Finite Group Databasebeta

← #7644400

Subgroups — #7644400

Order 512.

4786 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42375C214yesmaximal, complemented
2#42368C214yesmaximal, complemented
3#42137C214yesmaximal, complemented
4#42092C214yesmaximal, complemented
5#41317C214yesmaximal, complemented
6#41291C214yesmaximal, complemented
7#41257C214yesmaximal, complemented
8#41164C214yesmaximal, complemented
9#37504C212yesmaximal, complemented
10#37502C212yesmaximal, complemented
11#37500C212yesmaximal, complemented
12#37498C212yesmaximal, complemented
13#37425C211yesmaximal, characteristic, complemented
14#37393C211yesmaximal, characteristic, complemented
15#37317C211yesmaximal, characteristic, complemented
16#37296C211yesmaximal, characteristic, complemented
17#37288C212yesmaximal, complemented
18#37272C212yesmaximal, complemented
19#35654C212yesmaximal, complemented
20#35613C212yesmaximal, complemented
21#35591C212yesmaximal, complemented
22#35525C212yesmaximal, complemented
23#35315C211yesmaximal, characteristic, complemented
24#35271C211yesmaximal, characteristic, complemented
25#34614C212yesmaximal, complemented
26#34267C212yesmaximal, complemented
27#34070C211yesmaximal, characteristic, complemented
28C2×#537C2212yes—
29C2×#532C2211yescharacteristic
30C2×#529C2212yes—
31C2×#520C2212yes—
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2855C2212yes—
37#2854C2212yes—
38#2851C2211yescharacteristic
39#2851C2211yescharacteristic
40#2839C2214yes—
41#2837C2214yes—
42#2836C2214yes—
43#2836C2214yes—
44#2827C2214yes—
45#2826C2214yes—
46#2826C2214yes—
47#2825C2214yes—
48#2809C2214yes—
49#2800C2214yes—
50#2790C2214yes—
51#2783C2214yes—
52#2781C2214yes—
53#2780C2214yes—
54#2780C2214yes—
55#2779C2214yes—
56#2774C2214yes—
57#2751C2214yes—
58#2748C2214yes—
59#2744C2214yes—
60#2743C2214yes—
61#2740C2214yes—
62#2732C2214yes—
63#2730C2214yes—
64#2729C2214yes—
65#2721C2214yes—
66#2714C2214yes—
67#2714C2214yes—
68#2707C2214yes—
69#2699C2214yes—
70#2695C2214yes—
71#2688C2214yes—
72#2688C2214yes—
73#2686C2214yes—
74#2682C2214yes—
75#2682C2214yes—
76#2673C2214yes—
77#2671C2214yes—
78#2671C2214yes—
79#2671C2214yes—
80#2667C2214yes—
81#2664C2214yes—
82#2655C2214yes—
83#2652C2214yes—
84#2649C2214yes—
85#2649C2214yes—
86#2649C2214yes—
87#2649C2214yes—
88#2648C2214yes—
89#2648C2214yes—
90#2647C2211yescharacteristic
91#2647C2211yescharacteristic
92#2646C2214yes—
93#2645C2212yes—
94#2644C2212yes—
95#2643C2214yes—
96#2642C2211yescharacteristic
97#2641C2211yescharacteristic
98#2637C2214yes—
99#2636C2214yes—
100#2636C2214yes—
101#2635C2214yes—
102#2630C2214yes—
103#2630C2214yes—
104#2629C2212yes—
105#2629C2212yes—
106#2625C2212yes—
107#2624C2212yes—
108#2623C2214yes—
109#2620C2212yes—
110#2620C2212yes—
111#2618C2214yes—
112#2616C2212yes—
113#2615C2212yes—
114#2609C2214yes—
115#2600C2214yes—
116#2598C2214yes—
117#2598C2214yes—
118#2597C2214yes—
119#2596C2214yes—
120#2590C2214yes—
121#2587C2214yes—
122#2579C2214yes—
123#2577C2214yes—
124#2576C2214yes—
125#2575C2214yes—
126#2575C2214yes—
127#2559C2214yes—
128#2558C2214yes—
129#2553C2214yes—
130#2553C2214yes—
131#2535C2214yes—
132#2533C2214yes—
133#2531C2214yes—
134#2528C2214yes—
135#2526C2214yes—
136#2515C2214yes—
137#2512C2212yes—
138#2511C2212yes—
139#2508C2214yes—
140#2507C2212yes—
141#2506C2212yes—
142#2505C2214yes—
143#2502C2212yes—
144#2501C2212yes—
145#2497C2212yes—
146#2496C2212yes—
147#2493C2214yes—
148#2490C2212yes—
149#2489C2212yes—
150#2487C2212yes—
151#2486C2212yes—
152#2485C2214yes—
153#2484C2214yes—
154#2481C2214yes—
155#2481C2214yes—
156#2479C2214yes—
157#2478C2214yes—
158#2478C2214yes—
159#2473C2214yes—
160#2471C2214yes—
161#2470C2214yes—
162#2470C2214yes—
163#2468C2214yes—
164#2467C2214yes—
165#2457C2214yes—
166#2457C2214yes—
167#2456C2214yes—
168#2454C2214yes—
169#2454C2212yes—
170#2453C2212yes—
171#2448C2212yes—
172#2447C2212yes—
173#2444C2214yes—
174#2443C2214yes—
175#2442C2212yes—
176#2442C2212yes—
177#2441C2212yes—
178#2441C2212yes—
179#2432C2212yes—
180#2431C2212yes—
181#2429C2212yes—
182#2428C2212yes—
183#2425C2214yes—
184#2425C2214yes—
185#2421C2212yes—
186#2420C2212yes—
187#2419C2214yes—
188#2417C2212yes—
189#2416C2212yes—
190#2415C2212yes—
191#2414C2212yes—
192#2407C2212yes—
193#2407C2212yes—
194#2396C2214yes—
195#2392C2214yes—
196#2392C2214yes—
197#2392C2214yes—
198#2364C2214yes—
199#2364C2214yes—
200#2363C2214yes—
201#2362C2214yes—
202#2361C2214yes—
203#2361C2214yes—
204#2361C2214yes—
205#2360C2214yes—
206#2330C2211yescharacteristic
207#2330C2211yescharacteristic
208#2328C2212yes—
209#2328C2211yescharacteristic
210#2327C2212yes—
211#2327C2211yescharacteristic
212#2326C2212yes—
213#2326C2212yes—
214#2325C2212yes—
215#2325C2212yes—
216#2325C2212yes—
217#2325C2212yes—
218#2324C2212yes—
219#2324C2212yes—
220#2323C2212yes—
221#2323C2212yes—
222#2320C2212yes—
223#2319C2212yes—
224#2311C2212yes—
225C4×C22⋊Q8C2212yes—
226C4×C22⋊Q8C2212yes—
227C4×C22⋊Q8C2212yes—
228C4×#121C2212yes—
229C4×#121C2212yes—
230C4×#121C2212yes—
231#2297C2211yescharacteristic
232#2297C2211yescharacteristic
233#2297C2212yes—
234C2×#389C2212yes—
235#2290C2212yes—
236#2290C2212yes—
237#2290C2212yes—
238#2290C2212yes—
239#2285C2212yes—
240#2285C2211yescharacteristic
241#2274C2212yes—
242C2×#376C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2312yes—
245C22×#41C2311yescharacteristic
246#537—216no—
247#532—28no—
248C2×C4⋊Q8C2311yescharacteristic
249C2×C4⋊Q8C2311yescharacteristic
250C2×#127C2311yescharacteristic
251C2×#127C2311yescharacteristic
252#529—48no—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2311yescharacteristic
257C2×#125C2311yescharacteristic
258C2×#125C2312yes—
259C2×#125C2314yes—
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2312yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#121C2312yes—
276C2×#121C2312yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285#520—48no—
286C4×#41—44no—
287C4×#41—44no—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×#117C2312yes—
309C2×#117C2312yes—
310C2×#117C2311yescharacteristic
311C2×#117C2314yes—
312C2×#117C2314yes—
313C2×#117C2311yescharacteristic
314C2×#117C2312yes—
315C2×#117C2314yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2314yes—
319C22×C4⋊C4C2314yes—
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2312yes—
323C22×C42C2311yescharacteristic
324C22×C42C2312yes—
325#401C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
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#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
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#396C2314yes—
389#396C2314yes—
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#395C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#393C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#390C2314yes—
447#390C2312yes—
448#390C2312yes—
449#390C2312yes—
450#390C2314yes—
451#390C2314yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2312yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2312yes—
500#388C2314yes—
501#388C2312yes—
502#388C2312yes—
503#388C2312yes—
504#388C2312yes—
505#388C2312yes—
506#388C2312yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#387C2312yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2312yes—
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#386C2314yes—
550#386C2314yes—
551#386C2312yes—
552#386C2314yes—
553#386C2314yes—
554#386C2312yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2312yes—
563#386C2312yes—
564#386C2312yes—
565#386C2312yes—
566#386C2312yes—
567#386C2312yes—
568#386C2312yes—
569#386C2312yes—
570#386C2312yes—
571#386C2312yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#385C2312yes—
583#385C2314yes—
584#385C2312yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2312yes—
589#385C2312yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2312yes—
595#385C2312yes—
596#385C2312yes—
597#385C2312yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#384C2312yes—
610#384C2311yescharacteristic
611#384C2311yescharacteristic
612#384C2312yes—
613#384C2312yes—
614#383C2314yes—
615#382C2314yes—
616#382C2314yes—
617#382C2314yes—
618#382C2312yes—
619#382C2311yescharacteristic
620#382C2311yescharacteristic
621#381C2314yes—
622#381C2314yes—
623#381C2314yes—
624#381C2314yes—
625#381C2314yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2314yes—
631#380C2314yes—
632#380C2311yescharacteristic
633#380C2311yescharacteristic
634#380C2311yescharacteristic
635#380C2311yescharacteristic
636#380C2314yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671#376C2311yescharacteristic
672#376C2311yescharacteristic
673#376C2312yes—
674#376C2312yes—
675#376C2311yescharacteristic
676#376C2311yescharacteristic
677C2×#95C2312yes—
678C2×#95C2312yes—
679C2×#95C2314yes—
680C2×#41—24no—
681C2×#41—28no—
682C2×#41—42no—
683C2×#41—42no—
684C2×#41—42no—
685C2×#41—42no—
686C2×#41—44no—
687C2×#41—44no—
688C2×#41#4118yes—
689C22×Q8C2412yes—
690C22×Q8C2411yescharacteristic
691C22×Q8C2411yescharacteristic
692C22×D4C2412yes—
693C22×D4C2412yes—
694C22×D4C2414yes—
695C22×D4C2411yescharacteristic
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2412yes—
699C22×D4C2412yes—
700C22×D4C2414yes—
701C22×D4C2414yes—
702C22×D4C2414yes—
703C22×D4C2412yes—
704C22×D4C2411yescharacteristic
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2411yescharacteristic
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2414yes—
711C23×C4C2412yes—
712C23×C4C2412yes—
713C23×C4C2412yes—
714C23×C4C2411yescharacteristic
715C23×C4C2411yescharacteristic
716C23×C4C2414yes—
717C23×C4C2412yes—
718C23×C4C2414yes—
719C23×C4C2412yes—
720C23×C4C2412yes—
721C4⋊Q8—24no—
722C4⋊Q8—42no—
723#127—24no—
724#127—42no—
725#126—48no—
726#126—84no—
727#126—84no—
728#125—42no—
729#125—42no—
730#125—44no—
731#125—84no—
732#124—24no—
733#124—24no—
734#124—44no—
735#123—48no—
736#123—84no—
737#123—84no—
738#123—84no—
739#123—84no—
740C22⋊Q8—216no—
741C22⋊Q8—28no—
742C22⋊Q8—28no—
743C22⋊Q8—44no—
744C22⋊Q8—44no—
745#121—28no—
746#121—28no—
747#121—216no—
748#121—216no—
749#121—216no—
750#121—28no—
751#121—28no—
752#121—44no—
753#121—44no—
754#121—84no—
755#121—84no—
756#121—84no—
757C4×Q8—28no—
758C4×Q8—44no—
759C4×Q8—44no—
760C4×Q8—44no—
761C4×D4—28no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—44no—
765C4×D4—48no—
766C4×D4—44no—
767C4×D4—44no—
768C4×D4—44no—
769C4×D4—44no—
770C4×D4—48no—
771C4×D4—44no—
772C4×D4—44no—
773C4×D4—48no—
774C4×D4—84no—
775C4×D4—84no—
776C4×D4—84no—
777#117—28no—
778#117—44no—
779#117—42no—
780#117—42no—
781#117—48no—
782#117—48no—
783#117—44no—
784#117—84no—
785C2×C4⋊C4—28no—
786C2×C4⋊C4—48no—
787C2×C4⋊C4—44no—
788C2×C4⋊C4—84no—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2411yescharacteristic
850C2×C22⋊C4C2411yescharacteristic
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2411yescharacteristic
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C42—24no—
892C2×C42—24no—
893C2×C42—28no—
894C2×C42—44no—
895C2×C42—42no—
896C2×C42C2414yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2411yescharacteristic
919#95C2412yes—
920#95C2412yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
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#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977C24C2514yes—
978C24C2512yes—
979C24C2512yes—
980C24C2511yescharacteristic
981#41—416no—
982#41—432no—
983#41—416no—
984C2×Q8—24no—
985C2×Q8—22no—
986C2×Q8—24no—
987C2×Q8—24no—
988C2×Q8—41no—
989C2×Q8—41no—
990C2×Q8—41no—
991C2×Q8—41no—
992C2×Q8C2×#4114yes—
993C2×D4—24no—
994C2×D4—28no—
995C2×D4—24no—
996C2×D4—24no—
997C2×D4—28no—
998C2×D4—28no—
999C2×D4—24no—
1000C2×D4—22no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—41no—
1004C2×D4—41no—
1005C2×D4—42no—
1006C2×D4—42no—
1007C2×D4—44no—
1008C2×D4—42no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4—42no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—42no—
1023C2×D4—44no—
1024C2×D4—42no—
1025C2×D4—42no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4C2×#4118yes—
1031C2×D4C2×#4114yes—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—22no—
1035C22×C4—24no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—28no—
1039C22×C4—24no—
1040C22×C4—28no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—28no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4C2×#4114yes—
1077C22×C4C2×#4118yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C4⋊C4—28no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
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—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C22⋊C4—24no—
1151C22⋊C4—24no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—28no—
1161C22⋊C4—44no—
1162C22⋊C4—42no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—41no—
1175C22⋊C4—41no—
1176C22⋊C4—41no—
1177C22⋊C4—44no—
1178C22⋊C4—41no—
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—42no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C42—22no—
1204C42—22no—
1205C42—22no—
1206C42—22no—
1207C42—22no—
1208C42—24no—
1209C42—24no—
1210C42—24no—
1211C42—24no—
1212C42—24no—
1213C42—28no—
1214C42—22no—
1215C42—22no—
1216C42—42no—
1217C42—42no—
1218C42—42no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42H(5,𝔽2)14yes—
1226C23—22no—
1227C23—21no—
1228C23—22no—
1229C23—21no—
1230C23—22no—
1231C23—22no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—22no—
1236C23—24no—
1237C23—22no—
1238C23—24no—
1239C23—22no—
1240C23—22no—
1241C23—24no—
1242C23—22no—
1243C23—24no—
1244C23—24no—
1245C23—22no—
1246C23—24no—
1247C23—24no—
1248C23—22no—
1249C23—22no—
1250C23C22×#4114yes—
1251C23C22×#4112yes—
1252C23C2611yescharacteristic
1253Q8—44no—
1254Q8—44no—
1255Q8—48no—
1256D4—48no—
1257D4—44no—
1258D4—44no—
1259D4—48no—
1260D4—416no—
1261D4—48no—
1262D4—88no—
1263D4—88no—
1264D4—84no—
1265D4—84no—
1266D4—88no—
1267D4—88no—
1268D4—164no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—216no—
1276C2×C4—28no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—48no—
1331C2×C4—416no—
1332C2×C4—48no—
1333C2×C4—84no—
1334C2×C4—84no—
1335C2×C4—88no—
1336C2×C4—82no—
1337C2×C4—88no—
1338C2×C4—82no—
1339C2×C4—84no—
1340C2×C4—84no—
1341C2×C4—84no—
1342C2×C4—164no—
1343C2×C4—164no—
1344C2×C4C22×#4112yes—
1345C2×C4C22×#4114yes—
1346C2×C4C22×#4112yes—
1347C2×C4C2×H(5,𝔽2)14yes—
1348C2×C4C2×H(5,𝔽2)12yes—
1349C2×C4#58512yes—
1350C22—24no—
1351C22—22no—
1352C22—22no—
1353C22—24no—
1354C22—24no—
1355C22—22no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—44no—
1363C22—42no—
1364C22—42no—
1365C22—44no—
1366C22—42no—
1367C22—44no—
1368C22—42no—
1369C22—44no—
1370C22—42no—
1371C22—44no—
1372C22—44no—
1373C22—42no—
1374C22—44no—
1375C22—42no—
1376C22C23×#4111yescharacteristic
1377C22C22×H(5,𝔽2)11yescharacteristic
1378C22C2×#58511yescharacteristic
1379C22H(7,𝔽2)12yes—
1380C222−1+612yes—
1381C4—24no—
1382C4—24no—
1383C4—22no—
1384C4—41no—
1385C4—44no—
1386C4—44no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—42no—
1394C4—44no—
1395C4—42no—
1396C4—44no—
1397C4—44no—
1398C4—42no—
1399C4—42no—
1400C4—44no—
1401C4—42no—
1402C4—44no—
1403C4#345914yes—
1404C2—44no—
1405C2—42no—
1406C2—84no—
1407C2—82no—
1408C2C2×#345911yescharacteristic
1409C2#6285811yescharacteristic
1410C2#6286111yescharacteristic
1411C2#6287512yes—
1412C2#6288412yes—
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. #42375C2semidirect
2. #42368C2semidirect
3. #42137C2semidirect
4. #42092C2semidirect
5. #41317C2semidirect
6. #41291C2semidirect
7. #41257C2semidirect
8. #41164C2semidirect
9. #37504C2semidirect
10. #37502C2semidirect
11. #37500C2semidirect
12. #37498C2semidirect
13. #37425C2semidirect
14. #37393C2semidirect
15. #37317C2semidirect
16. #37296C2semidirect
17. #37288C2semidirect
18. #37272C2semidirect
19. #35654C2semidirect
20. #35613C2semidirect
21. #35591C2semidirect
22. #35525C2semidirect
23. #35315C2semidirect
24. #35271C2semidirect
25. #34614C2semidirect
26. #34267C2semidirect
27. #34070C2semidirect

Maximal subgroups

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

subgroupindex
#423752
#423682
#421372
#420922
#413172
#412912
#412572
#411642
#375042
#375022
#375002
#374982
#374252
#373932
#373172
#372962
#372882
#372722
#356542
#356132
#355912
#355252
#353152
#352712
#346142
#342672
#340702