Finite Group Databasebeta

← #7658452

Subgroups — #7658452

Order 512.

4517 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42783C213yesmaximal, complemented
2#42781C213yesmaximal, complemented
3#42775C213yesmaximal, complemented
4#42772C213yesmaximal, complemented
5#42768C213yesmaximal, complemented
6#42762C213yesmaximal, complemented
7#42713C213yesmaximal, complemented
8#42707C213yesmaximal, complemented
9#42526C213yesmaximal, complemented
10#42513C213yesmaximal, complemented
11#42473C213yesmaximal, complemented
12#42459C213yesmaximal, complemented
13#37637C213yesmaximal, complemented
14#37593C213yesmaximal, complemented
15#37581C213yesmaximal, complemented
16#36693C213yesmaximal, complemented
17#35996C211yesmaximal, characteristic, complemented
18#35957C211yesmaximal, characteristic, complemented
19#35920C211yesmaximal, characteristic, complemented
20#35910C211yesmaximal, characteristic, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35854C211yesmaximal, characteristic, complemented
23#35854C211yesmaximal, characteristic, complemented
24#35845C211yesmaximal, characteristic, complemented
25#35816C211yesmaximal, characteristic, complemented
26#35786C211yesmaximal, characteristic, complemented
27#35771C211yesmaximal, characteristic
28#35723C211yesmaximal, characteristic, complemented
29#34337C211yesmaximal, characteristic, complemented
30#34312C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×#519C2211yescharacteristic
41#2839C2213yes—
42#2839C2213yes—
43#2838C2213yes—
44#2838C2213yes—
45#2838C2213yes—
46#2838C2213yes—
47#2837C2211yescharacteristic
48#2837C2213yes—
49#2832C2213yes—
50#2832C2213yes—
51#2831C2213yes—
52#2831C2216yes—
53#2831C2213yes—
54#2830C2213yes—
55#2830C2213yes—
56#2829C2213yes—
57#2829C2213yes—
58#2800C2216yes—
59#2790C2216yes—
60#2775C2216yes—
61#2774C2216yes—
62#2772C2216yes—
63#2772C2216yes—
64#2770C2216yes—
65#2767C2216yes—
66#2766C2216yes—
67#2757C2216yes—
68#2754C2216yes—
69#2751C2216yes—
70#2723C2216yes—
71#2718C2216yes—
72#2705C2216yes—
73#2698C2216yes—
74#2665C2216yes—
75#2663C2216yes—
76#2660C2213yes—
77#2654C2216yes—
78#2652C2216yes—
79#2652C2216yes—
80#2651C2216yes—
81#2650C2216yes—
82#2650C2216yes—
83#2647C2216yes—
84#2645C2213yes—
85#2644C2216yes—
86#2644C2213yes—
87#2642C2213yes—
88#2640C2213yes—
89#2640C2213yes—
90#2637C2216yes—
91#2637C2216yes—
92#2629C2213yes—
93#2629C2213yes—
94#2628C2213yes—
95#2625C2213yes—
96#2625C2213yes—
97#2620C2213yes—
98#2592C2213yes—
99#2592C2213yes—
100#2584C2213yes—
101#2582C2213yes—
102#2581C2213yes—
103#2568C2213yes—
104#2567C2213yes—
105#2567C2213yes—
106#2566C2213yes—
107#2565C2213yes—
108#2563C2213yes—
109#2563C2213yes—
110#2562C2213yes—
111#2552C2213yes—
112#2552C2213yes—
113#2550C2213yes—
114#2550C2213yes—
115#2545C2213yes—
116#2538C2213yes—
117#2538C2213yes—
118#2530C2216yes—
119#2527C2216yes—
120#2513C2213yes—
121#2512C2216yes—
122#2512C2213yes—
123#2512C2213yes—
124#2511C2213yes—
125#2511C2213yes—
126#2511C2213yes—
127#2508C2216yes—
128#2502C2213yes—
129#2499C2213yes—
130#2497C2213yes—
131#2496C2213yes—
132#2496C2213yes—
133#2496C2213yes—
134#2496C2213yes—
135#2494C2213yes—
136#2492C2213yes—
137#2492C2213yes—
138#2490C2213yes—
139#2490C2213yes—
140#2490C2213yes—
141#2490C2213yes—
142#2489C2213yes—
143#2489C2213yes—
144#2489C2213yes—
145#2489C2213yes—
146#2489C2213yes—
147#2489C2213yes—
148#2486C2213yes—
149#2485C2213yes—
150#2465C2216yes—
151#2458C2216yes—
152#2454C2213yes—
153#2453C2213yes—
154#2453C2213yes—
155#2453C2213yes—
156#2452C2213yes—
157#2451C2213yes—
158#2447C2213yes—
159#2447C2213yes—
160#2446C2213yes—
161#2446C2213yes—
162#2442C2213yes—
163#2441C2213yes—
164#2441C2213yes—
165#2441C2213yes—
166#2440C2213yes—
167#2439C2213yes—
168#2429C2213yes—
169#2426C2213yes—
170#2423C2213yes—
171#2422C2213yes—
172#2422C2213yes—
173#2421C2213yes—
174#2415C2213yes—
175#2414C2213yes—
176#2401C2213yes—
177#2401C2213yes—
178#2399C2213yes—
179#2398C2213yes—
180#2398C2213yes—
181#2398C2213yes—
182#2396C2213yes—
183#2396C2213yes—
184#2396C2213yes—
185#2395C2213yes—
186#2395C2213yes—
187#2392C2213yes—
188#2370C2213yes—
189#2370C2213yes—
190#2367C2213yes—
191#2365C2213yes—
192#2363C2213yes—
193#2360C2213yes—
194#2356C2213yes—
195#2355C2213yes—
196#2352C2213yes—
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2213yes—
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208#2347C2213yes—
209#2346C2213yes—
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222#2330C2213yes—
223#2330C2213yes—
224#2324C2213yes—
225#2323C2213yes—
226#2320C2213yes—
227#2314C2213yes—
228C4×C4⋊Q8C2213yes—
229C4×#124C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2295C2213yes—
233#2293C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—28no—
242#557—44no—
243#557—44no—
244D4×Q8—44no—
245#548—28no—
246#548—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×#126C2316yes—
252C2×#126C2316yes—
253C2×#125C2313yes—
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#123C2316yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2316yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269#520—44no—
270#519—28no—
271#519—44no—
272C2×C4×Q8C2313yes—
273C2×C4×Q8C2313yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2316yes—
291C2×C4×Q8C2311yescharacteristic
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×#117C2313yes—
298C2×#117C2313yes—
299C2×#117C2313yes—
300C2×#117C2313yes—
301C2×#117C2313yes—
302C22×C4⋊C4C2313yes—
303#401C2313yes—
304#401C2313yes—
305#400C2316yes—
306#400C2313yes—
307#400C2313yes—
308#400C2313yes—
309#400C2313yes—
310#400C2313yes—
311#400C2313yes—
312#400C2316yes—
313#400C2316yes—
314#400C2316yes—
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#400C2311yescharacteristic
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2316yes—
330#399C2313yes—
331#399C2313yes—
332#399C2311yescharacteristic
333#399C2311yescharacteristic
334#399C2313yes—
335#399C2316yes—
336#398C2313yes—
337#398C2316yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#398C2313yes—
342#398C2311yescharacteristic
343#398C2313yes—
344#398C2313yes—
345#398C2313yes—
346#398C2316yes—
347#398C2316yes—
348#398C2311yescharacteristic
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2316yes—
353#398C2316yes—
354#398C2316yes—
355#398C2316yes—
356#397C2313yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2316yes—
369#397C2316yes—
370#397C2316yes—
371#397C2313yes—
372#397C2313yes—
373#397C2311yescharacteristic
374#397C2311yescharacteristic
375#397C2313yes—
376#397C2313yes—
377#397C2313yes—
378#397C2316yes—
379#397C2316yes—
380#397C2316yes—
381#397C2316yes—
382#397C2316yes—
383#397C2316yes—
384#396C2313yes—
385#396C2316yes—
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2313yes—
390#396C2311yescharacteristic
391#396C2311yescharacteristic
392#396C2313yes—
393#396C2313yes—
394#396C2313yes—
395#396C2316yes—
396#396C2316yes—
397#396C2316yes—
398#396C2316yes—
399#396C2316yes—
400#395C2313yes—
401#395C2313yes—
402#395C2316yes—
403#395C2316yes—
404#395C2313yes—
405#395C2313yes—
406#395C2313yes—
407#395C2313yes—
408#395C2313yes—
409#394C2313yes—
410#394C2311yescharacteristic
411#394C2311yescharacteristic
412#394C2313yes—
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2313yes—
417#394C2313yes—
418#394C2313yes—
419#394C2313yes—
420#394C2311yescharacteristic
421#394C2313yes—
422#394C2316yes—
423#393C2313yes—
424#393C2313yes—
425#393C2316yes—
426#393C2316yes—
427#393C2313yes—
428#393C2313yes—
429#393C2313yes—
430#393C2313yes—
431#393C2313yes—
432#393C2313yes—
433#393C2313yes—
434#392C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2313yes—
438#391C2313yes—
439#391C2313yes—
440#391C2316yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#391C2316yes—
445#391C2313yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2316yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#390C2316yes—
457#390C2316yes—
458#390C2313yes—
459#390C2313yes—
460#390C2313yes—
461#390C2313yes—
462#390C2313yes—
463#390C2313yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2316yes—
469#389C2316yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2316yes—
477#389C2316yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2311yescharacteristic
485#389C2313yes—
486#389C2313yes—
487#389C2316yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2316yes—
493#389C2316yes—
494#389C2313yes—
495#389C2316yes—
496#389C2316yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2316yes—
502#388C2316yes—
503#388C2316yes—
504#388C2313yes—
505#388C2316yes—
506#388C2313yes—
507#388C2313yes—
508#388C2311yescharacteristic
509#388C2313yes—
510#388C2313yes—
511#388C2311yescharacteristic
512#388C2313yes—
513#388C2316yes—
514#388C2316yes—
515#388C2316yes—
516#388C2316yes—
517#388C2316yes—
518#388C2316yes—
519#388C2316yes—
520#388C2316yes—
521#388C2316yes—
522#388C2316yes—
523#388C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2313yes—
529#387C2313yes—
530#387C2313yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2316yes—
537#387C2316yes—
538#387C2316yes—
539#387C2316yes—
540#387C2316yes—
541#387C2316yes—
542#387C2316yes—
543#387C2316yes—
544#387C2316yes—
545#387C2316yes—
546#387C2316yes—
547#387C2316yes—
548#386C2316yes—
549#385C2316yes—
550#385C2316yes—
551#385C2316yes—
552#385C2316yes—
553#385C2316yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2316yes—
560#384C2313yes—
561#384C2313yes—
562#383C2316yes—
563#382C2316yes—
564#382C2316yes—
565#382C2313yes—
566#382C2316yes—
567#382C2316yes—
568#382C2313yes—
569#382C2313yes—
570#381C2316yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2316yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2316yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2316yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2316yes—
622#376C2313yes—
623#376C2313yes—
624#376C2313yes—
625#376C2316yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2413yes—
640C22×Q8C2413yes—
641C22×Q8C2411yescharacteristic
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2411yescharacteristic
645C22×D4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2416yes—
650C4⋊Q8—212no—
651C4⋊Q8—46no—
652C4⋊Q8—46no—
653C4⋊Q8—46no—
654#126—86no—
655#126—86no—
656#125—212no—
657#125—212no—
658#125—46no—
659#125—46no—
660#125—46no—
661#125—46no—
662#124—212no—
663#124—46no—
664#123—86no—
665C22⋊Q8—212no—
666C22⋊Q8—46no—
667C22⋊Q8—46no—
668C22⋊Q8—46no—
669C22⋊Q8—86no—
670#121—212no—
671#121—46no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—212no—
684C4×Q8—212no—
685C4×Q8—212no—
686C4×Q8—46no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×Q8—86no—
691C4×Q8#4118yes—
692C4×D4—212no—
693C4×D4—46no—
694C4×D4—46no—
695C4×D4—46no—
696C4×D4—46no—
697#117—212no—
698#117—212no—
699#117—46no—
700#117—46no—
701#117—46no—
702C2×C4⋊C4—46no—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2416yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2411yescharacteristic
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2416yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2416yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2416yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2416yes—
819C2×C42C2413yes—
820C2×C42C2416yes—
821C2×C42C2416yes—
822C2×C42C2411yescharacteristic
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2416yes—
826C2×C42C2413yes—
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2416yes—
842#95C2416yes—
843#95C2411yescharacteristic
844#95C2413yes—
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2416yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2416yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2416yes—
870#95C2411yescharacteristic
871#95C2413yes—
872#95C2413yes—
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2413yes—
876#95C2416yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2416yes—
890#95C2416yes—
891#95C2416yes—
892#95C2416yes—
893#95C2416yes—
894#95C2416yes—
895C24C2511yescharacteristic
896C24C2513yes—
897C24C2511yescharacteristic
898#41—416no—
899C2×Q8—26no—
900C2×Q8—26no—
901C2×Q8—26no—
902C2×Q8—26no—
903C2×Q8—26no—
904C2×Q8—26no—
905C2×Q8—26no—
906C2×Q8—43no—
907C2×Q8—43no—
908C2×Q8—43no—
909C2×Q8—43no—
910C2×Q8—43no—
911C2×Q8—43no—
912C2×Q8—43no—
913C2×Q8—43no—
914C2×Q8—416no—
915C2×Q8—416no—
916C2×Q8C2×#4114yes—
917C2×Q8H(5,𝔽2)14yes—
918C2×Q82−1+414yes—
919C2×D4—26no—
920C2×D4—26no—
921C2×D4—26no—
922C2×D4—26no—
923C2×D4—41no—
924C2×D4—41no—
925C2×D4—41no—
926C2×D4—43no—
927C2×D4—43no—
928C2×D4—43no—
929C2×D4—43no—
930C2×D4—43no—
931C22×C4—26no—
932C22×C4—26no—
933C22×C4—26no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—46no—
941C22×C4—46no—
942C22×C4—46no—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2513yes—
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2513yes—
954C22×C4C2513yes—
955C22×C4C2513yes—
956C22×C4C2513yes—
957C22×C4C2513yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C22×C4C2511yescharacteristic
962C22×C4C2513yes—
963C22×C4C2513yes—
964C22×C4C2511yescharacteristic
965C22×C4C2513yes—
966C22×C4C2513yes—
967C22×C4C2511yescharacteristic
968C22×C4C2511yescharacteristic
969C22×C4C2513yes—
970C22×C4C2513yes—
971C4⋊C4—26no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—22no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—212no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—46no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—43no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—43no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—41no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—46no—
1023C4⋊C4—43no—
1024C4⋊C4—46no—
1025C4⋊C4—46no—
1026C4⋊C4—46no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4C2×#41112yes—
1032C22⋊C4—26no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—26no—
1036C22⋊C4—212no—
1037C22⋊C4—41no—
1038C22⋊C4—43no—
1039C22⋊C4—43no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—41no—
1043C22⋊C4—46no—
1044C22⋊C4—41no—
1045C22⋊C4—43no—
1046C22⋊C4—41no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C22⋊C4—46no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—43no—
1058C22⋊C4—43no—
1059C22⋊C4—43no—
1060C22⋊C4—41no—
1061C22⋊C4—43no—
1062C22⋊C4—43no—
1063C22⋊C4—43no—
1064C22⋊C4—46no—
1065C22⋊C4—43no—
1066C22⋊C4—46no—
1067C22⋊C4—43no—
1068C22⋊C4—43no—
1069C22⋊C4—46no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C42—26no—
1075C42—212no—
1076C42—26no—
1077C42—26no—
1078C42—26no—
1079C42—26no—
1080C42—26no—
1081C42—26no—
1082C42—26no—
1083C42—26no—
1084C42—26no—
1085C42—26no—
1086C42—43no—
1087C42—46no—
1088C42—43no—
1089C42—41no—
1090C42—46no—
1091C42—43no—
1092C42—46no—
1093C42—46no—
1094C42C2×#41112yes—
1095C23—21no—
1096C23—23no—
1097C23—21no—
1098C23—21no—
1099C23—23no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—23no—
1104C23—21no—
1105C23—23no—
1106C23—21no—
1107C23—23no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—23no—
1112C23—21no—
1113C23—21no—
1114C23—23no—
1115C23—21no—
1116C23C2611yescharacteristic
1117Q8—412no—
1118Q8—412no—
1119Q8—412no—
1120Q8—86no—
1121Q8—86no—
1122Q8#542116yes—
1123D4—44no—
1124D4—412no—
1125D4—86no—
1126D4—86no—
1127C2×C4—21no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—21no—
1131C2×C4—23no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—21no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—23no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—21no—
1206C2×C4—412no—
1207C2×C4—412no—
1208C2×C4—412no—
1209C2×C4—166no—
1210C2×C4C22×#4116yes—
1211C2×C4C22×#4112yes—
1212C2×C4C22×#4116yes—
1213C2×C4C2×H(5,𝔽2)16yes—
1214C2×C4C2×2−1+416yes—
1215C22—41no—
1216C22—41no—
1217C22—43no—
1218C22—43no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—43no—
1224C22—41no—
1225C22—41no—
1226C22—43no—
1227C22—41no—
1228C22—43no—
1229C22—41no—
1230C22—41no—
1231C22—43no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—43no—
1236C22C23×#4111yescharacteristic
1237C22C22×H(5,𝔽2)11yescharacteristic
1238C22C22×2−1+411yescharacteristic
1239C22H(7,𝔽2)11yescharacteristic
1240C222−1+611yescharacteristic
1241C222−1+611yescharacteristic
1242C222−1+611yescharacteristic
1243C4—22no—
1244C4—26no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—43no—
1249C4—43no—
1250C4—41no—
1251C4—41no—
1252C4—43no—
1253C4—43no—
1254C4—43no—
1255C4—43no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—43no—
1260C4—43no—
1261C4—43no—
1262C4—43no—
1263C4—43no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—43no—
1269C4—43no—
1270C4C2×#542112yes—
1271C2—81no—
1272C2—81no—
1273C2—83no—
1274C2C22×#54211yescharacteristic
1275C2#6285111yescharacteristic
1276C2#6286111yescharacteristic
1277C2#6304411yescharacteristic
1278C2#6305211yescharacteristic
1279C2#6305711yescharacteristic
1280C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35771C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42783C2semidirect
2. #42781C2semidirect
3. #42775C2semidirect
4. #42772C2semidirect
5. #42768C2semidirect
6. #42762C2semidirect
7. #42713C2semidirect
8. #42707C2semidirect
9. #42526C2semidirect
10. #42513C2semidirect
11. #42473C2semidirect
12. #42459C2semidirect
13. #37637C2semidirect
14. #37593C2semidirect
15. #37581C2semidirect
16. #36693C2semidirect
17. #35996C2semidirect
18. #35957C2semidirect
19. #35920C2semidirect
20. #35910C2semidirect
21. #35898C2semidirect
22. #35854C2semidirect
23. #35854C2semidirect
24. #35845C2semidirect
25. #35816C2semidirect
26. #35786C2semidirect
28. #35723C2semidirect
29. #34337C2semidirect
30. #34312C2semidirect
31. #34262C2semidirect

Maximal subgroups

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

subgroupindex
#427832
#427812
#427752
#427722
#427682
#427622
#427132
#427072
#425262
#425132
#424732
#424592
#376372
#375932
#375812
#366932
#359962
#359572
#359202
#359102
#358982
#358542
#358452
#358162
#357862
#357712
#357232
#343372
#343122
#342622