Finite Group Databasebeta

← #7658003

Subgroups — #7658003

Order 512.

4590 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41592C214yesmaximal, complemented
2#41583C214yesmaximal, complemented
3#41199C214yesmaximal, complemented
4#41194C214yesmaximal, complemented
5#41186C214yesmaximal, complemented
6#41176C214yesmaximal, complemented
7#39564C212yesmaximal, complemented
8#39563C212yesmaximal, complemented
9#39484C211yesmaximal, characteristic, complemented
10#39463C212yesmaximal
11#39366C211yesmaximal, characteristic, complemented
12#37938C212yesmaximal, complemented
13#37757C212yesmaximal, complemented
14#37582C212yesmaximal, complemented
15#37509C212yesmaximal, complemented
16#37504C212yesmaximal, complemented
17#36571C212yesmaximal, complemented
18#36196C211yesmaximal, characteristic, complemented
19#36151C211yesmaximal, characteristic, complemented
20#35887C214yesmaximal, complemented
21#35864C214yesmaximal, complemented
22#35337C211yesmaximal, characteristic, complemented
23#35257C212yesmaximal, complemented
24#34629C211yesmaximal, characteristic, complemented
25#34627C212yesmaximal, complemented
26#34314C212yesmaximal, complemented
27#34141C211yesmaximal, characteristic
28C2×#552C2212yes—
29C2×#544C2212yes—
30C2×#533C2212yes—
31C2×#532C2211yescharacteristic
32C2×C4×#41C2212yes—
33#2862C2211yescharacteristic
34#2859C2211yescharacteristic
35#2857C2212yes—
36#2857C2212yes—
37#2851C2212yes—
38#2851C2212yes—
39#2851C2212yes—
40#2839C2214yes—
41#2839C2214yes—
42#2836C2214yes—
43#2835C2214yes—
44#2830C2214yes—
45#2827C2214yes—
46#2799C2214yes—
47#2786C2214yes—
48#2786C2214yes—
49#2782C2214yes—
50#2764C2214yes—
51#2758C2214yes—
52#2758C2214yes—
53#2757C2214yes—
54#2751C2214yes—
55#2750C2214yes—
56#2743C2214yes—
57#2738C2214yes—
58#2729C2214yes—
59#2728C2214yes—
60#2726C2214yes—
61#2724C2214yes—
62#2719C2214yes—
63#2713C2214yes—
64#2713C2214yes—
65#2711C2214yes—
66#2709C2214yes—
67#2708C2214yes—
68#2692C2214yes—
69#2690C2214yes—
70#2666C2214yes—
71#2664C2214yes—
72#2655C2214yes—
73#2655C2214yes—
74#2655C2214yes—
75#2654C2214yes—
76#2653C2214yes—
77#2652C2214yes—
78#2652C2214yes—
79#2651C2214yes—
80#2650C2214yes—
81#2650C2214yes—
82#2647C2211yescharacteristic
83#2647C2211yescharacteristic
84#2647C2211yescharacteristic
85#2646C2214yes—
86#2645C2212yes—
87#2643C2214yes—
88#2642C2211yescharacteristic
89#2638C2214yes—
90#2638C2214yes—
91#2634C2214yes—
92#2633C2214yes—
93#2629C2211yescharacteristic
94#2629C2212yes—
95#2628C2212yes—
96#2628C2212yes—
97#2628C2212yes—
98#2625C2212yes—
99#2625C2212yes—
100#2625C2212yes—
101#2621C2212yes—
102#2621C2211yescharacteristic
103#2616C2212yes—
104#2616C2212yes—
105#2611C2214yes—
106#2601C2214yes—
107#2597C2214yes—
108#2596C2214yes—
109#2595C2214yes—
110#2589C2214yes—
111#2589C2214yes—
112#2588C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2588C2214yes—
117#2585C2214yes—
118#2583C2214yes—
119#2578C2214yes—
120#2573C2214yes—
121#2565C2212yes—
122#2562C2212yes—
123#2560C2214yes—
124#2559C2214yes—
125#2556C2214yes—
126#2556C2214yes—
127#2550C2212yes—
128#2536C2212yes—
129#2533C2214yes—
130#2533C2214yes—
131#2532C2214yes—
132#2529C2214yes—
133#2521C2214yes—
134#2520C2214yes—
135#2520C2214yes—
136#2509C2212yes—
137#2506C2212yes—
138#2505C2214yes—
139#2502C2212yes—
140#2499C2212yes—
141#2497C2212yes—
142#2497C2212yes—
143#2496C2212yes—
144#2495C2212yes—
145#2492C2214yes—
146#2492C2212yes—
147#2489C2214yes—
148#2489C2212yes—
149#2487C2212yes—
150#2485C2212yes—
151#2481C2214yes—
152#2478C2214yes—
153#2478C2214yes—
154#2477C2214yes—
155#2477C2214yes—
156#2477C2214yes—
157#2476C2214yes—
158#2475C2214yes—
159#2474C2214yes—
160#2473C2214yes—
161#2473C2214yes—
162#2466C2214yes—
163#2454C2214yes—
164#2453C2214yes—
165#2453C2214yes—
166#2453C2212yes—
167#2452C2214yes—
168#2451C2214yes—
169#2451C2212yes—
170#2450C2214yes—
171#2450C2214yes—
172#2449C2214yes—
173#2449C2214yes—
174#2446C2214yes—
175#2442C2212yes—
176#2439C2212yes—
177#2421C2214yes—
178#2421C2212yes—
179#2421C2212yes—
180#2417C2212yes—
181#2415C2212yes—
182#2415C2214yes—
183#2402C2214yes—
184#2401C2214yes—
185#2399C2214yes—
186#2398C2214yes—
187#2395C2214yes—
188#2395C2214yes—
189#2373C2214yes—
190#2373C2214yes—
191#2370C2212yes—
192#2370C2214yes—
193#2370C2214yes—
194#2368C2214yes—
195#2367C2212yes—
196#2367C2212yes—
197#2366C2212yes—
198#2365C2212yes—
199#2364C2212yes—
200#2364C2212yes—
201#2362C2212yes—
202#2362C2214yes—
203#2361C2212yes—
204#2361C2212yes—
205#2360C2212yes—
206#2359C2214yes—
207#2352C2212yes—
208#2351C2212yes—
209#2347C2212yes—
210#2344C2212yes—
211#2343C2214yes—
212#2336C2214yes—
213#2334C2214yes—
214#2331C2212yes—
215#2322C2214yes—
216#2317C2212yes—
217#2314C2211yescharacteristic
218#2314C2211yescharacteristic
219#2311C2212yes—
220#2311C2212yes—
221C4×C4⋊Q8C2211yescharacteristic
222C4×#125C2212yes—
223C4×#125C2211yescharacteristic
224C4×C22⋊Q8C2212yes—
225C4×C22⋊Q8C2212yes—
226C4×C22⋊Q8C2212yes—
227C4×C22⋊Q8C2212yes—
228C4×C22⋊Q8C2212yes—
229#2297C2212yes—
230#2296C2212yes—
231#2295C2212yes—
232#2293C2211yescharacteristic
233#2293C2211yescharacteristic
234C2×#389C2212yes—
235#2290C2212yes—
236#2290C2212yes—
237#2283C2212yes—
238#2274C2214yes—
239C42×D4C2211yescharacteristic
240C42×D4C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×C4×C4⋊C4C2211yescharacteristic
243C22×#41C2312yes—
244#552—216no—
245#544—48no—
246#533—48no—
247#532—28no—
248C2×C4⋊Q8C2311yescharacteristic
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2314yes—
253C2×#127C2311yescharacteristic
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2312yes—
257C2×#125C2311yescharacteristic
258C2×#125C2314yes—
259C2×#125C2312yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#124C2312yes—
264C2×#123C2314yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×#121C2311yescharacteristic
276C2×#121C2311yescharacteristic
277C2×#121C2312yes—
278C4×#41—48no—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2314yes—
283C2×C4×Q8C2312yes—
284C2×C4×Q8C2312yes—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2311yescharacteristic
296C2×#117C2312yes—
297C2×#117C2311yescharacteristic
298C2×#117C2312yes—
299C2×#117C2314yes—
300C2×#117C2311yescharacteristic
301C2×#117C2312yes—
302C2×#117C2314yes—
303C2×#117C2314yes—
304C2×#117C2312yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2314yes—
308C22×C4⋊C4C2312yes—
309C22×C42C2311yescharacteristic
310C22×C42C2312yes—
311C22×C42C2312yes—
312C22×C42C2312yes—
313#401C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
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#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
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#397C2314yes—
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#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#391C2314yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2312yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2312yes—
436#391C2314yes—
437#390C2314yes—
438#390C2314yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2312yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2312yes—
501#388C2312yes—
502#388C2312yes—
503#388C2312yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2312yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
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#387C2312yes—
549#387C2312yes—
550#386C2312yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2312yes—
556#386C2314yes—
557#386C2312yes—
558#386C2312yes—
559#386C2312yes—
560#386C2312yes—
561#386C2312yes—
562#386C2312yes—
563#386C2314yes—
564#386C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2312yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2312yes—
585#385C2312yes—
586#385C2312yes—
587#385C2314yes—
588#385C2314yes—
589#384C2311yescharacteristic
590#384C2312yes—
591#384C2311yescharacteristic
592#384C2311yescharacteristic
593#383C2314yes—
594#383C2314yes—
595#383C2314yes—
596#382C2312yes—
597#382C2311yescharacteristic
598#382C2312yes—
599#382C2311yescharacteristic
600#382C2311yescharacteristic
601#382C2312yes—
602#382C2314yes—
603#382C2314yes—
604#381C2314yes—
605#381C2314yes—
606#380C2312yes—
607#380C2312yes—
608#380C2312yes—
609#380C2312yes—
610#380C2312yes—
611#380C2312yes—
612#380C2312yes—
613#380C2312yes—
614#380C2312yes—
615#380C2314yes—
616#380C2312yes—
617#380C2314yes—
618#380C2314yes—
619#380C2312yes—
620#380C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2314yes—
628C4×C4⋊C4C2314yes—
629C4×C4⋊C4C2311yescharacteristic
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2314yes—
632C4×C4⋊C4C2314yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2314yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2311yescharacteristic
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2311yescharacteristic
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670#376C2311yescharacteristic
671#376C2314yes—
672#376C2314yes—
673#376C2311yescharacteristic
674C2×#95C2314yes—
675C2×#95C2311yescharacteristic
676C2×#95C2311yescharacteristic
677C43C2311yescharacteristic
678C43C2311yescharacteristic
679C2×#41—28no—
680C2×#41—28no—
681C2×#41—44no—
682C22×Q8C2412yes—
683C22×Q8C2412yes—
684C22×Q8C2414yes—
685C22×Q8C2414yes—
686C22×D4C2412yes—
687C22×D4C2412yes—
688C22×D4C2412yes—
689C22×D4C2411yescharacteristic
690C22×D4C2412yes—
691C22×D4C2411yescharacteristic
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2414yes—
697C23×C4C2412yes—
698C23×C4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2412yes—
701C23×C4C2411yescharacteristic
702C23×C4C2414yes—
703C23×C4C2412yes—
704C23×C4C2412yes—
705C4⋊Q8—24no—
706C4⋊Q8—24no—
707C4⋊Q8—28no—
708C4⋊Q8—44no—
709C4⋊Q8—48no—
710#127—24no—
711#126—216no—
712#126—48no—
713#125—216no—
714#125—28no—
715#125—24no—
716#125—48no—
717#125—48no—
718#125—44no—
719#125—48no—
720#124—28no—
721#123—216no—
722C22⋊Q8—28no—
723C22⋊Q8—28no—
724C22⋊Q8—28no—
725C22⋊Q8—48no—
726C22⋊Q8—48no—
727C22⋊Q8—48no—
728C22⋊Q8—48no—
729C22⋊Q8—44no—
730C22⋊Q8—48no—
731C22⋊Q8—44no—
732#121—24no—
733#121—24no—
734#121—28no—
735C4×Q8—28no—
736C4×Q8—44no—
737C4×Q8—44no—
738C4×Q8—44no—
739C4×Q8—44no—
740C4×Q8—48no—
741C4×D4—28no—
742C4×D4—24no—
743C4×D4—44no—
744C4×D4—44no—
745C4×D4—44no—
746C4×D4—44no—
747C4×D4—44no—
748C4×D4—44no—
749C4×D4—44no—
750C4×D4—44no—
751C4×D4#4118yes—
752#117—28no—
753#117—24no—
754#117—216no—
755#117—24no—
756#117—28no—
757#117—44no—
758#117—48no—
759#117—48no—
760#117—44no—
761C2×C4⋊C4—28no—
762C2×C4⋊C4—44no—
763C2×C4⋊C4—48no—
764C2×C4⋊C4—44no—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2411yescharacteristic
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
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⋊C4C2411yescharacteristic
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2412yes—
858C2×C42—24no—
859C2×C42—28no—
860C2×C42—44no—
861C2×C42—44no—
862C2×C42C2411yescharacteristic
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2411yescharacteristic
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892#95C2414yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2414yes—
896#95C2412yes—
897#95C2412yes—
898#95C2411yescharacteristic
899#95C2411yescharacteristic
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2412yes—
905#95C2414yes—
906#95C2412yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2414yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
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#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
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—
961C24C2512yes—
962C24C2512yes—
963C24C2511yescharacteristic
964#41—432no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—28no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—44no—
974C2×Q8—44no—
975C2×Q8—44no—
976C2×Q8—44no—
977C2×D4—24no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—22no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—42no—
988C2×D4—42no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4—42no—
992C2×D4C2×#4114yes—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—28no—
998C22×C4—22no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—24no—
1004C22×C4—22no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4C2×#4118yes—
1029C22×C42−1+414yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2514yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2512yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2512yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2511yescharacteristic
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—28no—
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—28no—
1060C4⋊C4—24no—
1061C4⋊C4—22no—
1062C4⋊C4—28no—
1063C4⋊C4—28no—
1064C4⋊C4—28no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—24no—
1070C4⋊C4—28no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4C2×#4114yes—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—24no—
1114C22⋊C4—28no—
1115C22⋊C4—24no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4C2×#4118yes—
1147C42—22no—
1148C42—22no—
1149C42—22no—
1150C42—28no—
1151C42—28no—
1152C42—24no—
1153C42—24no—
1154C42—24no—
1155C42—22no—
1156C42—24no—
1157C42—22no—
1158C42—22no—
1159C42—28no—
1160C42—42no—
1161C42—42no—
1162C42—42no—
1163C42—42no—
1164C42—42no—
1165C42—42no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—42no—
1174C42—42no—
1175C42C2×#4114yes—
1176C42H(5,𝔽2)14yes—
1177C23—21no—
1178C23—22no—
1179C23—21no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23C22×#4114yes—
1195C23C2×2−1+412yes—
1196C23C2611yescharacteristic
1197Q8—48no—
1198Q8—48no—
1199Q8—88no—
1200Q8—164no—
1201D4—44no—
1202D4—48no—
1203D4—48no—
1204D4—44no—
1205D4—48no—
1206D4—84no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—216no—
1218C2×C4—28no—
1219C2×C4—21no—
1220C2×C4—24no—
1221C2×C4—21no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—48no—
1269C2×C4—44no—
1270C2×C4—416no—
1271C2×C4—48no—
1272C2×C4—82no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—164no—
1279C2×C4C22×#4112yes—
1280C2×C4C22×#4114yes—
1281C2×C4C22×#4112yes—
1282C2×C4C22×#4112yes—
1283C2×C4C2×H(5,𝔽2)14yes—
1284C2×C4C2×H(5,𝔽2)12yes—
1285C2×C4C2×2−1+412yes—
1286C2×C4C2×2−1+412yes—
1287C2×C4#58514yes—
1288C22—22no—
1289C22—24no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—41no—
1294C22—41no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22C23×#4111yescharacteristic
1308C22C22×H(5,𝔽2)11yescharacteristic
1309C22C22×2−1+411yescharacteristic
1310C22C2×#58512yes—
1311C222−1+612yes—
1312C4—24no—
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—24no—
1317C4—24no—
1318C4—42no—
1319C4—44no—
1320C4—44no—
1321C4—41no—
1322C4—41no—
1323C4—44no—
1324C4—44no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—44no—
1330C4—44no—
1331C4—44no—
1332C4—42no—
1333C4—42no—
1334C4—44no—
1335C4#352014yes—
1336C2—42no—
1337C2—44no—
1338C2—82no—
1339C2#6268611yescharacteristic
1340C2C2×#352011yescharacteristic
1341C2#6286111yescharacteristic
1342C2#6295412yes—
1343C2#6295612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41592C2semidirect
2. #41583C2semidirect
3. #41199C2semidirect
4. #41194C2semidirect
5. #41186C2semidirect
6. #41176C2semidirect
7. #39564C2semidirect
8. #39563C2semidirect
9. #39484C2semidirect
11. #39366C2semidirect
12. #37938C2semidirect
13. #37757C2semidirect
14. #37582C2semidirect
15. #37509C2semidirect
16. #37504C2semidirect
17. #36571C2semidirect
18. #36196C2semidirect
19. #36151C2semidirect
20. #35887C2semidirect
21. #35864C2semidirect
22. #35337C2semidirect
23. #35257C2semidirect
24. #34629C2semidirect
25. #34627C2semidirect
26. #34314C2semidirect

Maximal subgroups

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

subgroupindex
#415922
#415832
#411992
#411942
#411862
#411762
#395642
#395632
#394842
#394632
#393662
#379382
#377572
#375822
#375092
#375042
#365712
#361962
#361512
#358872
#358642
#353372
#352572
#346292
#346272
#343142
#341412