Finite Group Databasebeta

← #7661974

Subgroups — #7661974

Order 512.

4727 conjugacy classes of subgroups.

The subgroup lattice has 1307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52284C213yesmaximal, complemented
2#42735C213yesmaximal, complemented
3#42734C213yesmaximal, complemented
4#42604C213yesmaximal, complemented
5#42596C213yesmaximal, complemented
6#42472C213yesmaximal, complemented
7#42466C213yesmaximal, complemented
8#40203C213yesmaximal, complemented
9#40151C213yesmaximal, complemented
10#40142C213yesmaximal, complemented
11#40001C213yesmaximal, complemented
12#39771C213yesmaximal, complemented
13#39213C213yesmaximal, complemented
14#37408C213yesmaximal, complemented
15#37357C213yesmaximal, complemented
16#37322C213yesmaximal, complemented
17#36585C211yesmaximal, characteristic, complemented
18#36474C211yesmaximal, characteristic, complemented
19#36467C211yesmaximal, characteristic, complemented
20#36457C211yesmaximal, characteristic, complemented
21#36432C211yesmaximal, characteristic, complemented
22#36431C211yesmaximal, characteristic, complemented
23#36059C211yesmaximal, characteristic, complemented
24#36018C211yesmaximal, characteristic
25#35983C211yesmaximal, characteristic, complemented
26#35948C211yesmaximal, characteristic, complemented
27#35748C211yesmaximal, characteristic, complemented
28#35711C211yesmaximal, characteristic, complemented
29#34335C211yesmaximal, characteristic, complemented
30#34295C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×Q82C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41#2862C2213yes—
42#2861C2213yes—
43#2860C2213yes—
44#2858C2213yes—
45#2855C2213yes—
46#2851C2213yes—
47#2831C2216yes—
48#2829C2216yes—
49#2800C2213yes—
50#2799C2213yes—
51#2796C2216yes—
52#2796C2216yes—
53#2793C2213yes—
54#2779C2213yes—
55#2777C2213yes—
56#2773C2213yes—
57#2767C2213yes—
58#2765C2213yes—
59#2764C2216yes—
60#2763C2216yes—
61#2762C2216yes—
62#2761C2216yes—
63#2759C2216yes—
64#2759C2211yescharacteristic
65#2757C2216yes—
66#2754C2216yes—
67#2751C2216yes—
68#2751C2213yes—
69#2751C2216yes—
70#2737C2216yes—
71#2731C2213yes—
72#2730C2213yes—
73#2730C2216yes—
74#2729C2213yes—
75#2723C2216yes—
76#2718C2213yes—
77#2715C2213yes—
78#2712C2216yes—
79#2712C2216yes—
80#2710C2213yes—
81#2700C2216yes—
82#2700C2216yes—
83#2700C2216yes—
84#2653C2216yes—
85#2651C2216yes—
86#2650C2216yes—
87#2644C2213yes—
88#2640C2216yes—
89#2640C2213yes—
90#2638C2216yes—
91#2632C2216yes—
92#2628C2213yes—
93#2628C2213yes—
94#2625C2213yes—
95#2619C2213yes—
96#2592C2213yes—
97#2592C2213yes—
98#2581C2213yes—
99#2580C2213yes—
100#2580C2213yes—
101#2568C2213yes—
102#2567C2213yes—
103#2566C2213yes—
104#2563C2213yes—
105#2562C2213yes—
106#2550C2213yes—
107#2550C2213yes—
108#2550C2213yes—
109#2550C2213yes—
110#2548C2213yes—
111#2548C2213yes—
112#2547C2213yes—
113#2546C2213yes—
114#2542C2213yes—
115#2536C2213yes—
116#2532C2216yes—
117#2527C2216yes—
118#2513C2213yes—
119#2513C2213yes—
120#2513C2213yes—
121#2513C2213yes—
122#2513C2213yes—
123#2513C2213yes—
124#2503C2213yes—
125#2499C2213yes—
126#2495C2213yes—
127#2495C2213yes—
128#2495C2213yes—
129#2494C2213yes—
130#2494C2213yes—
131#2494C2213yes—
132#2492C2213yes—
133#2492C2213yes—
134#2492C2213yes—
135#2491C2213yes—
136#2491C2213yes—
137#2491C2213yes—
138#2491C2213yes—
139#2491C2213yes—
140#2491C2213yes—
141#2491C2213yes—
142#2490C2213yes—
143#2489C2213yes—
144#2487C2213yes—
145#2485C2213yes—
146#2465C2216yes—
147#2461C2216yes—
148#2454C2213yes—
149#2452C2213yes—
150#2452C2213yes—
151#2452C2213yes—
152#2451C2213yes—
153#2451C2213yes—
154#2448C2216yes—
155#2447C2213yes—
156#2447C2216yes—
157#2447C2213yes—
158#2447C2213yes—
159#2447C2213yes—
160#2441C2213yes—
161#2440C2213yes—
162#2440C2213yes—
163#2439C2213yes—
164#2439C2213yes—
165#2439C2213yes—
166#2426C2213yes—
167#2426C2213yes—
168#2422C2213yes—
169#2420C2213yes—
170#2420C2213yes—
171#2420C2213yes—
172#2414C2213yes—
173#2414C2213yes—
174#2401C2213yes—
175#2398C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2395C2213yes—
179#2392C2213yes—
180#2369C2213yes—
181#2366C2213yes—
182#2365C2213yes—
183#2365C2213yes—
184#2363C2213yes—
185#2361C2213yes—
186#2356C2213yes—
187#2355C2213yes—
188#2355C2213yes—
189#2352C2213yes—
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2347C2213yes—
201#2346C2213yes—
202#2341C2211yescharacteristic
203#2341C2211yescharacteristic
204#2341C2211yescharacteristic
205#2341C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214#2332C2216yes—
215#2331C2213yes—
216#2331C2213yes—
217#2328C2213yes—
218#2326C2216yes—
219#2324C2213yes—
220#2320C2213yes—
221#2314C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×C4⋊Q8C2213yes—
224C4×#126C2213yes—
225C4×#124C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×#123C2213yes—
229C4×#121C2213yes—
230#2298C2213yes—
231#2295C2213yes—
232#2295C2213yes—
233#2290C2213yes—
234#2276C2211yescharacteristic
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—28no—
242Q82—44no—
243#557—44no—
244#550—28no—
245#548—44no—
246#548—44no—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×#127C2313yes—
256C2×#126C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#124C2316yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2316yes—
265C2×#124C2316yes—
266C2×#123C2313yes—
267C2×C22⋊Q8C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2316yes—
272C2×#121C2313yes—
273C2×#121C2313yes—
274C2×#121C2313yes—
275C2×#121C2313yes—
276#520—44no—
277#519—28no—
278C4×#41—44no—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2316yes—
296C2×C4×Q8C2311yescharacteristic
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2316yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C22×C4⋊C4C2313yes—
310C22×C42C2313yes—
311#401C2316yes—
312#401C2311yescharacteristic
313#400C2316yes—
314#400C2313yes—
315#400C2316yes—
316#400C2313yes—
317#400C2316yes—
318#400C2313yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#399C2316yes—
325#399C2316yes—
326#399C2313yes—
327#399C2313yes—
328#399C2313yes—
329#398C2316yes—
330#398C2313yes—
331#398C2316yes—
332#398C2313yes—
333#398C2313yes—
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#397C2316yes—
338#397C2316yes—
339#397C2316yes—
340#397C2316yes—
341#397C2316yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2313yes—
346#397C2313yes—
347#397C2316yes—
348#397C2316yes—
349#397C2311yescharacteristic
350#397C2316yes—
351#397C2316yes—
352#397C2311yescharacteristic
353#397C2313yes—
354#397C2313yes—
355#397C2316yes—
356#397C2313yes—
357#397C2313yes—
358#397C2313yes—
359#396C2316yes—
360#396C2316yes—
361#396C2313yes—
362#396C2313yes—
363#396C2313yes—
364#396C2313yes—
365#396C2313yes—
366#396C2313yes—
367#396C2313yes—
368#395C2316yes—
369#395C2316yes—
370#395C2316yes—
371#395C2313yes—
372#395C2316yes—
373#395C2311yescharacteristic
374#394C2316yes—
375#394C2313yes—
376#394C2313yes—
377#394C2316yes—
378#394C2316yes—
379#394C2316yes—
380#394C2316yes—
381#394C2313yes—
382#394C2313yes—
383#394C2313yes—
384#394C2313yes—
385#394C2316yes—
386#394C2313yes—
387#393C2316yes—
388#393C2316yes—
389#393C2313yes—
390#393C2316yes—
391#393C2313yes—
392#393C2316yes—
393#393C2316yes—
394#393C2316yes—
395#393C2316yes—
396#393C2316yes—
397#393C2311yescharacteristic
398#393C2311yescharacteristic
399#392C2316yes—
400#392C2313yes—
401#391C2311yescharacteristic
402#391C2316yes—
403#391C2313yes—
404#391C2316yes—
405#391C2316yes—
406#391C2313yes—
407#391C2313yes—
408#391C2316yes—
409#391C2316yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2316yes—
415#391C2316yes—
416#391C2316yes—
417#391C2313yes—
418#391C2313yes—
419#391C2316yes—
420#391C2313yes—
421#391C2313yes—
422#391C2311yescharacteristic
423#391C2313yes—
424#391C2311yescharacteristic
425#390C2316yes—
426#390C2313yes—
427#390C2313yes—
428#390C2316yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2316yes—
435#390C2313yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#390C2313yes—
443#390C2313yes—
444#390C2313yes—
445#390C2316yes—
446#390C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#388C2313yes—
475#388C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2316yes—
479#388C2313yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#388C2316yes—
484#388C2316yes—
485#388C2316yes—
486#388C2313yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2313yes—
492#388C2313yes—
493#388C2316yes—
494#388C2316yes—
495#388C2313yes—
496#388C2316yes—
497#388C2313yes—
498#388C2313yes—
499#388C2316yes—
500#388C2316yes—
501#388C2313yes—
502#388C2311yescharacteristic
503#388C2313yes—
504#388C2311yescharacteristic
505#388C2313yes—
506#388C2313yes—
507#388C2311yescharacteristic
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2313yes—
515#387C2316yes—
516#387C2316yes—
517#387C2313yes—
518#387C2313yes—
519#387C2316yes—
520#387C2313yes—
521#387C2316yes—
522#387C2313yes—
523#387C2313yes—
524#387C2316yes—
525#387C2313yes—
526#387C2313yes—
527#387C2313yes—
528#387C2313yes—
529#387C2313yes—
530#387C2313yes—
531#387C2311yescharacteristic
532#387C2311yescharacteristic
533#386C2316yes—
534#386C2313yes—
535#386C2316yes—
536#386C2316yes—
537#386C2313yes—
538#386C2316yes—
539#386C2313yes—
540#385C2313yes—
541#385C2316yes—
542#385C2313yes—
543#385C2313yes—
544#385C2316yes—
545#385C2316yes—
546#385C2316yes—
547#385C2316yes—
548#385C2316yes—
549#385C2313yes—
550#385C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#383C2311yescharacteristic
555#383C2316yes—
556#383C2316yes—
557#382C2313yes—
558#382C2313yes—
559#382C2313yes—
560#382C2313yes—
561#382C2313yes—
562#382C2316yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#381C2316yes—
569#381C2316yes—
570#381C2316yes—
571#381C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2316yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2316yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622#376C2313yes—
623#376C2316yes—
624#376C2313yes—
625C43C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2411yescharacteristic
638C22×Q8C2411yescharacteristic
639C22×Q8C2413yes—
640C22×Q8C2416yes—
641C22×Q8C2416yes—
642C22×Q8C2411yescharacteristic
643C22×D4C2413yes—
644C22×D4C2413yes—
645C22×D4C2416yes—
646C22×D4C2413yes—
647C22×D4C2413yes—
648C22×D4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2416yes—
653C23×C4C2413yes—
654C23×C4C2413yes—
655C4⋊Q8—212no—
656C4⋊Q8—212no—
657C4⋊Q8—212no—
658C4⋊Q8—46no—
659C4⋊Q8—46no—
660C4⋊Q8—46no—
661C4⋊Q8—46no—
662C4⋊Q8—46no—
663#127—212no—
664#126—46no—
665#125—46no—
666#125—46no—
667#124—412no—
668#124—46no—
669#124—46no—
670#124—46no—
671#124—46no—
672#124—86no—
673#124—86no—
674#123—46no—
675C22⋊Q8—412no—
676C22⋊Q8—46no—
677C22⋊Q8—46no—
678C22⋊Q8—46no—
679C22⋊Q8—86no—
680#121—212no—
681#121—212no—
682#121—46no—
683#121—46no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—212no—
696C4×Q8—212no—
697C4×Q8—212no—
698C4×Q8—46no—
699C4×Q8—46no—
700C4×Q8—86no—
701C4×Q8#4118yes—
702C4×D4—212no—
703C4×D4—46no—
704C4×D4—46no—
705C4×D4—46no—
706C4×D4—46no—
707C4×D4—46no—
708C4×D4—46no—
709C4×D4—86no—
710#117—212no—
711#117—212no—
712#117—46no—
713#117—46no—
714C2×C4⋊C4—46no—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2411yescharacteristic
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⋊C4C2416yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C22⋊C4C2411yescharacteristic
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2416yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2411yescharacteristic
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2416yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C42—46no—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2416yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2411yescharacteristic
826C2×C42C2413yes—
827C2×C42C2416yes—
828C2×C42C2413yes—
829C2×C42C2416yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2411yescharacteristic
834C2×C42C2413yes—
835C2×C42C2411yescharacteristic
836C2×C42C2413yes—
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2416yes—
848#95C2416yes—
849#95C2413yes—
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2416yes—
871#95C2413yes—
872#95C2413yes—
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2416yes—
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2416yes—
883#95C2413yes—
884#95C2416yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2416yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2416yes—
897#95C2416yes—
898#95C2416yes—
899#95C2416yes—
900#95C2416yes—
901#95C2416yes—
902#95C2416yes—
903C24C2511yescharacteristic
904C24C2513yes—
905C24C2513yes—
906#41—416no—
907#41—416no—
908C2×Q8—22no—
909C2×Q8—26no—
910C2×Q8—212no—
911C2×Q8—26no—
912C2×Q8—26no—
913C2×Q8—22no—
914C2×Q8—22no—
915C2×Q8—26no—
916C2×Q8—41no—
917C2×Q8—41no—
918C2×Q8—41no—
919C2×Q8—43no—
920C2×Q8—46no—
921C2×Q8—46no—
922C2×Q8—43no—
923C2×Q8—46no—
924C2×Q8—46no—
925C2×Q8—46no—
926C2×Q8—416no—
927C2×Q8C2×#4114yes—
928C2×Q8H(5,𝔽2)14yes—
929C2×Q82−1+414yes—
930C2×D4—26no—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—212no—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—26no—
937C2×D4—26no—
938C2×D4—43no—
939C2×D4—43no—
940C2×D4—46no—
941C2×D4—43no—
942C2×D4—46no—
943C2×D4—43no—
944C2×D4—43no—
945C2×D4—43no—
946C2×D4—43no—
947C2×D4—43no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—26no—
954C22×C4—26no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4—43no—
961C22×C4—43no—
962C22×C4—43no—
963C22×C4—46no—
964C22×C4—46no—
965C22×C4—46no—
966C22×C4C2511yescharacteristic
967C22×C4C2513yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2513yes—
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2511yescharacteristic
984C22×C4C2511yescharacteristic
985C22×C4C2513yes—
986C22×C4C2511yescharacteristic
987C22×C4C2513yes—
988C22×C4C2511yescharacteristic
989C22×C4C2511yescharacteristic
990C22×C4C2513yes—
991C22×C4C2511yescharacteristic
992C22×C4C2511yescharacteristic
993C22×C4C2513yes—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—22no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—22no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—43no—
1015C4⋊C4—41no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—41no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—41no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—46no—
1031C4⋊C4—46no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—46no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4C2×#41112yes—
1045C22⋊C4—26no—
1046C22⋊C4—22no—
1047C22⋊C4—26no—
1048C22⋊C4—26no—
1049C22⋊C4—26no—
1050C22⋊C4—26no—
1051C22⋊C4—22no—
1052C22⋊C4—26no—
1053C22⋊C4—22no—
1054C22⋊C4—26no—
1055C22⋊C4—43no—
1056C22⋊C4—46no—
1057C22⋊C4—46no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—43no—
1061C22⋊C4—43no—
1062C22⋊C4—43no—
1063C22⋊C4—46no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—43no—
1067C22⋊C4—43no—
1068C22⋊C4—43no—
1069C22⋊C4—46no—
1070C22⋊C4—46no—
1071C22⋊C4—46no—
1072C22⋊C4—43no—
1073C22⋊C4—46no—
1074C22⋊C4—43no—
1075C22⋊C4—46no—
1076C22⋊C4—43no—
1077C22⋊C4—46no—
1078C22⋊C4—46no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—46no—
1087C22⋊C4—43no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C42—26no—
1091C42—212no—
1092C42—26no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—22no—
1104C42—41no—
1105C42—43no—
1106C42—43no—
1107C42—41no—
1108C42—46no—
1109C42—43no—
1110C42—46no—
1111C42—43no—
1112C42—43no—
1113C42—43no—
1114C42C2×#41112yes—
1115C23—21no—
1116C23—23no—
1117C23—23no—
1118C23—23no—
1119C23—23no—
1120C23—21no—
1121C23—21no—
1122C23—23no—
1123C23—23no—
1124C23—23no—
1125C23—23no—
1126C23—23no—
1127C23—21no—
1128C23—23no—
1129C23—21no—
1130C23—21no—
1131C23—23no—
1132C23—23no—
1133C23—23no—
1134C23—23no—
1135C23—21no—
1136C23C2611yescharacteristic
1137Q8—44no—
1138Q8—44no—
1139Q8—412no—
1140Q8—812no—
1141Q8—86no—
1142Q8—166no—
1143Q8#542116yes—
1144D4—412no—
1145D4—412no—
1146D4—86no—
1147D4—812no—
1148D4—86no—
1149D4—86no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—23no—
1199C2×C4—21no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—23no—
1223C2×C4—21no—
1224C2×C4—23no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—412no—
1228C2×C4—412no—
1229C2×C4—412no—
1230C2×C4—86no—
1231C2×C4—86no—
1232C2×C4—166no—
1233C2×C4C22×#4116yes—
1234C2×C4C22×#4112yes—
1235C2×C4C22×#4116yes—
1236C2×C4C2×H(5,𝔽2)16yes—
1237C2×C4C2×2−1+416yes—
1238C2×C4#58512yes—
1239C2×C4#58512yes—
1240C22—43no—
1241C22—43no—
1242C22—41no—
1243C22—43no—
1244C22—43no—
1245C22—41no—
1246C22—41no—
1247C22—43no—
1248C22—43no—
1249C22—41no—
1250C22—43no—
1251C22—43no—
1252C22—43no—
1253C22—41no—
1254C22—43no—
1255C22—43no—
1256C22—43no—
1257C22—41no—
1258C22—41no—
1259C22—43no—
1260C22—43no—
1261C22C23×#4111yescharacteristic
1262C22C22×H(5,𝔽2)11yescharacteristic
1263C22C22×2−1+411yescharacteristic
1264C22C2×#58511yescharacteristic
1265C22C2×#58511yescharacteristic
1266C22H(7,𝔽2)11yescharacteristic
1267C222−1+611yescharacteristic
1268C4—22no—
1269C4—22no—
1270C4—26no—
1271C4—22no—
1272C4—43no—
1273C4—41no—
1274C4—41no—
1275C4—43no—
1276C4—43no—
1277C4—41no—
1278C4—43no—
1279C4—41no—
1280C4—43no—
1281C4—41no—
1282C4—43no—
1283C4—43no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—43no—
1289C4—43no—
1290C4—43no—
1291C4—43no—
1292C4—41no—
1293C4—41no—
1294C4—43no—
1295C4C2×#542112yes—
1296C2—83no—
1297C2—83no—
1298C2—81no—
1299C2C22×#54211yescharacteristic
1300C2#6289711yescharacteristic
1301C2#6292311yescharacteristic
1302C2#6300511yescharacteristic
1303C2#6301011yescharacteristic
1304C2#6303411yescharacteristic
1305C2#6306111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36018C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52284C2semidirect
2. #42735C2semidirect
3. #42734C2semidirect
4. #42604C2semidirect
5. #42596C2semidirect
6. #42472C2semidirect
7. #42466C2semidirect
8. #40203C2semidirect
9. #40151C2semidirect
10. #40142C2semidirect
11. #40001C2semidirect
12. #39771C2semidirect
13. #39213C2semidirect
14. #37408C2semidirect
15. #37357C2semidirect
16. #37322C2semidirect
17. #36585C2semidirect
18. #36474C2semidirect
19. #36467C2semidirect
20. #36457C2semidirect
21. #36432C2semidirect
22. #36431C2semidirect
23. #36059C2semidirect
25. #35983C2semidirect
26. #35948C2semidirect
27. #35748C2semidirect
28. #35711C2semidirect
29. #34335C2semidirect
30. #34295C2semidirect
31. #34262C2semidirect

Maximal subgroups

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

subgroupindex
#522842
#427352
#427342
#426042
#425962
#424722
#424662
#402032
#401512
#401422
#400012
#397712
#392132
#374082
#373572
#373222
#365852
#364742
#364672
#364572
#364322
#364312
#360592
#360182
#359832
#359482
#357482
#357112
#343352
#342952
#342622