Finite Group Databasebeta

← #8701634

Subgroups — #8701634

Order 512.

4213 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59877C212yesmaximal, complemented
2#59682C212yesmaximal, complemented
3#59459C212yesmaximal, complemented
4#59435C212yesmaximal, complemented
5#58617C214yesmaximal, complemented
6#56008C214yesmaximal, complemented
7#55895C214yesmaximal, complemented
8#52305C211yesmaximal, characteristic, complemented
9#51331C214yesmaximal, complemented
10#49195C214yesmaximal, complemented
11#48966C214yesmaximal, complemented
12#46013C211yesmaximal, characteristic
13#46006C211yesmaximal, characteristic, complemented
14#45998C211yesmaximal, characteristic
15#45213C212yesmaximal, complemented
16#45083C212yesmaximal, complemented
17#44969C212yesmaximal
18#42837C212yesmaximal, complemented
19#42837C212yesmaximal, complemented
20#42733C212yesmaximal, complemented
21#40191C212yesmaximal, complemented
22#39399C212yesmaximal, complemented
23#39001C212yesmaximal
24#37191C212yesmaximal, complemented
25#37153C212yesmaximal, complemented
26#37137C212yesmaximal, complemented
27#36447C211yesmaximal, characteristic, complemented
28#36313C211yesmaximal, characteristic, complemented
29#36300C211yesmaximal, characteristic
30C2×#563C2212yes—
31C2×#541C2214yes—
32#2863C2212yes—
33#2862C2211yescharacteristic
34#2860C2212yes—
35#2860C2212yes—
36#2859C2212yes—
37#2859C2211yescharacteristic
38#2858C2211yescharacteristic
39#2844C2212yes—
40#2838C2214yes—
41#2838C2214yes—
42#2833C2214yes—
43#2820C2212yes—
44#2820C2212yes—
45#2810C2211yescharacteristic
46#2808C2212yes—
47#2805C2212yes—
48#2795C2214yes—
49#2792C2214yes—
50#2792C2214yes—
51#2790C2214yes—
52#2790C2214yes—
53#2788C2214yes—
54#2788C2214yes—
55#2780C2214yes—
56#2779C2214yes—
57#2775C2214yes—
58#2775C2214yes—
59#2774C2214yes—
60#2773C2214yes—
61#2772C2214yes—
62#2771C2214yes—
63#2771C2214yes—
64#2767C2212yes—
65#2767C2212yes—
66#2767C2212yes—
67#2763C2214yes—
68#2762C2214yes—
69#2761C2214yes—
70#2758C2214yes—
71#2746C2214yes—
72#2738C2214yes—
73#2738C2214yes—
74#2737C2214yes—
75#2734C2212yes—
76#2732C2212yes—
77#2729C2214yes—
78#2727C2212yes—
79#2726C2211yescharacteristic
80#2726C2211yescharacteristic
81#2726C2211yescharacteristic
82#2725C2214yes—
83#2725C2214yes—
84#2723C2214yes—
85#2723C2214yes—
86#2721C2214yes—
87#2720C2214yes—
88#2720C2214yes—
89#2720C2214yes—
90#2719C2212yes—
91#2719C2214yes—
92#2719C2212yes—
93#2719C2212yes—
94#2718C2214yes—
95#2716C2214yes—
96#2713C2214yes—
97#2713C2214yes—
98#2704C2214yes—
99#2700C2214yes—
100#2695C2214yes—
101#2690C2214yes—
102#2690C2214yes—
103#2690C2214yes—
104#2689C2214yes—
105#2689C2214yes—
106#2689C2214yes—
107#2683C2212yes—
108#2674C2214yes—
109#2666C2214yes—
110#2664C2214yes—
111#2664C2214yes—
112#2654C2214yes—
113#2653C2214yes—
114#2650C2214yes—
115#2650C2214yes—
116#2645C2212yes—
117#2642C2214yes—
118#2637C2214yes—
119#2611C2214yes—
120#2611C2214yes—
121#2608C2214yes—
122#2604C2214yes—
123#2604C2214yes—
124#2601C2214yes—
125#2596C2214yes—
126#2595C2214yes—
127#2594C2214yes—
128#2594C2214yes—
129#2593C2214yes—
130#2587C2214yes—
131#2586C2214yes—
132#2586C2214yes—
133#2584C2214yes—
134#2574C2214yes—
135#2571C2212yes—
136#2571C2211yescharacteristic
137#2571C2212yes—
138#2568C2211yescharacteristic
139#2567C2212yes—
140#2567C2212yes—
141#2567C2211yescharacteristic
142#2567C2214yes—
143#2563C2212yes—
144#2556C2214yes—
145#2552C2211yescharacteristic
146#2552C2212yes—
147#2552C2212yes—
148#2551C2212yes—
149#2551C2212yes—
150#2550C2214yes—
151#2549C2214yes—
152#2548C2211yescharacteristic
153#2546C2211yescharacteristic
154#2545C2212yes—
155#2545C2212yes—
156#2545C2212yes—
157#2544C2212yes—
158#2542C2212yes—
159#2529C2214yes—
160#2528C2214yes—
161#2528C2214yes—
162#2525C2214yes—
163#2524C2214yes—
164#2521C2214yes—
165#2515C2214yes—
166#2514C2212yes—
167#2514C2212yes—
168#2513C2212yes—
169#2512C2212yes—
170#2512C2212yes—
171#2512C2212yes—
172#2512C2212yes—
173#2511C2212yes—
174#2511C2212yes—
175#2511C2212yes—
176#2508C2214yes—
177#2508C2212yes—
178#2506C2212yes—
179#2506C2212yes—
180#2506C2214yes—
181#2506C2212yes—
182#2505C2214yes—
183#2496C2214yes—
184#2495C2214yes—
185#2492C2214yes—
186#2488C2214yes—
187#2475C2214yes—
188#2474C2214yes—
189#2470C2214yes—
190#2469C2214yes—
191#2460C2214yes—
192#2454C2212yes—
193#2453C2212yes—
194#2452C2212yes—
195#2452C2212yes—
196#2452C2212yes—
197#2451C2212yes—
198#2451C2212yes—
199#2451C2212yes—
200#2451C2212yes—
201#2451C2212yes—
202#2448C2212yes—
203#2448C2212yes—
204#2448C2212yes—
205#2448C2212yes—
206#2447C2212yes—
207#2447C2212yes—
208#2447C2212yes—
209#2446C2212yes—
210#2446C2212yes—
211#2445C2212yes—
212#2441C2214yes—
213#2438C2214yes—
214#2438C2214yes—
215#2402C2212yes—
216#2402C2212yes—
217#2402C2212yes—
218#2382C2212yes—
219#2379C2212yes—
220#2373C2214yes—
221#2370C2214yes—
222#2369C2211yescharacteristic
223#2367C2212yes—
224#2367C2212yes—
225#2366C2211yescharacteristic
226#2365C2212yes—
227#2365C2212yes—
228#2365C2211yescharacteristic
229#2365C2211yescharacteristic
230#2356C2212yes—
231#2356C2212yes—
232#2354C2212yes—
233#2354C2212yes—
234#2351C2212yes—
235Q8×C4⋊C4C2212yes—
236Q8×C4⋊C4C2212yes—
237Q8×C4⋊C4C2211yescharacteristic
238Q8×C4⋊C4C2211yescharacteristic
239#2349C2212yes—
240#2346C2214yes—
241#2332C2214yes—
242#2331C2212yes—
243#2326C2212yes—
244#2326C2212yes—
245#2318C2214yes—
246C4×C4⋊Q8C2212yes—
247C4×C4⋊Q8C2212yes—
248C4×#125C2212yes—
249C4×#125C2212yes—
250C4×#125C2212yes—
251C4×#125C2212yes—
252C4×#125C2211yescharacteristic
253C4×#125C2211yescharacteristic
254C4×#125C2211yescharacteristic
255C4×#124C2212yes—
256#2295C2212yes—
257#2293C2212yes—
258C42×Q8C2211yescharacteristic
259#563—48no—
260#541—416no—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2314yes—
269C2×#127C2311yescharacteristic
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2311yescharacteristic
277C2×#125C2312yes—
278C2×#125C2311yescharacteristic
279C2×#125C2311yescharacteristic
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#123C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×#117C2314yes—
313C2×#117C2314yes—
314#401C2314yes—
315#401C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2312yes—
327#400C2312yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#389C2311yescharacteristic
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2311yescharacteristic
476#389C2311yescharacteristic
477#389C2311yescharacteristic
478#389C2312yes—
479#389C2312yes—
480#389C2311yescharacteristic
481#389C2311yescharacteristic
482#389C2314yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2312yes—
563#387C2314yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2314yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
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#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#384C2312yes—
628#384C2312yes—
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2312yes—
632#384C2314yes—
633#384C2314yes—
634#384C2312yes—
635#384C2312yes—
636#384C2311yescharacteristic
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#382C2311yescharacteristic
641#382C2312yes—
642#382C2311yescharacteristic
643#382C2311yescharacteristic
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2314yes—
651#382C2314yes—
652#382C2314yes—
653#382C2312yes—
654#382C2312yes—
655#381C2314yes—
656#381C2314yes—
657#381C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707#376C2312yes—
708#376C2314yes—
709#376C2314yes—
710C2×#95C2314yes—
711C43C2312yes—
712C43C2311yescharacteristic
713C43C2312yes—
714C22×Q8C2412yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2414yes—
718C22×Q8C2414yes—
719C22×Q8C2412yes—
720C22×D4C2412yes—
721C22×D4C2412yes—
722C22×D4C2412yes—
723C23×C4C2414yes—
724C23×C4C2414yes—
725C23×C4C2414yes—
726C4⋊Q8—28no—
727C4⋊Q8—44no—
728C4⋊Q8—44no—
729C4⋊Q8—42no—
730C4⋊Q8—42no—
731C4⋊Q8—48no—
732C4⋊Q8—42no—
733C4⋊Q8—48no—
734#127—42no—
735#126—216no—
736#126—48no—
737#126—48no—
738#126—48no—
739#126—48no—
740#125—28no—
741#125—24no—
742#125—28no—
743#125—24no—
744#125—44no—
745#125—42no—
746#125—48no—
747#125—48no—
748#125—48no—
749#125—44no—
750#125—44no—
751#125—48no—
752#124—28no—
753#124—44no—
754#124—44no—
755#124—44no—
756#124—44no—
757#123—48no—
758C22⋊Q8—48no—
759C22⋊Q8—48no—
760C22⋊Q8—48no—
761C22⋊Q8—48no—
762C22⋊Q8—48no—
763C4×Q8—24no—
764C4×Q8—28no—
765C4×Q8—48no—
766C4×Q8—44no—
767C4×Q8—44no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×Q8—44no—
771C4×Q8—42no—
772C4×Q8—42no—
773C4×D4—28no—
774C4×D4—44no—
775C4×D4—44no—
776C4×D4—44no—
777#117—48no—
778#117—48no—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2411yescharacteristic
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2411yescharacteristic
918C2×C42C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996C24C2514yes—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—22no—
1000C2×Q8—22no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—44no—
1004C2×Q8—42no—
1005C2×Q8—44no—
1006C2×Q8—42no—
1007C2×Q8—44no—
1008C2×Q8—44no—
1009C2×Q8—44no—
1010C2×Q8—42no—
1011C2×Q8—42no—
1012C2×Q8—44no—
1013C2×Q8—42no—
1014C2×Q82−1+414yes—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—24no—
1018C2×D4—24no—
1019C2×D4—42no—
1020C2×D4—42no—
1021C2×D4—42no—
1022C2×D4—42no—
1023C2×D4—42no—
1024C22×C4—28no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2512yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C4⋊C4—24no—
1062C4⋊C4—28no—
1063C4⋊C4—22no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—22no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—22no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—22no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—41no—
1096C4⋊C4—42no—
1097C4⋊C4—41no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—41no—
1101C4⋊C4—41no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4H(5,𝔽2)14yes—
1143C4⋊C42−1+414yes—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C42—28no—
1170C42—24no—
1171C42—24no—
1172C42—28no—
1173C42—22no—
1174C42—24no—
1175C42—24no—
1176C42—22no—
1177C42—24no—
1178C42—24no—
1179C42—22no—
1180C42—24no—
1181C42—24no—
1182C42—24no—
1183C42—24no—
1184C42—24no—
1185C42—24no—
1186C42—22no—
1187C42—22no—
1188C42—22no—
1189C42—41no—
1190C42—42no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—42no—
1195C42—42no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—42no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23C2611yescharacteristic
1209Q8—28no—
1210Q8—48no—
1211Q8—84no—
1212Q8—88no—
1213Q8—164no—
1214Q8—162no—
1215D4—48no—
1216D4—84no—
1217D4—162no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—88no—
1294C2×C4—88no—
1295C2×C4—164no—
1296C2×C4C2×H(5,𝔽2)14yes—
1297C2×C4C2×H(5,𝔽2)12yes—
1298C2×C4C2×2−1+412yes—
1299C2×C4C2×2−1+414yes—
1300C2×C4C2×2−1+414yes—
1301C2×C4C2×2−1+412yes—
1302C2×C4#58512yes—
1303C2×C4#58512yes—
1304C2×C4#58512yes—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22C22×H(5,𝔽2)11yescharacteristic
1313C22C22×2−1+411yescharacteristic
1314C22C22×2−1+411yescharacteristic
1315C22C2×#58511yescharacteristic
1316C22C2×#58511yescharacteristic
1317C22C2×#58511yescharacteristic
1318C222−1+611yescharacteristic
1319C4—24no—
1320C4—24no—
1321C4—24no—
1322C4—22no—
1323C4—22no—
1324C4—22no—
1325C4—44no—
1326C4—41no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—44no—
1333C4—41no—
1334C4—44no—
1335C4—41no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—44no—
1344C4—44no—
1345C4—42no—
1346C4#355314yes—
1347C2—84no—
1348C2C2×#355311yescharacteristic
1349C2#6294911yescharacteristic
1350C2#6295911yescharacteristic
1351C2#6296011yescharacteristic
1352C2#6302511yescharacteristic
1353C2#6303511yescharacteristic
1354C2#6303711yescharacteristic
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. #59877C2semidirect
2. #59682C2semidirect
3. #59459C2semidirect
4. #59435C2semidirect
5. #58617C2semidirect
6. #56008C2semidirect
7. #55895C2semidirect
8. #52305C2semidirect
9. #51331C2semidirect
10. #49195C2semidirect
11. #48966C2semidirect
13. #46006C2semidirect
15. #45213C2semidirect
16. #45083C2semidirect
18. #42837C2semidirect
19. #42837C2semidirect
20. #42733C2semidirect
21. #40191C2semidirect
22. #39399C2semidirect
24. #37191C2semidirect
25. #37153C2semidirect
26. #37137C2semidirect
27. #36447C2semidirect
28. #36313C2semidirect

Maximal subgroups

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

subgroupindex
#598772
#596822
#594592
#594352
#586172
#560082
#558952
#523052
#513312
#491952
#489662
#460132
#460062
#459982
#452132
#450832
#449692
#428372
#427332
#401912
#393992
#390012
#371912
#371532
#371372
#364472
#363132
#363002