Finite Group Databasebeta

← #7681604

Subgroups — #7681604

Order 512.

5013 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59786C214yesmaximal, complemented
2#59730C214yesmaximal, complemented
3#59615C214yesmaximal, complemented
4#59588C214yesmaximal, complemented
5#44644C214yesmaximal, complemented
6#44631C214yesmaximal, complemented
7#44311C214yesmaximal, complemented
8#44152C214yesmaximal, complemented
9#39554C212yesmaximal, complemented
10#39494C211yesmaximal, characteristic, complemented
11#39417C212yesmaximal, complemented
12#39356C211yesmaximal, characteristic, complemented
13#39143C212yesmaximal, complemented
14#38061C212yesmaximal, complemented
15#38057C212yesmaximal, complemented
16#36602C211yesmaximal, characteristic, complemented
17#36574C211yesmaximal, characteristic, complemented
18#36374C212yesmaximal, complemented
19#35671C212yesmaximal, complemented
20#35601C212yesmaximal, complemented
21#35332C211yesmaximal, characteristic, complemented
22#35300C212yesmaximal, complemented
23#34902C212yesmaximal, complemented
24#34312C212yesmaximal, complemented
25#34276C212yesmaximal, complemented
26#34125C211yesmaximal, characteristic, complemented
27C4×#541C211yesmaximal, characteristic, complemented
28C2×#548C2212yes—
29C2×#541C2211yescharacteristic
30C2×#541C2211yescharacteristic
31C2×#540C2211yescharacteristic
32C2×#536C2212yes—
33C2×#520C2212yes—
34C2×#519C2212yes—
35C2×C4×#41C2211yescharacteristic
36#2861C2212yes—
37#2859C2211yescharacteristic
38#2859C2212yes—
39#2858C2211yescharacteristic
40#2855C2212yes—
41#2854C2212yes—
42#2850C2212yes—
43#2802C2214yes—
44#2801C2214yes—
45#2783C2214yes—
46#2780C2214yes—
47#2780C2214yes—
48#2779C2214yes—
49#2765C2214yes—
50#2762C2214yes—
51#2762C2214yes—
52#2758C2214yes—
53#2757C2214yes—
54#2755C2214yes—
55#2752C2214yes—
56#2749C2214yes—
57#2725C2214yes—
58#2711C2214yes—
59#2707C2214yes—
60#2706C2214yes—
61#2705C2214yes—
62#2705C2214yes—
63#2704C2214yes—
64#2702C2214yes—
65#2683C2214yes—
66#2682C2214yes—
67#2645C2212yes—
68#2644C2212yes—
69#2642C2211yescharacteristic
70#2641C2211yescharacteristic
71#2629C2212yes—
72#2620C2212yes—
73#2620C2212yes—
74#2611C2214yes—
75#2608C2214yes—
76#2604C2214yes—
77#2602C2214yes—
78#2601C2214yes—
79#2597C2214yes—
80#2596C2214yes—
81#2594C2214yes—
82#2594C2214yes—
83#2593C2214yes—
84#2592C2212yes—
85#2591C2214yes—
86#2587C2214yes—
87#2587C2214yes—
88#2584C2214yes—
89#2584C2214yes—
90#2581C2212yes—
91#2578C2214yes—
92#2576C2214yes—
93#2576C2214yes—
94#2576C2214yes—
95#2570C2212yes—
96#2569C2214yes—
97#2560C2214yes—
98#2559C2214yes—
99#2559C2214yes—
100#2559C2214yes—
101#2558C2214yes—
102#2558C2214yes—
103#2558C2214yes—
104#2558C2214yes—
105#2556C2214yes—
106#2554C2214yes—
107#2553C2214yes—
108#2545C2212yes—
109#2529C2214yes—
110#2526C2214yes—
111#2525C2214yes—
112#2525C2214yes—
113#2522C2214yes—
114#2518C2214yes—
115#2518C2214yes—
116#2518C2214yes—
117#2516C2214yes—
118#2515C2214yes—
119#2514C2212yes—
120#2512C2212yes—
121#2509C2214yes—
122#2508C2214yes—
123#2505C2214yes—
124#2493C2214yes—
125#2493C2214yes—
126#2479C2214yes—
127#2477C2214yes—
128#2476C2214yes—
129#2475C2214yes—
130#2475C2214yes—
131#2474C2214yes—
132#2470C2214yes—
133#2470C2214yes—
134#2469C2214yes—
135#2469C2214yes—
136#2465C2214yes—
137#2464C2214yes—
138#2462C2214yes—
139#2461C2214yes—
140#2461C2214yes—
141#2459C2214yes—
142#2458C2214yes—
143#2457C2214yes—
144#2453C2212yes—
145#2453C2212yes—
146#2448C2212yes—
147#2446C2212yes—
148#2446C2212yes—
149#2445C2212yes—
150#2444C2214yes—
151#2442C2212yes—
152#2441C2212yes—
153#2434C2212yes—
154#2431C2212yes—
155#2430C2214yes—
156#2429C2212yes—
157#2426C2212yes—
158#2423C2212yes—
159#2420C2212yes—
160#2416C2212yes—
161#2415C2212yes—
162#2414C2214yes—
163#2413C2214yes—
164#2409C2212yes—
165#2407C2212yes—
166#2401C2214yes—
167#2396C2214yes—
168#2374C2214yes—
169#2370C2214yes—
170#2367C2214yes—
171#2367C2212yes—
172#2364C2214yes—
173#2363C2214yes—
174#2363C2212yes—
175#2362C2214yes—
176#2362C2214yes—
177#2360C2214yes—
178#2360C2212yes—
179#2360C2214yes—
180#2360C2214yes—
181#2359C2214yes—
182#2359C2214yes—
183#2359C2214yes—
184#2359C2214yes—
185#2359C2214yes—
186#2357C2212yes—
187#2357C2212yes—
188#2357C2212yes—
189#2352C2212yes—
190#2352C2214yes—
191#2351C2212yes—
192#2351C2212yes—
193#2347C2212yes—
194#2347C2212yes—
195#2347C2212yes—
196#2341C2212yes—
197#2341C2212yes—
198Q8×C22⋊C4C2212yes—
199#2336C2214yes—
200#2334C2214yes—
201#2330C2211yescharacteristic
202#2327C2211yescharacteristic
203#2327C2212yes—
204#2326C2212yes—
205#2326C2212yes—
206#2324C2212yes—
207#2324C2214yes—
208#2323C2214yes—
209#2323C2212yes—
210#2323C2212yes—
211#2320C2212yes—
212#2317C2212yes—
213#2314C2211yescharacteristic
214C4×C4⋊Q8C2211yescharacteristic
215C4×C4⋊Q8C2212yes—
216C4×C4⋊Q8C2212yes—
217C4×#125C2211yescharacteristic
218C4×#125C2214yes—
219C4×#126C2214yes—
220C4×#126C2214yes—
221C4×#124C2212yes—
222C4×#124C2214yes—
223C4×#124C2212yes—
224C4×#124C2212yes—
225C4×C22⋊Q8C2212yes—
226#2298C2214yes—
227#2297C2212yes—
228#2295C2212yes—
229C2×#391C2212yes—
230#2293C2211yescharacteristic
231#2293C2214yes—
232#2293C2212yes—
233#2293C2212yes—
234#2293C2211yescharacteristic
235#2293C2212yes—
236#2283C2212yes—
237#2283C2211yescharacteristic
238C42×Q8C2212yes—
239C42×Q8C2211yescharacteristic
240C42×Q8C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C4×#117C2212yes—
243C22×#41C2312yes—
244C22×#41C2311yescharacteristic
245C23×Q8C2312yes—
246#548—216no—
247#541—28no—
248#541—44no—
249#540—44no—
250#536—216no—
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2311yescharacteristic
254C2×#127C2311yescharacteristic
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#125C2311yescharacteristic
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2311yescharacteristic
263C2×#125C2311yescharacteristic
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×#121C2312yes—
280C2×#121C2314yes—
281C2×#121C2314yes—
282C2×#121C2312yes—
283C2×#121C2314yes—
284#520—48no—
285#519—48no—
286C4×#41—28no—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2312yes—
311C2×#117C2311yescharacteristic
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2314yes—
318C2×#117C2314yes—
319C2×#117C2314yes—
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2314yes—
322C22×C42C2311yescharacteristic
323C22×C42C2312yes—
324#401C2314yes—
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#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#393C2314yes—
392#393C2314yes—
393#392C2314yes—
394#392C2314yes—
395#392C2314yes—
396#391C2314yes—
397#391C2312yes—
398#391C2312yes—
399#391C2312yes—
400#391C2312yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2312yes—
410#390C2314yes—
411#390C2312yes—
412#390C2314yes—
413#390C2312yes—
414#390C2314yes—
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2314yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2314yes—
426#390C2314yes—
427#390C2314yes—
428#390C2312yes—
429#389C2312yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2312yes—
438#389C2312yes—
439#389C2314yes—
440#389C2314yes—
441#389C2312yes—
442#389C2314yes—
443#389C2312yes—
444#389C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2312yes—
472#388C2314yes—
473#388C2314yes—
474#388C2312yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2312yes—
490#388C2314yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
508#388C2314yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2314yes—
517#388C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
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#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#384C2311yescharacteristic
583#384C2312yes—
584#384C2312yes—
585#383C2314yes—
586#383C2314yes—
587#383C2312yes—
588#383C2312yes—
589#383C2311yescharacteristic
590#383C2311yescharacteristic
591#382C2311yescharacteristic
592#382C2314yes—
593#382C2312yes—
594#382C2312yes—
595#382C2314yes—
596#382C2314yes—
597#382C2312yes—
598#382C2312yes—
599#382C2312yes—
600#381C2311yescharacteristic
601#381C2314yes—
602#381C2314yes—
603#381C2312yes—
604#381C2312yes—
605#381C2311yescharacteristic
606#380C2312yes—
607#380C2314yes—
608#380C2314yes—
609#380C2312yes—
610#380C2314yes—
611#380C2312yes—
612#380C2312yes—
613#380C2312yes—
614#380C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2311yescharacteristic
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2314yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2311yescharacteristic
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2312yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671#376C2311yescharacteristic
672#376C2311yescharacteristic
673#376C2312yes—
674#376C2314yes—
675C2×#95C2314yes—
676C2×#95C2314yes—
677C43C2314yes—
678C43C2311yescharacteristic
679C43C2312yes—
680C43C2312yes—
681C43C2311yescharacteristic
682C2×#41—28no—
683C2×#41—24no—
684C2×#41—28no—
685C2×#41—44no—
686C2×#41—44no—
687C22×Q8—28no—
688C22×Q8—28no—
689C22×Q8—44no—
690C22×Q8C2411yescharacteristic
691C22×Q8C2412yes—
692C22×Q8C2414yes—
693C22×Q8C2412yes—
694C22×D4C2412yes—
695C22×D4C2412yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C22×D4C2414yes—
700C22×D4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2412yes—
705C23×C4C2412yes—
706C23×C4C2414yes—
707C23×C4C2411yescharacteristic
708C23×C4C2412yes—
709C23×C4C2411yescharacteristic
710C23×C4C2414yes—
711C23×C4C2414yes—
712C4⋊Q8—28no—
713C4⋊Q8—42no—
714C4⋊Q8#4118yescomplemented
715#127—42no—
716#126—216no—
717#126—48no—
718#126—48no—
719#125—216no—
720#125—24no—
721#125—48no—
722#125—42no—
723#125—42no—
724#125—48no—
725#124—28no—
726#124—216no—
727#124—28no—
728#124—28no—
729#123—216no—
730#123—216no—
731#123—48no—
732#123—48no—
733#123—48no—
734C22⋊Q8—28no—
735C22⋊Q8—28no—
736C22⋊Q8—216no—
737C22⋊Q8—216no—
738C22⋊Q8—216no—
739C22⋊Q8—44no—
740#121—216no—
741#121—28no—
742#121—48no—
743#121—48no—
744#121—44no—
745C4×Q8—28no—
746C4×Q8—24no—
747C4×Q8—24no—
748C4×Q8—28no—
749C4×Q8—28no—
750C4×Q8—28no—
751C4×Q8—48no—
752C4×Q8—48no—
753C4×Q8—44no—
754C4×Q8—44no—
755C4×Q8—44no—
756C4×Q8—44no—
757C4×Q8—44no—
758C4×D4—24no—
759C4×D4—28no—
760C4×D4—28no—
761C4×D4—216no—
762C4×D4—28no—
763C4×D4—48no—
764C4×D4—44no—
765C4×D4—48no—
766C4×D4#4118yes—
767#117—24no—
768#117—28no—
769#117—28no—
770#117—24no—
771#117—28no—
772#117—24no—
773#117—48no—
774#117—48no—
775#117—48no—
776#117—48no—
777#117—44no—
778C2×C4⋊C4—48no—
779C2×C4⋊C4—44no—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2414yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C42—28no—
877C2×C42—24no—
878C2×C42C2414yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2411yescharacteristic
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2411yescharacteristic
891C2×C42C2412yes—
892C2×C42C2414yes—
893C2×C42C2411yescharacteristic
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914#95C2414yes—
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#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2411yescharacteristic
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2411yescharacteristic
960#95C2412yes—
961#95C2412yes—
962#95C2411yescharacteristic
963#95C2411yescharacteristic
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975C24C2511yescharacteristic
976C24C2514yes—
977C24C2512yes—
978#41—432no—
979#41—416no—
980C2×Q8—22no—
981C2×Q8—24no—
982C2×Q8—28no—
983C2×Q8—28no—
984C2×Q8—24no—
985C2×Q8—24no—
986C2×Q8—24no—
987C2×Q8—24no—
988C2×Q8—24no—
989C2×Q8—44no—
990C2×Q8—432no—
991C2×Q8C2×#4118yes—
992C2×D4—24no—
993C2×D4—28no—
994C2×D4—28no—
995C2×D4—24no—
996C2×D4—28no—
997C2×D4—24no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—44no—
1001C2×D4—42no—
1002C2×D4—42no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4C2×#4114yes—
1012C22×C4—24no—
1013C22×C4—24no—
1014C22×C4—24no—
1015C22×C4—28no—
1016C22×C4—24no—
1017C22×C4—22no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—28no—
1021C22×C4—28no—
1022C22×C4—28no—
1023C22×C4—22no—
1024C22×C4—24no—
1025C22×C4—22no—
1026C22×C4—28no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—44no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4C2×#4118yes—
1043C22×C4C2511yescharacteristic
1044C22×C4C2512yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2514yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—22no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—28no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4C2×#4114yes—
1118C4⋊C4C2×#41116yes—
1119C22⋊C4—24no—
1120C22⋊C4—28no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—24no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
1144C22⋊C4—42no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—44no—
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⋊C4C2×#4118yes—
1163C42—22no—
1164C42—22no—
1165C42—24no—
1166C42—24no—
1167C42—24no—
1168C42—22no—
1169C42—22no—
1170C42—24no—
1171C42—28no—
1172C42—28no—
1173C42—24no—
1174C42—22no—
1175C42—28no—
1176C42—28no—
1177C42—24no—
1178C42—24no—
1179C42—42no—
1180C42—42no—
1181C42—44no—
1182C42—42no—
1183C42—42no—
1184C42—42no—
1185C42—42no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—42no—
1192C42—42no—
1193C42—42no—
1194C42—42no—
1195C42—44no—
1196C42C2×#4114yes—
1197C42C2×#4114yes—
1198C42H(5,𝔽2)14yes—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—21no—
1206C23—24no—
1207C23—24no—
1208C23—21no—
1209C23—21no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—22no—
1214C23—24no—
1215C23—24no—
1216C23—22no—
1217C23C22×#4114yes—
1218C23C2611yescharacteristic
1219Q8—28no—
1220Q8—216no—
1221Q8—416no—
1222Q8—48no—
1223D4—44no—
1224D4—48no—
1225D4—416no—
1226D4—48no—
1227D4—88no—
1228D4—164no—
1229D4—164no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—216no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—416no—
1290C2×C4—416no—
1291C2×C4—48no—
1292C2×C4—44no—
1293C2×C4—44no—
1294C2×C4—82no—
1295C2×C4—88no—
1296C2×C4—84no—
1297C2×C4—164no—
1298C2×C4—164no—
1299C2×C4C22×#4112yes—
1300C2×C4C22×#4114yes—
1301C2×C4C22×#4112yes—
1302C2×C4C22×#4118yes—
1303C2×C4C22×#4114yes—
1304C2×C4C22×#4112yes—
1305C2×C4C22×#4112yes—
1306C2×C4C2×H(5,𝔽2)14yes—
1307C2×C4C2×H(5,𝔽2)12yes—
1308C2×C4#58514yes—
1309C22—24no—
1310C22—24no—
1311C22—24no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—44no—
1318C22—44no—
1319C22—41no—
1320C22—44no—
1321C22—41no—
1322C22—44no—
1323C22—44no—
1324C22—42no—
1325C22—44no—
1326C22—44no—
1327C22—41no—
1328C22C23×#4111yescharacteristic
1329C22C23×#4111yescharacteristic
1330C22C22×H(5,𝔽2)11yescharacteristic
1331C22C2×#58512yes—
1332C222−1+612yes—
1333C4—24no—
1334C4—22no—
1335C4—24no—
1336C4—22no—
1337C4—24no—
1338C4—24no—
1339C4—28no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—44no—
1344C4—41no—
1345C4—44no—
1346C4—42no—
1347C4—41no—
1348C4—42no—
1349C4—44no—
1350C4—44no—
1351C4—42no—
1352C4—44no—
1353C4—42no—
1354C4—41no—
1355C4—44no—
1356C4#348114yes—
1357C2—44no—
1358C2—81no—
1359C2—84no—
1360C2C2×#348111yescharacteristic
1361C2#6281411yescharacteristic
1362C2#6286111yescharacteristic
1363C2#6293112yes—
1364C2#6300712yes—
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. #59786C2semidirect
2. #59730C2semidirect
3. #59615C2semidirect
4. #59588C2semidirect
5. #44644C2semidirect
6. #44631C2semidirect
7. #44311C2semidirect
8. #44152C2semidirect
9. #39554C2semidirect
10. #39494C2semidirect
11. #39417C2semidirect
12. #39356C2semidirect
13. #39143C2semidirect
14. #38061C2semidirect
15. #38057C2semidirect
16. #36602C2semidirect
17. #36574C2semidirect
18. #36374C2semidirect
19. #35671C2semidirect
20. #35601C2semidirect
21. #35332C2semidirect
22. #35300C2semidirect
23. #34902C2semidirect
24. #34312C2semidirect
25. #34276C2semidirect
26. #34125C2semidirect
27. C4×#541C2semidirect
714. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#597862
#597302
#596152
#595882
#446442
#446312
#443112
#441522
#395542
#394942
#394172
#393562
#391432
#380612
#380572
#366022
#365742
#363742
#356712
#356012
#353322
#353002
#349022
#343122
#342762
#341252
C4×#5412