Finite Group Databasebeta

← #8757564

Subgroups — #8757564

Order 512.

4778 conjugacy classes of subgroups.

The subgroup lattice has 1421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58887C212yesmaximal, complemented
2#57272C214yesmaximal, complemented
3#56927C214yesmaximal, complemented
4#56530C212yesmaximal, complemented
5#56419C212yesmaximal, complemented
6#55615C212yesmaximal, complemented
7#55604C212yesmaximal, complemented
8#53893C212yesmaximal, complemented
9#53794C212yesmaximal, complemented
10#53492C212yesmaximal, complemented
11#51509C214yesmaximal, complemented
12#50106C214yesmaximal, complemented
13#49704C214yesmaximal, complemented
14#47801C212yesmaximal, complemented
15#47788C212yesmaximal, complemented
16#46972C212yesmaximal, complemented
17#46966C212yesmaximal, complemented
18#46417C214yesmaximal, complemented
19#46226C212yesmaximal, complemented
20#46224C212yesmaximal, complemented
21#46224C212yesmaximal, complemented
22#45989C212yesmaximal, complemented
23#45986C212yesmaximal, complemented
24#45984C212yesmaximal, complemented
25#35328C211yesmaximal, characteristic, complemented
26#35200C211yesmaximal, characteristic, complemented
27#35190C211yesmaximal, characteristic, complemented
28C2×#562C2212yes—
29C2×#542C2214yes—
30C2×#537C2212yes—
31C2×#533C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2851C2212yes—
36#2851C2212yes—
37#2850C2212yes—
38#2850C2212yes—
39#2850C2212yes—
40#2850C2212yes—
41#2844C2212yes—
42#2836C2214yes—
43#2833C2212yes—
44#2832C2214yes—
45#2830C2212yes—
46#2825C2214yes—
47#2823C2212yes—
48#2820C2212yes—
49#2820C2212yes—
50#2819C2212yes—
51#2819C2212yes—
52#2815C2214yes—
53#2813C2214yes—
54#2800C2214yes—
55#2792C2212yes—
56#2790C2214yes—
57#2786C2214yes—
58#2784C2214yes—
59#2782C2212yes—
60#2779C2214yes—
61#2778C2214yes—
62#2778C2214yes—
63#2775C2214yes—
64#2773C2214yes—
65#2769C2212yes—
66#2766C2214yes—
67#2765C2214yes—
68#2762C2214yes—
69#2759C2214yes—
70#2758C2214yes—
71#2757C2214yes—
72#2749C2214yes—
73#2749C2214yes—
74#2747C2214yes—
75#2743C2214yes—
76#2737C2214yes—
77#2737C2214yes—
78#2733C2212yes—
79#2730C2214yes—
80#2729C2214yes—
81#2729C2214yes—
82#2729C2214yes—
83#2728C2212yes—
84#2724C2212yes—
85#2723C2214yes—
86#2717C2214yes—
87#2714C2214yes—
88#2714C2214yes—
89#2712C2214yes—
90#2710C2214yes—
91#2703C2214yes—
92#2703C2214yes—
93#2703C2214yes—
94#2700C2214yes—
95#2699C2212yes—
96#2699C2214yes—
97#2698C2214yes—
98#2696C2214yes—
99#2696C2214yes—
100#2695C2214yes—
101#2692C2214yes—
102#2691C2214yes—
103#2688C2214yes—
104#2688C2214yes—
105#2686C2214yes—
106#2683C2214yes—
107#2683C2214yes—
108#2681C2214yes—
109#2681C2214yes—
110#2680C2212yes—
111#2676C2214yes—
112#2676C2214yes—
113#2676C2214yes—
114#2676C2214yes—
115#2676C2214yes—
116#2676C2214yes—
117#2675C2214yes—
118#2675C2214yes—
119#2674C2214yes—
120#2674C2214yes—
121#2673C2214yes—
122#2673C2214yes—
123#2673C2214yes—
124#2671C2214yes—
125#2671C2214yes—
126#2661C2214yes—
127#2653C2214yes—
128#2649C2214yes—
129#2643C2214yes—
130#2638C2212yes—
131#2638C2212yes—
132#2635C2212yes—
133#2635C2212yes—
134#2631C2214yes—
135#2631C2214yes—
136#2621C2211yescharacteristic
137#2621C2211yescharacteristic
138#2619C2211yescharacteristic
139#2619C2211yescharacteristic
140#2610C2214yes—
141#2609C2212yes—
142#2604C2214yes—
143#2599C2212yes—
144#2599C2212yes—
145#2598C2212yes—
146#2598C2212yes—
147#2595C2214yes—
148#2582C2212yes—
149#2576C2214yes—
150#2573C2214yes—
151#2572C2212yes—
152#2568C2211yescharacteristic
153#2567C2211yescharacteristic
154#2564C2214yes—
155#2564C2214yes—
156#2563C2211yescharacteristic
157#2559C2214yes—
158#2555C2212yes—
159#2555C2214yes—
160#2555C2214yes—
161#2549C2214yes—
162#2548C2211yescharacteristic
163#2547C2211yescharacteristic
164#2546C2211yescharacteristic
165#2543C2212yes—
166#2543C2212yes—
167#2543C2212yes—
168#2543C2212yes—
169#2543C2214yes—
170#2542C2211yescharacteristic
171#2541C2211yescharacteristic
172#2536C2212yes—
173#2536C2212yes—
174#2535C2212yes—
175#2535C2212yes—
176#2530C2214yes—
177#2527C2214yes—
178#2510C2214yes—
179#2500C2212yes—
180#2499C2212yes—
181#2493C2214yes—
182#2485C2212yes—
183#2485C2212yes—
184#2481C2214yes—
185#2477C2214yes—
186#2474C2214yes—
187#2471C2214yes—
188#2471C2214yes—
189#2469C2214yes—
190#2467C2214yes—
191#2465C2214yes—
192#2465C2214yes—
193#2465C2214yes—
194#2458C2214yes—
195#2456C2214yes—
196#2456C2214yes—
197#2455C2214yes—
198#2455C2214yes—
199#2450C2214yes—
200#2450C2214yes—
201#2450C2214yes—
202#2449C2214yes—
203#2444C2214yes—
204#2438C2214yes—
205#2432C2212yes—
206#2431C2212yes—
207#2430C2214yes—
208#2430C2214yes—
209#2428C2214yes—
210#2426C2214yes—
211#2426C2214yes—
212#2426C2214yes—
213#2425C2214yes—
214#2425C2214yes—
215#2422C2214yes—
216#2414C2214yes—
217#2407C2214yes—
218#2407C2212yes—
219#2407C2214yes—
220#2407C2212yes—
221#2382C2212yes—
222#2379C2212yes—
223#2379C2212yes—
224#2377C2214yes—
225#2364C2214yes—
226#2329C2214yes—
227#2328C2212yes—
228#2327C2212yes—
229#2326C2212yes—
230#2326C2212yes—
231#2311C2212yes—
232#2283C2211yescharacteristic
233#2283C2211yescharacteristic
234C2×#382C2211yescharacteristic
235C22×#41C2311yescharacteristic
236C22×#41C2312yes—
237C22×#41C2312yes—
238#562—48no—
239#542—416no—
240#537—48no—
241#533—44no—
242#532—44no—
243#532—44no—
244C2×C4⋊Q8C2312yes—
245C2×C4⋊Q8C2311yescharacteristic
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2311yescharacteristic
248C2×C4⋊Q8C2311yescharacteristic
249C2×#127C2312yes—
250C2×#127C2311yescharacteristic
251C2×#127C2311yescharacteristic
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#125C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2314yes—
259C2×#124C2312yes—
260C2×#124C2314yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2312yes—
287C2×#121C2314yes—
288C2×#121C2312yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C4×#41—44no—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2311yescharacteristic
314C2×C4×D4C2311yescharacteristic
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2314yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×#117C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C2×#117C2311yescharacteristic
324C2×#117C2314yes—
325C2×#117C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330#401C2314yes—
331#401C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2312yes—
349#399C2312yes—
350#398C2314yes—
351#398C2312yes—
352#398C2312yes—
353#398C2312yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2312yes—
361#398C2312yes—
362#398C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2312yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2312yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2312yes—
378#397C2312yes—
379#397C2312yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#395C2312yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2312yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#394C2312yes—
406#394C2314yes—
407#394C2312yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2312yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2312yes—
422#394C2314yes—
423#394C2312yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#393C2312yes—
433#393C2312yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2312yes—
448#392C2314yes—
449#392C2314yes—
450#392C2314yes—
451#392C2312yes—
452#392C2312yes—
453#392C2312yes—
454#392C2312yes—
455#392C2312yes—
456#392C2314yes—
457#392C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2314yes—
465#392C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2314yes—
474#391C2312yes—
475#391C2314yes—
476#391C2314yes—
477#391C2314yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2314yes—
487#390C2314yes—
488#390C2314yes—
489#390C2314yes—
490#390C2314yes—
491#390C2314yes—
492#390C2314yes—
493#390C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
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#388C2314yes—
535#388C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
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#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
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#384C2312yes—
617#384C2312yes—
618#383C2314yes—
619#383C2314yes—
620#383C2312yes—
621#383C2312yes—
622#382C2312yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2311yescharacteristic
628#382C2311yescharacteristic
629#382C2312yes—
630#382C2312yes—
631#381C2314yes—
632#381C2314yes—
633#381C2312yes—
634#381C2312yes—
635#381C2314yes—
636#380C2312yes—
637#380C2312yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2312yes—
644#380C2312yes—
645#380C2312yes—
646#380C2314yes—
647#380C2312yes—
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2311yescharacteristic
650C4×C4⋊C4C2311yescharacteristic
651C4×C4⋊C4C2311yescharacteristic
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659#376C2312yes—
660#376C2312yes—
661C2×#95C2312yes—
662C2×#95C2314yes—
663C2×#95C2314yes—
664C2×#95C2312yes—
665C2×#41—24no—
666C2×#41—42no—
667C2×#41—44no—
668C2×#41—42no—
669C2×#41—44no—
670C2×#41—44no—
671C2×#41—44no—
672C2×#41—82no—
673C2×#41—82no—
674C22×Q8C2412yes—
675C22×Q8C2412yes—
676C22×Q8C2412yes—
677C22×Q8C2412yes—
678C22×Q8C2414yes—
679C22×Q8C2411yescharacteristic
680C22×D4C2411yescharacteristic
681C22×D4C2411yescharacteristic
682C22×D4C2411yescharacteristic
683C22×D4C2412yes—
684C22×D4C2414yes—
685C22×D4C2414yes—
686C22×D4C2412yes—
687C22×D4C2412yes—
688C22×D4C2412yes—
689C22×D4C2414yes—
690C22×D4C2414yes—
691C22×D4C2412yes—
692C22×D4C2412yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2414yes—
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C23×C4C2411yescharacteristic
708C23×C4C2411yescharacteristic
709C23×C4C2414yes—
710C23×C4C2414yes—
711C23×C4C2414yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2414yes—
715C4⋊Q8—28no—
716C4⋊Q8—42no—
717C4⋊Q8—42no—
718C4⋊Q8—42no—
719C4⋊Q8—42no—
720#127—42no—
721#127—42no—
722#127—44no—
723#126—48no—
724#126—48no—
725#125—28no—
726#124—28no—
727#124—28no—
728#124—28no—
729#124—48no—
730#124—44no—
731#124—48no—
732#124—84no—
733#124—84no—
734#123—48no—
735#123—48no—
736#123—48no—
737#123—48no—
738#123—84no—
739#123—84no—
740C22⋊Q8—216no—
741C22⋊Q8—48no—
742C22⋊Q8—48no—
743C22⋊Q8—48no—
744C22⋊Q8—48no—
745C22⋊Q8—44no—
746C22⋊Q8—44no—
747C22⋊Q8—44no—
748C22⋊Q8—44no—
749C22⋊Q8—84no—
750C22⋊Q8—82no—
751C22⋊Q8—84no—
752C22⋊Q8—82no—
753#121—44no—
754#121—44no—
755#121—44no—
756#121—44no—
757#121—44no—
758#121—44no—
759#121—48no—
760#121—48no—
761#121—48no—
762#121—48no—
763#121—48no—
764#121—48no—
765#121—48no—
766#121—48no—
767#121—82no—
768#121—84no—
769#121—84no—
770#121—84no—
771#121—84no—
772#121—82no—
773C4×Q8—42no—
774C4×Q8—42no—
775C4×Q8—44no—
776C4×Q8—44no—
777C4×Q8—48no—
778C4×D4—44no—
779C4×D4—44no—
780C4×D4—44no—
781C4×D4—44no—
782C4×D4—42no—
783C4×D4—42no—
784C4×D4—42no—
785C4×D4—42no—
786C4×D4—42no—
787C4×D4—42no—
788C4×D4—48no—
789C4×D4—84no—
790C4×D4—84no—
791#117—42no—
792#117—42no—
793#117—42no—
794#117—48no—
795#117—44no—
796C2×C4⋊C4—44no—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C22⋊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⋊C4C2411yescharacteristic
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2411yescharacteristic
853C2×C22⋊C4C2411yescharacteristic
854C2×C22⋊C4C2411yescharacteristic
855C2×C22⋊C4C2411yescharacteristic
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×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×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C42—24no—
895C2×C42—24no—
896C2×C42—24no—
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966C24C2514yes—
967C24C2514yes—
968C24C2511yescharacteristic
969C24C2511yescharacteristic
970C24C2511yescharacteristic
971#41—416no—
972#41—816no—
973#41—816no—
974C2×Q8—24no—
975C2×Q8—24no—
976C2×Q8—24no—
977C2×Q8—41no—
978C2×Q8—41no—
979C2×Q8—44no—
980C2×Q8—42no—
981C2×Q8—42no—
982C2×Q8—42no—
983C2×Q8—44no—
984C2×Q8—44no—
985C2×Q8—42no—
986C2×Q8—42no—
987C2×Q8—42no—
988C2×Q8—44no—
989C2×Q8—42no—
990C2×Q8H(5,𝔽2)14yes—
991C2×D4—22no—
992C2×D4—22no—
993C2×D4—28no—
994C2×D4—28no—
995C2×D4—22no—
996C2×D4—22no—
997C2×D4—22no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—41no—
1002C2×D4—41no—
1003C2×D4—41no—
1004C2×D4—41no—
1005C2×D4—44no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—42no—
1009C2×D4—42no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—42no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—42no—
1020C2×D4—42no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—42no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—42no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—28no—
1059C22×C4—42no—
1060C22×C4—41no—
1061C22×C4—41no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2514yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—41no—
1124C4⋊C4—41no—
1125C4⋊C4—41no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—41no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—41no—
1170C22⋊C4—41no—
1171C22⋊C4—41no—
1172C22⋊C4—41no—
1173C22⋊C4—41no—
1174C22⋊C4—41no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
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⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C42—22no—
1207C42—22no—
1208C42—22no—
1209C42—22no—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—24no—
1216C42—24no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—42no—
1223C42—42no—
1224C42H(5,𝔽2)14yes—
1225C23—21no—
1226C23—21no—
1227C23—22no—
1228C23—22no—
1229C23—24no—
1230C23—24no—
1231C23—24no—
1232C23—24no—
1233C23—21no—
1234C23—21no—
1235C23—21no—
1236C23—21no—
1237C23—21no—
1238C23—24no—
1239C23—24no—
1240C23—21no—
1241C23—24no—
1242C23—22no—
1243C23—24no—
1244C23—24no—
1245C23—24no—
1246C23—22no—
1247C23—24no—
1248C23—24no—
1249C23—22no—
1250C23—24no—
1251C23—22no—
1252C23—24no—
1253C23#58512yes—
1254C23C2611yescharacteristic
1255Q8—44no—
1256Q8—84no—
1257Q8—84no—
1258Q8—84no—
1259Q8—88no—
1260Q8—84no—
1261D4—44no—
1262D4—44no—
1263D4—44no—
1264D4—84no—
1265D4—84no—
1266D4—84no—
1267D4—88no—
1268D4—88no—
1269D4—88no—
1270D4—88no—
1271D4—84no—
1272D4—84no—
1273D4—84no—
1274D4—88no—
1275D4—164no—
1276D4—164no—
1277D4—164no—
1278D4—164no—
1279D4—164no—
1280C2×C4—28no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—44no—
1334C2×C4—44no—
1335C2×C4—44no—
1336C2×C4—44no—
1337C2×C4—82no—
1338C2×C4—82no—
1339C2×C4—82no—
1340C2×C4—82no—
1341C2×C4—88no—
1342C2×C4—88no—
1343C2×C4—88no—
1344C2×C4—164no—
1345C2×C4—164no—
1346C2×C4—164no—
1347C2×C4—164no—
1348C2×C4C2×H(5,𝔽2)12yes—
1349C2×C4C2×H(5,𝔽2)12yes—
1350C2×C4C2×H(5,𝔽2)12yes—
1351C2×C4C2×H(5,𝔽2)12yes—
1352C2×C4C2×H(5,𝔽2)12yes—
1353C2×C4C2×H(5,𝔽2)12yes—
1354C22—24no—
1355C22—22no—
1356C22—42no—
1357C22—41no—
1358C22—41no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—42no—
1363C22—42no—
1364C22—44no—
1365C22—44no—
1366C22—44no—
1367C22—44no—
1368C22—42no—
1369C22—44no—
1370C22—42no—
1371C22—41no—
1372C22—41no—
1373C22—44no—
1374C22—44no—
1375C22—41no—
1376C22—44no—
1377C22—41no—
1378C22—44no—
1379C22—41no—
1380C22—41no—
1381C22—44no—
1382C22—44no—
1383C22C22×H(5,𝔽2)11yescharacteristic
1384C22C22×H(5,𝔽2)11yescharacteristic
1385C22C2×#58511yescharacteristic
1386C22H(7,𝔽2)12yes—
1387C222−1+612yes—
1388C4—22no—
1389C4—22no—
1390C4—22no—
1391C4—22no—
1392C4—22no—
1393C4—22no—
1394C4—44no—
1395C4—44no—
1396C4—44no—
1397C4—44no—
1398C4—44no—
1399C4—44no—
1400C4—44no—
1401C4—44no—
1402C4—41no—
1403C4—44no—
1404C4—41no—
1405C4—41no—
1406C4—44no—
1407C4—41no—
1408C4—41no—
1409C4—41no—
1410C2—42no—
1411C2—84no—
1412C2—84no—
1413C2—81no—
1414C2—81no—
1415C2#6281811yescharacteristic
1416C2#6287411yescharacteristic
1417C2#6288611yescharacteristic
1418C2#6305212yes—
1419C2#6305912yes—
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. #58887C2semidirect
2. #57272C2semidirect
3. #56927C2semidirect
4. #56530C2semidirect
5. #56419C2semidirect
6. #55615C2semidirect
7. #55604C2semidirect
8. #53893C2semidirect
9. #53794C2semidirect
10. #53492C2semidirect
11. #51509C2semidirect
12. #50106C2semidirect
13. #49704C2semidirect
14. #47801C2semidirect
15. #47788C2semidirect
16. #46972C2semidirect
17. #46966C2semidirect
18. #46417C2semidirect
19. #46226C2semidirect
20. #46224C2semidirect
21. #46224C2semidirect
22. #45989C2semidirect
23. #45986C2semidirect
24. #45984C2semidirect
25. #35328C2semidirect
26. #35200C2semidirect
27. #35190C2semidirect

Maximal subgroups

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

subgroupindex
#588872
#572722
#569272
#565302
#564192
#556152
#556042
#538932
#537942
#534922
#515092
#501062
#497042
#478012
#477882
#469722
#469662
#464172
#462262
#462242
#459892
#459862
#459842
#353282
#352002
#351902