Finite Group Databasebeta

← #8096450

Subgroups — #8096450

Order 512.

4673 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53099C213yesmaximal, complemented
2#53082C213yesmaximal, complemented
3#53058C213yesmaximal, complemented
4#53039C213yesmaximal, complemented
5#53020C213yesmaximal, complemented
6#52974C213yesmaximal, complemented
7#52298C213yesmaximal, complemented
8#46340C213yesmaximal, complemented
9#46174C213yesmaximal, complemented
10#46056C213yesmaximal, complemented
11#46019C213yesmaximal, complemented
12#45998C213yesmaximal, complemented
13#45993C213yesmaximal, complemented
14#45633C213yesmaximal, complemented
15#45502C213yesmaximal, complemented
16#45485C213yesmaximal, complemented
17Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
18Q8×#125C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#36458C211yesmaximal, characteristic, complemented
21#36458C211yesmaximal, characteristic, complemented
22#36457C211yesmaximal, characteristic
23#36456C211yesmaximal, characteristic, complemented
24#36445C211yesmaximal, characteristic, complemented
25#36433C211yesmaximal, characteristic
26#36005C211yesmaximal, characteristic
27#35937C211yesmaximal, characteristic, complemented
28#35898C211yesmaximal, characteristic, complemented
29#35898C211yesmaximal, characteristic, complemented
30#35816C211yesmaximal, characteristic, complemented
31#35748C211yesmaximal, characteristic, complemented
32C2×#563C2216yes—
33C2×Q82C2211yescharacteristic
34C2×Q82C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#550C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#2868C2213yes—
40#2864C2213yes—
41#2860C2213yes—
42#2860C2213yes—
43#2859C2213yes—
44#2858C2213yes—
45#2857C2213yes—
46#2857C2213yes—
47#2854C2213yes—
48#2841C2216yes—
49#2838C2216yes—
50#2838C2216yes—
51#2837C2216yes—
52#2831C2216yes—
53#2830C2216yes—
54#2823C2216yes—
55#2821C2216yes—
56#2820C2216yes—
57#2814C2216yes—
58#2814C2216yes—
59#2793C2213yes—
60#2787C2213yes—
61#2774C2216yes—
62#2774C2213yes—
63#2773C2213yes—
64#2766C2213yes—
65#2762C2213yes—
66#2759C2213yes—
67#2738C2213yes—
68#2731C2216yes—
69#2729C2216yes—
70#2729C2216yes—
71#2727C2216yes—
72#2725C2213yes—
73#2723C2213yes—
74#2723C2216yes—
75#2721C2216yes—
76#2720C2213yes—
77#2718C2216yes—
78#2717C2216yes—
79#2716C2216yes—
80#2715C2216yes—
81#2715C2216yes—
82#2715C2213yes—
83#2713C2211yescharacteristic
84#2707C2213yes—
85#2702C2216yes—
86#2698C2213yes—
87#2695C2216yes—
88#2690C2216yes—
89#2683C2216yes—
90#2680C2216yes—
91#2677C2216yes—
92#2674C2213yes—
93#2674C2216yes—
94#2674C2216yes—
95#2674C2216yes—
96#2660C2213yes—
97#2644C2213yes—
98#2644C2213yes—
99#2629C2213yes—
100#2628C2213yes—
101#2624C2213yes—
102#2584C2213yes—
103#2580C2213yes—
104#2570C2213yes—
105#2570C2213yes—
106#2567C2213yes—
107#2567C2213yes—
108#2566C2213yes—
109#2563C2213yes—
110#2563C2213yes—
111#2552C2213yes—
112#2552C2213yes—
113#2551C2213yes—
114#2551C2213yes—
115#2551C2213yes—
116#2551C2213yes—
117#2551C2213yes—
118#2551C2213yes—
119#2550C2213yes—
120#2550C2213yes—
121#2548C2213yes—
122#2546C2213yes—
123#2542C2213yes—
124#2542C2213yes—
125#2538C2213yes—
126#2538C2213yes—
127#2538C2213yes—
128#2513C2213yes—
129#2513C2213yes—
130#2513C2213yes—
131#2513C2213yes—
132#2512C2213yes—
133#2512C2213yes—
134#2512C2213yes—
135#2512C2213yes—
136#2512C2213yes—
137#2512C2213yes—
138#2512C2213yes—
139#2512C2213yes—
140#2509C2213yes—
141#2508C2213yes—
142#2507C2213yes—
143#2507C2213yes—
144#2507C2213yes—
145#2507C2213yes—
146#2507C2213yes—
147#2506C2213yes—
148#2501C2213yes—
149#2500C2213yes—
150#2497C2213yes—
151#2497C2213yes—
152#2497C2213yes—
153#2497C2213yes—
154#2496C2213yes—
155#2496C2213yes—
156#2496C2213yes—
157#2496C2213yes—
158#2495C2213yes—
159#2495C2213yes—
160#2494C2213yes—
161#2494C2213yes—
162#2491C2213yes—
163#2491C2213yes—
164#2491C2213yes—
165#2491C2213yes—
166#2487C2213yes—
167#2485C2213yes—
168#2454C2213yes—
169#2454C2213yes—
170#2454C2213yes—
171#2452C2213yes—
172#2452C2213yes—
173#2452C2213yes—
174#2452C2213yes—
175#2452C2213yes—
176#2445C2213yes—
177#2445C2213yes—
178#2445C2213yes—
179#2445C2213yes—
180#2442C2213yes—
181#2441C2213yes—
182#2441C2213yes—
183#2440C2213yes—
184#2440C2213yes—
185#2440C2213yes—
186#2439C2213yes—
187#2439C2213yes—
188#2422C2213yes—
189#2422C2213yes—
190#2422C2213yes—
191#2420C2213yes—
192#2401C2213yes—
193#2401C2213yes—
194#2399C2213yes—
195#2396C2213yes—
196#2396C2213yes—
197#2395C2213yes—
198#2383C2216yes—
199#2376C2216yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204#2351C2211yescharacteristic
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
221#2341C2211yescharacteristic
222#2341C2211yescharacteristic
223#2341C2211yescharacteristic
224#2341C2211yescharacteristic
225#2341C2211yescharacteristic
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
239C22×#41C2311yescharacteristic
240#563—424no—
241Q82—44no—
242Q82—44no—
243#557—44no—
244#550—44no—
245C2×C4⋊Q8C2311yescharacteristic
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×C4⋊Q8C2316yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2316yes—
255C2×C4⋊Q8C2316yes—
256C2×#127C2313yes—
257C2×#126C2313yes—
258C2×#126C2313yes—
259C2×#126C2316yes—
260C2×#126C2316yes—
261C2×#126C2316yes—
262C2×#126C2316yes—
263C2×#125C2311yescharacteristic
264C2×#125C2313yes—
265C2×#125C2316yes—
266C2×#125C2313yes—
267C2×#125C2313yes—
268C2×#124C2316yes—
269C2×#124C2313yes—
270C2×#124C2316yes—
271C2×#123C2313yes—
272C2×#123C2316yes—
273C2×#123C2316yes—
274C2×#123C2316yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2316yes—
277C2×C22⋊Q8C2316yes—
278C2×C22⋊Q8C2313yes—
279C2×C22⋊Q8C2316yes—
280C2×C22⋊Q8C2316yes—
281C2×C22⋊Q8C2316yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284#520—44no—
285C4×#41—44no—
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2311yescharacteristic
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C22×C4⋊C4C2313yes—
310C22×C42C2313yes—
311#401C2313yes—
312#401C2313yes—
313#400C2313yes—
314#400C2316yes—
315#400C2316yes—
316#400C2313yes—
317#400C2316yes—
318#400C2313yes—
319#400C2316yes—
320#400C2313yes—
321#400C2313yes—
322#400C2311yescharacteristic
323#400C2311yescharacteristic
324#400C2313yes—
325#400C2313yes—
326#399C2313yes—
327#399C2316yes—
328#399C2313yes—
329#399C2316yes—
330#399C2316yes—
331#399C2313yes—
332#399C2316yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2313yes—
340#398C2313yes—
341#398C2316yes—
342#398C2316yes—
343#398C2313yes—
344#398C2316yes—
345#398C2311yescharacteristic
346#398C2311yescharacteristic
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#397C2313yes—
351#397C2316yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2313yes—
358#397C2313yes—
359#397C2316yes—
360#397C2313yes—
361#397C2316yes—
362#397C2316yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#396C2316yes—
369#396C2316yes—
370#396C2316yes—
371#396C2316yes—
372#396C2313yes—
373#396C2316yes—
374#396C2313yes—
375#396C2316yes—
376#396C2316yes—
377#396C2316yes—
378#396C2316yes—
379#396C2313yes—
380#396C2313yes—
381#396C2313yes—
382#396C2313yes—
383#396C2316yes—
384#395C2316yes—
385#395C2316yes—
386#395C2316yes—
387#395C2316yes—
388#395C2316yes—
389#395C2316yes—
390#395C2316yes—
391#395C2313yes—
392#395C2311yescharacteristic
393#395C2313yes—
394#395C2311yescharacteristic
395#395C2313yes—
396#395C2313yes—
397#394C2316yes—
398#394C2316yes—
399#394C2316yes—
400#394C2316yes—
401#394C2313yes—
402#394C2316yes—
403#394C2316yes—
404#394C2316yes—
405#394C2313yes—
406#393C2316yes—
407#393C2316yes—
408#393C2316yes—
409#393C2316yes—
410#393C2316yes—
411#393C2313yes—
412#393C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2316yes—
416#391C2313yes—
417#391C2316yes—
418#391C2311yescharacteristic
419#391C2311yescharacteristic
420#390C2316yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#390C2313yes—
437#390C2313yes—
438#390C2313yes—
439#390C2313yes—
440#390C2313yes—
441#390C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
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#389C2316yes—
464#389C2316yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2316yes—
469#389C2316yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2316yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2311yescharacteristic
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2316yes—
496#388C2316yes—
497#388C2316yes—
498#388C2313yes—
499#388C2316yes—
500#388C2313yes—
501#388C2316yes—
502#388C2316yes—
503#388C2316yes—
504#388C2316yes—
505#388C2313yes—
506#388C2316yes—
507#388C2313yes—
508#388C2313yes—
509#388C2313yes—
510#387C2311yescharacteristic
511#387C2311yescharacteristic
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2311yescharacteristic
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2313yes—
528#387C2316yes—
529#387C2313yes—
530#387C2316yes—
531#387C2313yes—
532#387C2313yes—
533#387C2311yescharacteristic
534#387C2313yes—
535#386C2316yes—
536#386C2316yes—
537#386C2313yes—
538#385C2316yes—
539#385C2316yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2313yes—
544#385C2313yes—
545#385C2313yes—
546#385C2313yes—
547#385C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2316yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#384C2313yes—
561#383C2313yes—
562#383C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#381C2313yes—
572#380C2313yes—
573#380C2316yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2316yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2316yes—
586#380C2313yes—
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×C4⋊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—
621C4×C22⋊C4C2313yes—
622#376C2313yes—
623C43C2313yes—
624C43C2313yes—
625C2×#41—24no—
626C2×#41—24no—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C22×Q8C2411yescharacteristic
632C22×Q8C2411yescharacteristic
633C22×Q8C2413yes—
634C22×Q8C2416yes—
635C22×Q8C2416yes—
636C22×Q8C2411yescharacteristic
637C22×D4C2413yes—
638C22×D4C2413yes—
639C22×D4C2413yes—
640C22×D4C2416yes—
641C23×C4C2413yes—
642C23×C4C2413yes—
643C23×C4C2413yes—
644C23×C4C2413yes—
645C23×C4C2416yes—
646C4⋊Q8—24no—
647C4⋊Q8—46no—
648C4⋊Q8—46no—
649C4⋊Q8—46no—
650C4⋊Q8—46no—
651C4⋊Q8—46no—
652C4⋊Q8—46no—
653C4⋊Q8—46no—
654C4⋊Q8—412no—
655C4⋊Q8—412no—
656C4⋊Q8—86no—
657#127—46no—
658#126—212no—
659#126—46no—
660#126—412no—
661#126—412no—
662#126—412no—
663#126—412no—
664#125—212no—
665#125—24no—
666#125—46no—
667#125—46no—
668#125—412no—
669#124—412no—
670#124—46no—
671#124—86no—
672#123—212no—
673#123—412no—
674#123—412no—
675#123—86no—
676C22⋊Q8—212no—
677C22⋊Q8—412no—
678C22⋊Q8—46no—
679C22⋊Q8—412no—
680C22⋊Q8—412no—
681C22⋊Q8—86no—
682C22⋊Q8—86no—
683#121—46no—
684#121—46no—
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—24no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—46no—
699C4×Q8—46no—
700C4×Q8—46no—
701C4×D4—46no—
702C4×D4—46no—
703C4×D4—46no—
704C4×D4—46no—
705C4×D4—46no—
706#117—46no—
707#117—46no—
708C2×C4⋊C4—46no—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
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×C4⋊C4C2413yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2416yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2416yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2416yes—
800C2×C22⋊C4C2416yes—
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2416yes—
813C2×C42—46no—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2411yescharacteristic
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2411yescharacteristic
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2416yes—
836C2×C42C2413yes—
837C2×C42C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2416yes—
868#95C2416yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
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#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2416yes—
897#95C2416yes—
898#95C2416yes—
899#95C2416yes—
900#95C2416yes—
901C24C2513yes—
902C24C2513yes—
903#41—416no—
904#41—416no—
905C2×Q8—26no—
906C2×Q8—22no—
907C2×Q8—22no—
908C2×Q8—22no—
909C2×Q8—22no—
910C2×Q8—41no—
911C2×Q8—41no—
912C2×Q8—43no—
913C2×Q8—43no—
914C2×Q8—46no—
915C2×Q8—46no—
916C2×Q8—46no—
917C2×Q8—46no—
918C2×Q8—46no—
919C2×Q8—46no—
920C2×Q8H(5,𝔽2)14yes—
921C2×Q82−1+414yes—
922C2×Q82−1+414yes—
923C2×D4—26no—
924C2×D4—26no—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—43no—
931C2×D4—43no—
932C2×D4—46no—
933C2×D4—46no—
934C2×D4—46no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—43no—
944C22×C4—43no—
945C22×C4—43no—
946C22×C4—43no—
947C22×C4—46no—
948C22×C4—46no—
949C22×C4—46no—
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2513yes—
955C22×C4C2511yescharacteristic
956C22×C4C2513yes—
957C22×C4C2513yes—
958C22×C4C2511yescharacteristic
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C22×C4C2511yescharacteristic
962C22×C4C2513yes—
963C22×C4C2513yes—
964C22×C4C2513yes—
965C22×C4C2513yes—
966C22×C4C2513yes—
967C22×C4C2513yes—
968C22×C4C2513yes—
969C22×C4C2513yes—
970C22×C4C2513yes—
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2511yescharacteristic
978C22×C4C2513yes—
979C4⋊C4—26no—
980C4⋊C4—26no—
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—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—26no—
1011C4⋊C4—22no—
1012C4⋊C4—43no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—46no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—46no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—43no—
1034C4⋊C4—46no—
1035C4⋊C4—46no—
1036C4⋊C4—46no—
1037C4⋊C4—43no—
1038C4⋊C4—46no—
1039C4⋊C4—46no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—46no—
1043C4⋊C4—46no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4H(5,𝔽2)14yes—
1047C4⋊C42−1+414yes—
1048C22⋊C4—26no—
1049C22⋊C4—26no—
1050C22⋊C4—26no—
1051C22⋊C4—26no—
1052C22⋊C4—26no—
1053C22⋊C4—26no—
1054C22⋊C4—26no—
1055C22⋊C4—26no—
1056C22⋊C4—26no—
1057C22⋊C4—26no—
1058C22⋊C4—43no—
1059C22⋊C4—43no—
1060C22⋊C4—46no—
1061C22⋊C4—43no—
1062C22⋊C4—43no—
1063C22⋊C4—43no—
1064C22⋊C4—46no—
1065C22⋊C4—46no—
1066C22⋊C4—46no—
1067C22⋊C4—46no—
1068C22⋊C4—43no—
1069C22⋊C4—46no—
1070C22⋊C4—46no—
1071C22⋊C4—46no—
1072C22⋊C4—46no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—46no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—46no—
1083C42—26no—
1084C42—26no—
1085C42—26no—
1086C42—26no—
1087C42—26no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—26no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—22no—
1099C42—22no—
1100C42—26no—
1101C42—41no—
1102C42—43no—
1103C42—43no—
1104C42—43no—
1105C42—46no—
1106C42—43no—
1107C23—23no—
1108C23—23no—
1109C23—23no—
1110C23—23no—
1111C23—23no—
1112C23—23no—
1113C23—23no—
1114C23—23no—
1115C23—23no—
1116C23—23no—
1117C23—23no—
1118C23—23no—
1119C23—23no—
1120C23—23no—
1121C23C2611yescharacteristic
1122Q8—44no—
1123Q8—44no—
1124Q8—86no—
1125Q8—166no—
1126Q8—166no—
1127Q8#563116yescomplemented
1128D4—412no—
1129D4—412no—
1130D4—86no—
1131D4—166no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—23no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—21no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—412no—
1210C2×C4—412no—
1211C2×C4—86no—
1212C2×C4—86no—
1213C2×C4—166no—
1214C2×C4C2×H(5,𝔽2)12yes—
1215C2×C4C2×H(5,𝔽2)12yes—
1216C2×C4C2×H(5,𝔽2)12yes—
1217C2×C4C2×H(5,𝔽2)16yes—
1218C2×C4C2×2−1+412yes—
1219C2×C4C2×2−1+412yes—
1220C2×C4C2×2−1+412yes—
1221C2×C4C2×2−1+416yes—
1222C2×C4C2×2−1+416yes—
1223C2×C4#58512yes—
1224C22—43no—
1225C22—43no—
1226C22—43no—
1227C22—43no—
1228C22—43no—
1229C22—43no—
1230C22—43no—
1231C22—43no—
1232C22—43no—
1233C22—43no—
1234C22—43no—
1235C22—43no—
1236C22—43no—
1237C22—43no—
1238C22C22×H(5,𝔽2)11yescharacteristic
1239C22C22×H(5,𝔽2)11yescharacteristic
1240C22C22×2−1+411yescharacteristic
1241C22C22×2−1+411yescharacteristic
1242C22C22×2−1+411yescharacteristic
1243C22C2×#58511yescharacteristic
1244C22H(7,𝔽2)11yescharacteristic
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—22no—
1251C4—22no—
1252C4—41no—
1253C4—43no—
1254C4—41no—
1255C4—41no—
1256C4—43no—
1257C4—43no—
1258C4—43no—
1259C4—43no—
1260C4—43no—
1261C4—43no—
1262C4—43no—
1263C4—43no—
1264C4—43no—
1265C4—43no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—43no—
1272C4—43no—
1273C4C2×#563112yes—
1274C2—83no—
1275C2—83no—
1276C2C22×#56311yescharacteristic
1277C2#6291611yescharacteristic
1278C2#6294311yescharacteristic
1279C2#6295211yescharacteristic
1280C2#6301511yescharacteristic
1281C2#6303711yescharacteristic
1282C2#6303911yescharacteristic
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. #53099C2semidirect
2. #53082C2semidirect
3. #53058C2semidirect
4. #53039C2semidirect
5. #53020C2semidirect
6. #52974C2semidirect
7. #52298C2semidirect
8. #46340C2semidirect
9. #46174C2semidirect
10. #46056C2semidirect
11. #46019C2semidirect
12. #45998C2semidirect
13. #45993C2semidirect
14. #45633C2semidirect
15. #45502C2semidirect
16. #45485C2semidirect
17. Q8×C4⋊Q8C2semidirect
18. Q8×#125C2semidirect
19. #36475C2semidirect
20. #36458C2semidirect
21. #36458C2semidirect
23. #36456C2semidirect
24. #36445C2semidirect
27. #35937C2semidirect
28. #35898C2semidirect
29. #35898C2semidirect
30. #35816C2semidirect
31. #35748C2semidirect
1127. Q8#563semidirect

Maximal subgroups

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

subgroupindex
#530992
#530822
#530582
#530392
#530202
#529742
#522982
#463402
#461742
#460562
#460192
#459982
#459932
#456332
#455022
#454852
Q8×C4⋊Q82
Q8×#1252
#364752
#364582
#364572
#364562
#364452
#364332
#360052
#359372
#358982
#358162
#357482