Finite Group Databasebeta

← #8701644

Subgroups — #8701644

Order 512.

3933 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59879C212yesmaximal, complemented
2#59684C212yesmaximal
3#59463C212yesmaximal, complemented
4#59448C212yesmaximal, complemented
5#55897C214yesmaximal, complemented
6#55397C214yesmaximal, complemented
7#55286C214yesmaximal, complemented
8#52305C211yesmaximal, characteristic, complemented
9#51313C214yesmaximal, complemented
10#49401C214yesmaximal, complemented
11#49327C214yesmaximal, complemented
12#46022C211yesmaximal, characteristic, complemented
13#46014C211yesmaximal, characteristic
14#46013C211yesmaximal, characteristic
15#45278C212yesmaximal, complemented
16#45156C212yesmaximal, complemented
17#44967C212yesmaximal, complemented
18#42845C212yesmaximal, complemented
19#42538C212yesmaximal, complemented
20#42536C212yesmaximal
21#40107C212yesmaximal, complemented
22#40105C212yesmaximal, complemented
23#40105C212yesmaximal, complemented
24#37203C212yesmaximal, complemented
25#37164C212yesmaximal, complemented
26#37143C212yesmaximal, complemented
27#36447C211yesmaximal, characteristic, complemented
28#36313C211yesmaximal, characteristic, complemented
29#36300C211yesmaximal, characteristic
30#2863C2212yes—
31#2863C2212yes—
32#2862C2211yescharacteristic
33#2860C2212yes—
34#2859C2212yes—
35#2859C2211yescharacteristic
36#2858C2211yescharacteristic
37#2836C2214yes—
38#2836C2214yes—
39#2827C2214yes—
40#2822C2212yes—
41#2820C2212yes—
42#2820C2212yes—
43#2810C2211yescharacteristic
44#2809C2212yes—
45#2808C2212yes—
46#2805C2212yes—
47#2805C2214yes—
48#2802C2214yes—
49#2801C2214yes—
50#2800C2214yes—
51#2793C2214yes—
52#2793C2214yes—
53#2793C2214yes—
54#2793C2214yes—
55#2793C2214yes—
56#2792C2214yes—
57#2790C2214yes—
58#2790C2214yes—
59#2790C2214yes—
60#2789C2214yes—
61#2788C2214yes—
62#2783C2214yes—
63#2783C2214yes—
64#2783C2214yes—
65#2783C2214yes—
66#2774C2214yes—
67#2773C2214yes—
68#2773C2214yes—
69#2772C2214yes—
70#2771C2214yes—
71#2770C2214yes—
72#2768C2214yes—
73#2767C2212yes—
74#2767C2212yes—
75#2767C2212yes—
76#2766C2214yes—
77#2766C2214yes—
78#2765C2214yes—
79#2765C2214yes—
80#2762C2214yes—
81#2762C2214yes—
82#2761C2214yes—
83#2757C2214yes—
84#2754C2214yes—
85#2750C2214yes—
86#2746C2214yes—
87#2744C2214yes—
88#2739C2214yes—
89#2732C2212yes—
90#2727C2212yes—
91#2726C2211yescharacteristic
92#2726C2211yescharacteristic
93#2726C2211yescharacteristic
94#2724C2212yes—
95#2721C2214yes—
96#2721C2214yes—
97#2721C2214yes—
98#2719C2214yes—
99#2719C2212yes—
100#2719C2212yes—
101#2719C2212yes—
102#2715C2214yes—
103#2707C2214yes—
104#2707C2214yes—
105#2700C2214yes—
106#2698C2214yes—
107#2667C2214yes—
108#2667C2214yes—
109#2666C2214yes—
110#2654C2214yes—
111#2652C2214yes—
112#2652C2214yes—
113#2644C2212yes—
114#2643C2214yes—
115#2637C2214yes—
116#2633C2214yes—
117#2611C2214yes—
118#2594C2214yes—
119#2590C2214yes—
120#2589C2214yes—
121#2587C2214yes—
122#2587C2214yes—
123#2585C2214yes—
124#2577C2214yes—
125#2577C2214yes—
126#2577C2214yes—
127#2576C2214yes—
128#2575C2214yes—
129#2573C2214yes—
130#2573C2214yes—
131#2573C2214yes—
132#2571C2211yescharacteristic
133#2571C2212yes—
134#2570C2212yes—
135#2570C2212yes—
136#2568C2211yescharacteristic
137#2567C2211yescharacteristic
138#2566C2212yes—
139#2566C2212yes—
140#2565C2212yes—
141#2565C2212yes—
142#2558C2214yes—
143#2556C2214yes—
144#2552C2212yes—
145#2552C2211yescharacteristic
146#2550C2212yes—
147#2550C2212yes—
148#2548C2211yescharacteristic
149#2546C2211yescharacteristic
150#2545C2212yes—
151#2545C2212yes—
152#2545C2212yes—
153#2544C2212yes—
154#2530C2214yes—
155#2529C2214yes—
156#2528C2214yes—
157#2525C2214yes—
158#2525C2214yes—
159#2524C2214yes—
160#2524C2214yes—
161#2521C2214yes—
162#2520C2214yes—
163#2518C2214yes—
164#2518C2214yes—
165#2516C2214yes—
166#2515C2214yes—
167#2514C2212yes—
168#2514C2212yes—
169#2514C2212yes—
170#2514C2214yes—
171#2514C2212yes—
172#2513C2212yes—
173#2513C2212yes—
174#2513C2212yes—
175#2512C2212yes—
176#2512C2212yes—
177#2511C2212yes—
178#2508C2212yes—
179#2508C2212yes—
180#2508C2212yes—
181#2508C2214yes—
182#2507C2214yes—
183#2506C2212yes—
184#2506C2214yes—
185#2505C2214yes—
186#2497C2214yes—
187#2493C2214yes—
188#2478C2214yes—
189#2475C2214yes—
190#2474C2214yes—
191#2454C2212yes—
192#2454C2212yes—
193#2454C2212yes—
194#2453C2212yes—
195#2453C2212yes—
196#2453C2212yes—
197#2453C2212yes—
198#2453C2212yes—
199#2452C2212yes—
200#2451C2212yes—
201#2448C2212yes—
202#2448C2212yes—
203#2448C2212yes—
204#2448C2212yes—
205#2447C2212yes—
206#2447C2212yes—
207#2447C2212yes—
208#2446C2212yes—
209#2446C2212yes—
210#2445C2212yes—
211#2421C2214yes—
212#2419C2214yes—
213#2402C2212yes—
214#2402C2212yes—
215#2402C2212yes—
216#2382C2212yes—
217#2379C2212yes—
218#2379C2212yes—
219#2374C2214yes—
220#2369C2211yescharacteristic
221#2368C2214yes—
222#2367C2212yes—
223#2367C2212yes—
224#2366C2211yescharacteristic
225#2365C2212yes—
226#2365C2211yescharacteristic
227#2365C2212yes—
228#2365C2211yescharacteristic
229#2357C2212yes—
230#2356C2212yes—
231#2355C2212yes—
232#2354C2212yes—
233#2351C2212yes—
234Q8×C4⋊C4C2212yes—
235Q8×C4⋊C4C2211yescharacteristic
236Q8×C4⋊C4C2211yescharacteristic
237Q8×C4⋊C4C2212yes—
238#2349C2212yes—
239#2343C2214yes—
240#2336C2214yes—
241#2334C2214yes—
242#2334C2214yes—
243#2330C2212yes—
244#2327C2212yes—
245#2326C2212yes—
246C4×#125C2212yes—
247C4×#125C2212yes—
248C4×#125C2212yes—
249C4×#125C2212yes—
250C4×#125C2212yes—
251C4×#125C2211yescharacteristic
252C4×#125C2211yescharacteristic
253C4×#125C2211yescharacteristic
254C4×#124C2212yes—
255C4×#124C2212yes—
256#2295C2212yes—
257#2293C2212yes—
258C42×Q8C2211yescharacteristic
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×#127C2311yescharacteristic
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#125C2311yescharacteristic
267C2×#125C2311yescharacteristic
268C2×#125C2312yes—
269C2×#125C2311yescharacteristic
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#124C2312yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#123C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×#117C2314yes—
298#401C2314yes—
299#401C2314yes—
300#401C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2312yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2312yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2312yes—
326#400C2312yes—
327#400C2312yes—
328#400C2312yes—
329#400C2312yes—
330#400C2312yes—
331#400C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2312yes—
348#398C2314yes—
349#398C2312yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2312yes—
363#398C2312yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#393C2314yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2312yes—
448#389C2311yescharacteristic
449#389C2312yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2312yes—
454#389C2312yes—
455#389C2311yescharacteristic
456#389C2311yescharacteristic
457#389C2311yescharacteristic
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2311yescharacteristic
462#389C2311yescharacteristic
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
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#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#387C2312yes—
535#387C2312yes—
536#387C2314yes—
537#387C2312yes—
538#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2314yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
549#387C2312yes—
550#387C2314yes—
551#387C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#384C2311yescharacteristic
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2312yes—
623#384C2312yes—
624#384C2312yes—
625#384C2314yes—
626#384C2314yes—
627#383C2314yes—
628#383C2314yes—
629#383C2314yes—
630#383C2314yes—
631#383C2314yes—
632#382C2312yes—
633#382C2312yes—
634#382C2311yescharacteristic
635#382C2311yescharacteristic
636#382C2311yescharacteristic
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2314yes—
647#382C2314yes—
648#382C2314yes—
649#382C2314yes—
650#382C2314yes—
651#381C2314yes—
652#381C2314yes—
653#381C2314yes—
654#381C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706#376C2312yes—
707#376C2314yes—
708C2×#95C2314yes—
709C43C2312yes—
710C43C2311yescharacteristic
711C43C2312yes—
712C22×Q8C2412yes—
713C22×Q8C2411yescharacteristic
714C22×Q8C2412yes—
715C22×Q8C2412yes—
716C22×D4C2412yes—
717C22×D4C2412yes—
718C22×D4C2412yes—
719C23×C4C2414yes—
720C23×C4C2414yes—
721C23×C4C2414yes—
722C4⋊Q8—28no—
723C4⋊Q8—42no—
724C4⋊Q8—42no—
725C4⋊Q8—42no—
726#127—42no—
727#126—48no—
728#126—48no—
729#125—44no—
730#125—44no—
731#125—44no—
732#125—48no—
733#125—42no—
734#125—42no—
735#125—42no—
736#125—44no—
737#125—44no—
738#125—44no—
739#125—44no—
740#124—28no—
741#124—44no—
742#124—44no—
743#124—44no—
744#124—44no—
745#123—48no—
746C22⋊Q8—48no—
747C4×Q8—24no—
748C4×Q8—44no—
749C4×Q8—44no—
750C4×Q8—44no—
751C4×Q8—44no—
752C4×Q8—44no—
753C4×Q8—44no—
754C4×Q8—42no—
755C4×Q8—42no—
756C4×D4—44no—
757C4×D4—44no—
758C4×D4—44no—
759C4×D4—44no—
760#117—48no—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876C2×C42C2411yescharacteristic
877C2×C42C2412yes—
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2412yes—
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2414yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980C24C2514yes—
981C2×Q8—24no—
982C2×Q8—22no—
983C2×Q8—22no—
984C2×Q8—24no—
985C2×Q8—24no—
986C2×Q8—24no—
987C2×Q8—42no—
988C2×Q8—42no—
989C2×Q8—42no—
990C2×Q8—42no—
991C2×Q8—42no—
992C2×Q82−1+414yes—
993C2×D4—24no—
994C2×D4—24no—
995C2×D4—24no—
996C2×D4—24no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—42no—
1000C2×D4—42no—
1001C2×D4—42no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4C2511yescharacteristic
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2514yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C4⋊C4—24no—
1040C4⋊C4—22no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—24no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—28no—
1055C4⋊C4—22no—
1056C4⋊C4—22no—
1057C4⋊C4—22no—
1058C4⋊C4—24no—
1059C4⋊C4—22no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—42no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—42no—
1071C4⋊C4—44no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
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—42no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C42—24no—
1146C42—22no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—24no—
1151C42—24no—
1152C42—24no—
1153C42—24no—
1154C42—24no—
1155C42—24no—
1156C42—22no—
1157C42—22no—
1158C42—22no—
1159C42—22no—
1160C42—22no—
1161C42—41no—
1162C42—44no—
1163C42—42no—
1164C42—44no—
1165C42—42no—
1166C42—42no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—42no—
1174C42—42no—
1175C42—42no—
1176C42—44no—
1177C23—24no—
1178C23—24no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—24no—
1184C23C2611yescharacteristic
1185Q8—28no—
1186Q8—48no—
1187Q8—84no—
1188Q8—162no—
1189D4—48no—
1190D4—84no—
1191D4—162no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—88no—
1270C2×C4—164no—
1271C2×C4—164no—
1272C2×C4C2×2−1+414yes—
1273C2×C4C2×2−1+412yes—
1274C2×C4#58512yes—
1275C2×C4#58512yes—
1276C2×C4#58512yes—
1277C2×C4#58512yes—
1278C2×C4#58512yes—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22C22×2−1+411yescharacteristic
1287C22C2×#58511yescharacteristic
1288C22C2×#58511yescharacteristic
1289C22C2×#58511yescharacteristic
1290C22C2×#58511yescharacteristic
1291C22C2×#58511yescharacteristic
1292C222−1+611yescharacteristic
1293C4—24no—
1294C4—22no—
1295C4—22no—
1296C4—22no—
1297C4—44no—
1298C4—41no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—41no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—41no—
1311C4—44no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—44no—
1317C4—42no—
1318C4—42no—
1319C4—44no—
1320C4#355314yes—
1321C2—84no—
1322C2C2×#355311yescharacteristic
1323C2#6294911yescharacteristic
1324C2#6296411yescharacteristic
1325C2#6296411yescharacteristic
1326C2#6303111yescharacteristic
1327C2#6303411yescharacteristic
1328C2#6303611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59879C2semidirect
3. #59463C2semidirect
4. #59448C2semidirect
5. #55897C2semidirect
6. #55397C2semidirect
7. #55286C2semidirect
8. #52305C2semidirect
9. #51313C2semidirect
10. #49401C2semidirect
11. #49327C2semidirect
12. #46022C2semidirect
15. #45278C2semidirect
16. #45156C2semidirect
17. #44967C2semidirect
18. #42845C2semidirect
19. #42538C2semidirect
21. #40107C2semidirect
22. #40105C2semidirect
23. #40105C2semidirect
24. #37203C2semidirect
25. #37164C2semidirect
26. #37143C2semidirect
27. #36447C2semidirect
28. #36313C2semidirect

Maximal subgroups

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

subgroupindex
#598792
#596842
#594632
#594482
#558972
#553972
#552862
#523052
#513132
#494012
#493272
#460222
#460142
#460132
#452782
#451562
#449672
#428452
#425382
#425362
#401072
#401052
#372032
#371642
#371432
#364472
#363132
#363002