Finite Group Databasebeta

← #8096260

Subgroups — #8096260

Order 512.

4717 conjugacy classes of subgroups.

The subgroup lattice has 1351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53148C213yesmaximal, complemented
2#53140C213yesmaximal, complemented
3#53138C213yesmaximal, complemented
4#53010C213yesmaximal, complemented
5#52982C213yesmaximal, complemented
6#52975C213yesmaximal, complemented
7#52303C213yesmaximal, complemented
8#46072C213yesmaximal, complemented
9#46057C213yesmaximal, complemented
10#46055C213yesmaximal, complemented
11#45714C213yesmaximal, complemented
12#45675C213yesmaximal, complemented
13#45670C213yesmaximal, complemented
14#45641C213yesmaximal, complemented
15#45626C213yesmaximal, complemented
16#45498C213yesmaximal, complemented
17#36578C211yesmaximal, characteristic, complemented
18#36577C211yesmaximal, characteristic, complemented
19Q8×#124C211yesmaximal, characteristic, complemented
20Q8×#121C211yesmaximal, characteristic, complemented
21#36482C211yesmaximal, characteristic, complemented
22#36475C211yesmaximal, characteristic, complemented
23#36467C211yesmaximal, characteristic, complemented
24#36435C211yesmaximal, characteristic, complemented
25#36434C211yesmaximal, characteristic, complemented
26#35983C211yesmaximal, characteristic, complemented
27#35771C211yesmaximal, characteristic, complemented
28#35748C211yesmaximal, characteristic, complemented
29#35737C211yesmaximal, characteristic, complemented
30#35723C211yesmaximal, characteristic, complemented
31#35711C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44#2864C2213yes—
45#2862C2213yes—
46#2861C2213yes—
47#2857C2213yes—
48#2857C2213yes—
49#2855C2213yes—
50#2854C2213yes—
51#2851C2213yes—
52#2850C2213yes—
53#2841C2216yes—
54#2839C2216yes—
55#2839C2216yes—
56#2837C2216yes—
57#2836C2216yes—
58#2831C2216yes—
59#2831C2216yes—
60#2831C2216yes—
61#2831C2216yes—
62#2827C2216yes—
63#2824C2216yes—
64#2808C2213yes—
65#2806C2213yes—
66#2798C2216yes—
67#2788C2216yes—
68#2783C2213yes—
69#2783C2213yes—
70#2781C2213yes—
71#2781C2213yes—
72#2772C2216yes—
73#2768C2216yes—
74#2761C2216yes—
75#2755C2216yes—
76#2755C2216yes—
77#2754C2216yes—
78#2751C2216yes—
79#2750C2216yes—
80#2750C2216yes—
81#2744C2213yes—
82#2744C2213yes—
83#2744C2216yes—
84#2741C2216yes—
85#2740C2216yes—
86#2739C2216yes—
87#2732C2213yes—
88#2730C2213yes—
89#2730C2213yes—
90#2704C2216yes—
91#2700C2216yes—
92#2696C2216yes—
93#2694C2213yes—
94#2694C2213yes—
95#2692C2216yes—
96#2692C2216yes—
97#2687C2216yes—
98#2686C2211yescharacteristic
99#2686C2213yes—
100#2682C2213yes—
101#2628C2213yes—
102#2628C2213yes—
103#2625C2213yes—
104#2625C2213yes—
105#2621C2213yes—
106#2620C2213yes—
107#2592C2213yes—
108#2582C2213yes—
109#2581C2213yes—
110#2581C2213yes—
111#2580C2213yes—
112#2570C2213yes—
113#2570C2213yes—
114#2568C2213yes—
115#2568C2213yes—
116#2568C2213yes—
117#2565C2213yes—
118#2563C2213yes—
119#2562C2213yes—
120#2547C2213yes—
121#2546C2213yes—
122#2545C2213yes—
123#2545C2213yes—
124#2542C2213yes—
125#2538C2213yes—
126#2538C2213yes—
127#2536C2213yes—
128#2535C2213yes—
129#2509C2213yes—
130#2508C2213yes—
131#2507C2213yes—
132#2506C2213yes—
133#2504C2213yes—
134#2503C2213yes—
135#2503C2213yes—
136#2499C2213yes—
137#2492C2213yes—
138#2492C2213yes—
139#2492C2213yes—
140#2492C2213yes—
141#2492C2213yes—
142#2491C2213yes—
143#2490C2213yes—
144#2489C2213yes—
145#2487C2213yes—
146#2487C2213yes—
147#2486C2213yes—
148#2485C2213yes—
149#2453C2213yes—
150#2453C2213yes—
151#2453C2213yes—
152#2452C2213yes—
153#2452C2213yes—
154#2451C2213yes—
155#2451C2213yes—
156#2451C2213yes—
157#2448C2213yes—
158#2448C2213yes—
159#2447C2213yes—
160#2447C2213yes—
161#2446C2213yes—
162#2446C2213yes—
163#2446C2213yes—
164#2446C2213yes—
165#2442C2213yes—
166#2442C2213yes—
167#2442C2213yes—
168#2440C2213yes—
169#2440C2213yes—
170#2440C2213yes—
171#2439C2213yes—
172#2439C2213yes—
173#2429C2213yes—
174#2429C2213yes—
175#2429C2213yes—
176#2429C2213yes—
177#2427C2213yes—
178#2427C2213yes—
179#2426C2213yes—
180#2426C2213yes—
181#2423C2213yes—
182#2421C2213yes—
183#2421C2213yes—
184#2421C2213yes—
185#2421C2213yes—
186#2421C2213yes—
187#2420C2213yes—
188#2420C2213yes—
189#2417C2213yes—
190#2417C2213yes—
191#2417C2213yes—
192#2417C2213yes—
193#2417C2213yes—
194#2416C2213yes—
195#2415C2213yes—
196#2414C2213yes—
197#2396C2213yes—
198#2396C2213yes—
199#2395C2213yes—
200#2395C2213yes—
201#2392C2213yes—
202#2392C2213yes—
203#2378C2216yes—
204#2378C2216yes—
205#2377C2216yes—
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208#2351C2211yescharacteristic
209#2351C2211yescharacteristic
210#2351C2211yescharacteristic
211#2351C2211yescharacteristic
212#2351C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214Q8×C4⋊C4C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226Q8×C22⋊C4C2211yescharacteristic
227Q8×C22⋊C4C2211yescharacteristic
228C4×#125C2213yes—
229C4×#124C2213yes—
230C4×#124C2213yes—
231C4×C22⋊Q8C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×#123C2213yes—
234C4×#123C2213yes—
235C4×#121C2213yes—
236C4×#121C2213yes—
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242Q82—44no—
243#557—44no—
244D4×Q8—44no—
245D4×Q8—44no—
246D4×Q8—44no—
247#548—44no—
248#548—44no—
249#548—44no—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×C4⋊Q8C2313yes—
257C2×#125C2313yes—
258C2×#125C2313yes—
259C2×#125C2313yes—
260C2×#124C2311yescharacteristic
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#124C2313yes—
265C2×#123C2313yes—
266C2×#123C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2316yes—
278C2×C22⋊Q8C2316yes—
279C2×C22⋊Q8C2313yes—
280C2×#121C2313yes—
281C2×#121C2311yescharacteristic
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285#520—44no—
286#519—44no—
287C2×C4×Q8—44no—
288C2×C4×Q8—44no—
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×Q8C2311yescharacteristic
300C2×C4×Q8C2313yes—
301C2×C4×Q8C2313yes—
302C2×C4×Q8C2313yes—
303C2×C4×Q8C2313yes—
304C2×C4×Q8C2313yes—
305C2×C4×Q8C2313yes—
306C2×C4×Q8C2313yes—
307C2×C4×Q8C2313yes—
308C2×C4×D4C2313yes—
309C2×C4×D4C2313yes—
310C2×C4×D4C2313yes—
311C2×C4×D4C2313yes—
312C2×C4×D4C2313yes—
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×#117C2313yes—
317C2×#117C2313yes—
318C2×#117C2313yes—
319C22×C4⋊C4C2313yes—
320C22×C4⋊C4C2313yes—
321C22×C4⋊C4C2313yes—
322C22×C42C2313yes—
323C22×C42C2313yes—
324#400C2316yes—
325#400C2313yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2316yes—
330#400C2316yes—
331#400C2316yes—
332#400C2316yes—
333#400C2313yes—
334#400C2316yes—
335#400C2316yes—
336#400C2316yes—
337#400C2316yes—
338#400C2316yes—
339#400C2316yes—
340#400C2313yes—
341#400C2313yes—
342#399C2313yes—
343#399C2316yes—
344#399C2316yes—
345#399C2313yes—
346#399C2313yes—
347#399C2313yes—
348#398C2316yes—
349#398C2316yes—
350#398C2316yes—
351#398C2316yes—
352#398C2316yes—
353#398C2313yes—
354#398C2316yes—
355#398C2316yes—
356#398C2316yes—
357#398C2313yes—
358#398C2316yes—
359#398C2316yes—
360#398C2313yes—
361#398C2313yes—
362#398C2313yes—
363#398C2313yes—
364#398C2316yes—
365#398C2316yes—
366#398C2313yes—
367#398C2313yes—
368#397C2316yes—
369#397C2316yes—
370#397C2313yes—
371#397C2316yes—
372#397C2316yes—
373#397C2313yes—
374#397C2313yes—
375#397C2316yes—
376#397C2316yes—
377#397C2316yes—
378#397C2316yes—
379#397C2313yes—
380#397C2316yes—
381#397C2313yes—
382#397C2311yescharacteristic
383#397C2313yes—
384#397C2313yes—
385#396C2316yes—
386#396C2316yes—
387#396C2316yes—
388#396C2313yes—
389#396C2313yes—
390#396C2316yes—
391#396C2316yes—
392#396C2313yes—
393#396C2313yes—
394#396C2316yes—
395#396C2313yes—
396#396C2313yes—
397#396C2313yes—
398#396C2313yes—
399#395C2313yes—
400#395C2316yes—
401#395C2316yes—
402#395C2316yes—
403#395C2311yescharacteristic
404#394C2316yes—
405#394C2313yes—
406#394C2316yes—
407#394C2316yes—
408#394C2313yes—
409#394C2313yes—
410#394C2311yescharacteristic
411#394C2311yescharacteristic
412#394C2313yes—
413#394C2313yes—
414#394C2311yescharacteristic
415#394C2313yes—
416#394C2313yes—
417#393C2316yes—
418#393C2316yes—
419#393C2316yes—
420#393C2316yes—
421#393C2313yes—
422#393C2316yes—
423#393C2311yescharacteristic
424#392C2313yes—
425#392C2313yes—
426#391C2313yes—
427#391C2313yes—
428#391C2313yes—
429#391C2313yes—
430#391C2313yes—
431#391C2316yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2316yes—
438#391C2316yes—
439#391C2316yes—
440#391C2316yes—
441#391C2313yes—
442#391C2313yes—
443#391C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#390C2313yes—
454#390C2313yes—
455#390C2313yes—
456#390C2313yes—
457#390C2313yes—
458#390C2313yes—
459#390C2313yes—
460#390C2316yes—
461#390C2313yes—
462#390C2313yes—
463#390C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2316yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#389C2316yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2316yes—
482#389C2316yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#388C2313yes—
495#388C2316yes—
496#388C2316yes—
497#388C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2313yes—
501#388C2316yes—
502#388C2313yes—
503#388C2316yes—
504#388C2313yes—
505#388C2316yes—
506#388C2313yes—
507#388C2316yes—
508#388C2316yes—
509#388C2313yes—
510#388C2313yes—
511#388C2313yes—
512#388C2311yescharacteristic
513#388C2313yes—
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#387C2311yescharacteristic
521#387C2313yes—
522#387C2313yes—
523#387C2313yes—
524#387C2313yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2313yes—
531#387C2316yes—
532#387C2316yes—
533#387C2313yes—
534#387C2316yes—
535#387C2316yes—
536#387C2316yes—
537#387C2313yes—
538#387C2316yes—
539#387C2316yes—
540#387C2313yes—
541#387C2313yes—
542#387C2313yes—
543#387C2313yes—
544#386C2313yes—
545#386C2316yes—
546#386C2316yes—
547#386C2313yes—
548#386C2316yes—
549#386C2313yes—
550#386C2316yes—
551#386C2316yes—
552#386C2311yescharacteristic
553#386C2313yes—
554#386C2311yescharacteristic
555#385C2316yes—
556#385C2316yes—
557#385C2316yes—
558#385C2316yes—
559#385C2313yes—
560#385C2313yes—
561#385C2313yes—
562#385C2311yescharacteristic
563#385C2313yes—
564#385C2313yes—
565#384C2313yes—
566#384C2313yes—
567#384C2313yes—
568#382C2313yes—
569#382C2316yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2313yes—
574#382C2313yes—
575#382C2313yes—
576#382C2313yes—
577#382C2313yes—
578#382C2313yes—
579#381C2316yes—
580#381C2316yes—
581#381C2316yes—
582#381C2313yes—
583#381C2311yescharacteristic
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2316yes—
594#380C2313yes—
595#380C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2316yes—
600#380C2316yes—
601#380C2316yes—
602#380C2313yes—
603#380C2311yescharacteristic
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×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C43C2313yes—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8—24no—
637C22×Q8—24no—
638C22×Q8—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8C2413yes—
643C22×Q8C2413yes—
644C22×Q8C2413yes—
645C22×Q8C2411yescharacteristic
646C22×Q8C2413yes—
647C22×Q8C2416yes—
648C22×Q8C2411yescharacteristic
649C22×D4C2413yes—
650C22×D4C2411yescharacteristic
651C22×D4C2411yescharacteristic
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2411yescharacteristic
656C23×C4C2413yes—
657C23×C4C2413yes—
658C23×C4C2413yes—
659C23×C4C2413yes—
660C23×C4C2411yescharacteristic
661C23×C4C2413yes—
662C23×C4C2411yescharacteristic
663C23×C4C2413yes—
664C23×C4C2416yes—
665C4⋊Q8—46no—
666C4⋊Q8—46no—
667C4⋊Q8—46no—
668C4⋊Q8—46no—
669C4⋊Q8—46no—
670C4⋊Q8—46no—
671C4⋊Q8—46no—
672#125—46no—
673#125—46no—
674#125—46no—
675#124—24no—
676#124—46no—
677#124—46no—
678#124—46no—
679#124—46no—
680#123—46no—
681#123—46no—
682C22⋊Q8—412no—
683C22⋊Q8—412no—
684C22⋊Q8—46no—
685C22⋊Q8—46no—
686C22⋊Q8—46no—
687C22⋊Q8—46no—
688C22⋊Q8—46no—
689C22⋊Q8—46no—
690C22⋊Q8—46no—
691C22⋊Q8—46no—
692C22⋊Q8—46no—
693C22⋊Q8—46no—
694C22⋊Q8—46no—
695#121—24no—
696#121—212no—
697#121—46no—
698#121—46no—
699#121—46no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—46no—
712C4×Q8—46no—
713C4×Q8—46no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×Q8—46no—
717C4×Q8—46no—
718C4×Q8—46no—
719C4×D4—46no—
720C4×D4—46no—
721C4×D4—46no—
722C4×D4—46no—
723C4×D4—46no—
724C4×D4—46no—
725C4×D4—46no—
726C4×D4—46no—
727#117—46no—
728#117—46no—
729#117—46no—
730C2×C4⋊C4—46no—
731C2×C4⋊C4—46no—
732C2×C4⋊C4—46no—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2416yes—
754C2×C4⋊C4C2416yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2411yescharacteristic
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2411yescharacteristic
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2416yes—
789C2×C22⋊C4C2411yescharacteristic
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2416yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2413yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2416yes—
835C2×C42—46no—
836C2×C42—46no—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2411yescharacteristic
849C2×C42C2416yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2413yes—
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857#95C2411yescharacteristic
858#95C2411yescharacteristic
859#95C2411yescharacteristic
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#95C2413yes—
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2416yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2416yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907#95C2416yes—
908#95C2416yes—
909#95C2416yes—
910#95C2416yes—
911#95C2416yes—
912#95C2416yes—
913#95C2416yes—
914#95C2416yes—
915#95C2416yes—
916#95C2416yes—
917#95C2416yes—
918C24C2511yescharacteristic
919C24C2513yes—
920C24C2511yescharacteristic
921C24C2511yescharacteristic
922#41—416no—
923C2×Q8—26no—
924C2×Q8—26no—
925C2×Q8—26no—
926C2×Q8—26no—
927C2×Q8—26no—
928C2×Q8—26no—
929C2×Q8—22no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—41no—
935C2×Q8—41no—
936C2×Q8—43no—
937C2×Q8—43no—
938C2×Q8—46no—
939C2×Q8—46no—
940C2×Q8—46no—
941C2×Q8—416no—
942C2×Q8—416no—
943C2×Q8—416no—
944C2×Q8H(5,𝔽2)14yes—
945C2×Q8H(5,𝔽2)14yes—
946C2×Q82−1+414yes—
947C2×D4—22no—
948C2×D4—22no—
949C2×D4—26no—
950C2×D4—26no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—26no—
954C2×D4—22no—
955C2×D4—41no—
956C2×D4—41no—
957C2×D4—41no—
958C2×D4—41no—
959C2×D4—41no—
960C2×D4—43no—
961C2×D4—43no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—43no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D42−1+414yes—
968C22×C4—22no—
969C22×C4—26no—
970C22×C4—26no—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—26no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—22no—
983C22×C4—22no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—41no—
987C22×C4—43no—
988C22×C4—43no—
989C22×C4—43no—
990C22×C4—43no—
991C22×C4—43no—
992C22×C4—46no—
993C22×C4—46no—
994C22×C4—46no—
995C22×C4C2511yescharacteristic
996C22×C4C2513yes—
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2513yes—
1001C22×C4C2513yes—
1002C22×C4C2513yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2513yes—
1005C22×C4C2513yes—
1006C22×C4C2513yes—
1007C22×C4C2513yes—
1008C22×C4C2513yes—
1009C22×C4C2513yes—
1010C22×C4C2511yescharacteristic
1011C22×C4C2511yescharacteristic
1012C22×C4C2511yescharacteristic
1013C22×C4C2513yes—
1014C22×C4C2513yes—
1015C22×C4C2513yes—
1016C22×C4C2513yes—
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2513yes—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—22no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—22no—
1041C4⋊C4—43no—
1042C4⋊C4—46no—
1043C4⋊C4—46no—
1044C4⋊C4—41no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—46no—
1048C4⋊C4—43no—
1049C4⋊C4—41no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—41no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—46no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—46no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C4⋊C4—46no—
1071C4⋊C4—46no—
1072C4⋊C4—46no—
1073C4⋊C4—43no—
1074C4⋊C4—43no—
1075C4⋊C4—43no—
1076C4⋊C4—43no—
1077C4⋊C4—46no—
1078C22⋊C4—26no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—26no—
1086C22⋊C4—22no—
1087C22⋊C4—26no—
1088C22⋊C4—26no—
1089C22⋊C4—22no—
1090C22⋊C4—46no—
1091C22⋊C4—43no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—43no—
1101C22⋊C4—43no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—46no—
1110C22⋊C4—46no—
1111C22⋊C4—46no—
1112C22⋊C4—46no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—46no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C42—26no—
1125C42—26no—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—26no—
1134C42—26no—
1135C42—22no—
1136C42—43no—
1137C42—43no—
1138C42—43no—
1139C42—43no—
1140C42—43no—
1141C42—46no—
1142C42—43no—
1143C42—43no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—23no—
1158C23—23no—
1159C23—21no—
1160C23—21no—
1161C23—23no—
1162C23—21no—
1163C23—23no—
1164C23—23no—
1165C23—23no—
1166C23—21no—
1167C23—21no—
1168C23—23no—
1169C23—21no—
1170C23C2×2−1+412yes—
1171C23C2×2−1+412yes—
1172C23C2611yescharacteristic
1173Q8—44no—
1174Q8—412no—
1175Q8—412no—
1176Q8—412no—
1177Q8—86no—
1178Q8—166no—
1179Q8#562116yes—
1180D4—44no—
1181D4—44no—
1182D4—44no—
1183D4—412no—
1184D4—86no—
1185D4—86no—
1186D4—86no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—23no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—21no—
1230C2×C4—23no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—21no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—21no—
1251C2×C4—23no—
1252C2×C4—21no—
1253C2×C4—23no—
1254C2×C4—23no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—21no—
1258C2×C4—23no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—23no—
1262C2×C4—44no—
1263C2×C4—44no—
1264C2×C4—412no—
1265C2×C4—412no—
1266C2×C4—412no—
1267C2×C4—412no—
1268C2×C4—86no—
1269C2×C4—86no—
1270C2×C4—166no—
1271C2×C4C2×H(5,𝔽2)16yes—
1272C2×C4C2×H(5,𝔽2)16yes—
1273C2×C4C2×2−1+412yes—
1274C2×C4C2×2−1+416yes—
1275C2×C4#58512yes—
1276C2×C4#58512yes—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—43no—
1293C22—41no—
1294C22—43no—
1295C22—43no—
1296C22—41no—
1297C22—41no—
1298C22—43no—
1299C22—41no—
1300C22—43no—
1301C22—41no—
1302C22—43no—
1303C22—41no—
1304C22—43no—
1305C22C22×H(5,𝔽2)11yescharacteristic
1306C22C22×H(5,𝔽2)11yescharacteristic
1307C22C22×2−1+411yescharacteristic
1308C22C22×2−1+411yescharacteristic
1309C22C2×#58511yescharacteristic
1310C22C2×#58511yescharacteristic
1311C222−1+611yescharacteristic
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—41no—
1316C4—41no—
1317C4—43no—
1318C4—43no—
1319C4—41no—
1320C4—41no—
1321C4—43no—
1322C4—43no—
1323C4—43no—
1324C4—43no—
1325C4—41no—
1326C4—43no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—43no—
1331C4—43no—
1332C4—43no—
1333C4—41no—
1334C4—43no—
1335C4—43no—
1336C4—43no—
1337C4—43no—
1338C4C2×#562112yes—
1339C2—42no—
1340C2—42no—
1341C2—81no—
1342C2—83no—
1343C2C22×#56211yescharacteristic
1344C2#6289311yescharacteristic
1345C2#6289711yescharacteristic
1346C2#6295311yescharacteristic
1347C2#6301511yescharacteristic
1348C2#6303211yescharacteristic
1349C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53148C2semidirect
2. #53140C2semidirect
3. #53138C2semidirect
4. #53010C2semidirect
5. #52982C2semidirect
6. #52975C2semidirect
7. #52303C2semidirect
8. #46072C2semidirect
9. #46057C2semidirect
10. #46055C2semidirect
11. #45714C2semidirect
12. #45675C2semidirect
13. #45670C2semidirect
14. #45641C2semidirect
15. #45626C2semidirect
16. #45498C2semidirect
17. #36578C2semidirect
18. #36577C2semidirect
19. Q8×#124C2semidirect
20. Q8×#121C2semidirect
21. #36482C2semidirect
22. #36475C2semidirect
23. #36467C2semidirect
24. #36435C2semidirect
25. #36434C2semidirect
26. #35983C2semidirect
27. #35771C2semidirect
28. #35748C2semidirect
29. #35737C2semidirect
30. #35723C2semidirect
31. #35711C2semidirect

Maximal subgroups

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

subgroupindex
#531482
#531402
#531382
#530102
#529822
#529752
#523032
#460722
#460572
#460552
#457142
#456752
#456702
#456412
#456262
#454982
#365782
#365772
Q8×#1242
Q8×#1212
#364822
#364752
#364672
#364352
#364342
#359832
#357712
#357482
#357372
#357232
#357112