Finite Group Databasebeta

← #7726941

Subgroups — #7726941

Order 512.

6584 conjugacy classes of subgroups.

The subgroup lattice has 1468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3559C211yesmaximal, characteristic, complemented
2C2×#3455C211yesmaximal, characteristic, complemented
3#51753C212yesmaximal, complemented
4#51546C212yesmaximal, complemented
5#51545C212yesmaximal, complemented
6#51545C212yesmaximal, complemented
7#47822C214yesmaximal, complemented
8#47800C214yesmaximal, complemented
9#44450C212yesmaximal, complemented
10#44082C212yesmaximal, complemented
11#43496C212yesmaximal, complemented
12#43495C212yesmaximal, complemented
13#39846C214yesmaximal, complemented
14#39415C212yesmaximal, complemented
15#39413C212yesmaximal, complemented
16#39376C212yesmaximal, complemented
17#39371C212yesmaximal, complemented
18#38365C214yesmaximal, complemented
19#38363C214yesmaximal, complemented
20#37540C211yesmaximal, characteristic, complemented
21#36972C214yesmaximal, complemented
22#36217C214yesmaximal, complemented
23#35464C214yesmaximal, complemented
24#35326C211yesmaximal, characteristic, complemented
25#35118C211yesmaximal, characteristic, complemented
26C2×#2611C211yesmaximal, characteristic, complemented
27#34222C211yesmaximal, characteristic, complemented
28#3559—216no—
29C2×#563C2212yescomplemented
30C2×#562C2212yescomplemented
31C2×#554C2212yescomplemented
32C2×#553C2212yes—
33C2×#553C2212yescomplemented
34C2×#547C2214yes—
35C2×#547C2212yes—
36C2×#544C2212yescomplemented
37#3455—216no—
38C2×#542C2212yes—
39C2×#542C2212yes—
40C2×#541C2212yes—
41C2×#540C2212yes—
42C2×#540C2212yescomplemented
43C2×#539C2212yes—
44C2×#539C2212yes—
45C2×#539C2212yes—
46C2×#539C2214yescomplemented
47C2×#538C2212yes—
48C2×#538C2212yes—
49C2×#537C2212yes—
50C2×#533C2211yescharacteristic
51C2×#532C2211yescharacteristic
52C2×#529C2211yescharacteristic
53C2×#529C2214yes—
54C2×#529C2214yes—
55C22×#125C2211yescharacteristic
56C2×#525C2212yes—
57C2×C4×#41C2212yes—
58C22×#117C2211yescharacteristic
59#2857C2212yes—
60#2855C2214yescomplemented
61#2853C2212yes—
62#2853C2214yescomplemented
63#2850C2212yes—
64#2849C2212yes—
65#2822C2214yescomplemented
66#2732C2214yes—
67#2729C2214yes—
68#2729C2214yes—
69#2728C2214yes—
70#2726C2214yescomplemented
71#2725C2214yes—
72#2724C2214yescomplemented
73#2721C2214yes—
74#2719C2214yescomplemented
75#2718C2214yes—
76#2718C2214yes—
77#2718C2214yescomplemented
78#2716C2214yes—
79#2713C2214yescomplemented
80#2710C2214yes—
81#2708C2214yes—
82#2708C2214yes—
83#2708C2214yescomplemented
84#2708C2214yescomplemented
85#2706C2214yes—
86#2704C2214yescomplemented
87#2703C2214yes—
88#2702C2214yes—
89#2701C2214yes—
90#2701C2214yescomplemented
91#2700C2214yes—
92#2700C2214yes—
93#2699C2214yes—
94#2698C2214yescomplemented
95#2698C2214yescomplemented
96#2689C2214yescomplemented
97#2689C2214yescomplemented
98#2689C2214yescomplemented
99#2688C2214yes—
100#2688C2214yes—
101#2687C2214yescomplemented
102#2674C2214yes—
103#2672C2214yescomplemented
104#2671C2214yes—
105#2671C2214yes—
106#2660C2211yescharacteristic, complemented
107#2660C2212yescomplemented
108#2658C2211yescharacteristic, complemented
109#2642C2212yescomplemented
110#2642C2211yescharacteristic, complemented
111#2640C2211yescharacteristic, complemented
112#2638C2214yes—
113#2634C2214yescomplemented
114#2630C2214yes—
115#2627C2211yescharacteristic
116#2627C2212yes—
117#2627C2212yes—
118#2626C2211yescharacteristic
119#2618C2211yescharacteristic
120#2617C2211yescharacteristic
121#2611C2212yes—
122#2611C2212yes—
123#2611C2212yes—
124#2611C2212yes—
125#2611C2212yes—
126#2611C2214yes—
127#2611C2214yes—
128#2611C2214yescomplemented
129#2610C2212yes—
130#2609C2214yes—
131#2604C2212yescomplemented
132#2604C2212yescomplemented
133#2602C2214yes—
134#2601C2214yes—
135#2600C2214yes—
136#2599C2212yes—
137#2598C2212yes—
138#2579C2214yes—
139#2565C2214yescomplemented
140#2564C2212yes—
141#2564C2214yes—
142#2564C2212yes—
143#2560C2214yes—
144#2559C2214yescomplemented
145#2557C2214yes—
146#2556C2214yescomplemented
147#2555C2214yes—
148#2553C2214yescomplemented
149#2549C2214yescomplemented
150#2549C2214yescomplemented
151#2543C2214yes—
152#2534C2214yes—
153#2521C2214yes—
154#2521C2214yes—
155#2519C2214yes—
156#2506C2214yescomplemented
157#2503C2212yes—
158#2502C2212yes—
159#2501C2214yes—
160#2499C2214yescomplemented
161#2498C2214yes—
162#2498C2214yescomplemented
163#2496C2214yescomplemented
164#2496C2214yescomplemented
165#2488C2214yes—
166#2488C2214yes—
167#2488C2214yes—
168#2488C2214yescomplemented
169#2486C2214yes—
170#2486C2214yescomplemented
171#2485C2214yescomplemented
172#2484C2214yes—
173#2484C2214yescomplemented
174#2481C2214yes—
175#2479C2214yes—
176#2475C2214yescomplemented
177#2473C2214yescomplemented
178#2446C2214yescomplemented
179#2446C2214yescomplemented
180#2444C2214yes—
181#2444C2214yes—
182#2444C2214yescomplemented
183#2443C2214yes—
184#2443C2214yes—
185#2443C2214yescomplemented
186#2440C2214yescomplemented
187#2425C2214yes—
188#2425C2214yes—
189#2425C2214yescomplemented
190#2424C2214yes—
191#2423C2214yescomplemented
192#2421C2214yescomplemented
193#2419C2214yes—
194#2419C2214yes—
195#2419C2214yes—
196#2419C2214yescomplemented
197#2419C2214yescomplemented
198#2419C2214yescomplemented
199#2419C2214yescomplemented
200#2418C2214yes—
201#2406C2214yes—
202#2404C2214yes—
203C2×#400C2211yescharacteristic
204C2×#399C2211yescharacteristic
205C2×#398C2211yescharacteristic
206C2×#397C2211yescharacteristic
207#2372C2212yescomplemented
208#2372C2212yescomplemented
209#2364C2212yes—
210#2364C2212yes—
211#2353C2214yescomplemented
212#2349C2214yes—
213D4×C4⋊C4C2214yes—
214#2339C2214yes—
215#2339C2214yes—
216#2339C2214yes—
217#2331C2212yescomplemented
218#2328C2212yescomplemented
219#2327C2212yescomplemented
220#2326C2212yescomplemented
221#2325C2214yes—
222#2322C2212yes—
223#2322C2214yes—
224#2321C2212yes—
225#2319C2212yescomplemented
226C4×#123C2214yescomplemented
227C4×#121C2212yes—
228C4×#121C2212yes—
229C2×#389C2212yes—
230C2×#388C2212yes—
231C2×#387C2212yes—
232C2×#387C2214yescomplemented
233C2×#385C2212yes—
234#2283C2211yescharacteristic
235#2275C2212yescomplemented
236C2×#376C2211yescharacteristic
237C22×#41C2314yes—
238C22×#41C2312yes—
239C24×C4C2311yescharacteristic
240#563—216no—
241#562—216no—
242#554—216no—
243#553—216no—
244#553—216no—
245#547—232no—
246#547—216no—
247#544—216no—
248#542—216no—
249#542—216no—
250#541—216no—
251#540—216no—
252#540—216no—
253#539—216no—
254#539—216no—
255#539—216no—
256#539—232no—
257#538—216no—
258#538—216no—
259#537—216no—
260#533—28no—
261#532D4116yescomplemented
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×#127C2311yescharacteristic
269#529—232no—
270#529—232no—
271#529—28no—
272C2×#126C2314yes—
273C2×#126C2312yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125—28no—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2311yescharacteristic
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2312yes—
290C2×#124C2311yescharacteristic
291C2×#124C2314yes—
292C2×#124C2314yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295#525—216no—
296C2×#123C2312yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2312yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2311yescharacteristic
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×#121C2311yescharacteristic
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2312yes—
335C2×#121C2314yes—
336C2×#121C2312yes—
337C2×#121C2312yes—
338C2×#120C2314yes—
339C2×#120C2312yes—
340C4×#41—216no—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2314yes—
350C2×C4×D4C2311yescharacteristic
351C2×C4×D4C2314yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×#117—28no—
365C2×#117C2312yes—
366C2×#117C2312yes—
367C2×#117C2312yes—
368C2×#117C2312yes—
369C2×#117C2312yes—
370C2×#117C2312yes—
371C2×#117C2314yes—
372C2×#117C2312yes—
373C22×C4⋊C4C2311yescharacteristic
374C22×C4⋊C4C2314yes—
375C22×C4⋊C4C2311yescharacteristic
376C22×C4⋊C4C2312yes—
377C22×C4⋊C4C2311yescharacteristic
378C22×C4⋊C4C2311yescharacteristic
379C22×C4⋊C4C2312yes—
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C4⋊C4C2314yes—
383C22×C4⋊C4C2312yes—
384C22×C22⋊C4C2311yescharacteristic
385C22×C22⋊C4C2311yescharacteristic
386C22×C22⋊C4C2312yes—
387C22×C22⋊C4C2312yes—
388C22×C42C2311yescharacteristic
389C22×C42C2314yes—
390C22×C42C2312yes—
391C22×C42C2311yescharacteristic
392#400C2312yes—
393#400C2312yes—
394#400C2314yes—
395#400C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2312yes—
400#400C2314yes—
401#400C2312yes—
402#400C2312yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#399C2312yes—
410#399C2312yes—
411#399C2314yes—
412#399C2312yes—
413#399C2314yes—
414#399C2312yes—
415#399C2312yes—
416#399C2314yes—
417#399C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2312yes—
429#398C2314yes—
430#398C2314yes—
431#398C2312yes—
432#398C2312yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#397C2314yes—
440#397C2312yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2312yes—
445#397C2312yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#395C2312yes—
464#395C2312yes—
465#395C2314yes—
466#395C2312yes—
467#395C2314yes—
468#395C2314yes—
469#395C2314yes—
470#394C2314yes—
471#394C2312yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#393C2314yes—
484#393C2312yes—
485#393C2312yes—
486#393C2312yes—
487#393C2314yes—
488#392C2312yes—
489#392C2314yes—
490#392C2314yes—
491#392C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2314yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2314yes—
502#391C2314yes—
503#390C2314yes—
504#390C2312yes—
505#390C2312yes—
506#390C2314yes—
507#390C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2312yes—
580#386C2314yes—
581#386C2312yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2312yes—
606#385C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#384C2314yes—
627#384C2312yes—
628#384C2314yes—
629#383C2312yes—
630#382C2314yes—
631#382C2312yes—
632#382C2312yes—
633#382C2314yes—
634#381C2314yes—
635#381C2312yes—
636#381C2314yes—
637#381C2312yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2311yescharacteristic
656#380C2311yescharacteristic
657#379C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671#376C2311yescharacteristic
672#376C2312yes—
673#376C2312yes—
674#376C2311yescharacteristic
675#376C2312yes—
676#376C2311yescharacteristic
677#376C2311yescharacteristic
678C2×#95C2311yescharacteristic
679C2×#95C2311yescharacteristic
680C2×#95C2314yes—
681C2×#95C2312yes—
682C2×#95C2312yes—
683C2×#95C2312yes—
684C2×#95C2314yes—
685C2×#95C2314yes—
686C2×#95C2312yes—
687C2×#95C2314yes—
688C2×#95C2312yes—
689C25C2411yescharacteristic
690C2×#41—216no—
691C2×#41—44no—
692C2×#41—44no—
693C2×#41—48no—
694C2×#41—48no—
695C2×#41C2×D4116yes—
696C22×Q8C2411yescharacteristic
697C22×Q8C2412yes—
698C22×Q8C2412yes—
699C22×Q8C2414yes—
700C22×Q8C2412yes—
701C22×D4C2412yes—
702C22×D4C2414yes—
703C22×D4C2414yes—
704C22×D4C2414yes—
705C22×D4C2414yes—
706C22×D4C2411yescharacteristic
707C22×D4C2414yes—
708C22×D4C2414yes—
709C22×D4C2412yes—
710C22×D4C2412yes—
711C22×D4C2412yes—
712C23×C4—24no—
713C23×C4—42no—
714C23×C4—42no—
715C23×C4C2412yes—
716C23×C4C2411yescharacteristic
717C23×C4C2412yes—
718C23×C4C2411yescharacteristic
719C23×C4C2412yes—
720C23×C4C2411yescharacteristic
721C23×C4C2411yescharacteristic
722C23×C4C2412yes—
723C23×C4C2414yes—
724C23×C4C2412yes—
725C23×C4C2414yes—
726C23×C4C2414yes—
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2414yes—
736C4⋊Q8—216no—
737C4⋊Q8—28no—
738C4⋊Q8—24no—
739C4⋊Q8—24no—
740C4⋊Q8—44no—
741C4⋊Q8C2×D418yes—
742#127C2×D418yes—
743#126—216no—
744#126—216no—
745#126—216no—
746#126—216no—
747#126—216no—
748#126—216no—
749#126—28no—
750#125—216no—
751#125—216no—
752#125—216no—
753#125—28no—
754#125—28no—
755#125—28no—
756#125—28no—
757#125—28no—
758#125—24no—
759#125—28no—
760#124—216no—
761#124—216no—
762#124—24no—
763#124—44no—
764#124C2×D4116yes—
765#123—216no—
766#123—216no—
767#123—216no—
768#123—216no—
769#123—216no—
770#123—216no—
771#123—28no—
772#123—216no—
773#123—216no—
774#123—216no—
775#123—216no—
776#123—216no—
777#123—48no—
778#123—48no—
779#123—44no—
780C22⋊Q8—28no—
781C22⋊Q8—28no—
782C22⋊Q8—216no—
783C22⋊Q8—24no—
784C22⋊Q8—28no—
785C22⋊Q8—28no—
786C22⋊Q8—216no—
787C22⋊Q8—216no—
788C22⋊Q8—216no—
789C22⋊Q8—216no—
790C22⋊Q8—216no—
791C22⋊Q8—216no—
792C22⋊Q8—216no—
793#121—28no—
794#121—28no—
795#121—216no—
796#121—216no—
797#121—216no—
798#121—216no—
799#121—28no—
800#121—216no—
801#121—28no—
802#121—24no—
803#121—216no—
804#121—48no—
805#121C2×D4116yes—
806#121C2×D4116yes—
807#120—216no—
808#120—44no—
809C4×Q8—28no—
810C4×Q8—28no—
811C4×Q8—28no—
812C4×Q8—28no—
813C4×Q8—24no—
814C4×D4—216no—
815C4×D4—216no—
816C4×D4—28no—
817C4×D4—28no—
818C4×D4—216no—
819C4×D4—28no—
820C4×D4—28no—
821C4×D4—216no—
822C4×D4—216no—
823C4×D4—28no—
824C4×D4—216no—
825C4×D4—24no—
826C4×D4—44no—
827C4×D4—44no—
828C4×D4—48no—
829C4×D4—48no—
830C4×D4C2×D4116yes—
831C4×D4C2×D4116yes—
832#117—28no—
833#117—216no—
834#117—28no—
835#117—28no—
836#117—28no—
837#117—28no—
838#117—28no—
839#117—28no—
840C2×C4⋊C4—24no—
841C2×C4⋊C4—24no—
842C2×C4⋊C4—28no—
843C2×C4⋊C4—24no—
844C2×C4⋊C4—28no—
845C2×C4⋊C4—24no—
846C2×C4⋊C4—216no—
847C2×C4⋊C4—28no—
848C2×C4⋊C4—44no—
849C2×C4⋊C4—48no—
850C2×C4⋊C4—44no—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2412yes—
904C2×C22⋊C4—24no—
905C2×C22⋊C4—24no—
906C2×C22⋊C4—44no—
907C2×C22⋊C4—44no—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C42—24no—
954C2×C42—216no—
955C2×C42—44no—
956C2×C42C2×D418yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2414yes—
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2411yescharacteristic
980#95C2411yescharacteristic
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2411yescharacteristic
987#95C2411yescharacteristic
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028C24—22no—
1029C24—22no—
1030C24—22no—
1031C24—42no—
1032C24—42no—
1033C24C2512yes—
1034C24C2512yes—
1035C24C2514yes—
1036C24C2511yescharacteristic
1037#41—432no—
1038#41—832no—
1039C2×Q8—22no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—28no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8C22×D418yes—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—28no—
1058C2×D4—28no—
1059C2×D4—28no—
1060C2×D4—28no—
1061C2×D4—22no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—44no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—42no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4C22×D4116yes—
1080C2×D4C22×D418yes—
1081C2×D4C22×D418yes—
1082C2×D4C22×D418yes—
1083C22×C4—22no—
1084C22×C4—22no—
1085C22×C4—24no—
1086C22×C4—22no—
1087C22×C4—24no—
1088C22×C4—22no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—22no—
1092C22×C4—22no—
1093C22×C4—22no—
1094C22×C4—28no—
1095C22×C4—28no—
1096C22×C4—24no—
1097C22×C4—28no—
1098C22×C4—28no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—28no—
1105C22×C4—28no—
1106C22×C4—42no—
1107C22×C4—42no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—42no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4—44no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—416no—
1138C22×C4C22×D414yes—
1139C22×C4C22×D4116yes—
1140C22×C4C22×D414yes—
1141C22×C4C22×D414yes—
1142C22×C4C2512yes—
1143C22×C4C2514yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2514yes—
1147C22×C4C2512yes—
1148C22×C4C2514yes—
1149C22×C4C2512yes—
1150C22×C4C2514yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2514yes—
1154C22×C4C2512yes—
1155C22×C4C2514yes—
1156C22×C4C2512yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2514yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C4⋊C4—24no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—28no—
1175C4⋊C4—28no—
1176C4⋊C4—28no—
1177C4⋊C4—24no—
1178C4⋊C4—28no—
1179C4⋊C4—28no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—28no—
1184C4⋊C4—28no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—24no—
1191C4⋊C4—22no—
1192C4⋊C4—22no—
1193C4⋊C4—28no—
1194C4⋊C4—28no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—28no—
1198C4⋊C4—28no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4C22×D418yes—
1217C4⋊C4C22×D418yes—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—24no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—24no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—28no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—24no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4C22×D4116yes—
1262C22⋊C4C22×D4116yes—
1263C42—24no—
1264C42—24no—
1265C42—28no—
1266C42—28no—
1267C42—28no—
1268C42—24no—
1269C42—28no—
1270C42—24no—
1271C42—24no—
1272C42—42no—
1273C42—42no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C42C22×D414yes—
1278C42C22×D414yes—
1279C42C22×D414yes—
1280C42C22×D414yes—
1281C23—22no—
1282C23—22no—
1283C23—24no—
1284C23—24no—
1285C23—24no—
1286C23—24no—
1287C23—24no—
1288C23—24no—
1289C23—22no—
1290C23—22no—
1291C23—24no—
1292C23—24no—
1293C23—22no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—24no—
1298C23—24no—
1299C23—48no—
1300C23—44no—
1301C23—82no—
1302C23—82no—
1303C23—84no—
1304C23C23×D418yes—
1305C23C23×D412yes—
1306C23#58512yes—
1307C23#58512yes—
1308C23C2611yescharacteristic
1309Q8—48no—
1310Q8—82no—
1311Q8—84no—
1312Q8—84no—
1313Q8—88no—
1314D4—232no—
1315D4—48no—
1316D4—48no—
1317D4—48no—
1318D4—48no—
1319D4—82no—
1320D4—88no—
1321D4—88no—
1322D4—88no—
1323D4—88no—
1324D4—164no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—28no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—44no—
1380C2×C4—44no—
1381C2×C4—416no—
1382C2×C4—48no—
1383C2×C4—48no—
1384C2×C4—48no—
1385C2×C4—48no—
1386C2×C4—44no—
1387C2×C4—48no—
1388C2×C4—88no—
1389C2×C4—88no—
1390C2×C4—82no—
1391C2×C4—88no—
1392C2×C4—84no—
1393C2×C4—88no—
1394C2×C4—82no—
1395C2×C4—88no—
1396C2×C4—84no—
1397C2×C4—88no—
1398C2×C4—164no—
1399C2×C4C23×D412yes—
1400C2×C4C23×D418yes—
1401C2×C4C23×D412yes—
1402C2×C4C23×D412yes—
1403C2×C4C23×D412yes—
1404C2×C4C23×D412yes—
1405C2×C4C23×D412yes—
1406C2×C4#58514yes—
1407C22—22no—
1408C22—22no—
1409C22—24no—
1410C22—24no—
1411C22—28no—
1412C22—28no—
1413C22—28no—
1414C22—44no—
1415C22—44no—
1416C22—44no—
1417C22—44no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—44no—
1425C22—44no—
1426C22—44no—
1427C22—44no—
1428C22—88no—
1429C22#348514yes—
1430C22C24×D411yescharacteristic
1431C22C2×#58511yescharacteristic
1432C22C2×#58511yescharacteristic
1433C22C2×#58512yes—
1434C222−1+612yes—
1435C4—22no—
1436C4—22no—
1437C4—28no—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—24no—
1443C4—42no—
1444C4—44no—
1445C4—42no—
1446C4—42no—
1447C4—44no—
1448C4—42no—
1449C4—44no—
1450C4—42no—
1451C4—42no—
1452C4—44no—
1453C4—42no—
1454C4—44no—
1455C4—42no—
1456C4—42no—
1457C4—44no—
1458C2—24no—
1459C2—48no—
1460C2—82no—
1461C2—82no—
1462C2C2×#348511yescharacteristic
1463C2#6281211yescharacteristic
1464C2#6285911yescharacteristic
1465C2#6290912yes—
1466C2#6293412yes—
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. C2×#3559C2semidirect
2. C2×#3455C2semidirect
3. #51753C2semidirect
4. #51546C2semidirect
5. #51545C2semidirect
6. #51545C2semidirect
7. #47822C2semidirect
8. #47800C2semidirect
9. #44450C2semidirect
10. #44082C2semidirect
11. #43496C2semidirect
12. #43495C2semidirect
13. #39846C2semidirect
14. #39415C2semidirect
15. #39413C2semidirect
16. #39376C2semidirect
17. #39371C2semidirect
18. #38365C2semidirect
19. #38363C2semidirect
20. #37540C2semidirect
21. #36972C2semidirect
22. #36217C2semidirect
23. #35464C2semidirect
24. #35326C2semidirect
25. #35118C2semidirect
26. C2×#2611C2semidirect
27. #34222C2semidirect
29. C2×#563C22semidirect
30. C2×#562C22semidirect
31. C2×#554C22semidirect
33. C2×#553C22semidirect
36. C2×#544C22semidirect
42. C2×#540C22semidirect
46. C2×#539C22semidirect
60. #2855C22semidirect
62. #2853C22semidirect
65. #2822C22semidirect
70. #2726C22semidirect
72. #2724C22semidirect
74. #2719C22semidirect
77. #2718C22semidirect
79. #2713C22semidirect
83. #2708C22semidirect
84. #2708C22semidirect
86. #2704C22semidirect
90. #2701C22semidirect
94. #2698C22semidirect
95. #2698C22semidirect
96. #2689C22semidirect
97. #2689C22semidirect
98. #2689C22semidirect
101. #2687C22semidirect
103. #2672C22semidirect
106. #2660C22semidirect
107. #2660C22semidirect
108. #2658C22semidirect
109. #2642C22semidirect
110. #2642C22semidirect
111. #2640C22semidirect
113. #2634C22semidirect
128. #2611C22semidirect
131. #2604C22semidirect
132. #2604C22semidirect
139. #2565C22semidirect
144. #2559C22semidirect
146. #2556C22semidirect
148. #2553C22semidirect
149. #2549C22semidirect
150. #2549C22semidirect
156. #2506C22semidirect
160. #2499C22semidirect
162. #2498C22semidirect
163. #2496C22semidirect
164. #2496C22semidirect
168. #2488C22semidirect
170. #2486C22semidirect
171. #2485C22semidirect
173. #2484C22semidirect
176. #2475C22semidirect
177. #2473C22semidirect
178. #2446C22semidirect
179. #2446C22semidirect
182. #2444C22semidirect
185. #2443C22semidirect
186. #2440C22semidirect
189. #2425C22semidirect
191. #2423C22semidirect
192. #2421C22semidirect
196. #2419C22semidirect
197. #2419C22semidirect
198. #2419C22semidirect
199. #2419C22semidirect
207. #2372C22semidirect
208. #2372C22semidirect
211. #2353C22semidirect
217. #2331C22semidirect
218. #2328C22semidirect
219. #2327C22semidirect
220. #2326C22semidirect
225. #2319C22semidirect
226. C4×#123C22semidirect
232. C2×#387C22semidirect
235. #2275C22semidirect
261. #532D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35592
C2×#34552
#517532
#515462
#515452
#478222
#478002
#444502
#440822
#434962
#434952
#398462
#394152
#394132
#393762
#393712
#383652
#383632
#375402
#369722
#362172
#354642
#353262
#351182
C2×#26112
#342222