Finite Group Databasebeta

← #8096465

Subgroups — #8096465

Order 512.

4329 conjugacy classes of subgroups.

The subgroup lattice has 1255 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53123C213yesmaximal, complemented
2#53067C213yesmaximal, complemented
3#53028C213yesmaximal, complemented
4#53023C213yesmaximal, complemented
5#52974C213yesmaximal, complemented
6#52965C213yesmaximal, complemented
7#52306C213yesmaximal, complemented
8#46347C213yesmaximal, complemented
9#46341C213yesmaximal, complemented
10#46180C213yesmaximal, complemented
11#46116C213yesmaximal, complemented
12#46113C213yesmaximal, complemented
13#46082C213yesmaximal, complemented
14#46078C213yesmaximal, complemented
15#46019C213yesmaximal, complemented
16#46001C213yesmaximal, complemented
17#36593C211yesmaximal, characteristic, complemented
18Q8×#126C211yesmaximal, characteristic, complemented
19Q8×#125C211yesmaximal, characteristic, complemented
20#36475C211yesmaximal, characteristic, complemented
21#36467C211yesmaximal, characteristic
22#36466C211yesmaximal, characteristic, complemented
23#36458C211yesmaximal, characteristic, complemented
24#36458C211yesmaximal, characteristic, complemented
25#36448C211yesmaximal, characteristic, complemented
26#35996C211yesmaximal, characteristic
27#35845C211yesmaximal, characteristic, complemented
28#35816C211yesmaximal, characteristic, complemented
29#35816C211yesmaximal, characteristic, complemented
30#35801C211yesmaximal, characteristic
31#35786C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38#2868C2213yes—
39#2864C2213yes—
40#2863C2213yes—
41#2863C2213yes—
42#2861C2213yes—
43#2860C2213yes—
44#2860C2213yes—
45#2859C2213yes—
46#2859C2213yes—
47#2843C2216yes—
48#2839C2216yes—
49#2839C2216yes—
50#2838C2216yes—
51#2837C2216yes—
52#2836C2216yes—
53#2836C2216yes—
54#2836C2216yes—
55#2831C2216yes—
56#2823C2216yes—
57#2814C2216yes—
58#2809C2213yes—
59#2793C2216yes—
60#2793C2216yes—
61#2791C2216yes—
62#2787C2216yes—
63#2777C2216yes—
64#2775C2213yes—
65#2775C2213yes—
66#2775C2213yes—
67#2775C2213yes—
68#2770C2216yes—
69#2769C2213yes—
70#2769C2213yes—
71#2766C2216yes—
72#2765C2216yes—
73#2738C2216yes—
74#2734C2213yes—
75#2731C2213yes—
76#2731C2213yes—
77#2729C2216yes—
78#2727C2213yes—
79#2727C2213yes—
80#2725C2216yes—
81#2725C2216yes—
82#2722C2216yes—
83#2721C2213yes—
84#2721C2213yes—
85#2721C2213yes—
86#2721C2211yescharacteristic
87#2720C2216yes—
88#2718C2216yes—
89#2716C2216yes—
90#2713C2216yes—
91#2707C2216yes—
92#2698C2216yes—
93#2677C2216yes—
94#2674C2216yes—
95#2629C2213yes—
96#2629C2213yes—
97#2629C2213yes—
98#2628C2213yes—
99#2625C2213yes—
100#2624C2213yes—
101#2592C2213yes—
102#2584C2213yes—
103#2584C2213yes—
104#2582C2213yes—
105#2581C2213yes—
106#2570C2213yes—
107#2570C2213yes—
108#2567C2213yes—
109#2566C2213yes—
110#2566C2213yes—
111#2565C2213yes—
112#2562C2213yes—
113#2552C2213yes—
114#2552C2213yes—
115#2552C2213yes—
116#2552C2213yes—
117#2552C2213yes—
118#2552C2213yes—
119#2552C2213yes—
120#2551C2213yes—
121#2550C2213yes—
122#2550C2213yes—
123#2546C2213yes—
124#2546C2213yes—
125#2538C2213yes—
126#2538C2213yes—
127#2514C2213yes—
128#2514C2213yes—
129#2513C2213yes—
130#2513C2213yes—
131#2512C2213yes—
132#2512C2213yes—
133#2512C2213yes—
134#2512C2213yes—
135#2511C2213yes—
136#2511C2213yes—
137#2511C2213yes—
138#2511C2213yes—
139#2509C2213yes—
140#2508C2213yes—
141#2507C2213yes—
142#2507C2213yes—
143#2507C2213yes—
144#2507C2213yes—
145#2507C2213yes—
146#2506C2213yes—
147#2502C2213yes—
148#2500C2213yes—
149#2497C2213yes—
150#2497C2213yes—
151#2497C2213yes—
152#2497C2213yes—
153#2497C2213yes—
154#2496C2213yes—
155#2496C2213yes—
156#2496C2213yes—
157#2495C2213yes—
158#2495C2213yes—
159#2495C2213yes—
160#2494C2213yes—
161#2492C2213yes—
162#2491C2213yes—
163#2490C2213yes—
164#2489C2213yes—
165#2486C2213yes—
166#2485C2213yes—
167#2454C2213yes—
168#2454C2213yes—
169#2453C2213yes—
170#2453C2213yes—
171#2453C2213yes—
172#2452C2213yes—
173#2452C2213yes—
174#2451C2213yes—
175#2448C2213yes—
176#2448C2213yes—
177#2447C2213yes—
178#2447C2213yes—
179#2442C2213yes—
180#2442C2213yes—
181#2441C2213yes—
182#2441C2213yes—
183#2441C2213yes—
184#2440C2213yes—
185#2440C2213yes—
186#2439C2213yes—
187#2423C2213yes—
188#2422C2213yes—
189#2422C2213yes—
190#2421C2213yes—
191#2396C2213yes—
192#2396C2213yes—
193#2396C2213yes—
194#2396C2213yes—
195#2395C2213yes—
196#2395C2213yes—
197#2383C2216yes—
198#2383C2216yes—
199#2378C2216yes—
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
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226C4×C4⋊Q8C2213yes—
227C4×C4⋊Q8C2213yes—
228C4×#125C2213yes—
229C4×#125C2213yes—
230C4×#126C2213yes—
231C4×#126C2213yes—
232C4×#126C2213yes—
233C4×#126C2213yes—
234C4×#124C2213yes—
235C42×Q8C2211yescharacteristic
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×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2316yes—
250C2×#126C2311yescharacteristic
251C2×#126C2313yes—
252C2×#126C2313yes—
253C2×#126C2313yes—
254C2×#126C2316yes—
255C2×#126C2316yes—
256C2×#125C2311yescharacteristic
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#125C2313yes—
263C2×#125C2313yes—
264C2×#125C2316yes—
265C2×#124C2313yes—
266C2×#124C2313yes—
267C2×#123C2316yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2316yes—
270C2×C22⋊Q8C2316yes—
271C2×#121C2313yes—
272#520—44no—
273#519—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×C4⋊C4C2313yes—
299#401C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2316yes—
303#400C2316yes—
304#400C2316yes—
305#400C2313yes—
306#400C2316yes—
307#400C2316yes—
308#400C2316yes—
309#400C2316yes—
310#400C2313yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2316yes—
315#400C2316yes—
316#400C2313yes—
317#399C2313yes—
318#399C2316yes—
319#399C2316yes—
320#399C2313yes—
321#399C2311yescharacteristic
322#399C2313yes—
323#399C2311yescharacteristic
324#399C2313yes—
325#398C2313yes—
326#398C2316yes—
327#398C2316yes—
328#398C2316yes—
329#398C2316yes—
330#398C2316yes—
331#398C2313yes—
332#398C2316yes—
333#398C2313yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2316yes—
343#398C2313yes—
344#398C2313yes—
345#398C2316yes—
346#398C2313yes—
347#398C2316yes—
348#398C2313yes—
349#398C2311yescharacteristic
350#398C2311yescharacteristic
351#398C2313yes—
352#397C2316yes—
353#397C2316yes—
354#397C2316yes—
355#397C2316yes—
356#397C2313yes—
357#397C2313yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2316yes—
363#397C2311yescharacteristic
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#396C2313yes—
368#396C2313yes—
369#396C2316yes—
370#396C2316yes—
371#396C2313yes—
372#396C2316yes—
373#396C2316yes—
374#396C2316yes—
375#396C2316yes—
376#396C2313yes—
377#396C2316yes—
378#396C2313yes—
379#396C2316yes—
380#396C2313yes—
381#396C2311yescharacteristic
382#396C2313yes—
383#395C2313yes—
384#395C2316yes—
385#395C2316yes—
386#395C2316yes—
387#395C2313yes—
388#395C2313yes—
389#395C2313yes—
390#394C2316yes—
391#394C2313yes—
392#394C2316yes—
393#394C2313yes—
394#394C2313yes—
395#394C2313yes—
396#393C2316yes—
397#393C2313yes—
398#393C2313yes—
399#393C2313yes—
400#393C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2316yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2313yes—
432#389C2311yescharacteristic
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2316yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2316yes—
447#389C2313yes—
448#389C2313yes—
449#389C2316yes—
450#389C2316yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2316yes—
455#389C2316yes—
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#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#388C2311yescharacteristic
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2316yes—
497#388C2316yes—
498#388C2316yes—
499#388C2313yes—
500#388C2316yes—
501#388C2313yes—
502#388C2316yes—
503#388C2316yes—
504#388C2316yes—
505#388C2311yescharacteristic
506#387C2311yescharacteristic
507#387C2311yescharacteristic
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2313yes—
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2311yescharacteristic
519#387C2313yes—
520#387C2313yes—
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2313yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2316yes—
531#387C2316yes—
532#387C2316yes—
533#387C2316yes—
534#387C2316yes—
535#387C2316yes—
536#387C2316yes—
537#387C2316yes—
538#387C2316yes—
539#385C2316yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2316yes—
544#385C2316yes—
545#384C2311yescharacteristic
546#384C2313yes—
547#384C2313yes—
548#384C2313yes—
549#384C2313yes—
550#384C2313yes—
551#384C2316yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2316yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#383C2313yes—
561#383C2313yes—
562#383C2313yes—
563#383C2313yes—
564#383C2316yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#381C2316yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2316yes—
585#380C2316yes—
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—
621C43C2313yes—
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×C4C2416yes—
640C4⋊Q8—46no—
641C4⋊Q8—46no—
642C4⋊Q8—46no—
643C4⋊Q8—46no—
644C4⋊Q8—46no—
645C4⋊Q8—86no—
646#126—24no—
647#126—212no—
648#126—46no—
649#126—412no—
650#126—46no—
651#126—86no—
652#125—24no—
653#125—46no—
654#125—46no—
655#125—46no—
656#125—46no—
657#125—46no—
658#125—46no—
659#125—46no—
660#125—86no—
661#124—46no—
662#124—46no—
663#123—86no—
664C22⋊Q8—412no—
665C22⋊Q8—46no—
666C22⋊Q8—86no—
667#121—46no—
668C4×Q8—24no—
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—46no—
682C4×Q8—46no—
683C4×Q8—46no—
684C4×Q8—46no—
685C4×Q8—46no—
686C4×D4—46no—
687C4×D4—46no—
688C4×D4—46no—
689#117—46no—
690#117—46no—
691#117—46no—
692C2×C4⋊C4—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⋊C4C2413yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2413yes—
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⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2411yescharacteristic
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2411yescharacteristic
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2411yescharacteristic
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2416yes—
797C2×C22⋊C4C2416yes—
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×C42C2413yes—
813C2×C42C2411yescharacteristic
814C2×C42C2413yes—
815C2×C42C2411yescharacteristic
816C2×C42C2416yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2411yescharacteristic
829#95C2413yes—
830#95C2413yes—
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#95C2411yescharacteristic
845#95C2411yescharacteristic
846#95C2411yescharacteristic
847#95C2411yescharacteristic
848#95C2411yescharacteristic
849#95C2416yes—
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#95C2416yes—
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—46no—
921C22×C4—46no—
922C22×C4—46no—
923C22×C4C2513yes—
924C22×C4C2511yescharacteristic
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C22×C4C2513yes—
928C22×C4C2513yes—
929C22×C4C2513yes—
930C22×C4C2513yes—
931C22×C4C2513yes—
932C22×C4C2513yes—
933C22×C4C2511yescharacteristic
934C22×C4C2511yescharacteristic
935C22×C4C2511yescharacteristic
936C22×C4C2511yescharacteristic
937C22×C4C2511yescharacteristic
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2511yescharacteristic
941C22×C4C2513yes—
942C22×C4C2513yes—
943C22×C4C2513yes—
944C22×C4C2513yes—
945C22×C4C2513yes—
946C22×C4C2511yescharacteristic
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2513yes—
952C4⋊C4—26no—
953C4⋊C4—26no—
954C4⋊C4—26no—
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—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—26no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—22no—
976C4⋊C4—26no—
977C4⋊C4—26no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—43no—
981C4⋊C4—41no—
982C4⋊C4—43no—
983C4⋊C4—43no—
984C4⋊C4—43no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—43no—
992C4⋊C4—43no—
993C4⋊C4—43no—
994C4⋊C4—46no—
995C4⋊C4—46no—
996C4⋊C4—43no—
997C4⋊C4—46no—
998C4⋊C4—46no—
999C4⋊C4—46no—
1000C4⋊C4—46no—
1001C4⋊C4—43no—
1002C4⋊C4—43no—
1003C4⋊C4—43no—
1004C4⋊C4—46no—
1005C4⋊C4—46no—
1006C4⋊C4—46no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—46no—
1010C4⋊C4—46no—
1011C4⋊C4—46no—
1012C4⋊C4—46no—
1013C4⋊C4—43no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—46no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—43no—
1024C4⋊C42−1+414yes—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—26no—
1028C22⋊C4—26no—
1029C22⋊C4—26no—
1030C22⋊C4—22no—
1031C22⋊C4—26no—
1032C22⋊C4—22no—
1033C22⋊C4—26no—
1034C22⋊C4—22no—
1035C22⋊C4—41no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C22⋊C4—41no—
1040C22⋊C4—43no—
1041C22⋊C4—46no—
1042C22⋊C4—46no—
1043C22⋊C4—43no—
1044C22⋊C4—46no—
1045C22⋊C4—43no—
1046C22⋊C4—43no—
1047C22⋊C4—46no—
1048C22⋊C4—43no—
1049C22⋊C4—43no—
1050C22⋊C4—43no—
1051C22⋊C4—43no—
1052C22⋊C4—46no—
1053C22⋊C4—46no—
1054C22⋊C4—43no—
1055C22⋊C4—43no—
1056C22⋊C4—43no—
1057C42—26no—
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—22no—
1071C42—26no—
1072C42—22no—
1073C42—26no—
1074C42—22no—
1075C42—46no—
1076C42—43no—
1077C42—43no—
1078C42—43no—
1079C42—43no—
1080C42—43no—
1081C42—43no—
1082C42—43no—
1083C23—21no—
1084C23—23no—
1085C23—21no—
1086C23—23no—
1087C23—21no—
1088C23—21no—
1089C23—23no—
1090C23—23no—
1091C23—21no—
1092C23—23no—
1093C23—23no—
1094C23—21no—
1095C23—23no—
1096C23—21no—
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—21no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—23no—
1126C2×C4—23no—
1127C2×C4—23no—
1128C2×C4—23no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—23no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—23no—
1138C2×C4—23no—
1139C2×C4—21no—
1140C2×C4—23no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—21no—
1145C2×C4—23no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—412no—
1185C2×C4—412no—
1186C2×C4—166no—
1187C2×C4C2×H(5,𝔽2)16yes—
1188C2×C4C2×2−1+412yes—
1189C2×C4C2×2−1+412yes—
1190C2×C4C2×2−1+412yes—
1191C2×C4C2×2−1+416yes—
1192C2×C4C2×2−1+416yes—
1193C2×C4#58512yes—
1194C2×C4#58512yes—
1195C22—41no—
1196C22—43no—
1197C22—41no—
1198C22—43no—
1199C22—41no—
1200C22—43no—
1201C22—43no—
1202C22—41no—
1203C22—41no—
1204C22—43no—
1205C22—41no—
1206C22—43no—
1207C22—41no—
1208C22—43no—
1209C22C22×H(5,𝔽2)11yescharacteristic
1210C22C22×2−1+411yescharacteristic
1211C22C22×2−1+411yescharacteristic
1212C22C22×2−1+411yescharacteristic
1213C22C2×#58511yescharacteristic
1214C22C2×#58511yescharacteristic
1215C22H(7,𝔽2)11yescharacteristic
1216C4—22no—
1217C4—22no—
1218C4—22no—
1219C4—22no—
1220C4—22no—
1221C4—41no—
1222C4—43no—
1223C4—43no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—43no—
1230C4—43no—
1231C4—43no—
1232C4—43no—
1233C4—43no—
1234C4—43no—
1235C4—43no—
1236C4—41no—
1237C4—41no—
1238C4—43no—
1239C4—41no—
1240C4—43no—
1241C4—43no—
1242C4—43no—
1243C4—43no—
1244C4C2×#563112yes—
1245C2—83no—
1246C2—81no—
1247C2C22×#56311yescharacteristic
1248C2#6289911yescharacteristic
1249C2#6294311yescharacteristic
1250C2#6295211yescharacteristic
1251C2#6303211yescharacteristic
1252C2#6303311yescharacteristic
1253C2#6303911yescharacteristic
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. #53067C2semidirect
3. #53028C2semidirect
4. #53023C2semidirect
5. #52974C2semidirect
6. #52965C2semidirect
7. #52306C2semidirect
8. #46347C2semidirect
9. #46341C2semidirect
10. #46180C2semidirect
11. #46116C2semidirect
12. #46113C2semidirect
13. #46082C2semidirect
14. #46078C2semidirect
15. #46019C2semidirect
16. #46001C2semidirect
17. #36593C2semidirect
18. Q8×#126C2semidirect
19. Q8×#125C2semidirect
20. #36475C2semidirect
22. #36466C2semidirect
23. #36458C2semidirect
24. #36458C2semidirect
25. #36448C2semidirect
27. #35845C2semidirect
28. #35816C2semidirect
29. #35816C2semidirect
31. #35786C2semidirect

Maximal subgroups

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

subgroupindex
#531232
#530672
#530282
#530232
#529742
#529652
#523062
#463472
#463412
#461802
#461162
#461132
#460822
#460782
#460192
#460012
#365932
Q8×#1262
Q8×#1252
#364752
#364672
#364662
#364582
#364482
#359962
#358452
#358162
#358012
#357862