Finite Group Databasebeta

← #8096678

Subgroups — #8096678

Order 512.

4335 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53123C213yesmaximal, complemented
2#53086C213yesmaximal, complemented
3#53082C213yesmaximal, complemented
4#53067C213yesmaximal, complemented
5#53020C213yesmaximal, complemented
6#52994C213yesmaximal, complemented
7#52298C213yesmaximal, complemented
8#46347C213yesmaximal, complemented
9#46158C213yesmaximal, complemented
10#46109C213yesmaximal, complemented
11#46105C213yesmaximal, complemented
12#46105C213yesmaximal, complemented
13#46079C213yesmaximal, complemented
14#45674C213yesmaximal, complemented
15#45523C213yesmaximal, complemented
16#45499C213yesmaximal, complemented
17Q8×#126C211yesmaximal, characteristic, complemented
18Q8×#125C211yesmaximal, characteristic, complemented
19#36467C211yesmaximal, characteristic
20#36466C211yesmaximal, characteristic, complemented
21#36458C211yesmaximal, characteristic, complemented
22#36447C211yesmaximal, characteristic, complemented
23#36445C211yesmaximal, characteristic, complemented
24#36445C211yesmaximal, characteristic, complemented
25#36432C211yesmaximal, characteristic
26#35957C211yesmaximal, characteristic, complemented
27#35920C211yesmaximal, characteristic, complemented
28#35898C211yesmaximal, characteristic, complemented
29#35801C211yesmaximal, characteristic
30#35786C211yesmaximal, characteristic, complemented
31#35786C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2863C2213yes—
39#2861C2213yes—
40#2860C2213yes—
41#2859C2213yes—
42#2859C2213yes—
43#2859C2213yes—
44#2857C2213yes—
45#2857C2213yes—
46#2855C2213yes—
47#2841C2216yes—
48#2839C2216yes—
49#2838C2216yes—
50#2837C2216yes—
51#2836C2216yes—
52#2836C2216yes—
53#2836C2216yes—
54#2831C2216yes—
55#2823C2216yes—
56#2820C2216yes—
57#2814C2216yes—
58#2805C2216yes—
59#2799C2216yes—
60#2793C2213yes—
61#2791C2216yes—
62#2787C2213yes—
63#2777C2216yes—
64#2776C2216yes—
65#2774C2213yes—
66#2773C2216yes—
67#2773C2216yes—
68#2773C2216yes—
69#2773C2213yes—
70#2766C2213yes—
71#2762C2213yes—
72#2759C2213yes—
73#2738C2213yes—
74#2729C2216yes—
75#2727C2216yes—
76#2725C2216yes—
77#2725C2211yescharacteristic
78#2725C2216yes—
79#2723C2213yes—
80#2722C2216yes—
81#2721C2216yes—
82#2721C2216yes—
83#2720C2213yes—
84#2720C2216yes—
85#2715C2213yes—
86#2713C2213yes—
87#2707C2213yes—
88#2702C2216yes—
89#2698C2213yes—
90#2698C2216yes—
91#2690C2216yes—
92#2690C2216yes—
93#2689C2216yes—
94#2674C2213yes—
95#2660C2213yes—
96#2645C2213yes—
97#2644C2213yes—
98#2629C2213yes—
99#2629C2213yes—
100#2624C2213yes—
101#2592C2213yes—
102#2584C2213yes—
103#2584C2213yes—
104#2584C2213yes—
105#2582C2213yes—
106#2582C2213yes—
107#2571C2213yes—
108#2567C2213yes—
109#2565C2213yes—
110#2565C2213yes—
111#2562C2213yes—
112#2552C2213yes—
113#2552C2213yes—
114#2552C2213yes—
115#2552C2213yes—
116#2552C2213yes—
117#2552C2213yes—
118#2551C2213yes—
119#2550C2213yes—
120#2550C2213yes—
121#2550C2213yes—
122#2550C2213yes—
123#2542C2213yes—
124#2542C2213yes—
125#2538C2213yes—
126#2538C2213yes—
127#2513C2213yes—
128#2513C2213yes—
129#2512C2213yes—
130#2512C2213yes—
131#2512C2213yes—
132#2512C2213yes—
133#2511C2213yes—
134#2511C2213yes—
135#2511C2213yes—
136#2511C2213yes—
137#2511C2213yes—
138#2511C2213yes—
139#2508C2213yes—
140#2508C2213yes—
141#2507C2213yes—
142#2507C2213yes—
143#2507C2213yes—
144#2507C2213yes—
145#2506C2213yes—
146#2506C2213yes—
147#2500C2213yes—
148#2499C2213yes—
149#2497C2213yes—
150#2497C2213yes—
151#2497C2213yes—
152#2497C2213yes—
153#2497C2213yes—
154#2496C2213yes—
155#2496C2213yes—
156#2496C2213yes—
157#2496C2213yes—
158#2496C2213yes—
159#2495C2213yes—
160#2494C2213yes—
161#2492C2213yes—
162#2491C2213yes—
163#2490C2213yes—
164#2489C2213yes—
165#2485C2213yes—
166#2485C2213yes—
167#2454C2213yes—
168#2454C2213yes—
169#2454C2213yes—
170#2454C2213yes—
171#2453C2213yes—
172#2453C2213yes—
173#2451C2213yes—
174#2451C2213yes—
175#2448C2213yes—
176#2448C2213yes—
177#2447C2213yes—
178#2447C2213yes—
179#2441C2213yes—
180#2441C2213yes—
181#2441C2213yes—
182#2441C2213yes—
183#2441C2213yes—
184#2441C2213yes—
185#2439C2213yes—
186#2439C2213yes—
187#2423C2213yes—
188#2422C2213yes—
189#2421C2213yes—
190#2420C2213yes—
191#2401C2213yes—
192#2401C2213yes—
193#2399C2213yes—
194#2396C2213yes—
195#2396C2213yes—
196#2395C2213yes—
197#2382C2216yes—
198#2378C2216yes—
199#2378C2216yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214Q8×C4⋊C4C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220#2341C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226C4×C4⋊Q8C2213yes—
227C4×#125C2213yes—
228C4×#125C2213yes—
229C4×#126C2213yes—
230C4×#126C2213yes—
231C4×#124C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×C22⋊Q8C2213yes—
234C4×#123C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240#557—44no—
241#557—44no—
242#557—44no—
243#548—44no—
244C2×C4⋊Q8C2313yes—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×#126C2311yescharacteristic
249C2×#126C2313yes—
250C2×#126C2316yes—
251C2×#126C2316yes—
252C2×#126C2316yes—
253C2×#125C2311yescharacteristic
254C2×#125C2313yes—
255C2×#125C2313yes—
256C2×#125C2316yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#125C2316yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#123C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2316yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2316yes—
271C2×#121C2313yes—
272#519—44no—
273C4×#41—44no—
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×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×#117C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C22×C42C2313yes—
299#401C2313yes—
300#401C2313yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2313yes—
305#400C2316yes—
306#400C2316yes—
307#400C2313yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2313yes—
312#400C2313yes—
313#400C2316yes—
314#400C2316yes—
315#400C2311yescharacteristic
316#400C2313yes—
317#400C2313yes—
318#400C2313yes—
319#400C2313yes—
320#399C2313yes—
321#399C2316yes—
322#399C2316yes—
323#399C2316yes—
324#399C2316yes—
325#399C2316yes—
326#399C2313yes—
327#399C2313yes—
328#398C2313yes—
329#398C2313yes—
330#398C2316yes—
331#398C2316yes—
332#398C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2313yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2316yes—
343#398C2316yes—
344#398C2313yes—
345#398C2313yes—
346#398C2313yes—
347#398C2316yes—
348#398C2313yes—
349#398C2311yescharacteristic
350#398C2316yes—
351#397C2313yes—
352#397C2316yes—
353#397C2313yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2313yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2316yes—
363#397C2313yes—
364#397C2313yes—
365#397C2311yescharacteristic
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#396C2316yes—
370#396C2316yes—
371#396C2316yes—
372#396C2316yes—
373#396C2313yes—
374#396C2313yes—
375#396C2316yes—
376#396C2316yes—
377#396C2316yes—
378#396C2313yes—
379#396C2316yes—
380#396C2316yes—
381#396C2311yescharacteristic
382#396C2311yescharacteristic
383#396C2311yescharacteristic
384#395C2316yes—
385#395C2316yes—
386#395C2313yes—
387#395C2313yes—
388#395C2316yes—
389#395C2313yes—
390#395C2313yes—
391#395C2313yes—
392#395C2313yes—
393#394C2316yes—
394#394C2316yes—
395#394C2316yes—
396#394C2313yes—
397#394C2313yes—
398#393C2316yes—
399#393C2313yes—
400#393C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2316yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2316yes—
413#391C2316yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#389C2311yescharacteristic
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2311yescharacteristic
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2316yes—
443#389C2313yes—
444#389C2313yes—
445#389C2316yes—
446#389C2316yes—
447#389C2316yes—
448#389C2316yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2316yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2316yes—
466#389C2316yes—
467#389C2316yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2316yes—
473#389C2316yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2311yescharacteristic
483#389C2311yescharacteristic
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2316yes—
492#388C2316yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2313yes—
497#388C2313yes—
498#388C2316yes—
499#388C2316yes—
500#388C2316yes—
501#388C2316yes—
502#388C2316yes—
503#388C2313yes—
504#388C2311yescharacteristic
505#388C2311yescharacteristic
506#387C2311yescharacteristic
507#387C2313yes—
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2316yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2313yes—
527#387C2316yes—
528#387C2313yes—
529#387C2316yes—
530#387C2316yes—
531#387C2316yes—
532#387C2313yes—
533#387C2316yes—
534#387C2316yes—
535#387C2316yes—
536#387C2313yes—
537#387C2313yes—
538#387C2313yes—
539#386C2313yes—
540#385C2316yes—
541#385C2313yes—
542#385C2313yes—
543#385C2313yes—
544#385C2313yes—
545#385C2313yes—
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2316yes—
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#383C2313yes—
561#383C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2316yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#381C2316yes—
571#381C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2316yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2316yes—
585#380C2313yes—
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⋊C4C2313yes—
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×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊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⋊C4C2313yes—
621#376C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41—24no—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2413yes—
633C22×Q8C2413yes—
634C22×Q8C2411yescharacteristic
635C22×D4C2413yes—
636C22×D4C2413yes—
637C23×C4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C4⋊Q8—46no—
642C4⋊Q8—46no—
643C4⋊Q8—46no—
644C4⋊Q8—46no—
645#126—24no—
646#126—46no—
647#126—86no—
648#126—86no—
649#126—86no—
650#125—24no—
651#125—412no—
652#125—46no—
653#125—46no—
654#125—46no—
655#125—46no—
656#125—46no—
657#125—46no—
658#125—46no—
659#125—86no—
660#124—46no—
661#124—46no—
662#123—46no—
663C22⋊Q8—212no—
664C22⋊Q8—46no—
665C22⋊Q8—412no—
666C22⋊Q8—46no—
667C22⋊Q8—86no—
668#121—46no—
669C4×Q8—24no—
670C4×Q8—24no—
671C4×Q8—24no—
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—46no—
683C4×Q8—46no—
684C4×Q8—46no—
685C4×Q8—46no—
686C4×Q8—46no—
687C4×D4—46no—
688C4×D4—46no—
689C4×D4—46no—
690#117—46no—
691#117—46no—
692#117—46no—
693C2×C4⋊C4C2413yes—
694C2×C4⋊C4C2413yes—
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2416yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2416yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2416yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2416yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2416yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C42—46no—
797C2×C42C2413yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813C2×C42C2413yes—
814C2×C42C2416yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2416yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2413yes—
824#95C2413yes—
825#95C2413yes—
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2411yescharacteristic
830#95C2411yescharacteristic
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2416yes—
851#95C2416yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
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#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883#95C2416yes—
884#95C2416yes—
885#95C2416yes—
886#95C2416yes—
887#95C2416yes—
888#95C2416yes—
889C24C2511yescharacteristic
890C24C2513yes—
891#41—416no—
892C2×Q8—26no—
893C2×Q8—26no—
894C2×Q8—26no—
895C2×Q8—26no—
896C2×Q8—26no—
897C2×Q8—43no—
898C2×Q8—43no—
899C2×Q8—43no—
900C2×Q8—43no—
901C2×Q8—43no—
902C2×Q8—43no—
903C2×Q8—43no—
904C2×Q8—416no—
905C2×Q8H(5,𝔽2)14yes—
906C2×Q82−1+414yes—
907C2×Q82−1+414yes—
908C2×D4—26no—
909C2×D4—26no—
910C2×D4—26no—
911C2×D4—43no—
912C2×D4—43no—
913C2×D4—43no—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—26no—
917C22×C4—26no—
918C22×C4—26no—
919C22×C4—26no—
920C22×C4—26no—
921C22×C4—26no—
922C22×C4—43no—
923C22×C4—43no—
924C22×C4—43no—
925C22×C4—43no—
926C22×C4C2511yescharacteristic
927C22×C4C2513yes—
928C22×C4C2511yescharacteristic
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2513yes—
932C22×C4C2513yes—
933C22×C4C2513yes—
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2513yes—
937C22×C4C2511yescharacteristic
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2511yescharacteristic
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2513yes—
955C4⋊C4—26no—
956C4⋊C4—26no—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—26no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—22no—
982C4⋊C4—26no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—43no—
986C4⋊C4—43no—
987C4⋊C4—43no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—43no—
997C4⋊C4—43no—
998C4⋊C4—46no—
999C4⋊C4—46no—
1000C4⋊C4—43no—
1001C4⋊C4—46no—
1002C4⋊C4—46no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—46no—
1006C4⋊C4—46no—
1007C4⋊C4—46no—
1008C4⋊C4—46no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—46no—
1012C4⋊C4—46no—
1013C4⋊C4—46no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—46no—
1017C4⋊C4—46no—
1018C4⋊C4—46no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—46no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C42−1+414yes—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—26no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—41no—
1036C22⋊C4—43no—
1037C22⋊C4—46no—
1038C22⋊C4—41no—
1039C22⋊C4—43no—
1040C22⋊C4—46no—
1041C22⋊C4—46no—
1042C22⋊C4—43no—
1043C22⋊C4—46no—
1044C22⋊C4—46no—
1045C22⋊C4—46no—
1046C22⋊C4—43no—
1047C22⋊C4—43no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C4—43no—
1053C22⋊C4—46no—
1054C22⋊C4—43no—
1055C22⋊C4—43no—
1056C22⋊C4—43no—
1057C22⋊C4—43no—
1058C42—26no—
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—22no—
1072C42—22no—
1073C42—26no—
1074C42—41no—
1075C42—43no—
1076C42—46no—
1077C42—43no—
1078C42—43no—
1079C42—43no—
1080C42—43no—
1081C42—46no—
1082C42—43no—
1083C23—21no—
1084C23—23no—
1085C23—21no—
1086C23—23no—
1087C23—21no—
1088C23—21no—
1089C23—23no—
1090C23—23no—
1091C23—23no—
1092C23—21no—
1093C23—21no—
1094C23—23no—
1095C23—21no—
1096C23—23no—
1097C23C2611yescharacteristic
1098Q8—412no—
1099Q8—86no—
1100Q8—86no—
1101Q8—86no—
1102Q8#563116yes—
1103D4—412no—
1104D4—86no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
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—21no—
1119C2×C4—21no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—21no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
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—21no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—412no—
1185C2×C4—412no—
1186C2×C4—86no—
1187C2×C4—86no—
1188C2×C4C2×H(5,𝔽2)16yes—
1189C2×C4C2×2−1+412yes—
1190C2×C4C2×2−1+412yes—
1191C2×C4C2×2−1+412yes—
1192C2×C4C2×2−1+416yes—
1193C2×C4C2×2−1+416yes—
1194C2×C4#58512yes—
1195C2×C4#58512yes—
1196C22—43no—
1197C22—41no—
1198C22—41no—
1199C22—43no—
1200C22—41no—
1201C22—43no—
1202C22—43no—
1203C22—41no—
1204C22—41no—
1205C22—43no—
1206C22—41no—
1207C22—41no—
1208C22—43no—
1209C22—43no—
1210C22C22×H(5,𝔽2)11yescharacteristic
1211C22C22×2−1+411yescharacteristic
1212C22C22×2−1+411yescharacteristic
1213C22C22×2−1+411yescharacteristic
1214C22C2×#58511yescharacteristic
1215C22C2×#58511yescharacteristic
1216C22H(7,𝔽2)11yescharacteristic
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—22no—
1221C4—22no—
1222C4—41no—
1223C4—43no—
1224C4—43no—
1225C4—43no—
1226C4—43no—
1227C4—41no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—43no—
1235C4—43no—
1236C4—43no—
1237C4—41no—
1238C4—43no—
1239C4—43no—
1240C4—43no—
1241C4—43no—
1242C4—43no—
1243C4—43no—
1244C4—43no—
1245C4C2×#563112yes—
1246C2—83no—
1247C2—81no—
1248C2C22×#56311yescharacteristic
1249C2#6291711yescharacteristic
1250C2#6295211yescharacteristic
1251C2#6295211yescharacteristic
1252C2#6301911yescharacteristic
1253C2#6303211yescharacteristic
1254C2#6303811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53123C2semidirect
2. #53086C2semidirect
3. #53082C2semidirect
4. #53067C2semidirect
5. #53020C2semidirect
6. #52994C2semidirect
7. #52298C2semidirect
8. #46347C2semidirect
9. #46158C2semidirect
10. #46109C2semidirect
11. #46105C2semidirect
12. #46105C2semidirect
13. #46079C2semidirect
14. #45674C2semidirect
15. #45523C2semidirect
16. #45499C2semidirect
17. Q8×#126C2semidirect
18. Q8×#125C2semidirect
20. #36466C2semidirect
21. #36458C2semidirect
22. #36447C2semidirect
23. #36445C2semidirect
24. #36445C2semidirect
26. #35957C2semidirect
27. #35920C2semidirect
28. #35898C2semidirect
30. #35786C2semidirect
31. #35786C2semidirect

Maximal subgroups

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

subgroupindex
#531232
#530862
#530822
#530672
#530202
#529942
#522982
#463472
#461582
#461092
#461052
#460792
#456742
#455232
#454992
Q8×#1262
Q8×#1252
#364672
#364662
#364582
#364472
#364452
#364322
#359572
#359202
#358982
#358012
#357862