Finite Group Databasebeta

← #7689942

Subgroups — #7689942

Order 512.

4798 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59962C213yesmaximal, complemented
2#59764C213yesmaximal, complemented
3#59446C213yesmaximal, complemented
4#59332C213yesmaximal, complemented
5#59264C213yesmaximal, complemented
6#45178C213yesmaximal, complemented
7#45172C213yesmaximal, complemented
8#45012C213yesmaximal, complemented
9#44904C213yesmaximal, complemented
10#39474C213yesmaximal, complemented
11#38969C213yesmaximal, complemented
12#38264C213yesmaximal, complemented
13#38260C213yesmaximal, complemented
14#36475C211yesmaximal, characteristic, complemented
15#36475C211yesmaximal, characteristic, complemented
16#36447C211yesmaximal, characteristic, complemented
17#36431C211yesmaximal, characteristic, complemented
18#36431C211yesmaximal, characteristic, complemented
19#36372C213yesmaximal, complemented
20#36171C213yesmaximal, complemented
21#36076C211yesmaximal, characteristic
22#36059C211yesmaximal, characteristic, complemented
23#36005C211yesmaximal, characteristic
24#35898C211yesmaximal, characteristic, complemented
25#34793C213yesmaximal, complemented
26#34336C211yesmaximal, characteristic, complemented
27#34263C211yesmaximal, characteristic, complemented
28#34263C211yesmaximal, characteristic, complemented
29#34184C211yesmaximal, characteristic, complemented
30C4×#550C211yesmaximal, characteristic
31#34125C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2864C2213yes—
39#2864C2213yes—
40#2859C2213yes—
41#2851C2213yes—
42#2851C2213yes—
43#2793C2216yes—
44#2781C2216yes—
45#2779C2216yes—
46#2773C2216yes—
47#2764C2216yes—
48#2761C2216yes—
49#2754C2216yes—
50#2751C2216yes—
51#2751C2216yes—
52#2738C2216yes—
53#2721C2216yes—
54#2707C2216yes—
55#2694C2216yes—
56#2694C2216yes—
57#2644C2213yes—
58#2644C2213yes—
59#2624C2213yes—
60#2624C2213yes—
61#2609C2216yes—
62#2601C2216yes—
63#2580C2213yes—
64#2580C2213yes—
65#2575C2216yes—
66#2573C2216yes—
67#2571C2213yes—
68#2570C2213yes—
69#2570C2213yes—
70#2570C2213yes—
71#2570C2213yes—
72#2566C2213yes—
73#2566C2213yes—
74#2558C2216yes—
75#2553C2216yes—
76#2552C2213yes—
77#2530C2213yes—
78#2530C2213yes—
79#2528C2213yes—
80#2528C2211yescharacteristic
81#2524C2216yes—
82#2517C2213yes—
83#2517C2216yes—
84#2517C2213yes—
85#2513C2213yes—
86#2513C2213yes—
87#2513C2213yes—
88#2513C2213yes—
89#2512C2213yes—
90#2512C2213yes—
91#2511C2213yes—
92#2509C2213yes—
93#2509C2213yes—
94#2508C2213yes—
95#2508C2213yes—
96#2508C2213yes—
97#2508C2213yes—
98#2507C2213yes—
99#2507C2213yes—
100#2506C2213yes—
101#2506C2213yes—
102#2506C2213yes—
103#2506C2213yes—
104#2506C2213yes—
105#2504C2213yes—
106#2501C2213yes—
107#2499C2213yes—
108#2498C2216yes—
109#2497C2213yes—
110#2496C2213yes—
111#2495C2213yes—
112#2495C2213yes—
113#2495C2213yes—
114#2494C2213yes—
115#2494C2213yes—
116#2493C2216yes—
117#2489C2213yes—
118#2488C2216yes—
119#2487C2213yes—
120#2486C2213yes—
121#2485C2213yes—
122#2477C2216yes—
123#2475C2216yes—
124#2470C2216yes—
125#2468C2216yes—
126#2460C2216yes—
127#2460C2213yes—
128#2460C2213yes—
129#2454C2213yes—
130#2454C2213yes—
131#2452C2213yes—
132#2452C2213yes—
133#2445C2213yes—
134#2445C2213yes—
135#2445C2213yes—
136#2445C2213yes—
137#2441C2213yes—
138#2441C2213yes—
139#2441C2213yes—
140#2439C2213yes—
141#2439C2213yes—
142#2422C2213yes—
143#2422C2213yes—
144#2420C2213yes—
145#2420C2213yes—
146#2419C2216yes—
147#2419C2216yes—
148#2415C2213yes—
149#2401C2213yes—
150#2401C2213yes—
151#2395C2213yes—
152#2395C2213yes—
153#2370C2213yes—
154#2370C2213yes—
155#2369C2213yes—
156#2366C2213yes—
157#2363C2213yes—
158#2363C2213yes—
159#2359C2216yes—
160#2359C2216yes—
161#2357C2213yes—
162#2357C2213yes—
163#2357C2213yes—
164#2357C2213yes—
165#2355C2213yes—
166#2354C2213yes—
167#2354C2213yes—
168#2354C2213yes—
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176#2351C2211yescharacteristic
177#2351C2211yescharacteristic
178#2351C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2211yescharacteristic
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185#2349C2213yes—
186#2349C2213yes—
187#2349C2213yes—
188#2349C2213yes—
189#2347C2213yes—
190#2347C2213yes—
191#2345C2213yes—
192#2345C2213yes—
193#2344C2213yes—
194#2344C2213yes—
195#2343C2216yes—
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199#2341C2211yescharacteristic
200#2341C2211yescharacteristic
201#2341C2211yescharacteristic
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2331C2213yes—
205#2330C2213yes—
206#2319C2213yes—
207#2319C2213yes—
208#2317C2213yes—
209#2317C2213yes—
210#2314C2213yes—
211#2314C2213yes—
212C4×#127C2213yes—
213C4×#125C2213yes—
214C4×#125C2213yes—
215C4×#125C2213yes—
216C4×#125C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×#121C2213yes—
220C4×#121C2213yes—
221#2298C2213yes—
222#2298C2213yes—
223#2295C2213yes—
224#2293C2213yes—
225#2293C2213yes—
226#2293C2213yes—
227#2293C2213yes—
228#2285C2213yes—
229#2283C2213yes—
230C2×#382C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C4×#117C2213yes—
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240#557—28no—
241#550—28no—
242C2×C4⋊Q8C2313yes—
243C2×#127C2313yes—
244C2×#126C2316yes—
245C2×#125C2313yes—
246C2×#125C2313yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2316yes—
251C2×#123C2316yes—
252C2×#123C2316yes—
253C2×#123C2316yes—
254C2×C22⋊Q8C2313yes—
255C2×C22⋊Q8C2313yes—
256C2×#121C2313yes—
257C2×#121C2313yes—
258#520—28no—
259#520—28no—
260C4×#41—28no—
261C4×#41—28no—
262C2×C4×Q8C2313yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×C4×D4C2313yes—
283C2×C4×D4C2313yes—
284C2×C4×D4C2313yes—
285C2×C4×D4C2313yes—
286C2×C4×D4C2313yes—
287C2×C4×D4C2316yes—
288C2×#117C2313yes—
289C2×#117C2313yes—
290C2×#117C2313yes—
291C2×#117C2313yes—
292C2×#117C2316yes—
293C2×#117C2313yes—
294C2×#117C2313yes—
295C2×#117C2316yes—
296C22×C4⋊C4C2313yes—
297C22×C4⋊C4C2313yes—
298C22×C42C2313yes—
299C22×C42C2313yes—
300#401C2311yescharacteristic
301#401C2313yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2316yes—
306#400C2316yes—
307#400C2316yes—
308#400C2313yes—
309#400C2311yescharacteristic
310#400C2313yes—
311#400C2311yescharacteristic
312#400C2313yes—
313#400C2313yes—
314#400C2313yes—
315#400C2313yes—
316#399C2316yes—
317#399C2316yes—
318#399C2316yes—
319#399C2313yes—
320#399C2313yes—
321#398C2316yes—
322#398C2316yes—
323#398C2316yes—
324#398C2316yes—
325#398C2316yes—
326#398C2311yescharacteristic
327#398C2313yes—
328#398C2316yes—
329#397C2313yes—
330#397C2316yes—
331#397C2313yes—
332#397C2313yes—
333#397C2316yes—
334#397C2316yes—
335#397C2316yes—
336#397C2316yes—
337#397C2316yes—
338#397C2313yes—
339#397C2313yes—
340#397C2313yes—
341#397C2313yes—
342#397C2313yes—
343#397C2313yes—
344#397C2313yes—
345#397C2313yes—
346#397C2313yes—
347#396C2316yes—
348#396C2316yes—
349#396C2316yes—
350#396C2316yes—
351#396C2316yes—
352#396C2313yes—
353#396C2313yes—
354#394C2313yes—
355#394C2316yes—
356#394C2316yes—
357#394C2316yes—
358#394C2316yes—
359#394C2313yes—
360#394C2313yes—
361#394C2313yes—
362#393C2316yes—
363#393C2316yes—
364#391C2313yes—
365#391C2316yes—
366#391C2313yes—
367#391C2313yes—
368#391C2313yes—
369#390C2313yes—
370#390C2313yes—
371#390C2316yes—
372#390C2316yes—
373#390C2313yes—
374#390C2313yes—
375#390C2313yes—
376#390C2313yes—
377#390C2313yes—
378#390C2313yes—
379#390C2313yes—
380#390C2313yes—
381#390C2313yes—
382#390C2313yes—
383#390C2313yes—
384#390C2313yes—
385#390C2313yes—
386#390C2313yes—
387#389C2311yescharacteristic
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2313yes—
394#389C2313yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2316yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#388C2316yes—
432#388C2316yes—
433#388C2316yes—
434#388C2316yes—
435#388C2316yes—
436#388C2313yes—
437#388C2313yes—
438#388C2316yes—
439#388C2316yes—
440#388C2316yes—
441#388C2316yes—
442#388C2316yes—
443#388C2316yes—
444#388C2316yes—
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2316yes—
449#388C2313yes—
450#388C2313yes—
451#388C2316yes—
452#388C2313yes—
453#388C2316yes—
454#387C2311yescharacteristic
455#387C2311yescharacteristic
456#387C2313yes—
457#387C2313yes—
458#387C2313yes—
459#387C2313yes—
460#387C2313yes—
461#387C2316yes—
462#387C2313yes—
463#387C2313yes—
464#387C2313yes—
465#387C2313yes—
466#387C2313yes—
467#387C2313yes—
468#387C2313yes—
469#387C2313yes—
470#387C2316yes—
471#387C2316yes—
472#387C2316yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2313yes—
478#387C2316yes—
479#387C2313yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2316yes—
488#387C2316yes—
489#387C2313yes—
490#387C2313yes—
491#387C2311yescharacteristic
492#387C2311yescharacteristic
493#387C2311yescharacteristic
494#387C2311yescharacteristic
495#387C2311yescharacteristic
496#386C2316yes—
497#386C2316yes—
498#386C2316yes—
499#386C2316yes—
500#386C2316yes—
501#385C2313yes—
502#385C2313yes—
503#385C2316yes—
504#385C2316yes—
505#385C2316yes—
506#385C2316yes—
507#385C2316yes—
508#385C2316yes—
509#385C2313yes—
510#385C2313yes—
511#385C2316yes—
512#385C2316yes—
513#385C2316yes—
514#384C2313yes—
515#384C2313yes—
516#384C2313yes—
517#384C2313yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#383C2316yes—
523#383C2316yes—
524#382C2313yes—
525#382C2313yes—
526#382C2313yes—
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2313yes—
535#382C2313yes—
536#382C2313yes—
537#382C2316yes—
538#382C2313yes—
539#382C2316yes—
540#382C2311yescharacteristic
541#381C2316yes—
542#381C2316yes—
543#381C2316yes—
544#381C2316yes—
545#380C2313yes—
546#380C2313yes—
547#380C2313yes—
548#380C2316yes—
549#380C2316yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2316yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2316yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
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⋊C4C2311yescharacteristic
598C4×C22⋊C4C2316yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615#376C2313yes—
616#376C2313yes—
617#376C2313yes—
618#376C2311yescharacteristic
619C2×#95C2316yes—
620C2×#95C2316yes—
621C43C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41#4118yes—
630C22×Q8C2413yes—
631C22×Q8C2411yescharacteristic
632C22×D4C2413yes—
633C22×D4C2413yes—
634C22×D4C2413yes—
635C22×D4C2416yes—
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2413yes—
639C23×C4C2416yes—
640C23×C4C2416yes—
641C23×C4C2413yes—
642C23×C4C2413yes—
643C23×C4C2413yes—
644C4⋊Q8—212no—
645#127—212no—
646#126—86no—
647#125—212no—
648#125—212no—
649#125—46no—
650#125—46no—
651#125—46no—
652#125—86no—
653#123—412no—
654#123—412no—
655#123—86no—
656C22⋊Q8—46no—
657C22⋊Q8—46no—
658#121—212no—
659#121—212no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
672C4×Q8—212no—
673C4×Q8#4118yes—
674C4×D4—212no—
675C4×D4—212no—
676C4×D4—212no—
677C4×D4—212no—
678C4×D4—212no—
679C4×D4—212no—
680C4×D4—212no—
681C4×D4—212no—
682C4×D4—212no—
683C4×D4—46no—
684C4×D4—46no—
685C4×D4—86no—
686#117—212no—
687#117—212no—
688#117—212no—
689#117—212no—
690#117—46no—
691#117—412no—
692#117—46no—
693#117—86no—
694C2×C4⋊C4—212no—
695C2×C4⋊C4—212no—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2411yescharacteristic
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⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2413yes—
760C2×C22⋊C4C2413yes—
761C2×C22⋊C4C2416yes—
762C2×C22⋊C4C2416yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2416yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2416yes—
773C2×C22⋊C4C2416yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2413yes—
788C2×C42—212no—
789C2×C42—212no—
790C2×C42C2411yescharacteristic
791C2×C42C2411yescharacteristic
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2411yescharacteristic
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2413yes—
811C2×C42C2416yes—
812C2×C42C2413yes—
813C2×C42C2416yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821#95C2413yes—
822#95C2413yes—
823#95C2413yes—
824#95C2413yes—
825#95C2416yes—
826#95C2416yes—
827#95C2416yes—
828#95C2416yes—
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2411yescharacteristic
834#95C2411yescharacteristic
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2411yescharacteristic
868#95C2416yes—
869#95C2416yes—
870#95C2411yescharacteristic
871#95C2416yes—
872#95C2413yes—
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2416yes—
889#95C2416yes—
890C24C2513yes—
891C24C2513yes—
892#41—232no—
893#41—416no—
894C2×Q8—26no—
895C2×Q8—43no—
896C2×Q8—43no—
897C2×Q8C2×#4114yes—
898C2×Q8C2×#4114yes—
899C2×Q82−1+414yes—
900C2×D4—26no—
901C2×D4—212no—
902C2×D4—26no—
903C2×D4—26no—
904C2×D4—26no—
905C2×D4—26no—
906C2×D4—26no—
907C2×D4—26no—
908C2×D4—43no—
909C2×D4—46no—
910C2×D4—46no—
911C2×D4C2×#41112yes—
912C22×C4—26no—
913C22×C4—26no—
914C22×C4—212no—
915C22×C4—212no—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—26no—
923C22×C4—26no—
924C22×C4—43no—
925C22×C4—46no—
926C22×C4—46no—
927C22×C4—43no—
928C22×C4—43no—
929C22×C4—43no—
930C22×C4—43no—
931C22×C4—43no—
932C22×C4—43no—
933C22×C4—46no—
934C22×C4—46no—
935C22×C4C2×#41112yes—
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2511yescharacteristic
939C22×C4C2511yescharacteristic
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2511yescharacteristic
944C22×C4C2513yes—
945C22×C4C2513yes—
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2513yes—
949C22×C4C2513yes—
950C22×C4C2511yescharacteristic
951C22×C4C2513yes—
952C22×C4C2511yescharacteristic
953C22×C4C2513yes—
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2513yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2513yes—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—212no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—26no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—22no—
989C4⋊C4—26no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—43no—
999C4⋊C4—43no—
1000C4⋊C4—43no—
1001C4⋊C4—46no—
1002C4⋊C4—43no—
1003C4⋊C4—46no—
1004C4⋊C4—46no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—46no—
1008C4⋊C4—43no—
1009C4⋊C4—46no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—43no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—46no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4C2×#41112yes—
1025C22⋊C4—26no—
1026C22⋊C4—26no—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—26no—
1030C22⋊C4—212no—
1031C22⋊C4—212no—
1032C22⋊C4—26no—
1033C22⋊C4—26no—
1034C22⋊C4—26no—
1035C22⋊C4—26no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4—46no—
1039C22⋊C4—43no—
1040C22⋊C4—43no—
1041C22⋊C4—46no—
1042C22⋊C4—43no—
1043C22⋊C4—43no—
1044C22⋊C4—43no—
1045C22⋊C4—46no—
1046C22⋊C4—43no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C22⋊C4—46no—
1050C22⋊C4—46no—
1051C22⋊C4—46no—
1052C22⋊C4—46no—
1053C22⋊C4—43no—
1054C22⋊C4—43no—
1055C22⋊C4—46no—
1056C22⋊C4—43no—
1057C42—22no—
1058C42—22no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—26no—
1067C42—26no—
1068C42—26no—
1069C42—26no—
1070C42—26no—
1071C42—26no—
1072C42—26no—
1073C42—22no—
1074C42—26no—
1075C42—22no—
1076C42—22no—
1077C42—43no—
1078C42—46no—
1079C42—43no—
1080C42—46no—
1081C42—43no—
1082C42—43no—
1083C42—43no—
1084C42—43no—
1085C42—43no—
1086C42—43no—
1087C42C2×#41112yes—
1088C23—23no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—23no—
1093C23—23no—
1094C23—23no—
1095C23—23no—
1096C23—23no—
1097C23—23no—
1098C23—23no—
1099C23—23no—
1100C23—23no—
1101C23C22×#4116yes—
1102C23C2611yescharacteristic
1103Q8—86no—
1104Q8#552116yes—
1105D4—224no—
1106D4—412no—
1107D4—412no—
1108D4—812no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—21no—
1121C2×C4—224no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—21no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—412no—
1189C2×C4—412no—
1190C2×C4—86no—
1191C2×C4—86no—
1192C2×C4—86no—
1193C2×C4—812no—
1194C2×C4—812no—
1195C2×C4C22×#4112yes—
1196C2×C4C22×#4116yes—
1197C2×C4C22×#4112yes—
1198C2×C4C22×#4116yes—
1199C2×C4C22×#4116yes—
1200C2×C4C2×2−1+416yes—
1201C2×C4#58512yes—
1202C2×C4#58512yes—
1203C2×C4#58512yes—
1204C22—26no—
1205C22—26no—
1206C22—26no—
1207C22—43no—
1208C22—43no—
1209C22—43no—
1210C22—43no—
1211C22—43no—
1212C22—43no—
1213C22—43no—
1214C22—43no—
1215C22—43no—
1216C22—43no—
1217C22—43no—
1218C22C23×#4111yescharacteristic
1219C22C23×#4111yescharacteristic
1220C22C22×2−1+411yescharacteristic
1221C22C2×#58511yescharacteristic
1222C22C2×#58511yescharacteristic
1223C22C2×#58511yescharacteristic
1224C22H(7,𝔽2)11yescharacteristic
1225C4—22no—
1226C4—22no—
1227C4—22no—
1228C4—22no—
1229C4—26no—
1230C4—22no—
1231C4—41no—
1232C4—43no—
1233C4—43no—
1234C4—43no—
1235C4—41no—
1236C4—41no—
1237C4—43no—
1238C4—43no—
1239C4—43no—
1240C4—41no—
1241C4—43no—
1242C4—41no—
1243C4—41no—
1244C4—43no—
1245C4—43no—
1246C4—41no—
1247C4—43no—
1248C4—41no—
1249C4—41no—
1250C4—43no—
1251C4—43no—
1252C4—41no—
1253C4C2×#552112yes—
1254C2—46no—
1255C2—83no—
1256C2C22×#55211yescharacteristic
1257C2#6281011yescharacteristic
1258C2#6281611yescharacteristic
1259C2#6295211yescharacteristic
1260C2#6300611yescharacteristic
1261C2#6301011yescharacteristic
1262C2#6303311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#550C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59962C2semidirect
2. #59764C2semidirect
3. #59446C2semidirect
4. #59332C2semidirect
5. #59264C2semidirect
6. #45178C2semidirect
7. #45172C2semidirect
8. #45012C2semidirect
9. #44904C2semidirect
10. #39474C2semidirect
11. #38969C2semidirect
12. #38264C2semidirect
13. #38260C2semidirect
14. #36475C2semidirect
15. #36475C2semidirect
16. #36447C2semidirect
17. #36431C2semidirect
18. #36431C2semidirect
19. #36372C2semidirect
20. #36171C2semidirect
22. #36059C2semidirect
24. #35898C2semidirect
25. #34793C2semidirect
26. #34336C2semidirect
27. #34263C2semidirect
28. #34263C2semidirect
29. #34184C2semidirect
31. #34125C2semidirect

Maximal subgroups

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

subgroupindex
#599622
#597642
#594462
#593322
#592642
#451782
#451722
#450122
#449042
#394742
#389692
#382642
#382602
#364752
#364472
#364312
#363722
#361712
#360762
#360592
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