—48no—
709C22⋊Q8—48no—
710C22⋊Q8—48no—
711C22⋊Q8—44no—
712#121—28no—
713#121—216no—
714#121—44no—
715#121—48no—
716#121—48no—
717#121—48no—
718#121—48no—
719#121—48no—
720#121—48no—
721#121—44no—
722#121—44no—
723C4×Q8—48no—
724C4×Q8—44no—
725C4×Q8—44no—
726C4×D4—28no—
727C4×D4—48no—
728C4×D4—48no—
729C4×D4—48no—
730C4×D4—48no—
731C4×D4—48no—
732C4×D4—44no—
733C4×D4—44no—
734C4×D4—48no—
735#117—28no—
736#117—42no—
737#117—42no—
738#117—44no—
739#117—48no—
740#117—44no—
741#117—44no—
742#117—48no—
743C2×C4⋊C4—216no—
744C2×C4⋊C4—44no—
745C2×C4⋊C4—42no—
746C2×C4⋊C4—44no—
747C2×C4⋊C4—42no—
748C2×C4⋊C4—44no—
749C2×C4⋊C4—48no—
750C2×C4⋊C4—44no—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C42—42no—
849C2×C42C2414yes—
850C2×C42C2412yes—
851C2×C42C2414yes—
852C2×C42C2412yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2412yes—
856C2×C42C2414yes—
857C2×C42C2412yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2412yes—
863C2×C42C2412yes—
864C2×C42C2411yescharacteristic
865C2×C42C2412yes—
866C2×C42C2411yescharacteristic
867#95C2412yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2412yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2412yes—
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—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911C24C2512yes—
912C24C2514yes—
913C24C2512yes—
914C24C2511yescharacteristic
915#41—432no—
916#41—416no—
917#41—88no—
918#41—832no—
919#41—816no—
920C2×Q8—22no—
921C2×Q8—28no—
922C2×Q8—28no—
923C2×Q8—28no—
924C2×Q8—22no—
925C2×Q8—42no—
926C2×Q8—42no—
927C2×Q8—42no—
928C2×Q8—41no—
929C2×Q8—41no—
930C2×Q8—44no—
931C2×Q8—44no—
932C2×Q8—41no—
933C2×Q8—44no—
934C2×Q8—42no—
935C2×Q8—44no—
936C2×Q8—44no—
937C2×Q8—41no—
938C2×Q8—816no—
939C2×Q82−1+418yes—
940C2×D4—24no—
941C2×D4—28no—
942C2×D4—24no—
943C2×D4—28no—
944C2×D4—28no—
945C2×D4—28no—
946C2×D4—24no—
947C2×D4—28no—
948C2×D4—28no—
949C2×D4—24no—
950C2×D4—28no—
951C2×D4—22no—
952C2×D4—42no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—41no—
957C2×D4—41no—
958C2×D4—42no—
959C2×D4—44no—
960C2×D4—41no—
961C2×D4—44no—
962C2×D4—42no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—42no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—41no—
973C2×D4—42no—
974C2×D4—42no—
975C2×D4—42no—
976C2×D4—42no—
977C2×D4H(5,𝔽2)14yes—
978C22×C4—24no—
979C22×C4—22no—
980C22×C4—24no—
981C22×C4—22no—
982C22×C4—24no—
983C22×C4—22no—
984C22×C4—24no—
985C22×C4—28no—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—28no—
989C22×C4—28no—
990C22×C4—28no—
991C22×C4—28no—
992C22×C4—24no—
993C22×C4—28no—
994C22×C4—28no—
995C22×C4—24no—
996C22×C4—28no—
997C22×C4—42no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—42no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—41no—
1012C22×C4—41no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2514yes—
1037C22×C4C2514yes—
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—28no—
1045C4⋊C4—24no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—24no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—41no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—41no—
1071C4⋊C4—44no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4H(5,𝔽2)18yes—
1092C22⋊C4—24no—
1093C22⋊C4—24no—
1094C22⋊C4—28no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—28no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C42—28no—
1138C42—28no—
1139C42—24no—
1140C42—28no—
1141C42—24no—
1142C42—41no—
1143C42—42no—
1144C42—41no—
1145C42—44no—
1146C42—44no—
1147C42—44no—
1148C42—42no—
1149C42—42no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C42—42no—
1154C42—42no—
1155C23—22no—
1156C23—24no—
1157C23—21no—
1158C23—24no—
1159C23—22no—
1160C23—21no—
1161C23—22no—
1162C23—22no—
1163C23—24no—
1164C23—24no—
1165C23—24no—
1166C23—24no—
1167C23—22no—
1168C23—24no—
1169C23—24no—
1170C23—24no—
1171C23—24no—
1172C23—22no—
1173C23—22no—
1174C23—24no—
1175C23C2×H(5,𝔽2)14yes—
1176C23#58512yes—
1177C23C2611yescharacteristic
1178Q8—48no—
1179Q8—48no—
1180Q8—44no—
1181Q8—88no—
1182Q8—88no—
1183Q8—82no—
1184Q8—84no—
1185D4—44no—
1186D4—416no—
1187D4—416no—
1188D4—48no—
1189D4—48no—
1190D4—88no—
1191D4—82no—
1192D4—88no—
1193D4—88no—
1194D4—84no—
1195D4—88no—
1196D4—84no—
1197D4—162no—
1198C2×C4—216no—
1199C2×C4—28no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—24no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—416no—
1248C2×C4—48no—
1249C2×C4—416no—
1250C2×C4—48no—
1251C2×C4—88no—
1252C2×C4—88no—
1253C2×C4—88no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—161no—
1258C2×C4—162no—
1259C2×C4—161no—
1260C2×C4—162no—
1261C2×C4C2×H(5,𝔽2)14yes—
1262C2×C4C2×H(5,𝔽2)12yes—
1263C2×C4C2×H(5,𝔽2)18yes—
1264C2×C4C2×2−1+418yes—
1265C2×C4C2×2−1+414yes—
1266C2×C4#58512yes—
1267C22—24no—
1268C22—24no—
1269C22—24no—
1270C22—22no—
1271C22—24no—
1272C22—41no—
1273C22—41no—
1274C22—42no—
1275C22—44no—
1276C22—44no—
1277C22—42no—
1278C22—44no—
1279C22—44no—
1280C22—42no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—42no—
1288C22—44no—
1289C22C22×H(5,𝔽2)11yescharacteristic
1290C22C22×H(5,𝔽2)12yes—
1291C22C22×2−1+412yes—
1292C22C2×#58511yescharacteristic
1293C22C2×#58511yescharacteristic
1294C4—28no—
1295C4—24no—
1296C4—24no—
1297C4—28no—
1298C4—22no—
1299C4—22no—
1300C4—44no—
1301C4—42no—
1302C4—42no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—44no—
1307C4—44no—
1308C4—44no—
1309C4—44no—
1310C4—42no—
1311C4—42no—
1312C4—44no—
1313C2—44no—
1314C2—42no—
1315C2—82no—
1316C2—84no—
1317C2#6281912yes—
1318C2#6282011yescharacteristic
1319C2#6301111yescharacteristic
1320C2#6303711yescharacteristic
1321C2#6303912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60048C2semidirect
2. #60046C2semidirect
3. #60044C2semidirect
4. #58588C2semidirect
5. #54859C2semidirect
6. #54850C2semidirect
7. #49703C2semidirect
8. #49635C2semidirect
9. #47795C2semidirect
10. #47752C2semidirect
11. #46620C2semidirect
12. #46423C2semidirect
13. #45091C2semidirect
14. #44758C2semidirect
15. #44441C2semidirect
16. #44435C2semidirect
17. #44181C2semidirect
18. #43779C2semidirect
19. #43553C2semidirect
20. #35740C2semidirect
21. #35715C2semidirect
22. #35532C2semidirect
23. #35530C2semidirect

Maximal subgroups

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

subgroupindex
#600482
#600462
#600442
#585882
#548592
#548502
#497032
#496352
#477952
#477522
#466202
#464232
#450912
#447582
#444412
#444352
#441812
#437792
#435532
#357402
#357152
#355322
#355302