Finite Group Databasebeta

← #7650326

Subgroups — #7650326

Order 512.

4886 conjugacy classes of subgroups.

The subgroup lattice has 1385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42973C211yesmaximal, characteristic, complemented
2#42952C211yesmaximal, characteristic
3#42638C212yesmaximal, complemented
4#42537C212yesmaximal, complemented
5#42517C211yesmaximal, characteristic, complemented
6#42506C211yesmaximal, characteristic, complemented
7#41272C214yesmaximal, complemented
8#41217C214yesmaximal, complemented
9#41101C214yesmaximal, complemented
10#40984C214yesmaximal, complemented
11#40315C214yesmaximal, complemented
12#40202C212yesmaximal, complemented
13#39866C212yesmaximal, complemented
14#39456C214yesmaximal, complemented
15#39406C212yesmaximal, complemented
16#39348C212yesmaximal, complemented
17#37816C214yesmaximal, complemented
18#37766C214yesmaximal, complemented
19#35589C212yesmaximal, complemented
20#35580C212yesmaximal, complemented
21#35549C212yesmaximal, complemented
22#35296C211yesmaximal, characteristic, complemented
23#35239C212yesmaximal, complemented
24#34879C211yesmaximal, characteristic, complemented
25#34763C212yesmaximal, complemented
26#34305C212yesmaximal, complemented
27#34214C211yesmaximal, characteristic, complemented
28C2×#553C2212yes—
29C2×#542C2214yes—
30C2×#539C2214yes—
31C2×#533C2211yescharacteristic
32C2×#529C2214yes—
33#2864C2211yescharacteristic
34#2858C2211yescharacteristic
35#2857C2214yes—
36#2854C2212yes—
37#2851C2214yes—
38#2844C2212yes—
39#2838C2214yes—
40#2836C2214yes—
41#2834C2212yes—
42#2824C2212yes—
43#2823C2212yes—
44#2792C2212yes—
45#2790C2214yes—
46#2789C2214yes—
47#2785C2212yes—
48#2782C2212yes—
49#2766C2214yes—
50#2765C2214yes—
51#2763C2212yes—
52#2751C2214yes—
53#2747C2214yes—
54#2725C2214yes—
55#2722C2214yes—
56#2722C2214yes—
57#2721C2214yes—
58#2721C2214yes—
59#2720C2214yes—
60#2720C2214yes—
61#2718C2214yes—
62#2718C2214yes—
63#2717C2214yes—
64#2710C2214yes—
65#2693C2212yes—
66#2692C2214yes—
67#2690C2214yes—
68#2687C2214yes—
69#2681C2214yes—
70#2680C2214yes—
71#2680C2212yes—
72#2680C2214yes—
73#2677C2212yes—
74#2675C2212yes—
75#2674C2214yes—
76#2672C2214yes—
77#2672C2214yes—
78#2672C2214yes—
79#2671C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2664C2214yes—
83#2660C2214yes—
84#2655C2214yes—
85#2653C2214yes—
86#2644C2212yes—
87#2638C2214yes—
88#2638C2214yes—
89#2637C2214yes—
90#2636C2214yes—
91#2636C2214yes—
92#2632C2214yes—
93#2629C2214yes—
94#2628C2211yescharacteristic
95#2623C2214yes—
96#2619C2211yescharacteristic
97#2612C2212yes—
98#2607C2214yes—
99#2604C2214yes—
100#2595C2214yes—
101#2594C2214yes—
102#2589C2214yes—
103#2580C2212yes—
104#2576C2214yes—
105#2576C2214yes—
106#2574C2214yes—
107#2574C2212yes—
108#2573C2212yes—
109#2572C2212yes—
110#2571C2212yes—
111#2570C2214yes—
112#2567C2212yes—
113#2560C2214yes—
114#2557C2214yes—
115#2556C2214yes—
116#2553C2212yes—
117#2553C2214yes—
118#2552C2212yes—
119#2552C2212yes—
120#2551C2212yes—
121#2550C2212yes—
122#2550C2214yes—
123#2549C2214yes—
124#2542C2212yes—
125#2537C2212yes—
126#2536C2214yes—
127#2524C2212yes—
128#2521C2214yes—
129#2519C2214yes—
130#2518C2214yes—
131#2515C2212yes—
132#2512C2212yes—
133#2512C2212yes—
134#2512C2212yes—
135#2510C2214yes—
136#2508C2212yes—
137#2507C2212yes—
138#2507C2212yes—
139#2506C2212yes—
140#2506C2212yes—
141#2501C2212yes—
142#2500C2212yes—
143#2496C2212yes—
144#2494C2212yes—
145#2494C2212yes—
146#2491C2212yes—
147#2491C2212yes—
148#2490C2212yes—
149#2488C2214yes—
150#2486C2212yes—
151#2485C2212yes—
152#2479C2214yes—
153#2478C2214yes—
154#2476C2214yes—
155#2474C2214yes—
156#2474C2214yes—
157#2471C2214yes—
158#2468C2214yes—
159#2468C2212yes—
160#2467C2214yes—
161#2465C2214yes—
162#2462C2214yes—
163#2461C2214yes—
164#2457C2214yes—
165#2457C2212yes—
166#2455C2212yes—
167#2455C2212yes—
168#2454C2212yes—
169#2454C2212yes—
170#2452C2212yes—
171#2449C2214yes—
172#2445C2212yes—
173#2443C2214yes—
174#2442C2212yes—
175#2442C2212yes—
176#2441C2214yes—
177#2440C2212yes—
178#2440C2212yes—
179#2440C2212yes—
180#2440C2212yes—
181#2438C2214yes—
182#2438C2214yes—
183#2438C2214yes—
184#2428C2212yes—
185#2427C2214yes—
186#2425C2214yes—
187#2425C2214yes—
188#2423C2214yes—
189#2422C2214yes—
190#2422C2212yes—
191#2421C2214yes—
192#2420C2214yes—
193#2416C2212yes—
194#2416C2212yes—
195#2402C2211yescharacteristic
196#2398C2211yescharacteristic
197#2396C2214yes—
198#2396C2211yescharacteristic
199#2395C2214yes—
200#2392C2211yescharacteristic
201#2373C2214yes—
202#2370C2212yes—
203#2364C2214yes—
204#2361C2212yes—
205#2361C2212yes—
206#2360C2214yes—
207#2360C2214yes—
208#2359C2214yes—
209#2355C2214yes—
210#2354C2212yes—
211Q8×C4⋊C4C2214yes—
212#2349C2214yes—
213D4×C4⋊C4C2212yes—
214#2346C2212yes—
215#2345C2212yes—
216#2335C2214yes—
217#2334C2214yes—
218#2334C2214yes—
219#2331C2212yes—
220#2331C2211yescharacteristic
221#2330C2212yes—
222#2330C2212yes—
223#2330C2212yes—
224#2328C2211yescharacteristic
225#2326C2214yes—
226#2324C2212yes—
227#2319C2212yes—
228#2317C2211yescharacteristic
229#2317C2211yescharacteristic
230C4×C4⋊Q8C2212yes—
231C4×C4⋊Q8C2212yes—
232C4×#126C2212yes—
233C4×#123C2214yes—
234C4×#123C2212yes—
235C4×#121C2214yes—
236C4×#121C2212yes—
237C4×#121C2212yes—
238#2295C2211yescharacteristic
239#2293C2212yes—
240#2290C2212yes—
241#2290C2214yes—
242#2285C2212yes—
243C2×#384C2211yescharacteristic
244#2283C2212yes—
245#2275C2212yes—
246#2274C2211yescharacteristic
247#2274C2211yescharacteristic
248C42×D4C2211yescharacteristic
249C4×#117C2211yescharacteristic
250C2×C4×C4⋊C4C2212yes—
251#553—216no—
252#542—416no—
253#539—416no—
254#533—28no—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2314yes—
259C2×#127C2311yescharacteristic
260#529—416no—
261C2×#126C2312yes—
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#125C2314yes—
271C2×#125C2314yes—
272C2×#124C2314yes—
273C2×#124C2314yes—
274C2×#124C2314yes—
275C2×#123C2314yes—
276C2×#123C2312yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2314yes—
314C2×#117C2311yescharacteristic
315C2×#117C2311yescharacteristic
316C2×#117C2311yescharacteristic
317C2×#117C2314yes—
318C2×#117C2314yes—
319C2×#117C2314yes—
320C2×#117C2311yescharacteristic
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2311yescharacteristic
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2314yes—
326C22×C42C2311yescharacteristic
327C22×C42C2312yes—
328C22×C42C2314yes—
329#401C2314yes—
330#401C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2312yes—
336#400C2311yescharacteristic
337#400C2314yes—
338#400C2312yes—
339#400C2312yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#399C2312yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2311yescharacteristic
353#398C2314yes—
354#398C2311yescharacteristic
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2312yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2312yes—
379#397C2314yes—
380#397C2311yescharacteristic
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2312yes—
401#396C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2311yescharacteristic
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#394C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2314yes—
420#394C2312yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2311yescharacteristic
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2312yes—
430#393C2314yes—
431#393C2311yescharacteristic
432#393C2314yes—
433#393C2312yes—
434#393C2314yes—
435#393C2312yes—
436#393C2314yes—
437#392C2312yes—
438#392C2312yes—
439#392C2314yes—
440#392C2311yescharacteristic
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#390C2314yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2314yes—
455#390C2312yes—
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#388C2312yes—
495#388C2312yes—
496#388C2312yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2312yes—
501#388C2312yes—
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
538#387C2314yes—
539#387C2312yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2312yes—
559#387C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2312yes—
563#386C2312yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2312yes—
575#385C2312yes—
576#385C2312yes—
577#385C2312yes—
578#385C2312yes—
579#385C2312yes—
580#385C2314yes—
581#385C2312yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2312yes—
599#384C2312yes—
600#384C2314yes—
601#384C2312yes—
602#384C2314yes—
603#384C2312yes—
604#384C2312yes—
605#384C2312yes—
606#384C2312yes—
607#384C2314yes—
608#384C2312yes—
609#383C2312yes—
610#383C2312yes—
611#383C2312yes—
612#382C2312yes—
613#382C2314yes—
614#382C2311yescharacteristic
615#382C2312yes—
616#382C2312yes—
617#382C2312yes—
618#382C2314yes—
619#382C2311yescharacteristic
620#382C2314yes—
621#382C2314yes—
622#382C2312yes—
623#381C2312yes—
624#381C2312yes—
625#381C2312yes—
626#381C2314yes—
627#381C2314yes—
628#380C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2314yes—
635#380C2312yes—
636#380C2314yes—
637#380C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2312yes—
641#380C2312yes—
642#380C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687#376C2312yes—
688#376C2314yes—
689#376C2311yescharacteristic
690#376C2311yescharacteristic
691C2×#95C2314yes—
692C2×#95C2314yes—
693C43C2311yescharacteristic
694C43C2311yescharacteristic
695C22×Q8C2414yes—
696C22×Q8C2411yescharacteristic
697C22×Q8C2414yes—
698C22×Q8C2412yes—
699C22×D4C2412yes—
700C22×D4C2411yescharacteristic
701C22×D4C2412yes—
702C22×D4C2414yes—
703C22×D4C2414yes—
704C22×D4C2414yes—
705C22×D4C2412yes—
706C22×D4C2412yes—
707C23×C4C2412yes—
708C23×C4C2412yes—
709C23×C4C2412yes—
710C23×C4C2412yes—
711C23×C4C2411yescharacteristic
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2414yes—
715C23×C4C2414yes—
716C23×C4C2412yes—
717C23×C4C2412yes—
718C23×C4C2414yes—
719C4⋊Q8—28no—
720C4⋊Q8—42no—
721C4⋊Q8—44no—
722C4⋊Q8—48no—
723#127—42no—
724#126—216no—
725#126—28no—
726#126—216no—
727#126—48no—
728#126—48no—
729#126—48no—
730#125—28no—
731#125—28no—
732#125—48no—
733#125—48no—
734#125—48no—
735#124—216no—
736#124—48no—
737#124—48no—
738#123—216no—
739#123—28no—
740#123—216no—
741#123—48no—
742#123—48no—
743#123—48no—
744#123—48no—
745#123—48no—
746C22⋊Q8—216no—
747C22⋊Q8—48no—
748C22⋊Q8—48no—
749C22⋊Q8—48no—
750C22⋊Q8—48no—
751C22⋊Q8—48no—
752C22⋊Q8—48no—
753C22⋊Q8—48no—
754#121—28no—
755#121—28no—
756#121—216no—
757#121—48no—
758#121—48no—
759#121—48no—
760#121—44no—
761C4×Q8—216no—
762C4×Q8—42no—
763C4×Q8—48no—
764C4×Q8—48no—
765C4×D4—28no—
766C4×D4—28no—
767C4×D4—28no—
768C4×D4—216no—
769C4×D4—28no—
770C4×D4—48no—
771C4×D4—44no—
772C4×D4—42no—
773C4×D4—48no—
774C4×D4—48no—
775C4×D4—48no—
776C4×D4—48no—
777#117—24no—
778#117—24no—
779#117—42no—
780#117—48no—
781#117—48no—
782#117—48no—
783#117#4118yes—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—42no—
786C2×C4⋊C4—44no—
787C2×C4⋊C4—42no—
788C2×C4⋊C4—48no—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C42—24no—
896C2×C42—28no—
897C2×C42—48no—
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2411yescharacteristic
946#95C2411yescharacteristic
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2411yescharacteristic
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2411yescharacteristic
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991C24C2514yes—
992C24C2511yescharacteristic
993C24C2512yes—
994C2×Q8—28no—
995C2×Q8—28no—
996C2×Q8—44no—
997C2×Q8—41no—
998C2×Q8—42no—
999C2×Q8—44no—
1000C2×Q8—44no—
1001C2×Q8—44no—
1002C2×Q8—42no—
1003C2×Q8—44no—
1004C2×D4—24no—
1005C2×D4—24no—
1006C2×D4—24no—
1007C2×D4—28no—
1008C2×D4—28no—
1009C2×D4—28no—
1010C2×D4—28no—
1011C2×D4—24no—
1012C2×D4—24no—
1013C2×D4—24no—
1014C2×D4—41no—
1015C2×D4—44no—
1016C2×D4—42no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—42no—
1023C2×D4—42no—
1024C2×D4—44no—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—24no—
1028C22×C4—24no—
1029C22×C4—28no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—28no—
1038C22×C4—28no—
1039C22×C4—28no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4C2×#4114yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2512yes—
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2511yescharacteristic
1077C22×C4C2511yescharacteristic
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—41no—
1121C4⋊C4—41no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—41no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—41no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4C2×#4118yes—
1144C22⋊C4—24no—
1145C22⋊C4—24no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—24no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—24no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—24no—
1163C22⋊C4—28no—
1164C22⋊C4—42no—
1165C22⋊C4—44no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—41no—
1173C22⋊C4—41no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—42no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4C2×#4118yes—
1188C22⋊C4H(5,𝔽2)18yes—
1189C42—24no—
1190C42—22no—
1191C42—22no—
1192C42—24no—
1193C42—24no—
1194C42—28no—
1195C42—28no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—22no—
1202C42—22no—
1203C42—22no—
1204C42—24no—
1205C42—44no—
1206C42—44no—
1207C42—42no—
1208C42—42no—
1209C42—44no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C42—44no—
1214C42C2×#4118yes—
1215C422−1+414yes—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—21no—
1220C23—22no—
1221C23—21no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—24no—
1230C23—24no—
1231C23—24no—
1232C23—24no—
1233C23C22×#4112yes—
1234C23C2×H(5,𝔽2)14yes—
1235C23C2611yescharacteristic
1236Q8—416no—
1237Q8—82no—
1238Q8—162no—
1239Q8—164no—
1240D4—416no—
1241D4—48no—
1242D4—44no—
1243D4—48no—
1244D4—88no—
1245D4—88no—
1246D4—162no—
1247D4—162no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—28no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—48no—
1310C2×C4—48no—
1311C2×C4—48no—
1312C2×C4—48no—
1313C2×C4—88no—
1314C2×C4—88no—
1315C2×C4—88no—
1316C2×C4—88no—
1317C2×C4—162no—
1318C2×C4—164no—
1319C2×C4—162no—
1320C2×C4C22×#4112yes—
1321C2×C4C22×#4118yes—
1322C2×C4C22×#4112yes—
1323C2×C4C2×H(5,𝔽2)14yes—
1324C2×C4C2×H(5,𝔽2)14yes—
1325C2×C4C2×2−1+414yes—
1326C2×C4C2×2−1+412yes—
1327C2×C4#58512yes—
1328C22—24no—
1329C22—24no—
1330C22—24no—
1331C22—24no—
1332C22—22no—
1333C22—42no—
1334C22—41no—
1335C22—41no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22C23×#4111yescharacteristic
1348C22C22×H(5,𝔽2)12yes—
1349C22C22×2−1+411yescharacteristic
1350C22C2×#58511yescharacteristic
1351C222−1+612yes—
1352C4—24no—
1353C4—28no—
1354C4—24no—
1355C4—24no—
1356C4—22no—
1357C4—42no—
1358C4—42no—
1359C4—44no—
1360C4—42no—
1361C4—44no—
1362C4—44no—
1363C4—44no—
1364C4—42no—
1365C4—44no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—44no—
1374C4—42no—
1375C4#346114yes—
1376C2—42no—
1377C2—44no—
1378C2—84no—
1379C2C2×#346111yescharacteristic
1380C2#6283411yescharacteristic
1381C2#6289111yescharacteristic
1382C2#6291512yes—
1383C2#6298512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42952C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42973C2semidirect
3. #42638C2semidirect
4. #42537C2semidirect
5. #42517C2semidirect
6. #42506C2semidirect
7. #41272C2semidirect
8. #41217C2semidirect
9. #41101C2semidirect
10. #40984C2semidirect
11. #40315C2semidirect
12. #40202C2semidirect
13. #39866C2semidirect
14. #39456C2semidirect
15. #39406C2semidirect
16. #39348C2semidirect
17. #37816C2semidirect
18. #37766C2semidirect
19. #35589C2semidirect
20. #35580C2semidirect
21. #35549C2semidirect
22. #35296C2semidirect
23. #35239C2semidirect
24. #34879C2semidirect
25. #34763C2semidirect
26. #34305C2semidirect
27. #34214C2semidirect

Maximal subgroups

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

subgroupindex
#429732
#429522
#426382
#425372
#425172
#425062
#412722
#412172
#411012
#409842
#403152
#402022
#398662
#394562
#394062
#393482
#378162
#377662
#355892
#355802
#355492
#352962
#352392
#348792
#347632
#343052
#342142